tag:blogger.com,1999:blog-47867841824881351712024-03-13T13:38:48.058+04:00Ron GeorgeRonhttp://www.blogger.com/profile/16268869622833968439noreply@blogger.comBlogger723125tag:blogger.com,1999:blog-4786784182488135171.post-91526551047023136592021-04-28T18:06:00.007+04:002021-04-29T00:11:53.051+04:00Studying India's Covid-19 Pandemic Response : Part 2<p style="text-align: justify;">Continued from the <b><span style="color: red;"><a href="https://www.georgeron.com/2021/04/india-covid-19-pandemic-response-research.html" target="_blank"><span style="color: red;">first post</span> </a></span></b>in this series...</p><p style="text-align: justify;"><br /></p><p style="text-align: justify;">Studying India's pandemic response won't be complete if we didn't concentrate on the factors taking place on a global level which in-turn affects everything down at a country level. </p><p style="text-align: justify;"><span style="text-align: left;">Let's start with addressing a fundamental issue at the heart of this crisis.</span></p><p style="text-align: justify;"><span style="text-align: left;">While it is not necessary to go into the statistics of the rise in cases and deaths around the world, one can easily see that the core mathematical pattern behind these is exponential in nature. So simple, that perhaps most people simply gloss over it, not understanding it's implications. </span></p><p style="text-align: justify;"><span style="text-align: left;">A famous lecture on exponential growth by Professor </span><span style="text-align: left;">Albert Allen Bartlett, an acclaimed professor of physics at the University of Colorado at Boulder, comes to mind. It is required watching by everyone and I think I'm ready to die on this hill. I'll leave that in the supplementary section below.</span></p><p style="text-align: justify;">That a burgeoning world population has outstripped the carrying capacity of the earth is something every kid is taught in school today. This comes with a loss in bio-diversity, with animals like CoV reservoirs (bats) coming into increasing contact with human habitation. <a href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7566801/" target="_blank"><span style="color: red;">This paper</span></a> takes a full look at this issue. </p><p></p><p style="text-align: justify;">Within this context, it would seem that critical systems should be constructed and managed to rapidly adapt and scale up for exponential rise in illnesses. Why? Simply because the adverse exponentials seems to occurring at an increased frequency. In other words, the extremes are becoming more frequent. </p><p style="text-align: justify;">In March, Chatham House hosted a Global C-19 Vaccine Supply Chain & Manufacturing Summit in which the main participants were CEPI (the Coalition for Epidemic Preparedness Innovations) and industry players. For a "summit" of this magnitude, it was telling that WHO was largely absent from the discussions. Not that WHO's leadership hasn't been questioned in this pandemic, to <a href="https://www.theguardian.com/news/2020/apr/10/world-health-organization-who-v-coronavirus-why-it-cant-handle-pandemic" target="_blank"><span style="color: red;">which this piece</span></a> is a good (long) read.</p><p style="text-align: justify;">An <a href="https://blogs.bmj.com/bmj/2021/03/17/scaling-up-covid-19-vaccine-production-what-are-the-problems-and-implications/" target="_blank"><span style="color: red;">opinion piece in the BMJ</span></a> noted the following after this summit, from which I quote : </p><p style="text-align: justify;"></p><blockquote><p style="text-align: justify;"><i>It is not widely known that current annual production of all vaccines in the world is about 5 billion doses. Yet this year the aim is to produce as much covid-19 vaccine as possible to meet projected demand—the organizers estimated about <span style="background-color: #fcff01;">9.5 billion doses</span> which has never been done before. To date, <span style="background-color: #fcff01;">production is less than 500 million doses</span> so there is a very long way to go. </i></p><p style="text-align: justify;"><i>Such a scale up of production will put a huge strain on the producers of the many inputs required to produce a vaccine and get it into the arms of millions of people. <span style="background-color: #fcff01;">One participant in the summit said that their vaccine required 280 separate inputs.</span> These range from the biological materials to grow the vaccine through a wide range of technical kit necessary for production to the vials that contain the finished product. On top of which vaccine production requires a range of highly-skilled technical personnel to manage what is, unlike most conventional medicines, a complex biological process—and such personnel are in short supply. </i></p><p style="text-align: justify;"><i>Given the complexity of the task, and the myriad of different circumstances affecting the multiplicity of input suppliers, <span style="background-color: #fcff01;">it is very difficult to anticipate exactly which critical supply problems will emerge or exactly how each of them might be dealt with</span>. What is clear is that such problems will likely arise, given the unprecedented scale-up, and producers, regulators and governments need to be alert in addressing them.</i></p></blockquote><p><br /></p><p style="text-align: justify;">Is it a surprise that in April, an Indian pharmaceutical giant at the heart of the biggest vaccine production effort in the world <a href="critical vaccine raw materials and n" target="_blank"><span style="color: red;">calls out publicly</span></a> for the USA to repeal it's sudden embargo on raw materials and free up the supply chain? The USA seems to have done what any country at the apex of this crisis would have done. Protecting critical vaccine raw materials became a national <i>defense</i> interest in an atmosphere of shortages. So these issues simply do not occur in vacuum, they are all interconnected.</p><p style="text-align: justify;">In summary, we have a simple but large-scale lack of appreciation for the exponential.</p><p style="text-align: justify;">With delayed responses, the timeframe within which manufacturing and logistics can scale up to meet an exponential crisis is woefully limited. Countries step in to protect their national interests. But a globalized world means you can't simply lock all doors on those who deal with you at many complex levels.</p><p style="text-align: justify;">It would seem that an entirely new top-down management system built to deal with the unique nature of these exponential events and high number of moving parts are the need of the hour. </p><p style="text-align: justify;">Despite having all the fancy systems in place, the question of coordination between different players in this vast system also needs addressed. What's the point in so-called "taskforces" if they're not used to maximum effect? Moreover, there could be players who are there to help, and players there specially ordained to <a href="https://newrepublic.com/article/162000/bill-gates-impeded-global-access-covid-vaccines" target="_blank"><span style="color: red;">throw a wrench into the works</span></a>. </p><p style="text-align: justify;">We'll need to take a look into those aspects of this multi-dimensional issue. But that's for another post. </p><p><br /></p><p style="text-align: center;"><b>SUPPLEMENT</b></p><p><b></b></p><p style="text-align: left;"><b>Arithmetic, Population and Energy - a talk by Al Bartlett</b></p><p><iframe allowfullscreen="" class="BLOG_video_class" height="266" src="https://www.youtube.com/embed/O133ppiVnWY" width="320" youtube-src-id="O133ppiVnWY"></iframe></p><p style="text-align: justify;"></p>Ronhttp://www.blogger.com/profile/16268869622833968439noreply@blogger.com0tag:blogger.com,1999:blog-4786784182488135171.post-49932360041790455162021-04-23T17:47:00.031+04:002021-04-24T04:53:44.419+04:00Studying India's Covid-19 Pandemic Response : Part 1<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://1.bp.blogspot.com/-Jk-h5n1NdfM/YILQO00VNCI/AAAAAAAAIQQ/lW4opxjYJMMrQmQ99V4t2vA3PobZ9NM9wCLcBGAsYHQ/s640/newFile-9.jpg" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="479" data-original-width="640" height="301" src="https://1.bp.blogspot.com/-Jk-h5n1NdfM/YILQO00VNCI/AAAAAAAAIQQ/lW4opxjYJMMrQmQ99V4t2vA3PobZ9NM9wCLcBGAsYHQ/w402-h301/newFile-9.jpg" width="402" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">India has emerged as the global epicenter of the covid-19 pandemic. Photo courtesy :<i> Independent</i></td></tr></tbody></table><p style="text-align: justify;"><br /></p><p style="text-align: justify;">Like hundreds of helpless expats, I sit in the middle east taking stock of the seriousness of the pandemic situation in India. For the last 2 days, the number of daily cases have topped 300,000. Hospitals overflowing, health services unable to cope, oxygen supply crunched, crematoriums exhuming bodies in car parks. The positivity rate is an all-time high of 30%. Vaccinations need to be at 10 million a day but moving at a snail's pace of 3 million a day. </p><p style="text-align: justify;">Unfortunately, one is faced with having to wade through 24/7 live ticker news and myriad of opinions and commentary on the situation in real-time. Often, you come across phrases and terms used to address the government's actions, such as "mismanagement", "complacency", "refusal to acknowledge shortcomings", "creaky system" or "rickety healthcare" and so on. </p><p style="text-align: justify;">What is going on?</p><p style="text-align: justify;">Management and systems engineering are topics that frankly interest me. Taking a step back and looking at this hot mess from a 10,000ft view, how can an average citizen understand the pandemic response policy, decision aid system and management strategy enacted by the current Modi administration specifically for this pandemic? </p><p style="text-align: justify;">Is it possible there is a resource somewhere that rewinds the tape back to day one and runs through all the actions of the government ? Is there a non-partisan book(s) or website anyone know of? India being home to a great business community and management intuitions, I'm concerned why more people are not looking at this crisis from a high level systems point of view.</p><p style="text-align: justify;">Of course, these might be concerns even you have. So worry not. Let's try to pick through this disaster piece by piece and unravel the mess playing out before us. I would first like to share a few resources that act as "primers" for reading (I've also included an interview).</p><p style="text-align: justify;"><br /></p><p style="text-align: justify;"><b>Primer :</b></p><p style="text-align: justify;"><b>1. What is the nature of the public health system currently established in India?</b> This handy website explores the current health systems in place in several countries. What I like about it is how it goes in-depth into the organizational structures of each nation's health system. Not highly detailed, but just enough. One can look up India and do the necessary reading. <a href="https://www.commonwealthfund.org/international-health-policy-center/countries"><span style="color: red;">https://www.commonwealthfund.org/international-health-policy-center/countries</span></a></p><p style="text-align: justify;"><b>2. "Combating the COVID-19 pandemic in a resource-constrained setting: insights from initial response in India" </b>This is a neat analysis of all actions pursued by the Indian government in the first 4 months of the first wave of the pandemic in India. A SWOT analysis of those actions are also contained in the paper. I thought it was very systematically researched. <a href="https://gh.bmj.com/content/5/11/e003416"><span style="color: red;">https://gh.bmj.com/content/5/11/e003416</span></a></p><p style="text-align: justify;"><b>3. "A critique of the Indian government’s response to the COVID-19 pandemic".</b> Self explanatory. An Indian economist exposes where the pandemic response has fallen short. Lots of points to take stock of. One needs to face these questions head-on. <a href="https://link.springer.com/article/10.1007/s40812-020-00170-x"><span style="color: red;">https://link.springer.com/article/10.1007/s40812-020-00170-x</span></a></p><p style="text-align: justify;"><b>4. "Modi Leadership Style Main Reason for India's Covid Mishandling" </b>An interview with Indian economist and historian Ramachandra Guha suggests the <span style="text-align: left;">principal blame and responsibility rests squarely on the Prime Minister’s shoulders. The analysis is on the leadership flaws in the highest man in power and the "yes men" built around him. </span><span style="text-align: left;"><a href="https://www.youtube.com/watch?v=AFVmsRmFE4Q"><span style="color: red;">https://www.youtube.com/watch?v=AFVmsRmFE4Q</span></a></span></p><p style="text-align: left;"><b>5. The EPC mess-up with the medical oxygen</b><span style="text-align: left;"><b> </b></span><span style="text-align: left;">I leave two articles and the original bid that was floated here : a) </span><span style="color: red;"><a href="https://scroll.in/article/992537/india-is-running-out-of%20oxygen-covid-19-patients-are-dying-because-the-gov%20ernment-wasted-time"><span style="color: red;">https://scroll.in/article/992537/india-is-running-out-of%20oxygen-covid-19-patients-are-dying-because-the-gov%20ernment-wasted-time </span></a> </span>and b) <span style="color: red;"><a href="https://www.thenewsminute.com/article/how-kerala-managing-its-medical-oxygen-supply-147579"><span style="color: red;">https://www.thenewsminute.com/article/how-kerala-managing-its-medical-oxygen-supply-147579</span></a> . </span><span>The Request for Bid from the Government :</span><span style="color: red;"> </span><a href="http://www.cmss.gov.in/sites/default/files/PSAPLANTTENDERDOCUMENT.pdf" style="color: red;"><span style="color: red;">http://www.cmss.gov.in/sites/default/files/PSAPLANTTENDERDOCUMENT.pdf</span></a></p><p style="text-align: left;"><b>6. "</b><span style="text-align: left;"><b>Ten scientific reasons in support of airborne transmission of SARS-CoV-2" </b></span><span style="text-align: left;"><a href="https://www.thelancet.com/journals/lancet/article/PIIS0140-6736(21)00869-2/fulltext"><span style="color: red;">https://www.thelancet.com/journals/lancet/article/PIIS0140-6736(21)00869-2/fulltext</span></a></span></p><p style="text-align: justify;"><b>7. "Biological Risks in India: Perspectives and Analysis" </b>This is a recent and noteworthy treatment of biological risks in India and stresses why India needs a firm 24/7 bio-disasters policy and purpose built institutions in place. <a href="https://carnegieendowment.org/2020/12/09/biological-risks-in-india-perspectives-and-analysis-pub-83399"><span style="color: red;">https://carnegieendowment.org/2020/12/09/biological-risks-in-india-perspectives-and-analysis-pub-83399</span></a></p><p style="text-align: justify;"><br /></p><p>Once we are done sifting through these articles and getting a handle of the problem, we can address sub-topics. That will be the subject of the next series of posts, which I hopefully will do soon. Thanks.</p><p style="text-align: center;">* * *</p>Ronhttp://www.blogger.com/profile/16268869622833968439noreply@blogger.com0tag:blogger.com,1999:blog-4786784182488135171.post-37102089468767692882021-02-07T20:54:00.023+04:002021-02-09T01:03:18.552+04:00Reverse Engineering Zwift Physics - A Fun Look<p> <b style="text-align: justify;">INTRO </b></p><div style="text-align: justify;">Last year, I performed a simple exercise to reverse engineer a cycling ride done on Fulgaz app to understand in-game variables being employed. I described it in <b><a href="http://www.georgeron.com/2020/08/Fulgaz-model-climbing-accuracy.html" target="_blank"><span style="color: red;">this post</span></a></b>. It was nice to receive a message from Fulgaz suggesting that I'd come very close to what they actually use for their sanctioned events. </div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">Overall, the Fulgaz app seemed very in-tune with the physics behavior we cyclists normally expect to encounter with cycling outdoors. Zwift, on the other hand is tricky. None of the in-game physics constants and parameters are known to the public. </div><div style="text-align: justify;"><br /></div><div style="text-align: justify;"><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-4NzkuW9z0Us/YCAdRfAKMuI/AAAAAAAAIJE/dhWgH96Ls-4AEZbOO8Ai0TS8wZI_9N2AACLcBGAsYHQ/s656/image_2021-02-07_210300.png" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" data-original-height="385" data-original-width="656" src="https://1.bp.blogspot.com/-4NzkuW9z0Us/YCAdRfAKMuI/AAAAAAAAIJE/dhWgH96Ls-4AEZbOO8Ai0TS8wZI_9N2AACLcBGAsYHQ/s320/image_2021-02-07_210300.png" width="320" /></a></div>Given many of us outdoor cyclists find the discrepancies between in-game Zwift physics and real world confusing, it is apt to ask whether Zwift is even based on an "earth" model.</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">With that fun question - <i>which world is Zwift in?</i> - I make an attempt to understand what makes the app work the way it does. Its far from perfect but hopefully it simulates your own thinking and you can go off and try to do something similar. </div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">Just don't send me any hate mail. My approach maybe far from perfect.</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;"><br /></div><div style="text-align: justify;"><p><b>MODELING TOOL</b></p><div>The modeling tool is the same one I used to model the Fulgaz performance. It takes more than 30 variables and allows breaking a course into many many small segments for steady speed analysis. </div><div><br /></div><div>For Zwift, I included some adjustments where the model would accept different g constants, drag co-efficient of bikes, altitude de-rates to power depending on whether a cyclist is acclimated or not, segment-by-segment rolling resistances and drag areas depending on the heading of the cyclist, direction of wind and the known characteristics of the road. </div><div><br /></div><div>In short, there's a lot of "handles" that I can pull in order to understand the whacky world of Zwift.</div><div><br /></div><div><br /></div><p><b>METHOD</b></p><p>I rode one lap of <b><a href="https://whatsonzwift.com/world/new-york/route/mighty-metropolitan" target="_blank"><span style="color: red;">Mighty Metropolitan</span></a></b> using my real bike hooked up to Computrainer. The in-game bike chosen was the 2021 Canyon Aeroad with Zipp 202 wheelset. My weight and height were set to 64.8 kg and 173cm respectively. The bike weight was assumed to be a race-ready 6.8kg, which came off some forums on the internet. </p><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://1.bp.blogspot.com/-p67qAA1O5Ss/YCAYEniyh8I/AAAAAAAAIIw/Qv_V2b1-XgoKZ5W0mEZVHew1Qr-PSxKCwCLcBGAsYHQ/s892/image_2021-02-07_204049.png" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="653" data-original-width="892" height="262" src="https://1.bp.blogspot.com/-p67qAA1O5Ss/YCAYEniyh8I/AAAAAAAAIIw/Qv_V2b1-XgoKZ5W0mEZVHew1Qr-PSxKCwCLcBGAsYHQ/w358-h262/image_2021-02-07_204049.png" width="358" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Fig 1 : A crazy twisty, windy course! Course details on <a href="https://veloviewer.com/segment/19181471" target="_blank"><b><span style="color: red;">Veloviewer</span></b></a>. </td></tr></tbody></table><br /><p>Power output was dual recorded. Primary source of power was dual-sided power pedals while Racermate maintained the load at 150W. This would also yield second by second transmission differences between the two sites of power application depending on where on the course I changed a gear or my cadence. Trainer load was held at a constant 150W. I freely chose a cadence.</p><p>Using a script for processing the GPX file, the course was broken into 60 segments in order to capture all the features of the terrain - flats, downhills and uphill sections. Specific sections that had the glass or road surfaces were marked for rolling resistance adjustments.</p><p>Model variables were tweaked as far as practical to match the model segment time to the Zwift recorded segment time and speeds which came off the raw GPX file. The strategies being :</p><p>1) Minimize the difference between average model speed and Zwift reported average speed for the course. </p><p>AND/OR</p><p>2) Minimize the difference between segment model speed and Zwift reported segment speed individually for uphills, flats and downhills. </p><p>The exercise seemed to often be a tradeoff between the above two. In principle, the two scenarios should be intertwined but the way I derived segment-segment information from the GPX data could have led to some errors. For example, the average speed in a segment was derived from the data which may have been acutely affected by outliers within that segment. </p><p>The best solution would balance the accuracy in average course speeds with the match within each of the segments. I ran a few scenarios to check the sensitivity of the model. </p><div><br /></div><div><b>ASSUMPTIONS</b></div><div><b><br /></b></div><div><div>A CdA of 0.22 sq.m was modeled from frontal area from Bassett et al. (Med Sci Sports Exerc 1999; 31:1665-1676) using my height and weight and co-efficient of drag Cd from Heil was computed as : </div><div><br /></div><div><div style="text-align: center;">Cd = 4.45 x mass (kg)^-0.45</div></div><div><br /></div><div>CdA factors were set to 90% on the flat and downhill sections assuming an aero position but 100% on the uphills. </div><div><br /></div><div>Is this CdA representative of the Zwift world? Probably. Earlier, I did some Aero testing using the Chung "regression method" with the same bike and weight settings on another course called <a href="https://whatsonzwift.com/world/yorkshire/route/queen-s-highway" target="_blank"><b><span style="color: red;">Queen's Highway</span></b></a>. The CdA that resulted was around 0.21 sq.m (Fig 2). The Crr values were bonkers so instead I tried the Chung "virtual elevation method" and achieved better results (Fig 3). </div><div><br /></div><div>In the VE method, the CdA was more like 0.0028 sq.m and Crr around 0.0032. To achieve that, I had to constrain Crr to 0.0032 and used Goal Seek to hone in on the CdA value in order to get the virtual elevation to match the expected elevation profile. Since CdA and Crr have an inverse relationship with each other, I can only find out how sensitive CdA is to a given Crr by changing the Crr value. For this exercise, I simply fixed Crr to 0.0032. </div><div><br /></div><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://1.bp.blogspot.com/-aCcbxsW1UEI/YCGC01EHwaI/AAAAAAAAIJQ/VPSz-LTFslE6QLvSbYE1jf6Vp8wmigOHACLcBGAsYHQ/s966/Zwift%2BCdA%2BTesting.JPG" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="572" data-original-width="966" height="273" src="https://1.bp.blogspot.com/-aCcbxsW1UEI/YCGC01EHwaI/AAAAAAAAIJQ/VPSz-LTFslE6QLvSbYE1jf6Vp8wmigOHACLcBGAsYHQ/w463-h273/Zwift%2BCdA%2BTesting.JPG" width="463" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Fig 2 : (click to view) Results of aero testing done by Chung method. Spreadsheet courtesy of Alex Simmons , Google Wattage Group</td></tr></tbody></table><br /><div><br /></div><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://1.bp.blogspot.com/-wlsnQzNbrCI/YCGm0fz7YBI/AAAAAAAAIJo/WxDqRCD3LOM9CdRvGzQMDuwGbEz82ZqNwCLcBGAsYHQ/s1441/CdA%2BVE%2BMethod.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="577" data-original-width="1441" height="217" src="https://1.bp.blogspot.com/-wlsnQzNbrCI/YCGm0fz7YBI/AAAAAAAAIJo/WxDqRCD3LOM9CdRvGzQMDuwGbEz82ZqNwCLcBGAsYHQ/w541-h217/CdA%2BVE%2BMethod.png" width="541" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Fig 3 : (click to view) Results of the Chung virtual elevation method. Spreadsheet courtesy of Alex Simmons, Google Wattage Group.</td></tr></tbody></table><br /><div><br /></div><div>From the above results, it appears my simulation tests using CdA between 0.22 and 0.29 sq.m and Crr of 0.003 was alright. However, I'm pretty unsure of modification factors used for the uphill, downhill and flats. Slope is hardly the reason for a rider to change his bike position, infact it must actually be speed that sets the body position. However, I've assumed speed to be low on the uphills to increase the CdA factors and high on the downhills and flats. </div></div><div><br /></div><div><div>The Crr of tarmac was chosen as 0.003, the same I used for Fulgaz. A Crr of 0.003 is representative of the performance of a high quality tire on a smooth road. Note that the Crr for glassy segments of 65% of tarmac is arbitrary and hypothetical. </div></div><div><br /></div><div><div>Other factors like acceleration due to gravity, relative humidity, altitude and air temperature in Mighty Metropolitan etc were all based on data from NYC. </div><div><br /></div></div><div><br /></div><p><b>RESULTS</b></p><p>I've attached the results from the tabulation below. </p><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://1.bp.blogspot.com/-cGFb1nNuAJo/YCAcpDs9MwI/AAAAAAAAII8/Q9u0tU6iwYoeLwj9tKuq5LNdVvu6fodzgCLcBGAsYHQ/s1163/Graph1.JPG" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="432" data-original-width="1163" height="210" src="https://1.bp.blogspot.com/-cGFb1nNuAJo/YCAcpDs9MwI/AAAAAAAAII8/Q9u0tU6iwYoeLwj9tKuq5LNdVvu6fodzgCLcBGAsYHQ/w563-h210/Graph1.JPG" width="563" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Fig 4 : (click to view) Tabulation of different case runs with the variables chosen to run the model. The first two runs are representative of earth while the rest are whackier attempts with whimsical variables.</td></tr></tbody></table><p><br /></p><p></p><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://1.bp.blogspot.com/-VErzMGlpoyA/YCAUGm7hs2I/AAAAAAAAIIk/M_aGUs5_44Ufd6wV524SAy_jljyzp8aZQCLcBGAsYHQ/s1189/Plot%2B1.JPG" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="652" data-original-width="1189" height="306" src="https://1.bp.blogspot.com/-VErzMGlpoyA/YCAUGm7hs2I/AAAAAAAAIIk/M_aGUs5_44Ufd6wV524SAy_jljyzp8aZQCLcBGAsYHQ/w560-h306/Plot%2B1.JPG" width="560" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Fig 5 : (click to view) Model performance compared to the "virtual" performance in Zwift for segmented distances of the course using the given variables in Case# 1. </td></tr></tbody></table><b></b><p></p><p><br /></p><b>DISCUSSION</b><p></p><div>As you can see through Fig 5, the model did well to bring down the overall error in overall course performance time and speed but seemed to struggle with matching Zwift recorded speed and time data for segments. In the best "earth" scenario Case #1 (see Fig 4), the model flew downhills but rode uphills and flats slower. But trying to make segment performance improve had a tradeoff on the course average performance as shown in Case #2. </div><div><br /></div><div>The segment specific speed and time matching were not that great. This could also stem from the errors in speed and time calculation within the segments themselves, which in turn stems from irregularities in the original GPX file. Moreover, since the GPX file is a continuous speed run of my avatar with one segment's speed input being linked to the output from a previous segment (such as steep downhill speeds leading to a climb), the transient nature would probably differ from a purely steady state analysis from the model. </div><div><br /></div><div>In other whacky attempts (#3-#6), I employed a "non-earth" scenario by manipulating air density and acceleration due to gravity. The best whacky attempt (#6) provided me a near identical error in course average performance speed and time as Scenario #1 but with improvements in the segment specific matching. These results are "whacky" because a change in the acceleration due to gravity and air density should also affect the CdA values, in other words they are all dependent on each other. However, I've ignored that obvious complexity and stopped further attempts here. </div><div><br /></div><div><br /></div><div><p><b>CONCLUSION</b></p></div><div>I tried to reverse engineer the physics variables and parameters set in the whacky world of Zwift. The model came close but a closer match can be achieved only with inputs of whimsical numbers. A purely steady state type cycling power model is perhaps not best to use for matching to running-segment data however overall, the model course time matched closely with Zwift course time. </div><div><br /></div><div>If you don't know what to make of this fun attempt, don't worry. I'm just as puzzled how the world of Zwift works. And perhaps I just said it. The <i>world </i>of Zwift may not even be a world on earth. We would perhaps like to assume so, but it might just be the case that we're in a parallel world as earth with similar names of cities and hypothetical physics. Perhaps those flying cars and glassy climbs where riders seem to have the ability to climb at 40kph and descend at 80kph are enough proof.</div><div><br /></div><div>As a cyclist who is clearly in-tune with the world around him and how his bike rides in that world for over 15 years, the way Zwift overreports speeds on flats and downhills seems overly flattering. That said, I love my in-game CdA and rolling resistances and whatever other Zwifty physics constants there might be. The enjoyment of Zwifting far overrules the eccentricities of this software.</div><div><br /></div><div><br /></div><div><div><p><b>REFERENCE :</b></p></div></div><div><p>My Strava activity is here : <b><a href="https://www.strava.com/activities/4741883532" target="_blank"><span style="color: red;">https://www.strava.com/activities/4741883532</span></a></b></p><p>The dual record is here : <b><a href="https://www.strava.com/activities/4741887869" target="_blank"><span style="color: red;">https://www.strava.com/activities/4741887869</span></a></b></p></div></div><div class="separator" style="clear: both; text-align: center;">* * *</div>Ronhttp://www.blogger.com/profile/16268869622833968439noreply@blogger.com0tag:blogger.com,1999:blog-4786784182488135171.post-41284670224252232532020-09-20T20:40:00.056+04:002020-09-22T15:52:05.641+04:00The Race of a Lifetime : Tadej POGAČAR's Stage 20 Time Trial Analysis<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://1.bp.blogspot.com/-x1kKeDLpBlg/X2dsZJ-cKjI/AAAAAAAAH_A/-WiHcZ4D2pMUcjLbTEr8XgQPjiXlIupGQCLcBGAsYHQ/s1430/013-RTX7WKGD%2B%25281%2529.jpg" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="924" data-original-width="1430" height="322" src="https://1.bp.blogspot.com/-x1kKeDLpBlg/X2dsZJ-cKjI/AAAAAAAAH_A/-WiHcZ4D2pMUcjLbTEr8XgQPjiXlIupGQCLcBGAsYHQ/w497-h322/013-RTX7WKGD%2B%25281%2529.jpg" width="497" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Photo courtesy : Steephill.tv</td></tr></tbody></table><p style="text-align: justify;"><br /></p><p style="text-align: justify;">Great comebacks are always a fascination for sports observers both from an entertainment and statistics perspective. Don't we all thrive for that moment when fortunes can be reversed and the underdog can win? In social psychology, this phenomenon even has a special name - <i>schadenfreude</i>.</p><p style="text-align: justify;">Such a reversal in fortune happened during Stage 20 of the 36.2 km individual time trial at the Tour de France when a 21 year old Tadej Pogačar reclaimed nearly 2 minutes over his nearest rival Primoz Roglič, all but securing the title of the coveted yellow jersey and taking home 500,000 Euros in hard won prize money.</p><p style="text-align: justify;">This was a rare feat to witness 20 days into the 3500 km Tour de France, and many had made up their minds that 57 seconds was a large chunk of time to win back from a highly motivated Primoz who had been in sitting in yellow for 11 days in a row. In the aftermath, the sport's pundits are going to be looking closely at how this was accomplished by the youngster, who beat just about every veteran of the time trial format available to contest that day.</p><p style="text-align: justify;">Allow me to devote a brief section below to the analysis of the actual time trial performance and the corresponding power demands without going too much into the mathematics of it all. Please note this analysis remains to be validated since the official performance data from Team UAE Emirates is unavailable to the public as of today. Sources of my information are highlighted below and where required, educated guesses are employed. I also discuss my results towards the end of the article.</p><p style="text-align: justify;"><br /></p><p><b>Assumptions & Considerations</b></p><p>I've used the following assumptions & considerations in this first order analysis :</p><p></p><ul style="text-align: left;"><li>Weight/Height : 66 kg/176 cm (<b><a href="http://www.uaeteamemirates.com/rider/tadej-pogacar/" target="_blank"><span style="color: red;">Source</span></a></b>)</li><li>Assumed Drag Area, CdA : T1/T2/T3/Finish = 0.22/0.24/0.3/0.3 sq.m (arbitrary but educated)</li><li>Assumed Rolling Resistance Co-efficient, Crr : 0.002-0.0023, 25mm width (Vittoria Corsa tubeless)</li><li>Assumed drivetrain efficiency : 98%</li><li>Bike T1-T2 : TT bike w/ rim profile 60mm/Full Disc at 8.3 kg</li><li>Bike T2-Finish : Road bike w/ rim profile 30mm/30mm at 6.8 kg (current UCI limit, <a href="https://dmcx.com/2020/08/14/tadej-pogacars-colnago-bike-size-2020/" target="_blank"><b><span style="color: red;">source</span></b></a>)</li><li>Gear : Aerodynamic skin-suit and streamlined TT helmet</li><li>Weather : Historical weather for 3-5pm local French time w/ winds 8.5-12 kph at 93-105 degrees range.</li><li>Roads : Good (smooth asphalt) w/ mountainous terrain</li><li>Course GPX source : Ritchie Porte's <a href="https://www.strava.com/activities/4083350744/" target="_blank"><span style="color: red;"><b>Strava data</b></span></a> </li><li>Performance time data : <span style="color: red;"><b><a href="https://www.procyclingstats.com/race/tour-de-france/2020/stage-20/today/time-splits" target="_blank"><span style="color: red;">Pro Cycling Stats</span></a> </b></span></li><li>Model used : A widely <a href="https://collections.lib.utah.edu/dl_files/b4/8e/b48ef26086091662c561e673d7bd990d77868437.pdf" target="_blank"><b><span style="color: red;">cited & validated</span></b></a> general purpose model of human power requirements in cycling</li><li>Secondary power data for comparison : Thomas de Gendt's<b><span style="color: red;"> <a href="http://www.georgeron.com/2020/09/tadej-pogacar-timetrial-poweroutput.html" target="_blank"><span style="color: red;">Strava data</span></a></span></b> for Stage 20</li></ul><p></p><div><br /></div><p><b>Method</b></p><p style="text-align: justify;">The race course was broken up into 4 segments corresponding to the official time checkpoints for the stage. A 1st order physics model was used in combination with official timings at those checkpoints to reverse calculate a suitable matching power output. I quote "suitable" as the numbers could change up or down depending on the actual conditions. From the potential locus of power outputs, this is a workable number for the rider, as I validate it below. </p><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://1.bp.blogspot.com/-fzfCNLHCOw8/X2eBQcMTNBI/AAAAAAAAH_s/eqGQI1A__64bSc7ubsSUuY3pBULNdFAlgCLcBGAsYHQ/s650/Stage%2Bmap.jpg" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="580" data-original-width="650" height="408" src="https://1.bp.blogspot.com/-fzfCNLHCOw8/X2eBQcMTNBI/AAAAAAAAH_s/eqGQI1A__64bSc7ubsSUuY3pBULNdFAlgCLcBGAsYHQ/w456-h408/Stage%2Bmap.jpg" width="456" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Stage 20 ITT course profile</td></tr></tbody></table><p><b><br />Results</b></p><p style="text-align: justify;">The modeling indicates that for the first two sections totaling 30.3 km, the use of a special purpose TT bike weighing in at an assumed 8.3 kg and a body shape of CdA 0.22 sq.m required an average power output of 427 Watts. The results indicate a positive split with an average power of 451 Watts for the 1st segment until T1 and 402 Watts for the 2nd segment T1-T2. </p><p style="text-align: justify;">In the vicinity of T2 at 30.3 km, <b><a href="https://www.youtube.com/watch?v=z9xbL3B4zQM" target="_blank"><span style="color: red;">a bike change</span></a></b> happened where the TT bike was exchanged for a lighter road bike due to requirements necessitated by the gradient. This climb is at an average 8% gradient, kicking up to 20% in places. The bike change cost anywhere from 6-8 seconds in total, depending on how you start and stop the watch. This time cost is factored into the overall performance time. </p><p style="text-align: justify;">Thus, in the last 5.9 km of this climb, the use of the assumed 6.8ckg road bike required an approximate average of 412 Watts at an estimated 6.2 W/kg (power to rider weight). The power demand for T2-T3 and T3-Finish of approximately 3.3 and 2.6 km each were 432 and 392 W (6.5 & 5.9 W/kg respectively).</p><p>The results are plotted in the image below :</p><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://1.bp.blogspot.com/-adnJbzBEuMg/X2nlMAP8M4I/AAAAAAAAIAg/pHh-IUzoGzwqpMOydd7sbhXg8A_oQ6bQQCLcBGAsYHQ/s879/Pogacar%2BPower%2BOutput%2BITT%2BTdf%2BStage%2B20.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="523" data-original-width="879" height="310" src="https://1.bp.blogspot.com/-adnJbzBEuMg/X2nlMAP8M4I/AAAAAAAAIAg/pHh-IUzoGzwqpMOydd7sbhXg8A_oQ6bQQCLcBGAsYHQ/w522-h310/Pogacar%2BPower%2BOutput%2BITT%2BTdf%2BStage%2B20.JPG" width="522" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td class="tr-caption" style="text-align: center;">(Click to zoom) : Actual performance times along with corresponding modeled average power outputs for Tadej Pogacar in the final individual time trial of Stage 20 of the 2020 Tour de France.</td></tr></tbody></table><p><br style="text-align: left;" /></p></td></tr></tbody></table><p><b><br />Discussion</b></p><div style="text-align: justify;">This is an unverified analysis done based on checkpoint timings obtained from<span style="background-color: white;"> <b><a href="https://www.procyclingstats.com/race/tour-de-france/2020/stage-20/today/time-splits" target="_blank"><span style="color: red;">Pro Cycling stats</span></a></b></span> and other publicly available information. An average power output of 419 Watts was required for this performance as per the modeling. What is definitely in question is the pacing profile over the course of time duration, which needs to be validated with real data.</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">Such a power output is not totally unrealistic for Tadej, given we know that in the 140km Mountain Stage on Stage 8 of the Tour, he displayed a <b><a href="https://www.strava.com/activities/4016249740/overview" target="_blank"><span style="color: red;">power output of 428 Watts</span></a></b> over the Col de Peyresourde, climbing it in one of the fastest times recorded in recent history and an estimated power to weight ratio of over 6.5 W/kg. This was after 2 massive climbs before it and 120 km in the legs.</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">The modeled power output of 412W on the final 5.9 km climb equates to a power to weight ratio of 6.2 Watts/kg. Compare this to Thomas de Gendt's <b><a href="https://www.strava.com/activities/4084111083/analysis/2582/3625" target="_blank"><span style="color: red;">data</span></a></b> from the same stage where he rode with an average of 405W at a power to weight of 5.9 Watts/kg. This is consistent with Thomas' performance data that shows he climbed 1:51 minutes slower than Tadej. </div><div style="text-align: justify;"><br /></div><div style="text-align: justify;"><div style="text-align: justify;">The overall data indicates a positive split of power across elapsed time duration. I justify this with two potentially valid points : </div><div style="text-align: justify;"><br /></div><div style="text-align: justify;"><div>1. High motivation at the start, giving the rider the urge to ride hard in the first half. Tadej was in fact chasing what looked like an improbable target, a 58 second deficit to win the Tour de France. He might have purposely fired all cylinders, thus accounting for a potential loss of valuable seconds later during the bike change and any other unforeseen events on the climb. </div><div><br /></div><div>2. The decrease in power output in the second half might be attributed to a combination of accumulated fatigue and/or a change of the power demand and the impact on feelings from a sudden change to a lighter bike on a steep climb. The "sudden" change to a new bike and the lack of objective power data from an absent head unit meant that Tadej had to guage his effort carefully. It could be that despite a drop in power and cadence, Tadej maintained the "same" or even "greater" level of perceived effort compared to previous flat sections of the course. However, this is just my speculation.</div></div></div><div style="text-align: justify;"><br /></div><div><div style="text-align: justify;">The choice of tire rolling resistances and drag areas although arbitrary, are not a totally wild guess. We know that Team UAE Emirates is sponsored by Vittoria in 2020, the tubeless varieties of which have reportedly exhibited some of the lowest rolling resistances at race speeds. Therefore, I have started off with an ideal case of 0.002 increasing this to 0.0023 at the climb. I figured the weaving on the climb at slow speeds combined with the quality of road on the gradient poses less than ideal conditions, justifying the small increase to Crr. </div><div><br /></div><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://1.bp.blogspot.com/-d-ogaAxF57A/X2d9RbJBOLI/AAAAAAAAH_g/JfivVMY6G8I2jGzr5LlV4jVdyG2sBCfVACLcBGAsYHQ/s1011/Vittoria%2Brolling%2Bresistances.jpg" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="616" data-original-width="1011" height="316" src="https://1.bp.blogspot.com/-d-ogaAxF57A/X2d9RbJBOLI/AAAAAAAAH_g/JfivVMY6G8I2jGzr5LlV4jVdyG2sBCfVACLcBGAsYHQ/w518-h316/Vittoria%2Brolling%2Bresistances.jpg" width="518" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Reported co-efficients of rolling resistance for some bicycle racing tires at race speeds. Source : Aerocoach</td></tr></tbody></table><div><br /><br /></div><div style="text-align: justify;">Professional TT riders are known to be slippery, exhibiting well under 0.25 sq.m of drag area in ideal conditions (smaller riders reportedly presenting less than 0.2 sq.m!) I have started off with an ideal scenario of 0.22 sq.m in the TT position due to Tadej's height and weight, increasing this to 0.3 sq.m on the climb which corresponds to a climbing position adopted with the hands on the hoods. Again, these numbers are arbitrarily chosen but there is no way at present to verify what the real numbers in open terrain might be. I do have some <a href="https://twitter.com/xavierdisley/status/1306201993732591617" target="_blank"><span style="color: red;"><b>references from a Twitter conversation</b></span></a> to believe that my choices are conservative for a top professional rider. </div><div style="text-align: justify;"><br /></div><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://1.bp.blogspot.com/-HDVoMgA-ROg/X2jomvNpyEI/AAAAAAAAIAI/v2WVg30fkeQ6zsLDT8oBl9rTz0VVYvRfgCLcBGAsYHQ/s979/CFD%2Bstudy.JPG" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="552" data-original-width="979" height="225" src="https://1.bp.blogspot.com/-HDVoMgA-ROg/X2jomvNpyEI/AAAAAAAAIAI/v2WVg30fkeQ6zsLDT8oBl9rTz0VVYvRfgCLcBGAsYHQ/w400-h225/CFD%2Bstudy.JPG" width="400" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">CFD simulation results showing the individual contributions of wheels, bicycle and rider to CdA as well as the net CdA. Source : Fabio Malizia, Katholieke Universiteit, Leuven</td></tr></tbody></table><br /><div style="text-align: justify;"><br /></div><div style="text-align: justify;">The total system weight with rider and all accessories is an unknown. A premium TT bike setup of 8.3kg and lightweight road bike setup of 6.3kg are not unexpected and matches recorded observations on the internet. However, the weight of his kit, shoes, helmet, bottle etc are unknowns. I have reasons to believe this will be under 1kg in total however the uncertainty in analysis from the final climb will stem from the uncertainty in system weight and rolling resistance. Regardless, the modeled power outputs are likely not very far off from the actual numbers. </div></div><div style="text-align: justify;"><br /></div><div style="text-align: justify;"><p style="text-align: left;"><b><br /></b></p><p style="text-align: left;"><b>Conclusion</b></p><p>I titled this race as the "race of a lifetime". Indeed, performances like these are hard to come by simply due to the immense difficulty of turning around such time advantages over a pile of fatigue and mental exhaustion 20 days into the Tour de France.</p><p>In some respects, Tadej's race performance has been likened to a pivotal moment in 1989 when the American Greg Lemond, bustling with energy and ready to try new technologies, beat the yellow jersey holder Laurent Fignon with the use of aerodynamic gear and in turn, winning the Tour de France. </p><p>Whether Tadej's victory was a matter of such marginal gains at the end of the day is debatable. Yes, two purpose made bikes were used in the time trial in an unusual manner, but this is increasingly becoming common in the top races these days. Moreover, unlike 1989, both Primoz and Tadej were arguably evenly matched in terms of technology, the funding and competent attention required to apply the technology. In fact, on race-day, they both undertook bike changes before the 6 km climb so any small variations in equipment came really down to supply differences from the equipment sponsors.</p><p>Did Tadej just ride his usual top race, as he does every time and was it Primoz who slowed and fizzled out? Well, I think that is clear to see. A race is indeed won by someone who slows the least. And what promoted this spectacular fall when the day demanded the best? Whether it was the massive pressure upon his Primoz's shoulders, or whether it was the failure of his power pacing model, or whether it was the fatigue, or ALL of the above, we will not know for sure. </p><p>What speaks to me from this performance is that marginal gains did not win, and something else contributed. Certainly Tadej rode the time trial of his life, and converted the opportunity of a lifetime to a magnificent victory. And I think in that moment, the individual qualities of what makes one rider better than another in the heat of the moment won. It really is a victory for the human element.</p><p>Years after his crushing defeat in the 1989 Tour, Laurent Fignon would write that despite getting over it, <i>"you never stop grieving over an event like that; the best you can manage is to contain the effect it has on your mind." </i>I hope that Primoz, as amazing a rider he has been to reach this level, is able to contain the effect of this race outcome on his mind and move on. He has more than a few good years of a top fight left in him at the very top. But an able and worthy opponent stands beside to check that in the form of Tadej Pogačar.</p></div><div style="text-align: justify;">Thanks for reading. Comments and observations welcome below.</div>Ronhttp://www.blogger.com/profile/16268869622833968439noreply@blogger.com0tag:blogger.com,1999:blog-4786784182488135171.post-55529434595551904182020-08-30T14:27:00.056+04:002020-08-31T13:17:57.959+04:00Fulgaz App : Validating Model Prediction & Performance Results<p style="text-align: justify;"><b>INTRO </b></p><p style="text-align: justify;">After my self-inflicted <i><a href="http://www.georgeron.com/2020/08/amateur-virtual-Tour-de-France.html" target="_blank"><span style="color: red;"><b>Poor Man's Tour de France</b></span></a></i> that ended on 22nd August, I took a week of recovery and lunged into the <b><a href="https://fulgaz.com/getting-started-with-fulgaz/" target="_blank"><span style="color: red;">Fulgaz</span></a></b> app's 3 week fundraising campaign called <b><a href="https://frenchtour2020.fulgaz.com/about" target="_blank"><span style="color: red;">French Tour</span></a></b>. This "curated" Tour campaign features most of the celebrated climbs of the Tour de France in the high Alps along with other famous circuits in and around France. With a real-time leaderboard and 381 virtual kilometres with 14000m of climbing over 21 stages, its a challenging event to keep my mind occupied while the actual Tour de France plays out. </p><p style="text-align: justify;">When riding the Tour in Fulgaz, you see a beautiful HD or 4K video of the course taken by a volunteer rider on a high resolution cam. The volunteer would obviously ride the course at their own capacity, so when you use the app, the speed of the footage can be set to "reactive", so effectively it'd speed up or slow down based on how closely you match the recording (for example, 1x, 0.9x, 0.8x or >1x). </p><p style="text-align: justify;">Being new to Fulgaz, I was quite impressed with the app's in-built features and sliders to "tune" nearly everything that would have appreciable impact on the ride - for example system weight, rolling resistance, drag area, even wind speed and direction. The speed with which the app loads is extremely fast, about a second on my Windows 10 pc with a 32gb RAM. Whats more, you can download all the high resolution videos to stave off any buffering troubles. A download would take 15 minutes for a full HD video on my modest internet connection. </p><p style="text-align: justify;">All this was fascinating, given that a) I'm quite new to indoor cycling apps and b) Zwift, another leading indoor cycling app of which I'm a paying customer, keeps a lot of these variables under tight secrecy so effectively you have little clue what is driving the model. </p><p style="text-align: justify;"><br /></p><p style="text-align: justify;"><b>MODELING</b></p><p style="text-align: justify;">Sometime ago, I built myself a cycling performance model for personal use. The model is built based on Martin et.al's <b><a href="https://collections.lib.utah.edu/dl_files/b4/8e/b48ef26086091662c561e673d7bd990d77868437.pdf" target="_blank"><span style="color: red;">power model</span></a></b> for cycling which I like to use for personal and coaching related estimation purposes. I can build as many segments of a course in the model and make tweaks to inspect how it changes my performance. This is handy for climbing and TT predictions and even drafting simulations. </p><p style="text-align: justify;">For Stage 3 of the French Tour, registrants would have to climb the 1200m vertical <i>Col du Galibier</i>. I was interested in knowing how my performance results in Fulgaz would compare with the model predictions for the same given power input. So I did the Galibier this morning, staying completely aerobic, sweating buckets, powers tuned to steady perfection with a Computrainer erg controller and a second Powertap pedal (those curious how I used the Computrainer with Fulgaz can send me an email or comment). Once I had my performance, I input the same powers into the model along with the driving variables input that I'd input into the app. Results are below. </p><p style="text-align: justify;"><br /></p><p style="text-align: justify;"><b>RESULTS</b></p><p style="text-align: justify;">Given the assumptions I used (stated in the graphic below), the app performance results and the model predictions converged very well, which I'm pleased with. This gives me further trust in the app. Note how the positive and negative errors negate each other over time. Also note that generally, the errors are within 5% and the average error for 17.9 segments I manually built is -0.26%. </p><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://1.bp.blogspot.com/-b2iYqFTJWKA/X0y6L-5XXQI/AAAAAAAAH88/da7ernRHBZEXpWvsG1fMRbU_RYwdxvl3QCLcBGAsYHQ/s1223/Fulgaz%2Bpredictions%2Bvs%2Bperformance.JPG" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="588" data-original-width="880" height="246" src="https://1.bp.blogspot.com/-b2iYqFTJWKA/X0y6L-5XXQI/AAAAAAAAH88/da7ernRHBZEXpWvsG1fMRbU_RYwdxvl3QCLcBGAsYHQ/w512-h246/Fulgaz%2Bpredictions%2Bvs%2Bperformance.JPG" width="512" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">(Click to view) "Virtual" performance in the Fulgaz app compared to model predictions for given power. The ride was done on a Computrainer using Fulgaz app. Strava results : <a href="https://www.strava.com/activities/3984801170"><span style="color: red;">https://www.strava.com/activities/3984801170</span></a></td></tr></tbody></table><br /><p style="text-align: justify;">I believe the errors are partly due to :</p><p style="text-align: justify;">1) The chosen granularity of the course, which is a km at a "constant elevation". In reality, the road might step up or step down several times within a kilometre. However, for my purposes, this would suffice.</p><p style="text-align: justify;">2) I did not ride km segments at "constant power". Infact, I modulated it based on how I felt. </p><p style="text-align: justify;">3) I've assumed a constant rolling resistance per segment of 0.003. If the Fulgaz app changes rolling resistance in real time based on the segment you're on, that could affect the speed slightly. </p><p style="text-align: justify;">Also note that I have not applied altitude power-attenuation ("de-rate") in the model, which is because this is a virtual environment. However, we know for a fact, from both tested runners and cyclists, that aerobic capacity drops at moderate to high altitudes, how much depending on acclimatization levels and individual attributes. So in reality, actual times are very likely going to be slower. How much slower is another conversation. I hope to tackle that in an upcoming post. </p><p style="text-align: justify;"><b><br /></b></p><p style="text-align: justify;"><b>CONCLUSION</b></p><div style="text-align: justify;">The close results from my model and the actual performance on Fulgaz makes the Fulgaz app a reliable training tool, <u>in so far </u>as it is used for constant, steady speed climbing (I have yet to test it for solo TT efforts against the wind). It also validates the Martin et.al model (which has probably been done several times before by several people). When I shared this article with Mike Clucas of Fulgaz, he essentially confirmed that my reverse engineering closely matches the inputs that drive their model, atleast in curated events such as the French Tour. </div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">This post generally speaks to the need for indoor cycling training apps to make transparent to a customer what is driving their in-game physics. If in-game physics is non transparent, predictions based on widely used open source models will be vastly different to in-app performance. </div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">If the variables that impact the in-game performance are not transparent, you can't effectively do "what-if" predictions as almost all cyclists do in real life (<i>"if I ride with x equipment and/or shed a few pounds, how would that affect my performance?"</i>). This does not help those who take their training and racing very seriously and like to pre-plan for the event.</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">One might argue that indoor cycling apps are built like "games", hence the physics can deviate to an extent simply because it is a game. But there can be impacts. Depending on the magnitude of the deviation, a host of things can be affected ranging from perceived exertion, fatigue, <b><a href="http://www.georgeron.com/2020/04/Critical-Power-Concept.html" target="_blank"><span style="color: red;">CP and W'</span></a></b> dynamics and most importantly the nutritional needs that an app based performance requires. Either-way, if you can't predict something with physics, it's <i>unverifiable</i>, <i>unpredictable and </i>might I add<i>,</i> possibly <i>unstable</i>. </div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">If on the other hand, all indoor cycling apps used a verifiable model, one could effectively standardize/minimize/account for a source of variability while the rest of the differentiation can be in the graphics, software performance and other perks unique to each app. </div><p style="text-align: justify;">I look forward to actually climbing the beautiful Galibier in reality, if I'm lucky enough to put together my coin collection and go to France. Huge thanks to everyone at Fulgaz for keeping me entertained during this tumultuous time.</p><p style="text-align: justify;">-Ron</p>Ronhttp://www.blogger.com/profile/16268869622833968439noreply@blogger.com0tag:blogger.com,1999:blog-4786784182488135171.post-54742075466477708382020-08-23T16:25:00.052+04:002020-08-26T00:47:29.541+04:00The Poor Man's Tour de France : Virtual Stage Racing in GT Mimicry<p style="text-align: justify;">Readers might recall that last year, I attempted <a href="http://www.georgeron.com/2019/06/amateur-grand-tour-science.html" target="_blank"><span style="background-color: white; color: red;"><b>a Poor Man's Giro d'Italia</b></span></a>, a tongue in cheek name for a stage racing simulation in which the objective was to follow the Giro while riding "short" stages pretty much everyday by myself on local roads. The main motivation behind the exercise was to collect data and compare them to research studies attempted into Grand Tours and Grand Tour racers. </p><p style="text-align: justify;">I'd wanted to replicate something like that this year but with some additional realism to racing. Obviously for this to happen, the intensities would have to be high and I'd have to race with other people. With the whole Covid-19 situation demolishing the race calendar throughout the world, I turned to <b><a href="https://www.zwift.com" target="_blank"><span style="color: red;">Zwift</span></a></b> for the obvious solution. </p><p style="text-align: justify;">And thereby, I began another self-inflicted stage racing attempt called Poor Man's Tour de France in July. </p><p style="text-align: justify;">I have a few points to make on this mini-adventure before I share the data :</p><p style="text-align: justify;">1. The races began on 17th July and lasted upto 21st August. All race results are recorded in my <b><a href="https://www.zwiftpower.com/profile.php?z=2229999" target="_blank"><span style="color: red;">Zwift power user profile</span></a></b>. I started Zwift as a beginner in the E/D category and moved up to C by Stage 13. (To download my data in Excel .csv format, you can click on the plot below in Figure 2 where it links to the tabulated data). </p><p style="text-align: justify;">2. All races were done with a single sided pedal based power meter and a heart rate monitor on a non-smart trainer. </p><p style="text-align: justify;">3. The trainer used was the <a href="https://www.feedbacksports.com/product/omnium-portable-trainer/" target="_blank"><span style="color: red;"><b>Feedback Sports Omnium Over-drive</b></span></a> unit. This is a roller unit which is extremely portable, and perhaps the most portable of all trainers. Owing to direct contact between tire and roller, rolling friction and the dynamics of tire pressure becomes a bit more important than direct-drive units. The unit has minimal inertia. therefore, there is little to no way to coast during racing. If you stop pedaling, you lose power and stop very quickly. On the plus side, riding with this trainer has considerably improved my pedaling conditioning. Due to the direct wheel-on-roller experience, I was also able to get instant audible feedback on stomping vs smooth pedaling patterns.</p><p style="text-align: justify;">4. Due to lack of a direct drive setup, I found I had constraints with the inherent power curve available within the above trainer. With the gearing available to me and that power curve, I rarely escalated past cruise powers greater than 200 Watts, for fear of damaging the rollers (I'd already damaged one earlier this year and lost nearly 3 weeks to have a replacement under warranty shipped out to me from Hong Kong!). This also limited the short maximal sprint power outputs I could display within 300 Watts (I was generally not interested in sprinting) </p><p style="text-align: justify;">5. Choice of daily distances were variable. Terrain type was a mix between rolling hill races, mountain stages, few crits and uphill time trials. I skewed the race stages more towards rolling hilly races. </p><p style="text-align: justify;">6. I felt racing every day on Zwift while maneuvering around time constraints as a parent to a 2 year old wasn't really easy. Therefore, I had a few more recovery days in between stages than what would be standard for a Tour. In general, I didn't exceed more than 3 days without a race but the norm was racing every second day as fatigue started accumulating. </p><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://1.bp.blogspot.com/-Gax9T_DvA7I/X0JoOpY6oII/AAAAAAAAH7I/TZ8jeJalfMsB26CT1cGVDWtoEX8tQ3MLwCLcBGAsYHQ/s1024/WhatsApp%2BImage%2B2020-08-23%2Bat%2B4.59.01%2BPM.jpeg" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="1024" data-original-width="768" height="512" src="https://1.bp.blogspot.com/-Gax9T_DvA7I/X0JoOpY6oII/AAAAAAAAH7I/TZ8jeJalfMsB26CT1cGVDWtoEX8tQ3MLwCLcBGAsYHQ/w384-h512/WhatsApp%2BImage%2B2020-08-23%2Bat%2B4.59.01%2BPM.jpeg" width="384" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><h4><span style="font-weight: normal;">Figure 1 : The author's "pain cave", cobbled together during Covid-19 shelter in place restrictions in UAE. Materials used : book shelf, baby high chair, normal chair, ironing stand, yoga block, a weighing machine, Feedback Omnium Overdrive trainer, road bike, laptop and a 19 inch wide screen monitor. </span></h4></td></tr></tbody></table><p style="text-align: justify;"><br />Below is the interactive data for all 21 stages of the Poor Man's Tour. Note that data is presented against a logarithmic y-axis to make the plot more readable. Scrolling over the data lines should show data points.</p><p><br /></p><h3 style="text-align: left;"><b>DATA RESULTS</b></h3><div><b><br /></b></div><div><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://1.bp.blogspot.com/-cVkMctSkQ3I/X0VWwEerH1I/AAAAAAAAH7s/eGNLHEHNOLMTBrcs-fwDB172z5xZjD8zgCLcBGAsYHQ/s1309/Capture.JPG" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="483" data-original-width="1309" height="189" src="https://1.bp.blogspot.com/-cVkMctSkQ3I/X0VWwEerH1I/AAAAAAAAH7s/eGNLHEHNOLMTBrcs-fwDB172z5xZjD8zgCLcBGAsYHQ/w512-h189/Capture.JPG" width="512" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Table 1 : List of races done during 21 day <i>Poor Man's Tour de France</i> on Zwift<br /></td></tr></tbody></table><b><br /></b></div><p style="text-align: center;">
<iframe aria-label="Interactive line chart" frameborder="0" height="500" id="datawrapper-chart-JdvG2" scrolling="no" src="https://datawrapper.dwcdn.net/JdvG2/3/" style="border: none; min-width: 100% !important; width: 0;" title="Poor Man's Tour de France : The Data"></iframe><script type="text/javascript">!function(){"use strict";window.addEventListener("message",(function(a){if(void 0!==a.data["datawrapper-height"])for(var e in a.data["datawrapper-height"]){var t=document.getElementById("datawrapper-chart-"+e)||document.querySelector("iframe[src*='"+e+"']");t&&(t.style.height=a.data["datawrapper-height"][e]+"px")}}))}();
</script></p><h3 style="text-align: center;"><span style="font-size: small; font-weight: normal;">Figure 2 : Data for 21 days from a self-inflicted stage racing simulation called <i>The Poor Man's Tour de France</i> (top to bottom) - Total heartbeats, calculated calories, Zwift reported calories, work done, elevation, Trimp points, average heart rate, bike stress, normalized power, average power, average cadence, distance, RPE, TSS/km, TSS/km, & duration. Note that BikeStress is a training metric native to Golden Cheetah which establishes race intensities as a function of duration and intensity. Click on the line to view the data. </span></h3><p style="text-align: center;"><br /></p><h3 style="text-align: left;"><b>DISCUSSION OF RESULTS</b></h3><p style="text-align: justify;"><b>1. Total Distance, Elevation & Calories :</b> Over the total of 21 stages, I completed 600km of racing with a net ascent of 8666m burning an estimated 12000-13000 kcals. This equates to 17% of the actual Tour de France distance with an elevation gain nearly the height of Mt. Everest. These are modest numbers.</p><p style="text-align: justify;"><b>2. Heart rate :</b> The range of racing heart rates were between 151-194 bpm across the 21 stages. The highest heart rates were featured in stages with high stochasticity in pacing effort. For example, the two crits I attempted on Stage 9 and Stage 14 both of which had rolling terrain showed the highest heart rates. However, there were other crits I attempted which did not feature high heart rates (for example Stage 18). Although the normalized power for those stages were also high, this does not explain the higher heart rates. Perhaps cadence is another factor that might offer a clue, meaning the stages with higher cadence could feature high heart rate. There may also be a hidden con-founder somewhere that is outside of this data (diet, sleep, fatigue, other activities in life...). </p><p style="text-align: justify;"><b>3. Power :</b> In terms of normalized power, the range was from 117W-193W over 21 days of racing. Interestingly, in the early stages, I was just getting used to riding at high intensities on a trainer and not wholly happy with the cooling air flow available to me. So the early stages featured low powers at high heart rates. As the stages evolved, I got fitter in terms of being able to deliver higher power to the pedals at similar heart rates. I also got myself a bigger industrial size fan which could push out more air volume! There was a plateauing phenomena in powers as racing progressed which I attribute to day-to-day fatigue and the inherent power curve limitations of the non-smart trainer. </p><p style="text-align: justify;"><b>4. Aggregate stress : </b>Over 21 days of riding, the aggregate TRIMP based stress was 3008 for a daily stress of 143 AU/day. The aggregate Bikestress (a correlate for TSS) was around 2124, giving a daily figure of 101 AU/day. These were all calculated in Golden Cheetah. Total kilojoules burned was 12036, resulting in an average of 573 KJ/day. On a per day basis, these numbers are higher than the same data from Poor Man's Giro d'Italia. </p><p style="text-align: justify;"><b>5. Distance specific intensity :</b> In terms of TSS/km and Trimp/km, two metrics that maybe indicative of ride intensity as a function of unit distance, the highest values were incurred in stages that featured either a mountain climb time trial, a mountain race or a high intensity crit race. For example, of all the stages, the ones I rode on Stage 3 (L'Etape du Tour Stage 3) and Stage 7 (Alpe du Zwift TT) posted the highest values of intensity per distance. This again <b><a href="http://www.georgeron.com/2019/06/amateur-grand-tour-science.html" target="_blank"><span style="color: red;">agrees with my findings</span></a></b> previously from Poor Man's Giro d'Italia and the research data I posted there from the Sanders et.al investigation of Grand Tour racing. With distance and per day stress metrics stated as above, one area of inquiry is whether there are differences in the numbers between indoor and outdoor racing. With constraints of air flow and cooling indoors, one might expect to see higher race intensities indoors. Comparing the Zwift racing data with last year's Poor Man's Giro, the distance specific intensity metric Trimp/km is definitely higher this year on Zwift. However, this is not exactly an apples-to-apples comparison because I did not do a true "stage racing simulation" last year. However, the argument that indoor intensities should be higher is a rational one and something to discuss and further explore. </p><p style="text-align: justify;"><b>6. RPE :</b> Across 21 days of racing, RPE varied from a low of 6 to 10! The hardest I felt was during Stage 2 (L'Etape du Tour) which featured a mountain ascent of 1538m. Because this was one of the earlier stages, I was in no shape to climb continuously for 3 hours with poor air flow. In the final 20 minutes, I did hop off the bike once to take a break, thinking I was going to have a heart attack. Part of the challenge that day in my pain cave was lack of air flow to cool myself for that long! The standard deviation in RPE across the stages was quite low, however, indicating that the intensity on all days were more or less quite similar to each other. </p><p style="text-align: justify;"><b>7. Cadence : </b>My average cadence across all stages was 83 and the highest cadence was during Stage 19 which was a rolling hills ITT of 28 kilometers in length, where I staved off fatigue by riding at 90+ cadence. I reckon the stages with high cadence were excellent stimulus to the VO2max region of training intensities. One of the things I'm pleased with as I attempted this challenge is that I got quite experienced with being able to regulate my cadence to tune my perceived effort within different racing situations. It may have been that this factor also affected my heart rates over the course of each day's race. </p><p style="text-align: justify;"><b>8. Nutrition :</b> In general, being able to race everyday on Zwift means having to rely heavily on carbohydrates; success seems to depend on how well the stores of glycogen are topped up between races. My fuel system is one that is biased towards carbohydrates, which may also be partly explained by the fact that I'm a habitual carbohydrate consumer. There were some days were I didn't have the luxury to manage the diet well to feel fully topped up before the next race. On days where I felt I needed an extra "boost", I used the top ergogenic aid known to man, that's right - Coca Cola! Caffeine works. </p><p style="text-align: justify;"><b>9. Race Competition :</b> In general, I have only good things to say about Zwift as it is a tremendous motivational tool. During the 21 stages, I enjoyed many days sitting in the peloton and sharing the effort that got us all across the line with good timings. But I was in no way a match for those who could utilize some of the "gaming" aspects of virtual racing.</p><p style="text-align: justify;">I think Zwift has to figure out some way to weed out sandbaggers. Although the final listings on Zwift Power website excludes those cheating below their actual categories, the race dynamics are affected by the presence of these individuals. For example, it is often the first 2-3 minutes of an e-race where your placement is made or broken due to massive power surges to find position. The presence of more able riders who are cheating below their category could compel others to ride just as hard in order to get on their wheel , as a result many gaps are formed disadvantaging the lower order riders who have "missed the draft". This point maybe moot. </p><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://1.bp.blogspot.com/-WmUhC11D0Js/X0J0SHbtVBI/AAAAAAAAH7U/TZwR4iXicAMwASluc-orT1H4vRPRk4oPgCLcBGAsYHQ/s2048/uZkw26-CxCneqNJM5me-qtz5CkEwCZHFPC01BeagScs-2048x1119.jpg" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="1119" data-original-width="2048" height="350" src="https://1.bp.blogspot.com/-WmUhC11D0Js/X0J0SHbtVBI/AAAAAAAAH7U/TZwR4iXicAMwASluc-orT1H4vRPRk4oPgCLcBGAsYHQ/w640-h350/uZkw26-CxCneqNJM5me-qtz5CkEwCZHFPC01BeagScs-2048x1119.jpg" width="640" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Figure 3 : The author in a "break" of select group of riders from the Namibian Race League <br />during Stage 17. <br /></td></tr></tbody></table><h3><b><br />CONCLUSION</b></h3><p style="text-align: justify;">The results discussed in the section above generally agrees with the data found from Grand Tours that the mountain stages are where the action really is in-terms of stress and intensity. Although the race intensities were high and the monotony day to day was also high. <span style="text-align: justify;">Zwift provided a great way to beat that monotony with the ability to select from numerous races spread across different maps with different competitors. For example, I found South Africans and Japanese race subtly different when compared to Brits! Maybe that is an imaginative observation, but it still is an observation. </span></p><p style="text-align: justify;">Overall, while I found I was making improvements in the duration specific power outputs as the races progressed, I found myself hitting a plateau due to a combination of fatigue and power curve limitations on the trainer. In other words, there were diminishing returns after a point. </p><p style="text-align: justify;">From the Poor Man's Tour de France racing challenge, I was quickly able to learn which e-races suit me and which races wouldn't. Therefore, the choice of many rolling hilly races was intentional. I also included mountain stages. Flat, all-out races were few. </p><p style="text-align: justify;">If I redid the Poor Man's Tour de France again, I'd figure out a way to balance out the percentage of race distance spread between mountains, flats and rollers. But I can't say if the actual Tour de France traditionally or even this year has actually been balanced either! Often we hear that the Tour stages are deliberately designed to suit some of the top French stars. That doesn't seem to be any different this year. </p><p style="text-align: justify;">In conclusion, with the constraints that were upon my time, I think this was sufficient racing stimulus. Due to the plateauing effect of power and the accumulating fatigue as the stages progressed, I had to draw the line somewhere to minimize the losses. </p><p style="text-align: justify;">With a few days left for the actual Tour de France, I will be able to smugly soak in the racing footage and maybe even pretend to co-relate to it with my own experience, ha!</p>Ronhttp://www.blogger.com/profile/16268869622833968439noreply@blogger.com0tag:blogger.com,1999:blog-4786784182488135171.post-52100436052247839842020-07-15T23:50:00.000+04:002020-07-16T01:07:15.285+04:00Tour de France : Key Statistics The following is an easily accessible graph showing key statistics for the Tour de France from the years 1903-2019.<br />
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I've highlighted some epochs in the data, namely the two World Wars and the 1990's doping era culminating in the Armstrong doping saga. For the wars, the plot makes it seem as if racing took place but this is just a visual effect. No racing took place during those years.<br />
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To go along with this data, you might also like my <b><a href="https://www.georgeron.com/2010/08/modern-bicycles-and-cycling-speeds-any.html"><span style="color: red;">previous post</span> </a></b>on modern bicycles and cycling speeds. There, I explored whether bicycles themselves have made any appreciable impact to speeds.<br />
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Hopefully this datasheet can be used in future years as a live plot.<br />
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All data obtained from <b><a href="http://www.letour.fr/"><span style="color: red;">www.letour.fr</span></a></b> and compiled with <a href="https://www.datawrapper.de/"><span style="color: red;"><b>Datawrapper</b></span></a>.<br />
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<br />Ronhttp://www.blogger.com/profile/16268869622833968439noreply@blogger.com0tag:blogger.com,1999:blog-4786784182488135171.post-86707638346517839482020-04-29T11:26:00.002+04:002020-09-01T03:55:09.767+04:00Functional Threshold Power : A Scientific Scrutiny<div dir="ltr" style="text-align: left;" trbidi="on">
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Certain entities in the world have originated competing claims about cycling performance concepts, test protocols, and training zones the rest of the world must adhere to. The astute athlete cum observer would want to find out which ones stand scientific scrutiny and separate myth from fact.<br />
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In that spirit, this post is an appraisal of the definition and estimation techniques of Functional Threshold Power (FTP) which are at the core of this power-based training concept. It follows from the <b><a href="http://www.georgeron.com/2020/04/Critical-Power-Concept.html"><span style="color: red;">last post</span></a></b>, where I explored a scientifically vetted threshold concept called critical power (CP) and most of its nuances, including application related issues.<br />
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This post attempts to explain with simple arguments and scientific references why FTP, although as "useful" a performance metric as it may be to some people, is a pseudo-scientific concept at best. </div>
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<b>I. Introduction to FTP : Definition and Estimation</b></div>
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FTP was conceptualized as a field-based practical method of estimating a threshold phenomena using cycling power meter technology. It is, like Critical Power, used as an endurance index to design training prescription as well as classify cycling talent. A threshold, as a reminder, is an intensity marker just above which physiological responses will sharply change whereas below it, attains a steady-state within a tolerance band. </div>
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The training concept was formalized by Coggan et.al in the book <i>Training and Racing with a Power Meter (TARWAPM) </i>in the early 2000s and an ecosystem was built around FTP consisting of sister metrics (NP, IF, TSS, etc) and software marketed by Training Peaks group. Some of the history behind how this all came to be is documented on TARWAPM's <b><a href="http://www.trainingandracingwithapowermeter.com/2010/04/brief-history-of-training-and-racing_1025.html"><span style="color: red;">blog page</span></a></b>.<br />
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<table cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://1.bp.blogspot.com/-PyFnd8Oh9lc/XqiYPjy1uwI/AAAAAAAAHu4/L75g5pQGO-c59BFN0FVHqNFxFJsnnNw0wCLcBGAsYHQ/s1600/Andrew%2BCoggan%2Bsigning%2Bbooks.jpg" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="540" data-original-width="720" height="240" src="https://1.bp.blogspot.com/-PyFnd8Oh9lc/XqiYPjy1uwI/AAAAAAAAHu4/L75g5pQGO-c59BFN0FVHqNFxFJsnnNw0wCLcBGAsYHQ/s320/Andrew%2BCoggan%2Bsigning%2Bbooks.jpg" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Andrew Coggan PhD signing copies of TARWAPM books. Source : TARWAPM's blog page. </td></tr>
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<span style="text-align: left;">Let me cut to the chase and quote the 3rd edition of TARWAPM's definition of FTP, marking in red some key terms that I will explore further : </span></div>
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<i>"FTP is the <span style="color: red;"><b>highest power</b></span> that a rider can sustain in a <b><span style="color: red;">quasi-steady state</span></b> <b><span style="color: red;">without fatiguing</span></b>. When power exceeds FTP, fatigue will occur much sooner (generally after <b><span style="color: red;">approximately one hour</span></b> in <b><span style="color: red;">well-trained cyclists</span></b>), whereas power just below FTP can be maintained considerably longer. </i>[1]" --- (1)</div>
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The text lists around 7 different methods to estimate FTP.</div>
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1) From a power & time-frequency distribution chart from cycling training and racing data.</div>
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2) From routine steady power intervals, repeats or longer climbs.</div>
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3) From normalized power (NP) during hard mass-start races of <span style="color: red;"><b>approximately one hour.</b></span></div>
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4) From a <b><span style="color: red;">one-hour time trial </span></b>by inspecting a smoothed time-series plot of power.</div>
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5) From a power duration model. obtained by testing for CP, and where the resulting model derived value of CP is suggested to be <b><span style="color: red;">interchangeable with FTP.</span></b></div>
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6) From the <b><span style="color: red;">proprietary mFTP</span></b> model in WKO4.</div>
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7) From the FTP testing protocol consisting of a 28-minute warmup, a main set of 20 minutes, and a cooldown of 10-15 minutes. </div>
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The 7th method is probably the most notoriously proliferated in cycling lexicon. The premise being that subtracting 5% from the main set time trial of 20 minutes after a hard warm-up will estimate FTP (hereby, called FTP20 for simplicity). A. Coggan has not until recently<span style="background-color: white;"> <a href="http://marktallonphd.com/the-myth-of-functional-threshold-power-ftp/"><b><span style="color: #e67c73;">distanced himself</span></b></a></span> from this estimation technique, saying that it was Allen Hunter's contribution and not his.</div>
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There are other methods of estimating FTP which is coded into popular programs like Zwift and Trainer Road and yet another confusing bunch of "new" test protocols on <b><a href="https://www.trainingpeaks.com/blog/the-physiology-of-ftp-and-new-testing-protocols/?fbclid=IwAR1OPOrd6NZT72tRwrkXla9J1z6zq_bUy9ODIVJHdZCAvO1p8KzfLaCsN5s"><span style="color: red;">Training Peaks' website</span></a></b>. The validity of these techniques are in question besides the obvious danger of under/overestimating some individuals. <u>Therefore, this post is purely focused on the original concept of FTP and its test protocols as codified in TARWAPM.</u> </div>
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<b>II. A Deeper Inspection of FTP</b><br />
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Let me inspect in slightly more detail the terms highlighted in red in the definition of FTP in (1). </div>
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<b>A) The Issue of "Quasi-steady State" </b></div>
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A quasi-steady state is meant to describe a transient situation where physiological variables such as blood lactate and VO2 are rising but remain within the zone of uncertainty. Using field power estimates, a quasi-steady state can be attributed to the variation of power values over the time duration. </div>
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Scientific studies demonstrate the ability to work at a "quasi-steady state" at critical power, where workloads are on the order of 10-15 Watts higher than what can be sustained for one hour. Critical power, from <b><a href="https://www.georgeron.com/2020/04/Critical-Power-Concept.html"><span style="color: red;">my previous post</span></a></b>, corresponds to a workload of approximately mid-way between lactate threshold (or gas exchange threshold) and VO2max.<br />
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Moreover, the time to exhaustion at that workload is lower, around 24 minutes or so. This has been demonstrated in both physically active subjects and competitive cyclists (see Figures 1,2 below). Besides, even a shorter maximal time trial lasting around 30 minutes was demonstrated to show quasi-steady-state behavior in both power outputs and physiological variables (see Figures 2B, 2C). </div>
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Therefore, the FTP concept systematically underestimates the wattage, or the workload that can be achieved at a quasi-steady state. From a lab testing standpoint, this same observation was noted with MLSS suggesting that a steady state in VO2 can be achieved even beyond the power at MLSS [15].</div>
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<tr><td style="text-align: center;"><a href="https://1.bp.blogspot.com/-e7zxZZJ-WzI/XqfZX49SlnI/AAAAAAAAHtk/2SL5lb9obG4ZVEpyFELwctGBOBX-TnnDgCLcBGAsYHQ/s1600/Time%2Bto%2Bexhaustion%2Band%2Bquasi%2Bsteady%2Bstate%2Bat%2BCP%2B%2528marked%2529.jpg" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="720" data-original-width="960" height="300" src="https://1.bp.blogspot.com/-e7zxZZJ-WzI/XqfZX49SlnI/AAAAAAAAHtk/2SL5lb9obG4ZVEpyFELwctGBOBX-TnnDgCLcBGAsYHQ/s400/Time%2Bto%2Bexhaustion%2Band%2Bquasi%2Bsteady%2Bstate%2Bat%2BCP%2B%2528marked%2529.jpg" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Figure 1 : The Poole et.al study showed that in physically active subjects, the group mean of metabolic demand when working at constant-load exercise at critical power, much higher than that of lactate threshold, resulted in steady state VO2. Time to exhaustion in these subjects was 17.7 +/- 1.2 minutes. From research reference [6].</td></tr>
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<tr><td style="text-align: center;"><a href="https://1.bp.blogspot.com/-BR4QgIUmaMI/XqfgMPSyl5I/AAAAAAAAHtw/12KRF3sow3MY3CxDrCM2d7pziLh8uWJeQCLcBGAsYHQ/s1600/Time%2Bto%2Bexhaustion%2Band%2Bquasi%2Bsteady%2Bstate%2Bat%2BCP%2B%2528competitive%2Bcyclists%2529.JPG" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="720" data-original-width="960" height="240" src="https://1.bp.blogspot.com/-BR4QgIUmaMI/XqfgMPSyl5I/AAAAAAAAHtw/12KRF3sow3MY3CxDrCM2d7pziLh8uWJeQCLcBGAsYHQ/s320/Time%2Bto%2Bexhaustion%2Band%2Bquasi%2Bsteady%2Bstate%2Bat%2BCP%2B%2528competitive%2Bcyclists%2529.JPG" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Figure 2 : The de Lucas study in competitive cyclists showed that quasi steady state VO2 was achieved at workloads at CP. Here again, the group mean for time to exhaustion was 22.9 +/ 7.5 minutes. From research reference [7].</td></tr>
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<tr><td style="text-align: center;"><a href="https://1.bp.blogspot.com/-1Bntc0GsI0I/XqlEhDLgqMI/AAAAAAAAHvE/tzNMO2ko7U0DLedkZnkHQ_XRATw9loF2gCEwYBhgL/s1600/Quasi%2Bsteady%2Bstate%2Bpower%2Boutputs%2Bduring%2B30km%2BTT.png" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="366" data-original-width="590" height="248" src="https://1.bp.blogspot.com/-1Bntc0GsI0I/XqlEhDLgqMI/AAAAAAAAHvE/tzNMO2ko7U0DLedkZnkHQ_XRATw9loF2gCEwYBhgL/s400/Quasi%2Bsteady%2Bstate%2Bpower%2Boutputs%2Bduring%2B30km%2BTT.png" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Figure 2B : Quasi-steady state power outputs were shown in intense 30 min TTs conducted on well-trained triathletes. See reference [12]. </td></tr>
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<tr><td style="text-align: center;"><a href="https://1.bp.blogspot.com/-zeO1VPAnlZ4/Xqhxmt2DMnI/AAAAAAAAHus/kR6jfV_UTbAwvWw40c_2CWbYQ9r10DW_QCLcBGAsYHQ/s1600/Quasi%2Bsteady%2Bstate%2Bduring%2B30km%2BTT.png" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="417" data-original-width="960" height="172" src="https://1.bp.blogspot.com/-zeO1VPAnlZ4/Xqhxmt2DMnI/AAAAAAAAHus/kR6jfV_UTbAwvWw40c_2CWbYQ9r10DW_QCLcBGAsYHQ/s400/Quasi%2Bsteady%2Bstate%2Bduring%2B30km%2BTT.png" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Figure 2C : Quasi steady states in metabolic demand and blood lactate values were shown in a much more intense, shorter TT lasting 30 minutes on well trained triathletes. Moreover, study demonstrates that subjects can sustain very high values of blood lactate for extended time, some > 10mM. See reference [12].<br />
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<b>B) The Issue of "Absence of Fatigue"</b><br />
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The highest workload one can sustain for about an hour does not or cannot occur in the absence of fatigue.<br />
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A well-documented study in well trained cyclists who completed a 4, 20 and 40km time trial demonstrated that central and peripheral fatigue occurred in all distances, including the 40km TT which took approximately 65 minutes to complete. The pattern of central vs peripheral fatigue shifts from peripheral dominant over 4km towards central fatigue over 20km. In other words, the decline in the ability to produce force residing within the central nervous system was higher in the longer time trials. Given this data, exercising at the highest workload corresponding to quasi steady-state in the "absence of fatigue" is notionally incorrect. </div>
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<tr><td style="text-align: center;"><a href="https://1.bp.blogspot.com/-PJFJ9QwXjds/Xqf3ld9XdZI/AAAAAAAAHt8/5h6ijR2GZmspFwlLlO9sgjnBoa2qtZZ6gCLcBGAsYHQ/s1600/Fatigue%2Bduring%2B4%2B20%2B40%2Bkm%2BTTs.jpg" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="720" data-original-width="960" height="300" src="https://1.bp.blogspot.com/-PJFJ9QwXjds/Xqf3ld9XdZI/AAAAAAAAHt8/5h6ijR2GZmspFwlLlO9sgjnBoa2qtZZ6gCLcBGAsYHQ/s400/Fatigue%2Bduring%2B4%2B20%2B40%2Bkm%2BTTs.jpg" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Figure 3 : Exercise induced impairment in the ability to produce muscular force measured in well trained cyclists who executed 4km, 20km and 40km time trials. Fatigue, central and peripheral, are prominent in all duration time trials with central fatigue being highest during longer time trials. Reference and adapted from [8]. </td></tr>
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<b>C) The Issue of "Highest Power" at Quasi-steady State </b><br />
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Following the arguments from A), the power output that can be sustained for "approximately" an hour does not correspond to the "highest power" for which a quasi steady-state can be achieved. The study referenced in Figure 3 shows that lactate values for the 20km TT also stabilized around the 8km mark and barely increases until the end spurt, despite being at a 15-20W higher than the 40km TT wattage.<br />
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FTP arbitrarily pegs a duration of "approximately" one hour to "highest power at quasi-steady state" which is not actually the case. What is obvious though, is that the workload at FTP is an unambiguously steady-state and therefore, is not the highest "quasi-steady state" intensity. </div>
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<tr><td style="text-align: center;"><a href="https://1.bp.blogspot.com/-spvLE97JuNs/XqgBk4ug_tI/AAAAAAAAHuI/J04NSwrru7UmTEhrP-7eycOodb7R6HcDgCLcBGAsYHQ/s1600/Lactate%2Bvalues%2Bat%2B20km%2Band%2B40km%2BTT.png" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="584" data-original-width="938" height="248" src="https://1.bp.blogspot.com/-spvLE97JuNs/XqgBk4ug_tI/AAAAAAAAHuI/J04NSwrru7UmTEhrP-7eycOodb7R6HcDgCLcBGAsYHQ/s400/Lactate%2Bvalues%2Bat%2B20km%2Band%2B40km%2BTT.png" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Figure 4 : Lactate values in a 20km TT stabilize at the 8km mark and barely increase <b>until the end spurt</b>, despite being a 15-20W higher than a 40km TT. The latter took 65min to complete, which going by FTP definition, would correspond to "approximately" one hour. Reference and adapted from [8]</td></tr>
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</b> <b>D) The Issue of "Functional Threshold" As a Surrogate for Laboratory-Based Testing</b><br />
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FTP originated as a practical field-based alternative to lactate threshold testing. "Threshold" in concept refers to sharp distinctions in physiological responses associated with exercise slightly below and above a specific intensity value. </div>
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However, as we have seen previously, the maximum intensity of "quasi-steady" state exercise has been shown to have sustainable durations much lesser than approximately an hour. So it is questionable why FTP should lay claim to accurately representing threshold in a wide group of people. </div>
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Having stated that, how do comparisons between FTP and laboratory indicators of threshold match up in scientific studies? </div>
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Let's take a look : </div>
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<b>1) FTP compared against individual anaerobic threshold (IAT) power: </b> Although empirical demonstrations have shown FTP20 and IAT are close, authors of one recent study stated: "<i>…it is difficult to accept FTP as a thoroughly valid concept. We found large limits of agreement between most variables, suggesting a high level of inter-individual variability in the relationship between FTP20 vs. FTP60 and between both measurements vs. IAT (me: stepwise lactate profile test).</i>" [2] </div>
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In other words, wide limits of agreement in a Bland-Altman plot shows that any agreement between a surrogate method (FTP) and a laboratory-based marker, here IAT, must be ambiguous.</div>
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<tr><td style="text-align: center;"><a href="https://1.bp.blogspot.com/-JPkKoEgC8w0/XqLhiTXzI6I/AAAAAAAAHsU/vohP3Wl4H0MCImmox7IfpaO7ZD8idndyACLcBGAsYHQ/s1600/LOA%2BFTP20%2BFTP60.JPG" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="434" data-original-width="1411" height="122" src="https://1.bp.blogspot.com/-JPkKoEgC8w0/XqLhiTXzI6I/AAAAAAAAHsU/vohP3Wl4H0MCImmox7IfpaO7ZD8idndyACLcBGAsYHQ/s400/LOA%2BFTP20%2BFTP60.JPG" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Figure 5 : Bland altman plot of FTP20 compared to individual anaerobic threshold (IAT) in 23 well trained cyclists. See reference [2].</td></tr>
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<b>2) Against maximum lactate steady state (MLSS) power: </b>The same authors from the study above compared FTP with another threshold concept called MLSS and found generally good agreement. However, even in this study, wide limits of agreement were bserved between FTP20 and MLSS among different groups of cyclists with different training statuses, implying ambiguous agreement between the two when we look at heterogeneous samples [3]</div>
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<tr><td style="text-align: center;"><a href="https://1.bp.blogspot.com/-KLC5ks6quSI/XqLkMaNKtYI/AAAAAAAAHsg/zR2xWFSOmn08MsPdjcyjVRv8Wzy6jhhSACLcBGAsYHQ/s1600/LOA%2BFTP20%2BMLSS.JPG" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="348" data-original-width="1106" height="125" src="https://1.bp.blogspot.com/-KLC5ks6quSI/XqLkMaNKtYI/AAAAAAAAHsg/zR2xWFSOmn08MsPdjcyjVRv8Wzy6jhhSACLcBGAsYHQ/s400/LOA%2BFTP20%2BMLSS.JPG" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Figure 6: Comparison of FTP20 with MLSS in 15 cyclists - 7 trained and 8 well trained. See reference [3].</td></tr>
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</b> Another study that studied validity to MLSS concluded: <i>"The results indicate that the PO at FTP95% is different to MLSS, and that changes in the PO at MLSS after training were not reflected by FTP95%. Even when using an adjusted percentage (ie, 88% rather than 95% of FTP20), the large variability in the data is such that it would not be advisable to use this as a representation of MLSS." </i>[14]<br />
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<b>3) Against Lactate Threshold (LT) power: </b>Foster et.al came to a similar conclusion as the previous two studies when comparing LT and FTP20. They wrote: <i>".....caution should be taken when using the FTP interchangeably with the LT as the bias between markers seems to depend on the athletes’ fitness status. Whereas the FTP provides a good estimate of the LT in trained cyclists, in recreational cyclists, FTP may underestimate LT." </i>[4]</div>
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<tr><td style="text-align: center;"><a href="https://1.bp.blogspot.com/-y2tvKc6BVew/XqLpr5JZILI/AAAAAAAAHss/ifGBTZW99mwkU-XQ2KGv4uTc-Pa-H1yOwCLcBGAsYHQ/s1600/LOA%2BFTP20%2BLT.JPG" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="380" data-original-width="520" height="233" src="https://1.bp.blogspot.com/-y2tvKc6BVew/XqLpr5JZILI/AAAAAAAAHss/ifGBTZW99mwkU-XQ2KGv4uTc-Pa-H1yOwCLcBGAsYHQ/s320/LOA%2BFTP20%2BLT.JPG" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Figure 7 : Limits of agreement between FTP and lactate threshold studied in 20 healthy cyclists. See reference [4]. </td></tr>
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<b>4) FTP Compared Against A Range of Blood Lactate Threshold Markers: </b>One study compared FTP20 with a range of laboratory-based blood lactate measurements, such as LT, LT at 4mmol blood lactate, Dmax derived LT, and IAT (LT = lactate threshold). The main objective was to find the best correlate of FTP in a single study. </div>
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They demonstrated that all computations resulted in numbers that differed significantly from FTP20. Despite the strongest correlation being between FTP and LT4.0, a large dispersion of approximately 100 Watts was found in the inter-individual data questioning their equivalence. The study concluded: "...<i>we suggest that FTP does not have an </i><i>equivalent physiological basis to any of the tests used herein and, therefore, cannot be used </i><i>interchangeably.</i>" [9] </div>
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<tr><td style="text-align: center;"><a href="https://1.bp.blogspot.com/-PFKIFoiGu6w/XqMQ5yp1ALI/AAAAAAAAHs4/Ltep1gjwPPEPgmq7m20Nu8PWEbL87dpjQCLcBGAsYHQ/s1600/FTP%2Bvs%2BBLA%2Bmarkers.JPG" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="510" data-original-width="692" height="293" src="https://1.bp.blogspot.com/-PFKIFoiGu6w/XqMQ5yp1ALI/AAAAAAAAHs4/Ltep1gjwPPEPgmq7m20Nu8PWEbL87dpjQCLcBGAsYHQ/s400/FTP%2Bvs%2BBLA%2Bmarkers.JPG" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Figure 8 : FTP compared to a host of lactate parameters in 20 competitive cyclists. See reference [9].</td></tr>
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The overall picture from the previous studies shows that claiming FTP can be used as an accurate surrogate for laboratory-based measures of threshold is at best, unfounded.</div>
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<b>E) The Issue of FTP20 method and "False Sense of Precision" </b><br />
<br />
As a matter of practical convenience, the second and third editions of TARWAPM suggested the FTP20 method as a way to estimate 60 minute FTP.<br />
<br />
The issue with this technique is that the 95% computation is probably an average for a large group of cyclists but not exactly applicable to you or I mainly due to inter-individual variability [5]. Some people will be at 93%, some at 90%, some at 85%. This was also shown by A. Coggan himself (see Figure 9).<br />
<br />
One prominent exercise physiologist told me: "A value of 92-93% is probably closer on average, whereas a value of 95% would, therefore bring the estimated threshold back towards 30MMP (30 minute mean maximal power)!"<br />
<div style="text-align: left;">
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<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td><a href="https://1.bp.blogspot.com/-WZvcanetRWQ/XqgGYqx7guI/AAAAAAAAHuU/Xgk4eP7_eFcIke_oWJvMftdqIjErkEq3ACLcBGAsYHQ/s1600/Screen%2BShot%2B2016-09-19%2Bat%2B19.48.46.png" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="509" data-original-width="504" height="320" src="https://1.bp.blogspot.com/-WZvcanetRWQ/XqgGYqx7guI/AAAAAAAAHuU/Xgk4eP7_eFcIke_oWJvMftdqIjErkEq3ACLcBGAsYHQ/s320/Screen%2BShot%2B2016-09-19%2Bat%2B19.48.46.png" width="316" /></a></td></tr>
<tr><td class="tr-caption" style="font-size: 12.8px;">Figure 9 : 95% of 20min power is not necessarily one hour FTP. Source : Facebook fan-page of TARWAPM.</td></tr>
</tbody></table>
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<br /></div>
<div style="text-align: left;">
<span style="text-align: justify;">As published by A. Coggan in a whitepaper in March 2003, the real effect of employing an arbitrary correction factor to 20 min power may simply be to convey a false sense of precision [10].</span></div>
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<span style="text-align: justify;"><br />
</span></div>
<div style="text-align: left;">
<span style="text-align: justify;">While its understood that he would like to distance himself from the FTP20 method, I would add that continuing to perpetrate the false sense of precision in the TARWAPM book does not make false sense of precision go away. </span><span style="text-align: justify;">Besides, the entire discussion of whether the correction factor should be 95%, or 90% does not take away from the fact that FTP is arbitrary linked to "approximately one hour" with an unfounded claim to being the "highest workload" at quasi-steady state. Will two wrongs make a right?</span></div>
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<b>F) The Issue of FTP derived as CP from W-time plot</b><br />
<br />
In my <b><a href="http://www.georgeron.com/2020/04/Critical-Power-Concept.html"><span style="color: red;">previous post</span></a></b>, we looked into several research studies showing how critical power defines the boundary between heavy and severe intensity. In numerous research studies, work-rates at markers of thresholds such as LT and MLSS were found to be lower than work-rates at CP. In fact, it falls somewhere midway between LT and VO2max, depending on which study you look at. </div>
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<br /></div>
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With that information available, CP is a high-intensity workload that may be sustained only approximately 30 minutes or less. Therefore, approximately one hour of power (FTP) and CP should not be considered interchangeable in principle without data. As one research team noted, a fresh study involving a wider cohort of subjects is worthwhile to continue to test this idea of interchangeability [11]. </div>
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In a study conducted by Morgan et.al, FTP20 and CP correlated with each other but the limits of agreement were found to be relatively large (+ 10.9 to -13.1%) such that the authors argued: <i>"...limits of agreement between CP and FTP in this study may be too large to be practically meaningful for athletes and coaches, and that the agreement between the two variables may be coincidental."</i> [5]</div>
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The idea advanced in TARWAPM Ed.3 that FTP can be estimated from a linearized Work-Time plot and considered interchangeable with Critical Power is unfounded.<br />
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<b>G) The Issue of Secret Sauce In Modeled FTP</b><br />
<br />
In TARWAPM, one of the methods to estimate FTP is from modeling it from a collection of mean maximal power (MMP) values collected in a specific time frame window. The value of FTP is the resulting parameter solved from the fit, called modeled FTP or mFTP.<br />
<br />
However, mFTP modeling is only available in the proprietary software WKO4 (now WKO5). On the Wattage forums, A.Coggan has claimed that data from over 200 MMP values show mFTP to be 60 +/- 13 min, and he's used this as an argument to claim that FTP is sustained for "approximately" an hour.<br />
<br />
TARWAPM calls the modeling technique the "secret sauce" implying that the proprietary fitting method is not available for open scrutiny, only its outputs are. This roadblock might explain why most studies have used the FTP20 estimation technique to explore their research questions. Compare this to the CP concept which is pretty much open-source and tenable to research to advance our understanding in wide groups of people and wide groups of sporting activities.<br />
<br />
<br />
<b>H) The Issue of FTP Based Stress Metrics and One Hour </b><br />
<br />
While TARWAPM's definition that FTP is based "approximately around an hour" continues to be proliferated, other metrics in the FTP ecosystem such as the Bannister style "Training Stress Score" (TSS) is still arbitrarily pegged to an hour. The math in the formula for TSS has been designed in such a fashion as to result in 1 hour at FTP = 100 TSS. This indicates that the formula was designed with an arbitrarily fixed value in mind for convenience, rather than basing it on physiological reality. Since training prescription and fitness performance charts in the FTP ecosystem are based on TSS, flaws are propagated throughout the mathematics chain.</div>
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<b>III. Conclusion</b></div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
FTP was borne out of a perceived need for field testing convenience and one might add, an entrepreneurial excitement to build a quantification ecosystem when power-meters hit the market beginning in the late 1990s. </div>
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<br /></div>
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As a purely performance-based metric, FTP is "useful", just as critical power concept and modeling for CP is useful. However, in comparison to CP, the number of papers scrutinizing FTP has been woefully and remarkably small in number. Many of them demonstrates that the validity of FTP is in question. </div>
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I conclude with a summary of reasons why FTP must be approached with caution by whomsoever is using it or plans to adopt it : </div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
1) FTP's definition that it is the "highest" workload one can sustain a quasi-steady state is not demonstrated in studies. This might systematically under-estimate the intensity where quasi-steady states can be achieved. This also implies that FTP is an intensity area where one is <u>unambiguously</u> at steady state. </div>
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<br /></div>
<div style="text-align: justify;">
2) FTP's claim to be a valid and accurate surrogate for lab-based testing for a range of thresholds is unfounded. Besides, any claims that the concepts like critical power and FTP can be interchanged through modeling work is unfounded and probably a serious error. There have been recent calls by scientists to consider CP alone as the gold standard when the goal is to define maximum lactate steady state [13].</div>
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<br /></div>
<div style="text-align: justify;">
3) FTP's claim that it is approximately one hour of power that can be sustained without fatigue is most definitely incorrect. </div>
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<br /></div>
<div style="text-align: justify;">
4) Despite acknowledgement of variability, accompanying metrics in the FTP ecosystem like Training Stress Scores continue to be arbitrarily pegged to an hour (1 hour at FTP = 100 TSS). This continues to spread the already wide spread confusion that FTP is 1-hour power which it is not. </div>
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<br /></div>
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5) Widely profilerated estimation techniques for FTP, such as the FTP20 method is incorrect. As the originator of the FTP concept describes, it simply yields a false sense of precision. However, the proliferation of this false sense in the TARWAPM book does not make false sense of precision go away.</div>
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<br /></div>
<span style="text-align: justify;">Regardless of its conceptual flaws, I acknowledge that FTP has found favor with coaches and athletes who use it simply for its training value. </span>However, testimonials and anecdotal evidence are separate from science. Claims made about FTP and its accompanying ecosystem warrant additional scientific scrutiny. The collection of knowledge we currently have from research suggests that those claims are weak and not based on scientific fact.<br />
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<div style="text-align: justify;">
<b>REFERENCES</b></div>
</div>
<div>
<div style="text-align: justify;">
<br /></div>
</div>
<div>
<div>
<div style="text-align: justify;">
1. Allen Hunter. Training and Racing with a Power Meter . VeloPress. Kindle Edition. </div>
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<div>
<div style="text-align: justify;">
<br /></div>
</div>
<div>
<div style="text-align: justify;">
2. Borszcz, Fernando & Tramontin, Artur & Bossi, Arthur & Carminatti, Lorival & Costa, Vitor. (2018). Functional Threshold Power in Cyclists: Validity of the Concept and Physiological Responses. International Journal of Sports Medicine. 39. 10.1055/s-0044-101546. </div>
</div>
<div>
<div style="text-align: justify;">
<br /></div>
</div>
<div>
<div style="text-align: justify;">
3. Borszcz, Fernando & Tramontin, Artur & Costa, Vitor. (2019). Is the Functional Threshold Power Interchangeable With the Maximal Lactate Steady State in Trained Cyclists?. International Journal of Sports Physiology and Performance. 14. 1029-1035. 10.1123/ijspp.2018-0572. </div>
</div>
<div>
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</div>
<div>
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4. Valenzuela, Pedro L. & Morales, Javier S. & Foster, Carl & Lucia, Alejandro & de la Villa, Pedro. (2018). Is the Functional Threshold Power (FTP) a Valid Surrogate of the Lactate Threshold?. International Journal of Sports Physiology and Performance. 13. 10.1123/ijspp.2018-0008. </div>
</div>
<div>
<div style="text-align: justify;">
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</div>
</div>
</div>
</div>
<div>
<div style="text-align: justify;">
5. Morgan, Paul & Black, Matthew & Bailey, Stephen & Jones, Andrew & Vanhatalo, Anni. (2018). Road cycle TT performance: Relationship to the power-duration model and association with FTP. Journal of Sports Sciences. 10.1080/02640414.2018.1535772. </div>
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<br /></div>
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6. Poole, David & Ward, Susan & Gardner, Gerald & Whipp, Brian. (1988). Metabolic and respiratory profile of the upper limit for prolonged exercise in man. Ergonomics. 31. 1265-79. 10.1080/00140138808966766. </div>
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<br /></div>
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7. de Lucas, Ricardo & Mendes de Souza, Kristopher & Costa, Vitor & Grossl, Talita & Guglielmo, Luiz Guilherme. (2013). Time to exhaustion at and above critical power in trained cyclists: The relationship between heavy and severe intensity domains. Science & Sports. 28. e9- e14. 10.1016/j.scispo.2012.04.004. </div>
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<br /></div>
<div style="text-align: justify;">
8. Thomas, Kevin & Goodall, Stuart & Stone, Mark & Howatson, Glyn & Gibson, Alan & Ansley, Les. (2014). Central and Peripheral Fatigue in Male Cyclists after 4-, 20-, and 40-km Time Trials. Medicine and science in sports and exercise. 47. 10.1249/MSS.0000000000000448. </div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
9. Jeffries, Owen & Simmons, Richard & Patterson, Stephen & Waldron, Mark. (2019). Functional Threshold Power Is Not Equivalent to Lactate Parameters in Trained Cyclists. Journal of Strength and Conditioning Research. 1. 10.1519/JSC.0000000000003203. </div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
10. Coggan, Andrew. (2003). Training and racing using a power meter: an introduction. </div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
11. McGRATH, Eanna & Mahony, Nick & Fleming, Neil & Donne, Bernard. (2019). Is the FTP Test a Reliable, Reproducible and Functional Assessment Tool in Highly-Trained Athletes?. International journal of exercise science. 12. 1334-1345.</div>
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<br /></div>
<div style="text-align: justify;">
12. Perrey, Stephane & Grappe, Fred & Girard, A & Bringard, Aurélien & Alain, Groslambert & William, Bertucci & Rouillon, J. (2003). Physiological and Metabolic Responses of Triathletes to a Simulated 30-min Time-Trial in Cycling at Self-Selected Intensity. International journal of sports medicine. 24. 138-43. 10.1055/s-2003-38200. </div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
13. Jones, Andrew & Burnley, Mark & Black, Matthew & Poole, David & Vanhatalo, Anni. (2019). The maximal metabolic steady state: redefining the ‘gold standard’. Physiological Reports. 7. 10.14814/phy2.14098.<br />
<br />
14. Inglis, Erin Calaine & Iannetta, Danilo & Passfield, Louis & Murias, Juan. (2019). Maximal Lactate Steady State Versus the 20-Minute Functional Threshold Power Test in Well-Trained Individuals: “Watts” the Big Deal?. International Journal of Sports Physiology and Performance. 1-7. 10.1123/ijspp.2019-0214. </div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">15. Bräuer, Elisabeth & Smekal, Gerhard. (2020). VO2 Steady State at and Just Above Maximum Lactate Steady State Intensity. International Journal of Sports Medicine. 41. 10.1055/a-1100-7253. </div>
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Ronhttp://www.blogger.com/profile/16268869622833968439noreply@blogger.com0tag:blogger.com,1999:blog-4786784182488135171.post-77962158638952179422020-04-03T21:32:00.001+04:002021-04-08T20:58:11.336+04:00Critical Power Concept in Exercise : Critique And Applications<div dir="ltr" style="text-align: left;" trbidi="on">
<div style="text-align: justify;">
This referenced article serves as a broad exploration into the power duration relationship and the parameters that result from the hyperbolic power-Tlim characteristic.<br />
<u><b><br />
</b></u> <u><b><br />
</b></u> <u><b>I. INTRODUCTION</b></u><br />
<br />
It is well established that work requiring high speed and power output is short lived but that at low speed and power can be prolonged. This relationship has been shown in a number of living species, including humans, horses, mouse and salamanders. In human activities, it's validity has been shown for running, cycling, swimming and rowing. It is valid for any activity where the limits of sustainable oxygen consumption is sufficiently challenged.<br />
<br />
Within this power-duration curve, there is a maximum level of speed or power that can be tolerated beyond which exercise tolerance until termination can be predicted.<br />
<br />
That particular threshold value of speed or power is called "critical velocity" or "critical power". The literature provides an "expanded" definition to be the highest steady state metabolic rate (i.e intensity) that can be sustained solely by oxidative energy provision beyond which homeostasis is lost and exercise tolerance is limited.<br />
<br />
Although in lay-speak, we tend to associate "thresholds" with points beyond which things "blow up " in the body, the transitions between intensity regions as far as fatigue related variables go is much more "gradual", as one recent study showed [33].<br />
<br />
Regardless, any exercise crossing critical power happens on borrowed time as the organism shifts away from sustaining muscle activity exclusively through aerobic pathways and starts concurrently relying on finite anaerobic stores. A slow rise in VO2 kicks in accelerating the drive towards VO2max and eventual exercise termination.<br />
<br />
For sports, critical power is an index of aerobic endurance. It was found to have strong positive correlations with skeletal muscle capillarity, particularly around type I fibers, and type I fiber composition [14].<br />
<br />
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://1.bp.blogspot.com/-b_5MzxSP4VQ/XrGywInBnZI/AAAAAAAAHws/bafR_8nLTlY_XPplEBd4bWVF1qmbroh8ACLcBGAsYHQ/s1600/Capillarity%2Band%2BCP.JPG" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="793" data-original-width="628" height="400" src="https://1.bp.blogspot.com/-b_5MzxSP4VQ/XrGywInBnZI/AAAAAAAAHws/bafR_8nLTlY_XPplEBd4bWVF1qmbroh8ACLcBGAsYHQ/s400/Capillarity%2Band%2BCP.JPG" width="316" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">The association of Critical Power and capillarity in two athletes with different CPs. Source [14].</td></tr>
</tbody></table>
<br />
In a recent review, Jones et.al called CP the "gold standard" when the goal was to determine the maximal metabolic steady state [11]. This appears to be one of the few resolutions to some long standing criticisms of the CP paradigm and lack of validity in relation to metabolic steady state.<br />
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<br />
<br />
<div style="text-align: justify;">
<b><u>II. PHYSIOLOGICAL BASIS FOR CP</u></b></div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
Exercise concepts must have good descriptions that link back to what actually takes place in the body. A good model would have a bio-energetic basis. In this respect, critical power (CP) has well established scientific underpinnings, unlike "other" training concepts in commercial circulation today. (There are of course models that are simply empirical, and do not help us understand how model parameters relate to something within our own bodies)</div>
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<br /></div>
<div style="text-align: justify;">
CP is thought to represent the highest rate of aerobic energy supply available for exercise. On an intensity spectrum, it forms the lower limit for the severe exercise intensity regime and an upper limit for the heavy exercise intensity regime. </div>
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<div class="separator" style="clear: both; text-align: center;">
<a href="https://1.bp.blogspot.com/-Bve_myy-UhE/XSiSF1kC-qI/AAAAAAAAHYU/Oy2zHmhWF-4Uz3G7JX9VTVviXPkaIzPZgCLcBGAs/s1600/Effect%2Bof%2Bwork%2Babove%2BCP.PNG" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="738" data-original-width="427" height="640" src="https://1.bp.blogspot.com/-Bve_myy-UhE/XSiSF1kC-qI/AAAAAAAAHYU/Oy2zHmhWF-4Uz3G7JX9VTVviXPkaIzPZgCLcBGAs/s640/Effect%2Bof%2Bwork%2Babove%2BCP.PNG" width="369" /></a></div>
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</div>
<div style="text-align: center;">
<span style="font-size: x-small;">The breakdown of metabolic control variables when exercising above CP. Black dots = baseline values. Gray = new values at work > CP. Source [2].</span></div>
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In this severe intensity regime, intramuscular metabolic control breaks down, and such exhaustive exercise results in the attainment of low end-exercise pH, [bicarbonate] and [PCr] values irrespective of the chosen work rate and a continuous increase in blood [lactate], pulmonary VO2 rate and ventilation relative to baseline values.<br />
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CP becomes the "threshold" beyond which metabolic control is lost by the individual. </div>
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<div style="text-align: justify;">
Beyond CP, a slow component of VO2 that was previously under control, rises so steeply so as to speed up the body's breathing path to VO2max attainment within the span of a few minutes. The slow component of VO2 is thought to arise from the incremental use of fast twitch muscle fiber. Considering this, exercise above CP always happens on 'borrowed time'. </div>
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Some 85% of the slow VO2 rise is linked to the recruitment of energetically costly fast-twitch (FT) muscle fibres as work intensity increases. The energy cost per unit force output is higher for FT fibers than for slow twitch (ST) fibers. The slow component of VO2 is not unique to humans; the same has been demonstrated in horses when they are exercised above their lactate threshold. [3]</div>
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<div class="separator" style="clear: both; text-align: center;">
<a href="https://1.bp.blogspot.com/-et2UMMCoRRY/XSiSEOxEYVI/AAAAAAAAHYM/pjgtq_mVCnYCJoddxGjNdSWftqB6ApBEgCLcBGAs/s1600/VO2%2Bslow%2Bcomponent.PNG" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="769" data-original-width="697" height="400" src="https://1.bp.blogspot.com/-et2UMMCoRRY/XSiSEOxEYVI/AAAAAAAAHYM/pjgtq_mVCnYCJoddxGjNdSWftqB6ApBEgCLcBGAs/s400/VO2%2Bslow%2Bcomponent.PNG" width="362" /></a></div>
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</div>
<div style="text-align: center;">
<span style="font-size: x-small;">The steep rise of slow component of VO2 at work > CP. Source [1]</span></div>
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<div style="text-align: justify;">
<br />
In the hyperbolic critical power model, the term W' (vocally called <i>W prime</i>) represents a constant amount of work that can be performed above CP and is notionally equivalent to an energy store consisting of O2 reserves, high energy phosphates and a source related to anaerobic glycolysis. The higher the sustained power output above the CP, the more rapidly the W' will be expended, and the greater will be the rate at which metabolites which have been associated with the fatigue process accumulate. </div>
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The average time to exhaustion in work done above CP maybe in the order of 10-15 minutes at most depending on the size of the athlete's anaerobic reserves and motivation. In some laboratory tests, the average time to exhaustion in test subjects at work above CP was 13 minutes [1]. </div>
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Even at CP, physiological steady state is not necessarily achieved. The time to failure at CP ranged from 25 minutes 1 second to 40 minutes 3 seconds [2]. This inter-individual variability hints to the obvious possibility that better trained athletes can sustain exercise at CP longer than less aerobically trained individuals. Some of this variation may also be linked to unfamiliarity with exercising at the estimated CP ("learning effect"). </div>
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<div style="text-align: justify;">
One definition of CP is that it is the "highest, non-steady-state intensity that can be maintained for a period in excess of 20 minutes, but generally no longer than 40 minutes." [2]<br />
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CP has been found to be influenced by the carbohydrate availability. Researchers found that 2 hours of high intensity activity can decrease CP over time and that carbohydrate feeding negated some of the decrease [12]. The time rate of fall in muscle glycogen also exhibits inter-individual differences, so the time course of decrease of CP in turn also varies from person to person depending on their physiology. </div>
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<br />
<b><u>III. CP MODELS</u></b><br />
<u><b><br />
</b></u>Traditionally, CP is determined from multi-duration tests conducted over several days in the laboratory. The resulting work rate vs duration (Power-time, or p-t) relation can be mathematically modeled various fits :<br />
<br />
1) The <i>exponential CP model</i> (Hopkins et.al) - Nonlinear<br />
2) The <i>3-parameter CP model </i>(Morton et.al) - Nonlinear<br />
3) The <i>2-parameter CP model</i> (Hill et.al) - Nonlinear<br />
4) The <i>linear model</i> (Moritani et.al) - Linear<br />
5) The <i>inverse time CP model</i> (Whipp et.al) - Linear<br />
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These mathematics behind the model are shown below :<br />
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<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://1.bp.blogspot.com/-EUJhP_OOJbM/XogFCfQPoDI/AAAAAAAAHps/VQ7b-IW_ToQbuZGu7Qb3-8c_bg07YnjQACLcBGAsYHQ/s1600/Models.JPG" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="155" data-original-width="801" height="76" src="https://1.bp.blogspot.com/-EUJhP_OOJbM/XogFCfQPoDI/AAAAAAAAHps/VQ7b-IW_ToQbuZGu7Qb3-8c_bg07YnjQACLcBGAsYHQ/s400/Models.JPG" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">CP models and their mathematical representation. Source [9].</td></tr>
</tbody></table>
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Although there doesn't seem to a consensus on what is the best model, there has been relatively more attention and research on the hyperbolic forms [7]. This focus of this writeup is primarily in the use of the 2-parameter hyperbolic model which may not be the best model but is the most simple to apply.<br />
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Note : This year, a new paper was published detailing an "omni duration" power duration model. Basically, the authors describe an adopted discontinuous mathematical function that helps some of the traditional CP models achieve a better fit at very long durations (more on protocol and duration dependancies below). Details of this model is within the paper in reference [10].<br />
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<b><u>2-PARAMETER MODEL</u></b><br />
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The 2-parameter hyperbolic form of the p-t relation is shown below from a paper on the topic, clearly demarcating boundaries of moderate, heavy and severe intensity domains [1].<br />
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Two parameters are of interest in this model :<br />
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1) Critical power, CP : This is the horizontal asymptote of the hyperbola, which when read off the y-axis, yields a value of power that could "theoretically" be sustained for ever but in reality, corresponds to a maximal duration of 60 minutes or less. Its units are in Watts.<br />
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2) W prime, W' : This is curvature constant of the model, signifying a constant "work" that can be done above critical power. Its units are in kilojoules.<br />
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Below CP, physiological balance is attained. This corresponds to the heavy and moderate areas in the plot. Above CP, VO2 is driven towards maximum and eventual exercise failure. That area is shown as the severe intensity region.<br />
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<a href="https://1.bp.blogspot.com/-uanjovrvBAw/XSiSBJTxyQI/AAAAAAAAHYI/9xYgtBFUkmsnMr6Zcd8z8JzELivT0bm8ACLcBGAs/s1600/Critical%2Bpower%2Bintensity%2Bspectrum.PNG" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="635" data-original-width="757" height="335" src="https://1.bp.blogspot.com/-uanjovrvBAw/XSiSBJTxyQI/AAAAAAAAHYI/9xYgtBFUkmsnMr6Zcd8z8JzELivT0bm8ACLcBGAs/s400/Critical%2Bpower%2Bintensity%2Bspectrum.PNG" width="400" /></a></div>
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<span style="font-size: x-small;"> The geometrical descriptions of CP. Source [1]</span><br />
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<span style="text-align: justify;">In terms of power output and oxygen consumption, the second plot shows the values represented on the exercise intensity regime.</span></div>
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<tr><td class="tr-caption" style="text-align: center;">Range of attainable power output in a young male along with the oxygen consumption attained. Shown in the intensity range are lactate threshold (LT) and critical Power (CP) along with VO2max, the point which results in termination of exercise. Source [8]</td></tr>
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The hyperbola may also be linearized, in which case the linear relationship becomes one between work done and time duration. The y-intercept would then correspond to W' while the slope of the line would be critical power or velocity. The linear Moritani model is not discussed further here.</div>
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<b><u>IV. ASSUMPTIONS IN THE 2 PARAMETER CP MODEL</u></b><br />
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Any model is a mathematical simplification of a real world phenomena and by nature, is never fully correct. As far as whole body CP concept is concerned, four major assumptions in the simple 2 parameter CP model has been documented :<br />
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1. There are only two components to the energy supply system, termed aerobic and anaerobic.<br />
2. Aerobic supply is unlimited in capacity but rate limited, the limiting parameter being CP.<br />
3. The anaerobic capacity is not rate limited but capacity limited.<br />
4. Exhaustion, by implication, termination of exercise, occurs when all of the anaerobic work capacity is exhausted.<br />
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The treatment of these assumptions has been done beautifully by Morton, and the reader interested in understanding the details of each assumption need to read the reference [5] below. My conclusions from Morton's paper is as follows :<br />
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Assumption 1 : There are only two components to the energy supply system, termed aerobic and anaerobic. <i>Yes, this is largely true but only to an extent. The body has more than two energy systems.</i><br />
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Assumption 2 : Aerobic supply is unlimited in capacity but rate limited, the limiting parameter being CP. <i>This is not true, the aerobic capacity clearly has a limit in all humans. However, the statement that it is rate limited is correct. There is clearly a limit and you might define it by CP.</i><br />
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Assumption 3 : The anaerobic capacity is not rate limited but capacity limited. <i>True, explosive power generated from anaerobic capacity is limited. It is not true that it is rate limited.</i><br />
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</i> Assumption 4 : Exhaustion, by implication, termination of exercise, occurs when all of the anaerobic work capacity is exhausted. <i>The human engine does not necessarily terminate exercise when all the glycogen stores, consequently, anaerobic work capacity, is exhausted. Research proves that at the point of exercise termination, there is still glycogen left in the body. The fine proof is that when nearing exhaustion, if the power output is just slightly lowered, subjects exercising should be able to continue on despite still working at supra-maximal power outputs.</i><br />
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All models have assumptions and to be able to validate the model also means that the assumptions should be correct. If they deviate from reality, the model is wrong, sometimes dead wrong. Like CP, similar assumptions can be generated the concept of FTP and the astute athlete and coach can treat each assumption and try to understand at what point the usage of the model fails and is inapplicable to the athlete.<br />
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Note : Around 9 total assumptions about the 2 parameter CP model have been treated in the paper by Morton [5].<br />
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<b><u>V. WEAKNESSES OF CP MODELS</u></b></div>
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Like any mathematical model, GIGO principle applies. All models are wrong, being a simplistic representation of reality. The CP models are not immune from this deficiency. Other concepts such as FTP also suffer from model related errors.<br />
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Some of the weaknesses in CP modeling are listed as follows :<br />
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<b>1) Estimated CP and real CP maybe different :</b> Critical power is a parameter estimated from the hyperbolic relationship between power and time or the linear relationship from work and time. There is no guarantee that the estimation from model fits consisting of limited test points actually point to the "real CP", i.e the real physiological boundary demarcating heavy and severe intensities. Unless ofcourse, the parameter is experimentally validated in the lab against the real procedure to determine CP (multiple lab visits at different test durations).<br />
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<b>2) Model and protocol dependency :</b> In a very practical research study, scientists compared several models for estimating CP using different combinations of time-to-exhaustion exercise sessions in 13 young recreational cyclists. They not only found that the 3 parameter CP model fit the data best, but when they compared model fits from time duration combinations having more of the short durations, CP was over-estimated and W' under-estimated [9].<br />
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<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://1.bp.blogspot.com/-3V60mBbZ2B0/Xo5OVVwaCOI/AAAAAAAAHqg/beuUcX6v4qAzD6Kp_hsLQ_gdpK4M5ggIgCLcBGAsYHQ/s1600/Criterion%2Bvalidity%2B%2528W%2529.JPG" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="734" data-original-width="757" height="387" src="https://1.bp.blogspot.com/-3V60mBbZ2B0/Xo5OVVwaCOI/AAAAAAAAHqg/beuUcX6v4qAzD6Kp_hsLQ_gdpK4M5ggIgCLcBGAsYHQ/s400/Criterion%2Bvalidity%2B%2528W%2529.JPG" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><span style="font-size: 12.8px;">Absolute difference (watt) between CP modeling techniques and the criterion model (3-P CP) are presented along with 90% confidence interval around each difference and effect size calculation. Source [9].</span></td></tr>
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In particular to our interest, the 2-parameter CP model was closest to the criterion measure only when mean duration combinations such as 7, 12 and 19 minutes were chosen, whereas when durations were consistently < 10 minutes, the model values were far from accurate [9].<br />
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There has been reports of large variations in the calculated value of W' arising from different models, particularly in sub-classes of athletes such as elite athletes [6].<br />
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Sub-discussions that arise from model time duration dependencies are as follows :<br />
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<b>2.1) Effect of exclusively very short durations in the model :</b> When critical power is calculated from slope of the work-duration relationship using short supra-maximal exercises, the resulting power from models is higher than the power output which corresponds to a lab measured lactate "steady state" work intensity. The critical power also tends to be lower than maximal aerobic power [6].<br />
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</span><span style="text-align: justify;"><b>2.2) Effect of exclusively long durations in the model </b>: When critical power is calculated from very long sub-maximal exercise durations, the resulting power from the models tends to be lower than the power output which corresponds to a lab measured lactate steady state work intensity such as OBLA (onset of blood lactate) [6]. </span></div>
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<b>2.3) Weakness of some non-linear models :</b> Due to the hyperbolic form of the CP model, small errors in CP translate to large errors in sustainable time duration. This reduces the predictive validity of CP when the model is misapplied by practitioners. The non-linear 2 parameter CP model suffers from a distinct weakness : As time approaches 0 seconds, power becomes infinite and at exhaustion, all of the muscular energy reserves associated with W' are exhausted. This is ofcourse, not necessarily true and the 3 parameter model was formulated to address this weakness, by bringing in an additional Pmax term.<br />
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<b>2.4) Weakness of linear models :</b> Linear models are often linearized from non-linear observations and as such introduce statistical errors simply from the linearization process. For example, it is possible that the fit parameters computed from linearized models yield higher values compared to their original non-linear forms.<br />
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<b><u>VI. MANAGING TESTING AND USE OF CP MODELS</u></b></div>
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To get around some of the weaknesses of CP models, careful application is necessary. I can suggest a few things :<br />
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<b>1) Getting the right "intensity" :</b> Critical power is a "heavy" work output above which a slow rise in VO2 can speed the approach to VO2max and eventual exhaustion. As such, it has been suggested that critical power should only be calculated from exhaustion times corresponding to "heavy sub-maximal exercises". The recommended exhaustion time range is suggested as 6 - 30 minutes [6]. Below and above this range, the validity of the classic CP models are questionable.<br />
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This idea that CP is a heavy intensity also brings a concern of long tests like 20 minute tests. The sub-maximal nature of a 20 minute test brings into question its reliability.<br />
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The data that is fed into the model matters. Garbage in, garbage out. While conducting tests, effort must be feel "strong" and motivation needs to be very high. Deflated and/or inflated values of power or speed will skew the results one way or the other when modeling.<br />
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<b>2) Which CP model to use :</b> Since the nature of the power-duration curve is a non-linear hyperbola, statistically speaking the best model fit would be a non-linear fit without transformation of any of the variables for linearization.<br />
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The non-linear 2 and 3 parameter CP models should be preferred over a linear model. However, the 3 parameter CP model was proposed by Morton as a way to get around flaws of the 2 parameter CP model (see section IV). Therefore, of all the 5 models, the 3 parameter CP model would be the sound choice. But this also means 4 or more trials need to be conducted.<br />
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Linear models systematically inflate CP than do non-linear models and there is ample evidence from literature that time to fatigue is drastically shortened when testing at work intensities estimated from linear models. This alone would support the move away from linear models.<br />
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<b>3) Choice of test durations :</b> Owing to research done in [9], it is best to include a mix of test durations in order to balance the short supra-maximal with the long sub-maximal. 2 and 3 duration tests can be analyzed by linear CP and 2 parameter model. 4 durations or greater can be analyzed with the 3 parameter CP model and linear CP models.<br />
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- For 2 durations : Pick from a range of 10-20 minutes. Avoid very short and very long durations like 3 and 20 minutes.<br />
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- For 3 durations : 7, 12 and 15 minutes. If glyoclytic capacity needs to be tested, 3, 10 and 15 minutes is a good spread.<br />
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- Pacing : All short duration trials should be done in time trial mode to exhaustion but not "ALL-OUT". Example, a 3 minute test is an aerobic time trial to exhaustion, not a maximal sprint mixed with an aerobic effort.<br />
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- The 3-parameter hyperbolic CP model (Morton model) is deemed protocol independant and works with 4 or more test durations. But I've also been told that when you have a trial that is too close to 20 min, you might get odd values for the Pmax parameter (too high values), which is not realistic.<br />
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- Ideally, testing within specific durations would be conducted on different days. For a single day test, maximum 2 or 3 tests are recommended spaced by ample break but done this way, the impact of prior testing on a subsequent test performance has to be assessed.<br />
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<b>5) Validate the model :</b> Experimental validation is the only way to check if a model derived estimates of CP is representative of physiological CP. Until that happens, a model calculated value holds a presumption that it is accurate when it may not be. For example, a model might yield an inflated estimate of CP which would be above true physiological CP as measured in a lab leading to loss of maintenance of homeostasis.<br />
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<b><u>VII. INTERVENTION STUDIES </u></b><br />
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</u></b> CP and W' are not just parameters of a fitting model. That there are some underpinning physiological relations to them are shown by intervention studies designed to manipulate either one independently of each other. For example, studies show that training adaptations are specific to either CP or W'. Nutritional and external gaseous interventions also affect the parameters.<br />
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Broadly, some of the studies and their references are listed below for further exploration :<br />
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1. Endurance training in normal subjects results in an increase in critical power with little or no change in W' [16, 17, 18].<br />
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2. Endurance training enhances critical power and end test power in a 3min all out test [19, 20].<br />
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3. Sprint cycle training with long rest intervals improves W′ [21].<br />
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4. W' is sensitive to, and modified by resistance training with no change in CP [22, 23].<br />
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5. W' is sensitive to creatine supplementation [24, 25, 26, 27].<br />
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6. Hypoxia systematically reduces CP with no significant impact W' [28]. Conversely, hyperoxia improves CP [31].<br />
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7. Supra-CP fatigue inducing work with different recovery durations affects the reconstitution dynamics of W' in different ways, without having an effect on CP [29].<br />
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8. Glycogen depletion has been shown to result in a decrease in W' [30].<br />
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</u></b> <b><u>VIII. FIELD MEASUREMENT OF CP</u></b><br />
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<b>1) Multi-duration testing :</b> The established lab practice to model CP is done using several bouts of constant load exercise done at varying durations to failure over several days. These bouts are administered in random order and the recommended exercise duration to exhaustion range from 1-20 minutes. The time to exhaustion in these exercises is plotted power output. The hyperbolic 2-parameter Whipp model when fit through this data yields CP and W', where CP is the horizontal asymptote of the curve and W' is the area between the curve and CP which represents a fixed quantity of work that can be done above CP before approaching complete exhaustion. However, the choice of durations would need to be scrutinized to yield a critical power that resembles a severe intensity workload.<br />
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<b>2) A 3 minute all out test (3MAOT)</b> has been scientifically established to point towards critical power. The idea with this test is that it is possible to deplete W’ in reasonably short time. Therefore, the idea of the test is to perform work all-out in a span of 3 minutes and deplete W'. The last 30 seconds of the 3 min all out test is supposedly close to the critical power.<br />
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There are indications from the scientific community that the 3MAOT field test overestimates CP and underestimates W' so therefore, it is not a reliable measure of capacity in "well trained athletes".<br />
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<tr><td style="text-align: center;"><a href="https://1.bp.blogspot.com/-xCPL8ZSAAwk/Xod4DbZ9KUI/AAAAAAAAHpg/FW0D9D6FdY4xRdqcTZTUUXGNbFKd34fKwCLcBGAsYHQ/s1600/Critical%2Bpower%2Bfrom%2B3%2Bmin%2Btest.PNG" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="286" data-original-width="400" height="228" src="https://1.bp.blogspot.com/-xCPL8ZSAAwk/Xod4DbZ9KUI/AAAAAAAAHpg/FW0D9D6FdY4xRdqcTZTUUXGNbFKd34fKwCLcBGAsYHQ/s320/Critical%2Bpower%2Bfrom%2B3%2Bmin%2Btest.PNG" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">CP calculated from a 3MAOT test. Source [4].</td></tr>
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<b>3) Software CP modeling ; </b>Traditionally, CP is determined by acquiring power-time series data over several visits and fitting a chosen model to the data. However, lab visits are expensive and time consuming. With the proliferation of GPS and power meters, these can be reproduced by acquiring mean maximal power and duration data in a given sport over a time span such as recent weeks or months. Once that data is acquired, software can be used to plot the data as a p-t chart. Model fitting is done to solve for the parameters.<br />
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<b><u>IX. TRAINING APPLICATIONS</u></b><br />
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</b> <b>1) </b><b>Predicting Time to Exhaustion :</b> The most fundamental application for the critical power (or velocity) model is to help determine the time to exhaustion during work performed above CP. The very purpose of modeling is to find out parameters that can be used with the power output to determine time to exhaustion.<br />
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With the simple 2 parameter hyperbolic form using power and work done, time to exhaustion can be represented as :<br />
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<b>Tlim = W′ /(P − CP)</b><br />
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As an example, setting W' = 20 KJ, CP = 250W, P = 300W :<br />
Tlim = 20,000 J / (300W - 250W) = 400s = 6.66 minutes.<br />
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Similarly, in the distance and speed domain :<br />
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</b> <b>Tlim = (D - D')/CS</b><br />
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Setting Critical Speed (CS) = 6 m/s, D = 1600m, D' = 200m :<br />
Tlim = (1600m - 200m) / 6m/s = 233.3s = 3.88 minutes.<br />
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This way, the time duration using a given estimated critical power or speed can be predicted.<br />
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</b> <b>2) Training Zone Descriptions :</b> Once the critical power (or critical speed) has been determined, training descriptions can be communicated to an athlete.<br />
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The following training levels described by Dr. Skiba can be a decent start. These levels may have to be modified depending on the athlete and race performances and/or tests.<br />
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Recovery (Light): Less than 56% (or go by feel)<br />
Level 2 (Moderate), Endurance : 56-75% of CP<br />
Level 3 (Heavy), Tempo : 76-90% CP<br />
Level 4 (Very Heavy), Critical Power : 91-105% of CP<br />
Level 5 (Severe), VO2max : 106-120% of CP<br />
Anaerobic Capacity (Extreme) : > 120% of CP<br />
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Bettina Karsten in a well-written thesis summed up CP training zones or intensity domains as defined in the literature. She gave extensive scientific references for these "zones". Background reading can be done beginning at section 2.3.1 in reference [32].<br />
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As she also highlighted in her work, exercise is a continuum and therefore the absolute "strictness" of these demarcation markers have not been fully demonstrated within research literature to date [32].<br />
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<tr><td style="text-align: center;"><a href="https://1.bp.blogspot.com/-Pdh74xjKJjA/Xq8iasAA9yI/AAAAAAAAHv8/N2OSTIo4HMsZjWGFCn0QsIgNPec46m5TACLcBGAsYHQ/s1600/Critical%2BPower%2BZones.JPG" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="795" data-original-width="692" height="400" src="https://1.bp.blogspot.com/-Pdh74xjKJjA/Xq8iasAA9yI/AAAAAAAAHv8/N2OSTIo4HMsZjWGFCn0QsIgNPec46m5TACLcBGAsYHQ/s400/Critical%2BPower%2BZones.JPG" width="347" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Broad CP based training intensity domains. Source [32]. </td></tr>
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<tr><td style="text-align: center;"><a href="https://1.bp.blogspot.com/-rLo5KZrBv9E/Xq8kYT2UQ_I/AAAAAAAAHwI/0Ax8ZbLjJ2EH9QW6XKL7osNoizGSyO2FgCLcBGAsYHQ/s1600/Critical%2BPower%2BZones%2Band%2BAdaptations.JPG" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="745" data-original-width="902" height="330" src="https://1.bp.blogspot.com/-rLo5KZrBv9E/Xq8kYT2UQ_I/AAAAAAAAHwI/0Ax8ZbLjJ2EH9QW6XKL7osNoizGSyO2FgCLcBGAsYHQ/s400/Critical%2BPower%2BZones%2Band%2BAdaptations.JPG" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Training zones and exercise intensity domains. Source [32]. </td></tr>
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<b>3) Interval Training Prescription : </b>One of the promising areas for using the critical power concept is to explore promoting targeted anaerobic and aerobic effects in an athletes. HIIT training can be prescribed for individuals proportionate to their D' or W'. By setting intervals to deplete a fixed percentage of W' and controlling the rest, individuals can complete a fixed distance at different speeds relative to their criticals. Examples of approaches are provided in [15].<br />
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</b> <b>4) Race Pacing Strategy :</b> Pacing prescription may also be set for races where the use of running power is prevalent. A 10K race for a talented runner maybe targeted using 95-100% CP. A 5K race performance maybe targeted within a range of 100-105% CP. Again, experimentation is necessary with these ranges and no guidance can be offered set in stone, as courses are different and CP itself may exhibit small day-to-day variations.<br />
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For prolonged duration high intensity events, CP is purported to decrease over time. If that is true, it is not clear how effectively one could employ CP to set pace prescription [12]. However, the studies reveal that carbohydrate feeding of around 60g/hour should be an important strategy to negate considerable decreases in CP over long durations [12]. I also suggest the use of a multi-pronged approach for marathons and ultra-marathons, involving the use of pace, heart rate and perceived exertion.<br />
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<b>5) Potential in anti-doping : </b>A paper was published arguing that the CP model could be useful for doping detection mainly based on the predictable sensitivities of its parameters to ergogenic aids and other performance-enhancing interventions [13]. I understand this proposal is still in its early stages and needs to be vetted.<br />
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<b>6) Educative value :</b> Critical power models have educative value behind them. They can teach concepts underpinning human endurance and record performances.<br />
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Curve fitting is easily done in Microsoft Excel.<br />
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Filipe Maturana, a PhD candidate, built <b><span style="color: red;"><a href="https://shiny.fmattioni.me/CPapp/"><span style="color: red;">an app</span> </a></span></b>developed on R Shiny which allows you to model CP using a number of time to exhaustion trials. This would be a good model to play around with for what-if analyses.<br />
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Using that app, I ran a simple example of how two different combinations of time and power data yield two different values of CP and W' estimate when using a simple linear CP model. The power and time to exhaustion data was taken from the reference in [9] and the duration combinations used as inputs to the two scenarios were 3+20 minutes and 12+20 minutes. <br />
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<tr><td style="text-align: center;"><a href="https://1.bp.blogspot.com/-IuAeMtO2PZE/Xo8l2RrEv0I/AAAAAAAAHqw/me3cQH7LuLo91LQ4EfIacVgX74oCN8JUwCLcBGAsYHQ/s1600/Linear%2Bmodel%2B12%2Band%2B20.JPG" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="811" data-original-width="1596" height="202" src="https://1.bp.blogspot.com/-IuAeMtO2PZE/Xo8l2RrEv0I/AAAAAAAAHqw/me3cQH7LuLo91LQ4EfIacVgX74oCN8JUwCLcBGAsYHQ/s400/Linear%2Bmodel%2B12%2Band%2B20.JPG" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Model output showing how different combinations of power duration data can yield different values of CP. </td></tr>
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<b><u>X. CONCLUSION</u></b><br />
<b><u><br />
</u></b> While there are several exercise concepts out there, the critical power model has been one of the most rigorously studied one in scientific literature, with several lab studies validating the model for athletes. The number of parameters are small (CP and W') and they have physiological meanings.<br />
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In this post, only one form of this model - the hyperbolic 2 parameter model - was described in a somewhat broad manner. There are several other models including 3 parameter and extended CP models. In future, this post will be expanded to include a treatment of those other models.<br />
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The concern over test protocol, quality of data and error propagation carries across to any CP model. The practitioner must be careful in the use of these models to advise exercise prescription, specially to talented elite athletes. Lab based physiological profiles will be better suited to making informed decisions in these athletes.<br />
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However, in a vast majority of recreational athletes, proper use of the field based testing protocol and the modeling based on the data will yield a useful approximation of the endurance capacity of an individual. That it is conceptually the highest power output or speed at physiological steady state is useful in training prescription. Practitioners will also be pleased in utilizing a very scientifically vetted training concept.<br />
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What remains to be seen is how the critical power concept marries with the central nervous system theory of fatigue. That the ultimate limiter of exercise performance is not the muscle but the brain was introduced more than a century ago by scientists.<br />
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Implicit in the effectiveness of applying the critical power concept is this idea that the performance that is analyzed must be the maximal in nature, implying that the central drive must be maximum for that performance. The role of motivation and internal drive is significant enough to warrant further investigations as part of the critical power concept.<br />
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Readers are advised to expand on their knowledge and read the papers referenced below.<br />
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<b><u>REFERENCES</u></b></div>
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1. Jones, A. M., Vanhatalo, A., Burnley, M., Morton, R. H., & Poole, D. C. (2010). Critical power: implications for determination of VO2max and exercise tolerance. Med Sci Sports Exerc, 42(10), 1876-90.</div>
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2. Brickley, G., Doust, J., & Williams, C. (2002). Physiological responses during exercise to exhaustion at critical power. European journal of applied physiology, 88(1-2), 146-151.</div>
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3. Langsetmo, I., Weigle, G. E., Fedde, M. R., Erickson, H. H., Barstow, T. J., & Poole, D. C. (1997). VO2 kinetics in the horse during moderate and heavy exercise. Journal of Applied Physiology, 83(4), 1235-1241</div>
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4. Miller, M. C., & Macdermid, P. W. (2015). Predictive validity of critical power, the onset of blood lactate and anaerobic capacity for cross-country mountain bike race performance. Sport Exerc Med Open J, 1(4), 105-110.<br />
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5. Morton, R.H. The critical power and related whole-body bioenergetic models. Eur J Appl Physiol 96, 339–354 (2006).<br />
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6. Vandewalle, Henry & Vautier, J-F & Kachouri, M & Lechevalier, J & Monod, H. (1997). Work-exhaustion time relationships and the critical power concept. A critical review. The Journal of sports medicine and physical fitness. 37. 89-102.<br />
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7. H. Monod & J. Scherrer (1965) The Work Capacity Of a Synergic Muscular Group, Ergonomics, 8:3, 329-338, DOI: 10.1080/00140136508930810<br />
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8. Mark Burnley & Andrew M. Jones (2018) Power–duration relationship: Physiology, fatigue, and the limits of human performance, European Journal of Sport Science, 18:1,<br />
1-12, DOI: 10.1080/17461391.2016.1249524<br />
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9. Mattioni Maturana, Felipe & Fontana, Federico & Pogliaghi, Silvia & Passfield, Louis & Murias, Juan. (2017). Critical power: How different protocols and models affect its determination. Journal of Science and Medicine in Sport. 21. 10.1016/j.jsams.2017.11.015.<br />
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10. Puchowicz, Michael & Baker, Jonathan & Clarke, David. (2020). Development and field validation of an omni-domain power-duration model. Journal of Sports Sciences. 38. 1-13. 10.1080/02640414.2020.1735609.<br />
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11. Jones, Andrew & Burnley, Mark & Black, Matthew & Poole, David & Vanhatalo, Anni. (2019). The maximal metabolic steady state: redefining the ‘gold standard’. Physiological Reports. 7. 10.14814/phy2.14098.<br />
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12. Clark, Ida & Vanhatalo, Anni & Thompson, Christopher & Joseph, Charlotte & Black, Matthew & Blackwell, Jamie & Wylie, Lee & Tan, Rachel & Bailey, Stephen & Wilkins, Brad & Kirby, Brett & Jones, Andrew. (2019). Dynamics of the power-duration relationship during prolonged endurance exercise and influence of carbohydrate ingestion. Journal of Applied Physiology. 127. 10.1152/japplphysiol.00207.2019.<br />
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13. Puchowicz, M. J., Mizelman, E., Yogev, A., Koehle, M. S., Townsend, N. E., & Clarke, D. C. (2018). The Critical Power Model as a Potential Tool for Anti-doping. Frontiers in physiology, 9, 643. https://doi.org/10.3389/fphys.2018.00643<br />
<br />
14. Mitchell, Emma & Martin, Neil & Bailey, Stephen & Ferguson, Richard. (2018). Critical power is positively related to skeletal muscle capillarity and type I muscle fibers in endurance trained individuals. Journal of Applied Physiology. 125. 10.1152/japplphysiol.01126.2017.<br />
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15. Pettitt, Robert. (2016). Applying the Critical Speed Concept to Racing Strategy and Interval Training Prescription. International Journal of Sports Physiology and Performance. 11. 10.1123/ijspp.2016-0001.<br />
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16. Porszasz, Janos & Emtner, Margareta & Goto, Shinichi & Somfay, Attila & Whipp, Brian & Casaburi, Richard. (2005). Exercise training decreases ventilatory requirements and exercise-induced hyperinflation at submaximal intensities in patients with COPD. Chest. 128. 2025-34. 10.1378/chest.128.4.2025.<br />
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17. Gaesser GA, Wilson LA. Effects of continuous and interval training on the parameters of the power-endurance time relationship for high-intensity exercise. International Journal of Sports Medicine. 1988 Dec;9(6):417-421. DOI: 10.1055/s-2007-1025043.<br />
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18. Poole, David & Ward, Susan & Whipp, Brian. (1990). The effects of training on the metabolic and respiratory profile of high-intensity cycle ergometer exercise. European journal of applied physiology and occupational physiology. 59. 421-9. 10.1007/BF02388623.<br />
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19. Jenkins, David & Quigley, Brian. (1992). Endurance training enhances critical power. Medicine and science in sports and exercise. 24. 1283-9. 10.1249/00005768-199211000-00014.<br />
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20. Vanhatalo, Anni & Doust, Jonathan & Burnley, Mark. (2008). A 3-min All-out Cycling Test Is Sensitive to a Change in Critical Power. Medicine and science in sports and exercise. 40. 1693-9. 10.1249/MSS.0b013e318177871a.<br />
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21. Jenkins, David & Quigley, Brian. (1993). The influence of high-intensity exercise training on the W-Trelationship. Medicine and science in sports and exercise. 25. 275-82. 10.1249/00005768-199302000-00019.<br />
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22. Bishop, David John & Jenkins, D. (1996). The influence of resistance training on the critical power function & time to fatigue at critical power. Australian journal of science and medicine in sport. 28. 101-5.<br />
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23. Sawyer, Brandon & Stokes, David & Womack, Christopher & Morton, Richard & Weltman, Arthur & Gaesser, Glenn. (2013). Strength Training Increases Endurance Time to Exhaustion During High-Intensity Exercise Despite No Change in Critical Power. Journal of strength and conditioning research / National Strength & Conditioning Association. 28. 10.1519/JSC.0b013e31829e113b.<br />
<br />
24. Vanhatalo, Anni & Jones, Andrew. (2009). Influence of Creatine Supplementation on the Parameters of the “All-Out Critical Power Test”. Journal of Exercise Science & Fitness - J EXERC SCI FIT. 7. 9-17. 10.1016/S1728-869X(09)60002-2.<br />
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25. Fukuda, David & Smith-Ryan, Abbie & Kendall, Kristina & Dwyer, Teddi & Kerksick, Chad & Beck, Travis & Cramer, Joel & Stout, Jeffrey. (2010). The Effects of Creatine Loading and Gender on Anaerobic Running Capacity. Journal of strength and conditioning research / National Strength & Conditioning Association. 24. 1826-33. 10.1519/JSC.0b013e3181e06d0e.<br />
<br />
26. Smith, Jimmy & Stephens, Daniel & Hall, Emily & Jackson, Allen & Earnest, Conrad. (1998). Effect of oral creatine ingestion on parameters of the work rate-time relationship and time to exhaustion in high-intensity cycling. European journal of applied physiology and occupational physiology. 77. 360-5. 10.1007/s004210050345.<br />
<br />
27, Miura, Akira & Kino, Fumiko & Kajitani, Saori & Sato, Haruhiko & Fukuba, Yoshiyuki. (1999). The Effect of Oral Creatine Supplementation on the Curvature Constant Parameter of the Power-Duration Curve for Cycle Ergometry in Humans.. The Japanese journal of physiology. 49. 169-74. 10.2170/jjphysiol.49.169.<br />
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28. Dekerle, Jeanne & Mucci, Patrick & Carter, H. (2011). Influence of moderate hypoxia on tolerance to high-intensity exercise. European journal of applied physiology. 112. 327-35. 10.1007/s00421-011-1979-z.<br />
<br />
29. Ferguson, Carrie & Rossiter, Harry & Whipp, B & Cathcart, A & Murgatroyd, Scott & Ward, Susan. (2010). Effect of recovery duration from prior exhaustive exercise on the parameters of the power-duration relationship. Journal of applied physiology (Bethesda, Md. : 1985). 108. 866-74. 10.1152/japplphysiol.91425.2008.<br />
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30. Miura, Akira & Sato, Haruhiko & Whipp, B & Fukuba, Yoshiyuki. (2000). The effect of glycogen depetion on the curvature constant parameter of the power-duration curve for cycle ergometry. Ergonomics. 43. 133-41. 10.1080/001401300184693.<br />
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31. Goulding, Richie & Roche, Denise & Marwood, Simon. (2019). Effect of Hyperoxia on Critical Power and V[Combining Dot Above]O2 Kinetics during Upright Cycling. Medicine & Science in Sports & Exercise. 52. 1. 10.1249/MSS.0000000000002234.<br />
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32. Karsten, Bettina. (2014). Analysis of Reliability and Validity of Critical Power Testing in the Field. Thesis Paper. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.643129<br />
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33. Pethick, Jamie; Winter, Samantha L.; Burnley, Mark Physiological Evidence that the Critical Torque Is a Phase Transition Not a Threshold, Medicine & Science in Sports & Exercise: May 4, 2020 - Volume Publish Ahead of Print - Issue - doi: 10.1249/MSS.0000000000002389</div>
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Ronhttp://www.blogger.com/profile/16268869622833968439noreply@blogger.com0tag:blogger.com,1999:blog-4786784182488135171.post-2310435182773512932019-06-16T08:47:00.000+04:002019-06-16T08:58:58.776+04:00The Poor Man's Giro : Amateur Science in a GT Mimicry<div dir="ltr" style="text-align: left;" trbidi="on">
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Early in May, I set out to do something in the name of science. I'd read about the <a href="https://www.researchgate.net/publication/329872713_Physical_Demands_and_Power_Profile_of_Different_Stage_Types_within_a_Cycling_Grand_Tour"><span style="color: red;">physical demands of grand tour racing</span></a> in research papers and wondered what that would translate to for an amateur rider who works 5 days a week in a day job.<br />
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The idea was simple. I set out to ride roughly 1/8th the daily distances in the 2019 Giro d'Italia. Each ride tried to capture the intent and spirit of the pro rides.<br />
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For example, if one day was the ITT, I'd go out and smash a little ITT of my own. If there was a mountain stage, then I'd go out and do some hill repeats (we do not have mountain passes in Abu Dhabi ! ). If the ride called for a flat stage, I'd go out on a 40km ride and end with a "solo sprint".<br />
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The challenge was called "Poor Man's Giro". I even created a little flyer for it and <b><a href="https://twitter.com/RonGeorge_Dubai/status/1126786327226269697"><span style="color: red;">shared it on Twitter</span></a></b> with the likes of sports analytics guru Alan Couzens and exercise scientist Stephen Seiler. <br />
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All rides were attempted in the searing heat of Abu Dhabi. The rides were supported by nutrition from Secret Training U.A.E.<br />
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<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://1.bp.blogspot.com/-_bWMCRkqYew/XQW7K8pTM3I/AAAAAAAAHWM/p5-OvcOXKmcpwhwzE7jrY5saEpHYne5KwCLcBGAs/s1600/%2523PoorMansGiro.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="720" data-original-width="960" height="240" src="https://1.bp.blogspot.com/-_bWMCRkqYew/XQW7K8pTM3I/AAAAAAAAHWM/p5-OvcOXKmcpwhwzE7jrY5saEpHYne5KwCLcBGAs/s320/%2523PoorMansGiro.png" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Fig 1 : Too poor to be a pro and ride a Grand Tour? The Poor Man's challenge is an answer!</td></tr>
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Now, I faced a few challenges which I need to declare before we get started. Namely :<br />
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1) In addition to my day job, I also coach a running club and so squeezing in rides everyday became a challenge.<br />
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2) I went on vacation round about the 20th pro stage so I ended up completing just 18 "stages".<br />
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3) A couple of rides had to be done indoors on a Cybex ergometer.<br />
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4) I took one rest day more than necessary. It was inevitable. Too busy to squeeze a ride in one or two occasions.<br />
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5) My time trial bike was not fitted with a power meter so power output wasn't captured for two TT's.<br />
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95% of the rides were done on a Colnago C40 road bike outfitted with a Powertap powermeter to capture the workload. Daily rides were uploaded into Strava and synced with GC to power the analytics.<br />
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<b>Data Results</b><br />
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Below is the data from 18 rides. BikeStress is GC's implementation of Training Peak's TSS when they got rid of the "TSS" trademark from their software. TRIMPS have been calculated most likely using zonal points. IsoPower is GC's implementation of TrainingPeak's NP, again after getting rid of trademarked metrics.<br />
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<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://1.bp.blogspot.com/-7YFhXXjN9AM/XQW6igXSsfI/AAAAAAAAHWE/UiM6hML41CkyZmJnYledYneRbYY_XO-agCLcBGAs/s1600/poormans%2Bgiro%2Btable.PNG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="487" data-original-width="1315" height="147" src="https://1.bp.blogspot.com/-7YFhXXjN9AM/XQW6igXSsfI/AAAAAAAAHWE/UiM6hML41CkyZmJnYledYneRbYY_XO-agCLcBGAs/s400/poormans%2Bgiro%2Btable.PNG" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Fig 2 : Ride, workload and stress parameters from each day's ride of the Poor Man's Giro</td></tr>
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To add a little bit of extra science to the investigation, daily HR and HRV related parameters were measured using a Faros ECG device hooked up to a Polar H10 chest strap. Protocol followed was 5 min supine-standing orthostatic format.<br />
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All the data was analyzed in Kubios to extract the mathematical nature of sympathetic and parasympathetic function. A self coded script threw the data onto a spreadsheet and automatically plotted the variables.<br />
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<a href="https://1.bp.blogspot.com/-kkM0aghTCKk/XQXFjKSnxtI/AAAAAAAAHWo/5xofASacaUMXBd6CRtGYDGRQnWzXo3HdgCLcBGAs/s1600/HRV1.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="416" data-original-width="738" height="225" src="https://1.bp.blogspot.com/-kkM0aghTCKk/XQXFjKSnxtI/AAAAAAAAHWo/5xofASacaUMXBd6CRtGYDGRQnWzXo3HdgCLcBGAs/s400/HRV1.PNG" width="400" /></a></div>
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<a href="https://1.bp.blogspot.com/-NWQGVeIIOv0/XQXFjPcoMSI/AAAAAAAAHWs/6FlApFD1Z2MocuLjrxTIMJ5h0QFDrg_xQCLcBGAs/s1600/HRV3.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="416" data-original-width="738" height="225" src="https://1.bp.blogspot.com/-NWQGVeIIOv0/XQXFjPcoMSI/AAAAAAAAHWs/6FlApFD1Z2MocuLjrxTIMJ5h0QFDrg_xQCLcBGAs/s400/HRV3.PNG" width="400" /></a></div>
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<tr><td style="text-align: center;"><a href="https://1.bp.blogspot.com/-cxCtYEQadhg/XQXFjGB22iI/AAAAAAAAHWk/SOiwrNnXSVgJOBSKu4hcdS9_uWVNQWdIQCLcBGAs/s1600/HRV2.PNG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="415" data-original-width="738" height="223" src="https://1.bp.blogspot.com/-cxCtYEQadhg/XQXFjGB22iI/AAAAAAAAHWk/SOiwrNnXSVgJOBSKu4hcdS9_uWVNQWdIQCLcBGAs/s400/HRV2.PNG" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Fig 3 : Sets of plots showing the HR/HRV related parameters for the duration of Poor Man's Giro</td></tr>
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<b>Discussion of Results</b><br />
<b><br /></b>
We understand from the Grand Tours research done by<span style="color: red;"> <b><a href="https://www.researchgate.net/publication/329872713_Physical_Demands_and_Power_Profile_of_Different_Stage_Types_within_a_Cycling_Grand_Tour">Sanders et.al</a></b></span> that the stress associated with a time trial (TT) as a function of distance is the highest among flat (FLAT), semi-mountaineous (SMT) and mountain stages (MT).<br />
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The authors find a typical average TT speed of 36.5 +- 12.9 kph, an average power output of 371 W at 177+/ 10 bpm, TRIMPS of 33 +/ 32 AU and a TSS of 62 +/ 32 AU. That translates to a TRIMPS/km = 3.39 +/- 1.39 and a TSS/km = 3.39 +/ 0.17 AU/km.<br />
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The table 2 from their research paper is very instructive of the performance parameters across the spectrum of stages. Borrowed and pasted below for quick reference.<br />
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<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://1.bp.blogspot.com/-K-t-2cdB2eg/XQW-OqijGyI/AAAAAAAAHWY/3-95RnCiA7AQWbjThpA7_CMDK75mV_AXwCLcBGAs/s1600/Race%2Bcharacteristics%2Bof%2BGTs.PNG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="507" data-original-width="968" height="208" src="https://1.bp.blogspot.com/-K-t-2cdB2eg/XQW-OqijGyI/AAAAAAAAHWY/3-95RnCiA7AQWbjThpA7_CMDK75mV_AXwCLcBGAs/s400/Race%2Bcharacteristics%2Bof%2BGTs.PNG" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Fig 4 : Typical performance characteristics from Grand Tours from Time Trials (TT), Flats (FLAT), semi-mountaineous (SMT) and mountain stages (MT). </td></tr>
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This can be compared to my own ride characteristics from Fig 2.<br />
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<b>Time Trials</b> : Agreeing with the research, the RPE associated with a solo TT is high, around 8.5-9. TRIMP points are 62 vs 58 (mine) which translates to a TRIMPS/km of between 4-5. This is the highest among all rided that I attempted.<br />
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<b>Flat Stages</b> : Agreeing with the research, the RPE associated with a flat stage is around 5 (pro =5.8). TRIMP points are 298 vs 94 (mine) which tranlates to around 1/3rd the heart related stress mainly due to the reduction in distance attempted. This translates to a TRIMPS/km of around 2 (pro = 1.55). Power output is around 137 W average giving an average TSS/km of 2.9-3 (pro = 1.14). I presume pros show a lesser power related stress per km riding such long stages due to the draft effect.<br />
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<b>Mountain Stages</b> : The ride done on May 25 is a perfect example of a flat ride ending with several hill repeats to mimic the feel of climbing a mountain. The TSS/km and TRIMPS/km came out to 3.8 and 3 respectively, compared to the pro stats of 1.97 and 2.1 AU/km. So the stress was a bit greater on my part, and I probably intentionally made it that way when thinking about climbing.<br />
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<b>Daily Accumulation Rates : </b>For 3 weeks, the accumulation of stress was as follows :<br />
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The sum total of TRIMPS gained over 18 stages = 1937 AU = 108 TRIMPS/day.<br />
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The same for TSS (aka BikeStress in GC language) = 1386 AU = 77 TSS/day.<br />
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Total workload = 6467 KJ, with an accumulation rate = 359 KJ/day.<br />
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<b>Daily HR and HRV related fatigue : </b>The days after the hardest rides (TT's and MTs) on 11th, 18th and 28th May respectively show significant drops in time related HRV parameters such as rMSSD and conversely high supine resting pulses. <br />
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Although all these parameters showed cyclical variations day in and day out, one standout feature was the steady rise in chronic HRV and the steady drop in chronic resting heart rates over the course of 18 days (chronic = long term).<br />
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Infact, the drop in resting heart rate, when compared to similar data from the beginning of year show the difference very clearly. The long term difference seems to be a decrease of around 5 beats/min compared to the period prior to starting this mini challenge.<br />
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<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://1.bp.blogspot.com/-fe_U0Fi0THE/XQXH4LG2DHI/AAAAAAAAHW8/MgiSyjZayjQLOI37oEz5ha0QJd0BQ5wkQCLcBGAs/s1600/HRV4.PNG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="416" data-original-width="738" height="225" src="https://1.bp.blogspot.com/-fe_U0Fi0THE/XQXH4LG2DHI/AAAAAAAAHW8/MgiSyjZayjQLOI37oEz5ha0QJd0BQ5wkQCLcBGAs/s400/HRV4.PNG" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Fig 5 : Highlighted section showing the supine resting heart rate (daily acute and chronic over 7 days) compared with data from March 2019. </td></tr>
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<b>Conclusion</b><br />
<b><br /></b>
Keeping with the spirit of amateur scientific investigation, an 18 day grand tour was mimicked during the period of the 2019 Giro d'Italia. Despite the limitations of a decreased work load, the aim of trying and matching atleast 1/8th the distance was more or less accomplished.<br />
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From the data. I conclude that heart related fitness parameters improved during those days, which shows the effect of a 108 TRIMPS/day and 77 TSS/day loading pattern. However, the data doesn't show the "delayed" effect of improvement that must have come +1 or +2 weeks after the 3 week training was concluded.<br />
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I hope to expand on this research during the period of the Tour de France. If you wish to join me in a Poor Man's TDF, please join ! Let's learn together. I can be <b><a href="https://www.researchgate.net/publication/329872713_Physical_Demands_and_Power_Profile_of_Different_Stage_Types_within_a_Cycling_Grand_Tour"><span style="color: red;">found on Twitter</span></a></b>.<br />
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Ronhttp://www.blogger.com/profile/16268869622833968439noreply@blogger.com0tag:blogger.com,1999:blog-4786784182488135171.post-77981097868832258342019-03-31T21:37:00.003+04:002019-03-31T21:48:23.614+04:00Machine Learning and Learning Humans<div dir="ltr" style="text-align: left;" trbidi="on">
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Perhaps I'm behind the times, but the field of 'machine learning' is all the rage these days. I only purport to know what it's all about from simple definitions found on the internet.<br />
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What I do understand is that 'Machine Learning' is a sub-field in the broad world of what's termed artificial intelligence. Using tools to teach artificial machines to automatically learn and improve their experiential knowledge based on collections of data sounds exciting and promising.<br />
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But do we really know how humans reason? At best, what we have are models of how humans are supposed to think intelligently. And perhaps more correctly, research has a model(s) of how a sub-set of humans from this planet are supposed to think 'intelligently' and make decisions on a daily basis. In other words, everything we know about what humans know about intelligent thinking is from a pool of subjects that volunteer to participate in research. Is my thinking far fetched?</div>
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Now, do humans need formal rules to make inferences? If Carly knows that chicken pox is associated with dark spots on the skin and that Jim has dark spots, she infers that Jim might have chicken pox. Did this conclusion require logic? No. It is entirely possible Carly used the content of the sentences to make a deduction, to imagine possibilities. </div>
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The news media lately has been filled with humans trying to understand 'difficult, complex' topics, topics we have no precedent to learn from or use to navigate to a solution.<br />
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For instance, Brexiteers have little clue how to get <a href="https://www.irishtimes.com/opinion/brexit-complexity-and-the-tangle-of-european-minds-1.3797014"><b><span style="color: red;">Britain out of the European Union</span></b></a> without incurring a series of dark uncertainties few really know about. <b><a href="https://leehamnews.com/2019/03/22/bjorns-corner-the-ethiopian-airlines-flight-302-crash-part-2/"><span style="color: red;">Flight accident investigators</span></a></b> scramble for answers how airplanes, an electronic 'thinking' machine made by humans, nose dived twice into the ground killing over 300 people in two separate instances less than 6 months apart. Separately, safety experts sing positive songs over completely <b><a href="https://www.independent.co.uk/news/world/europe/automatic-speed-limit-europe-cars-lorries-etsc-road-safety-2022-a8841361.html"><span style="color: red;">automating speed limits</span></a></b> in cars by 2020. We want to try and wrest control out of the human being, because ... it must be exciting.<br />
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<b><a href="https://www.sciencedaily.com/releases/2019/03/190329144223.htm"><span style="color: red;">Others look for clues on the ground</span></a></b> explaining the precise moments of a meteor impact that apparently led to the disappearance of dinosaurs. This is another interesting piece of development and I wonder whether any machines were truly involved in this study. Why would you need a machine to study this issue anyway?</div>
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News stories show the complexities behind real learning, real decision making. Can machines really imagine possibilities using content and 'meanings' behind that might lead to reasonings based outside logic? And do we know enough of how humans make meaning to data in examples not needing logic before we take it as a given that machines can 'learn' the same things too, if we only force them to think in certain ways. Are explorations in these two fields - human learning, and machine learning, going in parallel and feed into each other? </div>
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What do we <i>not know</i> about humans that we don't put into machines, which eventually might lead to the creation of what essentially are incomplete models of humans? </div>
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We try to mimic decision making in 'artificial intelligence' based on a limited set of knowledge we have about humans. The biases in that knowledge forms the underbelly of 'machine intelligence' we will have in our transportation systems, our appliances, and perhaps even in the robot that will help deliver your baby tomorrow. Aldoux Huxley's 'brave new world' is really an uncertain world. </div>
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Ronhttp://www.blogger.com/profile/16268869622833968439noreply@blogger.com1tag:blogger.com,1999:blog-4786784182488135171.post-67509535752817680052018-12-24T00:14:00.000+04:002018-12-24T10:08:53.296+04:00Surface Related VO2 Changes Not Reflected In Stryd Power - An Examination of Aubrey et.al<div dir="ltr" style="text-align: left;" trbidi="on">
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In a recent paper by Aubrey et.al published in the Journal of Strength and Conditioning Research, significant differences in oxygen consumption were reported from treadmill to overground running without evidence of a corresponding change in Stryd reported running power. Details can be found <b><a href="https://www.researchgate.net/profile/Jamie_Burr/publication/325775874_An_Assessment_of_Running_Power_as_a_Training_Metric_for_Elite_and_Recreational_Runners/links/5b27c822a6fdcca0f09c0a06/An-Assessment-of-Running-Power-as-a-Training-Metric-for-Elite-and-Recreational-Runners.pdf?origin=publication_detail"><span style="color: red;">here</span></a></b>. </div>
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Two quick pieces of summary : </div>
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a) The main bit of detail is that there was a significant change in VO2 not reflected in corresponding power readings between treadmill and overground running.</div>
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b) The other statement made in the paper is that a weak correlation was found between oxygen cost and power:weight ratio across all runners, elite or recreational, suggesting that "running power as assessed with the Stryd Power Meter, is not a great reflection of the metabolic demand of running in a <b>mixed ability population of runners</b>".</div>
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<b><a href="https://blog.stryd.com/2018/12/19/using-appropriate-mathematical-and-physiological-analyses-shows-that-stryd-power-is-strongly-correlated-to-metabolic-rate-across-speed/"><span style="color: red;">In a rebuttal</span></a></b> of point b) in the paper, Dr. Snyder from Stryd accused the authors of "fatal methodological flaws" when they chose to normalize both metabolic rate and power/weight ratio with speed while pointing to a weak correlation between the two variables (r = 0.29, p = 0.02). </div>
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Dr. Snyder's rebuttals are examined with the help of data from our old friends, Dutch researchers from the Secret of Running group. From their <b><a href="https://hetgeheimvanhardlopen.nl/wp-content/uploads/2016/11/3-The-running-economy-of-14-test-runners.pdf"><span style="color: red;">blog</span></a></b>, I extracted mean VO2 and mean power/weight ratios from treadmill testing belonging to a subset of 6 runners in random fashion.</div>
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<span style="color: blue;">Statement 1 : <i>Rate of oxygen consumption is approximately proportional to speed (linearly dependent upon speed with a y-intercept of close to zero) across both elite and recreational runners (Batliner et al., 2018). This means all values for the rate of oxygen consumption measure when normalized by speed <b>(otherwise known as cost of transport)*</b> will be approximately constant, giving virtually no variation in these values <b>other than that due to noise or subject variation</b>. Therefore, regardless of Stryd power’s dependence upon speed, no correlation would be expected between the normalized measures. </i></span></div>
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Aubrey et.al normalized metabolic rate in ml/kg/min with speed measured in m/s. Such a division does not result automatically in the oxygen cost of transport. </div>
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Infact, the actual formula is :</div>
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<b>Oxygen cost = <span style="border: 0px solid rgb(204 , 204 , 204); box-sizing: inherit; color: #222222; font-family: "hnr"; font-size: 17px; text-align: left;">60/3.6*VO</span><span style="border: 0px solid rgb(204 , 204 , 204); box-sizing: inherit; color: #222222; font-family: "hnr"; font-size: 17px; text-align: left;">2 </span><span style="border: 0px solid rgb(204 , 204 , 204); box-sizing: inherit; color: #222222; font-family: "hnr"; font-size: 17px; text-align: left;">(ml O</span><span style="border: 0px solid rgb(204 , 204 , 204); box-sizing: inherit; color: #222222; font-family: "hnr"; font-size: 17px; text-align: left;">2</span><span style="border: 0px solid rgb(204 , 204 , 204); box-sizing: inherit; color: #222222; font-family: "hnr"; font-size: 17px; text-align: left;">/kg/min)/v (m/s) --- 1)</span></b></div>
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So by calling this normalization "cost of transport", Dr. Snyder is not dimensionally correct because the x-axis in the Aubrey paper shows values ranging from 9 to 17 (see Figure 1 in their paper). Such low double digit values cannot align with the oxygen cost of running, which is in the triple digits. </div>
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Behavior of oxygen consumption with speed can be examined from the data of Secret of Running. The plot in Fig.1 shows that for 6 different subjects, metabolic rate is mostly linearly proportional to speed. </div>
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<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://3.bp.blogspot.com/-X99slcBdHyA/XB_JR2854TI/AAAAAAAAHI0/SrUZQBObZNkMLJFgXD_Hnt7zckyH_68ewCLcBGAs/s1600/Figure%2B1.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="434" data-original-width="690" height="250" src="https://3.bp.blogspot.com/-X99slcBdHyA/XB_JR2854TI/AAAAAAAAHI0/SrUZQBObZNkMLJFgXD_Hnt7zckyH_68ewCLcBGAs/s400/Figure%2B1.JPG" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Fig 1 : Metabolic rate vs running speed measured in 6 subjects. Source of data : Secret of Running (Dijk, Megen). </td></tr>
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Converting these values to an oxygen cost of running with the appropriate formula in 1) transforms the plot into the following plot in Fig.2. As Dr. Snyder states, the linear relationship between speed and oxygen consumption becomes nearly constant save for noise and subject variation. Infact, when looking at this plot, the data looks less noisy for some runners (4,5,6) and more noisy for others (1,2,3). What is the source of this variation? Some explanation would be good. </div>
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<tr><td style="text-align: center;"><a href="https://1.bp.blogspot.com/-Ndf036a4PKU/XB_MqWbXWdI/AAAAAAAAHJM/5_3fSQ_QoukR2cOC49zV0VUOG-XMJkMWgCLcBGAs/s1600/Figure%2B2.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="429" data-original-width="690" height="247" src="https://1.bp.blogspot.com/-Ndf036a4PKU/XB_MqWbXWdI/AAAAAAAAHJM/5_3fSQ_QoukR2cOC49zV0VUOG-XMJkMWgCLcBGAs/s400/Figure%2B2.JPG" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Fig 2 : Oxygen cost of running vs running speed in 6 subjects. Source of data : Secret of Running (Dijk, Megen). </td></tr>
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What does research say about this relationship? According to the plot in Fig.3, there is a "general absence" of a change in oxygen cost as running speed increases. However, because of the noise from the Stryd sensor, this constant relationship is not exactly seen.</div>
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From looking at Fig.2, we cannot make the claim that some individuals somehow magically reduce their oxygen cost as speed increases. The fundamental source of these fluctuations appear to be noise. It is precisely this noisy bit that requires further examination if such devices are to be applied among elite runners as a "surrogate" measure of oxygen cost. Not that I didn't warn about it on the Stryd <b><a href="https://www.facebook.com/groups/strydcommunity/permalink/1733507240280666/"><span style="color: red;">Facebook page many moons ago</span></a></b>. </div>
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<tr><td style="text-align: center;"><a href="https://3.bp.blogspot.com/-pTjbTp9KpEc/XB_NVJjuoSI/AAAAAAAAHJY/-381I0XkkR0qEiDXpQIcQviEJH6I4wSrQCLcBGAs/s1600/Figure%2B3.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="513" data-original-width="698" height="293" src="https://3.bp.blogspot.com/-pTjbTp9KpEc/XB_NVJjuoSI/AAAAAAAAHJY/-381I0XkkR0qEiDXpQIcQviEJH6I4wSrQCLcBGAs/s400/Figure%2B3.jpg" width="400" /></a></td></tr>
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<span style="color: blue;"><i>Statement 2 : Stryd power’s strong linear correlation with rate of oxygen consumption, however, indicates increasing Stryd power with increasing speed, meaning any variability would be reduced by normalization with speed. Thus, any correlation whatsoever between the normalized measures would be small and due to chance, unaccounted for nonlinearities, or subject variation, not the dominant linear relation with speed that underlies both non-normalized measures.</i></span></div>
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The relationship between Stryd power/weight ratio and treadmill speed can be examined in the Secret of Running data. By way of algorithmic implementation, Stryd power/weight in strongly linear in speed (Fig.4). But on closer inspection, not all subjects show linear proportionality. Infact, in this data, there doesn't appear to be anything close to perfectly linear relationship. Almost all datapoints show a wavy pattern. </div>
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Some appear comical. Subject 6 shows markedly high power ramp beween 15 and 16 kph compared to that between 16 and 17kph. </div>
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Subject 1 on the other hand exhibits something that looks like a curvilinear relationship. </div>
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What is the cause of these artifacts? </div>
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There is no reason why some runners should take more effort to "jump" between two speeds compared to other speeds. The treadmill test is a continuously administered test with no "breaks" in between each speed. The other explanation could be the choice of value of VO2. It hasn't been explained by the authors of Secret of Running on what basis they chose steady state values. Were some intervals shorter than others, affecting the average of VO2 in that interval? </div>
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<tr><td style="text-align: center;"><a href="https://2.bp.blogspot.com/-8YmlKG4eSxY/XB_Qv7s0UmI/AAAAAAAAHJw/6DvgiUN28pwNJthjFOgzZbQIg6owbRkygCLcBGAs/s1600/Figure%2B4.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="434" data-original-width="686" height="252" src="https://2.bp.blogspot.com/-8YmlKG4eSxY/XB_Qv7s0UmI/AAAAAAAAHJw/6DvgiUN28pwNJthjFOgzZbQIg6owbRkygCLcBGAs/s400/Figure%2B4.JPG" width="400" /></a></td></tr>
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Normalizing the power/weight values by speed will dimensionally yield the energy cost of running through the formula :</div>
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<span style="border: 0px solid rgb(204 , 204 , 204); box-sizing: inherit; color: #222222; font-family: "hnr"; font-size: 17px; font-weight: bolder;">ECOR (kJ/kg/km) = P (Watt/kg)/v (m/s) ---- 2)</span></div>
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When the above data is normalized by speed using the expression in 2), we get the following plot. Again, due to random variations in the Stryd data, none of the subjects show a constancy in energy cost of running.</div>
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<tr><td style="text-align: center;"><a href="https://1.bp.blogspot.com/-RTqGC33z07E/XB_S5YEpRcI/AAAAAAAAHJ8/FmkrhMk5TfgWb5hdcfSWzY20CjprCy-pACLcBGAs/s1600/Figure%2B5.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto; text-align: center;"><img border="0" data-original-height="431" data-original-width="684" height="251" src="https://1.bp.blogspot.com/-RTqGC33z07E/XB_S5YEpRcI/AAAAAAAAHJ8/FmkrhMk5TfgWb5hdcfSWzY20CjprCy-pACLcBGAs/s400/Figure%2B5.JPG" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Fig. 5 : ECOR (calculated) in 6 subjects. Source of data : Secret of Running (Dijk, Megen). </td></tr>
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The authors in Secret of Running have argued that the differences in ECOR among runners is of a fundamental nature due to some being more experienced and more "efficient" than others. They suggest in their literature and books that it is important to reduce ECOR and that the Stryd powermeter is sensitive enough to measure ECOR. </div>
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However, I challenge this idea. I suggest that these authors re-examine if changes in ECOR are really due to training status and running experience or simply due to random variations in the data as Fig. 5 and Dr. Snyder's assertion shows! Otherwise, different interpretations from different people appear to conflict. </div>
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<i><span style="color: blue;">Statement(s) 3 : [...] there is still a very strong linear relationship between the rate of oxygen consumption values and the Stryd power values. This strong dependence is obviously significantly reduced when these values are normalized by speed, giving a value only slightly larger than that found in the paper.</span></i></div>
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<i><span style="color: blue;">[....]Stryd power data are tailored to the individual, with power calculations being performed using input data for each specific subject, not across subjects. Therefore, if one were to actually validate Stryd power’s values as a training metric, as the paper’s title implies, correlation coefficients between rate of oxygen consumption and Stryd power should only be performed on a subject-by-subject basis</span></i></div>
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In keeping with Dr. Snyder's advice of analying Stryd data strictly on a subject-by-subject basis, I plot W/kg and metabolic rate of individual subjects separately on one plot and examine the strength of trendline linearity (Fig 6). Each subject's trendline and co-efficient of determination is shown. The plot shows that changes in metabolic rate explain anywhere from 96% to 98% of the variation in W/kg. The relationship is strong but far from 100%. It also shows a similar picture to the data I have collected from my <b><a href="http://www.georgeron.com/2018/12/examination-of-link-between-oxygen.html"><span style="color: red;">own laboratory VO2max testing</span></a></b>. </div>
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<tr><td style="text-align: center;"><a href="https://4.bp.blogspot.com/-w4rgvm79ztM/XB_YpbRbvFI/AAAAAAAAHKU/Vn4vUBhG6wo5ZQSA3bVwABjyWymKhhrPQCLcBGAs/s1600/Figure%2B7.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="430" data-original-width="686" height="250" src="https://4.bp.blogspot.com/-w4rgvm79ztM/XB_YpbRbvFI/AAAAAAAAHKU/Vn4vUBhG6wo5ZQSA3bVwABjyWymKhhrPQCLcBGAs/s400/Figure%2B7.JPG" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Fig. 5 : Energy cost lof running (calculated) vs cxygen cost of running (calculated). Source of data : Secret of Running (Dijk, Megen). </td></tr>
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What Aubrey et.al did in their paper (Figure 1) was pool all runner's data together by normalizing the metabolic rate and power/weight ratio by running speed. If we do the same for dataset from Secret of Running, all relationships are blunted and the plot essentially becomes a scatter of points (Fig.6). </div>
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<tr><td style="text-align: center;"><a href="https://4.bp.blogspot.com/-bkuvHEwjL7k/XB_aDCM53PI/AAAAAAAAHKg/3ZzYK-In62sCAP_8uJvMXnVMD5IC-JkRwCLcBGAs/s1600/Figure%2B8.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="433" data-original-width="693" height="248" src="https://4.bp.blogspot.com/-bkuvHEwjL7k/XB_aDCM53PI/AAAAAAAAHKg/3ZzYK-In62sCAP_8uJvMXnVMD5IC-JkRwCLcBGAs/s400/Figure%2B8.JPG" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Fig 6 : Normalized specific power vs normalized VO2. Source of data : Secret of Running (Dijk, Megen). </td></tr>
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So the methodological error explained by Dr. Snyder seems to be correct. Aubrey et.al must explain why they took this approach and on which former pieces of literature they borrowed this kind of analysis.</div>
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Stryd power and VO2 show a significant linear relationship. This relationship is pegged in two ways. </div>
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1) The Stryd powermeter, by way of algorithm, reports increased watts with increased running speed on flat surfaces. </div>
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2) By VO2 being positively proportional to speed on flat land running.</div>
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<span style="color: blue;"><i>Statement 4 : Data collection methods are not consistent across surfaces, making effective comparison across surfaces impossible.</i></span></div>
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That Aubrey et.al didn't fully explain data collection methods is a genuine accusation. However, on the same token, articles published by Secret of Running that were used in the chain emailing marketing efforts by Stryd also lacked tremendous clarity on how the authors conducted the tests. </div>
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For example, the authors Dijk & Megen stated that the <b><a href="http://hetgeheimvanhardlopen.nl/wp-content/uploads/2017/02/17.-The-Energy-Cost-of-Running-on-hills.pdf"><span style="color: red;">energy cost of running increases uphill</span></a></b>. The exact magnitude of the increase is in question. Is the nature of the specific increase just due to how the numerator in the algorithm (W/kg) is scaled to increase faster than the denominator (speed) and on what basis were the scaling factors decided? The correlational aspects of Stryd power and above ground gradient running is left to be explored and explained in scientific literature.<br />
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<b>Conclusion </b><br />
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<span style="color: blue;"><b>The methodological "fatal flaw" explained by Dr. Snyder in the Aubrey paper seems to be correct. Aubrey et.al must explain why they took this approach and on which former pieces of literature they borrowed this kind of analysis from. A proper explanation for this choice is desired.</b></span></div>
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<span style="color: blue;"><b>On cross-examining statements made with other data from Secret of Running group, Stryd power to weight ratio has a significant positively proportional relationship with speed. However, the data is not exactly linear, more wavy due to the presence of random variations and subject related issues and the slope of a linear trend line varies with subject. </b></span><br />
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<span style="color: blue;"><b>Both the energy cost of running and the oxygen cost of running calculated by normalizing power/weight ratio and metabolic rate by speed respectively are not exactly constant when seen in practice. Constancy is shown in literature but real data appears wavy, sometimes monotonically decreasing in certain runners. This maybe due to random errors in the sensor and variations in sensor placement as well as experimental issues in the VO2 data but these facts needs to be appreciated. </b></span><br />
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<span style="color: blue;"><b>Therefore, the Stryd as a powermeter must be used to make assertions about metabolic fitness only within subjects, as oppoed to across subjects.</b></span></div>
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<span style="color: blue;"><b>If we assume for a moment that Aubrey et.al indeed did due diligence and considered steady state VO2 values across both treadmill and above ground running, the Stryd research team has left some explaining to do why the observed differences in oxygen cost did not reflect in a corresponding difference in Stryd power. At the heart of this explanation lies several extrapolations various people are making on the internet about energy cost of running, running efficiency and oxygen economy, all on the basis of algorithms and no direct measurements of force or power. </b></span></div>
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Ronhttp://www.blogger.com/profile/16268869622833968439noreply@blogger.com0tag:blogger.com,1999:blog-4786784182488135171.post-54829510209288449302018-12-23T01:11:00.002+04:002018-12-24T00:18:49.485+04:00Examination of the Link Between Oxygen Uptake (VO2) and Stryd Run Power<div dir="ltr" style="text-align: left;" trbidi="on">
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Footpods utilizing 3D inertial measurement units to calculate external running power have been discussed <b><a href="http://www.georgeron.com/2017/09/the-physics-of-running-power.html"><span style="color: red;">previously on my blog</span></a></b> several times. </div>
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One of the purported advantages touted by product developers is the ability of the running "power meter" to track and inform about instantaneous metabolic rate (VO2). With the Stryd power pod, the existing support for this position has been that running power and VO2 are linearly proportional. </div>
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Infact, a linear relationship has been<b><span style="color: red;"><a href="https://www.georgeron.com/2017/03/actionable-intelligence-for-running.html"> <span style="color: red;">shown on my blog</span></a></span></b> earlier from a single VO2max test when we look at steady state values. But since the time I wrote it, I have gathered more data in order to re-examine the nature of this relationship in light of fitness changes in the body. </div>
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<b>Experiment </b><br />
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I completed two VO2max tests in a running laboratory a year apart in 2017 and 2018. Both tests were conducted by an experienced consultant who is also a PhD in Physiology & Exercise Sciences. Name withheld. </div>
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On both tests, I wore a Stryd footpod on my shoes and ran with a self-selected cadence. Key information : I also wore different shoes but the position of the pods themselves were standardized by mounting on the second criss-cross lacing from bottom. In 2017, I wore a Mizuno Ronin 5 and in 2018, I wore a Mizuno Sonic.</div>
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Treadmill grade was set to 1% and speed was increased by 2kph every 2 minutes until complete exhaustion. In 2017, I exhausted at 16kph. In 2018, I was fitter and exhausted at 18kph. </div>
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There was no change in equipment - treadmill, masks or gas analyzers, heart rate chest strap and metabolic carts - used between the two tests. Physiological variables that changed were my body weight and running fitness between the two periods. I was 64kg in 2017 and just shy of 61kg in 2018.<br />
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I ran my personal best 10K of 41 minutes in January 2018 and posted several track PR's in the later months. Compared to 2017, actual performance data indicated increased running fitness. </div>
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By special request, I gained all the raw data from both tests corresponding to several variables measured during the test for my own record.</div>
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<b>Summary of Results</b><br />
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A 30s rolling average of weight normalized metabolic rate and the corresponding instantaneous heart rate against time are shown in separate plots below (Figs. 1, 2). Tabulated data shows that in 2018, I had significantly lower heart rates to achieve similar running speeds on the treadmill. I was fit enough to run into the 18kph territory and extended my time to exhaustion by a whopping 3 minutes. </div>
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The VO2 trace on the other hand shows an increase in oxygen consumption in 2018 with a corresponding increase in power to weight ratio. The differences are significant. For example, at 16kph, the difference in oxygen consumption between both years are significant (p less than 0.05, f=68.96).</div>
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The strength of the correlation between oxygen demand and Stryd power weakened between 2017 and 2018, going from 99% in the former to being able to explain 96% of the variance in the latter. The particular relationship between 2018 oxygen consumption and power seems not exactly linear (Fig. 3). </div>
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<tr><td class="tr-caption" style="text-align: center;">Fig 1 : Tabulated summary showing VO2, Stryd power and corresponding heart rate for 6 different speed regimes.</td></tr>
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<tr><td class="tr-caption" style="text-align: center;">Fig 2 : VO2 and heart rate - time traces compared between two years.</td></tr>
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<tr><td class="tr-caption" style="text-align: center;">Fig 3 : Strength of correlation between VO2 and Stryd power to weight ratio in two tests.</td></tr>
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The specific percentage changes at each speed is shown for VO2 and power:weight ratio (Figs. 4, 5). Instantaneous VO2 measured by a metabolic cart is a scatter of points before achieving steady state so a boxplot of distribution is shown with the median value being used to calculate % changes. The same has been done for Stryd power. Outliers are also shown but median values are not affected by outliers.</div>
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<tr><td class="tr-caption" style="text-align: center;">Fig 4 : Comparison of VO2 distribution</td></tr>
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<tr><td class="tr-caption" style="text-align: center;">Fig 5 : Comparison of Stryd power:weight ratio</td></tr>
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<b>Discussion</b></div>
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Shown above is two VO2max tests done within a year and a few days. On both tests, I wore a Stryd footpod on two different shoes. </div>
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Specific discussion points are as follows. Note :<br />
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1) The correlation between Stryd power to weight and lab tested VO2 is strong, however the degree of the correlation weakens from 2017 to 2018. The reported requirement for higher power to weight ratios and decreased economy for the same speeds conflicts with the lowered heart rate data and the increased time to exhaustion and higher speed attained on the second test. In other words, one set of data indicating worsened power-speed efficiency appears to conflict with the actual performance on the test. Interpretations are open.<br />
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2) The boxplot distribution of VO2 at specific speeds are wide ranging and show the organic nature of oxygen rate according to the interval timing, run mechanics and the usage of elastic structures in the body. The boxplot distribution of algorthmic watts on the other hand is tight, which might potentially mislead when interpreting which value of run power corresponds to what oxygen demand. Therefore, caution must be exercised when comparing athlete(s) on the basis of run power to make value judgments of economical running. What is certain here is that Stryd power should be stated to be proportional only to steady state values of VO2, not transient data. If for example, a runner would run outdoors in heat conditions with a slowly rising component of VO2 which is a completely organic way the body functions, the meaning of the correlation of VO2 and Stryd power measured in one set of controlled conditions is lost in another. </div>
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3) The substantial decrease in heart rates to run the same speeds during the test show increased cardiovascular fitness. This correlates very well with the Polar Run Index recorded with Polar V800 for a period of 365 days between March 2017 and March 2018 (Fig. 6). In fact, around the January 2018 time frame, I'd been posting Run Indices in the 58-59 range which <b><a href="http://r-cane.blogspot.com/2014/11/polar-running-index.html"><span style="color: red;">predicts</span></a></b> my 5K/10K times within a margin of 1-2 minutes compared to actual performance. </div>
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<tr><td class="tr-caption" style="text-align: center;">Fig 6 : Author's Polar Run Index time series scatter obtained from Polar Flow for a period of 365 days from March 2017 - March 2018</td></tr>
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4) An inspection of preferred cadences on the two tests indicates non-signficant differences. The changes in cadence could not possibly explain the increased metabolic rate.<br />
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<tr><td class="tr-caption" style="text-align: center;">Fig 7 : Chosen stride rates between two VO2 tests conducted in 2017 and 2018.</td></tr>
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5) An inspection of the speed error (device speed minus target belt speed) between the two years show increased error in the second year but within 2%. The reason for the increased error is not known, as calibration factors were not changed within the footpod. </div>
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<tr><td class="tr-caption" style="text-align: center;">Fig 8 : Computed % error in run speed = 100 x (Device measured speed - Belt Speed)/(Belt Speed) </td></tr>
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6) The main variables that changed between the two tests were fitness, weight and the shoes worn. There is a possibility that simply wearing the meter on different shoes gave different readings but logically there is no reason why this should be so. However, on the Stryd forums, a variability in power measurements due to variations in mounting has been reported by users. </div>
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7) Interpretations should be kept in context of sample size (n=1), the period of time between the two tests in which many things not accounted for may have changed (systematic changes in sensors, stiffness between shoe and treadmill interface, motivation, hydration status, calibration error).</div>
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<b>Other Studies</b></div>
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1) In an outdoor setting, Aubrey et. al found statistically strong differences in oxygen consumption between different running surfaces that were not reflected in the strength of the differences in Stryd power to weight ratio (Aubrey, 2018). The device used was the first gen Stryd power meter worn on the chest. </div>
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2) In an indoor study studying the influence of a change in cadence on running economy and Stryd power in competitive collegiate runners, investigators found that only 31% of the variability in running economy coudd be explained by power (Austin, 2018). They cautioned that the Stryd's power measures may not be sufficiently accurate to estimate differences in running economy of competitive runners. The device used was the second gen Stryd power meter worn on the shoe as a footpod. </div>
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<b>Conclusion</b></div>
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<b><span style="color: blue;">A positive correlation exists between Stryd power and metabolic demand IN STEADY STATE. However, in light of the reported case here and the two other peer reviewed and published studies, caution must be exercised when applying Stryd power for metabolic profiling specifically due to points explored above. The value of a footpod powermeter </span></b><b><span style="color: blue;">to inform about "real time" metabolic demand </span></b><b><span style="color: blue;">in situations where minute but critical transient VO2 changes might be prevelant is suspect. </span></b><br />
<b><span style="color: blue;"><br /></span></b><b><span style="color: blue;">The true accuracy of this relationship is unknown in a large sample of runners in different environmental conditions as found in real world running. Interventions in running , such as change in shoes, change of mechanics, circadian rythms, travel fatigue etc may reflect in VO2 but not in run power. This is a hypothesis, some of which is just starting to be shown in the research community. We hope the research community can come forward with more topic ideas and explorations.</span></b></div>
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<b><span style="color: blue;">As reported here, a worsened power-speed efficiency did not correlate with the increased time to exhaustion, higher speeds and better heart rate fitness achieved in the second VO2 test. This study shows there is both teneble and actionable value in longitudinal heart rate monitoring over long periods of time. Conventional measures such as heart rate is not superceded or replaced by running power meters but should be considered an essential ingredient of a holistic performance monitoring approach. </span></b></div>
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<b>References </b><br />
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Austin, C., Hokanson, J., McGinnis, P., & Patrick, S. (2018). The Relationship between Running Power and Running Economy in Well-Trained Distance Runners. Sports, 6(4), 142. http://doi.org/10.3390/sports6040142<br />
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Rachel Aubry, Geoff Power, J. B. (2018). An Assessment of Running Power as a Training Metric for Elite and Recreational Runners. Journal of Strength and Conditioning Research, 32(8), 2258–2264. http://doi.org/10.1002/mrdd.20080<br />
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Polar Run Index Table </div>
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Ronhttp://www.blogger.com/profile/16268869622833968439noreply@blogger.com2tag:blogger.com,1999:blog-4786784182488135171.post-40824717660214989802018-11-18T09:14:00.001+04:002018-12-17T14:39:27.481+04:00GPS Inaccuracy is a Non-Problem<div dir="ltr" style="text-align: left;" trbidi="on">
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There are those who say running is not a skill. Sure, unlike soccer or archery, it may not need massive amounts of skill but the ability to pace by the internal "calibrator" in your head is absolulely a learned skill. That takes long hours of practice and generous amounts of emotional intelligence. Some people have more of EI than others. Perhaps women are better long distance pacers for this reason? The debate continues.</div>
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The other day, I ran a<span style="color: red;"> <b><a href="https://flow.polar.com/training/analysis/2987975545">relatively decent 10K</a></b></span> with a simple tried-and-true method I always employ : hit kilometer landmarks at specific times. The race, an annual staple in the Abu Dhabi calender, is not AIIMS certified, but is run on a course that is reliable enough for most of us 8am-5pm working animals. The course is also an easy out and back with stretches of long road and one roundabout so the effect of loops and not running tangets around those loops is absolutely minimal. </div>
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The trusted V800 GPS on my wrist always goes as a supplement, never a primary mode of pacing. Not surprisingly, the device would beep the kilometer split on-point in the beginning stretches of the race (corresponding to the position of kilometer signage) but as the race progressed, anywhere between 10-20 metres before the marked landmark.<br />
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It's important to put this into perspective. At my running speed, the watch beeped 3-5 seconds before the actual km marker. Over the course of 42:08 minutes, I ran 10.17km according to the watch but the race distance was reported to be 10km. In other words, assuming that the course was marked out correctly, the receiver on my wrist relying on a system of 24 global positioning satellites in orbit would under-report distance by 1-2%. </div>
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Is that really something to make a big hoopla about?<br />
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<b>Don't Fuss, We're Finely Tuned Machines</b></div>
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An experienced 10K road runner running would be consistently pacing within 1-5% of previous timings from race to race. They really are fined tuned machines. They already an ingrained sense of pace from long hours of training and racing. The GPS doesn't come to much benefit except to help assess whether they are roughly where they need to be. </div>
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A beginner road marathoner on the other hand might be more reliant on the GPS. They feel they need the training wheel to help guide them along, perhaps more out of a sense of anxiousness that anything can go wrong on such a long distance if they were off from where they need to be. </div>
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I argue that even these second class of individuals don't really need to depend primarily on GPS pace. With lots of hours of correct training, the human brain learns the forces and patterns of a marathon pace most comfortable and sustainable for a period of 2-4 hours. The primary reason for the trepidation in these runners is lack of adequate training. It's not GPS thats the problem.<br />
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<b>Get a Hold of Precision, not Inaccuracy</b></div>
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In a review of a ridiculous measurement of the same segment of road measuring 10km around 1000 times by GPS, the German mathematician Helmut Winter (who was also responsible for creating the timing systems in Kipchoge's world record Berlin marathon) wrote on <b><a href="http://run.hwinter.de/?p=7637"><span style="color: red;">his blog</span></a></b> : <b><i>"The most important result of the analyses was a standard deviation of the distribution of about 2 m for a total distance of 10,000 m, ie a relative dispersion of the data of about 0.2 per thousand. The deviation from the mean of the measured distance was less than 10 cm in the regime."</i></b><br />
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Even during training, I argue that a minor device deviation is a non-factor if you knew that it was precisely off everytime. </div>
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For example, if the watch says you run 7:57 min/mile but you covered really only about 3.75 miles in 30 minutes, you know that you really ran 8:00 min/mile so the watch over-estimated pace by about 3s/mile everytime. Over the course of a 3:30:00 marathon, the actual difference between what you actually ran and what the watch says you ran is a mere 150-200m.</div>
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On race day, even with tired bodies and weather fluctuations, such a runner can turn to the biological calibrator as primary guide and use a supplemental strategy of running every mile 3s/mile faster than what the watch should actually say in order to accomodate for the margin of error.<br />
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<b>Physiology is Not That Fussy</b></div>
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What about those who think if you don't hit training paces point blank, the sky will come crashing down?<br />
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Physiological reality is that there is an upper bound and lower bound to most training zones. A 20s/mile tolerance band to a threshold zone would be considerably more than the 3s/mile deviation in your GPS. Moreover, it is far better to incorporate multipace training to get your feet wet and learn different aspects of the water being tested.<br />
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<b>Conclusion</b><br />
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We forget that the point of training is to roughly hit the bullseye everytime and get on with life. Multipace training was how the Olympic stars of previous years broke world records! Instead, some hobby runners today want military grade accuracy, perhaps to land a missile in a specific spot of an ocean somewhere with a $500 watch. They can't sleep if device reported distance was off by 2%.</div>
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My argument is that trained humans are fined tuned machines to begin with. Distance road runners (which comprise probably 80-90% of the running population) can gain a ingrained sense of sustainable pace from long hours of training.</div>
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GPS inaccuracy is really a non-problem. What is a problem is that it is turned into a problem by those looking to dip into your pocket while marketing their own product. And one has to be wary about such hidden agendas. </div>
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Ronhttp://www.blogger.com/profile/16268869622833968439noreply@blogger.com0tag:blogger.com,1999:blog-4786784182488135171.post-39764916021906055852018-10-11T08:11:00.002+04:002019-03-15T16:25:00.842+04:00Monitoring & Applying Heart Rate : A Primer<div dir="ltr" style="text-align: left;" trbidi="on">
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<b><u>I. Introduction</u></b><br />
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At the core of a runner's body is a variable pump that manages to spectacularly manipulate it's blood flow output. At rest, the heart pumps roughly 250 ml/min of blood (the idling state), but this can increase two orders of magnitude to upto 22,000 ml/min during maximal exercise (redline). In highly trained athletes, maximal flow volume is of the order of 40,000 ml/min. If you look at the ratio, 40,000/250 is nearly160x times the value at rest.</div>
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Cardiac output is the product of heart rate (HR, beats per minute) and stroke volume (SV, ml per beat) expressed as :</div>
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<b><span style="color: red;">Cardiac Output = HR x SV </span></b></div>
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The amount of oxygen that can be removed from circulating blood and used by the working tissues in a given time period is called "VO2". An individual's maximum utilization capacity is represented by maximum oxygen consumption or what is commonly known as "VO2max" in exercise literature. When exercise intensities exceed this aerobic capacity, sources of energy outside of the aerobic system (glycolotic, alactic etc) have to be utilized to support the movement task. </div>
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Mathematically, VO2 is the product of cardiac output and the amount of oxygen extracted from the blood. The difference between the amount of oxygen within the arterial blood and that within the venous blood returning to the heart is termed the arteriovenous O2 difference (a-VO2diff). This constitutes the extraction capacity of blood.<br />
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Combining these variables yields the famous Fick's equation :<br />
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<b><span style="color: red;">VO2max = </span><span style="color: red;">HRmax</span><span style="color: red;"> x </span><span style="color: red;">SVmax</span><span style="color: red;"> x </span><span style="color: red;">a-VO2diffmax </span>---- EQUATION 1</b><br />
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Research indicates that despite increasing age, maximum HR is more or less stable. Therefore, little benefit can be obtained by heart rate increase and any endurance training benefits is derived from the second and third terms in EQUATION 1. In other words, the more stroke volume your heart has and the more oxygen extraction is possible between arterial and venous blood return, the more is VO2max which can then be used to extract more speed out of your running.<br />
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<b><u>II. Characteristics of HR Benefiting it's Field Application</u></b><br />
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HR has proven beneficial for normal day-to-day athletes because it shows a satisfactory correlation with physiological variables such as oxygen consumption rate (VO2) and blood lactate accumulation Due to it's correlation with VO2, HR been used to estimate VO2max as well.<br />
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It is also somewhat correlated to metabolic substrate use during exercise (the "Am I using more of Fats or More of Carbohydrate" question) and has been used to estimate energy expenditure in field conditions.<br />
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However, two caveats to the use of HR as a surrogate measure of physiological capacity :<br />
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1) The prediction of VO2max from HR is said to rely upon several assumptions and it has been shown that the results can deviate up to 20% from the true value.<br />
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2) There appears to be general consensus that this method provides a satisfactory estimate of energy expenditure on a group level, but is not very accurate for individual estimations.<br />
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3) HR by itself only answers the "how many beats per minute" question but not the "how much stroke volume per beat" question. Therefore, specific questions about adaptation to training may not be directly answered by just HR alone.<br />
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4) HR is affected by variables - such as weather conditions, hydration status and day-to-day variations such as fatigue. For example, scientific literature states an approximate variation of 3 beats/min in HRmax from day to day.<br />
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5) There appears to be a steady increase in HR during activity, a phenomenon termed "cardiac drift".<br />
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Due to these reasons, it is a <u>satisfactory</u> variable to use in the field mainly for the following :<br />
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A) To monitor exercise intensity by quantifying time spent in demarcated HR zones. The demarcation of zones is subject to various schools of thought, some being more representative or less representative of athlete physical condition. Generally in practice, HR zones coincide with the accumulation of lactic acid in the blood, with HR associated with low lactate values assigned to low intensity and higher lactate values assigned to high intensity.<br />
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B) It is valid in correlating internal load, such as Training Impulse (a metric generated with the knowledge of HR) to training outcomes such as fitness, fatigue or performance. For example, a study done in cyclists found that a weekly accumulation of individualized TRIMP of 650 units was necessary to maintain improvements in aerobic fitness (power output at 2 mmol/ L).<br />
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C) It is used to inform the daily state of an athlete through measurement of a resting pulse. For example, an over-reached state of fatigue may be accompanied by a higher-than-normal resting HR or sleeping HR.<br />
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<u>HR is not an objective measure of work rate.</u> Some good examples why this isn't so :<br />
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1) A sudden increase (or decrease) in work-rate, i.e running or cycling power, may not coincide with an immediate rise in HR. Due to the "laggy" non-linear response of HR, it is not ideal to use to inform about work rate changes.<br />
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2) At the same work rate, HR is known to slowly drift to higher values despite working at the same external load. Scientific studies show that this is partly co-related to dehydration.<br />
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3) In hot environments, cardiac drift has been shown to correlate with core body temperature increase. It has also been shown that in hot environments, VO2max can also be lowered. Therefore, a prediction of VO2max using HR becomes baseless.<br />
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4) In high altitudes, HR increases inspite of little to no change in VO2 or external load. Therefore, the HR-VO2 curve "right-shifts" and makes sea-level HR zone methodologies suspect. Recovery characteristics of heart rates due to acclimitization are very individual.<br />
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<b><u>III. APPLICATIONS </u></b><br />
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<b><u>A. Monitoring Heart Rate During Running</u></b><br />
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Input output characteristics are well studied with step inputs. A high intensity interval training session (HIIT) does exactly this - it involves step increases in pace or external power and holding said pace for a prescribed interval. This offers a good chance to study heart rate behavior.</div>
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Attached below is data from a subject (me) obtained from a HIIT training session where power, heart rate monitor and GPS as a secondary mode of monitoring pace (primary mode = time per lap) were all used in conjuction with each other.</div>
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The protocol was 4 x 5 minute intervals at a pedestrian 1:44 per 400m. The dynamics of HR is shown below in relation to running speed and mass specific external running power :</div>
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<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://1.bp.blogspot.com/-wIL7ojkNLDU/W72LtGxSOvI/AAAAAAAAHA4/A_fgRBEH24wqfgAM-SH1gdLtwHb-DZdUQCLcBGAs/s1600/Cardio%2Bdynamics.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="474" data-original-width="1270" height="148" src="https://1.bp.blogspot.com/-wIL7ojkNLDU/W72LtGxSOvI/AAAAAAAAHA4/A_fgRBEH24wqfgAM-SH1gdLtwHb-DZdUQCLcBGAs/s400/Cardio%2Bdynamics.png" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Fig 1 : Stacked data showing running power, heart rate and running speed with time from an interval session.</td></tr>
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<span style="text-align: justify;"><br />The most prominent observation is that in response to step increaes in power requirement (W/kg) or pace, heart rate takes several seconds to increase. This is called <i>cardiac lag</i>. This lag is simply a manifestation of an organic pump in our body that can only increase its beating frequency in a finite time as opposed to an instantaneous response. </span><br />
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<span style="text-align: justify;">One of the aims of this workout was to stay within 90-95% VO2. Since heart rate is a surrogate of VO2 and assuming external variables have been controlled for, I might conclude that the aim has been fulfilled in the first 3 of the 4 intervals. At the 4th interval, HRmax has been essentially reached. This value of HRmax completely agrees with value of HRmax reached during laboratory VO2max tests done earlier in the year. Therefore, I might conclude that at virtually no point did I cross my maximum aerobic ceiling until perhaps the very last interval. And it was at this point that I called off the 5 minute session. </span><br />
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Therefore, if the aim of the workout was to increase time spent at VO2max, this session wouldn't exactly provide the requirement. However, if the aim was to maximize time spent at between 90-95% of VO2max within the limited time allottment, then I conclude it met the aim mostly.<br />
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Another use of HR during such an interval session is to monitor the recovery dynamics. With the same amount of rest in between each interval, one finds that the baseline HR reached at the end of each recovery gets progressively higher. Conversely, this means that in each subsequent interval, it would take lesser time for HR to climb to the maximal values necessitated by the workout.</div>
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In the following diagram (click to zoom), the black lines indicate the slope of HR rise, the blue line would indicate the slope of HR fall and the thick red lines are the baseline HR reached at each recovery.</div>
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<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://4.bp.blogspot.com/-arSUUqmV1u8/W72R5u3RXpI/AAAAAAAAHBI/RpwiHks5jHUKx38FDbkQhSU1WGh7Zi8sACLcBGAs/s1600/Cardiodynamics2.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="385" data-original-width="1461" height="105" src="https://4.bp.blogspot.com/-arSUUqmV1u8/W72R5u3RXpI/AAAAAAAAHBI/RpwiHks5jHUKx38FDbkQhSU1WGh7Zi8sACLcBGAs/s400/Cardiodynamics2.png" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Fig 2: Heart rate dynamics during an interval running session</td></tr>
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Looking at the data, the slope of HR rise during the first and last 5 minute interval were +0.06 beats/second and +0.04 beats/second respectively. This indicates that the slope tends to the flatten out at the higher HRs. Secondly, the recovery slope is more or less the same, roughly -0.3 beats/second in the first recovery span and -0.28 beats/second after the final interval.</div>
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However the body's need to supply oxygen keeps HR elevated so within a given recovery time, the baseline recovery HR continues to climb. This, together with the effort signals sensed by the nervous system might indicate to the runner that they would need to stop at some point.<br />
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<b><u>B. Determining Maximum Heart Rate</u></b></div>
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Maximum heart rate can be readily determined by running uphill on a slope of 3-4% gradient at your 1500m pace for 3-4 minutes. I find that slopes tend to accelerate the rise of HR compared to the same running paces on flat, simply because of the need for more muscle involvement.<br />
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Without maximum heart rate from an actual field test, it can be determined on the basis of the Seal's formula :</div>
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<span style="color: red;"><b>Max HR = 207 - (0.7 x Age) </b></span><b style="text-align: left;">---- EQUATION 2</b></div>
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The formula can under-estimate actual heart rate by upto 10-20 bpm so caution is advised.<br />
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<b><u>C. Other Uses of Heart Rate </u></b><br />
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Some other uses of heart rate have very good application for overtraining prevention and are described below :<br />
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<b><u>Surrogate metric for operational efficiency :</u></b> The comparison of HR along with corresponding running pace or power can be used to understand if the running is efficient with respect to the same course and temperature conditions. In an earlier post, I looked at the <b><a href="https://www.georgeron.com/2017/07/heart-rate-to-power-ratio-metric-for.html"><span style="color: red;">ratio of running power to heart rate</span></a></b> as a potential application of this technique. So I won't expand on this here, but suffice to say it is an interesting area for personal exploration.<br />
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<b><u>Dehydration : </u></b>With dehydration, blood volume decreases leading to less blood pumped with each heart-beat. Earlier, a study published in the Journal of Applied Physiology found that heart rate increased 7 beats per minute for each 1% loss in bodyweight from dehydration. In other words, for a 68 kg runner, a loss of 1-2% of bodyweight which would increase heart rate by about 7-14 beats per minute. This cardiac drift phenomenon increases heart rate with distance and duration.<br />
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A runner has two ways to compensate for dehydration related heart rate increase.<br />
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A) The most obvious way to counteract HR drift is to stay hydrated before and during the exercise.<br />
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B) Account partially for drift and allow heart rate to increase to about +7 beats more than the prescribed maximum by the end of the run. But that might lead to more stress on the body so this is an 'aggressive HR strategy'.<br />
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C) Account for this 7 beat increase by starting , let's say a 1 hour tempo run, at 7-10 beats lower than prescribed. But this might means that the runner will not get the pace simulation for muscle loading and adaptation. This is a 'conservative HR strategy'.<br />
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<b><u>Checking recovery :</u></b> A potentially good benefit of monitoring heart rate is to help avoid overtraining. If a morning heart rate reading is higher than baseline readings during recovery days, it might be an indication of predominance in nervous system sympathetic activity. In simple words, this means the body is either trying hard to cope with hard training or it is stressed out and needs a break.<br />
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Monitoring waking HR rates is a simple way to check for onset of fatigue or even illness. How valid is it? Only you can collect your own data and decide for yourself. A snapshot of 41 days of supine resting HR from my own data collection indicates that there are days when HR is up and days when HR is down. Over 41 days, the long term trend is one showing a decrease in resting HR which might mean the heart is either adapting and pumping more blood per beat or that my training sessions are not as stressful as they were earlier.<br />
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<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://4.bp.blogspot.com/-GnRvdDWsXw0/W9G3Kszg69I/AAAAAAAAHCc/AVUqSsniYlI23LIM2nXjGSHm0TgqLMTpgCLcBGAs/s1600/HR%2Bmorning_Ron.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="527" data-original-width="930" height="226" src="https://4.bp.blogspot.com/-GnRvdDWsXw0/W9G3Kszg69I/AAAAAAAAHCc/AVUqSsniYlI23LIM2nXjGSHm0TgqLMTpgCLcBGAs/s400/HR%2Bmorning_Ron.JPG" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Fig 3 : Supine resting HR for 41 days from the author using an ECG holter. </td></tr>
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<b><u>D. Concerns Regarding Heart Rate</u></b></div>
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In my experience coaching, some runners, especially the older individuals, get alarmed upon receiving notification that their maximum HR has been reached. Here are some thoughts on this observation :</div>
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1. I would ask if the maximum HR been plugged into the watch correctly. Typically, a smart watch these days can automatically input maximum HR from stressful workouts into the settings. But normally, this is left to the user to input. Therefore, my question still stands. Has the user entered the correct "field-based" maximum HR into the watch's settings?<br />
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2. Has the HR chest strap been wetted ? Moisture and salt helps the electrode 'conduct'. I also do not believe in the reliability of wrist based HR monitors and have exclusively used chest strap systems from Polar for many years. </div>
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2. Going by the idea that HR is a surrogate for VO2, a slowly climbing HR is a good sign the workout is delivering oxygen to working muscles in the way it's supposed to. However, it's apt to understand this 'rise' with perceived effort. Is it normal rise or a dehydration or heat related rise?</div>
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When the running speed is too high, the runner's body dissipates heat at a faster rate than if the speed were slower. At the same time, if ambient humidity is also high then sweat evaporation is reduced, and the only other significant way of body cooling is through heat convection from dilated skin surface blood vessels. For this to happen, the blood has to be shunted away from working muscles to the skin.</div>
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Without adequate muscular blood supply, the runner may go anaerobic and must soon reduce or stop due to inability to manage heat and/or supply the muscles with oxygen. There is a mismatch between the aim of the workout and the selected running speed. The runner must now correct themselves by re-calibrating their speed.</div>
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Outside of correcting for these factors, if a high HR is still observed, it is prudent to check with a medical practicioner and get an ECG based reading for cardiac health. Just remember, everyone is different. Your neighbour may have a maximum heart rate of 170 but you might be crossing 200. That speaks nothing of either of your athletic capabilities. It is as statistical as one person having bigger feet than another. </div>
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REFERENCES<br />
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1. https://www.ncbi.nlm.nih.gov/pubmed/12762827</div>
Ronhttp://www.blogger.com/profile/16268869622833968439noreply@blogger.com0tag:blogger.com,1999:blog-4786784182488135171.post-22227802879700337532018-04-06T17:36:00.000+04:002019-03-27T11:44:38.151+04:00The Running Locomotor : Cost of Transport and Work Efficiency<div dir="ltr" style="text-align: left;" trbidi="on">
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<i><span style="color: blue;">The technically minded performance runner would want to be deeply interested in the inner workings of the human locomotor, and the numerical possibilities associated with the business of running and running performance. Through a series of articles, I hope to probe into and gain a deeper understanding of these possibilities. As Prof. di Prampero wrote in the Journal of Sports Medicine in 1986, man is the only machine to be able to move about and also understand how he does it at the same time. </span></i><br />
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One can draw interesting parallels between the power production processes at the cellular level in the human body and the 4 stroke combustion engine. </div>
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In the latter, a governing thermodynamic cycle requires that a mass flow of combustibles flow into a chamber as a "batch" process. A mix of gasoline and air is introduced into the combustion chamber, said mix is compressed to high pressures, said mix is then ignited by a spark plug consequently intiating the power stroke which delivers useful mechanical power to a flywheel. In the final stroke, exhaust products are expelled out of the combustion chamber. </div>
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Muscle is a chemical engine in the human locomotor. Electron microscopy has revealed, quite beautifully, that there exists a molecular "power-stroke" that is ultimately responsible for muscle contractions. </div>
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Very simplistically, the requirement to deliver contractile force causes a "spark" from an innervating motor unit strong enough to activate clusters of muscle fibers according to the size of the demand.<br />
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Substrates chemically combine in coupled reactions and the energy used to make ATP. All human movement is paid in ATP. At the muscle sacromere level, the hydrolysis of a molecule of ATP hydrolysis leads to the cross-bridging of the protein myosin over another protein actin causing contraction of a sacromere.<br />
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A <b><a href="https://www.youtube.com/watch?v=oHDRIwRZRVI"><span style="color: red;">great video</span></a></b> shows this elaborate molecular "power-stroke" in actin-myosin overlap. For academic purposes, <b><a href="https://biologicalwiki.wikispaces.com/The+way+things+move%2C+looking+under+the+hood+of+molecular+motor+proteins"><span style="color: red;">one can read</span></a></b> about fascinating molecular motors. Research on motility within muscle has spanned several decades and we still only continue to learn about the molecular agents responsible for muscle contraction.<br />
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<b><u>I. Cost of Transport </u></b><br />
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The cost of transport becomes a decision maker for vehicle purchase. For example, a 40mpg family sedan will consume approximately 7 liters of fuel per 100km. A figure like this is considered 'good' by today's standards and gets a strong weighting factor in purchase.<br />
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In the human locomotor, oxygen uptake reflects the quantity of ATP used when aerobic metabolism can provide all of the energy at a given steady state running speed.<br />
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Given the conditions that running is steady state and no accumulation of lactic acid takes place, the oxygen cost of sub-maximal running (ml O2/kg/min) above resting value is known to be a linear function of running speed. This oxygen cost, when expressed on a per minute basis, becomes the "metabolic power".<br />
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Metabolic power divided by speed of movement yields cost of transport.<br />
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<div style="text-align: left;">
<b><span style="color: blue;">COT = Metabolic Power Demand </span></b><b style="text-align: center;"><span style="color: blue;"><span style="background-color: white; font-family: "arial" , sans-serif; font-size: 16px; text-align: left;">÷ </span></span></b><b><span style="color: blue;">Running Speed</span></b></div>
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where units are :<br />
Cost of Transport, COT = mlO2/kg/m<br />
Metabolic Power Demand (net or gross) = ml/kg/min<br />
Running Speed = m/min<br />
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Note : COT is also called Cost of Running or simply Energy to Run (ECOR, Cr, Er etc) in some works. If expressed as an energy cost (J/kg/m), the volume of oxygen uptake has to be converted to it's energy equivalent.<br />
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Net metabolic power demand and running speed assumes linearity to a good degree; the slope becomes COT. As science consuming readers, we might be able to hold confidence in the linearity between metabolic power demand and running speed upto maximum metabolic power because a large collection of published studies show this correlation (Fig 1).<br />
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The linear relationship essentially means that COT is independant of running speed. That is, regardless of the speed of running, the runner's energy expenditure per unit distance is constant.<br />
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<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://1.bp.blogspot.com/-Ih8unVjeh8o/WrdRTaIVPrI/AAAAAAAAGyc/F_C8h9sfW9c5RSaEY3aHno0KGYQfcWtzgCLcBGAs/s1600/Gross%2Benergy%2Bcost%2Bof%2Brunning%2Bon%2Btreadmill.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="760" data-original-width="666" height="400" src="https://1.bp.blogspot.com/-Ih8unVjeh8o/WrdRTaIVPrI/AAAAAAAAGyc/F_C8h9sfW9c5RSaEY3aHno0KGYQfcWtzgCLcBGAs/s400/Gross%2Benergy%2Bcost%2Bof%2Brunning%2Bon%2Btreadmill.JPG" width="350" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Fig 1 : Data accumulated from 10 studies (n=130) for adults performing treadmill running (8-20 kph speeds) show the linear relationship between oxygen cost (ml/kg/min) and running speed (kmph). In this dataset, the average regression line approximates. Oxygen cost (ml/kg/min) = 2.203 + (3.163 x kph). If VO2 = A + B x Speed, A = 2.203 +/- 8.285 and B = 3.163 +/- 0.474. Males (71.5%), females (28.5%), trained (50%), untrained (1.5%) and unknown training status (18.5%). Reference [3]. </td></tr>
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Fig 2 shows COT values for several runners from a popular marathon in Geneva published in [7]. It is interesting to note that for the same sub-maximal running speeds, COT differs among the runners sometimes upto 20%!<br />
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Therefore, calculating COT yields an excellent barometer by which to judge different runners just as fuel consumption guides vehicle purchase.<br />
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Runners with a low COT have greater margin to push speed leading to superior performance to cover a given distance. Following that thought, we might consider that the hypothetical runner with a superior COT would be the one to break the marathon sub 2 hour barrier.<br />
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<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://2.bp.blogspot.com/-FJ1-KsMk0sQ/WsdM9QNgtsI/AAAAAAAAG2Q/NT_y3FTMWMQZKKjpnayjYpJTEQrCJ_d9QCLcBGAs/s1600/COT%2Bfor%2Bvarious%2Brunners.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="496" data-original-width="744" height="266" src="https://2.bp.blogspot.com/-FJ1-KsMk0sQ/WsdM9QNgtsI/AAAAAAAAG2Q/NT_y3FTMWMQZKKjpnayjYpJTEQrCJ_d9QCLcBGAs/s400/COT%2Bfor%2Bvarious%2Brunners.JPG" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Fig 2 : Energy cost of running (COT) at constant speed on flat terrain as a function of speed. Filled symbols refer to the two less economical and open symbols to the two most economical among 36 subjects taking part in the “Marathon International de Genève”. Reference [7].</td></tr>
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<b><u>II. Influencing Factors of COT</u></b><br />
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<b>A) Substrate Use </b><br />
<b><br /></b>It is essential to know in what proportions the human locomotor uses fats and carbohydrates to fuel exercise in order to derive the energy equivalents of their associated consumptions. Metabolic substrate use is dependant on intensity of run and variable of interest is decide fat-carb use and aerobic and anaerobic regime of operation is the respiratory exchange ratio.<br />
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For example, if the intensity is low enough in constant speed running and <b><a href="https://en.wikipedia.org/wiki/Respiratory_exchange_ratio"><span style="color: red;">respiratory exchange ratio</span></a></b> (RER) is 0.7, the human locomotor is known to operate in a predominantly aerobic fashion oxidising fats (palmitate). Based on this knowledge, a calorific equivalent of 19.6 J/mlO2 is used for this operational regime.<br />
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However, when exercise intensity increases and RER approaches 1, fraction of glucose (carbs) aerobically metabolised must be account for. Glucose yields 21.1 kJ/mLO2 and is therefore volumetrically 7% more energetic than fats. (diesel automobile enthusiasts will fondly remark that diesel fuel is volumetrically more efficient than petrol and that we ought to use diesel more!).<br />
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Under the simplifying assumption of zero anaerobic contribution, an average value of 20.9 J/mlO2 is used in literature to account for both fats and glucose oxidation, although this average value corresponds to a RER = 0.96.<br />
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Beyond a respiratory exchange ratio = 1, the human locomotor is anaerobic and equivalency value of 20.9 J/mlO2 without inclusion of the energy contribution of lactate introduces an error into the calculations. Therefore, improper assumptions about substrate use can lead to error-prone estimates of energy production depending on training status of the runner.<br />
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<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://1.bp.blogspot.com/-BjDn5zlcy-Q/WtCvLfkkwdI/AAAAAAAAG3o/8QiLZmSb9GY5SBz3jUIW6Kp3feb2euJLQCLcBGAs/s1600/BLA%2Bvs%2Bno%2BBLA%2Binclusion.png" imageanchor="1" style="margin-left: auto; margin-right: auto; text-align: center;"><img border="0" data-original-height="527" data-original-width="725" height="290" src="https://1.bp.blogspot.com/-BjDn5zlcy-Q/WtCvLfkkwdI/AAAAAAAAG3o/8QiLZmSb9GY5SBz3jUIW6Kp3feb2euJLQCLcBGAs/s400/BLA%2Bvs%2Bno%2BBLA%2Binclusion.png" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Fig 3 : The red lines indicate the corrected VO2 equivalent of running as a function of running intensity in sloped and level running conditions when blood lactate contribution is accounted for. Black lines neglect this contrbution. In this particular study on trained runners, the difference of neglecting lacate contribution amounted to a mean value of 0.02 mlO2/kg/m for level running and 0.03 mlO2/kg/m for sloped running. Reference [11].</td></tr>
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<b>Aerobic Regime</b><br />
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The shape of the aerobic COT in relation to running intensity has been reported to mildly curvilinear that tends to flatten out with intensity. The net oxygen consumption in the following relation is dependant on subject and assumes that during locomotion, the resting metabolism remains unchanged.<br />
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<b style="color: blue; text-align: center;"><br /></b>
<b style="color: blue; text-align: center;">Aerobic COT = [Net Oxygen Consumption x Calorific Equivalent] </b><b style="text-align: center;"><span style="color: blue;"><span style="background-color: white; font-family: "arial" , sans-serif; font-size: 16px; text-align: left;">÷ </span></span></b><b style="color: blue; text-align: center;">Speed</b></div>
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<b style="color: blue; text-align: center;"><br /></b></div>
where units are :<br />
Aerobic COT = J/kg/m<br />
Net Oxygen Consumption = ml/kg/min [Reported to be between 3.5-5 ml O2/kg/min]<br />
Calorific Equivalent = J/ml<br />
Caloric Equivalent of Aerobic Metabolism (Fat & Carb) = 20.9 J/mlO2 (average value)<br />
Speed = m/s<br />
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<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://4.bp.blogspot.com/-0iDtRe6J5qA/WrdkCVijsHI/AAAAAAAAGys/860KEqZvk6Yqlycl28LTZb8E9hFiAK8wwCLcBGAs/s1600/Non-athletes%2BAerobic%2BCOT.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="419" data-original-width="505" height="331" src="https://4.bp.blogspot.com/-0iDtRe6J5qA/WrdkCVijsHI/AAAAAAAAGys/860KEqZvk6Yqlycl28LTZb8E9hFiAK8wwCLcBGAs/s400/Non-athletes%2BAerobic%2BCOT.JPG" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Fig 4 : Non-linear increase of aerobic COT in several non-athletic male subjects (n=29) while running indoors. Reference [4]. </td></tr>
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<b>Anaerobic Regime</b><br />
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When the energy demand exceeds the locomotor's aerobic capacity, the fraction of energy production from anaerobic sources come into the picture. A byproduct of anaerobic metabolism is lactate, therefore measurements of blood lactate ([bLA]) in standardized laboratory protocols constitute a valid cardiorespiratory assessment of exercise intensity. Not accounting for [bLA]'s energy contribution (what literature calls "oxygen debt") may have varying degrees of error based on the subject measured on and the exercise intensities (Fig 3).<br />
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The precise shape of the anaerobic COT in relation to running intensity has been reported to be sharply curvilinear. The net increase in blood lactate (net bLA) is multiplied by an equiavalent of 60 J/kg/mM or 3 mlO2/kg/mM to determine the net energetic value of lactate. When divided by the overall distance covered, one gets the net anaerobic COT.<br />
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<b style="color: blue; text-align: center;">AnaerobicLa COT = [Net bLA x O2 equivalent x Caloric Equivalent of Carb. Oxid.] </b><b style="text-align: center;"><span style="color: blue;"><span style="background-color: white; font-family: "arial" , sans-serif; font-size: 16px; text-align: left;">÷ </span></span></b><b style="color: blue; text-align: center;">Distance</b><br />
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where units are :<br />
Anaerobic La COT = Anerobic Lactate COT, ml/kg/m<br />
Net bLA rise = mM/l<br />
O2 Equivalent of bLA accumulation = ml/mM/kg. This is between 2.7 and 3.3 mlO2/mM/kg (swimming to running) .<br />
Caloric Equivalent of Carb. Oxidatation (glucose) = 21.131 J/mlO2<br />
Distance = m (running time x speed)<br />
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<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://1.bp.blogspot.com/-2cDxfcIXhe8/WrdnEaY3ixI/AAAAAAAAGy4/ubkpGcxE5b413L4K38vc4_9Jpl9IyxrkACLcBGAs/s1600/Non-athletes%2BAnaerobic%2BCOT.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="416" data-original-width="507" height="327" src="https://1.bp.blogspot.com/-2cDxfcIXhe8/WrdnEaY3ixI/AAAAAAAAGy4/ubkpGcxE5b413L4K38vc4_9Jpl9IyxrkACLcBGAs/s400/Non-athletes%2BAnaerobic%2BCOT.JPG" width="400" /></a></td></tr>
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<tr><td class="tr-caption"><span style="font-size: x-small;">Fig 5 : Non-linear increase of anaerobic COT in several non-athletic male subjects (n=29) while running indoors. Reference [4]. </span></td></tr>
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A third contribution to energy supply comes from anaerobic alactic stores, or the cleavage of phospocreatine PCr but this is only prominent in short distances under maximal running conditions. For example, in the 400m sprint, 10-12% of total energy has been reported to come from this contribution. However, in long distance running, this contribution maybe conveniently neglected.</div>
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<b style="color: blue; text-align: center;">AaerobicaLa COT = </b><b style="color: blue; text-align: center;">[PCr x O2 equivalent x Caloric Equivalent of PCr] </b><b style="text-align: center;"><span style="color: blue;"><span style="background-color: white; font-family: "arial" , sans-serif; font-size: 16px; text-align: left;">÷ </span></span></b><b style="color: blue; text-align: center;">Distance</b></div>
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The metabolically derived COT, COTm is a summation of anerobic and aerobic contributions. </div>
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<span style="color: blue;"><b>COTm (J/kg/m) = Aerobic COT + Anaerobic La COT </b></span></div>
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COTm from a large number of studies done on athletic subjects approach the value of 0.9 kcal/kg/km or 3.7 J/kg/m in indoor conditions without environmental influences. Under the same conditions, the non-linear shapes of the aerobic and anaerobic COT combine to produce a net linear shape in COTm as shown in Fig 1.<br />
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<b>B) Environmental Conditions : Accelerated Running</b><br />
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The above discussion is valid for indoor settings. In an outdoor running environment, the influence of air resistance starts to play a substantial role in fast running. Furthermore, accelerated running out of block starts such as track running incurs a kinetic cost of accelerating the body from zero to final speed in the acceleration phase.<br />
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The energy cost of overcoming wind resistance is particularly appreciable beyond 5 m/s. For a man of 1.75m and 70kg in mass, wind resistance only accounts for 6.5% of the total cost although it can and have been known to affect speeds significantly in short distance track races.<br />
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Even under still wind conditions, runners "create" their own wind by virtue of moving speed. Speeds approaching the sub-2 hour marathon barrier (5.8 m/s) under still wind conditions will require +8% higher energy compared to running with no air resistance (Pugh, 1970).<br />
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<b>C) Environmental Conditions : Slope of Terrain</b><br />
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A strong environmental condition known to affect COT is the slope of the running surface. Fig 5 distills the work of some prominent researchers on slope effects. Recall that Minetti's regression 5th order equations for slope effects on running cost are <b><a href="http://www.georgeron.com/2017/11/the-govss-running-power-algorithm-and.html"><span style="color: red;">also reflected in the GOVSS power</span></a></b> calculation algorithm.<br />
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So we see that upto a slope of 2%, COT is linear. Running on a slopes of 3-5% will require upwards of 10J/kg/m! Therefore, higher work loads can be accumulated under hill running in a given amount of time compared to flat running and this has implications for training. On the other hand, in a race or long hiking situation on very steep terrain, the runner is faced with how to minimize energy costs of travel. There is advantages in traversing up a zigzag path to artifically flatten the slope.<br />
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<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://1.bp.blogspot.com/-EVDniRbe2Gw/WsdOs3HmZeI/AAAAAAAAG2g/yF581WI_4BMB3IaHPgqynZSjXr2QoINoQCLcBGAs/s1600/COT%2Bdepending%2Bon%2Bslope.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="541" data-original-width="737" height="292" src="https://1.bp.blogspot.com/-EVDniRbe2Gw/WsdOs3HmZeI/AAAAAAAAG2g/yF581WI_4BMB3IaHPgqynZSjXr2QoINoQCLcBGAs/s400/COT%2Bdepending%2Bon%2Bslope.JPG" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Fig 6 : COT along the direction of motion as a function of the incline of the terrain. COT is independant of speed and only depends on slope. Reference [7].</td></tr>
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<b>D) Environmental Conditions : Heat and Humidity</b><br />
<b><br /></b>
The running machine faces a substantial reduction in work capacity in hot and humid climates. The reasons are seen below.<br />
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Considering the running locomotor and the ambient surroundings (ground + air) as a thermodynamic system, heat production is a function of energy cost, speed and weight :<br />
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<span style="color: blue;"><b>Heat Production = COTm x Speed x Weight</b></span><br />
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where units are :<br />
Heat production = Watts<br />
COTm = Joules/kg/m<br />
Speed = m/s<br />
Weight = kg<br />
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On the other hand, heat dissipation is a function of surface area (or mathematically the square root of body surface area). Heat dissipated by means of conduction, radiation and evaporation added to the storage of heat within the body must balance heat production.<br />
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<b><span style="color: blue;">Heat Production = Heat Lost in (Conduction + Evaporation + Radiation) + Heat Stored in Body</span></b><br />
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The technical issues that lead to an impact on running speed are the following :<br />
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1. The running locomotor's aerobic capacity or VO2max could shrink, hence there is a derate in aerobic potential.<br />
2. The running locomotor faces a cardiovascular drift running in the heat.<br />
3. Heat production is constrained by speed and weight<br />
4. Heat dissipation is constrained by body surface area, temperature and relative humidity<br />
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<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://3.bp.blogspot.com/-rMeNDFB7_iE/WtDf3le7b6I/AAAAAAAAG4Y/0wMwUF6EP1ofWvMvisQzXWgpw5Hb3cFJwCLcBGAs/s1600/COT%2Bheat%2Bproduction.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="411" data-original-width="604" height="271" src="https://3.bp.blogspot.com/-rMeNDFB7_iE/WtDf3le7b6I/AAAAAAAAG4Y/0wMwUF6EP1ofWvMvisQzXWgpw5Hb3cFJwCLcBGAs/s400/COT%2Bheat%2Bproduction.png" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Fig 7 : Heat production (W, Y-axis) as a function of running velocity (X-axis) and COT. Iso-temperature lines are shown in bold. Reference [12]. </td></tr>
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Ultimately, what this entails is a substaintial % decrease in sustainable speed in hot, humid environment dictated by the need to be able to cool the body. This leads to the following realities :<br />
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1. Distance runners are smaller than middle-distance runners to limit heat production, because weight has a 2-fold effect on heat production compared to heat dissipation.<br />
2. Long distance running speed is temperature derated in hot climate because the running locomotor seeks to maintain heat balance without letting core body temperature rise to dangerous levels. For example, marathons in temperatures of 20± 25°C are 6%±10% slower than marathons in temperatures of 10±12°C.<br />
3. Increasing age possibly has a multiplicative effect on COT degradation as well as the effect of the ability to shed weight.<br />
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Noakes et.al published an interesting graph indicating speed cutoffs to maintain estimated heat balance. Observe that for heavier runners, the speed derate are higher. These are only indications, rather than absolute values as they mentioned in their paper.<br />
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<tr><td style="text-align: center;"><a href="https://3.bp.blogspot.com/-PXmQ8kXBuZk/WtDg7YRyCpI/AAAAAAAAG4k/JnAkfKzV_ogbU36E7s1eyVi3XRHE3JCyQCLcBGAs/s1600/Temperature%2Bderate%2Bof%2Bspeed.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="362" data-original-width="631" height="228" src="https://3.bp.blogspot.com/-PXmQ8kXBuZk/WtDg7YRyCpI/AAAAAAAAG4k/JnAkfKzV_ogbU36E7s1eyVi3XRHE3JCyQCLcBGAs/s400/Temperature%2Bderate%2Bof%2Bspeed.JPG" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Fig 8 : Illustration of the derate in running speeds where heat production and maximum heat dissipation are in balance. Illustation provided are indications, not absolute values. Reference [13]. </td></tr>
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<b><br /></b><b>E) Environmental Conditions : Altitude</b><br />
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It is known that COT falls with rising altitude. Overground sea-level oxygen cost of running has been reported by Daniels et.al to be 4.5% greater than that measured at an altitude of 2,300m.<br />
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This has been attributed to the a) greater reliance on carbohydrate at high altitude for the same absolute running speed, which serves to explain the lower metabolic cost since the oxygen uptake for metabolising carbohydrate is lower than that for fats and b) lower work of ventilation due to lesser resistance to breathing [8]. However, since carbohydrate stores are low and due to low partial pressures of oxygen at great heights, these advantages are negated and the human runner has to compromise on work intensity to survive over long high altitude distances.<br />
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<b><br /></b><b>F) Other Contributers to COT : Training Status, Mass and Size</b><br />
<b><br /></b>
Training status has the ability to affect the Overall COT. Though literature is filled with estimates ranging from 6-24% reduction, an estimate of 8% can be expected in beginner runners on a 10 week training program, anywhere between 2-7% in endurance runners and about 7.5% after 9 weeks on an explosive training regimen. However, all of these estimates are subject to the specific protocol administered and calculations used.<br />
<br />
Humans adapt with running training. They lose fat mass, build muscle and may alter their biomechanics in a way that elicits more tendon contribution in energy storage. Certainly the fat mass loss with training is something all runners are familiar with. Loss of fat around distal areas of the limb possibly lead to higher reductions in COT. The reduction of every 100 grams of mass from around the feet can lead to nearly 1% reduction in COT. This reduction is fairly consistent across a range of running speeds.<br />
<div>
<b><br /></b></div>
Several researchers noted that size and stature invariably affect the oxgen cost of running, with larger individuals having a lower energy cost and younger children haivng a higher energy cost. An analysis of studies report a gross estimate of 2% increase in the gross energy cost of running from ages 18 to 8 years.<br />
<br />
A Size-Independant Cost of Transport by dividing COT by the product of mass and height did not solve the interdependancies of mass to oxygen consumption. Alternative hypothesis suggest that the larger the body dimension, the larger the amount of energy stored and released through the stretch-shortening cycle of the leg extensor muscle (see below).<br />
<br />
Under the dictation of some of the above influencers, a correction to the laboratory estimate COTm can be written as :<br />
<br />
<div style="text-align: center;">
<div style="text-align: left;">
<span style="color: blue;"><b>COT = COTm + Correction Due to Combination of (Wind + Altitude + Slope) Effects</b></span></div>
</div>
<div style="text-align: center;">
<br /></div>
<b><br /></b>
<b><u>III. Predicting Time For Covering Distances</u></b><br />
<div>
<b><br /></b></div>
The overall cost of transport is a powerful metric. Knowing COT and the maximum metabolic power in proper units helps assess what is the maximum possible speed the human locomotor can achieve.<br />
<br />
<div style="text-align: center;">
<div style="text-align: left;">
<span style="color: blue;"><b>Maximum Running Speed (m/s) = Maximum Metabolic Power <span style="background-color: white; font-family: "arial" , sans-serif; font-size: 16px; text-align: left;">÷ </span>Overall COT</b></span></div>
</div>
<div style="text-align: center;">
<div style="text-align: left;">
<br /></div>
</div>
where units are :<br />
Maximum Running Speed = m/s<br />
Maximum Metabolic Power = W/kg or J/kg/s<br />
Overall COT = J/kg/m<br />
<br />
Since operating at the maximum metabolic power results in fatigue in the locomotor within approximately 7 minutes (runner dependant), the following equation allows the prediction of time to cover short distances upto 3000m :<br />
<br />
<div style="text-align: center;">
<div style="text-align: left;">
<b><span style="color: blue;">Best Short Distance Running Time (s) = Distance <span style="text-align: center;"><span style="background-color: white; font-family: "arial" , sans-serif; font-size: 16px; text-align: left;">÷ </span></span>Maximum Running Speed</span></b></div>
</div>
<div style="text-align: center;">
<div style="text-align: left;">
<br /></div>
</div>
For longer distances requiring more than 420 seconds of running time, it is impossible for the locomotor to sustain maximum metabolic power without fatigue. In this running regime, only a fraction of maximum metabolic power can be sustained and therefore, the endurance time is approximated by :<br />
<div style="text-align: left;">
<br /></div>
<div style="text-align: center;">
<div style="text-align: left;">
<span style="color: blue;"><b>Best Endurance Speed (m/s) = Highest Fraction of Maximum Metabolic Power <span style="background-color: white; font-family: "arial" , sans-serif; font-size: 16px; text-align: left;">÷ </span>Overall COT</b></span></div>
</div>
<div>
<div style="text-align: left;">
<br /></div>
</div>
<div style="text-align: center;">
<div style="text-align: left;">
<b><span style="color: blue;">Best Long Distance Running Time (s) = Distance <span style="background-color: white; font-family: "arial" , sans-serif; font-size: 16px; text-align: left;">÷ </span>Best Endurance Speed</span></b></div>
</div>
<div>
<b><span style="color: blue;"><br /></span></b></div>
So herein lies a secret to running. For a given metabolic power, best endurance speed is achieved by being able to race at a higher fraction of that metabolic power. But since metabolic power is itself under several environmental influences such as heat and altitude, there are uncertainties to such simple predictions.<br />
<br />
<b><br /></b><b><u>IV. Towards Optimizing Cost of Transport</u></b><br />
<br />
<div style="text-align: justify;">
Fascinatingly, both mechanical engine and human locomotory movements exhibit a "non-linear" shape to cost of operation.<br />
<br />
Consider that the fuel combusting mechanical engine has a speed and torque dependant <b><a href="http://x-engineer.org/automotive-engineering/internal-combustion-engines/performance/brake-specific-fuel-consumption-bsfc/"><span style="color: red;">optimum fuel efficiency</span></a></b>. Driving a car "too slow" or "too fast" introduces a bigger penalty on brake fuel consumption than a more optimum cruise speed somewhere in between. Therefore, an "island" that contains the optimum fuel consumption is by design placed at mid-engine speeds and high torque.<br />
<br />
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td><a href="https://1.bp.blogspot.com/-K6ivJXJFg4s/Wrc_PrnzImI/AAAAAAAAGx0/lpgKBBuRsDoyWUL4EeGpXiPZWSRNaVdogCLcBGAs/s1600/BSFC%2Bof%2Bengine.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="539" data-original-width="891" height="241" src="https://1.bp.blogspot.com/-K6ivJXJFg4s/Wrc_PrnzImI/AAAAAAAAGx0/lpgKBBuRsDoyWUL4EeGpXiPZWSRNaVdogCLcBGAs/s400/BSFC%2Bof%2Bengine.JPG" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="font-size: 12.8px;">Fig 9 : Optimum island for specific brake fuel consumption in an engine. Reference [1]</td></tr>
</tbody></table>
<table cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: justify;"><tbody>
<tr><td style="text-align: center;"><span style="text-align: justify;"></span><br />
<div style="text-align: justify;">
<span style="text-align: justify;">Similarly, when COT data is collected for several runners, an optima for low COT shows up at a specific value of running speed. For example, in the data below, minimum COT appears to be around 11.1 kph. Therefore, just like the mechanical engine, there is an optimal movement load and speed for lowest costs. </span></div>
<span style="text-align: justify;">
</span></td></tr>
</tbody></table>
<div style="text-align: justify;">
<br /></div>
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: justify;"><tbody>
<tr><td style="text-align: center;"><a href="https://1.bp.blogspot.com/-ySEU0DHIKhI/WrdAg6o9SaI/AAAAAAAAGyA/NPu-k4NCYPwjXP2DMbVIEdVy_7InU8GsgCLcBGAs/s1600/Optimal%2BO2%2Bconsumption%2Bin%2Brunning.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="581" data-original-width="886" height="261" src="https://1.bp.blogspot.com/-ySEU0DHIKhI/WrdAg6o9SaI/AAAAAAAAGyA/NPu-k4NCYPwjXP2DMbVIEdVy_7InU8GsgCLcBGAs/s400/Optimal%2BO2%2Bconsumption%2Bin%2Brunning.JPG" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Fig 10 : Optimal speed to minimize COT in 9 trained runners. Reference [2]</td></tr>
</tbody></table>
</div>
<div style="text-align: justify;">
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
<br />
At a kinematic level, speed is determined by the product of stride frequency and stride rate. The running locomotor attains a minima in COT at an optimum stride frequency that varies from individual to individual.<br />
<br />
A set of data from 12 subjects in Fig 8 show a U shaped profile in COT with respect to stride frequency. A similar behavior is also seen in cyclists, where the optimum pedaling frequency for low metabolic cost is around 60rpm. Yet, cyclists impose a self selected 90rpm possibly to reduce torque demand and muscular effort.<br />
<br />
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://2.bp.blogspot.com/-EdhFbWMMcnU/Wscay8isXGI/AAAAAAAAG1A/sJ_iZqS4ueIrvSL02Eal2xH0Se_ksXkwQCLcBGAs/s1600/COT%2Bstride%2Bfrequency.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="293" data-original-width="468" height="250" src="https://2.bp.blogspot.com/-EdhFbWMMcnU/Wscay8isXGI/AAAAAAAAG1A/sJ_iZqS4ueIrvSL02Eal2xH0Se_ksXkwQCLcBGAs/s400/COT%2Bstride%2Bfrequency.JPG" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Fig 11 : Relation between cost of transport (COT) and stride frequency for 12 physically fit and experienced runners. Reference [5].</td></tr>
</tbody></table>
<br />
Scientists tell us that metabolic cost is primarily linked to the cost of producing muscular force. So could optimal movement speed be governed by the force and speed of muscular firing?<br />
<br />
For example, it is known muscles are governed fundamentally by force-length and force-velocity relationships. At a whole body level, it is also known that human runners incur the least operational cost at an optimally selected stride frequency. These relationships are fundamentally non-linear in nature and subject to inter-individual differences.<br />
<br />
Secondly, operating the locomotor with a shorter ground contact time involves fast fiber contractions (faster muscle firing) leading to higher energy costs. This explanation has served very well in understanding why <b><span style="color: red;"><a href="http://www.georgeron.com/2017/01/running-science-part-1-ground-contact.html"><span style="color: red;">smaller animals have higher metabolic costs and COTs</span></a></span></b>.<br />
<br />
The practical takeaway from this discussion is that a self imposed step frequency may or may not necessarily correspond to the optimum required to achieve minimum metabolic cost and minimum COT. There is some trainability value in this aspect.<br />
<div>
<br /></div>
</div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
<b><u>V. Apparent Efficiency of Running</u></b><br />
<b><br /></b></div>
</div>
<div style="text-align: justify;">
In addition to the costs of transport, knowing efficiency as it relates to the maximum extractable work for a given metabolic input is also required to analyze the performance of any engine.<br />
<br />
What's the efficiency of running?<br />
<br />
At this juncture, we need to define the apparent efficiency of running. The apparent efficiency can be seen as the end result of all possible losses and energy saving mechanisms during complete cycles of running motion.<br />
<br />
<b><span style="color: blue;">Apparent Efficiency = Total Mechanical Work Done / Metabolic Cost</span></b><br />
<br />
where total mechanical work done = external work + internal work<br />
<br />
Apparent efficiency can be either expressed as "gross" or "net" depending on whether the energy cost of vital functions that are not directly related to exercise (e.g. the O2 consumption of the brain, of the gut, kidneys and internal organs, as well as the minor fraction due other organs' metabolism) is included in the metabolic cost (the denominator).<br />
<br />
<b><span style="color: blue;">Apparent Efficiency (Gross) = Total Mechanical Work Done / Gross Metabolic Cost</span></b><br />
<b><span style="color: blue;"><br /></span></b>
<br />
<div>
<b><span style="color: blue;">Apparent Efficiency (Net) = Total Mechanical Work Done / Net Metabolic Cost</span></b></div>
<div>
<b><span style="color: blue;"><br /></span></b></div>
Where Net Metabolic Cost = Observed Metabolic Cost - Resting Metabolic Cost<br />
Resting Metabolic Cost = Approx. 300 mlO2/min (≈ 1.5 kcal/min or ≈ 100 W) for an adult man of about 70 kg body mass and is essentially unaffected by the exercise.<br />
<br />
Muscular contractions require splitting of ATP, the energy currency in the body. To synthesize ATP can take several substrate routes but if we assume exercise to be fundamentally aerobic, then the amount of oxygen processed in unit time becomes a proxy for the power of cellular energy production.<br />
<br />
The process leading to the splitting of ATP in the isolated muscle comprises two steps and each of these steps have an associated efficiency.<br />
<br />
<div style="text-align: left;">
1. ATP-synthesis/energy liberation from decomposition of nutritients : Phosphorylative coupling</div>
<div style="text-align: left;">
2. Energy liberation during ATP-splitting/ATP Hydrolysis : Mechanical coupling</div>
<div style="text-align: left;">
<br /></div>
<div style="text-align: left;">
<span style="text-align: justify;"><b><span style="color: blue;">Overall muscle contraction efficiency = </span></b></span><b><span style="color: blue;">Phosphorylative coupling efficiency x Mechanical coupling Efficiency</span></b></div>
<div style="text-align: left;">
<br /></div>
<div style="text-align: justify;">
A range of reported values for phosphorylative coupling efficiency and mechanical coupling have been reported in literature (Fig. 12) Certaintly, it appears that aerobic work is more efficient overall with the ATP resynthesis efficiency being as high 64% which when multiplied with a modest 40% for ATP hydrolysis efficiency yields an overall efficiency = 25.6%. On the other hand, anaerobic muscle efficiency maybe somewhat lower at 21.5% as reported by Margaria. </div>
<div style="text-align: left;">
<br /></div>
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://1.bp.blogspot.com/-UqbIUQ6KZ44/Wsc-m0g61yI/AAAAAAAAG1k/7wuEtsj66m0YjxdqNHbFMtPUDCqeMVUggCLcBGAs/s1600/Muscle%2Befficiency%2Bvalues%2Breported%2Bin%2Bliterature.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="393" data-original-width="511" height="307" src="https://1.bp.blogspot.com/-UqbIUQ6KZ44/Wsc-m0g61yI/AAAAAAAAG1k/7wuEtsj66m0YjxdqNHbFMtPUDCqeMVUggCLcBGAs/s400/Muscle%2Befficiency%2Bvalues%2Breported%2Bin%2Bliterature.png" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Fig 12 : Components in ATP turnover efficiency in human muscle. Reference [6].</td></tr>
</tbody></table>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: left;">
<span style="text-align: justify;">However, running is not purely contraction movement, rather a mixture of positive work (the push-off) where ATP is split to apply force against the terrain and negative eccentric work (the landing) that dissipates energy while the terrain applies force on the body. It is then the apparent efficiency of positive-negative work that deserves attention. </span></div>
</div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
Researchers discovered several decades ago that the summation of the theoretical oxygen requirement to power the different parts of the body during endurance running is over-estimated by approximately 50% when they compared theory to empirical data from level running experiments. In other words, the apparent work efficiency of whole body running was greater than the 25% efficiency for isolated muscle contraction.<br />
<br />
How much greater? 40% or more for level running (Fig 13, 14).<br />
<br />
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://2.bp.blogspot.com/-vkkH6R8K0iM/WsdGC9mqRGI/AAAAAAAAG10/pkAgJClOJWUrAjsGwn4zIeJQuNbJvhP5QCLcBGAs/s1600/Range%2Bof%2Befficiencies%2Breported%2Bfor%2Brunning.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="675" data-original-width="846" height="318" src="https://2.bp.blogspot.com/-vkkH6R8K0iM/WsdGC9mqRGI/AAAAAAAAG10/pkAgJClOJWUrAjsGwn4zIeJQuNbJvhP5QCLcBGAs/s400/Range%2Bof%2Befficiencies%2Breported%2Bfor%2Brunning.png" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Fig 13 : Values of mechanical efficiency from several studies. </td></tr>
</tbody></table>
<br />
Scientists agree that a reason for high apparent efficiency has partly to do with the fact that during the landing phase of running, passive, elastic elements that are connected to muscle bellies in the human body absorb some of the elongation of the muscle, store and release energy into the next phase of the cycle. </div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
In other words, the human runner can activate "pre-stretch" in series connected elastic elements in the musculotendon unit just before touchdown, thereby storing energy which is then re-used for powering the next takeoff. The reduction in oxygen consumption is explained by the reduction in concentric response from the muscle and the lowered speed of contraction.<br />
<br />
What this simply means is that work done by tendons does not have to be performed by muscles - therefore, tendons reduce muscle work, and therefore metabolic cost, during running.<br />
<br />
This fact is empirically supported, with many studies showing that runners perform the work of running with an efficiency that exceeds that of isolated muscle (Cavagna et al., 1964; Heglund et al., 1982; Minetti et al., 1999). These observations support the idea that tendons do much of the work ‘for free’, thus increasing the apparent efficiency. This does not violate the principle of the second law of thermodynamics, as some people mistakenly claim.<br />
<br />
<br />
<b><u>VI. Spring Mechanics and Efficiency</u></b><br />
<div>
<br /></div>
Human locomotors naturally oscillate like a bouncing ball in order to run forward. As discussed in <b><span style="color: red;"><a href="http://www.georgeron.com/2017/01/actionable-intelligence-for-running.html"><span style="color: red;">another post</span>,</a></span></b> human running can be approximated very well by a linear spring-mass model. However, because some energy is lost at each step due to friction and heat (attenuation), muscles need to constantly add some energy to the system to power forward movement.<br />
<br />
Inspite of this little complication, the relation of COT to speed, stride frequency and the elastic behavior of the human running motion can all be fascinatingly tied up to support the metabolic cost of force production hypothesis.<br />
<br />
The empirical finding on a treadmill was that humans chose a self-selected stride frequency corresponding to one which minimized metabolic energy expenditure, maximises apparent work efficiency and which corresponds closely to the calculated natural frequency of the "spring" (assuming damped harmonic motion).<br />
<br />
The beautiful plot in Fig. 9 reveals more details. At low, medium and high running speeds (5.3 kph - 11.1 kph), human runners' freely chose a running cadence that corresponded to the minimum metabolic cost and maximum apparent efficiency.<br />
<br />
This was despite the fact that mechanical power was greater at low cadences due to higher vertical work against gravity and lower at higher cadences due to a minimzation in vertical work done. In other words, these studies suggest that the running locomotor is somewhat blind to mechanical power minimization and instead the goal is to optimize cadence around the point where work efficiency is highest and metabolic cost lowest.<br />
<br />
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://1.bp.blogspot.com/-e2gMm2ldUDQ/WsctdrUZqiI/AAAAAAAAG1U/ouQC2oXkshgdesreG2jBPUgIzjXZ5U0MgCLcBGAs/s1600/Freely%2Bchosen%2Bcadence.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="624" data-original-width="848" height="292" src="https://1.bp.blogspot.com/-e2gMm2ldUDQ/WsctdrUZqiI/AAAAAAAAG1U/ouQC2oXkshgdesreG2jBPUgIzjXZ5U0MgCLcBGAs/s400/Freely%2Bchosen%2Bcadence.JPG" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Fig 14 : The ratio of imposed step frequency and freely chosen cadence approaches 1 at the point where metabolic cost is minimized and apparent efficiency is maximized. Reference [9].</td></tr>
</tbody></table>
<br />
<br />
One also notices in Fig 9 that the apparent work efficiency increases as the speed increases, the magnitude is more than double (50%) of the metabolic efficiency of converting chemical energy to work in isolated human muscle (25%).</div>
<div style="text-align: justify;">
<br />
<br />
<b><u>Conclusion </u></b><br />
<b><span style="color: blue;"><br /></span></b></div>
<div style="text-align: justify;">
The human engine is likened to a mechanical engine, where molecular motors power the strokes responsible for movement while converting only a portion of the input energy to actual work. This post explored two key areas which influence human running performance - the cost of transport and the apparent efficiency.<br />
<br />
Cost of transport is driven by metabolic substrate use and the effect of environment upon cost.<br />
<br />
The learning process in endurance running is mostly about finding how to strike a balance between this need to achieve speed on one hand and minimizing cost of transport and maximizing efficiency on the other. It boils down to the cost of producing force at the molecular level and researchers are only beginning to understand that there maybe a tradeoff between force and efficiency, i.e some fundamental mechanistic limitations prevent muscles being both powerful and efficient at the same time [10].<br />
<br />
Numerous technologies are available today to aid the human runner to find their "pace"; these however are simply aids and the best runners still appear to run mostly by "feel". We know very little about how the human locomotor judges and acts upon internal and external feedback signals by way of sensory control systems but the fact is that it happens. So it becomes essential to investigate what those effort governance theories are and what the supporting observations might be. This aspect will be tackled in a future post. </div>
<div style="text-align: justify;">
<b><br /></b>
<b><br /></b></div>
<div style="text-align: justify;">
<b>REFERENCES </b><br />
<b><u><br /></u></b></div>
<div style="text-align: justify;">
[1] Brake Specific Fuel Consumption (BSFC) – x-engineer.org. (2018). X-engineer.org. http://x-engineer.org/automotive-engineering/internal-combustion-engines/performance/brake-specific-fuel-consumption-bsfc/</div>
<div style="text-align: justify;">
[2] Mayhew, J. L. (1977). Oxygen cost and energy expenditure of running in trained runners. British Journal of Sports Medicine, 11(3), 116–121.</div>
<div style="text-align: justify;">
[3] Leger, L., & Mercier, D. (1984). Gross energy cost of horizontal treadmill and track running. Sports medicine, 1(4), 270-277.</div>
<div style="text-align: justify;">
[4] Beneke R, Leithäuser RM. Energy Cost of Running Related to Running Intensity and Peak Oxygen Uptake. Dtsch Z Sportmed. 2017; 68: 196-202.</div>
<div>
[5] Lieberman DE, Warrener AG, Wang J, Castillo ER. Effects of stride frequency and foot position at landing on braking force, hip torque, impact peak force and the metabolic cost of running in humans. Journal of Experimental Biology [Internet]. 2015;218 :3406-3414.<br />
[6] Scott, Christopher B. A Primer for the Exercise and Nutrition Sciences: Thermodynamics, Bioenergetics, Metabolism. Humana Press, 2010.</div>
<div style="text-align: justify;">
[7] di Prampero. Mechanical efficiency, work and heat output in running uphill or downhill. Annales Kinesiologiae. 2011.<br />
[8] Fletcher JR and MacIntosh BR (2017) Running Economy from a Muscle Energetics Perspective. Front. Physiol. 8:433. doi: 10.3389/fphys.2017.00433<br />
[9] Cavagna, G. The Resonant Step Frequency in Human Running. Pflügers Archiv. 1997; 6:678–684<br />
[10] Barclay, C. (2017). The basis of differences in thermodynamic efficiency among skeletal muscles. Clinical and Experimental Pharmacology and Physiology, 44(12):1279-1286<br />
[11] REIS, Victor Machado, OLIVEIRA, Diogo Roberto, CARNEIRO, André Luiz, FERNANDES, Hélder Miguel, & SCOTT, Christopher. (2016). Inclusion of blood lactate O2 equivalent in the VO2-intensity regression at level and 10.5% grade running. Revista Brasileira de Educação Física e Esporte, 30(2), 255-261. https://dx.doi.org/10.1590/1807-55092016000200255<br />
[12] Arsac, L. M., Deschodt-Arsac, V., & Lacour, J. (2013). Influence of individual energy cost on running capacity in warm, humid environments. European Journal of Applied Physiology, 113(10), 2587-2594. doi:10.1007/s00421-013-2696-6<br />
[13] Dennis, S. C., & Noakes, T. D. (1999). Advantages of a smaller bodymass in humans when distance-running in warm, humid conditions. European Journal of Applied Physiology, 79(3), 280-284. doi:10.1007/s004210050507<br />
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Ronhttp://www.blogger.com/profile/16268869622833968439noreply@blogger.com0tag:blogger.com,1999:blog-4786784182488135171.post-62202494977621376522018-02-10T23:06:00.002+04:002018-02-16T22:23:15.530+04:00Technical Analysis of a 1:38:00 RAK Half Marathon<div dir="ltr" style="text-align: left;" trbidi="on">
<div style="text-align: justify;">
Going sub 1:40:00 in any half marathon is considered a decently competitive time achievement for age groupers.<br />
<br />
Consider that this year at the RAK Half, only 12% of the competing runners (both male and female) posted a gross time better than 1:40:00 and the rest 88% were slower. By net time, I assume this percentage will be still lower.<br />
<br />
In this year's RAK Half, I bested the previous year's race time by nearly 14 minutes and certainly, I've never run a half this fast since college years, so therefore it is an all-time PB at this distance.</div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
What does it take to run sub 1:40:00? I would like to share some of my own data to shed some technical light on the subject.<br />
<br />
Note : Please click all images to zoom in.<br />
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<b><u>Race Day Ambient Conditions</u></b><br />
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The morning of race saw a starting time temperature of 15 deg C, 88% humidity with 11 kph northerly winds (most likely measured at 10m height off the ground). Barometric pressure was 1014mbar. </div>
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Between 7 and 9am, the temperature rose maybe 2 degree C at most.</div>
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These conditions yield a calculated air density of 1.2203 kg per cubic meter and a WBGT (wet bulb globe temperature) of around 16 deg C. </div>
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<b><u>Race Course</u></b><br />
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The AIMS certified course is<a href="https://www.youtube.com/watch?v=PUgbLuH3G5A"> <span style="color: red;"><b>21.1 km long</b></span></a>. The course is mostly very flat with 30-40m of total ascent making it suitable for a flat out race.<br />
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Incline data as a function of distance :<br />
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<b><u>Weight Trend </u></b><br />
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The trend of weight (without shoes etc) several weeks leading into the race is shown below. The weight trend hovers over 62-63 kg. At the time of the race, adding the mass of shoes and running attire to that figure would put me at a racing weight of approximately 63 kg.<br />
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<b><u>HRV Trend 3 Weeks Before Race</u></b><br />
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A monitoring of daily heart rate variability 3 weeks from race day revealed that :<br />
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1) RMSSD fluctuated with highs reaching the weekend (Friday) of weeks 3 and 2 before the race. Hourly tapering of runs (last 2 weeks) showed a decrease in daily RMSSD.<br />
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2) Log transformed RMSSD normalized to R-R intervals, an indicator of fatigue, actually increased during the time 3 weeks before the race and declined during the last taper week.<br />
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Not reading too much into this but 1) and 2) might indicate a readiness to perform & heightened parasympathetic activity during tapering period. My weekly hours and average training paces for the last 3-4 weeks to the race are included in the 3rd plot below.<br />
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Certainly interesting and deserves more study.<br />
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<b><u>HR Trimp Performance Chart Trend</u></b><br />
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The following image shows TRIMP performance chart (generated in Golden Cheetah) along a 2.5 month period from Nov 20 2017 to race day on Feb 9 2018 (I ran a 10K race in early November 2017 so I chose to start tracking PMC then). </div>
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While absolute values are not important, the trend says I was more or less in a maintenance phase in the months of Nov and Dec by running an average of 3-4 km every day. In the month of January 2018, I picked that dosage upto >4 km every day. Therefore, I accumulated some residual fatigue indicated by the stress balance line (yellow) following which a taper period relaxed the stress balance to -4 just before race day. Overall fitness (blue line) increased gradually to a peak a week before race day. </div>
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It is interesting to keep the -4 stress balance in context with the race performance achieved at the race. Atleast what the curve shows is that I went into the race slightly fatigued but not at a level that made me dysfunctional. </div>
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Certainly, a performance management chart can be made using the language of external power and RSS, but to me, TRIMP and HR based PMC is much more trust-able when I want to assess heart stress.<br />
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<u><b>Race Data</b></u><br />
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Aggregated run data is shown below from several devices, namely the Polar V800, Runscribe+ (beta) and Stryd powermeters.<br />
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<b>Net Time : </b>1:38:00 (Data from GPS and 2x accelerometers)</div>
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<b>Pace</b> : 4:32 min/km | 7:18 min/mile | 13.23 kph | 8.22 mph | 3.67 m/s</div>
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<b>Ave. External Running Power :</b> 234 Watts (to move center of mass)</div>
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<b>Ave. External Power to weight ratio </b>: 3.7 W/kg </div>
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<b>External Power Intensity</b> : 95-98 % of Critical External Power </div>
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<b>Basis of Critical Power</b> : Exponential fit over 90 Day power duration curve</div>
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<b>Normalized External Race Power </b>: 233 W</div>
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<b>GOVSS Power</b> : 373 W (a proxy for internal + external run power)</div>
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<b>Ave. Heart Rate</b> : 190 bpm</div>
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<b>Racing HR as % </b> : 91% (Karvonen method)</div>
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<b>HR Zone Distribution</b> (Polar) </div>
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<b>Total Steps</b> : 18,584 </div>
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<b>Ave. Step Length</b> : 1.16 m | 3.8 ft</div>
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<b>Ave. Stride Length </b>: 2.32 m | 7.6 ft</div>
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<b>Ave. Step Rate</b> : 191 steps a minute</div>
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<b>Ave. Stride Rate</b> : 95 strides per minute </div>
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<b>Estimated Vertical Oscillation of Center of Mass </b>: 0.061 m</div>
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<b>Ave. Ground Contact Time</b> : 0.215 seconds</div>
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<b>Estimated Leg Spring Stiffness</b> : 11 kN/m</div>
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<b>Ave. Impact Shock</b> : 12.2 G (correlates with vertical ground impact force)</div>
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<b>Ave. Braking Shock</b> : 10.6 G (correlates with horizontal braking forces)</div>
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<b><u>Kinematic Variables & Their Distribution Over Time </u></b><br />
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The following series of time series screenshots show box plot distributions of kinematic variables, something I really like. On the Y-axis is dependant variables of interest (such as ground contact time) and on the X-axis is time. </div>
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<b>Step Rate </b></div>
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Half way point</div>
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Median : 189 spm<br />
Overall, high cadence and very even throughout. </div>
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<a href="https://1.bp.blogspot.com/-6esJL1iD5hc/Wn7uwP42aoI/AAAAAAAAGoM/PsMFkKdaeZgttARdbn7XOmk765dAX0dGQCLcBGAs/s1600/Step%2Brate%2Bdist.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em; text-align: center;"><img border="0" data-original-height="345" data-original-width="1557" height="139" src="https://1.bp.blogspot.com/-6esJL1iD5hc/Wn7uwP42aoI/AAAAAAAAGoM/PsMFkKdaeZgttARdbn7XOmk765dAX0dGQCLcBGAs/s640/Step%2Brate%2Bdist.png" width="640" /></a><br />
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<b>Ground Contact Time</b></div>
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Half way point</div>
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Median : 0.218 s<br />
<span style="font-family: "times new roman";">Overall, low GCT and very even which speaks for the evenness in step rate and footstrike type.</span></div>
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<b>Flight Ratio</b></div>
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Half way point </div>
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Median : 30.9%<br />
Overall, a slightly fluctuating proportion of flight time around the 30% mark. In all my past data at these paces, I have not seen numbers substantially higher than 30%.</div>
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<b>Stride Length </b></div>
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Half way point </div>
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Median : 8.4 ft (2.56 m)</div>
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<b>Stride Length (Left/Right Distribution)</b></div>
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A bit doubtful on the data but interestingly, it's showing that a decrease in SL in one of the feet is complemented by an increase in the other foot. The dark blue curve must be for the right foot. I'd have to continue to monitor this in past and future data to understand if this is a real variation between left and right sides or just noise.</div>
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<b>Footstrike Type</b></div>
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Half way point </div>
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Median : 9 (Between midfoot and forefoot)<br />
This data comes from accelerometers strapped to the heel but eitherway, the indication is not far from what I thought it'd be. </div>
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<b>Impact Force</b></div>
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Half way point</div>
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Median : 12.4 G<br />
This is not an indication of actual force but certainly a proxy for negative vertical acceleration. 5-15 Gs is a normal range. </div>
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<a href="https://2.bp.blogspot.com/-lm60Za0O7T4/Wn7uvgQGLxI/AAAAAAAAGoY/BUiPuKQEgVE8FcQZaBE5woXs2VYyVXnpwCEwYBhgL/s1600/Impact%2Bforce%2Bdist.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="339" data-original-width="1550" height="138" src="https://2.bp.blogspot.com/-lm60Za0O7T4/Wn7uvgQGLxI/AAAAAAAAGoY/BUiPuKQEgVE8FcQZaBE5woXs2VYyVXnpwCEwYBhgL/s640/Impact%2Bforce%2Bdist.png" width="640" /></a></div>
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<b>Braking Force</b></div>
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Half way point </div>
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Median : 10.9 G<br />
<span style="font-family: "times new roman";">This is not an indication of actual force but certainly a proxy for negative horizontal acceleration. 4-13 G's is a normal range.</span></div>
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<a href="https://2.bp.blogspot.com/-Mnl_UJgY7SI/Wn7ut-GBDgI/AAAAAAAAGok/3Nj-1FrCCuwillPsPrTJJMrvaCxPn7hCQCEwYBhgL/s1600/Braking%2Bforce%2Bdist.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="336" data-original-width="1547" height="138" src="https://2.bp.blogspot.com/-Mnl_UJgY7SI/Wn7ut-GBDgI/AAAAAAAAGok/3Nj-1FrCCuwillPsPrTJJMrvaCxPn7hCQCEwYBhgL/s640/Braking%2Bforce%2Bdist.png" width="640" /></a></div>
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<b>Run Power (GOVSS)</b></div>
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Half way point </div>
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Median : 421.6 W<br />
GOVSS power involves a computation of internal and external power to run and uses an efficiency correction upon metabolic demand. In other words, this plot gives an indication of total metabolic demand with time.</div>
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<a href="https://3.bp.blogspot.com/-kE5F5qMJpXU/Wn7uumkvTBI/AAAAAAAAGoc/1EjHMOQ0snc9a4sVUte89l_tv9s5ppVGQCEwYBhgL/s1600/GOVSS%2Bpower%2Bdist.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="343" data-original-width="1569" height="138" src="https://3.bp.blogspot.com/-kE5F5qMJpXU/Wn7uumkvTBI/AAAAAAAAGoc/1EjHMOQ0snc9a4sVUte89l_tv9s5ppVGQCEwYBhgL/s640/GOVSS%2Bpower%2Bdist.png" width="640" /></a></div>
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<b>Pace and Power Splits</b></div>
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Maximum variation in pace = 21 seconds/km.<br />
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<u><b>Conclusion </b></u><br />
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<div style="text-align: justify;">
Readers might <b><a href="http://www.georgeron.com/2017/02/actionable-intelligence-for-running-4.html"><span style="color: red;">recall my post</span></a></b> on my dismal performance in the same race in 2017. In that year, I dragged myself across the finish line in 1:52:00 and went back home pissed and determined to get better next year. </div>
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In that post, I revealed pace and power histograms and some other interesting metrics. This season, a self-coached and methodical running streak from September 2017 resulted in a strong performance and a 12th place in my age category. </div>
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<a href="https://1.bp.blogspot.com/-Qdqxo04NIsI/Wn9Gb2xseaI/AAAAAAAAGp4/LscizI6-Rpo1nQZlD2HTS6YxMfDTm70LQCLcBGAs/s1600/Race%2Bcomparison.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="474" data-original-width="1485" height="125" src="https://1.bp.blogspot.com/-Qdqxo04NIsI/Wn9Gb2xseaI/AAAAAAAAGp4/LscizI6-Rpo1nQZlD2HTS6YxMfDTm70LQCLcBGAs/s400/Race%2Bcomparison.JPG" width="400" /></a></div>
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I still think the most basic of all tools - a training log and a simple stopwatch - should inform most runners how structured their plans are, if they are making improvements and how much rest they are getting in between. </div>
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The plethora of data metrics from inertial measurement units, heart rate monitors and GPS devices are nice to have and for the added tradeoff in analysis time, you get some marginal improvements in information which may or may not suit everyone.</div>
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Yet, we should not lose sight of the forest for the trees. Summing up some greater generalities about achieving sub 1:40:00, I have the following points :</div>
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<b>1) Specificity of training :</b> Commit a purpose to most runs, if not all runs.</div>
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<b>2) Reverse your gear :</b> Work backwards from shorter distances. You must break barriers in short distance (aerobic) racing to get faster at longer distances. Remember our friend, <b><span style="color: red;"><a href="http://www.georgeron.com/2017/09/the-fatigue-factor-for-running-womens.html"><span style="color: red;">Riegel</span>?</a></span></b> A 44:00 10K will lobby harder for your sub 1:40:00 half campaign than one slower. </div>
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<b>3) Run slow to run fast :</b> Increase volume of low intensity runs and optimize volume of fast runs. </div>
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<b>4) Be a good guest : </b>Our friend is Mr. Improvement, we'd like him in our house. Complement training sessions with adequate rest in between; an extensive endurance run may take 8-12 hours for supercompensation timing while an intensive anaerobic training session might require 40-60 hours for the same. Doing stupid things when these bodily changes are taking place will shut the front door on Mr. Improvement. Corny, but this is fact. </div>
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<b>5) The journey counts :</b> Take a year to work towards the half marathon goal of 1:40:00. Run with friends, run often, have fun.</div>
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Ronhttp://www.blogger.com/profile/16268869622833968439noreply@blogger.com0tag:blogger.com,1999:blog-4786784182488135171.post-48694206781796056562018-01-27T22:27:00.000+04:002018-01-31T23:55:06.993+04:00Ground Contact Variables Affect External Running Power Derived From Accelerometry<div dir="ltr" style="text-align: left;" trbidi="on">
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In my <a href="http://www.georgeron.com/2017/12/stryd-running-power-model.html"><b><span style="color: red;">previous post</span></b></a>, I reviewed Stryd's running power model. While looking into Stryd's whitepaper and reading several other journal papers, I suspected that if running powermeter algorithms employed summation of energy changes at center of mass, then could variation in detected ground contact variables explain some of the striking variations in reported power between competing accelerometer platforms in the market?<br />
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Ground contact variables are things like ground contact force, ground contact time, stance time, step time, step rate, vertical oscillation and so on. Minimizing errors between detected variables and laboratory equipment may minimize variations in computed power, however we are yet to understand how these accelerometers work in outside running relative to variety of footstrikes and terrain types and how those errors vary relative to actual variables.</div>
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To understand what the effect of ground contact variables is on computed running power, I played around with some hard numbers and did a sensitivity analysis using a power model I built.</div>
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First, I got in touch with Professor Alberto Minetti to get some raw force plate data for running. Professor Minetti is widely regarded as an expert in the biomechanics of running and is an honorary research professor at Accademia Nazionale dei Lincei in Rome, Italy. He also leads the Laboratory of Physiomechanics of Locomotion at the Department of Pathophysiology and Transplantation at the University of Milan.</div>
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Prof. Minetti shared force plate data for a shod front foot striker running at 4 m/s, which is 14.4 kph or 6:42 min/mile. </div>
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I then developed a model to estimate the rate of changes in external work done using the EESA algorithm (see <b><a href="http://www.georgeron.com/2017/12/stryd-running-power-model.html"><span style="color: red;">previous post</span></a></b>). The model applies the same computation algorithm for external power as described in several sources in literature. </div>
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<b>I. Effect of Variation in Detected Ground Contact Time On Running Power</b></div>
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Stryd's whitepaper showed that the error in ground contact time between force plate and their footpod IMU is 2.83%. The running speed and footstrike type within the data was not discussed. These images from my previous post are reproduced here. </div>
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<tr><td style="text-align: center;"><a href="https://4.bp.blogspot.com/-B6wieEQNg4I/WmydG1dPxUI/AAAAAAAAGhM/3U6yOh1Q8wkRun4dol8ZRWFqBZUDSYlIACLcBGAs/s1600/1.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="624" data-original-width="807" height="308" src="https://4.bp.blogspot.com/-B6wieEQNg4I/WmydG1dPxUI/AAAAAAAAGhM/3U6yOh1Q8wkRun4dol8ZRWFqBZUDSYlIACLcBGAs/s400/1.JPG" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Figure 1 : Modeled vs actual vertical force-time signatures in a rear-footed runner for an unspecified running speed. Base image courtesy of Stryd. Markups by the me. Observe that the Stryd thinks the footstrike is front footed when the force-time signature from the forceplate shows a rear foot strike.</td></tr>
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<tr><td style="text-align: center;"><a href="https://3.bp.blogspot.com/-KYQj4Tij2xo/Wmyejb5x2mI/AAAAAAAAGhc/indrOFijxUAl8Lj7SbgqNNeV-q6maPS_wCLcBGAs/s1600/2.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="321" data-original-width="400" height="320" src="https://3.bp.blogspot.com/-KYQj4Tij2xo/Wmyejb5x2mI/AAAAAAAAGhc/indrOFijxUAl8Lj7SbgqNNeV-q6maPS_wCLcBGAs/s400/2.JPG" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Figure 2 : Plot showing goodness-of-fit of modeled GCT to force plate measurements. The average error is stated to be 2.83%. The number of runners, running speeds, shoes worn, footstrike mechanics and slope on the treadmill are all unknown which raises the question of how the error varies as a function of each of those factors. Image courtesy of Stryd.</td></tr>
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<span style="text-align: justify;">Now to the data from Prof. Minetti and my model :</span></div>
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Time signatures of the forces in the front foot striking runner are shown in Figure 3, where Fx, Fy and Fz are antero-posterial (A-P, or horizontal), vertical and medio-lateral forces respectively. Mechanical energy changes for all steps in the data and per step are shown in Figures 4 & 5 respectively. </div>
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<tr><td style="text-align: center;"><a href="https://3.bp.blogspot.com/-3xHmhkWUqnU/WmyiEhRaNZI/AAAAAAAAGhs/aVzSVgJPERYlpb15ROeRW5RYAFm--cTPQCLcBGAs/s1600/3.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="562" data-original-width="860" height="261" src="https://3.bp.blogspot.com/-3xHmhkWUqnU/WmyiEhRaNZI/AAAAAAAAGhs/aVzSVgJPERYlpb15ROeRW5RYAFm--cTPQCLcBGAs/s400/3.JPG" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Figure 3 : Force-time signatures for a 67kg front foot striking shod runner running at 4 m/s. Force plate data of Minetti, Milan (Italy). Force plate acquisition frequency = 1000 Hz.</td></tr>
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<tr><td style="text-align: center;"><a href="https://1.bp.blogspot.com/-cY7RX6JSrC8/WmymwrwoKKI/AAAAAAAAGh8/hVZYH6MSOC4xFJbniv5YaFSrRLw5jAXAwCLcBGAs/s1600/4.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="407" data-original-width="649" height="250" src="https://1.bp.blogspot.com/-cY7RX6JSrC8/WmymwrwoKKI/AAAAAAAAGh8/hVZYH6MSOC4xFJbniv5YaFSrRLw5jAXAwCLcBGAs/s400/4.JPG" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Figure 4 : Mechanical energy changes for a 67kg front foot striking shod runner running at 4 m/s for 3 steps.</td></tr>
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<tr><td style="text-align: center;"><a href="https://3.bp.blogspot.com/-ZN11vP14nj0/Wmymwi9AvbI/AAAAAAAAGh4/aQFEGbHWrfYwvaLnu3F89dhSUGORU_m2ACLcBGAs/s1600/5.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="408" data-original-width="650" height="250" src="https://3.bp.blogspot.com/-ZN11vP14nj0/Wmymwi9AvbI/AAAAAAAAGh4/aQFEGbHWrfYwvaLnu3F89dhSUGORU_m2ACLcBGAs/s400/5.JPG" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Figure 5 : Mechanical energy changes for a 67kg front foot striking shod runner running at 4 m/s for a single step.</td></tr>
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External power (Pext), vertical power (Pv), horizontal power (Px) and lateral power (Pz) are shown in the tabulated data in Figure 6 for a -5 to +5% variation in detected ground contact times. </div>
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<tr><td style="text-align: center;"><a href="https://3.bp.blogspot.com/-_Wrr09_cgB4/Wmy40KmjBrI/AAAAAAAAGiw/EIQzmgyo-5UtrY5rLpWLzS2YwBHm3PQxgCLcBGAs/s1600/6.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="191" data-original-width="364" height="208" src="https://3.bp.blogspot.com/-_Wrr09_cgB4/Wmy40KmjBrI/AAAAAAAAGiw/EIQzmgyo-5UtrY5rLpWLzS2YwBHm3PQxgCLcBGAs/s400/6.JPG" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Figure 6 : External running power and it's 3D components per step for a rear footed shod runner running at 4 m/s. Values were computed using the EESA algorithm (or Cavagna method) as described in literature for a range of ground contact times from -5% to +5% relative to the highlighted base value. Computer model was developed by Ron George. </td></tr>
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<span style="color: blue;"><b>As shown in Figure 6, a variation of -5 to +5% in detected ground contact time has an impact of <u>-5 to +5%</u> in estimated external running power, all other factors kept the same. </b></span><br />
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<b style="color: blue; text-align: justify;">Here, you can see power extending from 365 Watts to 331 Watts because of the error in vertical force-time signatures. </b><br />
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<b style="color: blue; text-align: justify;">A computational difference between platforms for ground contact time can arise from 3 </b><br />
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<span style="color: blue;"><b>1. Errors in estimated ground force-time signatures from accelerometry.</b></span></div>
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<span style="color: blue;"><b>2. Inability to differentiate between rear foot strike and front foot strike and suble variations in between.</b></span></div>
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<span style="color: blue;"><b>3. Variations in the minimum force threshold set in the power algorithm while computing ground contact time. In literature, the threshold value from a minimum of 10 N to as large as 50 N, which translates to an appreciable difference in estimated stance times for a given running speed. </b></span></div>
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This is just one source of variation possible between different accelerometers in reported power. Another example of variation is from differences in estimated vertical oscillation or vertical translation of the center of mass. </div>
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<b>II. Effect of Variation in Detected Vertical Oscillation On Running Power</b></div>
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The Stryd whitepaper revealed that an error of 3.18% existed between force plate vertical oscillation and that derived from the footpod. This is shown in Figure 7. </div>
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<tr><td class="tr-caption" style="text-align: center;">Figure 7 : Estmated vs actual vertical oscillation in the Stryd footpod. Stated average error with respect to force plate = 3.18%. Base image courtesy of Stryd. Markups by me.</td></tr>
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What does an error of 3.18% in vertical oscillation mean? It simply means that there is a difference in the vertical landing force that the footpod detects relative to force plate data. Since vertical velocity and vertical oscillation are single and double integrals of detected vertical accelarations respecitvely, any error in the acceleration signal translates into errors in the vertical oscillation.<br />
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Now to the data from Prof. Minetti and my model :</div>
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External power (Pext), vertical power (Pv), horizontal power (Px) and lateral power (Pz) are shown in the tabulated data in Figure 8 for a -5 to +5% variation in accelerometer derived vertical oscillations.</div>
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<tr><td style="text-align: center;"><a href="https://4.bp.blogspot.com/-blCLeLc7GVE/Wmy59M1xLhI/AAAAAAAAGjA/DznN5TtE0BEjTB5Up2WLV0mr9X7zg2iQgCLcBGAs/s1600/7.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="191" data-original-width="330" height="231" src="https://4.bp.blogspot.com/-blCLeLc7GVE/Wmy59M1xLhI/AAAAAAAAGjA/DznN5TtE0BEjTB5Up2WLV0mr9X7zg2iQgCLcBGAs/s400/7.JPG" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Figure 8 : External running power and it's 3D components per step for a front footed shod runner running at 4 m/s. Values were computed using the EESA algorithm (or Cavagna method) as described in literature for a range of vertical oscillations from -5% to +5% relative to the highlighted base value. Computer model was developed by Ron George. </td></tr>
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<span style="color: blue;"><b>As shown in Figure 8, a variation of -5 to +5% in derived vertical oscillation has an impact of <u>-0.3 to +1%</u> in estimated external running power respectively, all other factors kept the same. </b></span></div>
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<b style="color: blue;">Here, you can see power extending from 347 Watts to 351 Watts because of the error in vertical force-time signatures. </b></div>
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<span style="color: blue;"><b>A computational difference between platforms for vertical oscillation can arise from errors in the vertical acceleration and vertical force-time signatures computed by the device. </b></span></div>
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<b>III. Effect of Variation in Horizontal Speed On Running Power</b></div>
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The Stryd whitepaper revealed that an error of 5% existed between force plate horizontal speed and that derived from the footpod. This is shown in Figure 9. </div>
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<tr><td class="tr-caption" style="text-align: center;">Figure 9 : Stryd modeled forward speed change compared to force plate measures. Indicated accuracy = 95%. Grade of running surface unknown, but presumably level. Image courtesy of Stryd.</td></tr>
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Now to the data from Prof. Minetti and my model :</div>
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External power (Pext), vertical power (Pv), horizontal power (Px) and lateral power (Pz) are shown in the tabulated data in Figure 10 for a -5 to +5% variation in accelerometer derived horizontal speed. </div>
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<tr><td style="text-align: center;"><a href="https://4.bp.blogspot.com/-uiFJhBxHJ1Q/WmzcbuPND5I/AAAAAAAAGjk/KwaHhtusj5spnlOswhOBJQJh0xPBWRzKwCLcBGAs/s1600/10.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="209" data-original-width="360" height="231" src="https://4.bp.blogspot.com/-uiFJhBxHJ1Q/WmzcbuPND5I/AAAAAAAAGjk/KwaHhtusj5spnlOswhOBJQJh0xPBWRzKwCLcBGAs/s400/10.JPG" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Figue 10 : External running power and it's 3D components per step for a front footed shod runner running at 4 m/s. Values were computed using the EESA algorithm (or Cavagna method) as described in literature for a range of horizontal speeds from -5% to +5% relative to the highlighted base value. Computer model was developed by Ron George.</td></tr>
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<span style="color: blue;"><b>As shown in Figure 10, a variation of -5 to +5% in derived horizontal speed has an impact of <u>-7 to +16%</u> in estimated external running power respectively, all other factors kept the same. </b></span></div>
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<span style="color: blue;"><b>Here, you can see power extending from 324 Watts to 402 Watts because of the error in horizontal force-time signatures. </b></span></div>
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<span style="color: blue;"><b>This analysis is a little incomplete because if horizontal speed changes, so can the vertical force-time signature. Therefore, there are multiplicative effects on computed power from the coupling of horizontal speed and vertical force.</b></span></div>
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<span style="color: blue;"><b>A computational difference between platforms for horizontal speed can arise from errors in the horizontal acceleration and horizontal force-time signatures computed by the device. </b></span></div>
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<b>CONCLUSION</b></div>
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A running powermeter that utilizes ground contact variables in it's calculation of running power can spell out a range of values for power depending on variation in those ground contact inputs. </div>
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The impact of error in three of these ground contact variables, chiefly vertical oscillation, ground contact time and horizontal speed, were explored in this article by independantly varying force time signatures and inspecting their impact on computed power. </div>
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Other sources of error exist. For example, if an accelerometer and the algorithm used cannot distinguish between a front footed strike and a rear footed one, the underlying force impulse characteristic is misjudged. Misjudging impact force-time signature impacts the computed potental energy change and hence potential work. </div>
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Based on the analysis for one front foot runner at 4 m/s, one observes that some of the striking differences in reported power between accelerometer platforms like Stryd and Garmin may lie in the variations in derived ground contact variables. Out of the three explored variables, errors in vertical and horizontal force time signatures can make an appreciable impact on the theoretically computed power (See Figures 6 & 10). </div>
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It is my hope that this writeup gives runners and coaches a qualitative and quantitative feel for the impact of accelerometer error upon the new metric of running power. <b>Basing training prescription on faulty devices and secondary & tertiary metrics derived from them can carry a risk</b>. Not being aware of such risk within new technology has implications for both undertraining and over-reaching.</div>
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Ronhttp://www.blogger.com/profile/16268869622833968439noreply@blogger.com0tag:blogger.com,1999:blog-4786784182488135171.post-61350807381402957562017-12-10T00:09:00.000+04:002018-01-27T19:55:49.481+04:00Technical Review of Stryd's Running Power Model<div dir="ltr" style="text-align: left;" trbidi="on">
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In <b><a href="http://www.georgeron.com/2017/11/the-govss-running-power-algorithm-and.html"><span style="color: red;">my last post</span></a></b>, I reviewed GOVSS Running Power, which is the model adopted by Runscribe Plus. </div>
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As a recap : <span style="color: blue;"><b>GOVSS power</b></span> is a total energy model which includes both the external and the internal cost to move the limbs in relation to center of mass. It also accounts for wind and the kinetic component that play a prominent role during rapid, high speed transient running events such as a track sprint. </div>
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<span style="font-family: inherit;">In this post, I review the <span style="color: blue;"><b>External Energy Summation Approach (EESA)</b></span> applied to center of mass which can then be converted to an external power (Part A). I will describe the model in a bit, but one observation before that.</span><br />
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</span> <span style="font-family: inherit;">In a </span><b style="font-family: inherit;"><a href="https://storage.googleapis.com/stryd_static_assets/stryd-metric-validation.pdf"><span style="color: red;">Stryd whitepaper</span></a></b><span style="font-family: inherit;"> published yesterday, the writeup suggested that ground reaction forces are being employed in the calculation of components of power. After reading that, I hold a level of confidence that the EESA algorithm is used in some capacity, either at a very complex level or a very simplistic level with some inhouse modifications. </span><br />
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I also review the same whitepaper and appraise the validation they've disclosed (Part B) and describe several aspects of what it shows AND do not show. Readers who are scientifically inclined like me will be interested in this section. </div>
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I also point the reader to my <b><a href="http://www.georgeron.com/2017/09/the-physics-of-running-power.html"><span style="color: red;">Primer on Running Power</span></a></b> in order to get a feel for the changes in mechanical energy during running and how a 9 / 10-DOF IMU basically works. </div>
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<b><u><span style="font-size: large;">PART A : Fundamentals</span></u></b></div>
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<b>I. EESA Approach for Calculating External Power</b><br />
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In the EESA approach, the vertical (Y), anterio-posteral (X, fore-aft) and lateral ground reaction forces (Z) are used to calculate the instantaneous speed of body center of mass. </div>
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The resulting velocities are used to calculate the change in potential energy function and kinetic energy function to <b><span style="color: blue;">lift and accelerate the body center of mass.</span></b> (Note : EESA has been coined by me, for lack of a better term).</div>
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The potential energy function tracks the work done to lift the center of mass.The kinetic energy function contains the velocities to move in a forward and lateral direction. In common running situations, lateral motion maybe neglected but keeping with the intent to account for all 3D motion, the lateral kinetic energy is also included in the general equation. </div>
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The computational equations have been summed up in this mathematical infographic in Figure 1. <span style="font-family: "calibri" , sans-serif; font-size: 13.5pt; line-height: 107%;">F<sub>x</sub></span>, <span style="font-family: "calibri" , sans-serif; font-size: 13.5pt; line-height: 107%;">F<sub>y</sub> </span> and <span style="font-family: "calibri" , sans-serif; font-size: 13.5pt; line-height: 107%;">F<sub>z</sub></span> are the forces in the forward, vertical and lateral directions. Their speed counterparts are expressed as <span style="font-size: 13.5pt; text-align: left;">v</span><sub style="text-align: left;">x</sub><span style="font-size: 13.5pt; text-align: left;">, v</span><sub style="text-align: left;">y</sub><span style="font-size: 13.5pt; text-align: left;"> </span>and <span style="font-size: 13.5pt; text-align: left;">v</span><sub style="text-align: left;">y</sub>. Please click to zoom in.</div>
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<tr><td class="tr-caption" style="text-align: center;">Figure 1 : EESA computational approach for total external power for running. Adapted from Minetti et.al (2002). Click to zoon in.</td></tr>
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Referring to Figure 1, the <span style="color: blue;"><b>EESA algorithm</b></span> is the following :<br />
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STEP 1 : The X, Y and Z velocity functions are an integral of the ratio of the respective ground reaction forces and mass, or in other words the axis specific accelerations. After integration is performed, a constant has to be added to the right side which maybe different for level running and gradient running (Cavagna constant). </div>
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STEP 2 : Since velocity is a vector, the resultant running velocity is calculated by the sum of the squares of the 3D velocities.</div>
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STEP 3 : Kinetic energy as a function of time is half of mass times the resultant velocity squared.</div>
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STEP 4 : Vertical displacement of center of mass is the integral of vertical velocity with respect to time. After integration is performed, a constant has to be added on the right side (Cavagna constant).</div>
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STEP 5 : The potential energy as a function of time is mass times gravitational acceleration times the vertical displacement of center of mass.</div>
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STEP 6 : The total energy of the center of mass as a function of time is a summation of the potential and kinetic energies. This will fluctuation function in time, with a minimum occuring at the middle of stance phase. For level running, the curve is symmetric. For gradient running, the curve is lopsided to the right side for uphills and to the left side for downhills. </div>
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STEP 7 : External Power is the time derivative of the summation of changes in potential and kinetic energy functions. </div>
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This is the generalized form of EESA.<br />
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<tr><td class="tr-caption" style="text-align: center;">Figure 2 : Kinetic energy, potential energy and total external energy functions vs grade. Fluctuations in total external energy as a function of grade show asymmetrical profiles for uphills and downhills and a symmetrical profile for level grade. On the downhills, the decrease in total external energy is progressively more than subsequent increases as grade steepens (net energy dissipation). On the uphills, the increase in total external energy is progressively more than it decreases as grade steepens (net energy addition). Adapted from Snyder et.al (2012). Markups by me.</td></tr>
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The <span style="color: blue;"><b>disadvantages</b> </span>of the EESA model are the following :<br />
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<b><span style="color: blue;">A) It accounts only for the external power</span></b> to move center of mass. It does not take into the account another source of cost demand, that to swing the arms and the legs. Since it is not a total energy requirement to run, magnitude of calculated power will be lesser compared to a total energy approach such as GOVSS.<br />
<b><span style="color: blue;">B) It doesn't tell us what goes on inside the body.</span></b> External mechanical work reflects the overall behavior of the whole
body center of mass mechanics. Unfortunately, this black box approach seldom provides us with a direct understanding of what is going on inside the body. It is difficult to draw specific relationships using just sheer "watts" to things like forces, moments and storage-recoil mechanisms at the level of joints, muscles and tendons.</div>
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<b>II. Stryd Model</b><br />
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<span style="text-align: justify;">Chief features as I observe are :</span><br />
<span style="text-align: justify;"><br /></span><span style="text-align: justify;"><b>Ground forces estimated from acceleration signatures :</b> From the whitepaper, it seems that Stryd employs the equations in the EESA framework for external power in it's model. Otherwise, there'd be little meaning behind their efforts to approximate ground forces.</span><br />
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<span style="text-align: justify;">Ground forces are estimated from the acceleration-time signatures in the 3 axes multiplied by mass of the subject runner. What the whitepaper attempts to show is a validation of that force profile against force plate data. There is absolutely no measurement of forces, they are only estimated from the accelerations.</span><br />
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<b>Leg symmetry assumption :</b> Since the Stryd comes simply as one footpod, the mechanics in one leg is assumed to be an overall representation of the body's movement. This assumption carries through into the external power calculation.</div>
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<b>Scaling factors for power on gradients :</b> For outdoor gradient running, the ratio of negative and positive potential and kinetic energies are no longer in the ratio of 1:1 and mirrored (see Figure 1).<br />
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Stryd employs scaling factors for uphills to account for the greater degree of concentric work, in effect increasing the modeled external power. Conversely, they employ a negative scaling for downhills to account for the greater eccentric work. People have found varying degrees of correlation when comparing to their rates of perceived exertion.</div>
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These scaling factors came as a firmware update to Stryd users in early 2017. There has been little in the way of documentation and validaton of the approach for a wide range of runners so this area is an unknown. More about this is discussed in Part B.III below.</div>
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<b>Indoor running distance / speed may differ :</b> A small desirable nuance in the model might be for indoor running where the Stryd model would account for the difference in treadmill belt speeds when estimating a relative forward velocity. I do not think this is the case which explains why several people find a small discrepancy between treadmill recorded distance / pace and Stryd distance / pace. I think that the magnitude of this discrepancy maybe less than 5%. </div>
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<b>Form Power :</b> Stryd adds a distinction by singling out vertical work rate done "in place", i.e the power required to displace the center of mass vertically without considering forward displacement. This is expressed as a separate metric called <span style="color: blue;"><b>Form Power</b></span> which other platforms do not highlight. I take the liberty to express it in the following form :</div>
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<span style="color: blue;"><b>Lifting In-Place Power (due to vertical oscillation)</b> = <b>Step Rate</b> x <b>m</b> x <b>g</b> x <b>V<sub>disp</sub></b></span><br />
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</span> <span style="text-align: left;">Vdisp (m) = Vertical Oscillation [total vertical distance covered by center of mass]</span></div>
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Step Frequency (Hz) = 1/(Aerial Time + Ground Contact Time) = 1/60 x (Step Rate)<br />
m (kg) = mass<br />
g (m/s<sup>2</sup>) = gravitational acceleration<br />
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I've called it lifting in-place power to distinguish it from slope lifting power when running up a hill. </div>
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Take note that this component of power is directly proportional to step frequency. Since step frequency is made up of the inverse of the sum of aerial time and contact time, this would suggest that increasing step frequency is done by decreasing contact time and/or decreasing aerial time. This couples with and affects Vdisp.</div>
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<span style="text-align: justify;">The consensus in literature around lifting-in-place power is conflicting. Some studies show that low vertical oscillations are correlated with better running economy (lower metabolic cost) while some studies show the exact opposite (higher metabolic cost). </span></div>
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<span style="text-align: justify;">The latter point is interesting actually. It has been suggested that dropping vertical oscillation must be accompanied by an increase in step frequency (see figure above). But this increases the internal work needed to sustain high step frequencies, thereby increasing the overall metabolic cost and worsening running economy. Studies have published data backing this negative correlation. A confounding variable in these studies maybe how adapted and well trained the runners were to sustain high step frequencies. </span><br />
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<span style="text-align: justify;">One point is clear. Studies that have looked at leg kinematics during actual running races find that top tier runners are almost always front foot strikers and show the lowest ground contact times compared to the rest of the field (eg Hasegawa et.al, 2007). Again, this gives more power to ground contact time being an actionable variable. In this way, atleast in my mind, ground contact time and vertical oscillation are "coupled" variables which are again related to the running speed, as the figure above shows. </span><br />
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<span style="text-align: justify;">Another point to keep in mind is that leg spring action contributes some of the force (and power) needed to oscillate upwards. Therefore, a runner with good spring mechanics provides lesser net force to lift himself than one without. This must mean not all vertical oscillation is "waste", as energy is recycled. The net positive power to oscillate is therefore lower than the suggested calculated value of lifting-in-place power. </span><br />
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<span style="text-align: justify;">For example, a 64kg runner at 3 Hz step frequency and 5cm of vertical oscillation requires a lifting-in-place power = 95 W. But if 30% of that is supplied by leg spring, the rest 70% is the net positive power that the runner must produce. This equates to around 66 W. </span><br />
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<b style="text-align: justify;">Leg Spring Stiffness</b><span style="text-align: justify;"> : Another distinction that Stryd offers is displaying a mathematically calculated leg spring stiffness from</span><b style="text-align: justify;"><span style="color: red;"><a href="http://www.georgeron.com/2017/01/running-science-part-1-ground-contact.html"> <span style="color: red;">some of the equations</span></a></span></b><span style="text-align: justify;"> I described in a previous post. This maybe displayed for information only and I do not believe it is used to treat energy savings due to spring biomechanics. See part B.V below for more on this.</span><br />
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<b style="text-align: justify;">RSS : </b><span style="text-align: justify;">Native to Stryd is the Running Stress Score (RSS) that is a single number quantifying the effect of a daily run. One notes that this stress calculation is non-linear in nature as it credits higher volume and intensity in an exponential way. This thinking is similar to the weighted TRIMP method that assigns exponentially increasing weighting factors as exercise intensity increases. Although I don't know the exact algorithm used, </span><b style="text-align: justify;"><a href="http://www.georgeron.com/2017/08/an-equation-for-running-stress-score-rss.html"><span style="color: red;">a simple formula I developed </span></a></b><span style="text-align: justify;">approaches within 3% of Stryd RSS. This is based on Stryd's own RSS rules for different intensity zones. </span><br />
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It's as follows :</div>
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<b style="color: blue; font-family: inherit;"><span style="background-color: white; text-align: left;">RSS/min = A x e^(B x Pext/CP)</span></b></div>
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<span style="font-family: inherit;"><span style="background-color: white; color: #333333; font-family: inherit; text-align: left;">where parameter A = 0.0758</span></span><br />
<span style="color: #333333; font-family: inherit; text-align: left;">parameter B = </span><span style="color: #333333; font-family: inherit; text-align: left;">3.1297</span></div>
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<span style="font-family: inherit;"><span style="background-color: white; color: #333333; text-align: left;">Pext = External mechanical power</span></span></div>
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<span style="font-family: inherit;"><span style="background-color: white; color: #333333; text-align: left;">CP = Stryd Critical Power</span></span><br />
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<b>Wind :</b> The Stryd does not take wind into consideration. However, there are several reports of gusts negatively affecting reported power which seem to be a bug that is being investigated. See Part B.VII for more on this subject.</div>
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<b><u><span style="font-size: large;">PART B : Stryd Whitepaper Review</span></u></b></div>
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<b>I. Review of Stryd's Vertical Force-Time Curve</b><br />
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Vertical power is the rate of change in potential energy. Multiple studies have shown that this component constitutes the majority share in the metabolic cost of normal running.</div>
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Since the Stryd footpod has no means to measure force directly, in order to get the correct estimate of force, the IMU must capture the time course of instantaneous vertical acceleration profile which is proportional to the force signature. </div>
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Continuing on, in order to get an accurate estimate of changes in potential work, the footpod IMU must capture time course of vertical displacement of center of mass. </div>
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An image showing the first of these elements is in Figure 2.<br />
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<tr><td class="tr-caption" style="text-align: center;">Figure 3 : Modeled vs actual vertical force-time signatures in a rear-footed runner for an unspecified running speed. Base image courtesy of Stryd. Markups by the me. </td></tr>
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It is not known what speed the runner was running at but looking at the force signature, it is clear that it was a rear foot runner. The model estimation and force plate data nearly match, particularly when you look at the highest peak vertical force which is important in derivative calculations of impulse and leg spring stiffness.<br />
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Some key observations as far as <span style="color: red;"><b><span style="color: blue;">vertical force-time</span> </b></span>(Figure 1) is concerned :<br />
<br />
<div style="text-align: justify;">
<b>1) Misrepresentation of first footstrike peak :</b> The Stryd models a nice rounded single peak force when there were actually two. This is significant because the footpod thinks that the footstrike is fore-footed when in reality it's rear-footed. The implications are :</div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
a) The Stryd model neglects first impact peak. If the first rear-foot strike peak is completely neglected, that initial impact peak of landing will be distributed over an inaccurate and wider period of delta time which will suggest that there is no shock loading, when in reality there is.<br />
b) Stryd's force profile estimation for a forward moving (or backward moving) fore-footed runner might be alright but it might be grossly over-looking rear footed mechanics by missing the first impact peak altogether. </div>
<div style="text-align: justify;">
c) If a runner changes gait mechanics on the fly due to the effect of different running surfaces or due to fatigue in a long race, this 'tuning' may not be captured properly by the model.<br />
d) Gradients may substantially influence these errors. To get an idea of grade influences on the vertical force-time profile from empirical studies, please see Appendix image A4. </div>
<div style="text-align: justify;">
<br /></div>
<b>2) Mismatch of contact time : </b>Although the actual and estimated signals are close, Stryd under-estimates initial footstrike and over-estimates the actual takeoff point with respect to time (Figure 2).<br />
<div>
<br /></div>
This has some implications, namely :<br />
<br />
a) The ground contact time (GCT) is over-estimated. From the image, I estimate atleast 15-20 milliseconds greater than the force plate.<br />
b) The stance-averaged vertical ground reaction force during GCT does not match 1-to-1 with the actual force plate data.<br />
c) As a consequence of b), the Stryd estimated ground reaction impulse given by the product of force and GCT is different to the actual impulse.<br />
d) Any calculation of aerial times, step lengths and step times using GCT will propagate the error through.<br />
e) Since leg spring stiffness (LSS) is driven by GCT and involves a duty factor calculation treated with the maximum vertical ground reaction force, errors propogate into the LSS model as well.<br />
f) Since the tests were carried out in the laboratory, the effect of gradients and different speeds on the error in GCT remains unknown.<br />
<br />
<div style="text-align: justify;">
<b>3) Effect of Running Speed on Force-Time Curve Not Discussed :</b> Stryd does not show the effect of running speed on the goodness-of-fit for vertical force curve.</div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
That this important element is missing in the whitepaper prevents a discussion on the influence of variations among broader running speeds and broader gait mechanics. Within literature, researchers have found that simplistic vertical force-time curve models derived from spring mass models lose their goodness-of-fit as the running speed increases due to the presence of high frequency components from the acceleration of the lower limb. </div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
This is where I'd exercise some caution. With the current state-of-the-art, I wonder if IMU's may still not be practical for application to short-distance, high speed track racing.</div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
<b>4) Impact of Shoe Type to Force-Time Curve Not Discussed : </b>The impact of variations in footwear to the measured parameters is unknown. This is also an influencer of vertical ground reaction force profiles.</div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
<b>5) Impact of Treadmill Slope to Force-Time Curve Not Discussed : </b>The whitepaper lacks a review of the force-time profile accuracy under the influence of slope (see Appendix image A4). Since step period generally decreases as slope increases and increases as slope decreases, what influence high running speeds have on the model fit when the slopes are greater than 7 degrees inclination is something important to document. </div>
<div style="text-align: justify;">
<br /></div>
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://2.bp.blogspot.com/-pzubsrHRcKU/WiwyeDgyr9I/AAAAAAAAGZo/TxQJHIoMLx85mRtOTp2OzMfYhGPEI9VTgCLcBGAs/s1600/Capture14.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="527" data-original-width="656" height="321" src="https://2.bp.blogspot.com/-pzubsrHRcKU/WiwyeDgyr9I/AAAAAAAAGZo/TxQJHIoMLx85mRtOTp2OzMfYhGPEI9VTgCLcBGAs/s400/Capture14.JPG" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Figure 4 : Plot showing goodness-of-fit of modeled GCT to force plate measurements. The average error is stated to be 2.83%. The number of runners, running speeds, shoes worn, footstrike mechanics and slope on the treadmill are all unknown which raises the question of how the error varies as a function of each. Image courtesy of Stryd.</td></tr>
</tbody></table>
<div style="text-align: justify;">
<br /></div>
The second element in estimating potential energy changes is <b><span style="color: blue;">vertical oscillation</span></b>, shown in Figure 3.<br />
<br />
<br />
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://1.bp.blogspot.com/-wLhZEPH62JU/Wiu5kUmZDTI/AAAAAAAAGYU/saXVMhMOVqMKM6Ogx99R2dz1xgtsu0X6QCLcBGAs/s1600/Capture7.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="648" data-original-width="948" height="272" src="https://1.bp.blogspot.com/-wLhZEPH62JU/Wiu5kUmZDTI/AAAAAAAAGYU/saXVMhMOVqMKM6Ogx99R2dz1xgtsu0X6QCLcBGAs/s400/Capture7.JPG" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Figure 5: Estmated vs actual vertical oscillation across a wide range of runners. Sample size is not disclosed. Experimental method and running speeds to generate the plot is unknown. Stated average error with respect to force plate = 3.18%. Base image courtesy of Stryd. Markups by me.</td></tr>
</tbody></table>
<br />
Some key observations as far as vertical oscillation is concerned :<br />
<div>
<br /></div>
<div style="text-align: justify;">
<b>1) A close fit : </b>A 3.18% average error in vertical oscillation has been shown which is quite good. It is desirable to understand the experimental method, equipment used and the sample size of the runners to put this into context.<br />
<b>2) Error Propagation :</b> I understand that a small error propagates into the Form Power calculation due to vertical oscillation error.</div>
<div style="text-align: justify;">
<b>3) The effect of gait parameters on this variation is not documented.</b> The estimation error with respect to gait parameters such as velocity and step duration should be additionally plotted, for example, in the form of a Bland-Altman plot.</div>
<div style="text-align: justify;">
<b>4) Explanation of influencing factors behind error :</b> I'm very interested to know if 3% average error is the best achievable given current level of technology. It is desirable to get some sort of explanation to the influencers of this error. Do random influences play into this?<br />
<br /></div>
<br />
<b>II. Review of Stryd's Horiztonal Force Model</b><br />
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
<b><span style="color: blue;">Horizontal power</span></b> is a function of the rate of changes in kinetic energy. Studies have suggested that the horizontal work, particularly that component of generating horizontal propulsive force, constitutes more than one-third of the total cost of steady speed running.</div>
<div style="text-align: justify;">
<br /></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://3.bp.blogspot.com/-Dg6p01YvDkQ/Wiwt4ysmpSI/AAAAAAAAGZc/cqXG7e0duUgxO5LXVhEeWbcp4UCp1nG4QCLcBGAs/s1600/Capture12.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="428" data-original-width="688" height="248" src="https://3.bp.blogspot.com/-Dg6p01YvDkQ/Wiwt4ysmpSI/AAAAAAAAGZc/cqXG7e0duUgxO5LXVhEeWbcp4UCp1nG4QCLcBGAs/s400/Capture12.JPG" width="400" /></a></div>
<div style="text-align: justify;">
<br /></div>
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://1.bp.blogspot.com/-meFwwutKaWs/WiwuEyVO3hI/AAAAAAAAGZk/NmsllxDNXdIEHM9CSluD0IEU3OBBPRowQCLcBGAs/s1600/Capture13.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="519" data-original-width="661" height="251" src="https://1.bp.blogspot.com/-meFwwutKaWs/WiwuEyVO3hI/AAAAAAAAGZk/NmsllxDNXdIEHM9CSluD0IEU3OBBPRowQCLcBGAs/s320/Capture13.JPG" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Figure 6 : Stryd modeled forward speed change compared to force plate measures. Indicated accuracy = 95%. Grade of running surface unknown, but presumably level. Image courtesy of Stryd. </td></tr>
</tbody></table>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
A review shows the following :</div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
<b>1) Accuracy is decent :</b> Like the vertical force-time profile, the horizontal force-time profile is presumably derived from the horizontal acceleration signature from the IMU. Stryd states that it captures the speed attenuation during the contact phase with 95% accuracy. This is not bad when considering that this anterio-posterior dynamics is a difficult one to capture.</div>
<div style="text-align: justify;">
<b>2) Error Propagation : </b>A 5% error in estimation of kinetic energy change propagates a proportional error into the work and power calculations. </div>
<div style="text-align: justify;">
<b>3) Influence of speed and slope not discussed : </b>Like in the case of the modeled vertical force-time profile, the influence of different speeds and slopes on the goodness-of-fit are not specifically mentioned. This is important to document in order to compare how the fit varies under different situations. See Appendix image A4 for grade influences on horizontal force-time curve curves.</div>
<div style="text-align: justify;">
<span style="text-align: left;"><b><br /></b></span>
<span style="text-align: left;"><b><br /></b></span>
<span style="text-align: left;"><b>III. Basis of concentric and eccentric work scaling factors not discussed :</b> A technical basis for the scaling factors employed by the Stryd model to account for the dominance of concentric or eccentric work during gradient running is desirable (see Part A.II and Figure 1). </span><br />
<span style="text-align: left;"><br /></span>
<span style="text-align: left;">This correction was made as a firmware update in early 2017. </span><br />
<span style="text-align: left;"><br /></span>
<span style="text-align: left;">While I understand this is part of the secret sauce, some pedantic questions are necessary to be asked if we want to remain true to the estimation of a power : </span><br />
<span style="text-align: left;"><br /></span>
<span style="text-align: left;">A)</span><b style="text-align: left;"><span style="color: blue;"> Is the scaling used related more to vertical and horiontal ground forces or is it calibrated with metabolic costs?</span></b><span style="text-align: left;"> What was the validation study behind these and will those findings translate well for the general public?</span><br />
<span style="text-align: left;"><br /></span>
<span style="text-align: left;">B) <b><span style="color: blue;">I</span></b></span><b style="text-align: left;"><span style="color: blue;">s the power scaling a continuous linear decrease</span></b><span style="text-align: left;"> for downhill grades and </span><b style="text-align: left;"><span style="color: blue;">a continuous linear increase </span></b><span style="text-align: left;">for uphill grades? </span></div>
<div style="text-align: justify;">
<br />
<span style="text-align: left;">Let's suppose scaling is calibrated against metabolic costs. If power follows a strictly linear decrease for steep downhills while the metabolic cost decrease sharply, this will suggest that the metabolic efficiency increases. Conversely, if power follows a strictly linear increase for uphills while the metabolic cost follows a curvilinear relation to grade , that might suggest that metabolic efficiency becomes progressively worse. There are individual variations playing into metabolic cost dynamics on grade. </span><br />
<span style="text-align: left;"><br /></span><span style="text-align: left;">For downhills, a strict metabolic cost decrease may not even hold. For example, it has been documented that <span style="color: blue;"><b>beyond a grade of -9 degrees, </b></span><b><span style="color: blue;">the metabolic rate actually increases,</span></b> presumably from the high eccentric cost to maintain balance of center of mass. In other words, there is an optimum downhill angle beyond which metabolic cost increases. </span><br />
<span style="text-align: left;"><br /></span>
<span style="text-align: left;">How that scaling curve has been calibrated is of much interest to me, and I assume, to other scientifically minded runners.</span><br />
<span style="text-align: left;"><br /></span>
<span style="text-align: left;">C) Some reports indicate runners </span><span style="text-align: left;">losing RPE-power correlation for gradient running. </span><span style="text-align: left;">This begs the question whether the scaling factors should be something that is best left for the runner to tune and calibrate through the settings instead of being driven down from Stryd. </span><br />
<span style="text-align: left;"><br /></span>
<span style="text-align: left;"><br /></span>
<span style="text-align: left;"><b>VI. A Review of Stryd Statement on Correlation with VO2</b></span><br />
<span style="text-align: left;"><b><br /></b></span>
Stryd states in the whitepaper that : "The external mechanical power reported by Stryd has a well established relationship with metabolic expenditure based on testing conducted by Stryd and other third party research teams. "<br />
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
Now I have done this too in the <a href="http://www.georgeron.com/2017/03/actionable-intelligence-for-running.html"><b><span style="color: red;">past during a VO2max test</span></b></a>, plotting the relationship of VO2 to W/kg. This can be done by absolutely anyone. </div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
I consider the statement regarding "well-established relationship" to be a sleight of hand. In other words, if I take a powermeter that is algorithmically modeled in such away that external power is linearly proportional to running speed (atleast on flat terrain), ofcourse a VO2 test is going to show that ave VO2 at each speed is proportional to external power! This relationship has been "pegged" from the beginning due to speed being an input in the model. <b><span style="color: blue;">There is no unique science in this.</span></b></div>
<div style="text-align: justify;">
<br />
The linear relationship of VO2 to power is encouraging in as far as it only tells us that model algorithm involving speed works.</div>
<div style="text-align: justify;">
<br />
The next question would be : <b><span style="color: blue;">Can you use a running power meter be used to predict running economy? </span></b>This carries a risk of mis-estimation because we do not know how transferable such simple relations are going from indoors to outdoors.<br />
<br />
The estimation gets worse when it is a formula derived from a book which based it on data from a limited sample of runners that you weren't a part of. I do not believe you can estimate metabolic cost this way with any reliable degree of accuracy just like HR or HR based formulas cannot estimate caloric expenditure with any reliable degree of accuracy.<br />
<br />
Indeed, a study from the University of Guelph and presented at the recent Canadian Society for Exercise Physiology (CSEP) annual meeting in Winnipe challenged the idea.<br />
<br />
The researchers found a significant difference in running economy between treadmill and track running for 11 experienced elite runners as measured by standard metabolic measurements. But in the same study, the Stryd power meter and formulaic implementations of economy couldn't pick up any difference between the two surfaces.</div>
<div style="text-align: left;">
<br /></div>
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://2.bp.blogspot.com/-3n7an6xRbA0/Wi7w5JPdlrI/AAAAAAAAGc4/XPP0r3WJc6k-U9qZXLo6FVGr7l_UhZJUQCLcBGAs/s1600/Capture1.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="584" data-original-width="737" height="316" src="https://2.bp.blogspot.com/-3n7an6xRbA0/Wi7w5JPdlrI/AAAAAAAAGc4/XPP0r3WJc6k-U9qZXLo6FVGr7l_UhZJUQCLcBGAs/s400/Capture1.JPG" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Figure 7 : Plot showing VO2 as a function of specific external power reported by Stryd. Since power is linearly proportional to speed, such a relationship is already mostly pegged by design of the algorithm.</td></tr>
</tbody></table>
</div>
<br />
<b>OTHER ASPECTS : </b><br />
<br />
<b>V. Leg Spring Stiffness : Information Only Or Actually Used?</b><br />
<span style="text-align: justify;"><br />
</span> <span style="text-align: justify;">For level running, we understand from scientific literature that the storage and recoil of energy in the lower limbs restores an appreciable amount of energy into the positive work phase. Thus, the mechanical efficiency of running maybe greater than 30% depending on the skill and mechanics of the runner. This efficiency of running </span><b style="text-align: justify;"><a href="http://www.georgeron.com/2017/09/the-physics-of-running-power.html"><span style="color: red;">has a documented</span></a></b><span style="text-align: justify;"> linear relationship to running speed. </span><br />
<span style="text-align: justify;"><br /></span>
<span style="text-align: justify;">Stryd calculates leg spring stiffness (LSS) </span><b style="text-align: justify;"><a href="http://www.georgeron.com/2017/01/running-science-part-1-ground-contact.html"><span style="color: red;">using published models</span></a></b><span style="text-align: justify;"> derived from the mass-spring paradigm. But it is unclear how Stryd's model employs the stiffness into the mechanical work calculations to account for a "savings" in concentric work requirements. In contrast, the GOVSS model appreciates there maybe savings from efficiency increases as a function of speed and corrects the power demand depending on running speed.</span><br />
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
So the question is whether leg spring stiffness is simply a metric displayed for information only or whether it is actually used in the model in a fashion as described in the para above? If it is not used, then someone can question the actual value of this. The LSS metric remains one of the most confusing metrics from a trainability standpoint.<br />
<br />
<br />
<div style="text-align: left;">
<b>VI. Apparent Mechanical Efficiency of Running = 25%</b></div>
<div style="text-align: left;">
<b><br /></b></div>
<div style="text-align: left;">
The <b><span style="color: blue;">apparent mechanical efficiency</span></b> of running is defined as :</div>
<div style="text-align: left;">
<br /></div>
<div style="text-align: left;">
<b>Meff, a</b> = ratio of external power (Pext) and metabolic rate (Pmet). Meff, a = Pext/Pmet.</div>
<div style="text-align: left;">
<br /></div>
<div style="text-align: left;">
The <b><span style="color: blue;">gross mechanical efficiency</span></b> of running is differentiated as :</div>
<div>
<br /></div>
<div style="text-align: left;">
<b>Meff,g</b> = ratio of total power (Ptot) and metabolic rate (Pmet). Meff,g = Ptot/Pmet.</div>
<div style="text-align: left;">
<br /></div>
In the context of a Stryd powermeter, we should be concerned about the apparent mechanical efficiency.<br />
<br />
As alluded to in section V, human running involves energy storage and recoil going from the negative to positive phase. Several researchers have found that upto 40-50% of the energy stored during the eccentric phase can be returned to the concentric phase within the short time span of ground contact time for which those muscles remain in a loaded state.<br />
<br />
<span style="text-align: justify;"><b><span style="color: blue;">Maximum possible elastic energy storage</span></b> is defined in some papers (such as those written by Kram et.al) to be the difference between initial and minimum external energy of center of mass during the stance phase. <span style="color: blue;"><b>Energy return </b></span>is defined in the same papers to be the difference between the ending and minimum </span>external energy of center of mass during the stance phase. The <b><span style="color: blue;">maximum possible energy storage and recovery</span></b> is then taken as the smaller of these two values.<br />
<br />
To me, the way the efficiency is defined and what it takes into account (or what it doesn't) explains a lot of the differences in calculated efficiency between different running power models now arriving in the market. I suspect that an apparent mechanical efficiency value of 25% is artificially low, atleast for running on level and shallow slopes, if it didn't take into account energy storage and recovery mechanics between the negative and positive phases of running.<br />
<br />
<br /></div>
<div style="text-align: justify;">
<div style="text-align: left;">
<b>VII. Effect of Wind on Stryd's Performance</b></div>
<div style="text-align: left;">
<b><br /></b></div>
<div style="text-align: justify;">
The Stryd powermeter has no way to account for wind effects in the power calculation. In this respect, it will under-report power by a factor proportional to the correct relative velocity cubed. By "correct", I mean that the wind measured has to be applied at the height of the runner, and not what is reported from a 10m or 30m wind tower. </div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
That said, one of the "buggy" issues, as has been reported by several people both on the <b><a href="http://club.stryd.com/t/wind-effect-on-power-pioneer-vs-pod/2605/4"><span style="color: red;">Stryd support forums</span></a></b> and the <b><a href="https://groups.google.com/forum/#!forum/runningpower"><span style="color: red;">Running Power Google Groups</span></a></b>, is the sensitivity of power to sudden wind gusts. Reports indicate that gusts cause unsteady spikes in power for some and dips in the reported power for others, which is physically incorrect if you were trying to maintain speed in the face of a headwind. </div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
The root technical fault maybe with the barometer, which thinks that the a sudden pressure front is a change in pressure altitude. How that information is relayed through sensor fusion and into the Stryd algorithm to mess up the reported power is a mystery to me. Judging by the forums, even Stryd's engineers have a challenge grappling with this issue.<br />
<br />
The fact that they may need several consistently gusty days outside to test what's wrong might mean the delay of a corrective action for users.</div>
<div>
<b><br /></b></div>
</div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
<b><br />
</b></div>
<b>VIII. Conclusions</b><br />
<span style="text-align: justify;"><br /></span>
<span style="text-align: justify;">Stryd's description of the external running power model and a comparison of modeled variables against force plate data has been long in the making. It is appreciated but delivered a bit late.</span><br />
<span style="text-align: justify;"><br /></span>
<span style="text-align: justify;">From a brief reading, I assess that they employ the general EESA approach to external power with some "in-house" tweaking for uphills and downhills to account for net energy addition or dissipation. </span><br />
<span style="text-align: justify;"><br /></span>
<span style="text-align: justify;">Stryd is thinking several things, some unique, some literature driven, about the kinematics of running. I give them credit for that. However, it does not stop the questions about how the model employed will validate for a large number of runners in actual usage. This same question also goes for the GOVSS run power model. </span><br />
<span style="text-align: justify;"><br /></span>
<span style="text-align: justify;">The effect of running speed, footstrike variations and slopes on those errors were largely missing from the whitepaper. This was the most important aspect I would have liked to see. This unfortunately prevents an assessment of how closely IMUs can correctly decifer footstrike patterns across a broad range of runners, running speeds and terrain.</span><br />
<span style="text-align: justify;"><br /></span>
<span style="text-align: justify;">Though the stated errors in key variables and things like force-time curves are small, those errors propagate into the calculations of derived metrics. Users must be aware of this when trying to introduce running interventions to effect a change in some of these metrics. </span><br />
<span style="text-align: justify;"><br /></span>
<span style="text-align: justify;">It is hoped that this technical review will encourage them to release another round of whitepapers so we can understand that aspect. An independant scientific review from other laboratories is also desirable in order to establish the degree of reproducibility in these numbers. </span><br />
<span style="text-align: justify;"><br /></span>
<span style="text-align: justify;">With Stryd and Runscribe having published their running models, the lights fall onto Garmin. With a far greater user base, they should find impetus to publish their running power framework soon or risk a lukewarm interest from the market.</span><br />
<div style="text-align: justify;">
<br />
<b><span style="color: blue;">In the next post, I'll explore how errors in estimated ground reaction forces translate into errors in the external power calculations from the EESA method. Stay tuned...</span></b></div>
<br />
<br />
<br />
<div style="text-align: center;">
<b><u>APPENDIX</u></b></div>
<div>
<b><br />
</b></div>
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<tr><td class="tr-caption" style="text-align: center;">Figure A1 : An illustration of vertical ground reaction force-time curve along the gait cycle. Courtesy Weyand et.al (2010).</td></tr>
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<tr><td class="tr-caption" style="text-align: center;">Figure A2 : An illustration of the horizontal ground reaction force-time curve (lower plot). Courtesy Farley & Ferris.<br />
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<tr><td class="tr-caption" style="font-size: 12.8px;">Figure A3 : Specific vertical force-time profiles for unshod rearfoot-striker, shod <br />
rear foot-striker and a barefoot forefoot-striker at 3.5 m/s running speed. Courtesy Liebermann et.al (2010).<br />
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Figure A4 : Vertical and horizontal force-time curves for a 73kg subject running at 3 m/s over the indicated grades. For the vertical force profile, the first impact peak substantially increases as grade plummets. On the uphills, the second peak substantially increases to the point where at +9 degrees, the slope is rounded. Peak vertical forces decrease as grade steepens. For the horizontal force profile, the negative part of the S curve substantially increases as grade plummets while the curve more or less assumes a half sinusoid. On the uphills, the positive part of the S curve substantially increases as the grade increases while the curve as a whole more or less assumes a half sinusoid. Courtesy Gotschall et.al (2005).<br />
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Figure A5 : Submaximal VO2 is linearly related to speed. Courtesy Kram et.al. </div>
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Ronhttp://www.blogger.com/profile/16268869622833968439noreply@blogger.com7tag:blogger.com,1999:blog-4786784182488135171.post-35344952367344881992017-11-11T12:53:00.000+04:002017-12-13T08:04:55.864+04:00Technical Review of the Runscibe GOVSS Running Power Model<div dir="ltr" style="text-align: left;" trbidi="on">
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I would like to discuss the Gravity Ordered Velocity Stress Score (GOVSS) model for running, provide some comments in blue italics and simultaneously compare to Coggan metrics such as NP, IF and TSS (all trademarked under Training Peaks).<br />
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Tim Clark at Runscribe told me their RS+ will now incorporate the Skiba GOVSS model. Being open in what they are implementing is greatly appreciated. </div>
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Just off the bat : Dr. Andrew Coggan recently commented on the Stryd Forum that many of his metrics and guidelines developed for cycling don't 'necessarily' apply to running, nor should one consider TSS, rTSS, sTSS, BikeScore, GOVSS, RSS etc as completely interchangeable. </div>
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That said, here's the GOVSS algorithm as proposed by Phil Skiba, 2006 :</div>
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1. Find the athlete’s velocity at LT by a 10 km to one hour maximal run. </div>
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<i><span style="color: blue;">Note : Presumably the thinking behind this is that a true 10K intensity is the maximum intensity in the intensity continuum where a delicate homeostatic balance in physiological parameters is maintained. Research has also shown that speed or power at LT is a valid predictor of endurance CYCLING performance (r = 0.88 for cycling, Coyle. el al 1991). In cycling, the previous statement has been debated because cycling is so much more than a single discipline of TT'ing. Running on the other hand is predominantly a time trial against the clock so applying a LT limited power model may not be so unreasonable. This is probably also the basis for Stryd's CP and RSS paradigm. </span></i></div>
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2. Convert this LT limited velocity to a LT limited power value using Equation 7. "Lactate limited power" may also be called "lactate adjusted power". </div>
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<i><span style="color: blue;">Note : The equation converts a "threshold" velocity to a "threshold" power using Prof. di Prampero's power-balanced supply-demand equation for running energetics which expresses the metabolic RATE of running in terms of COST of energy C. The equation is then modified into a power by multilying with a speed specific efficiency. The efficiency that is used in power equation can be rated to different speeds with a simple linear equation based on the finding that efficiency varies linearly 0.5-0.7 at 8.33 m/s (30 km/h) in a reasonably linear fashion (Cavangna and Kaneko 1976, Arsac 2001). A 5th order regression model from Minetti (2002) is used to apply a general running surface to the cost for better acounting for slope effects. </span></i></div>
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3. Analyze the data from a particular workout from an athlete’s log, computing 120 second rolling averages from velocity and slope data. </div>
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<i><span style="color: blue;">Note - Before applying rolling averages, the following equations are applied to figure out instantaneous GOVSS based power. Equations are from the reference down in the bottom of this article.</span></i><br />
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<tr><td class="tr-caption" style="text-align: center;">Fig 1 a,b,c : Series of equations used to convert energy cost of running to lactate adjusted power</td></tr>
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<i><span style="color: blue;">Referring to Fig 1a, <b>Caero, the energy cost of overcoming air resistance</b> = k.n<sup>‑1</sup>.d<sup>2</sup>.t<sup>2</sup>,
and k is the constant of air friction (in kg<sup>-1</sup>. m<sup>-1</sup> )
with n = 0.5. </span></i><i><span style="color: blue;"><b>Ckin, the energy cost of acceleration</b> = 0.5.n<sup>-1</sup>.d t<sup>-2</sup> , with n = 0.25. It is important to note that equation was minimally "modified" to suit events ranging from 800m to 5K. But the original form was successfully used to predict performances for middle and long distance running. </span></i></div>
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<i><span style="color: blue;">Referring to Fig 1b, the equation describes the velocity independant energy cost <b>C</b> to cover any distance. In the absense of a slope, this defaults to 3.6 - 4.2 J·kg<sup>-1</sup>·m<sup>-1</sup>. In the presence of a slope i, it becomes a 5th order regression equation. </span></i></div>
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<i><span style="color: blue;">Referring to Fig 1c, the equation <b>converts metabolic rate to a mechanical power to weight ratio</b> available for locomotion by multiplying metabolic cost with the separate efficiencies. This becomes a total power cost to run as it includes both the cost of things like COM motion and limb swing. </span></i></div>
<i><span style="color: blue;"><br /></span></i><i><span style="color: blue;">All values of cost C (kinetic, air resistance and slope related) are <b>calculated as rolling averages over 120 seconds</b>. Skiba wrote that this was to account for the fact that the original 5th order cost of running model was validated to the 800m. </span></i></div>
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4. Raise the values in step 3 to the 4th power. </div>
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<i><span style="color: blue;">Note - Skiba investigated LT dynamics in relation to running speed in a group of running subjects and applied a simple power fit (as Coggan did with his data). The regression fit said that the lactate levels in the body were a function of the speed of running raised to the power of 3.5. The power exponent was 4.2 in the top 10% of the subjects and 2.5 in the bottom 10%. A power exponent of 3.5 became a middle ground to apply to the entire population of tested subjects (N = 94). Presumably, the 3.5 has got rounded up to 4 by Skiba to make it easy to apply but I question this. Why not just stick to the original exponent?</span></i><br />
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<tr><td class="tr-caption" style="text-align: center;">Fig 2 : The basis behind an exponent in the power model (Point 4). </td></tr>
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5. Average values from step 4. </div>
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<i><span style="color: blue;">Note - Same algorithm as Coggan's Normalized Power.</span></i></div>
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6. Take the 4th root of step 5. This is the Lactate-Normalized Power. </div>
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<span style="color: blue;"><i>Note : The general idea behind normalizing is that a normalized power is an ESTIMATED power output that an athlete can maintain for the same physiological cost if the power output had been perfectly constant. Even though the approach wrt Coggan's NP calculation remains similar, where the difference lies is in that whereas NP s a 30 second rolling average, LT NP for running is a 120 second rolling average. In cycling, 30 seconds was found to be a response time for many physiological variables but some have come out and contradicted the usefulness of NP. I won't go into that.</i></span></div>
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7. Divide Lactate Normalized Power by Threshold Power from step 2 to get the Intensity Weighting Fraction. <br />
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<i><span style="color: blue;">Note : IWF is similar to the IF concept. </span></i></div>
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8. Multiply the Lactate Normalized Power by the duration of the workout in seconds to obtain the normalized work performed in joules. </div>
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<i><span style="color: blue;">Note : Key idea that can be lost on people here is that this is a normalized work in KJ and it is a TOTAL amount of work because the power equation in Step 2 used a metabolic efficiency to convert metabolic rate to power. </span></i></div>
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9. Multiply value obtained in step 8 by the Intensity Weighting Fraction to get a raw training stress value. </div>
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<span style="color: blue;"><i>Note : The resulting training stress, is by virtue of the math, expressed in work KJ . This may not relate to a TSS implementation of KJ because of the difference in mathematics involved (see above points). </i></span></div>
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10. Divide the values from step 9 by the amount of work performed during the 10k to 1 hr test (threshold power in watts x number of seconds). </div>
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<i><span style="color: blue;">Note : This step is basically again normalizing the amount of "normalized work" from the workout file to the amount of work from the LT test. </span></i></div>
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11. Multiply the number from step 10 by 100 to obtain the final training stress in GOVSS. </div>
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<i><span style="color: blue;">Note : The Coggan TSS is graded based on a similar idea that a 1 hour ride at FTP corresponds to 100 TSS. Therefore, GOVSS also becomes relative to the score of 100. </span></i><br />
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Hopefully the details in the algorithm show in what respects the GOVSS is different relative to a cycling based TSS.<br />
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<b>Implementation Examples</b><br />
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Below is an example of GOVSS calculated power for a runner performing intervals at 20 kph and running at about 199 SPM on a slope of 0%. The model uses a calculated frontal area of 0.48sq.m to estimate the aero contribution for power. You can play around with this power model <b><a href="https://runscribe.com/power/"><span style="color: red;">here</span></a></b>.<br />
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<tr><td class="tr-caption" style="text-align: center;">Fig 3 : Estimated GOVSS power to run at steady state at 20 kph on flat ground. <br />
Runner weight = 64 kg. Assumed wind = 0 kph. </td></tr>
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Below is a GOVSS PMC from my running data implemented in Golden Cheetah. This is just to show you an example.<br />
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<tr><td style="text-align: center;"><a href="https://2.bp.blogspot.com/-Bisms3gtNxQ/WgbDReLe1xI/AAAAAAAAGOw/RrXtdwmpurMFH-g-Ge_kOUwqCsDNTPa2ACLcBGAs/s1600/GOVSS%2BPMC.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="872" data-original-width="1540" height="226" src="https://2.bp.blogspot.com/-Bisms3gtNxQ/WgbDReLe1xI/AAAAAAAAGOw/RrXtdwmpurMFH-g-Ge_kOUwqCsDNTPa2ACLcBGAs/s400/GOVSS%2BPMC.JPG" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Fig 4 : Example of a GOVSS implementation in Golden Cheetah. GC's Triscore PMC uses GOVSS for runs. However, the GOVSS is possibly based on pace, rather than power. This needs confirming with Mark Liveradge. </td></tr>
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<b>Concluding Remarks </b></div>
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1. The GOVSS model takes into account the energy cost of running and how that varies as a function of running gradient, acceleration and wind resistance. For example, even in slow to medium speed running regimes as those in endurance running, the energy cost to tackle wind resistance is alone atleast 8%.<br />
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2. The GOVSS model gives the total energy expenditure of running per km and therefore, includes the effects of internal power needed to swing the arms and legs relative to center of mass (see <b><a href="http://www.georgeron.com/2017/09/the-physics-of-running-power.html"><span style="color: red;">Physics of Running Power</span></a></b>). Therefore, a GOVSS based power may end up being higher than a purely external power that does not account for these aspects.<br />
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3. GOVSS relies heavily on measured speed and gradient. Errors in measurement propagate to the calculated GOVSS power.<br />
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4. It still has be known whether the originators of some of the equations behind GOVSS intended to have it be applied to distances ranging from 3K all the way to the marathon. This point needs investigation and testing. </div>
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5. GOVSS for running and TSS for cycling use different mathematics and philosophy. TSS from cycling applied for running will be a mis-application, as implied by Andrew Coggan. </div>
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6. As with TSS, the GOVSS scoring scheme relies on base data from a sample population of runners who were tested under controlled settings in a laboratory. The statistical power of such fits and accompanying simplications are not always high Application of scoring metrics to a general population of athletes who are not tested in the laboratory come with the acceptance of a risk of deviation. </div>
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7. Scoring workouts to a curve based on 100 brings it's own debate. </div>
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For example, the popular notion of an FTP as corresponding to the maximum power that can be applied to a bike in approximately 1 hour has been challenged by Dr. Coggan himself several times. It is somewhat of an urban legend, popular but untrue. </div>
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The “approximately one hour” component of the definition has since been clarified to range between 30-75 minutes, depending on the individual. </div>
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Similarly, the CP reported by Stryd Powercenter is said to reflect a sustainable duration of about 50 minutes as per Stryd. </div>
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If the TTE in a cycling and running situation are different numbers and if this varies from individual to individual, one could then question the use of the value of 100 in the grading as that corresponding to a 1 hour duration. </div>
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In the absence of better alternatives to apply in an athlete's Performance Management chart, the GOVSS, TSS, RSS etc all can be used purely for their modeling value but practitioners must refrain from using them interchangeably. </div>
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<b>Reference</b></div>
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Calculation of Power Output and Quantification of Training Stress in Distance Runners: The Development of the GOVSS Algorithm (Skiba, 2006) : <a href="http://runscribe.com/wp-content/uploads/power/GOVSS.pdf"><span style="color: red;"><b>Link</b></span></a></div>
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Ronhttp://www.blogger.com/profile/16268869622833968439noreply@blogger.com0tag:blogger.com,1999:blog-4786784182488135171.post-39210120475965827622017-09-29T20:03:00.002+04:002017-12-11T22:53:07.938+04:00The Physics of Running Power <div dir="ltr" style="text-align: left;" trbidi="on">
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<b>Physics of Running Power </b><br />
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There is a certain theorm we were taught in school that goes something like this : The kinetic energy of a system of particles is the kinetic energy associated with the movement of the center of mass and the kinetic energy associated to the movement of the particles relative to the center of mass. </div>
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This is called Koenig's theorm.<br />
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In humans (bipeds), as the center of mass is propelled, fore and hind limbs are alternatively in contact with the ground, while the upper limbs oscillate freely both during the stance and the swing phase. This results in a linked multi-segment system.<br />
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Koenig's theorm can be applied to this system to model the mechanical work done in running. </div>
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<b>A. External Work </b><br />
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The human runner consists of a central trunk and <b>n</b> number of rigid segments each of mass <b>m</b>. The total mass <b>M</b> of the runner is considered to be lumped at center of gravity. </div>
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The <b>potential energy</b> while running is represented by <b>M.g.H</b>, where H is the vertical height of center of gravity from ground. </div>
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The <b>kinetic energy</b> of M is <b>1/2.M.Vcg^2 </b>where Vcg is the velocity of center of gravity.<b> </b></div>
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<i>The </i><b style="font-style: italic;">total external work Wext</b><i> comprises of the </i><b style="font-style: italic;">sum of kinetic and potential energy</b>. </div>
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<b>B. Internal Work</b></div>
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The <b>kinetic energy of ith segment</b> relative to body center of gravity is <b>1/2.mi.Vr,i^2 </b>where Vr,i is the linear velocity of that segment relative to body center of gravity. </div>
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The <b>rotational kinetic energy</b> of the ith segment relative to body center of gravity is <b>1/2.Ki.</b><b style="background-color: white; color: #222222; font-family: sans-serif; font-size: 14px;">ω</b><b>i^2 </b>where Ki is the radius of gyration of the ith segment around it’s own centre of mass and <span style="background-color: white; color: #222222; font-family: sans-serif; font-size: 14px;">ω</span>i is the angular velocity of that segment.</div>
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<i>The <b>total internal work Wint</b> is the summation of every segment's linear kinetic and rotational kinetic energies. </i></div>
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The computational scheme of calculating internal work assumes that energy transfers take place between segments of the same limb but not between limbs or between trunk and limb. </div>
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The total mechanical work done for running is then the simultaneous summation of total external work done and total internal work done for a particular instant. </div>
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I've represented this in a rather quirky picture with the physical equations underneath. </div>
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<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://4.bp.blogspot.com/-c-P_Hilo7EU/Wc5B8ScXzCI/AAAAAAAAGIY/-nWaqlDoLPAMNymueBN9ZLbolffe585pQCLcBGAs/s1600/Power_run_model.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="661" data-original-width="1085" height="387" src="https://4.bp.blogspot.com/-c-P_Hilo7EU/Wc5B8ScXzCI/AAAAAAAAGIY/-nWaqlDoLPAMNymueBN9ZLbolffe585pQCLcBGAs/s640/Power_run_model.png" width="550" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Fig 1 : Illustration showing the physical equations in external work and internal work as contributions to total work. Kleg here is a lumped stiffness constant for the leg. The yellow dot represents the center of mass and the vertical amplitude of it's movement represents vertical oscillation. </td></tr>
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<span style="text-align: justify;"><i>Power is the rate of doing work. </i></span><br />
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<span style="text-align: justify;">For example, if the runner in the picture commits 5 Joules of total mechanical work per kilogram every second, power = 5 Watts/kg (1 W = 1 Joule/second). </span><br />
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<b>C. How Mechanical Energy Changes With Running Motion</b><br />
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<i>A cycle of running motion from touchdown to touchdown of the same leg is called the stride.</i> Total mechanical work done can be resolved over many strides to see how it varies. </div>
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Some data from empirical testing is shown in Fig. 2 to get an understanding of change in work done. For an idea of magnitude of work, a scale of 100 Joules is shown on the right. </div>
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Observe the troughs and peaks in mechanical energy. The largest oscillations in energy come from the lower leg comprising of the thigh and the foot. Cavagna has written that the lower limb is itself responsible for about 80-90% of internal work. </div>
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The physical understanding here is that every time the leg is on ground around mid-stance phase, potential energy is at it's minima, therefore mechanical energy of center of mass also attains minima (red lines). </div>
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The maxima in mechanical energy of center of mass is attained at the peak of flight phase after a maximum in trailing foot pushoff work and when potential energy is at it's maxima (green lines). </div>
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<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://3.bp.blogspot.com/-iQ_P0GT2_qY/Wc5Iig8K3sI/AAAAAAAAGI8/6yKkQOY3ujEXoZpfOpuU_ZBWQoz7i2V2ACLcBGAs/s1600/Mechanical%2BEnergy.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="613" data-original-width="437" height="400" src="https://3.bp.blogspot.com/-iQ_P0GT2_qY/Wc5Iig8K3sI/AAAAAAAAGI8/6yKkQOY3ujEXoZpfOpuU_ZBWQoz7i2V2ACLcBGAs/s400/Mechanical%2BEnergy.png" width="285" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Fig 2 : Variation in mechanical energy of given sites in the human body as a function of running phase</td></tr>
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<i>Duty factor is the percentage of the total time between strides (or steps) that a single foot is on the ground. </i><span style="text-align: left;">Values for duty factor can vary from 50 to 90 percent, but are typically in the 60 to 80 percent range. </span></div>
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<span style="text-align: left;">As duty factor increases, an individual spends more time with his feet on ground and this has implications for the maxima in mechanical energy, or maxima in power. </span></div>
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<span style="text-align: left;">In other words, we might consider that it increases the time spent around the minima of mechanical energy, which thereby might decrease the overall mechanical energy of the center of gravity and overall running velocity. </span></div>
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<span style="text-align: left;">But given the same forward speed, the only way to decrease duty factor is to increase leg turnover rate, or cadence. </span></div>
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<span style="text-align: left;">Somewhere between too high a cadence and too low a cadence, most good runners will strike a balance to optimize ground speed, time spent on the ground and total mechanical work done. </span></div>
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<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://4.bp.blogspot.com/-82_dll7sGlU/Wc5tOr1sMXI/AAAAAAAAGJ0/H6sSyEoBEmYUlPClqQZ-WNQk2DbPf3NGwCLcBGAs/s1600/Wint%2BWext%2Brunning%2Bspeed.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="603" data-original-width="1092" height="220" src="https://4.bp.blogspot.com/-82_dll7sGlU/Wc5tOr1sMXI/AAAAAAAAGJ0/H6sSyEoBEmYUlPClqQZ-WNQk2DbPf3NGwCLcBGAs/s400/Wint%2BWext%2Brunning%2Bspeed.JPG" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Fig 3 : Variation of Wint, Wext and total work done at 3 different running speeds as a function of running phase</td></tr>
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<b>D. Average Work and Average Power</b><br />
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<span style="text-align: justify;">The "average work done" for a duration of say 10 minutes means resolving these peaks and valleys of an up and down work signal into it's average. </span><br />
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The mechanical work done curve can be transformed to a mechanical power curve by turning it into a rate per second. The average mechanical power is about resolving this curve of peaks and troughs to an average value representing that curve. </div>
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<span style="text-align: justify;">A math trick is to remember that the average value of any function can be represented in</span><span style="color: red; text-align: justify;"><a href="http://tutorial.math.lamar.edu/Classes/CalcI/AvgFcnValue.aspx"> <b><span style="color: red;">integral form</span></b></a></span><span style="text-align: justify;">. Integration can be electronically implemented. To clean up the resulting curves for presentation, signals can be sent through filters and/or computationally 'smoothed' over a desired interval of time. </span><br />
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<b>E. Mechanical Efficiency </b><br />
<span style="text-align: justify;"><br /></span><span style="text-align: justify;">Human beings have a maximal efficiency of converting chemical energy in food to contractile muscle work of about 25%. Let's call this contractile efficiency as Contr_Eff.</span><br />
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<span style="text-align: justify;">In human locomotion, mechanical efficiency can be expressed in terms of how much total work you put out relative to the net metabolic cost of running. This is Run_Eff. Walking efficiency can be labelled Walk_Eff.</span><br />
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<span style="text-align: justify;">The energy cost of running is expressed as ml O2 consumed per kg per m. This can be converted to a metabolic power (units of J per kg per m) using the conversion of volumetric oxygen to joules. The net metabolic cost is nothing but the cost of running minus the cost of stationary standing.</span><br />
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<i>The ratio of total mechanical work per kg per m (or total power) and the net metabolic cost of running is defined as the mechanical efficiency : </i></div>
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<a href="https://1.bp.blogspot.com/--ObF0V7OuN8/Wc5fU72oGwI/AAAAAAAAGJg/ww3Vmenkxnoayw8Fv1vS6rEpKTOaQB4zQCLcBGAs/s1600/Efficiency.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="70" data-original-width="365" height="60" src="https://1.bp.blogspot.com/--ObF0V7OuN8/Wc5fU72oGwI/AAAAAAAAGJg/ww3Vmenkxnoayw8Fv1vS6rEpKTOaQB4zQCLcBGAs/s320/Efficiency.JPG" width="320" /></a></div>
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Presumably, for well trained runners, efficiency is better than that for average runners. Such <b><a href="https://www.ncbi.nlm.nih.gov/pubmed/22634972"><span style="color: red;">has been said</span> </a></b>about East African runners.<br />
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Researchers like Cavagna have seen that there are 4 trends to efficiency when they looked at motion on level surfaces :<br />
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1. Run_Eff > Contr_Eff. Apprently, this is due to the storage and use of elastic energy through the action of recoil in the lower legs between each cycle of running. The wider the separation between both, the better is the uptake of recoil elements in running.<br />
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2. Run_Eff > Walk_Eff. This is presumably because potential and kinetic energy are out of phase in walking (rolling egg), but nicely synchronized and in-phase during running (think of a pogo stick).<br />
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3. Run_Eff increases linearly with speed, starting at 45% and maximising somewhere between 70-80%.<br />
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4. Walk_Eff maximises at intermediate speeds with values of 35-40%. It then falls off with further increase in speeds. This is interesting and possibly explains why the human considers running instead of walking when speed is past a certain threshold.<br />
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<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://2.bp.blogspot.com/-FkhAuSC1prA/WeOpYNZcstI/AAAAAAAAGLU/ZEWyXCkROig642NAiJTKLtBHKi-BRS0igCLcBGAs/s1600/Efficiency_1.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="604" data-original-width="620" height="311" src="https://2.bp.blogspot.com/-FkhAuSC1prA/WeOpYNZcstI/AAAAAAAAGLU/ZEWyXCkROig642NAiJTKLtBHKi-BRS0igCLcBGAs/s320/Efficiency_1.JPG" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Fig 4 : Variation of mechanical efficiency, internal (Wint), external (Wext) and total work (Wtot) and net metabolic energy cost (En exp) with speed in running and walking regimes. Source : Cavagna (1976).</td></tr>
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<b>F. Contribution of Internal Work to Total Mechanical Work</b><br />
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As shown in Fig 4, things really depend on the magnitude of running speed.<br />
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Researchers like Cavagna have shown that when the log of internal power is plotted against a log of speed, the resulting linear line approaches a slope of 2. Which simply means that internal power, as a crude approximation, may vary as a square of running speed.</div>
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For example, in the graph I have stuck below in Fig.5, one sees that beyond a speed of 17 kph, internal work starts to become a greater percentage of total work done and exceeds external work. </div>
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The magnitudes of numbers are interesting for perspective. Below 17 kph, external mechanical work (Wext) varies from a high of nearly 1.5 to a low of 1.1 J/kg/m. Internal mechanical work (Win) varies from a low of 0.5 J/kg/m to a high of 1.1 J/kg/m. </div>
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Above 17 kph, Wext varies from a high of 1.1 J/kg/m to a low of 1 J/kg/m while Wint increases from 1.1 J/kg/m to 1.6 J/kg/m.<br />
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<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://3.bp.blogspot.com/-w0YYHClhsdc/Wc5v2jDthzI/AAAAAAAAGJ8/jHoBEFhc0OcdiZ38NV2yggzskef_bvThwCLcBGAs/s1600/Internal%2Band%2BExternal%2BWork.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="585" data-original-width="514" height="400" src="https://3.bp.blogspot.com/-w0YYHClhsdc/Wc5v2jDthzI/AAAAAAAAGJ8/jHoBEFhc0OcdiZ38NV2yggzskef_bvThwCLcBGAs/s400/Internal%2Band%2BExternal%2BWork.png" width="351" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Fig 5 : Plot of changes in Wint (black) and Wext (red) as fractions of Wtot (green) over a continuum of running speeds</td></tr>
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For this example, if speed were a modest 7:00 min/mile (13.8 kph), this means that Wint is around 0.7 J/kg/m and Wext is around 1.3 J/kg/m. In other words, the Wint and Wext % of total mechanical power is 32% and 68% respectively. </div>
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<span style="text-align: justify;">Presumably this means that short distance, maximal intensity runners might benefit in knowing the magnitude of internal work done, or internal power. It also means a 10K runner running at 7:00 min/mile spends 30% of his total power internally. That's a sizeable chunk of running workload. </span></div>
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<b>G. What Do Running Powermeters Measure and Not Measure? </b><br />
<span style="text-align: justify;"><br /></span><span style="text-align: justify;"><b>What they Measure : </b></span><br />
<span style="text-align: justify;"><br /></span><span style="text-align: justify;">Running powermeters such as the Stryd and Runscribe are inherently </span><span style="text-align: justify;">9-axis IMUs. By combining it with a barometric sensor, you get the ability to measure acceleration (X,Y,Z) and orientation but also altitude by measuring the atmospheric pressure and using the difference between that and sea level atmospheric pressure. This is called pressure altitude. </span><br />
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<span style="text-align: justify;">Among the electrically talented, these chips are also called TenDOFs or '10-degree of freedoms' which is a fusion of 3 chipsets and a barometer which communicate to each other through sensor fusion algorithms (like a Kalman filter). The function of each of the chips are summed up below :</span><br />
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3 DOF Accelerometer : Senses acceleration in 3 directions - X, Y, Z</div>
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3 DOF Gyroscope : Senses angular velocity in 3 directions - Roll, pitch, yaw</div>
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3 DOF Magnetometer : Senses true orientation in 3 directions (compass)</div>
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Averaging the data that comes from the 3 chipsets is said to produce a better estimate of motion than that obtained using accelerometer data alone.</div>
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<b><span style="color: red;"><a href="https://www.digikey.com/en/articles/techzone/2012/jul/a-designers-guide-to-mems-sensors"><span style="color: red;">This is a great page</span> </a></span></b>to learn about how accelerometers work. If you want to get a practical idea of how an accelerometer works, you can play around <b><a href="https://play.google.com/store/apps/details?id=com.google.android.apps.forscience.whistlepunk"><span style="color: red;">with this app</span></a></b> Google built. Basically it uses the sensors in your phone to give you an X and Y axis acceleration while running, but you're on your own about what to do with it.<br />
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Runscribe also has a <b><a href="https://runscribe.com/data-tools/"><span style="color: red;">RawData tool</span> </a></b>to inspect the raw file for the original signals. This forms part of their Science Package for researchers</div>
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Devices like Stryd are coded with a sleep mode when not active to save battery power. They 'wake up' when motion is sensed and start collecting run data only when a certain threshold in motion is passed.</div>
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The hard part is figuring out the coding. Because the raw data from 10dof's can be noisy, they have to be filtered to present meaningful motion data. </div>
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<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://1.bp.blogspot.com/-WrO85y-3YNE/Wf9M4SIw_dI/AAAAAAAAGM4/Qlue0wNfwxY8XxzpMn6I79ZjuDtdWOHuwCLcBGAs/s1600/Capture.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="573" data-original-width="919" height="248" src="https://1.bp.blogspot.com/-WrO85y-3YNE/Wf9M4SIw_dI/AAAAAAAAGM4/Qlue0wNfwxY8XxzpMn6I79ZjuDtdWOHuwCLcBGAs/s400/Capture.JPG" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Fig 6: An image explaining the components on a GY-80 10DOF chipset.</td></tr>
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<span style="text-align: justify;">Since an accelerometer can integrate acceleration to get velocity and double integrate to get position, algorithms involving changes in velocity and position are easily implemented. </span><br />
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<span style="text-align: justify;">Focusing on kinematics means these devices do not use any hardware to actually measure force and therefore save on lot of cost and footprint size. </span><br />
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Fig 7: An image showing the assembly view of a Stryd powermeter</div>
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<span style="text-align: justify;">Unlike cycling powermeters, running powermeters have zero strain gages, therefore there is no direct measurement of force. The device simply uses a model that uses measured parameters to approximate running power. </span><br />
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<tr><td style="text-align: center;"><a href="https://2.bp.blogspot.com/-EumBWrGM22E/WgWHWlT0TTI/AAAAAAAAGOA/dKrOAEOJ3AsHNHcNh-8pZ3qnDPIrotm2ACEwYBhgL/s1600/Capture7.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="679" data-original-width="1040" height="260" src="https://2.bp.blogspot.com/-EumBWrGM22E/WgWHWlT0TTI/AAAAAAAAGOA/dKrOAEOJ3AsHNHcNh-8pZ3qnDPIrotm2ACEwYBhgL/s400/Capture7.JPG" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Fig 8 : A close look at the electronics inside a Stryd powermeter</td></tr>
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<span style="text-align: justify;">Now precisely what algorithm the Stryd uses to measure power is not known. <b><a href="https://www.stryd.com/support#garmin"><span style="color: red;">On their website</span></a></b>, in a little blurb within the FAQ section, Stryd claims that by "approximating" the time-course of ground reaction force in the horizontal and vertical direction and multiplying it with velocity components integrated from acceleration, they can calculate power. This is shown in a screen capture from one of Stryd's Youtube videos.</span><br />
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<tr><td style="text-align: center;"><a href="https://2.bp.blogspot.com/-gKcGi3adyhI/WgNNl8Cog7I/AAAAAAAAGNc/d0CM1Wp9VAEA3oDBthWDL1ZXrCCR_pBNwCLcBGAs/s1600/Vertical%2Band%2Bhorizontal%2Bforces.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="471" data-original-width="846" height="222" src="https://2.bp.blogspot.com/-gKcGi3adyhI/WgNNl8Cog7I/AAAAAAAAGNc/d0CM1Wp9VAEA3oDBthWDL1ZXrCCR_pBNwCLcBGAs/s400/Vertical%2Band%2Bhorizontal%2Bforces.JPG" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Fig 9 : An image from Stryd's Youtube video featuring Dr. Andrew Coggan which shows the horizontal and vertical ground reaction force on the left and the accelerometer derived 'shape and form' of those forces on the right. Since the time Stryd dropped a chest mounted sensor for a footpod, they have claimed that the reproduction of ground reaction forces have become better (link in my post) </td></tr>
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<span style="text-align: justify;"> </span><br />
<span style="text-align: justify;">The methodological debate here is how the model is approximating the ground reaction forces and with what level of accuracy does it capture that data for level and gradient running and for soft vs hard surfaces. We will not know the answer to that. That is the secret sauce after all.</span><br />
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<span style="text-align: justify;"><span style="text-align: justify;"><b><a href="http://www.georgeron.com/2017/04/actionable-intelligence-for-running.html"><span style="color: red;">I was told</span></a></b> that values of external power had been calibrated against force plate treadmills in the laboratory within a range of 10 cm of shoe mounting height. We are </span><b style="text-align: justify;"><a href="https://www.dcrainmaker.com/2015/01/stryd-first-running.html"><span style="color: red;">told by others that the data</span></a></b><span style="text-align: justify;"> is reasonably accurate. </span></span><br />
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<span style="text-align: justify;">Stryd resolves power into a horizontal power and a form power, the latter which represents the cost of perpendicular bouncing in place. Stryd is marketing this as 'wasted' effort. The sum of horizontal and vertical powers become total power. </span><br />
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<span style="text-align: justify;">Other power models such as that used by Garmin take a different approach and they swear by the accuracy of their models.</span><br />
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<span style="text-align: justify;">If two powermeters yield different values of calculated power, we can assume that majority of the differences stem from precisely what algorithm is being used. The rest of the differences are probably due to how the signals are filtered, processed and implemented in code and smoothed before they are presented to the user. </span><br />
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<span style="text-align: justify;">I've </span><b style="text-align: justify;"><a href="http://www.georgeron.com/2017/03/actionable-intelligence-for-running.html"><span style="color: red;">conducted experiments</span></a></b><span style="text-align: justify;"> with the Stryd during a laboratory VO2max test and there was reasonable correlation between power and metabolic cost. I do not know if similar correlational power would exist in outdoor running with weather and running surface factored in. Stryd has conducted an outdoor VO2 test using a metabolic cart loading onto a pickup and claim that power tracks running economy. </span><br />
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<span style="text-align: justify;">Because external power is relatively more "stable" than heart rate and pace, it becomes a "useful" perhaps 'objective' parameter to design stress scores and performance management charts around. As a messenger of training intensity and training load, it is useful. </span><br />
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There are a few key things to question when using low cost accelerometry to study human motion, particularly the messy problem of running.<br />
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1. Inter-device reproducability : Given a bunch of running powermeters from the same OEM, to what degree will each device converge upon a similar value given a controlled running task?<br />
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2. Intra-device reproducability : Given several identical running tasks over a period of time, to what degree will a given device reproduce metrics over that time?<br />
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3. Validity : Given a "measurement" from a running powermeter, to what degree are the results meaningful , i.e what co-relation do they have in relation to real physiological demands of running?<br />
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Criterion validity measures how well the data corresponds to gold standards of measuring the same thing. Convergent validity is the extent to which the measurements made by the sensor are associated with those made with other assessment methods that intend to measure the same or similar aspects.<br />
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<b>Where to Apply the Sensors : </b><br />
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There are devices that measure running power hitting the market that are affixed to different positions on the body. Some, like Garmin's pods, are affixed to the shorts. Some, like the Runscribe and Stryd, are mounted on the shoes, either at the heels or on the laces. An earlier version of the Stryd, called Pioneer, came as a chest mounted strap.<br />
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There is a debate on what is the best position. For consistent measurement, mounting at the shorts and the chest is said to be problematic since the pod also exhibits motion when the fat layer and short waistline moves relative to the core of the body.<br />
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However, using the same argument, the Stryd foodpod exhibits relative motion on certain shoes as the foot-mount bracket "slips" on the laces. I suppose any mounting position, if properly controlled, is valid. But it does seem that the foot-mounting positions seems to be the least worst among all three positions.<br />
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<span style="text-align: justify;"><b>What They Don't Measure : </b></span></div>
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Estimating the true workload of running is a tricky business due to a couple of reasons.<br />
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1) First, in level running at constant speed, there is a substantial recovery of elastic energy at each stride, that brings about a corresponding reduction in the mechanical work performed by the active muscles. In other words, when your muscles shorten to propel you forwards, some of the energy it uses has been stored from the previous stretch cycle.<br />
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On non-level running surfaces, the portion of negative eccentric work starts to become a significant factor on appreciably steep downhill slopes, where the leg muscles are working to both brake and stabilise the human runner from toppling forward. In this regime, use of elastic recoil maybe lesser than on level running.<br />
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For these reasons, it is inappropriate and erronous to assume a running efficiency value equal to that of purely isotonic work (i. e. on the order of 25 %).<br />
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Powermeters can't tell you want is truly going on with the elastic recovery portion of running, however some algorithms like Leg Spring Stiffness (LSS) maybe a step in this direction. One also has to realize that LSS maybe subject to various interpretations depending on the mathematical implementation. <span style="color: red;"><b><a href="http://www.georgeron.com/2017/01/running-science-part-1-ground-contact.html">See this post</a></b> </span>for an overview.<br />
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2) Secondly, powermeters do not sense internal power. In literature, researchers have summed up the kinetic energy needed to move all important limbs in running, multiplied them by two for contra-laterality and divided by the stride time (2 steps) to express that in terms of power (W).<br />
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A problem with the above calculation is that it might over-estimate the amount of actual muscular power. Consider the case where if the energy can be "transferred" from one limb to the other due to speed and momentum without any muscular contraction actually happening, the total work you calculate is greater than that actually being used.<br />
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Sensing internal work is most likely hardware and computational intensive. Studies show that for the same running speed, different methods of calculating internal power yield around a 1000% difference between highest and lowest values. </div>
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3) Running powemeters do not factor in wind and therefore, any extra workload to move against stiff aerodynamic resistance is unaccounted for.<br />
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For example, in metabolic terms, a +4.5 mph headwind translates to a +5% increase in VO2 according to data from Dr. Jack Daniels. For maintaining the same pace, the running powermeter will "lag" behind metabolic intensity because wind resistance is not factored for.<br />
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Since fast runners "create" their own wind even in calm conditions, not being able to assess a true intensity of working in the fluid medium could be an issue, particularly in places with high air densities and air pressures. This might present a problem to a runner with an inflexible pacing plan.<br />
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4) Similarly, external power does not factor in a temperature. It is left to the runner to calibrate a power based pacing strategy against the ambient temperature and humidity.<br />
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While power is said to be "objective", it does not in any way diminish the need for the runner to calibrate against perceived effort and possibly, even heart rate. A sensible approach is one that is holistic, especially if runner in question is someone known to push their body to the extremes. </div>
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<b>H. The Implications of Not Knowing a "Total" Running Power</b></div>
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1) <i>One does not know the true mechanical workload of a run. </i><br />
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True workload is true total workload. Unless you're a kangaroo, humans commit internal work to run. How an algorithmic estimation fares against true intensity among different runners, of different age groups, of different geographical backgrounds, on different terrain - all carry an uncertainty to it. At the heart of why you would want to measure the intensity of an exercise is the ability to get valid information.<br />
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2) <i>For faster runners, not being able to assess Wint means not knowing a sizeable proportion of total workload that may contribute (or deduct) from movement efficiency. </i><br />
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Maximal running elicits high amounts of joint torque and power in fractions of seconds. Short distance track runners who use a substantial portion of limb power to propel forwards are probably better off with traditional or slightly more advanced techniques of training to extract maximum potential. </div>
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3) <i>Metrics using external mechanical power may not actually explain performance differences among runners and may not be helpful to address biomechanical issues.</i><br />
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The complexity with running lies in the fact that for the same speed, there are wide variations in economy among runners. We still don't exactly know what makes East African runners so good at what they do but various theories have been provided, one of them being running economy.<br />
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Traditionally, economy has been measured in metabolic terms. For example, if you need 200 ml O2/kg/min to run at 7:00/mile, that's your running economy at that speed.<br />
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With the coming of power sensors, a commercial market of sorts has opened up to introduce new ways to interpret this data. There's a plethora of metrics thats pouring out from these efforts.<br />
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It is my humble opinion that some caution must be exercised when basing value judgements using efficiency metrics calculated using external power.<br />
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For example, Stryd's analysts <b><a href="https://blog.stryd.com/2017/10/04/stryd-brings-the-lab-to-the-road/"><span style="color: red;">write</span></a></b> that running efficiency is 20-25% and that 40% efficiency is "inhuman" without distinguishing between a total running output and external running output. Expressing clarity in what goes into the effiiency calculation avoids confusion. As we have seen before, mechanical efficiency can be substantially different based on speed, running surface and elastic energy recoil. </div>
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In another example, Andrew Coggan and TrainingPeaks have introduced a "novel" metric called <b>Running Effectiveness</b>. This is a complex metric that is based on a ratio of speed (in m/s) over external power to weight ratio (W/kg). </div>
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Notwithstanding the need to get several things correct in this ratio and filter for course and weather decoupling to get a sensibly stable number, it must be borne in mind that the power in the denominator is still an "external power" only. </div>
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Therefore, trying to use Running Effectiveness for basing value judgements about runners maybe methodologically flawed. Depending on speed, a major chunk of total power - internal power - is not factored in. <br />
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Similarly, the inverse of the above metric is packaged into a metric called <b>Energy Cost of Running (ECOR)</b> by the authors of the book <i>Secret of Running</i>. In the book, they implore runners to monitor this metric and try to reduce energy cost.<br />
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Personally, from more than 10 months of running data, I do not have confidence that any decrease I'm seeing in ECOR isn't simply a function of normal variability in the data. Therefore, the analyst must be aware that a change that is less than or within the tolerance attributable to device variability is not conclusively a positive change purely from training.<br />
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The general advice to reduce cost of running is absolutely well taken, but hang on. Again, ECOR is calculated using only external power and presents a possibly limited picture of true cost. If you accomplish reducing ECOR in your runs, so what? Is an improvement in ECOR actually tied to something happening within the body?<br />
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Therefore, I do not think it is helpful to use a surrogate cost of running based on external power for cross-comparisons when you do not address and control for a major chunk of running biomechanics which is the movement of the limbs.<br />
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As Donald Rumsfeld once remarked, there's known unknowns and unknown unknowns. Internal power is a known unknown. The unknown unknown is what fraction of total power the internal power really is and how that varies among people. A reduction in ECOR or an increase in RE may not disclose the entire picture.</div>
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Carrying an evidence based approach in the application of such metrics is advisable. For example, a validation study could be conducted on an appropriate sample of runners to assess the correlational power of metrics like Running Effectiveness in relation to being able to explain actual performance variations among runners.<br />
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<b><u>ALSO READ :</u></b><br />
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<b><a href="http://www.georgeron.com/2017/12/stryd-running-power-model.html"><span style="color: red;">Technical Review of the Stryd Power Model</span></a></b><br />
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<b>REFERENCES</b><br />
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External, internal and total work in human locomotion.<br />
P. A. Willems, G. A. Cavagna, N. C. Heglund<br />
J Exp Biol. 1995 Feb; 198(Pt 2): 379–393.</div>
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Ronhttp://www.blogger.com/profile/16268869622833968439noreply@blogger.com0tag:blogger.com,1999:blog-4786784182488135171.post-29239392691622684702017-09-25T00:24:00.003+04:002017-10-04T10:11:33.391+04:00Berlin Marathon 2017 : Estimating Eliud Kipchoge's Running Power <div dir="ltr" style="text-align: left;" trbidi="on">
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<span style="font-family: inherit;">Eluid Kipchoge pounded out the tarmac at the Berlin Marathon today with the 5th fastest marathon time of 2:03:32. </span></div>
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<span style="font-family: inherit;">Berlin was wet and windy this year and Kipchoge had no benefit of drafting in the latter stages. We know that cost of running against the wind becomes significant after 20kph. </span><br />
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</span> <span style="font-family: inherit;">The extra power to run against the wind and maintain pace on wet roads may partly explain the huge difference in finishing time between Nike's Sub2 attempt at the Monza track and today's IAAF sanctioned marathon. Conditions</span><span style="font-family: inherit;"> also meant Kipchoge didn't even beat his own personal best of 2:03:05 today at the marathon. </span><br />
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<span style="font-family: inherit;">The average pace from the determined veteran especially at the middle of the race today was astonishing, so I decided to take a stab at estimating running power from pace data. </span><br />
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</span> <span style="font-family: inherit;">Many thanks to Dr. Pietro Prampero from beautiful Italy for helping out with some of the math surrounding metabolic power. </span><br />
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<span style="font-family: inherit;">Earlier in the day, Ross Tucker posted Kipchoge's 5km splits overlaid on other key pieces of information on his <b><a href="https://twitter.com/Scienceofsport"><span style="color: red;">Twitterfeed</span></a></b>. These are possibly unofficial, but to dive into the numbers, they'll do fine for now. Many thanks to him as well.</span></div>
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<tr><td class="tr-caption" style="text-align: center;">Fig 1 : 5K split data for Kipchoge at Berlin Marathon 2017. Courtesy Ross Tucker, Science of Sport.</td></tr>
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<b><u>Method 1 : Estimating Kipchoge's Marathon Power from Riegel Profile</u></b></div>
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<tr><td class="tr-caption" style="text-align: center;">Fig 2 : Riegel slope for Kipchoge's best times. Resulting fatigue factor = 1.0236.</td></tr>
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Kipchoge's best times at the 10K, Half Marathon and Marathon distances are 00:28:11, 00:59:25 and 2:03:05 respectively. Using those times to construct his Riegel fatigue factor on the Ln Speed vs Ln Distance graph gives a result of 1.02369 (Fig 2). Contrast this with the general men's <b><a href="http://www.georgeron.com/2017/09/kipchoge-running-power-marathon.html"><span style="color: red;">road racing Riegel fatigue factor</span></a></b> of 1.0497.<br />
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<span style="font-family: inherit;">Using this fatigue factor to predict Kipchoge's absolute best time from the half marathon time of 00:59:25 results in 2:00:47! This is just 22 seconds more than the actual time he ran at Monza during Nike Breaking2's 'deeply pampered' attempt. So we know this is somewhat possible but somewhat also impossible on an IAAF course.</span></div>
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<span style="font-family: inherit;">Some amateur predictions of best power to weight ratios in the different classes of runners was posted on Stryd's facebook page in September. The numbers of best in class power to weight ratios were obtained using formulae popularized in the Secret of Running book. A screenshot of the exact posting is below for reference in Fig 3 (click to zoom in). </span></div>
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<span style="font-family: inherit;">If we assume that these best in class ratios are for external power only, then we can assume that Kipchoge's 10K time of 00:28:11 might be very close to 100% of his critical power. If Kipchoge's weight is 56kg, this results in a <b><span style="color: red;">10K power of 386 W for 6.9W/kg</span></b>, equalling the table of best in class ratios.</span></div>
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<span style="font-family: inherit;">If that's the case, the recommended pacing from Stryd's guideline for the marathon is 89.9% of 100% CP which is the 10K power. Using 10K power of 386W, this results in a <span style="color: red;"><b>marathon external power of 347 W</b></span>.</span></div>
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<span style="font-family: inherit;">Is this predicted by Riegel? Using the uncorrected Riegel exponent of -0.0236 applied to an assumed half marathon power of 364 W (6.5W/kg) results in a <b><span style="color: red;">Riegel predicted marathon power of 352 W</span></b>.</span></div>
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<tr><td class="tr-caption" style="text-align: center;">Fig 3 : Power to Weight ratios for different classes, posted by Michael Arend on <a href="https://www.facebook.com/photo.php?fbid=1715567668474922&set=p.1715567668474922&type=3&theater&ifg=1"><b><span style="color: red;">Stryd's Facebook forum</span></b></a>.</td></tr>
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<b><u>Method 2 : Estimating Kipchoge's Running Power from Metabolic Power</u></b><br />
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<span style="text-align: center;">For outdoor running, the product of the mass and distance normalized energy cost of outdoor running (<span style="font-family: inherit; text-align: left;">Cr</span><span style="font-family: inherit; font-size: x-small; text-align: left;">out</span>), and the forward ground speed (v) yields the net metabolic power necessary to move at the speed in question.</span><br />
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</span> <span style="text-align: center;">Gross Metabolic Power, W/kg = </span><span style="text-align: justify;">Cr</span><span style="font-size: x-small; text-align: justify;">out </span><span style="text-align: center;"> x v ..... 1) </span><br />
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<span style="font-family: inherit;">where units are :</span></div>
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<span style="font-family: inherit;"><span style="text-align: justify;">Cr</span><span style="font-size: x-small; text-align: justify;">out </span><span style="text-align: justify;">in </span> J/kg.m</span></div>
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<span style="font-family: inherit;">v in m/s</span></div>
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</span> <span style="font-family: inherit;">The metabolic power is required to reconstitute the ATP utilised for work performance, regardless of the actual oxygen consumption which may be equal, greater, or smaller than the metabolic power itself.</span><br />
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</span> <span style="font-family: inherit;">During constant speed running on flat compact terrain the net energy cost of running (above resting, Cr) is independent of speed and amounts on an average to 4 J/kg.m [Lacour and Bourdin, Eur. J. Appl. Physiol., 2015]. This is strictly true for treadmill running in which case the energy for overcoming the air resistance is nil.</span><br />
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</span> <span style="font-family: inherit;">When running on terrain in the absence of wind, the overall Cr<span style="font-size: x-small;">out</span>, including the energy expenditure against the air resistance is larger than that applying to treadmill running (Cr_<span style="font-size: x-small;">Tr</span>) by an amount proportional to the square of the air velocity (which in this case is equal to the ground speed, v):</span><br />
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</span><span style="font-family: inherit; text-align: center;">Cr</span><span style="font-family: inherit; font-size: x-small; text-align: center;">out</span><span style="font-family: inherit; text-align: center;"> </span><span style="font-family: inherit; text-align: center;"> = Cr_</span><span style="font-family: inherit; font-size: x-small; text-align: center;">Tr </span><span style="font-family: inherit; text-align: center;"> + k’.v</span><span style="font-family: inherit; font-size: 18.6667px; text-align: left;">²</span><span style="font-family: inherit; text-align: center;"> ..... 2) </span><br />
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</span> <span style="text-align: left;">The values of the constant k’ (J.s2 .m-3.kg-1) reported in the literature range from ≈ 0.012 [Pugh, J. Physiol., 1971, di Prampero J. Sport Med.,1986] to ≈ 0.018 [Tam et al., Eur. J. Appl. Physiol., 2012].</span><br />
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Based on average Berlin marathon speed for Kipchoge and an assumed average k’ = 0.015, <span style="text-align: center;">Cr</span><span style="font-size: x-small; text-align: center;">out</span> = 4.49 J/kg/m. This cost of running is assumed to stay constant over the duration of the marathon, but in reality, it may even increase. </div>
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Equation 2) also shows that the effects of the air resistance are not as high as one would expect; indeed, up to a speed ≤ 20 km/h, the energy expenditure against the wind accounts for ≤ 9 – 14 % of the total cost.</div>
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To establish a time of 2:03:32, Kipchoge ran at an average pace of 5.7 m/s. If we assume this to have been his maximum aerobic speed, vaer,max, his maximum aerobic metabolic power can be estimated from the relation :</div>
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<span lang="EN-GB" style="text-align: center;"><span lang="EN-GB"><span lang="EN-GB" style="text-align: center;"><span lang="EN-GB"><br />
</span></span></span></span><span lang="EN-GB" style="text-align: center;"><span lang="EN-GB"><span lang="EN-GB" style="text-align: center;"><span lang="EN-GB">Maximum Gross Metabolic Power, W/kg = </span></span><span lang="EN-GB" style="font-family: inherit; text-align: center;"><span lang="EN-GB" style="font-size: 12pt;">(v</span><span lang="EN-GB" style="font-size: 10pt;">aer,max</span><span lang="EN-GB" style="font-size: 12pt;"> x </span></span><span style="font-family: inherit; text-align: center;">Cr</span><span style="font-family: inherit; font-size: x-small; text-align: center;">out</span><span style="font-family: inherit; text-align: center;"> ) / F ...... 3)</span></span></span><br />
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</span> <span style="text-align: center;">where F is the fraction of maximum metabolic power.</span><br />
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Elite marathoners are known to utilise 75-85% of their aerobic maximums for the marathon. An assumed F = 0.85 means Kipchoge's maximum gross metabolic power = 30 W/kg.<br />
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</span> Assuming 20.1 Joules of energy per ml of O2 , Kipchoge's VO2max = <b><span style="color: red;">89.7 ml O2/kg/min.</span></b><br />
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</span> <span style="font-family: inherit;">Also, if we assume a modest conversion efficiency of 23%, then :</span></div>
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<b><span style="font-family: inherit;">Kipchoge's Mechanical Running Power = 23% of 30 W/kg = <span style="color: red;">6.9 W/kg</span></span></b></div>
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<span style="font-family: inherit;">A lower fraction F will mean higher mechanical power demand to run at this speed, so for the same metabolic efficiency, it benefits Kipchoge to operate at a high fraction of his aerobic potential. This shows the importance to elite marathoners of increasing F and decreasing <span style="text-align: center;">Cr</span><span style="font-size: x-small; text-align: center;">out</span><span style="text-align: center;"> t</span>o it's minimum possible. </span></div>
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<span style="font-family: inherit;">How much optimization is possible becomes the eternal question for discussion. </span></div>
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<b><span style="font-family: inherit;"><u>Method 3 : Estimating Kipchoge's Running Power from Regression Curves</u></span></b></div>
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<span style="font-family: inherit;">The Berlin Marathon course is more or less flat, with some 35m of elevation gain in total. Since power is more or less directly proportional to speed on flat terrain, I needed a simple regression equation expressing power as a function of pace for running.</span></div>
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<span style="font-family: inherit;">Diving into old research papers, Cavagna et. al's 1967 work on external work in level running is not a bad place to start.</span></div>
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<span style="font-family: inherit;">Cavagna wrote then that in running, the potential and kinetic energy of the body do not interchange but are simultaneously taken up and released by the muscles with a rate increasing markedly with the speed.</span></div>
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<span style="font-family: inherit;">If that is correct, then total external mechanical work done during running must be in phase. In other words, external work done is approximately equal to sum of work done in forward motion and work done against gravity. </span></div>
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<b><span style="font-family: inherit;">W<span style="font-size: x-small;">ext </span>~ Work done to lift center of mass + Work done to move forward</span></b></div>
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<span style="font-family: inherit;">From experiements done on experienced males performing constant pace runs in a heavily instrumented indoor corridor, Cavagna et.al plotted a graph of cal/kg/min (external power) vs average forward speed and found the following relationships (filled dots represent running) : </span></div>
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<tr><td style="text-align: center;"><a href="https://4.bp.blogspot.com/-PQEEdzuKoY0/WcgLOyIMwcI/AAAAAAAAGGc/2QGdF1YCXdMPtrJMf86E8I8woqivSlC6wCLcBGAs/s1600/4.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><span style="font-family: inherit;"><img border="0" data-original-height="661" data-original-width="868" height="352" src="https://4.bp.blogspot.com/-PQEEdzuKoY0/WcgLOyIMwcI/AAAAAAAAGGc/2QGdF1YCXdMPtrJMf86E8I8woqivSlC6wCLcBGAs/s400/4.JPG" width="400" /></span></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><span style="font-family: inherit;">Fig 3 : Empirical data for pace vs external mechanical power for experienced runners. Cavagna (1976). </span></td></tr>
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<span style="font-family: inherit;">With a little bit of graphics trick, the equation of the regression line was extracted as :</span></div>
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<span style="font-family: inherit; font-size: 14pt; vertical-align: baseline;">Cal/kg/min = (4.8223 x km/hr speed) + 8.9124</span><br />
<span style="font-family: inherit; font-size: 14pt; text-align: left;">R² = 0.9997</span></div>
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<span style="font-family: inherit;">Based on splits and an easy regression formula from Cavagna's data, the table of estimated power/weight values for 42.195 kms converted to external mechanical power, Watts/kg are shown below :</span></div>
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<tr><td style="text-align: center;"><a href="https://3.bp.blogspot.com/--3u-lWwnpn8/WclEYZEI9eI/AAAAAAAAGHM/3U4lVEBUCSQNur85cCPHcEPBy2C6wDhowCLcBGAs/s1600/Running%2BPower_Kipchoge.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><span style="font-family: inherit;"><img border="0" data-original-height="280" data-original-width="513" height="217" src="https://3.bp.blogspot.com/--3u-lWwnpn8/WclEYZEI9eI/AAAAAAAAGHM/3U4lVEBUCSQNur85cCPHcEPBy2C6wDhowCLcBGAs/s400/Running%2BPower_Kipchoge.JPG" width="400" /></span></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><span style="font-family: inherit;">Fig 4 : Table of calculated power to weight ratio's (external) per given amount of distance at the Berlin Marathon 2017. </span></td></tr>
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<span style="font-family: inherit;">The power to weight numbers are truly astonishing as to seem almost unlikely, since it is based on a trend line. Therefore, I call it a 'high' estimate in the column.</span><br />
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</span> <span style="font-family: inherit;">From Cavagna's own graph, you can see a variance of 0.7 W/kg for the same running speed of 20 kph. So at the low end, you end up with a mechanical power to weight ratio of <b><span style="color: red;">6.8 W/kg</span></b>. This more or less matches the estimate using Method 2. </span></div>
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<span style="font-family: inherit;">I think the best we can do right now is express mechanical power within a range, the large uncertainty is justified due to insufficient empirical data. However, it is a first good guess.</span><br />
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<span style="font-family: inherit;">If Kipchoge's weight is assumed to be 56 kg, this results in the following range for power, accomodating all the numbers from Methods 1-3 :</span></div>
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<span style="color: red; font-family: inherit; font-size: large;">Range, Mechanical Power (Kipchoge) = 350-420 Watts</span></div>
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<span style="font-family: inherit;"><b><u>Weaknesses of Various Estimation Methods</u></b></span></div>
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The estimations are not without issues : </div>
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1) <b>Riegel factor mis-predictions </b>: The external mechanical power results from Method 1 are constructed using time prediction Riegel formulas applied to power. It is understood that this is external power as distinct from internal power. Riegel fatigue factors are specific to Kipchoge but the Riegel method has been known to sometimes over-predict and sometimes under-predict actual timings. One would assume the same inaccuracies to fall through to power. This is specifically because course and weather patterns are not accounted for in these simple formulae.<br />
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2) <b>Validity of Riegel exponent for power</b> : While power is proportional to pace, we don't know if the Riegel exponents can be applied to external mechanical power in the same way as it is done to time. There is no evidence that external power scales the same way for world class runners. Do good runners get better at running faster but while conserving mechanical power and increasing mechanical efficiency? Without answers to such questions, a blind application of Riegel exponents to scale external power to world class runners maybe erronous.<br />
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3)<b> Power to weight ratios for world class runners</b> : A<span style="font-family: inherit;">ny classification of external mechanical power as a function of body mass^1 for world class runners vs recreational runners done by individuals is unvalidated by science. To generate these tables, a Riegel exonent of -0.07 is also used by the creator of the tables which maybe erronous. The issue is that we are not sure if it's external mechanical power alone that separates the best from the rest or if other factors such as mechanical efficiency also help explain the differences. It goes back to all the complexities behind what makes good runners or really good runners the way they are. We are also not sure if body mass^1 in the power to weight ratio number is correct. We might find that an allometric exponent applied to body mass in the ratio might have a higher correlation to metabolic cost. Physically, this might mean that world class runners, especially east Africans, who are smaller in stature, might exhibit higher mechanical efficiencies while running.</span><br />
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4) <b>Assumptions of VO2 utilization and metabolic efficiency</b> : Methods 2-3 make assumptions about fractional VO2 utilization and metabolic efficiency that seem almost arbitrary. There is no empirical data specific to Kipchoge to back this up. I'm also not sure if runners like Kipchoge can getaway with a lower VO2 utilization by relying heavily on carbohydrate rich drinks throughout the run. 85%, while in the range of some papers in literature, is on the high side. Is 85% of VO2 for a marathon sustainable in practice?</div>
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5) <b>Savings due to pacers</b> : The calculation neglects a shielding factor in the beginning of the race due to the formation of pace makers. Therefore, it speaks nothing about the savings from those initial stages of the race. Fluid phenomena can only be simulated using fluid codes that are expensive and take time. An example is <b><a href="https://www.linkedin.com/pulse/uncovering-aerodynamic-trickery-behind-nikes-breaking-ferguson"><span style="color: red;">Siemens' fluid simulation of Nike's Breaking2</span></a></b> attempt published on Linkedin.<br />
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6) <b>Savings from shoes</b> : Any effect the shoes had on his run is neglected. Is there some hidden juice in the spring carbon plate? Should it be deemed important, why could a debutant marathoner Guye Adola stick with Kipchoge 98% of the way without any publicized aids on his feet? That's up for debate. My argument is that any aid obtained from the shoes is negligible in the big scheme of things. </div>
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<span style="font-family: inherit;"><b><u>Conclusion</u></b></span><br />
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<span style="font-family: inherit;">From first order mathematical relations, I estimate that absolute external power Kipchoge used to run the Berlin Marathon in 2:03:32 is in the range 350-420 Watts. The mechanical power was established using three methods and several assumptions. The Riegel power prediction is the most conservative. The latter two methods predict numbers on the high side. </span><br />
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<span style="font-family: inherit;">Popular social media site Strava's analysis into Kipchoge's pacing structure shows that Kipchoge had just 8 seconds of total variation in pace throughout the duration of the marathon. That somewhat matches Ross's 5K split data as well. </span></div>
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<span style="font-family: inherit;">Since power is proportional to pace on flat terrain, we can "assume" a proportionally tight variation on actual external power. </span><br />
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<span style="font-family: inherit;">The post acknowledges that calculated external power values maybe on the high side for a thin, lightweight runner such as Kipchoge. </span><span style="font-family: inherit;">Weaknessess of the estimations were spelled out in a separate section above. </span><br />
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<span style="font-family: inherit;">Kipchoge can run with lower power numbers by economizing on his cost of running and maximizing on the fraction of his aerobic potential.</span><br />
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<span style="font-family: inherit;">Given that his competitors, themselves top names in the running business, couldn't seem to hang on neither today nor at Monza inspite of a systematically pampered course must tell something about Kipchoge's high fractional VO2 utilization and low cost of running. This remains to be verified. </span><br />
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</span> <b><span style="font-family: inherit;"><u>References</u></span></b><br />
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</span> <span style="font-family: inherit;">1. Cavagna, G. A., Thys, H., & Zamboni, A. (1976). The sources of external work in level walking and running. The Journal of Physiology, 262(3), 639–657.</span><br />
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</span> <span style="font-family: inherit;">2. Joyner, M. J., & Coyle, E. F. (2008). Endurance exercise performance: the physiology of champions. The Journal of Physiology, 586(Pt 1), 35–44.</span><br />
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</span> <span style="font-family: inherit;">3. Strava analysis of pace variance,<span style="color: red;"> <b><a href="https://blog.strava.com/berlin-marathon-14921/">Link</a></b></span> :</span><br />
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</span> <span style="font-family: inherit;">4. Riegel Fatigue Factors for Men's (Updated) : <b><a href="http://www.georgeron.com/2017/09/new-fatigue-factors-for-running-mens.html"><span style="color: red;">Link</span></a></b></span><br />
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Ronhttp://www.blogger.com/profile/16268869622833968439noreply@blogger.com1tag:blogger.com,1999:blog-4786784182488135171.post-44732521351382636812017-09-23T21:02:00.003+04:002017-09-23T21:51:32.602+04:00Dubai Desert Road Run 10K Race 1 : The Metrics<div dir="ltr" style="text-align: left;" trbidi="on">
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Today's Dubai Desert Road Run 10K packed a quality field of 392 with some of the fastest male and female runners in Dubai showing up. As many observed, this became a fast race for a season opener and there was plenty of visible excitement in the air to complement the energy.<br />
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<b>Overall Standings</b></div>
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The top 100 in standings show who's done their homework over the summer. I'm somewhere in there. It seems to me that older individuals are getting faster while (we) the whatsapp generation continue to tumble down in fitness. Need to reduce thumbing up and down stupid messages and run more! </div>
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<a href="https://4.bp.blogspot.com/-z5mh40lNRbg/WcaAB33b_VI/AAAAAAAAGFE/JOD7eIK93x0oNlxMatgjU1BwTKJp5GdrACLcBGAs/s1600/21994164_1572028219528012_8892735914771493045_o.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1100" data-original-width="850" height="400" src="https://4.bp.blogspot.com/-z5mh40lNRbg/WcaAB33b_VI/AAAAAAAAGFE/JOD7eIK93x0oNlxMatgjU1BwTKJp5GdrACLcBGAs/s400/21994164_1572028219528012_8892735914771493045_o.jpg" width="307" /></a></div>
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<tr><td class="tr-caption" style="text-align: center;">Fig 1 : Official results, top 100 at Desert Road Run 10K Race 1</td></tr>
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I didn't exactly throw a kitchen sink at the race. Starting a bit on the conservative side and tossing a negative split cost me a bit of ground to cover in the later part. However, for the same course and same race for more or less similar ambient temperature profile, I broke a 3 min PR from 2013 which is interesting. As you can tell, I do not do a lot of these 10K's.</div>
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The following data table are my numbers from the race. Cost of running and running economy are surrogate values calculated purely from external mechanical power and running speed. I also choose to leave critical power and/or FTP from the data table. The -ve splitting today meant dabbling with something like a -3% to +20% CP distribution beginning to end, capping with a final kick at + 60% CP.</div>
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<tr><td class="tr-caption" style="text-align: center;">Fig 2 : Run data for Desert Road Run 10K Race 1<br />
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<b>A Look at Riegel Fatigue Factor</b><br />
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Readers will note that I extensively explored Riegel fatigue factors for both world class male and female racing in this <b><a href="http://www.georgeron.com/2017/09/new-fatigue-factors-for-running-mens.html"><span style="color: red;">post</span></a></b> and this <b><a href="http://www.georgeron.com/2017/09/the-fatigue-factor-for-running-womens.html"><span style="color: red;">post</span></a></b>. Many readers on Facebook expressed the concern for applicability of the exponents to everyday age-groupers.<br />
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Very conveniently, I ran a constant pace 3K (00:12:12) and a 5K TT (00:23:40) within 1 month's gap of each well before today's race. The first and second TT were in Abu Dhabi, by the Corniche, an obviously humid place to run due to the effect of water. Today's race in Dubai was in-land, a tad bit on the cooler side and much less humid.<br />
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The slope of Ln Speed to Ln Distance, when corrected to the Riegel fatigue factor becomes <b>1.0995</b> with a 51.7% regression fit. This exponent predicts a 10K time of 00:51:00 from previous 5K time. Actual finish time however was 00:46:18.<br />
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<tr><td class="tr-caption" style="text-align: center;">Fig 3: Riegel exponent for race and pre-10K time trials executed in the months of August and September 2017</td></tr>
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Which means nearly 5 minutes is unexplained by Riegel and that's inexcusable for my finishing time and placing. The poor linear fit of the slope is most likely due to insufficient data or variabilities in course, temperature and pacing strategy.<br />
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I will build this up as I accumulate more seasonal data for other distances and hopefully I can get a more composite picture of what the final fatigue factor is.<br />
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Well done to all runners today. See you soon. -Ron</div>
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Ronhttp://www.blogger.com/profile/16268869622833968439noreply@blogger.com0tag:blogger.com,1999:blog-4786784182488135171.post-72660595069243528792017-09-19T22:50:00.004+04:002017-09-19T23:46:12.414+04:00New Fatigue Factors for Running : Men's Road and Track Racing<div dir="ltr" style="text-align: left;" trbidi="on">
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<tr><td class="tr-caption" style="text-align: center;">Zersenay Tadese during the unbroken world record half marathon at Lisbon in 2010.</td></tr>
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<span style="font-family: inherit;">Readers will recall that in a <b><a href="http://www.georgeron.com/2017/09/the-fatigue-factor-for-running-womens.html"><span style="color: red;">recent post</span></a></b>, I did an exercise to calculate Riegel fatigue factors from updated world record performance times for women's road and track racing. </span><span style="font-family: inherit;">I then ran some numbers on a near-world class local female runner aged almost 40 to predict her half marathon time from her most recent 10K time. The Riegel model predicted the closest times to her actual finishing time compared to several other models widely available on the internet. </span></div>
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In this post, I attempt the same thing for men's road and track racing.<br />
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<b>I. Fatigue Factors for Men's Road Racing</b></div>
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<span style="font-family: inherit;">I constructed a table with the latest road racing world record times for men. The following ln-ln plot of time to distance results in a slope of -0.0497 (<i style="color: #222222; text-align: start;">R</i><sup style="color: #222222; line-height: 1; text-align: start;">2</sup><span style="color: #222222;"> </span> = 0.8101). When corrected into the fatigue factor form, it results in a number <b>1.0497</b>. This is a bit different to Riegel's estimation of <b>1.07732</b> back in the day, a percentage decrease of 2.5%. </span></div>
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<tr><td class="tr-caption" style="text-align: center;">Fig 1 : ln-ln graph of men's world class road racing bests</td></tr>
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<tr><td class="tr-caption" style="font-size: 10.4px;">Fig 2 : Table showing the data behind the updated Riegel model for world class men's road racing.</td></tr>
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<span style="font-family: inherit;">Apart from Stanley Biwott's 1:27:13 30K, no major recent records have been set in other distances. This shows the strength of Kimetto and Tedese's placings in the long and mid-distance categories. These records haven't been broken for several years although EliUd Kipchoge seems very hungry in 2017. A world record attempt at the marathon may mean taking out the half marathon world record in the process. </span></div>
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<b>II. Fatigue Factors for Men's Track Racing</b></div>
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The following ln-ln plot of time to distance for men's track results in a slope of -0.0777 (<i style="color: #222222;">R</i><sup style="color: #222222; line-height: 1;">2</sup>= 0.9901). When corrected into the fatigue factor form, it results in a number 1.0777. </div>
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<span style="font-family: inherit;"><span style="font-size: small;">There are two interesting aspects to this number. First, the linear fit is very close to actual results. Secondly, this number is very close to Riegel's</span><span style="font-size: small;"> estimation of </span><b>1.07732</b><span style="font-size: small;"> back in the late 1970's.</span></span></div>
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<tr><td style="text-align: center;"><a href="https://4.bp.blogspot.com/-uU0w7PMGrYk/WcFZLwdm_6I/AAAAAAAAGDk/JHssyaOCWQY4O66IV5A3ZyIHuQQuZx0sgCEwYBhgL/s1600/Mens%2BTrack%2BGraph.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="399" data-original-width="576" height="276" src="https://4.bp.blogspot.com/-uU0w7PMGrYk/WcFZLwdm_6I/AAAAAAAAGDk/JHssyaOCWQY4O66IV5A3ZyIHuQQuZx0sgCEwYBhgL/s400/Mens%2BTrack%2BGraph.JPG" width="400" /></a></td></tr>
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<tr><td class="tr-caption" style="font-size: 12.8px;">Fig 3 : ln-ln graph of men's world class track racing bests<br />
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<tr><td class="tr-caption" style="font-size: 10.4px;">Fig 4 : Table showing the data behind the updated Riegel model for world class men's track racing.<br />
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No recent upheavals have happened in men's track racing, with the last record in the 25k and 30K distance being established in 2011. El Guerrouj, Bekele and Gebrselassie's records meanwhile have stood the test of time proving the remarkable forms they were in when they competed.<br />
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<b>III. Application to a World Class Local Male Runner Y</b></div>
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<span style="font-family: inherit;"><span style="color: #333333;">I applied the Riegel fatigue factor for young male world class road racing to a 30 year old long distance runner Y to see how off the predictions are when using his 10K time to predict half marathon time. Both the races were held in the U.A.E and just a couple of months apart. </span></span><br />
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<span style="font-family: inherit;"><span style="color: #333333;">Runner Y is a local running celebrity of sorts, having established record times in everything from your weekend park run predictor to the RAK half marathon. </span></span><br />
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<span style="font-family: inherit;"><span style="color: #333333;">The math behind the following predictions were already explained in the </span><b><a href="http://www.georgeron.com/2017/09/the-fatigue-factor-for-running-womens.html"><span style="color: red;">past post</span></a></b><span style="color: #333333;">. </span></span><br />
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<span style="font-family: inherit;"><span style="color: #333333;">Riegel fatigue factor = </span><b style="color: #333333;">1.0497</b><br /><span style="color: #333333;">Individual : Y, local male sponsored athlete</span><br /><span style="color: #333333;">Age Bracket : 30-35</span><br /><span style="color: #333333;">Actual 10K time (T1) = 31:40</span><br /><span style="color: #333333;">Predicted 21.1K time (T2) = </span><b><span style="color: red;">1:09:21</span></b><br /><span style="color: #333333;">Actual 21.1K time = </span><b><span style="color: red;">1:06:10</span></b><br /><br /><span style="color: #333333;">Outcome : The prediction was under-estimated by 3 minutes 11 seconds. Runner Y finished in 1st place at the half marathon. The 2nd placed male runner finished in 1:15:06. For that difference in outcome between first and second place, the Riegel method still predicts the podium. So in a corrupted yet logical way, it appears that the difference of 00:03:11 is something we can live with. </span></span><br />
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<b style="font-family: Verdana, sans-serif; font-size: 13px;">IV. Comparison of Riegel Predictions to Other Time Prediction Models for Runner Y</b></div>
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<span style="font-family: inherit;">The following table compares Y's actual performance with old and new Riegel models and several other running predictors easily available on the internet. Please keep in mind that the case study was to predict half marathon time using 10K time.</span><br />
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<tr><td style="text-align: center;"><a href="https://1.bp.blogspot.com/-yTTKK-BOvuM/WcFwwhDuQRI/AAAAAAAAGEc/KheRpc80GgcNfrj1SaWvoLUPHyMdZ_C-wCLcBGAs/s1600/Men%2527s%2BRoad%2BModel%2BComparisons.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="231" data-original-width="373" height="198" src="https://1.bp.blogspot.com/-yTTKK-BOvuM/WcFwwhDuQRI/AAAAAAAAGEc/KheRpc80GgcNfrj1SaWvoLUPHyMdZ_C-wCLcBGAs/s320/Men%2527s%2BRoad%2BModel%2BComparisons.JPG" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Fig 5 : Comparison of updated Riegel prediction for men's road racing against 10 other models widely available on the internet. The error in prediction in also calculated and shown.</td></tr>
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<span style="color: #333333; font-weight: normal;">As shown in the table, the updated Riegel method performs the best prediction among several other models. In the women's case as well, it performed the best half marathon </span><b><a href="http://www.georgeron.com/2017/09/the-fatigue-factor-for-running-womens.html"><span style="color: red;">prediction</span></a></b><span style="color: #333333;">. </span></div>
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<span style="color: #333333;">Please note that the Runner's World predictor tool did not work. The times entered were outside the "limits" of the tool, which perhaps is something deliberately programmed by them to prevent application for elite athletes. </span></div>
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<b style="font-family: Verdana, sans-serif; font-size: 13px;">V. Conclusion</b></div>
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<span style="font-family: inherit;">In this writeup, I updated the fatigue factor or what people term the Riegel exponent to include road racing and track racing data for men. The updated fatigue factor for world class road racing = 1.0497 and that for world class track racing = 1.0777. </span></div>
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As opposed to women's racing, what is remarkable is that several of the men's records in both track and road have stood the test of time. Very few records have been broken in recent years. This further re-inforces the fact that there is more news to cover in women's racing, it's alive and kicking and these are exciting times. </div>
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Men have some catching up to do. </div>
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<span style="font-family: inherit;"><br />I used the updated Riegel model for men's road racing to predict the half marathon performance of a 30-35 age bracket world class road runner living in the U.A.E. The Riegel model appears to give the best prediction when compared to 10 other models. Further, the updated Riegel fatigue factor gives a better prediction in the case study that the number from Riegel's original paper. </span><br />
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<span style="font-family: inherit;">When considering both the men's and women's prediction I wrote about, the Riegel method appears to be a simple and reliable method that anyone could easily program. The fatigue factor can also be tweaked to fit the data of specific runners.<br /><br />Since world records are being broken year after year, it seems justified that running prediction calculators for world class runners should update their fatigue factors as new data comes in.<br /><br />Coaches are advised to guide with application and interpretation issues for recreational runners especially those above the age categories that the model was made from. As shown in this post, prediction tools are <b>only a guideline.</b> </span><br />
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<span style="font-family: inherit;">Therefore, two words of caution :<br /><br />A. The understanding is that specific data for a runner takes precedence over estimations done using data for world class athletes, the latter which can detrimentally over-estimate race time if mis-applied.<br /><br />B. Specific data involving similarities in race course and weather conditions takes precedence over distributed data containing a variety of different races courses and weather. In general, it is better to avoid exceptionally tough courses and/or conditions involving generous amounts of assistors, such as a tailwind or rabbits, from the dataset.</span></div>
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<b style="color: #333333; font-family: Verdana, sans-serif; font-size: 13px;">References</b><br />
<b style="color: #333333; font-family: Verdana, sans-serif; font-size: 13px;"><br /></b><span style="font-family: inherit;"><span style="color: #333333;">Riegel, Peter S. “Athletic Records and Human Endurance: A Time-vs.-Distance Equation Describing World-Record Performances May Be Used to Compare the Relative Endurance Capabilities of Various Groups of People.” </span><i style="box-sizing: inherit; color: #333333; line-height: inherit; text-align: start;">American Scientist</i><span style="color: #333333;">, vol. 69, no. 3, 1981, pp. 285–290. </span><b><a href="http://runningtrainingplan.com/downloads/AthleticeRecordsHumanEndurance.pdf"><span style="color: red;">Link to paper</span></a><span style="color: #333333;"><span id="goog_2114470840"></span><a href="https://www.blogger.com/"></a><span id="goog_2114470841"></span></span></b><span style="color: #333333;">.</span></span></div>
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Prediction Models :</div>
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<span style="color: #333333; font-weight: normal;">Runner's World Predictor : </span><b><a href="https://www.runnersworld.com/tools/race-time-predictor"><span style="color: red;">Link</span></a></b><span style="color: #333333;">.</span></div>
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<span style="color: #333333;">Daniel's Equivalence Predictor : </span><b><a href="https://runsmartproject.com/calculator/"><span style="color: red;">Link</span></a></b><span style="color: #333333;">.</span></div>
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<span style="color: #333333;">McMillian Race Predictor : </span><b><a href="https://www.mcmillanrunning.com/"><span style="color: red;">Link</span></a></b><span style="color: #333333;">.</span></div>
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<span style="color: #333333;">Godwin Race Predictor : </span><b><a href="http://fasterrunning.com/calculator"><span style="color: red;">Link</span></a></b><span style="color: #333333;">.</span></div>
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<span style="color: #333333;">Purdy, Cameron & VO2 Max Predictors : </span><b><a href="http://tools.runnerspace.com/gprofile.php?do=title&title_id=801&mgroup_id=45577"><span style="color: red;">Link</span></a></b><span style="color: #333333;">.</span></div>
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Ronhttp://www.blogger.com/profile/16268869622833968439noreply@blogger.com0tag:blogger.com,1999:blog-4786784182488135171.post-54171172415216590212017-09-09T20:44:00.000+04:002017-09-10T09:16:00.059+04:00Alberto Contador On His Final Angliru : Climbing Speed & Power to Weight Ratio<div dir="ltr" style="text-align: left;" trbidi="on">
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<a href="https://3.bp.blogspot.com/-JhpRpOD8ses/WbQWmvcAkvI/AAAAAAAAGB4/QSVfaUTHsEIllvhQ9fXiLNDF6c0WQcKRACEwYBhgL/s1600/Capture.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="491" data-original-width="954" height="205" src="https://3.bp.blogspot.com/-JhpRpOD8ses/WbQWmvcAkvI/AAAAAAAAGB4/QSVfaUTHsEIllvhQ9fXiLNDF6c0WQcKRACEwYBhgL/s400/Capture.JPG" width="400" /></a></div>
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This post is modeled on the calculation method shown <b><a href="http://www.georgeron.com/2008/09/alberto-contador-on-angliru-climbing.html"><span style="color: red;">in a past post </span></a></b>where I calculated Contador's VAM and power to weight ratio on the Angliru during the 2008 Vuelta a'Espana.</div>
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Today, Contador won the final mountain stage of the Vuelta, and again on the Alto d'Angliru.</div>
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My preliminary calculation suggests that Contador climbed 950 height meters in a time of roughly 35 minutes. I clocked his climbing time from the 9.3K to go mark.</div>
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The estimation is therefore :</div>
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The Ferrari method to estimate power to watt ratio is therefore :</div>
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<a href="https://4.bp.blogspot.com/-MyjFmjvfT0M/WbQXTSIo2-I/AAAAAAAAGCE/1zO9zzBkLHQJofOfgiNzd1WZlk7uvYqtgCLcBGAs/s1600/Contador_PWR_992017.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="111" data-original-width="442" height="80" src="https://4.bp.blogspot.com/-MyjFmjvfT0M/WbQXTSIo2-I/AAAAAAAAGCE/1zO9zzBkLHQJofOfgiNzd1WZlk7uvYqtgCLcBGAs/s320/Contador_PWR_992017.JPG" width="320" /></a></div>
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His VAM today is less than my estimation for his <a href="http://www.georgeron.com/2008/09/alberto-contador-on-angliru-climbing.html"><span style="color: red;"><b>2008 VAM</b></span></a> (done for the last 4K and quite high due to road steepness in the last sections), his power to weight ratio is also less than my estimation for his 2008 power to weight ratio. </div>
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However, reductions seem reasonable for a man at the twilight of his career and do not make room for suspicion. The power to weight ratio displayed at the end of a grand tour is remarkable nevertheless.</div>
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This is a clean performance unless further data instructed otherwise. </div>
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The calculations are based on the following raw data.</div>
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Ronhttp://www.blogger.com/profile/16268869622833968439noreply@blogger.com0