Sunday, May 7, 2017

The Sub-2Hr Marathon Attempt : Chasing Smallest Meaningful Changes Through Aerodynamics

We tried. Sub-2 is 20 odd seconds closer, thank you.

Such might have been Nike's drumbeat yesterday, as a months long planning and execution process bordering on OCD brought Eluid Kipchoge to run the fastest recorded marathon in human history. At 2:00:24, the attempt to break the sub-2 mark may have failed, but the feat of running 2 hours at an average speed of 5.84 m/s is astonishing to me as a runner.

The climate made for perfect running conditions. Temperatures were in the cool teens. A windrose chart shows winds were mostly ESE during the day. With the orientation of the track in the NNE-SSW direction and a counter clockwise running direction, a headwind would be felt if at all only at the southern short end of the track. Rest everywhere, you'd see either a tailwind or a sidewind. With near perfect pacelining and draft coverage even from a moving vehicle however, the task at hand looked daunting from get-go.

A whole 2 minutes.

So how did we get here?

Until now, the fall in the marathon world records have been very non-linear. Perhaps this is reflective of the course specific nature of marathon times as well as influence from a host of externalities such as training, hydration and climate. But some simple stats help understand the level of difficulty involved in every incremental improvement towards sub-2.

Fall in Marathon World Records

IAAF standardized marathons began in 1921. The marathon record in 1925 was 2:18:40. It took 28 years for the world record to fall 10.35 minutes, i.e 621 seconds. Put in a somewhat corrupted way, if you were to spread that among 28 years, that's not more than an average of 22 seconds per year.

Source : IAAF

From 1953, it took just 14 years to shave off another 538 seconds. Or, an average of 38 seconds time decrease per year which is an interesting rate of decrease, a subject for another day. But from thereon, it took almost 47 years to knock off another 399 seconds. That's a tiny decrease of 8 seconds average per year.

A better visual shows how the time knocked off between each marathon asymptotes to a window about 43 seconds wide. See below. I've included Kipchoge's time only for perspective of the advantage he had from a controlled strategy. However, the time is not recognized by IAAF.

Given this simple history, it would seem plausible that the remaining 178 seconds would be knocked off. But the question is how long that would take.

If we consider a 'generous' average of 30 second decrease per year, breaking 2:00:00 would take just 6 years. But if the task is considered exponentially difficult and we accept that only a 1 second decrease per year is possible at this level of racing, it would take a whopping 178 years to achieve. So is there an opportunity between these two extremes? Will it be 15 years or 20 years?

That's where the Nike's experiment fits in. Kipchoge and gang showed that even under the most controlled of conditions (some in clear violation of international marathon rules) and with the best athletes and level of technology available today, we humans are still shy of the barrier by 26 seconds. Close enough to warrant another try? Well, that's the debate.

The Smallest Meaningful Change

The best distance runners from Africa are nearly equal in abilities these days. Their training is similar. They eat similar kinds of foods. They live at the same altitudes. So what must be the differentiator among them?

Sports practitioners talk about the "smallest meaningful change" defined as the minimum change in performance worthy enough to determine differences between top competitors. For example, if a group of elite runners trained for months and showed a between-athlete standard deviation of 10 seconds in a 20K running test, the smallest meaninful change would be 0.2 x 20 = 4 seconds. In other words, anything above 4 seconds is an appreciable change. Anything less and it's just day-to-day noise.

Take another perhaps more representative example. Berlin 2014 was where the current world record shattered. In the last 5 years, the average standard deviation between the times of the 3 podium placers was just a minute and 25 seconds. The smallest meaningful change in an elite runner's performance for positive differentiation would be 0.2 x 85 = 17 seconds.

For today's elite marathoners showing such a tight cluster in finishing times, 17 seconds means everything in the world.

Nike publicly put their money in the aerodynamics basket as they pitched the marketing effort of the Sub-2Hr. Not much in the way of technical data has emerged from Monza. Therefore, I got curious enough to evaluate running energy savings on the table from just aerodynamics alone.

The Effect of Drafting off Other Runners

In human powered land transport, oxygen cost increases as a square of wind velocity. Experienced middle distance track runners can attest to the energy savings experienced even with a small amount of drafting. 

Pugh (1971) showed that at 4.5 m/s, his runner saved 0.250 l/min in oxygen cost by running behind another runner within a separation distance of 1 m. He extrapolated this figure to 0.332 l/min for a speed of 6 m/s and stated that for outdoor conditions, a runner can expect to overcome 80% of the energy cost of overcoming air resistance through shielded running.

Source : Pugh (1971)

In any mass event, it is not reasonable to be within touching distance of a runner in front of you. Pugh measured dynamic air pressure with a Pitostatic tube and showed that even at a separation distance of 1 m, air pressure was still only 7% of the value upstream of the lead runner. This might mean there are potential benefits to be had even at larger separation distances.

Source : Pugh (1971)

I also assume that like in cycling team time trial efforts, the leading runner can experience benefits as well by virtue of reduction in airflow separation in the wake due to the presence of a runner close behind. I'm not aware of any studies which have looked at the cost savings on the leading runner.

In an ideal marathon situation, it maybe possible for the favorites, all excellent in fitness and form, to getaway and stick with a tightly knit pacing formation until the very last kilometers of the course. The one competitor who will make most of this formation and slow down the least can be expected to win.

An analogy can be borrowed from long distance thoroughbred horse racing. The best finishing horses almost always spend the most time drafting. The horse that slows down the least emerges the winner.

Furthermore, thoroughbred horse racing is an interesting example because it exhibits a similar cluster of best times as seen in human marathons (although this has been the case for a longer period of years). If this means both horse racing and marathon running have 'plateaued' in terms of race times, looking to the next frontier to improve timing is justified.

Source : Five Thirty Eight

The Effect of Drafting off A Pace Car

At Monza, Nike used laser lights to guide the runners within an arrow formation which effectively shielded main-man Kipchoge from three directions. But we saw a pace car driving 10-15 metres before the lead runners which could have also potentially changed the flow field. The Sports Scientists joked that the unsung award for this sub2 attempt ought to go to the Tesla.

But must we exaggerate the effect of a vehicle 10-20 metres ahead of you? Certainly in the image above, it doesn't seem the runners would have a "massive" advantage at the distance they are positioned behind the car.

Infact, the difference in air pressure and x direction air speed is dependant on where you are behind the car. I did a simple 2D CFD simulation to show that the effect isn't is great as some may think it is. Since the simulation takes a long time to run, I ran it for a few milliseconds of real-world time. The road boundary is assumed to be moving at 5.84m/s and at the left end of the domain, the boundary condition for air velocity = 2.77m/s and air pressure of 100000 Pascal.

In the first image, I have sliced a cross-section in the X-direction at roughly the height of the car behind the car. The bold black line shows the profile of the difference in P - Po, where P = instantaneous air pressure and Po is the initial air pressure of 100000 Pascal. In the second, I've shown the distribution of horizontal air velocity in the same plane as above.

Summary : Yes, there is a reduction in both parameters which gets bigger the closer you are to the car. For example, in the P-Po simulation, the air pressure behind the car at where I think the runners were is only some 14.8 Pascals less than pressure upstream of the car, therefore total pressure is still intact. Therefore, at the distance the runners were shown in the live telecast, the effect is not "as great" as people are making it out to be.

However, the question is also whether it was justified to use such a prop in the first place. That's the debate in the running community.

The Effect of Reynold's Number (Re) on Running Drag 

Mechanical power for a runner to overcome air resistance is proportional to drag co-efficient CD, the relative velocity between wind and runner vr, horizontal running speed vf, air density ρ and the frontal area of the runner A, projected perpendicular to flow of air. 

In general, the dependance of power to overcome drag on speed is cubed and the dependance on density, area and CD are all to the power of 1. A step change in running speed on a zero wind day will triple the power requirements, all else kept the same.

Pugh (1971) estimated for a subject runner at a treadmill speed of 4.47 m/s and wind velocity of 14.14 m/s, wind pressure was 6.24 kgf which required a horizontal power of 27.89 kgf.m/s.

CD is dependant on Reynold's number, a useful dimensionless co-efficient in fluid dynamics. 

A running human can be approximated as a cylinder. While at low Reynold's number, the regime is one of laminar flow, rarely is this the case for a running human. Let's look at a simple example calculation using a bluff body approximation :

At this Reynold's number (Re) of 63,000, flow is all turbulent.

There is a 'critical' Reynold's number where a precipitous drop in drag co-efficient is exhibited, atleast in theory. For a cylinder, this is qualitatively shown below.

Source : Pugh (1971)

A table from Pugh (1971) also quantifies the curve shape of drag co-effcient as a function of Reynold's number.  Notice this effect first occuring at Reynold's number somewhere between 20,000 - 25,000. 

Source : Pugh (1971)

If I consider Kipchoge's smaller stature, a chest circumference of 90 cm instead of 100 cm and a speed of 5.84 m/s, I estimate an Re = 110,800. Comparing this value to the plot above, it already "seems" his drag co-efficient was in a low place, if not the optimal place for his speed. Again, this is an estimation. It would be quite nice to see whether Nike researchers found this in practice.

The Effect of Frontal Area on Running Drag

Ideally, a talented runner will have an optimized frontal area and will neither be too short or too tall. For example, a runner with a height of 179.9 cm, weighing 65 kg and having a surface area of 1.78 sq.m has a projected frontal area of 0.478 sq.m.

Perhaps Kipchoge was perfectly suited for the task. At a height of 168 cm with a race weight of 57 kg, Kipchoge's frontal area would have been 168/179.9 x 0.478  = 0.446 sq.m (notice I employed a simple ratio from the previous example).

Compared to the example runner, this reduction in Kipchoge's frontal area equates to a reduction in drag force of nearly 7%, all else kept the same.

Projected area is directly dependant on height and weight and to an extent, the type of running motion and running lean angle exhibited during the gait. Optimizing the latter two aspects should not come at the expense of running economy.

The Effect of Shoe on Running Drag

Nike's PR mainly revolved around a pair of shoes designed for Kipchoge called Zoom Vaporfly 4%. The shoe has an interesting shape and is streamlined at the back end. The purported benefits are 4% in energy savings through a carbon sole plate, although there is no published data from Nike to back this.

Some data from the research arena is starting to come out. A study supported by Nike and the laboratory of Rodger Kram (one of the few experts on the planet to know a thing or two about running energetics) found it took 4% lesser energy to run in the prototype Nike's compared to two other shoes.

Fascinatingly, one of the two control shoes was the Adidas Adios Boost 2, the same shoe worn by Kimetto while toppling the current world record. There's only an abstract available from the study and some key points are underlined below.

I certainly have my doubts over the 4% number, but if we assumed this were correct, then I have projected time savings that an ordinary runner could potentially experience. The calculated savings seem huge on account of economy improvement through the shoes itself, which is why I doubt we can apply the 4% number from the study to any running situation as is.

The running feet exhibits both translational speed of the runner and the rotational speed through the leg swing and leg pitch. An elite marathoner runs at step rates of around 3 Hz. The legs will swing a total of 14,400 times in an ideal scenario. That's 7,200 times each leg is thrown about. 

Cycling is another area which approximates the rotation and forward translation of the feet, although in a more constrained way.

Gibertini et. al tested three cycling shoe configurations in a wind tunnel and noted that a well fitting laced shoe exhibited the least power demand, around 15W in total. Given that this was a laced shoe, perhaps we could compare the numbers to that of a running shoe for perspective.

Source : Gibertini (2010)

The air speed in this cycling study was more than 2 times that of marathon running speed so it might not be entirely representative. Moreover, even during controlled running motion, African runners tend to show great degrees of knee lift, leg turnover and swing angle which differ from that of cycling.

Qualitatively, the crank angle based power diagram highlights that shoe drag power is a function of where the feet is during it's rotational motion. Drag power was greatest at top dead center  (Θ = 0) and least when the shoe was at 90 degrees before bottom dead center (Θ = 90).

Perhaps this idea can be extended to the running scenario by assuming that shoe drag might be the most when the lifted foot is at it's highest point and least when both feet are off the ground on the sample plane during mid-stance. I'm unaware of an actual study done in this fashion with running shoes.

Other reseachers have pointed to the benefits of a "dimpled" frontal shoe surface.

Finally, notice that none of the runners that attempted this event wore socks. One study by Ashford et. al compared a dozen socks on a form tested under the wind tunnel and found little variation in drag co-efficient among them. A couple of socks exhibited a drop in CD at low Reynold's numbers which maybe just a reflection of optimized behavior during lower running speeds.  In hunting for mere seconds to win a race, this maybe a potential avenue to look into. Any benefits though have to be traded-off with potential discomfort and blisters during a fast running attempt.

Source : Ashford (2011)

Another fairly obvious aspect was tight fitting clothes. Notice that none of the runners tucked their shirts into their shorts as many amateur runners do in marathons. Also, just Tedese, Desisa and Kipchoge wore arm warmers among all runners. I'm assuming it was more than just for warming the skin.


In the grand scheme of things, most marathon world records these days are pre-dominantly mental. Who can suffer the most for the longest? 

Having said that, my observations in this post are limited to aerodynamics alone. Summarizing key ideas :

1) In the best case scenario, I estimate that the 2 hour marathon record will be broken within the next 6 years. In the most conservative scenario, we'll be long dead before that happens. I'm an optimist however. 

2) Top podium worthy marathon timings are often spread by less than a minute and a half. The degree of improvements necessary are small and to be placed within context of the smallest meaningful change. The degree of enhancements from aerodynamics may help push past this threshold of beneficial change.  

Side point : This may also limit the scope of commercially sold running instruments for tracking performance if they do not have the required fidelity/sensitivity to capture small improvements. 

3) Running in a scientifically optimal ambient climate sets the density and viscosity of surrounding air for the optimal Reynold's number. Temperatures below 50 deg C may not be ideal.  The conditions in Monza have been noted to be picture perfect for sub 2 hour attempt. It was not too cold to for non-optimal Reynold's numbers and not too hot to demand increased cooling. 

4) Wind creates drag force which requires externally supplied power to overcome. It general, it increases as a cube of speed. As a rough rule of thumb, a +5 mph head wind relative to calm conditions increases oxygen demand by approximately 5% relative to calm conditions. Conversely, a tailwind decreases the horizontal power demand of running. Note that wind speed shall be considered at the center of gravity of the runner, not at the 10m wind station.

5) Optimal drag co-efficient is a function of Reynold's number and further on running speed and anthropomorphic aspects. Running posture may affect the frontal area presented to the wind. 

6) Optimizing clothing to improve aerodynamics is justified for small incremental performance benefits. Even shoes and socks may contribute to reduced power demand of fighting drag. A lack of adequate published literature in this area presents a good opportunity for engineers, biomechanists and sports scientists to get together.

Reference :

LG, Pugh, The influence of wind resistance in running and walking and the mechanical efficiency of work against horizontal or vertical forces. J Physiol. 1971 Mar;213(2):255-76. 

Sunday, April 23, 2017

Commentary : The Environmental Impact of Pre-Ride Food Choice and Driving to a Bike Ride

This is an Earth Day special commentary that I wrote on my Facebook page. The post was inspired by a similar opinion post along the same lines written by Thorpe & Keith from the Keith Group. They provide a host of reasonable references from where the numbers were picked.

The environmental impact of "getting to a ride" by car is analyzed below. What is also interesting to think about is the environmental burden due to choice of diet, which makes big marginal differences depending on what you put in your mouth.

Attached below are some graphs from a simple estimation of CO2equivalent emissions for a cyclist commuting for a typical 100km weekend ride. 

In one set of graphs, the cyclist is assumed to have eaten a 'typical American' diet and vehicle emissions were derived from test data for assumed 90kph driving speed. 

In scenario 1, driving distance = 20km in a conventional 4 door automatic petrol engined 2L Honda Civic. 

In scenario 2, driving distance = 20km in an automatic petrol engined 3.6L Porsche Panamera 4 PDK (Euro 5). 

In scenario 3, I look purely at impact of driving a fuel efficient, ULS diesel powered 2L Skoda Octavia Hatchback (Euro 5) as support vehicle for the cyclist (commute to ride is neglected). However, due to support function, the Skoda will be driven the 100km at a slow speed matching the cyclist (let's say 30-33 kph). Only the diet for the cyclist is taken into account, while that of the driver's is neglected.

Please note that life cycle environental impact of production of the vehicles, the bicycles and the construction of a public road system that the cyclist and driver utilize are neglected in the analysis.

The comparison is interesting if you account for the slow speed fuel efficiency degradation of any conventional vehicle. If you assume a 15% fuel efficiency derate due to low speed vehicular losses in the Skoda, then on a per km basis, I believe it makes little difference to be driving a Civic fast to the ride or a Skoda slow as a support car - they are more or less equally polluting regardless of what the sticker fuel efficiency is.  Meanwhile, it is approx 30% more polluting to carry bikes on a Porche when driven at similar highway speeds as a Civic, no surprise there.

The takeway? Reduce driving, carpool if possible and keep the luxury car at home. When driving, drive at the sweet spot fuel consumption speed. In urban environments, it helps to live close to a cycle track.

And finally, reduce or eliminate the use of conventional fuel support cars on long rides as pollution is spread over a larger area. If that's not possible, choose lighter cars with smaller displacement engines and reduce the number of start-stops. Start-stops cause relatively more pollution than constant speed driving regime due to the repeated accelerations and decelerations the vehicle must go through.

What is also interesting is to look at the effect of the cyclist's diet for this ride. In the first set of graphs above, I have assumed the cyclist to eat a typical diet with a life cycle burden of 2.6 gCO2eq/kcal. The carbon intensity of that ride on that diet is an average of 30-40 times less than driving the respective cars on a per km basis. 

However, if the same cyclist chose to eat a high protein meat rich Paleo diet with a pollution burden of 5.4g CO2eq/kcal, the difference is halved. For example, in the case of driving the Civic to the Paleo fueled ride, driving is only 15 times more polluting than cycling relative to a normal diet. Stunning if you think about it.

What I'm pointing to (as others have pointed out) is that on a gram of CO2eq per km basis, the high meat rich diet can be worser off than the transportation fuel in terms of the embedded carbon intensity (what goes into the production of the fuels). The reason can be attributed to the carbon intensive nature of raising cattle to produce beef. 

So the takeaway from this second analysis is that when possible, substitute lesser energy intensive forms of protein in your diet for fueling the ride. And while it, keep the beef away from the support car driver!

Post script : 

Just because cyclists reduce or avoid consuming a meat rich diet does not necessarily mean that the product will not be produced. Supermarkets will still carry the meat and someone else will buy and consume it. So on a global level, perhaps we'll see the same environmental burden of meat consumption.

However, if you account for the fact that products are sold because of relative consumer demand, if one segment of the market shifts outlook and reduces meat consumption, we can assume that somewhere else in the chain, production maybe cut. I'm not sure if its as simple an analysis as that and what timescales it takes to shift mindset overall. Something to think about though.

Saturday, April 22, 2017

GIANT Duathlon 16/17 Season Finale : Results and Analysis

Image courtesy : Paul Venn / Race.ME

The final duathlon in the Giant Duathlon series was held on April 14, 2017 at the District One cycling track in Dubai. The race format was 3k-25k-3k for a total distance of 31k. 

In a previous post, I described the runing dynamics data from race 4. In this post, I will use a similar level of analysis of race performance and will be comparing to the data in race 4.

The full results are hosted on the Race.ME results page here and my splits are shown there. The top 30 in men's overall times are posted at the end of this post.

The strategy going into this race was simple - throttle down the first run a notch and put everything you have for the day into the cycling aspect. Because this was a fast cycling track, I knew that the most of the field would be thinking along those lines.

For comparison purposes, I made a table of my timings for all 5 duathlon races this season along with a key piece of information - my training stress balance as a function of TRIMP. This is shown in Figure 1.

Figure 1 : Comparison of race performances over 5 x GIANT duathlons during the 2016/17 season.

TSB is an algorithmic surrogate for "freshness" or "readiness to perform". It is understood that the more negative it is immediately before an event, the more fatigue you bring into the race.

However, surrogates are just that - surrogates. Trimp or TSS based training stress balances are helpful, but I think they do not capture the stress in an adult working man's life who needs to commit 40-50 hours on a day job per week. In future posts, I'll be examining some interesting areas of physiology which might capture that aspect.

Graphing all my race timings from race 1 through race 5 helps form a visual story of what went on this season. This is shown in Figure 2.

Figure 2 : Plot of splits in 5 x Giant Duathlons during the 2016/17 season.

As shown above, I improved overall race timing in race 5 by 6.3% compared to race 1 and it would be my best overall timing this season.

Furthermore, duathlons are influenced by course. In race 3, there was a +4.9% degradation in overall timing compared to race 1 which was held on the same track. 

The reason is attributed to the poor visibility and foggy conditions in race 3 which pretty much hampered the average cycling speeds due to the technical nature of the course.  I also described in a past post about an inadvertent cramp during the last run segment which lost me atleast a minute in that race. 

Between race 5 and race 2 (same course), I improved overall timing by 4.9% mainly due to high motivation and better conditioning. All those brick sessions and gym workouts have helped.

Looking at transition times, the trends is one that shows decreasing t1 and t2 times. It appears feasible that minor improvements can be made here considering that I pulled out of transition in race 4 an average of 45 seconds. 

But I should think the transitions are also influenced by architecture of the transition zones. Race organisers optimizing the length and entrance/exit of the transition during race 4 helped me shave 10-15 seconds compared to other courses.

Running Dynamics 

Shown in the plot below is a composite of run dynamics for race 5. It shows run power (W), form power (W), ground contact times (ms) and leg spring stiffness (KN/m) vs duration. I also show an estimated average power for the biking duration. Unfortunately, I did not measure biking power due to a pairing handicap on the Polar V800s.

Figure 3 : Composite plot showing power and running dynamics in each split during the final duathlon race of 2016/17 season.

As the running started out, there was an overreaching in power due to the initial excitement and surge. As things settled down, I moved into a rhythm of 256W average. GCT was 210ms for a cadence of 93.

Form power is a surrogate for the metabolic cost of perpendicular bouncing. The form power data in the middle of run 1 looks rubbish due to data loss but overall, I displayed a mean form power : total average power ratio of 0.24, i.e about 24% of power was devoted to vertical motion. How much of that can be improved upon is debatable. What I do want to emphasize is that in all cases, vertical oscillation data says I limited it to < 3 inches, which is good rough guideline.

The story of the second run is that all metrics, by virtue of accumulated fatigue, worsened relative to the first run. This is shown in Figures 4 and 5.

Running power fell by 11.7% and pace fell by 10.6%. There was in increase in ground contact time of 9.5%, possibly the body's response to limit metabolic cost.

The surrogate of energy cost of running, ECOR, increased by 0.73% which may not be statistically significant to corroborate the increase in ground contact time (GCT).

Running economy (RE), a ratio of speed generated to power to weight ratio saw a fraction of a decrease.

I also kept cadence nearly the same as the first run. This may have been a way to compensate for the fall in stride length and gait push-off power.

Also note in Figure 3 the overreach in power towards the end of run 2. That is me pushing myself up a short hill just before the finish line. Power then dropped on the downhill segment and climbed back up again slightly for the home stretch on grass. By then I was flattened.

Figure 4 : Tabulated running dynamics from race 5 of the Giant Duathlon series, season 2016/17.

Figure 5 : Tabulated % change in running dynamics metrics in run split 2 compared to run split 1 during race 5 of the Giant Duathlon. 

What I thought would be interesting is to compare the fatiguing aspects of the second run in race 5 against the numbers in race 4.

Figure 6 : Running dynamics compared, race 4 vs race 5.

As expected, I ran a faster race in race 4. A major reason for the slower running metrics in race 5 was from the strategy to go slower in the running to perform in cycling.

Which brings me to state that duathlon is a fascinating exercise in energy management.  The mental and physical exertion of the short format was pretty taxing on the body all season and the excellent competition from my peers in the 30-39 age group kept me on my toes. Kudos to all those guys.

Training, self-coaching and making improvements have been fun. Tracking training volume and fitness changes through good data collection and record keeping has helped quite a bit. Keeping a tab on data comes natural to me from my engineering background and a major effort going forward would be to cut down on the sheer number of metrics and focus on actionable aspects. Keeping it simple stupid works.

The top 30 times from race 5 is shown below. Most of the fastest times in the race were from those in my age category, shown highlighted in yellow. The deficit I have to make up to be among the top 5 is a matter of 8-10 minutes. Thinking about that gives me some chills, it's a big gulf to cover.

If some optimization is carefully distributed among the various segments of the duathlon, I believe it is possible to narrow down the deficit but the question is by how much. Moreover, duathlon is a changing landscape with old competitors leaving, new ones coming along etc. This makes for pleasant surprises in each race. Sometimes you're the hammer, but often times you're the nail.

I also understand that the organisers may be considering cutting down the number of GIANT duathlon races for the next season, which means the room for error gets smaller. It's a shame because folks like me want to do nothing with swimming and duathlon is a way to show my A game. A lower number of races will be challenging, but hopefully a motivating aspect as well.

Thank you for following.

Figure 7 : Top 30 in the overall men's standings in race 5 of the Giant Duathlon series. Total competitors = 165. 

Image of motor

Image of mundane object to apply motor

Sunday, April 2, 2017

Actionable Intelligence for Running Part 8 : Effect of Shoe Type and Footpod Mounting Position on LSS and Power

Update, April 6 2017 : Since writing this post, several comments have been triggered on Stryd's Facebook community

Stryd developers acknowledged the data sharing exercise and this led to a conversation about the "sweetspot" in mounting height where this device has been validated. The sweetspot is somewhere 10cm and below. Andrew Coggan PhD is also pretty active in these discussions :

*  *  *

In Part 3 of this series, I had conducted an experiment with the Stryd to understand what had a bigger effect on LSS - running cadence or ground contact time (GCT). While high step frequency is related to high LSS, I found that lesser GCT's have a stronger correlation with high LSS than was higher cadence. I also found that at a fixed step rate, there existed a monotonic positive relationship between speed and LSS. 

Since then, I've analyzed much more data and plugged them into my own spreadsheet models. I'm fairly certain to have cracked the math behind LSS, i.e knowing what parameters affect LSS.

However, before I put my entire weight in the LSS train, it was important for me to answer one question. Does shoe type and where you mount the Stryd footpod affect the reported values? This a fundamental topic not only with the Stryd but any consumer device that measures athletic performance.

The reason it's fundamental is that when you track your own changes longitudinally over the course of a season or several seasons, you need to be sure that the % change in your own performance is greater than the noise introduced by the device you're using to measure with. If instead, the noise is greater than the % change, any change you say you made through training is unclear or baseless scientifically.

Discovering what is the "noise" in the Stryd LSS data is the subject of the post. Results are organized into two sections - 1) with the Stryd correctly oriented with the pointed edge facing down, and 2) an earlier test with the Stryd oriented in the upward direction. In each of these orientations, 2D position (X,Y) of the footpod was varied on the laces. I also tested with 3-4 different brands of shoes at two different running speeds.

Readers will find the results in section one with the Stryd in the correct orientation useful, as it is the recommended installation position. However, it will also be interesting to see what happens when the footpod is oriented in the wrong direction.

Actionable intelligence is highlighted in blue.

Motivation for Experiment

Attached below is a table of run data I have consolidated spanning 2 months. I've also included body weight and landing style as best as I recall.

Fig 1 : Collection of some run data from Jan 24-March 31,2017. Click to zoom.

Some runs didn't make sense in the context of a "few parameters".

A low GCT 800m track race run on clay track in Asics spikes yielded lower LSS (9.8kN/m) than during a slow jog on a tiled footpath in the Under Armor Bandit 2 (10.8 kN/m).

Meanwhile, a 2:53 interval run done in Nike Lunarlon Lunarglides on a purpose built concrete bike path showed high LSS (12 kN/m) but a similar GCT interval done in Mizuno's at faster pace was 0.5 kN/m lower.

More recently, a high speed VO2 max test done in a test lab with Mizuno's at somewhat lower power output than the track race also showed high LSS (10.6 kN/m). Puzzling that the slow jog in the Under Armor shoes displayed a slightly great amount of LSS for a GCT that was 50% higher than that in the VO2 test.

The complete list of LSS values are within -6% / +16% of the mean value of LSS in the table. One question to answer would be whether this much spread in the reported LSS is normal in the context of wearing different kinds of shoes. In that respect, it would also be interesting to study how different shoes and footpod mounting positions affect the reported LSS.

Design of Experiment

Fig 2 : Experimental equipment included 4 shoes, a Stryd and a Cybex 770 Treadmill which has it's own display of power.

Step 1. Round up 4 running shoes/sneakers from my collection (all I have). Label them A-D. Some basic characteristics about these shoes are shown below. Because I do not own a low drop shoe, the best I could find was a pair of Fox Motion sneakers from 2011/2012 which had a drop of 8mm. 

Fig 3 : Description of shoes used in the experiment.

Step 2. Choose 2 treadmill belt speeds to carry out test. Speed 1 = 10kph. Speed 2 = 12kph. Speed 1 would be run for 5 minutes and Speed 2 would be run for 3 minutes preserving a basic duration vs intensity relationship. 

Step 3. Choose two mounting positions for the Stryd footpod. Position in 2D space was defined as the X-Y distance of the footpod on the shoe. X distance was measured from medial malleolus of the tibia-foot interface to the center of footpod. Y distance was measured from the floor up to center of footpod. 

Fig 4 : Definition of X and Y footpod mounting positions.

The X-Y positions on all 4 shoes were as follows :

Fig 5 : Data table of X-Y positions of footpod. Click to zoom.

Step 4. Randomly assign the shoe A-D to run the test in. Within each shoe selected, randomly assign running speed with mounting position 1. The experiment table below will speak for itself. 

Note that in the interest of time, all shoes were tested twice to check repeatability except for shoe D. All shoes were tested atleast once with mounting position 2. All shoes were tested a total of 5 times each, except for shoe D. 18 tests were conducted in all, spanning more than 2.5 hours. 

Fig 6 : Protocol for randomized testing. Click to zoom.

Step 5. "As far as possible", all run tests for a specific speed would be carried out at similar cadence and the same running style. This was done to control step rate.  Note that I did not use a metronome which would have been a better way to control step rate. I accept that there would be some variation in step rate.

Step 6. All tests would be conducted using the Styrd App on treadmill mode. Treadmill would be set to 1% incline to mimic the stress of running outdoors.

Step 7. Collect data into post processors for analysis.

Part I

- With Stryd Footpod Mounted With Pointed End Facing Down (Recommended Position)
- Controlled Cadence

Results and Discussion 

In this test, I used only shoes A, B and C due to lack of time.

I controlled cadence using a metronome tone set to 90 cadence (180 steps per minute). Results table is shown in Fig.7.

Fig 7 & 8 : Results table for controlled cadence tests using 3 shoes and 2 footpod mounting heights with the Stryd installed in the recommended orientation. Cadence was controlled in this test using a metronome tone set to 90 cadence. 

Conclusion : LSS registered increased values at increased mounting height regardless of shoe or running speed.

Sample std deviation (10kph belt speed) = 0.93kN/m
Sample std deviation (12kph belt speed) = 0.65kN/m
%Variation from mean (10kph belt speed) = -9% / + 12.3%
%Variation from mean (12 kph belt speed) = -4.2% / + 8.9%

Variation appears to decrease with speed, although this test is limited to two speeds.

If the Stryd can show this much variation just from moving it's position higher on the shoe, I think it is best I control this position on a given shoe for my training going forward. However, when changing shoes, I understand that the absolute position from center of pod to the ground can still change due to the different exterior designs among shoes.  

This also means comparing my LSS longitudinally across a season to track improvements is a bit troublesome until I know that the pod had more or less the same ground height when installed on the shoe I chose to wear.

I'm happy to hear about the discoveries with your own device if variations are any different.

Part II (Optional Reading)

- With Stryd Footpod Mounted With Pointed End Facing Up (Not The Recommended Position)
- Uncontrolled Cadence

Results and Discussion 

II.A Effect of Mounting Position 

A 3 minute test conducted at 10kph belt before the 18 tests showed that freely chosen step rate = 178 spm. The step rate objective was to try as far as possible to stick with one cadence for a specific speed, without frying myself at cadences I'm not used to.

The full results table is shown below and sorted by shoe tested and then by ascending order of speed and ascending order of GCT. This makes repeatability and mounting position comparisons easy. Click to zoom in.

Fig 9 : Results table sorted by shoe type and ascending order of speed and GCT.  Click to zoom.

Eyeballing the data, within each subset of shoe tests, the highest LSS value reported by Stryd was for mounting position 2. It would then seem that the position of the device somehow influences LSS. However, if the data is organized in ascending order of GCT, the high values of LSS correspond to the lowest GCT values. In other words, lesser the time spent with feet on ground, higher LSS. It is possible that the combination of shoe type and the GCT is manifested in the difference in LSS values.

At the same time, the corresponding step rates unfortunately change as well. But the good news is that cadence variation is less than 3% so I did an almost good job. If mounting position is considered as the base position, then % variations in SPM, GCT and LSS with a given shoe and speed are as follows :

Fig 10 : % Change in LSS from footpod mounting positions 1 and 2 at a given running speed. Click to zoom.

With tests conducted on shoes A and B, variation in Stryd reported SPM was less than +/- 2.5% while in shoes C and D, SPM was limited to +/- 1%. Variation in reported GCT in mounting position 2 relative to mounting position 1 were less than 5% in all 4 shoes. Variation in corresponding LSS were all within +10%.

With shoes C and D, the change in LSS is the same as in shoes A and B even though cadence was extremely close. Therefore, whether it is the mounting position itself that is influencing GCT and LSS is not clear from the data above. It appears something else is influencing the modeled LSS. 

II.B Effect of Shoe Type

The results table is organized based on speed to help in shoe comparison.

Fig 11 : Results table sorted by speed. Click to zoom.

Eyeballing the data table, there doesn't seem to be any appreciable effect from shoe, except for line items where the footpod was mounted higher. This is my first hypothesis.

Digging further, I was interested to find a couple of things.

First, what is the standard deviation of Stryd reported speed, SPM, GCT and LSS sorted by treadmill belt speed with different mounting positions included in data? Results are tabulated below.

Fig 12 : Standard deviation of pace, SPM, GCT and LSS at 10 and 12kph belt speed between 4 different shoes. Click to zoom.

Second, what is the standard deviation of Stryd reported speed, SPM, GCT and LSS sorted by treadmill belt speed at a fixed mounting position? For this, I had to remove the data for mounting position 2 so that all shoes were compared on mounting position 1 (closer to ground).

Fig 13 : Standard deviation of pace, SPM, GCT and LSS at 10 and 12kph belt speed between 4 different shoes for a given mounting height. Click to zoom.

Comparing both the tables in Figs 10 and 11, the standard deviation in reported LSS gets small at a given mounting position. Infact, it is not entirely true that the X-Y distance at mounting position 1 for all shoes are the same, so it is possible the absolute mounting position has a finite influence here. The right way to conduct this experiment would have been to fix the absolute mounting position for all shoes, but I doubt this is really possible since different shoes have different exterior structural design.

Because the data indicates it is possible that shoes can have an influence on the reported LSS values, it is necessary to express the uncertainty in GCT and LSS.

Fig 14 : 95% confidence intervals calculated for GCT and LSS at 10 and 12 kph belt speeds. Click to zoom.

The influence of shoes could be due to the relative mounting position differences amongst them. I'm not entirely sure at this point. Whatever it might be, the findings here tell me that it is important to establish an uncertainty range when I talk about my own LSS to others : 

At 10kph and average 173spm : 

GCT falls between 256.1 +/- 3 ms (95% confidence).
LSS falls between 10.47 +/- 0.248 kN/m (95% confidence). 
Power falls between 196.7 +/- 1W (95% confidence).

At 12kph and average 177spm : 

GCT falls between 229.7 +/- 2 ms (95% confidence).
LSS falls between 10.46 +/- 0.317 kN/m (95% confidence).
Power falls between 233.5 +/- 1.8W (95% confidence).

The influence of shoe type on GCT, LSS and power is finite (but small) within the context of mounting positions and shoes tested by me. The other finding is that as speed increases, the influence of shoe type and mounting position increases, which widens the 95% confidence interval on GCT, LSS and Power. At both speeds, the effect of my shoes and mounting positions are extremely small on power. 

Since weight, footpod mounting position and shoes seem to have some influence on LSS, I would prefer to express LSS as :

 [ LSS +/- 3% (LSS) kN/m ] ÷ Weight

II.C Interaction Effects on LSS and Power

The above investigations ignore interaction effects of shoe and mounting positions with other parameters like step rate and GCT for example.

The two mounting positions I arbitrarily labelled 1 and 2 have different absolute X-Y values. Even though differences are small, there is a difference. Therefore, I thought it would be best to express the position of the footpod as a mounting height Y and ignore the X position which is assumed to have no bearing in what the footpod measures.

To get an understanding of relative effects of key inputs on LSS, I assumed there are 4 independant factors within the experiment that would affect LSS either by themselves or through interaction effects. I did not consider speed as independant as I figured speed would be a manifestation of step rate and GCT.

Key factors considered :
Shoe type 1-4
Mounting heights, Y
Device reported step rate
Device reported GCT

Interaction Effects Considered

Main Effects 
Shoe alone
Mounting height

Shoe + Mounting pos
Shoe + SPM
Shoe + GCT
Mounting height + SPM
Mounting height + GCT

Shoe + Mounting height + SPM
Shoe + Mounting height + GCT
Shoe + SPM + GCT
Mounting height + SPM + GCT (s)

Shoe + Mounting height + SPM + GCT

A pareto chart (influence chart) of the interaction effects on LSS (kN/m) at a default and widely used significance level of alpha = 0.05 is as follows :

Fig 13 : Pareto chart of standalone + interaction effects on LSS organized by importance. Only GCT, Shoe+GCT and Shoe+GCT+Mounting Height (Y) play a significant role at α = 0.05. Click to zoom.

Fig 14 : Normal plot of standardized effects. Significant factors like GCT, Shoe+GCT and Shoe+GCT+Mounting Height (Y) are negatively correlated to LSS. Click to zoom.

The interaction study might be proof of the earlier assessment that as standalone factors, shoe and footpod mounting height haved played no significant role in the reported LSS in the experiment. However, the combination of shoe type, mounting height and GCT seem to be influencing LSS more significantly than other factors.  

One disadvantage of this study is that I do not include the leg attack angle as a parameter. Infact, from a model I have developed, I know that leg attack angles influences LSS a great deal! It could be that while mounted on different shoes, the landing angle the accelerometer thinks in is different. 

Shoe type and mounting height, in so far as this set of data is concerned, have negligible effect on reported power for the two speeds considered. 

The study also helps prove an earlier post in Part 3 that :

1) GCT is a predominant factor in the LSS model, even more so than step rate (pareto chart Fig 13). 
2) GCT and LSS are negatively correlated. Lower GCT equates to higher LSS. 

If building LSS is considered "free speed"then focusing on injury limiting biomechanics that yield lower GCT appears fruitful. 

I also understand that any exercise intervention to improve my own LSS should bring out positive LSS changes (post intervention) greater than the maximum uncertainty range I have indicated here, which is 3%. This is done so that I can safely consider the changes in LSS are not just from day to day running variations in GCT and higher order shoe and footpod influences.

My interpretations are open to discussion.

In the next post, I'll be taking Stryd to the mountains. Stay tuned!