Sunday, December 10, 2017

Technical Review of Stryd's Running Power Model

In my last post, I reviewed GOVSS Running Power, which is the model adopted by Runscribe Plus. 

As a recap : GOVSS power is a total energy model which includes both the external and the internal cost to move the limbs in relation to center of mass. It also accounts for wind and the kinetic component that play a prominent role during rapid, high speed transient running events such as a track sprint. 

In this post, I review the External Energy Summation Approach (EESA) applied to center of mass which can then be converted to an external power (Part A). I will describe the model in a bit, but one observation before that.

In a Stryd whitepaper published yesterday, the writeup suggested that ground reaction forces are being employed in the calculation of components of power.   After reading that, I hold a level of confidence that the EESA algorithm is used in some capacity, either at a very complex level or a very simplistic level with some inhouse modifications. 

I also review the same whitepaper and appraise the validation they've disclosed (Part B) and describe several aspects of what it shows AND do not show. Readers who are scientifically inclined like me will be interested in this section. 

I also point the reader to my Primer on Running Power in order to get a feel for the changes in mechanical energy during running and how a 9 / 10-DOF IMU basically works. 

PART A : Fundamentals

I. EESA Approach for Calculating External Power

In the EESA approach, the vertical (Y), anterio-posteral (X, fore-aft) and lateral ground reaction forces (Z) are used to calculate the instantaneous speed of body center of mass. 

The resulting velocities are used to calculate the change in potential energy function and kinetic energy function to lift and accelerate the body center of mass. (Note : EESA has been coined by me, for lack of a better term).

The potential energy function tracks the work done to lift the center of mass.The kinetic energy function contains the velocities to move in a forward and lateral direction. In common running situations, lateral motion maybe neglected but keeping with the intent to account for all 3D motion, the lateral kinetic energy is also included in the general equation. 

The computational equations have been summed up in this mathematical infographic in Figure 1.  FxFy  and Fz are the forces in the forward, vertical and lateral directions. Their speed counterparts are expressed as vx, vy and vy. Please click to zoom in.

Figure 1 : EESA computational approach for total external power for running. Adapted from Minetti (2002). Click to zoon in.

Referring to Figure 1, the EESA algorithm is the following :

STEP 1 : The X, Y and Z velocity functions are an integral of the ratio of the respective ground reaction forces and mass, or in other words the axis specific accelerations. After integration is performed, a constant has to be added to the right side which maybe different for level running and gradient running (Cavagna constant). 
STEP 2 : Since velocity is a vector, the resultant running velocity is calculated by the sum of the squares of the 3D velocities.
STEP 3 : Kinetic energy as a function of time is half of mass times the resultant velocity squared.
STEP 4 : Vertical displacement of center of mass is the integral of vertical velocity with respect to time. After integration is performed, a constant has to be added on the right side (Cavagna constant).
STEP 5 : The potential energy as a function of time is mass times gravitational acceleration times the vertical displacement of center of mass.
STEP 6 : The total energy of the center of mass as a function of time is a summation of the potential and kinetic energies. This will fluctuation function in time, with a minimum occuring at the middle of stance phase. For level running, the curve is symmetric. For gradient running, the curve is lopsided to the right side for uphills and to the left side for downhills. 
STEP 7 : Power - Pext - is the time derivative of the summation of potential and kinetic energy functions.

This is the generalized form of EESA.

Figure 2 : Kinetic energy, potential energy and total external energy functions vs grade. Fluctuations in total external energy as a function of grade show asymmetrical profiles for uphills and downhills and a symmetrical profile for level grade. On the downhills, the decrease in total external energy is progressively more than subsequent increases as grade steepens (net energy dissipation). On the uphills, the increase in total external energy is progressively more than it decreases as grade steepens (net energy addition).  Adapted from Snyder (2012). Markups by me.

The disadvantages of the EESA model are the following :

A) It accounts only for the external power to move center of mass. It does not take into the account another source of cost demand, that to swing the arms and the legs. Since it is not a total energy requirement to run, magnitude of calculated power will be lesser compared to a total energy approach such as GOVSS.
B) It doesn't tell us what goes on inside the body. External mechanical work reflects the overall behavior of the whole body center of mass mechanics. Unfortunately, this black box approach seldom provides us with a direct understanding of what is going on inside the body. It is difficult to draw specific relationships using just sheer "watts" to things like forces, moments and storage-recoil mechanisms at the level of joints, muscles and tendons.

II. Stryd Model

Chief features as I observe are :

Ground forces estimated from acceleration signatures : From the whitepaper, it seems that Stryd employs the equations in the EESA framework for external power in it's model. Otherwise, there'd be little meaning behind their efforts to approximate ground forces.

Ground forces are estimated from the acceleration-time signatures in the 3 axes multiplied by mass of the subject runner. What the whitepaper attempts to show is a validation of that force profile against force plate data. There is absolutely no measurement of forces, they are only estimated from the accelerations.

Leg symmetry assumption : Since the Stryd comes simply as one footpod, the mechanics in one leg is assumed to be an overall representation of the body's movement. This assumption carries through into the external power calculation.

Scaling factors for power on gradients : For outdoor gradient running, the ratio of negative and positive potential and kinetic energies are no longer in the ratio of 1:1 and mirrored (see Figure 1).

Stryd employs scaling factors for uphills to account for the greater degree of concentric work, in effect increasing the modeled external power. Conversely, they employ a negative scaling for downhills to account for the greater eccentric work. People have found varying degrees of correlation when comparing to their rates of perceived exertion.

These scaling factors came as a firmware update to Stryd users in early 2017. There has been little in the way of documentation and validaton of the approach for a wide range of runners so this area is an unknown. More about this is discussed in Part B.III below.

Indoor running distance / speed may differ : A small desirable nuance in the model might be for indoor running where the Stryd model would account for the difference in treadmill belt speeds when estimating a relative forward velocity. I do not think this is the case which explains why several people find a small discrepancy between treadmill recorded distance / pace and Stryd distance / pace. I think that the magnitude of this discrepancy maybe less than 5%. 

Form Power : Stryd adds a distinction by singling out vertical work rate done "in place", i.e the power required to displace the center of mass vertically without considering forward displacement. This is expressed as a separate metric called Form Power which other platforms do not highlight. I take the liberty to express it in the following form :

Lifting In-Place Power (due to vertical oscillation) = Step Rate x m x g x Vdisp

where :

Vdisp (m) = Vertical Oscillation [total vertical distance covered by center of mass]
Step Frequency (Hz) = 1/(Aerial Time + Ground Contact Time) = 1/60 x (Step Rate)
m (kg) = mass
g (m/s2) = gravitational acceleration

I've called it lifting in-place power to distinguish it from slope lifting power when running up a hill. 

Take note that this component of power is directly proportional to step frequency. Since step frequency is made up of the inverse of the sum of aerial time and contact time, this would suggest that increasing step frequency is done by decreasing contact time and/or decreasing aerial time. This couples with and affects Vdisp.

The consensus in literature around lifting-in-place power is conflicting. Some studies show that low vertical oscillations are correlated with better running economy (lower metabolic cost) while some studies show the exact opposite (higher metabolic cost). 

The latter point is interesting actually. It has been suggested that dropping vertical oscillation must be accompanied by an increase in step frequency (see figure above). But this increases the internal work needed to sustain high step frequencies, thereby increasing the overall metabolic cost and worsening running economy. Studies have published data backing this negative correlation. A confounding variable in these studies maybe how adapted and well trained the runners were to sustain high step frequencies. 

One point is clear. Studies that have looked at leg kinematics during actual running races find that top tier runners are almost always front foot strikers and show the lowest ground contact times compared to the rest of the field (eg Hasegawa, 2007). Again, this gives more power to ground contact time being an actionable variable. In this way, atleast in my mind, ground contact time and vertical oscillation are "coupled" variables which are again related to the running speed, as the figure above shows. 

Another point to keep in mind is that leg spring action contributes some of the force (and power) needed to oscillate upwards. Therefore, a runner with good spring mechanics provides lesser net force to lift himself than one without. This must mean not all vertical oscillation is "waste", as energy is recycled. The net positive power to oscillate is therefore lower than the suggested calculated value of lifting-in-place power. 

For example, a 64kg runner at 3 Hz step frequency and 5cm of vertical oscillation requires a lifting-in-place power = 95 W. But if 30% of that is supplied by leg spring, the rest 70% is the net positive power that the runner must produce. This equates to around 66 W. 

Leg Spring Stiffness : Another distinction that Stryd offers is displaying a mathematically calculated leg spring stiffness from some of the equations I described in a previous post. This maybe displayed for information only and I do not believe it is used to treat energy savings due to spring biomechanics. See part B.V below for more on this.

RSS : Native to Stryd is the Running Stress Score (RSS) that is a single number quantifying the effect of a daily run. One notes that this stress calculation is non-linear in nature as it credits higher volume and intensity in an exponential way. This thinking is similar to the weighted TRIMP method that assigns exponentially increasing weighting factors as exercise intensity increases. Although I don't know the exact algorithm used, a simple formula I developed approaches within 3% of Stryd RSS. This is based on Stryd's own RSS  rules for different intensity zones. 

It's as follows :

RSS/min = A x e^(B x Pext/CP)

where  parameter A = 0.0758
parameter B =  3.1297
Pext = External mechanical power

CP = Stryd Critical Power

Wind : The Stryd does not take wind into consideration. However, there are several reports of gusts negatively affecting reported power which seem to be a bug that is being investigated. See Part B.VII for more on this subject.

PART B : Stryd Whitepaper Review

I. Review of Stryd's Vertical Force-Time Curve

Vertical power is the rate of change in potential energy. Multiple studies have shown that this component constitutes the majority share in the metabolic cost of normal running.

Since the Stryd footpod has no means to measure force directly, in order to get the correct estimate of force, the IMU must capture the time course of instantaneous vertical acceleration profile which is proportional to the force signature. 

Continuing on, in order to get an accurate estimate of changes in potential work, the footpod IMU must capture time course of vertical displacement of center of mass. 

An image showing the first of these elements is in Figure 2.

Figure 3 : Modeled vs actual vertical force-time signatures in a rear-footed runner for an unspecified running speed. Base image courtesy of Stryd. Markups by the me. 

It is not known what speed the runner was running at but looking at the force signature, it is clear that it was a rear foot runner. The model estimation and force plate data nearly match, particularly when you look at the highest peak vertical force which is important in derivative calculations of impulse and leg spring stiffness.

Some key observations as far as vertical force-time (Figure 1) is concerned :

1) Misrepresentation of first footstrike peak : The Stryd models a nice rounded single peak force when there were actually two. This is significant because the footpod thinks that the footstrike is fore-footed when in reality it's rear-footed. The implications are :

a) The Stryd model neglects first impact peak. If the first rear-foot strike peak is completely neglected, that initial impact peak of landing will be distributed over an inaccurate and wider period of delta time which will suggest that there is no shock loading, when in reality there is.
b) Stryd's force profile estimation for a forward moving (or backward moving) fore-footed runner might be alright but it might be grossly over-looking rear footed mechanics by missing the first impact peak altogether. 
c) If a runner changes gait mechanics on the fly due to the effect of different running surfaces or due to fatigue in a long race, this 'tuning' may not be captured properly by the model.
d) Gradients may substantially influence these errors. To get an idea of grade influences on the vertical force-time profile from empirical studies, please see Appendix image A4. 

2) Mismatch of contact time : Although the actual and estimated signals are close, Stryd under-estimates initial footstrike and over-estimates the actual takeoff point with respect to time (Figure 2).

This has some implications, namely :

a) The ground contact time (GCT) is over-estimated. From the image, I estimate atleast 15-20 milliseconds greater than the force plate.
b) The stance-averaged vertical ground reaction force during GCT does not match 1-to-1 with the actual force plate data.
c) As a consequence of b), the Stryd estimated ground reaction impulse given by the product of force and GCT is different to the actual impulse.
d) Any calculation of aerial times, step lengths and step times using GCT will propagate the error through.
e) Since leg spring stiffness (LSS) is driven by GCT and involves a duty factor calculation treated with the maximum vertical ground reaction force, errors propogate into the LSS model as well.
f) Since the tests were carried out in the laboratory, the effect of gradients and different speeds on the error in GCT remains unknown.

3) Effect of Running Speed on Force-Time Curve Not Discussed : Stryd does not show the effect of running speed on the goodness-of-fit for vertical force curve.

That this important element is missing in the whitepaper prevents a discussion on the influence of variations among broader running speeds and broader gait mechanics. Within literature, researchers have found that simplistic vertical force-time curve models  derived from spring mass models lose their goodness-of-fit as the running speed increases due to the presence of high frequency components from the acceleration of the lower limb.  

This is where I'd exercise some caution. With the current state-of-the-art, I wonder if IMU's may still not be practical for application to short-distance, high speed track racing.

4) Impact of Shoe Type to Force-Time Curve Not Discussed : The impact of variations in footwear to the measured parameters is unknown. This is also an influencer of vertical ground reaction force profiles.

5) Impact of Treadmill Slope to Force-Time Curve Not Discussed : The whitepaper lacks a review of the force-time profile accuracy under the influence of slope (see Appendix image A4). Since step period generally decreases as slope increases and increases as slope decreases, what influence high running speeds have on the model fit when the slopes are greater than 7 degrees inclination is something important to document. 

Figure 4 : Plot showing goodness-of-fit of modeled GCT to force plate measurements. The average error is stated to be 2.83%. The number of runners, running speeds, shoes worn, footstrike mechanics and slope on the treadmill are all unknown which raises the question of how the error varies as a function of each.  Image courtesy of Stryd.

The second element in estimating potential energy changes is vertical oscillation, shown in Figure 3.

Figure 5: Estmated vs actual vertical oscillation across a wide range of runners. Sample size is not disclosed. Experimental method and running speeds to generate the plot is unknown. Stated average error with respect to force plate = 3.18%. Base image courtesy of Stryd. Markups by me.

Some key observations as far as vertical oscillation is concerned :

1) A close fit : A 3.18% average error in vertical oscillation has been shown which is quite good. It is desirable to understand the experimental method, equipment used and the sample size of the runners to put this into context.
2) Error Propagation : I understand that a small error propagates into the Form Power calculation due to vertical oscillation error.
3) The effect of gait parameters on this variation is not documented. The estimation error with respect to gait parameters such as velocity and step duration should be additionally plotted, for example, in the form of a Bland-Altman plot.
4) Explanation of influencing factors behind error : I'm very interested to know if 3% average error is the best achievable given current level of technology. It is desirable to get some sort of explanation to the influencers of this error. Do random influences play into this?

II. Review of Stryd's Horiztonal Force Model

Horizontal power is a function of the rate of changes in kinetic energy. Studies have suggested that the horizontal work, particularly that component of generating horizontal propulsive force, constitutes more than one-third of the total cost of steady speed running.

Figure 6 : Stryd modeled forward speed change compared to force plate measures. Indicated accuracy = 95%. Grade of running surface unknown, but presumably level. Image courtesy of Stryd. 

A review shows the following :

1) Accuracy is decent : Like the vertical force-time profile, the horizontal force-time profile is presumably derived from the horizontal acceleration signature from the IMU. Stryd states that it captures the speed attenuation during the contact phase with 95% accuracy. This is not bad when considering that this anterio-posterior dynamics is a difficult one to capture.
2) Error Propagation : A 5% error in estimation of kinetic energy change propagates a proportional error into the work and power calculations. 
3) Influence of speed and slope not discussed : Like in the case of the modeled vertical force-time profile, the influence of different speeds and slopes on the goodness-of-fit are not specifically mentioned. This is important to document in order to compare how the fit varies under different situations. See Appendix image A4 for grade influences on horizontal force-time curve curves.

III. Basis of concentric and eccentric work scaling factors not discussed : A technical basis for the scaling factors employed by the Stryd model to account for the dominance of concentric or eccentric work during gradient running is desirable (see Part A.II and Figure 1). 

This correction was made as a firmware update in early 2017. 

While I understand this is part of the secret sauce, some pedantic questions are necessary to be asked if we want to remain true to the estimation of a power : 

A) Is the scaling used related more to vertical and horiontal ground forces or is it calibrated with metabolic costs? What was the validation study behind these and will those findings translate well for the general public?

B) Is the power scaling a continuous linear decrease for downhill grades and a continuous linear increase for uphill grades? 

Let's suppose scaling is calibrated against metabolic costs. If power follows a strictly linear decrease for steep downhills while the metabolic cost decrease sharply, this will suggest that the metabolic efficiency increases. Conversely, if power follows a strictly linear increase for uphills while the metabolic cost follows a curvilinear relation to grade , that might suggest that metabolic efficiency becomes progressively worse. There are individual variations playing into metabolic cost dynamics on grade.  

For downhills, a strict metabolic cost decrease may not even hold. For example, it has been documented that beyond a grade of -9 degrees, the metabolic rate actually increases, presumably from the high eccentric cost to maintain balance of center of mass. In other words, there is an optimum downhill angle beyond which metabolic cost increases. 

How that scaling curve has been calibrated is of much interest to me, and I assume, to other scientifically minded runners.

C) Some reports indicate runners losing RPE-power correlation for gradient running. This begs the question whether the scaling factors should be something that is best left for the runner to tune and calibrate through the settings instead of being driven down from Stryd. 

VI. A Review of Stryd Statement on Correlation with VO2

Stryd states in the whitepaper that : "The external mechanical power reported by Stryd has a well established relationship with metabolic expenditure based on testing conducted by Stryd and other third party research teams. "

Now I have done this too in the past during a VO2max test, plotting the relationship of VO2 to W/kg. This can be done by absolutely anyone. 

I consider the statement regarding "well-established relationship" to be a sleight of hand.  In other words, if I take a powermeter that is algorithmically modeled in such away that external power is linearly proportional to running speed (atleast on flat terrain), ofcourse a VO2 test is going to show that ave VO2 at each speed is proportional to external power! This relationship has been "pegged" from the beginning due to speed being an input in the model. There is no unique science in this.

The linear relationship of VO2 to power is encouraging in as far as it only tells us that model algorithm involving speed works.

The next question would be : Can you use a running power meter be used to predict running economy? This carries a risk of mis-estimation because we do not know how transferable such simple relations are going from indoors to outdoors.

The estimation gets worse when it is a formula derived from a book which based it on data from a limited sample of runners that you weren't a part of.  I do not believe you can estimate metabolic cost this way with any reliable degree of accuracy just like HR or HR based formulas cannot estimate caloric expenditure with any reliable degree of accuracy.

Indeed, a study from the University of Guelph and presented at the recent Canadian Society for Exercise Physiology (CSEP) annual meeting in Winnipe challenged the idea.

The researchers found a significant difference in running economy between treadmill and track running for 11 experienced elite runners as measured by standard metabolic measurements. But in the same study, the Stryd power meter and formulaic implementations of economy couldn't pick up any difference between the two surfaces.

Figure 7 : Plot showing VO2 as a function of specific external power reported by Stryd. Since power is linearly proportional to speed, such a relationship is already mostly pegged by design of the algorithm.


V. Leg Spring Stiffness : Information Only Or Actually Used?

For level running, we understand from scientific literature that the storage and recoil of energy in the lower limbs restores an appreciable amount of energy into the positive work phase. Thus, the mechanical efficiency of running maybe greater than 30% depending on the skill and mechanics of the runner. This efficiency of running has a documented linear relationship to running speed. 

Stryd calculates leg spring stiffness (LSS) using published models derived from the mass-spring paradigm. But it is unclear how Stryd's model employs the stiffness into the mechanical work calculations to account for a "savings" in concentric work requirements. In contrast, the GOVSS model appreciates there maybe savings from efficiency increases as a function of speed and corrects the power demand depending on running speed.

So the question is whether leg spring stiffness is simply a metric displayed for information only or whether it is actually used in the model in a fashion as described in the para above? If it is not used, then someone can question the actual value of this. The LSS metric remains one of the most confusing metrics from a trainability standpoint.

VI. Apparent Mechanical Efficiency of Running = 25%

The apparent mechanical efficiency of running is defined as :

Meff, a = ratio of external power (Pext) and metabolic rate (Pmet). Meff, a = Pext/Pmet.

The gross mechanical efficiency of running is differentiated as :

Meff,g = ratio of total power (Ptot) and metabolic rate (Pmet). Meff,g = Ptot/Pmet.

In the context of a Stryd powermeter, we should be concerned about the apparent mechanical efficiency.

As alluded to in section V, human running involves energy storage and recoil going from the negative to positive phase. Several researchers have found that upto 40-50% of the energy stored during the eccentric phase can be returned to the concentric phase within the short time span of ground contact time for which those muscles remain in a loaded state.

Maximum possible elastic energy storage is defined in some papers (such as those written by Kram to be the difference between initial and minimum external energy of center of mass during the stance phase. Energy return is defined in the same papers to be the difference between the ending and minimum external energy of center of mass during the stance phase. The maximum possible energy storage and recovery is then taken as the smaller of these two values.

To me, the way the efficiency is defined and what it takes into account (or what it doesn't) explains a lot of the differences in calculated efficiency between different running power models now arriving in the market. I suspect that an apparent mechanical efficiency value of 25% is artificially low, atleast for running on level and shallow slopes, if it didn't take into account energy storage and recovery mechanics between the negative and positive phases of running.

VII. Effect of Wind on Stryd's Performance

The Stryd powermeter has no way to account for wind effects in the power calculation. In this respect, it will under-report power by a factor proportional to the correct relative velocity cubed. By "correct", I mean that the wind measured has to be applied at the height of the runner, and not what is reported from a 10m or 30m wind tower. 

That said, one of the "buggy" issues, as has been reported by several people both on the Stryd support forums and the Running Power Google Groups, is the sensitivity of power to sudden wind gusts. Reports indicate that gusts cause unsteady spikes in power for some and dips in the reported power for others, which is physically incorrect if you were trying to maintain speed in the face of a headwind. 

The root technical fault maybe with the barometer, which thinks that the a sudden pressure front is a change in pressure altitude. How that information is relayed through sensor fusion and into the Stryd algorithm to mess up the reported power is a mystery to me. Judging by the forums, even Stryd's engineers have a challenge grappling with this issue.

The fact that they may need several consistently gusty days outside to test what's wrong might mean the delay of a corrective action for users.

VIII. Conclusions

Stryd's description of the external running power model and a comparison of modeled variables against force plate data has been long in the making. It is appreciated but delivered a bit late.

From a brief reading, I assess that they employ the general EESA approach to external power with some "in-house" tweaking for uphills and downhills to account for net energy addition or dissipation. 

Stryd is thinking several things, some unique, some literature driven, about the kinematics of running. I give them credit for that.  However, it does not stop the questions about how the model employed will validate for a large number of runners in actual usage.  This same question also goes for the GOVSS run power model. 

The effect of running speed, footstrike variations and slopes on those errors were largely missing from the whitepaper. This was the most important aspect I would have liked to see. This unfortunately prevents an assessment of how closely IMUs can correctly decifer footstrike patterns across a broad range of runners, running speeds and terrain.

Though the stated errors in key variables and things like force-time curves are small, those errors propagate into the calculations of derived metrics. Users must be aware of this when trying to introduce running interventions to effect a change in some of these metrics.  

It is hoped that this technical review will encourage them to release another round of whitepapers so we can understand that aspect.  An independant scientific review from other laboratories is also desirable in order to establish the degree of reproducibility in these numbers.  

With Stryd and Runscribe having published their running models, the lights fall onto Garmin. With a far greater user base, they should find impetus to publish their running power framework soon or risk a lukewarm interest from the market.

In the next post, I'll explore how errors in estimated ground reaction forces translate into errors in the external power calculations from the EESA method. Stay tuned...


Figure A1 : An illustration of vertical ground reaction force-time curve along the gait cycle. Courtesy Weyand (2010).

Figure A2 : An illustration of the horizontal ground reaction force-time curve (lower plot). Courtesy Farley & Ferris.

Figure A3 : Specific vertical force-time profiles for unshod rearfoot-striker, shod
rear foot-striker and a barefoot forefoot-striker at 3.5 m/s running speed.  Courtesy Liebermann (2010).

Figure A4 : Vertical and horizontal force-time curves for a 73kg subject running at 3 m/s over the indicated grades. For the vertical force profile, the first impact peak substantially increases as grade plummets. On the uphills, the second peak substantially increases to the point where at +9 degrees, the slope is rounded. Peak vertical forces decrease as grade steepens. For the horizontal force profile, the negative part of the S curve substantially increases as grade plummets while the curve more or less assumes a half sinusoid. On the uphills, the positive part of the S curve substantially increases as the grade increases while the curve as a whole more or less assumes a half sinusoid. Courtesy Gotschall (2005).

Figure A5 : Submaximal VO2 is linearly related to speed. Courtesy Kram 

Saturday, November 11, 2017

Technical Review of the Runscibe GOVSS Running Power Model

I would like to discuss the Gravity Ordered Velocity Stress Score (GOVSS) model for running, provide some comments in blue italics and simultaneously compare to Coggan metrics such as NP, IF and TSS (all trademarked under Training Peaks).

Tim Clark at Runscribe told me their RS+ will now incorporate the Skiba GOVSS model. Being open in what they are implementing is greatly appreciated. 

Just off the bat : Dr. Andrew Coggan recently commented on the Stryd Forum that many of his metrics and guidelines developed for cycling don't 'necessarily' apply to running, nor should one consider TSS, rTSS, sTSS, BikeScore, GOVSS, RSS etc as completely interchangeable. 

That said, here's the GOVSS algorithm as proposed by Phil Skiba, 2006 :

1. Find the athlete’s velocity at LT by a 10 km to one hour maximal run.   

Note : Presumably the thinking behind this is that a true 10K intensity is the maximum intensity in the intensity continuum where a delicate homeostatic balance in physiological parameters is maintained. Research has also shown that speed or power at LT is a valid predictor of endurance CYCLING performance (r = 0.88 for cycling, Coyle. el al 1991). In cycling, the previous statement has been debated because cycling is so much more than a single discipline of TT'ing. Running on the other hand is predominantly a time trial against the clock so applying a LT limited power model may not be so unreasonable. This is probably also the basis for Stryd's CP and RSS paradigm. 

2. Convert this LT limited velocity to a LT limited power value using Equation 7. "Lactate limited power" may also be called "lactate adjusted power".  

Note : The equation converts a "threshold" velocity to a "threshold" power using Prof. di Prampero's power-balanced supply-demand equation for running energetics which expresses the metabolic RATE of running in terms of COST of energy C. The equation is then modified into a power by multilying with a speed specific efficiency. The efficiency that is used in power equation can be rated to different speeds with a simple linear equation based on the finding that efficiency varies linearly 0.5-0.7 at 8.33 m/s (30 km/h) in a reasonably linear fashion (Cavangna and Kaneko 1976, Arsac 2001).  A 5th order regression model from Minetti (2002) is used to apply a general running surface to the cost for better acounting for slope effects.  

3. Analyze the data from a particular workout from an athlete’s log, computing 120 second rolling averages from velocity and slope data.   

Note - Before applying rolling averages, the following equations are applied to figure out instantaneous GOVSS based power. Equations are from the reference down in the bottom of this article.

Fig 1 a,b,c : Series of equations used to convert energy cost of running to lactate adjusted power
Referring to Fig 1a, Caero, the energy cost of overcoming air resistance = k.n‑1.d2.t2, and k is the constant of air friction (in kg-1. m-1 ) with n = 0.5. Ckin, the energy cost of acceleration = 0.5.n-1.d t-2 , with n = 0.25.  It is important to note that equation was minimally "modified" to suit events ranging from 800m to 5K. But the original form was successfully used to predict performances for middle and long distance running. 

Referring to Fig 1b, the equation describes the velocity independant energy cost C to cover any distance. In the absense of a slope, this defaults to 3.6 - 4.2 J·kg-1·m-1.  In the presence of a slope i, it becomes a 5th order regression equation. 

Referring to Fig 1c, the equation converts metabolic rate to a mechanical power to weight ratio available for locomotion by multiplying metabolic cost with the separate efficiencies. This becomes a total power cost to run as it includes both the cost of things like COM motion and limb swing. 

All values of cost C (kinetic, air resistance and slope related) are calculated as rolling averages over 120 seconds. Skiba wrote that this was to account for the fact that the original 5th order cost of running model was validated to the 800m. 

4. Raise the values in step 3 to the 4th power.  

Note - Skiba investigated LT dynamics in relation to running speed in a group of running subjects and applied a simple power fit (as Coggan did with his data). The regression fit said that the lactate levels in the body were a function of the speed of running raised to the power of 3.5. The power exponent was 4.2 in the top 10% of the subjects and 2.5 in the bottom 10%.  A power exponent of 3.5 became a middle ground to apply to the entire population of tested subjects (N = 94). Presumably, the 3.5 has got rounded up to 4 by Skiba to make it easy to apply but I question this. Why not just stick to the original exponent?

Fig 2 : The basis behind an exponent in the power model (Point 4). 

5. Average values from step 4.  

Note - Same algorithm as Coggan's Normalized Power.

6. Take the 4th root of step 5. This is the Lactate-Normalized Power.   

Note : The general idea behind normalizing is that a normalized power is an ESTIMATED power output that an athlete can maintain for the same physiological cost if the power output had been perfectly constant. Even though the approach wrt Coggan's NP calculation remains similar, where the difference lies is in that whereas NP s a 30 second rolling average, LT NP for running is a 120 second rolling average.  In cycling, 30 seconds was found to be a response time for many physiological variables but some have come out and contradicted the usefulness of NP. I won't go into that.

7. Divide Lactate Normalized Power by Threshold Power from step 2 to get the Intensity Weighting Fraction. 

Note : IWF is similar to the IF concept. 

8. Multiply the Lactate Normalized Power by the duration of the workout in seconds to obtain the normalized work performed in joules.  

Note : Key idea that can be lost on people here is that this is a normalized work in KJ and it is a TOTAL amount of work because the power equation in Step 2 used a metabolic efficiency to convert metabolic rate to power.  

9. Multiply value obtained in step 8 by the Intensity Weighting Fraction to get a raw training stress value.  

Note : The resulting training stress, is by virtue of the math, expressed in work KJ . This may not relate to a TSS implementation of KJ because of the difference in mathematics involved (see above points). 

10. Divide the values from step 9 by the amount of work performed during the 10k to 1 hr test (threshold power in watts x number of seconds).  

Note : This step is basically again normalizing the amount of "normalized work" from the workout file to the amount of work from the LT test. 

11. Multiply the number from step 10 by 100 to obtain the final training stress in GOVSS. 

Note :  The Coggan TSS is graded based on a similar idea that a 1 hour ride at FTP corresponds to 100 TSS. Therefore, GOVSS also becomes relative to the score of 100.  

Hopefully the details in the algorithm show in what respects the GOVSS is different relative to  a cycling based TSS.

Implementation Examples

Below is an example of GOVSS calculated power for a runner performing intervals at 20 kph and running at about 199 SPM on a slope of 0%. The model uses a calculated frontal area of 0.48sq.m to estimate the aero contribution for power. You can play around with this power model here.

Fig 3 : Estimated GOVSS power to run at steady state at 20 kph on flat ground.
Runner weight = 64 kg. Assumed wind = 0 kph.  

Below is a GOVSS PMC from my running data implemented in Golden Cheetah. This is just to show you an example.

Fig 4 : Example of a GOVSS implementation in Golden Cheetah. GC's Triscore PMC uses GOVSS for runs. However, the GOVSS is possibly based on pace, rather than power. This needs confirming with Mark Liveradge. 

Concluding Remarks 

1. The GOVSS model takes into account the energy cost of running and how that varies as a function of running gradient, acceleration and wind resistance. For example, even in slow to medium speed running regimes as those in endurance running, the energy cost to tackle wind resistance is alone atleast 8%.

2. The GOVSS model gives the total energy expenditure of running per km and therefore, includes the effects of internal power needed to swing the arms and legs relative to center of mass (see Physics of Running Power). Therefore, a GOVSS based power may end up being higher than a purely external power that does not account for these aspects.

3. GOVSS relies heavily on measured speed and gradient. Errors in measurement propagate to the calculated GOVSS power.

4. It still has be known whether the originators of some of the equations behind GOVSS intended to have it be applied to distances ranging from 3K all the way to the marathon. This point needs investigation and testing. 

5. GOVSS for running and TSS for cycling use different mathematics and philosophy. TSS from cycling applied for running will be a mis-application, as implied by Andrew Coggan. 

6. As with TSS, the GOVSS scoring scheme relies on base data from a sample population of runners who were tested under controlled settings in a laboratory. The statistical power of such fits and accompanying simplications are not always high Application of scoring metrics to a general population of athletes who are not tested in the laboratory come with the acceptance of a risk of deviation. 

7. Scoring workouts to a curve based on 100 brings it's own debate. 

For example, the popular notion of an FTP as corresponding to the maximum power that can be applied to a bike in approximately 1 hour has been challenged by Dr. Coggan himself several times. It is somewhat of an urban legend, popular but untrue. 

The “approximately one hour” component of the definition has since been clarified to range between 30-75 minutes, depending on the individual. 

Similarly, the CP reported by Stryd Powercenter is said to reflect a sustainable duration of about 50 minutes as per Stryd. 

If the TTE in a cycling and running situation are different numbers and if this varies from individual to individual, one could then question the use of the value of 100 in the grading as that corresponding to a 1 hour duration. 

In the absence of better alternatives to apply in an athlete's Performance Management chart, the GOVSS, TSS, RSS etc all can be used purely for their modeling value but practitioners must refrain from using them interchangeably. 


Calculation of Power Output and Quantification of Training Stress in Distance Runners: The Development of the GOVSS Algorithm (Skiba, 2006) : Link

Friday, September 29, 2017

The Physics of Running Power

Physics of Running Power 

There is a certain theorm we were taught in school that goes something like this : The kinetic energy of a system of particles is the kinetic energy associated with the movement of the center of mass and the kinetic energy associated to the movement of the particles relative to the center of mass.  

This is called Koenig's theorm.

In humans (bipeds), as the center of mass is propelled, fore and hind limbs are alternatively in contact with the ground, while the upper limbs oscillate freely both during the stance and the swing phase. This results in a linked multi-segment system.

Koenig's theorm can be applied to this system to model the mechanical work done in running. 

A. External Work 

The human runner consists of a central trunk and n number of rigid segments each of mass m. The total mass M of the runner is considered to be lumped at center of gravity. 

The potential energy while running is represented by M.g.H, where H is the vertical height of center of gravity from ground.  

The kinetic energy of M is 1/2.M.Vcg^2 where Vcg is the velocity of center of gravity. 

The total external work Wext comprises of the sum of kinetic and potential energy

B. Internal Work

The kinetic energy of ith segment relative to body center of gravity is 1/2.mi.Vr,i^2 where Vr,i is the linear velocity of that segment relative to body center of gravity. 

The rotational kinetic energy of the ith segment relative to body center of gravity is 1/2.Ki.ωi^2 where Ki is the radius of gyration of the ith segment around it’s own centre of mass and ωi is the angular velocity of that segment.

The total internal work Wint is the summation of every segment's linear kinetic and rotational kinetic energies. 

The computational scheme of calculating internal work assumes that energy transfers take place between segments of the same limb but not between limbs or between trunk and limb. 

The total mechanical work done for running is then the simultaneous summation of total external work done and total internal work done for a particular instant.  

I've represented this in a rather quirky picture with the physical equations underneath. 

Fig 1 : Illustration showing the physical equations in external work and internal work as contributions to total work. Kleg here is a lumped stiffness constant for the leg. The yellow dot represents the center of mass and the vertical amplitude of it's movement represents vertical oscillation. 

Power is the rate of doing work. 

For example, if the runner in the picture commits 5 Joules of total mechanical work per kilogram every second, power = 5 Watts/kg (1 W = 1 Joule/second). 

C. How Mechanical Energy Changes With Running Motion

A cycle of running motion from touchdown to touchdown of the same leg is called the stride. Total mechanical work done can be resolved over many strides to see how it varies. 

Some data from empirical testing is shown in Fig. 2 to get an understanding of change in work done. For an idea of magnitude of work, a scale of 100 Joules is shown on the right.  

Observe the troughs and peaks in mechanical energy. The largest oscillations in energy come from the lower leg comprising of the thigh and the foot. Cavagna has written that the lower limb is itself responsible for about 80-90% of internal work. 

The physical understanding here is that every time the leg is on ground around mid-stance phase, potential energy is at it's minima, therefore mechanical energy of center of mass also attains minima (red lines). 

The maxima in mechanical energy of center of mass is attained at the peak of flight phase after a maximum in trailing foot pushoff work and when potential energy is at it's maxima (green lines). 

Fig 2 : Variation in mechanical energy of given sites in the human body as a function of running phase

Duty factor is the percentage of the total time between strides (or steps) that a single foot is on the ground. Values for duty factor can vary from 50 to 90 percent, but are typically in the 60 to 80 percent range. 

As duty factor increases, an individual spends more time with his feet on ground and this has implications for the maxima in mechanical energy, or maxima in power. 

In other words, we might consider that it increases the time spent around the minima of mechanical energy, which thereby might decrease the overall mechanical energy of the center of gravity and overall running velocity.  

But given the same forward speed, the only way to decrease duty factor is to increase leg turnover rate, or cadence. 

Somewhere between too high a cadence and too low a cadence, most good runners will strike a balance to optimize ground speed, time spent on the ground and total mechanical work done. 

Fig 3 : Variation of Wint, Wext and total work done at 3 different running speeds as a function of running phase

D. Average Work and Average Power

The "average work done" for a duration of say 10 minutes means resolving these peaks and valleys of an up and down work signal into it's average. 

The mechanical work done curve can be transformed to a mechanical power curve by turning it into a rate per second. The average mechanical power is about resolving this curve of peaks and troughs to an average value representing that curve. 

A math trick is to remember that the average value of any function can be represented in integral form. Integration can be electronically implemented. To clean up the resulting curves for presentation, signals can be sent through filters and/or computationally 'smoothed' over a desired interval of time. 

E. Mechanical Efficiency 

Human beings have a maximal efficiency of converting chemical energy in food to contractile muscle work of about 25%. Let's call this contractile efficiency as Contr_Eff.

In human locomotion, mechanical efficiency can be expressed in terms of how much total work you put out relative to the net metabolic cost of running. This is Run_Eff. Walking efficiency can be labelled Walk_Eff.

The energy cost of running is expressed as ml O2 consumed per kg per m. This can be converted to a metabolic power (units of J per kg per m) using the conversion of volumetric oxygen to joules. The net metabolic cost is nothing but the cost of running minus the cost of stationary standing.

The ratio of total mechanical work per kg per m (or total power) and the net metabolic cost of running is defined as the mechanical efficiency : 

Presumably, for well trained runners, efficiency is better than that for average runners. Such has been said about East African runners.

Researchers like Cavagna have seen that there are 4 trends to efficiency when they looked at motion on level surfaces :

1. Run_Eff > Contr_Eff. Apprently, this is due to the storage and use of elastic energy through the action of recoil in the lower legs between each cycle of running. The wider the separation between both, the better is the uptake of recoil elements in running.

2.  Run_Eff > Walk_Eff. This is presumably because potential and kinetic energy are out of phase in walking (rolling egg), but nicely synchronized and in-phase during running (think of a pogo stick).

3.  Run_Eff increases linearly with speed, starting at 45% and maximising somewhere between 70-80%.

4.  Walk_Eff maximises at intermediate speeds with values of 35-40%. It then falls off with further increase in speeds. This is interesting and possibly explains why the human considers running instead of walking when speed is past a certain threshold.

Fig 4 : Variation of mechanical efficiency, internal (Wint), external (Wext) and total work (Wtot) and net metabolic energy cost  (En exp) with speed in running and walking regimes. Source : Cavagna (1976).

F. Contribution of Internal Work to Total Mechanical Work

As shown in Fig 4, things really depend on the magnitude of running speed.

Researchers like Cavagna have shown that when the log of internal power is plotted against a log of speed, the resulting linear line approaches a slope of 2. Which simply means that internal power, as a crude approximation, may vary as a square of running speed.

For example, in the graph I have stuck below in Fig.5, one sees that beyond a speed of 17 kph, internal work starts to become a greater percentage of total work done and exceeds external work. 

The magnitudes of numbers are interesting for perspective. Below 17 kph, external mechanical work (Wext) varies from a high of nearly 1.5 to a low of 1.1 J/kg/m. Internal mechanical work (Win) varies from a low of 0.5 J/kg/m to a high of 1.1 J/kg/m. 

Above 17 kph, Wext varies from a high of 1.1 J/kg/m to a low of 1 J/kg/m while Wint increases from 1.1 J/kg/m to 1.6 J/kg/m.

Fig 5 : Plot of changes in Wint (black) and Wext (red) as fractions of Wtot (green) over a continuum of running speeds

For this example, if speed were a modest 7:00 min/mile (13.8 kph), this means that Wint is around 0.7 J/kg/m and Wext is around 1.3 J/kg/m. In other words, the Wint and Wext % of total mechanical power is 32% and 68% respectively. 

Presumably this means that short distance, maximal intensity runners might benefit in knowing the magnitude of internal work done, or internal power. It also means a 10K runner running at 7:00 min/mile spends 30% of his total power internally. That's a sizeable chunk of running workload. 

G. What Do Running Powermeters Measure and Not Measure? 

What they Measure : 

Running powermeters such as the Stryd and Runscribe are inherently 9-axis IMUs. By combining it with a barometric sensor, you get the ability to measure acceleration (X,Y,Z) and orientation but also altitude by measuring the atmospheric pressure and using the difference between that and sea level atmospheric pressure. This is called pressure altitude. 

Among the electrically talented, these chips are also called TenDOFs or '10-degree of freedoms' which is a fusion of 3 chipsets and a barometer which communicate to each other through sensor fusion algorithms (like a Kalman filter). The function of each of the chips are summed up below :

3 DOF Accelerometer : Senses acceleration in 3 directions - X, Y, Z
3 DOF Gyroscope : Senses angular velocity in 3 directions - Roll, pitch, yaw
3 DOF Magnetometer : Senses true orientation in 3 directions (compass)

Averaging the data that comes from the 3 chipsets is said to produce a better estimate of motion than that obtained using accelerometer data alone.

This is a great page to learn about how accelerometers work. If you want to get a practical idea of how an accelerometer works, you can play around with this app Google built. Basically it uses the sensors in your phone to give you an X and Y axis acceleration while running, but you're on your own about what to do with it.

Runscribe also has a RawData tool to inspect the raw file for the original signals. This forms part of their Science Package for researchers

Devices like Stryd are coded with a sleep mode when not active to save battery power. They 'wake up' when motion is sensed and start collecting run data only when a certain threshold in motion is passed.

The hard part is figuring out the coding. Because the raw data from 10dof's can be noisy, they have to be filtered to present meaningful motion data. 

Fig 6: An image explaining the components on a GY-80 10DOF chipset.

Since an accelerometer can integrate acceleration to get velocity and double integrate to get position, algorithms involving changes in velocity and position are easily implemented. 

Focusing on kinematics means these devices do not use any hardware to actually measure force and therefore save on lot of cost and footprint size. 

Fig 7: An image showing the assembly view of a Stryd powermeter
Unlike cycling powermeters, running powermeters have zero strain gages, therefore there is no direct measurement of force. The device simply uses a model that uses measured parameters to approximate running power. 

Fig 8 : A close look at the electronics inside a Stryd powermeter

Now precisely what algorithm the Stryd uses to measure power is not known. On their website, in a little blurb within the FAQ section, Stryd claims that by "approximating" the time-course of ground reaction force in the horizontal and vertical direction and multiplying it with velocity components integrated from acceleration, they can calculate power. This is shown in a screen capture from one of Stryd's Youtube videos.

Fig 9 : An image from Stryd's Youtube video featuring Dr. Andrew Coggan which shows the horizontal and vertical ground reaction force on the left and the accelerometer derived 'shape and form' of those forces on the right. Since the time Stryd dropped a chest mounted sensor for a footpod, they have claimed that the reproduction of ground reaction forces have become better (link in my post) 
The methodological debate here is how the model is approximating the ground reaction forces and with what level of accuracy does it capture that data for level and gradient running and for soft vs hard surfaces. We will not know the answer to that. That is the secret sauce after all.

I was told that values of external power had been calibrated against force plate treadmills in the laboratory within a range of 10 cm of shoe mounting height. We are told by others that the data is reasonably accurate. 

Stryd resolves power into a horizontal power and a form power, the latter which represents the cost of perpendicular bouncing in place. Stryd is marketing this as 'wasted' effort. The sum of horizontal and vertical powers become total power. 

Other power models such as that used by Garmin take a different approach and they swear by the accuracy of their models.

If two powermeters yield different values of calculated power, we can assume that majority of the differences stem from precisely what algorithm is being used. The rest of the differences are probably due to how the signals are filtered, processed and implemented in code and smoothed before they are presented to the user. 

I've conducted experiments with the Stryd during a laboratory VO2max test and there was reasonable correlation between power and metabolic cost. I do not know if similar correlational power would exist in outdoor running with weather and running surface factored in. Stryd has conducted an outdoor VO2 test using a metabolic cart loading onto a pickup and claim that power tracks running economy.  

Because external power is relatively more "stable" than heart rate and pace, it becomes a "useful" perhaps 'objective' parameter to design stress scores and performance management charts around. As a messenger of training intensity and training load, it is useful. 

There are a few key things to question when using low cost accelerometry to study human motion, particularly the messy problem of running.

1. Inter-device reproducability : Given a bunch of running powermeters from the same OEM, to what degree will each device converge upon a similar value given a controlled running task?

2. Intra-device reproducability : Given several identical running tasks over a period of time, to what degree will a given device reproduce metrics over that time?

3. Validity : Given a "measurement" from a running powermeter, to what degree are the results meaningful , i.e what co-relation do they have in relation to real physiological demands of running?

Criterion validity measures how well the data corresponds to gold standards of measuring the same thing. Convergent validity is the extent to which the measurements made by the sensor are associated with those made with other assessment methods that intend to measure the same or similar aspects.

Where to Apply the Sensors : 

There are devices that measure running power hitting the market that are affixed to different positions on the body. Some, like Garmin's pods, are affixed to the shorts. Some, like the Runscribe and Stryd, are mounted on the shoes, either at the heels or on the laces. An earlier version of the Stryd, called Pioneer, came as a chest mounted strap.

There is a debate on what is the best position. For consistent measurement, mounting at the shorts  and the chest is said to be problematic since the pod also exhibits motion when the fat layer and short waistline moves relative to the core of the body.

However, using the same argument, the Stryd foodpod exhibits relative motion on certain shoes as the foot-mount bracket "slips" on the laces. I suppose any mounting position, if properly controlled, is valid. But it does seem that the foot-mounting positions seems to be the least worst among all three positions.

What They Don't Measure : 

Estimating the true workload of running is a tricky business due to a couple of reasons.

1) First, in level running at constant speed, there is a substantial recovery of elastic energy at each stride, that brings about a corresponding reduction in the mechanical work performed by the active muscles.  In other words, when your muscles shorten to propel you forwards, some of the energy it uses has been stored from the previous stretch cycle.

On non-level running surfaces, the portion of negative eccentric work starts to become a significant factor on appreciably steep downhill slopes, where the leg muscles are working to both brake and stabilise the human runner from toppling forward. In this regime, use of elastic recoil maybe lesser than on level running.

For these reasons, it is inappropriate and erronous to assume a running efficiency value equal to that of purely isotonic work (i. e. on the order of 25 %).

Powermeters can't tell you want is truly going on with the elastic recovery portion of running, however some algorithms like Leg Spring Stiffness (LSS) maybe a step in this direction. One also has to realize that LSS maybe subject to various interpretations depending on the mathematical implementation. See this post for an overview.

2) Secondly, powermeters do not sense internal power.  In literature, researchers have summed up the kinetic energy needed to move all important limbs in running, multiplied them by two for contra-laterality and divided by the stride time (2 steps) to express that in terms of power (W).

A problem with the above calculation is that it might over-estimate the amount of actual muscular power. Consider the case where if the energy can be "transferred" from one limb to the other due to speed and momentum without any muscular contraction actually happening, the total work you calculate is greater than that actually being used.

Sensing internal work is most likely hardware and computational intensive.  Studies show that for the same running speed, different methods of calculating internal power yield around a 1000% difference between highest and lowest values. 

3) Running powemeters do not factor in wind and therefore, any extra workload to move against stiff aerodynamic resistance is unaccounted for.

For example, in metabolic terms, a +4.5 mph headwind translates to a +5% increase in VO2 according to data from Dr. Jack Daniels. For maintaining the same pace, the running powermeter will "lag" behind metabolic intensity because wind resistance is not factored for.

Since fast runners "create" their own wind even in calm conditions, not being able to assess a true intensity of working in the fluid medium could be an issue, particularly in places with high air densities and air pressures. This might present a problem to a runner with an inflexible pacing plan.

4) Similarly, external power does not factor in a temperature. It is left to the runner to calibrate a power based pacing strategy against the ambient temperature and humidity.

While power is said to be "objective", it does not in any way diminish the need for the runner to calibrate against perceived effort and possibly, even heart rate. A sensible approach is one that is holistic, especially if runner in question is someone known to push their body to the extremes. 

H. The Implications of Not Knowing a "Total" Running Power

1) One does not know the true mechanical workload of a run. 

True workload is true total workload. Unless you're a kangaroo, humans commit internal work to run. How an algorithmic estimation fares against true intensity among different runners, of different age groups, of different geographical backgrounds, on different terrain - all carry an uncertainty to it. At the heart of why you would want to measure the intensity of an exercise is the ability to get valid information.

2) For faster runners, not being able to assess Wint means not knowing a sizeable proportion of total workload that may contribute (or deduct) from movement efficiency. 

Maximal running elicits high amounts of joint torque and power in fractions of seconds. Short distance track runners who use a substantial portion of limb power to propel forwards are probably better off with traditional or slightly more advanced techniques of training to extract maximum potential. 

3) Metrics using external mechanical power may not actually explain performance differences among runners and may not be helpful to address biomechanical issues.

The complexity with running lies in the fact that for the same speed, there are wide variations in economy among runners. We still don't exactly know what makes East African runners so good at what they do but various theories have been provided, one of them being running economy.

Traditionally, economy has been measured in metabolic terms. For example, if you need 200 ml O2/kg/min to run at 7:00/mile, that's your running economy at that speed.

With the coming of power sensors, a commercial market of sorts has opened up to introduce new ways to interpret this data. There's a plethora of metrics thats pouring out from these efforts.

It is my humble opinion that some caution must be exercised when basing value judgements using efficiency metrics calculated using external power.

For example, Stryd's analysts write that running efficiency is 20-25% and that 40% efficiency is "inhuman" without distinguishing between a total running output and external running output. Expressing clarity in what goes into the effiiency calculation avoids confusion. As we have seen before, mechanical efficiency can be substantially different based on speed, running surface and elastic energy recoil. 

In another example, Andrew Coggan and TrainingPeaks have introduced a "novel" metric called Running Effectiveness. This is a complex metric that is based on a ratio of speed (in m/s) over external power to weight ratio (W/kg). 

Notwithstanding the need to get several things correct in this ratio and filter for course and weather decoupling to get a sensibly stable number, it must be borne in mind that the power in the denominator is still an "external power" only. 

Therefore, trying to use Running Effectiveness for basing value judgements about runners maybe methodologically flawed. Depending on speed, a major chunk of total power - internal power - is not factored in.

Similarly, the inverse of the above metric is packaged into a metric called Energy Cost of Running (ECOR) by the authors of the book Secret of Running. In the book, they implore runners to monitor this metric and try to reduce energy cost.

Personally, from more than 10 months of running data, I do not have confidence that any decrease I'm seeing in ECOR isn't simply a function of normal variability in the data. Therefore, the analyst must be aware that a change that is less than or within the tolerance attributable to device variability is not conclusively a positive change purely from training.

The general advice to reduce cost of running is absolutely well taken, but hang on. Again, ECOR is calculated using only external power and presents a possibly limited picture of true cost. If you accomplish reducing ECOR in your runs, so what? Is an improvement in ECOR actually tied to something happening within the body?

Therefore, I do not think it is helpful to use a surrogate cost of running based on external power for cross-comparisons when you do not address and control for a major chunk of running biomechanics which is the movement of the limbs.

As Donald Rumsfeld once remarked, there's known unknowns and unknown unknowns. Internal power is a known unknown. The unknown unknown is what fraction of total power the internal power really is and how that varies among people. A reduction in ECOR or an increase in RE may not disclose the entire picture.

Carrying an evidence based approach in the application of such metrics is advisable. For example, a validation study could be conducted on an appropriate sample of runners to assess the correlational power of metrics like Running Effectiveness in relation to being able to explain actual performance variations among runners.


Technical Review of the Stryd Power Model


External, internal and total work in human locomotion.
P. A. Willems, G. A. Cavagna, N. C. Heglund
J Exp Biol. 1995 Feb; 198(Pt 2): 379–393.