Sunday, June 16, 2019

The Poor Man's Giro : Amateur Science in a GT Mimicry

Early in May, I set out to do something in the name of science. I'd read about the physical demands of grand tour racing in research papers and wondered what that would translate to for an amateur rider who works 5 days a week in a day job.

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.

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".

The challenge was called "Poor Man's Giro". I even created a little flyer for it and shared it on Twitter with the likes of sports analytics guru Alan Couzens and exercise scientist Stephen Seiler. 

All rides were attempted in the searing heat of Abu Dhabi. The rides were supported by nutrition from Secret Training U.A.E.

Fig 1 : Too poor to be a pro and ride a Grand Tour? The Poor Man's challenge is an answer!

Now, I faced a few challenges which I need to declare before we get started. Namely :

1) In addition to my day job, I also coach a running club and so squeezing in rides everyday became a challenge.

2) I went on vacation round about the 20th pro stage so I ended up completing just 18 "stages".

3) A couple of rides had to be done indoors on a Cybex ergometer.

4) I took one rest day more than necessary. It was inevitable. Too busy to squeeze a ride in one or two occasions.

5) My time trial bike was not fitted with a power meter so power output wasn't captured for two TT's.

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.

Data Results

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.

Fig 2 : Ride, workload and stress parameters  from each day's ride of the Poor Man's Giro

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.

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.

Fig 3 : Sets of plots showing the HR/HRV related parameters for the duration of Poor Man's Giro

Discussion of Results

We understand from the Grand Tours research done by Sanders 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).

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.

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.

Fig 4 : Typical performance characteristics from Grand Tours from Time Trials (TT), Flats (FLAT), semi-mountaineous (SMT) and mountain stages (MT).  

This can be compared to my own ride characteristics from Fig 2.

Time Trials : 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.

Flat Stages : 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.

Mountain Stages : 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.

Daily Accumulation Rates : For 3 weeks, the accumulation of stress was as follows :

The sum total of TRIMPS gained over 18 stages = 1937 AU = 108 TRIMPS/day.

The same for TSS (aka BikeStress in GC language) = 1386 AU = 77 TSS/day.

Total workload = 6467 KJ, with an accumulation rate = 359 KJ/day.

Daily HR and HRV related fatigue : 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. 

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).

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.

Fig 5 : Highlighted section showing the supine resting heart rate (daily acute and chronic over 7 days) compared with data from March 2019. 


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.

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.

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 found on Twitter.

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Sunday, March 31, 2019

Machine Learning and Learning Humans

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.

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.

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?

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. 

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.

For instance, Brexiteers have little clue how to get Britain out of the European Union without incurring a series of dark uncertainties few really know about. Flight accident investigators 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 automating speed limits in cars by 2020. We want to try and wrest control out of the human being, because ... it must be exciting.

Others look for clues on the ground 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?

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? 

What do we not know about humans that we don't put into machines, which eventually might lead to the creation of what essentially are incomplete models of humans? 

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. 

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Monday, December 24, 2018

Surface Related VO2 Changes Not Reflected In Stryd Power - An Examination of Aubrey

In a recent paper by Aubrey 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 here

Two quick pieces of summary : 

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.

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 mixed ability population of runners".

In a rebuttal 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). 

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 blog, I extracted mean VO2 and mean power/weight ratios from treadmill testing belonging to a subset of 6 runners in random fashion.

Statement 1 : 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 (otherwise known as cost of transport)* will be approximately constant, giving virtually no variation in these values other than that due to noise or subject variation. Therefore, regardless of Stryd power’s dependence upon speed, no correlation would be expected between the normalized measures. 

Aubrey 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. 

Infact, the actual formula is :

Oxygen cost = 60/3.6*VO(ml O2/kg/min)/v (m/s)  --- 1)

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.  

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. 

Fig 1 : Metabolic rate vs running speed measured in 6 subjects. Source of data : Secret of Running (Dijk, Megen). 

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. 

Fig 2 : Oxygen cost of running vs running speed in 6 subjects. Source of data : Secret of Running (Dijk, Megen). 

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.

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 Facebook page many moons ago

Fig 3 : Oxygen cost in three different population groups

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.

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. 

Some appear comical. Subject 6 shows markedly high power ramp beween 15 and 16 kph compared to that between 16 and 17kph. 

Subject 1 on the other hand exhibits something that looks like a curvilinear relationship. 

What is the cause of these artifacts? 

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? 

Fig 4 : Stryd power/weight ratio vs running speed in 6 subjects. Source of data : Secret of Running (Dijk, Megen).
Normalizing the power/weight values by speed will dimensionally yield the energy cost of running through the formula :

ECOR (kJ/kg/km) = P (Watt/kg)/v (m/s)  ---- 2)

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.

Fig. 5 : ECOR (calculated) in 6 subjects. Source of data : Secret of Running (Dijk, Megen). 

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. 

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. 

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.
[....]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

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 own laboratory VO2max testing

Fig. 5 : Energy cost lof running (calculated) vs cxygen cost of running (calculated).  Source of data : Secret of Running (Dijk, Megen). 

What Aubrey 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). 

Fig 6 : Normalized specific power vs normalized VO2.  Source of data : Secret of Running (Dijk, Megen). 

So the methodological error explained by Dr. Snyder seems to be correct. Aubrey must explain why they took this approach and on which former pieces of literature they borrowed this kind of analysis.

Stryd power and VO2 show a significant linear relationship. This relationship is pegged in two ways. 

1) The Stryd powermeter, by way of algorithm, reports increased watts with increased running speed on flat surfaces. 

2) By VO2 being positively proportional to speed on flat land running.

Statement 4 : Data collection methods are not consistent across surfaces, making effective comparison across surfaces impossible.

That Aubrey 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. 

For example, the authors Dijk & Megen stated that the energy cost of running increases uphill. 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.


The methodological "fatal flaw" explained by Dr. Snyder in the Aubrey paper seems to be correct. Aubrey 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.

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.  

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. 

Therefore, the Stryd as a powermeter must be used to make assertions about metabolic fitness only within subjects, as oppoed to across subjects.

If we assume for a moment that Aubrey 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. 

Sunday, December 23, 2018

Examination of the Link Between Oxygen Uptake (VO2) and Stryd Run Power

Footpods utilizing 3D inertial measurement units to calculate external running power have been discussed previously on my blog several times. 

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. 

Infact, a linear relationship has been shown on my blog 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. 


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. 

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.

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. 

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.

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. 

By special request, I gained all the raw data from both tests corresponding to several variables measured during the test for my own record.

Summary of Results

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. 

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).

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).  

Fig 1 : Tabulated summary showing VO2, Stryd power and corresponding heart rate for 6 different speed regimes.

Fig 2 : VO2 and heart rate - time traces compared between two years.

Fig 3 : Strength of correlation between VO2 and Stryd power to weight ratio in two tests.

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.

Fig 4 : Comparison of VO2 distribution

Fig 5 : Comparison of Stryd power:weight ratio


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. 

Specific discussion points are as follows. Note :

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.

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. 

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 predicts my 5K/10K times within a margin of 1-2 minutes compared to actual performance. 

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

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.

Fig 7 : Chosen stride rates between two VO2 tests conducted in 2017 and 2018.

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. 

Fig 8 : Computed % error in run speed = 100 x (Device measured speed - Belt Speed)/(Belt Speed)  

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. 

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).

Other Studies

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. 

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. 


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 to inform about "real time" metabolic demand in situations where minute but critical transient VO2 changes might be prevelant  is suspect.  

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.

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. 


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.

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.

Polar Run Index Table 

Sunday, November 18, 2018

GPS Inaccuracy is a Non-Problem

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.

The other day, I ran a relatively decent 10K 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. 

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.

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%. 

Is that really something to make a big hoopla about?

Don't Fuss, We're Finely Tuned Machines

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. 

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. 

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.

Get a Hold of Precision, not Inaccuracy

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 his blog : "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."

Even during training, I argue that a minor device deviation is a non-factor if you knew that it was precisely off everytime. 

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.

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.

Physiology is Not That Fussy

What about those who think if you don't hit training paces point blank, the sky will come crashing down?

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.


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%.

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.

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. 

Thursday, October 11, 2018

Monitoring & Applying Heart Rate : A Primer

I. Introduction

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.

Cardiac output is the product of heart rate (HR, beats per minute) and stroke volume (SV, ml per beat) expressed as :

Cardiac Output = HR x SV 

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. 

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.

Combining these variables yields the famous Fick's equation :

VO2max = HRmax  x  SVmaxa-VO2diffmax    ---- EQUATION 1

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.

II. Characteristics of HR Benefiting it's Field Application

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.

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.

However, two caveats to the use of HR as a surrogate measure of physiological capacity :

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.

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.

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.

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.

5) There appears to be a steady increase in HR  during activity, a phenomenon termed "cardiac drift".

Due to these reasons, it is a satisfactory variable to use in the field mainly for the following :

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.

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).

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.

HR is not an objective measure of work rate. Some good examples why this isn't so :

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.

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.

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.

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.


A. Monitoring Heart Rate During Running

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.

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.

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 :

Fig 1 : Stacked data showing running power, heart rate and running speed with time from an interval session.

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 cardiac lag. 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. 

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.   

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.

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.

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.

Fig 2: Heart rate dynamics during an interval running session

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.

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.

B. Determining Maximum Heart Rate

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.

Without maximum heart rate from an actual field test, it can be determined on the basis of the Seal's formula :

Max HR = 207 - (0.7 x Age) ---- EQUATION 2

The formula can under-estimate actual heart rate by upto 10-20 bpm so caution is advised.

C. Other Uses of Heart Rate 

Some other uses of heart rate have very good application for overtraining prevention and are described below :

Surrogate metric for operational efficiency : 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 ratio of running power to heart rate 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.

Dehydration : 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.

A runner has two ways to compensate for dehydration related heart rate increase.

A) The most obvious way to counteract HR drift is to stay hydrated before and during the exercise.

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'.

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'.

Checking recovery :  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.

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.

Fig 3 : Supine resting HR for 41 days from the author using an ECG holter. 

D. Concerns Regarding Heart Rate

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 :

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?

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. 

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?

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.

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.

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. 



Friday, April 6, 2018

The Running Locomotor : Cost of Transport and Work Efficiency

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. 

One can draw interesting parallels between the power production processes at the cellular level in the human body and the 4 stroke combustion engine. 

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. 

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. 

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.

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.

great video shows this elaborate molecular "power-stroke" in actin-myosin overlap. For academic purposes, one can read 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.

I. Cost of Transport 

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.

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.

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".

Metabolic power divided by speed of movement yields cost of transport.

COT = Metabolic Power Demand ÷ Running Speed

where units are :
Cost of Transport, COT  = mlO2/kg/m
Metabolic Power Demand (net or gross) = ml/kg/min
Running Speed = m/min

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.

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).

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.

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]. 

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%!

Therefore, calculating COT yields an excellent barometer by which to judge different runners just as fuel consumption guides vehicle purchase.

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.

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].

II. Influencing Factors of COT

A) Substrate Use 

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.

For example, if the intensity is low enough in constant speed running and respiratory exchange ratio (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.

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!).

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.

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.

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].

Aerobic Regime

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.

Aerobic COT = [Net Oxygen Consumption x Calorific Equivalent] ÷ Speed

where units are :
Aerobic COT = J/kg/m
Net Oxygen Consumption  = ml/kg/min [Reported to be between 3.5-5 ml O2/kg/min]
Calorific Equivalent = J/ml
Caloric Equivalent of Aerobic Metabolism (Fat & Carb) = 20.9 J/mlO2  (average value)
Speed = m/s

Fig 4 : Non-linear increase of aerobic COT in several non-athletic male subjects (n=29) while running indoors. Reference [4].   

Anaerobic Regime

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).

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.

AnaerobicLa COT = [Net bLA x O2 equivalent x Caloric Equivalent of Carb. Oxid.] ÷ Distance

where units are :
Anaerobic La COT = Anerobic Lactate COT, ml/kg/m
Net bLA rise  = mM/l
O2 Equivalent of bLA accumulation = ml/mM/kg. This is between 2.7 and 3.3 mlO2/mM/kg (swimming to running) .
Caloric Equivalent of Carb. Oxidatation (glucose) = 21.131 J/mlO2
Distance = m (running time x speed)

Fig 5 : Non-linear increase of anaerobic COT in several non-athletic male subjects (n=29) while running indoors. Reference [4]. 
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.

AaerobicaLa COT = [PCr x O2 equivalent x Caloric Equivalent of PCr] ÷ Distance

The metabolically derived COT, COTm is a summation of anerobic and aerobic contributions. 

COTm (J/kg/m) = Aerobic COT + Anaerobic La COT 

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.

B) Environmental Conditions : Accelerated Running

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.

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.

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).

C) Environmental Conditions : Slope of Terrain

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 also reflected in the GOVSS power calculation algorithm.

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.

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].

D) Environmental Conditions : Heat and Humidity

The running machine faces a substantial reduction in work capacity in hot and humid climates. The reasons are seen below.

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 :

Heat Production = COTm x Speed x Weight

where units are :
Heat production = Watts
COTm = Joules/kg/m
Speed = m/s
Weight = kg

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.

Heat Production = Heat Lost in (Conduction + Evaporation + Radiation) + Heat Stored in Body

The technical issues that lead to an impact on running speed are the following :

1. The running locomotor's aerobic capacity or VO2max could shrink, hence there is a derate in aerobic potential.
2.  The running locomotor faces a cardiovascular drift running in the heat.
3.  Heat production is constrained by speed and weight
4.  Heat dissipation is constrained by body surface area, temperature and relative humidity

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]. 

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 :

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.
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.
3. Increasing age possibly has a multiplicative effect on COT degradation as well as the effect of the ability to shed weight.

Noakes 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.

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]. 

E) Environmental Conditions : Altitude

It is known that COT falls with rising altitude. Overground sea-level oxygen cost of running has been reported by Daniels to be 4.5% greater than that measured at an altitude of 2,300m.

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.

F) Other Contributers to COT : Training Status, Mass and Size

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.

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.

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.

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).

Under the dictation of some of the above influencers, a correction to the laboratory estimate COTm can be written as :

COT = COTm + Correction Due to Combination of (Wind + Altitude + Slope) Effects

III. Predicting Time For Covering Distances

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.

Maximum Running Speed (m/s) = Maximum Metabolic Power ÷ Overall COT

where units are :
Maximum Running Speed = m/s
Maximum Metabolic Power = W/kg or J/kg/s
Overall COT = J/kg/m

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 :

Best Short Distance Running Time (s)  = Distance ÷ Maximum Running Speed

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 :

Best Endurance Speed (m/s) = Highest Fraction of Maximum Metabolic Power ÷ Overall COT

Best Long Distance Running Time (s) = Distance ÷ Best Endurance Speed

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.

IV. Towards Optimizing Cost of Transport

Fascinatingly, both mechanical engine and human locomotory movements exhibit a "non-linear" shape to cost of operation.

Consider that the fuel combusting mechanical engine has a speed and torque dependant optimum fuel efficiency. 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.

Fig 9 : Optimum island for specific brake fuel consumption in an engine. Reference [1]

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. 

Fig 10 : Optimal speed to minimize COT in 9 trained runners. Reference [2]

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.

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.

Fig 11 : Relation between cost of transport (COT) and stride frequency for 12 physically fit and experienced runners. Reference [5].

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?

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.

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 smaller animals have higher metabolic costs and COTs.

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.

V. Apparent Efficiency of Running

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.

What's the efficiency of running?

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.

Apparent Efficiency = Total Mechanical Work Done / Metabolic Cost

where total mechanical work done = external work + internal work

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).

Apparent Efficiency (Gross) = Total Mechanical Work Done / Gross Metabolic Cost

Apparent Efficiency (Net) = Total Mechanical Work Done / Net Metabolic Cost

Where Net Metabolic Cost = Observed Metabolic Cost - Resting Metabolic Cost
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.

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.

The process leading to the splitting of ATP in the isolated muscle comprises two steps and each of these steps have an associated efficiency.

1. ATP-synthesis/energy liberation from decomposition of nutritients : Phosphorylative coupling
2. Energy liberation during ATP-splitting/ATP Hydrolysis : Mechanical coupling

Overall muscle contraction efficiency =  Phosphorylative coupling efficiency x Mechanical coupling Efficiency

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. 

Fig 12 : Components in ATP turnover efficiency in human muscle. Reference [6].

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. 

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.

How much greater? 40% or more for level running (Fig 13, 14).

Fig 13 : Values of mechanical efficiency from several studies. 

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. 

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.

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.

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.

VI. Spring Mechanics and Efficiency

Human locomotors naturally oscillate like a bouncing ball in order to run forward. As discussed in another post, 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.

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.

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).

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.

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.

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].

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%).


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.

Cost of transport is driven by metabolic substrate use and the effect of environment upon cost.

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].

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. 


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[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
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