Sunday, March 26, 2017

NYUAD Ultimate Athletics Track Meet : 800m and 400m

On the 16th of March, I decided to drive over to NYUAD and test myself in the Ultimate Athletics 800m and 400m timed events. Medals were up for grabs for the 1st - 3rd places. 

Long story short, I managed a podium in the men's seniors category in both the 800m and 400m events, spaced about 45 minutes apart. I went limping back home and was happy to shampoo the sand off from my hair. 

To be fair, it was a heck of a windy day (Beufort scale 4) so there wasn't much of a turnout at the event. Which was good because I was wearing an ugly pair of Hypersprint 6 neon track shoes by Asics and was praying that no one would see me. 

But those who turned up were pretty solid runners. In the 800m, I ran with one of the top teenage female running stars in Dubai - Megan Dingle - and was hanging on for dear life. Definitely felt 100 years older. 

In the 400m, I was served some solid African competition but in hindsight, that turned out to be a great testosterone booster because I turned out my fastest 400m. In both events, I managed a PR from the last indoor meet at the same place.

A couple of preliminary photos from the action (check out the massive number of spectators!) :

The results were encouraging for someone who has had virtually no track running since last September 2016. I had great hopes to set up the Stryd powermeter and record data from the run. Unfortunately, the device didn't wake itself up during the second shorter run (the 400m), meaning I only captured data from the first 800m run. Bit of an annoyance.

From the data I did capture for the 800m, things went as follows :

Time : 2:30"
Pace : 5.3537 m/s
Cadence : 102 spm
Estimated VO2 : 55 ml/kg/min
Power to weight ratio : 5.30 W/kg 
Form Power : 64W
Vertical Oscillation : 6 cm
Leg Spring Stiffness : 10 kN/m
Ground Contact Time : 176ms
Run Effectiveness (RE) = 1.01 m/s / W/kg
Energy Cost of Running = 0.98 kJ/kg/km

A couple of things from the data :

1) You notice that even though power picks up in the first 20seconds of the race, the other variables such as GCT, LSS, VO etc take time to activate. This is bizarre and I label it a lag from the Powercenter screenshot. I grow discouraged from the behavior of Stryd on short, fast track runs. 

2) In the final lap, about 200m from the finish was a nice burst of 20kph headwind smack against the face. This was where I slowed down a bit but consciously picked up my legs in order not to fall behind (or fall off!). The delta in wattage from initial part of the race to this point was about 110W.

3) Knowing from a previous RAK half marathon race that my FTP maybe between 200-205W, the intensity factor of the 800m was approximately 330W ave / 200W = 1.65. 

Race results, in old school paper form. 

Highlight of the night was to get introduced to some solid fast twitchers from Zimbabwe (if I recall correctly). Somehow this 63kg slow twitcher was keeping up but it was a hard effort. I'll look forward to more, NYUAD!

Saturday, March 18, 2017

Actionable Intelligence for Running Part 7 : Running Power Characteristics During a Duathlon

In Part 6 of this series, I inspected data from a VO2 lab test data and graphed it's relationship to my corresponding power to weight ratio for 6 different running speeds. What I discovered what the non-linear nature of VO2 (rising and settling dynamics) and the inability of a linear equation to predict instantaneous oxygen cost from a power to weight ratio. 

In general, what was encouraging to see the was the proportional rise in both VO2 and power to weight ratio as speed increased and this credits the Stryd footpod as a steady state "running cost" predictor even though it is an accelerometer / bouce meter, i.e it does not directly measure mechanical power but algorithmically outputs power based on components of velocity extracted from acceleration data.   

I also ended the post by stating that the Stryd does not account for outdoor wind resistance nor for the effect of temperature and humidity, so using an indoor treadmill based correlational equation is likely to underpredict the true cost of running outdoors, especially against winds pushing past Beufort scale #6.

Readers familiar with my previous posts on the GIANT Duathlon Series will know that this race frequently brings some top athletes from the region to the start line. The race format is 3K run, 25K bike, 3K run. This is my third season as a duathlete.

In this post, I'd like to inspect running power during the two running splits of Race#4 held on March 10, 2017. 

Equipment and Personal Data

Running Shoes : Mizuno Wave Ronin 2 (Pre-2010, yes I hold onto old stuff)
Shoes Weight (pair) : 7.5 oz.
Heel to Toe Drop : 9mm
Footpod : Stryd 
Body Weight (unclad) : 63.5 kg
Training (conditioning) : 8-10 hours weekly

Fig 1 : Mizuno Wave Ronin 2

The Course 

The Data

Elsewhere, I will describe in a short race report the feelings and effort going through this race. In a nutshell, it's been one of my best performances to date, having placed 8th in my age category. However, it keeps getting more difficult race by race to move up and 1:17:36 is nothing to boast about.

Fig 2 : GIANT Duathlon 2017 Race 4 results (30-39 Age Category)

The Stryd and Stages powermeter will not automatically pair to the Polar V800 as sport mode changes in a duathlon. Further, the V800 does not have a power feature within running. Therefore, I relied on offline data saved on the footpod for post-processing.

Below is a composite plot showing running power and biomechanical characteristics of the race. Note that cycling has been ignored except to trace an average cycling power for that duration.

Fig 3 : Composite plot showing running power, form power, ground contact time, vertical oscillation and leg spring stiffness from the two running splits of the Giant duathlon Race#4 on March 10, 2017.

Focusing in on the two run splits, the performance variables are tabulated below :

Fig 4 : Performance tabulation of key power and biomechanical variables during the two running splits of GIANT Duathlon Race# 4.
Please note that speed was calculated from the distance vs time relationship from the clocked results of the race and not from the footpod.


All highlighted items - speed, avg. power, power to weight ratio, form power to avg power ratio, cadence and LSS suffered in the second run leg. Considering these facts, the effect of fatigue during short high intensity sprint duathlon is clear to see.

The delta between these variables (those in Run 2 minus those in Run 1) expressed in percentage are as follows :

Fig 5 : Calculated percentage differences in running performance variables in Run 2 compared to Run 1.

1. A 10.5% decrease in run power resulted in a 10.7% decrease in pace in run # 2. Knowing the proportional relationship between VO2 and running power from Part 6, I conclude that the internal running engine ran a bit out of steam. 

Fatigue is multifactorial, not just cardiovascular. There was a short duration decrease in power about 1/4th of the way into run # 2 which in reality coincided with a slight tightening of the right leg muscle where I had to throttle down power to 180W for a few seconds.

However, there were no cramps and no stopping to loosen the legs. The salt instake for the day was good considering the ingestion of both a GU gel worth of 180mg of sodium and an aerodynamic water bottle filled with water + 380mg serving of sodium in 50g of electrolyte mix. 

Some others who have seen my data comment that this is an example of predominantly "metabolic fatigue".

2. Form power, i.e the cost of "perpendicular bouncing" as a percentage of total external running power, was 8% higher in run # 2 than run # 1 (external running power does not account for the swing in upper and lower body limbs).

3. Ground contact time (GCT) was 9.76% greater in run # 2.

4. Leg spring stiffness (LSS), extensively discussed in Part 1, Part 2 and Part 3 of this series, was 2.9% higher in run # 2. Cadence decreased and GCT increased between the two runs, but as previously discovered by experiment, the effect of change of GCT on LSS is greater than is the effect of cadence on LSS (Part 2)

5. Run effectiveness (m/s over W/kg), a surrogate for running economy, decreased by a tiny fraction of a % in run # 2 compared to run # 1. 

Within each of the splits, the behavior of the RE trend (fraction of instantaneous RE over average RE) was a mildy increasing one for run # 1 and flat for run # 2. Please note that the calculated value of RE is sensitive to the data and abnormal spikes in speed or drop in power will result in higher than usual RE values.

My conclusions from the above data study for sprint duathlon are as follows :

In an ideal scenario :

a) Leg turnover would be similar in the two run legs. Longer swing times during the start of the second run affect GCT which consequently has bigger impact upon LSS than the lowering of step rate alone.

b) Vertical "bouncing" as a fraction of total power would be reduced in the second run so that more of the horizontal component makes up the total power. However, I  must confess my understanding on components of power is not on par with the coaching community. I believe one has to bounce to an extent to generate the potential energy needed to activate the storage potential of the leg spring, so an optimum must be struck between too little bouncing and too much bouncing. Too much bouncing is understandable since energy is being used to elevate and lower the center of mass and perhaps some of that could be acively focused instead on moving forward. Form power is something to continue experimenting with.

c) Nutrition points would be more optimally placed during the race to allow proper absorption by body before the demands of the second run. Ideally, this would allow a more even power to weight ratio between both the run splits. Race strategy is knowing exactly at what points to ingest and that can have a pronounced effect on performance during the second run split.

d) Based on 400m and 800m track results, I have the potential for RE > 1.00. What that will mean for performance in the second run split is something to be tried out. Racing is always learning by trial and error. In these short high intensity events, you always have to push your body past the limit to place well but you also have to throttle things down a notch to first finish ! 

Saturday, March 11, 2017

Actionable Intelligence for Running Part 6 : Relationship Between Oxygen Uptake (VO2) and Running Power

In Part 5, I mapped out the power displayed by the Cybex 770T "powermeter" treadmill against changes in speed, grade and weight. The displayed power was based on calibration with the AC motor frequency. It was an interesting exercise, showing how treadmill measured power is linearly related to the 3 parameters. A similar experiment can be done using the Stryd App by changing grade and speed however one would also have to change the weight and I didnt choose to mess with that. Mapping the information from the treadmill display reading gives me reasonably good information for indoor workouts. 

Today's post examines something much more fundamental : the relationship between volume of oxygen uptake against external mechanical power measured by Stryd (as opposed to total mechanical power, see Appendix Fig.2). The objective of this test was to examine how closely related are measured VO2 and footpod based running power. The insights I got from this test are given at the end of this post in blue italics.

Procedure & Preliminary Result

A week ago, I participated in a 20 minute graded VO2max test at a well established professional sports medicine laboratory in Dubai. The test was conducted on a lab worthy treadmill and using all standard equipment as employed in standardized VO2max tests at other facilities.  

Treadmill belt speed was increased from 8km/hr to 16km/hr in 3 min increments to capture not only the "linearly" rising component of VO2 but also the "settling" value at each speed. The machine was set to 1% incline as is standard practice.

The test ended at what point the sports consultant Dr.Ramzy Ross thought was a reasonable place to stop based on maximal VO2 stabilization, HR and samples of my blood lactate taken at regular intervals by prick method. Two lactate turnpoints were discovered.

During the test, I was wearing the Stryd footpod on my right shoe. Because operating the Stryd phone app was impossible during the fatiguing test, I relied on saved offline data to form the following conclusions.

VO2 curve can be approximated as linear but it really isn't. Below is the result from the preliminary graded VO2max test. I've hidden absolute values of VO2, the point being to show here the "rising" component and the "settling" component of the VO2 curve (blue color). 

Fig 1 ; Preliminary result showing HR and specific VO2 during course of a graded VO2 max test performed on the author. Incline grade = 1%.

Since instantaneous power data was from a foodpod not related to the VO2 equipment, careful stitching of the data had to be done. In other words, if the raw data from the VO2 test has a different sampling time than the Stryd data (every second), you will not be able to piece together the two information correctly.

Relationship of VO2 to Running Power

After some post processing, the best way I have found to present the data with respect to speed is through individual box plots of VO2 and power. In the following figure, both power and VO2 are normalized to weight.

Fig 2 ; Box plot of VO2 values with corresponding power to weight ratios at specific speeds during a graded VO2max test performed by the author. Median values of VO2 range are connected only for sake of representation.


1. Because of the fluctuation of oxygen demand and the nature of the stabilization curve, VO2 data exhibits a range of values at specific speeds (represented by the boxes in Fig.2). The range of Stryd measured power to weight values is, on the other hand, tighter (which is good). Connecting median values of VO2 box plots, it can be seen that an increase in speed accompanies both an increase in VO2 and power to weight ratio.

2. A linear regression relationship between range of VO2 values and the range of power to weight values suggests the following math, based on a R squared value of 52%. In other words, looking at the entire range of non-linear VO2 values, only a little more than half of that data is explained by corresponding power to weight values through a linear equation. This is specifically because of the nature of the VO2 curve - it is not linear.

3.  It is possible to look at the mean (or perhaps median) values of VO2 and mean values of power to weight ratio for each speed and correlate both of them. Mean values can signify the "steady state" value of VO2. This way, the relationship becomes more linear and the linear trend line shows an R-sq value of 99%. This helps to "approximate" a steady state metabolic cost from just power data alone.

Fig 3 ; Linear trend between mean value of VO2 max and mean power to weight ratio for specific speeds during a graded VO2max test performed by the author. 

4. When the VO2max test incorporates a blood lactate test, it is possible to know what values of VO2, HR and also running power correspond to the lactate turnpoints (lactate thresholds). It is believed in the latest exercise science literature that lactate is not a waste, rather it is a source of energy and also a prevention mechanism against fatigue. However, a host of processess associated with fatigue occur around the lactate turnpoints. By having knowledge of the power values associated with these turnpoints, it is now directly possible to target "high power" training zones around those markers, rather than using someone else's interpretation of what your thresholds should be. 

Please note that in making the above statement, indoor running power and outdoor running power are assumed to be close if you do not account for wind resistance. Please see appendix plots showing a narrow band of power values (185-190W) for jogging at 6mph. 

6. If you assume 20.1 Joules of energy per ml of O2, the steady state VO2 values can be converted to a steady state metabolic energy cost. Subtracting the resting metabolic rate requirements from this value then gives you a relationship between net metabolic rate per kg and mechanical power to weight ratio for steady state running. Dividing the mechanical power to weight ratio by the net metabolic rate per kg gives you a predicted efficiency. 

My resting metabolic rate from past data (Weight = 65kg) = 68 kcal/h = 1.216 W/kg

For a running speed of 12kph, this translates to :

VO2, ml/kg/min = 8.8766(3.41W/kg)+ 8.2972 = 38.56 ml/kg/min = 775.056 J/kg/min = 12.92 W/kg

Net Metabolic Rate = 12.92 - 1.216 = 11.70 W/kg

Predicted efficiency = (Power/Weight )/ (Net Metabolic Rate / Weight) = 3.41/11.70 = 29.14%

7. VO2 and power values are very individual and vary with training (or lack of). I do not believe it is correct to use someone else's VO2 data and use their VO2-power correlations to derive one's own physiological "state". The Dutch researchers Hans van Dijk and Ron van Megen have written on their blog that test data from 14 runners show differences in the VO2-power relationship because some happen to be more economical than others. Caution should be exercised while estimating VO2 from power, especially at submaximal running speeds.

In other words, there is no one absolute formula to estimate VO2 using power values and such approximations do not substitute for actual lab testing. That said, it is encouraging to see the proportional relationship of oxygen demand and measured running power for use in one's own study of training and racing performance. 

Stay tuned for more. In the next post, I will show how I utilized running power metrics during a local duathlon in Dubai.


Stryd does not account for wind resistance so on level ground, I'd be suprised if the power readings are too different between treadmill and outdoor running. See the two plots below, where at a slow jog at 6mph (10min/mile), I'm seeing a 180-190 wattage band for both scenarios. Such observations, I believe, are device dependant. Please experiment extensively with your footpod for establishing indoor and outdoor power values.

Appendix Fig 1: Two plots showing running power at a slow jog of 6mph while running indoor and outdoor (both circled). 

Appendix Fig 2: Components of external power measured by Stryd which flows into the metabolic cost of running. Slide adapted by Andrew Coggan, where he took a graphic developed by Hoogkamer, Taboga, and Kram, which depicts the various metabolic costs of running and their power components. 

Monday, February 27, 2017

Actionable Intelligence for Running Part 5 : Mapping Treadmill Power Against Speed, Weight and Incline

In part 4 of this series, I made baby steps with a commercially available footpod called Stryd and ran with it in in what is billed the 'fastest half marathon in the world'. I measured only power and made some indirect assessments of what would be a safe threshold power level to run that distance with current fitness level. I also looked at running effectiveness.

Today, I kept the Stryd aside and turned to a neat powermeter treadmill at the home gym called the Cybex 770T with Intelligent Suspension. In Part 2, I explained how this treadmill uses an AC motor with a variable frequency inverter drive. Treadmill belt speed is based on output frequency to the motor and according to the OEM, it would need no calibration. Infact, I measured the belt speed and even measured the time it would take for 10 revolutions. Comparing this to the treadmill speed readout gave a 1:1 match. 

The objective of today's short test was to study how the treadmill maps power output to speed, mass and grade. 

Objective : Curiosity, mostly. How does machine power vary with pace and mass? Perhaps mapping this would help in comparisons when doing the same with Stryd powermeter (to be tried later).

Test Protocol : Enter my correct weight of 64.5kg into the machine. Keep speed constant at 8kph (7:30 min/km) pace and get power readouts at 0%, 1%, 2%, 3%, 4%, 5% and 10% incline settings. Repeat this sequence with 10 kmph (6:00 min/km) and 12 kmph (4:36 min/km) speeds. I repeated the same experiment by entering weights of 70kg (+5 kg mass increase) and 80 kg (+10 kg). The total number of readings taken were 63.

Results :

Power output readings to corresponding mass and grouped by pace are shown below.

Fig.1 : Power table for 3 speeds and 3 weights for 7 different grades as measured on Cybex 770T.

For a given running pace, the power reading was linearly related to grade. Below, I show example of linear power lines for my weight 64.5kg and 70kg and 80kg for running pace 13kph (4:36 min/km). Also, both the y intercept (power at 0 grade) and slope of the line increase with mass. 

Fig.2 : Power vs Treadmill incline for weight input of 64.5kg (yellow line), 70kg (orange line) and 80kg (green line).

To understand how power is mapped to speed, pace and mass, I performed a linear regression on the response Power with predictors speed, pace and weight input to the machine.

The regression equation I obtained was :

TREADMILL POWER (W) = - 225 + (7.46 x GRADE) + (3.00 x MASS) 
+ (18.8 x Speed)   [tested for running speeds only > 8kph]

where grade is expressed in % , Mass in kg, and Speed in kph.

An equation is derived to map treadmill belt power to running speed, grade setting and pace for the Cybex 770T treadmill. The key takeaway is that maintaining the same power on an incline as on level ground running is impossible unless running pace is slowed down. For perspective, if a 64kg person ran on this treadmill at 8kph with a 10% incline setting, he'd have to slow speed by 1 min/km or more to match the same power reading obtained with a 0% incline.

My finding is that for a given weight, the power reading increases by 1.4 times between 0% and 10% grade. My finding is also that for a given grade, power increases by 1.24 times between 64.5 kg and 80 kg. 

The equation tends to slightly overpredict at lower speeds and underpredict at higher speeds for a given weight. It also tends to slightly overpredict at lower weights and underpredict at higher weights for a given speed. The sweetspot of the prediction seems to be at a pace of around 10 kph where errors are less than 2%.

In the next post, I'll compare running uphill and power numbers using the Stryd to see if these same general takeaways are maintained. Ciao!

Monday, February 13, 2017

Actionable Intelligence for Running Part 4 : Pacing by Power & Running Effectiveness

In Part 3 of this series, I continued looking into Leg Spring Stiffness (LSS) relationship with speed and time. I found that LSS is a function of speed and while it has been considered by some in the running community to be linearly increasing with speed, I found no evidence of strict linearity. 

Some limited data from long runs suggested that  LSS may also drop with duration, hinting that running form was being affected. That information is subject for further confirmation from new runs.

This post focuses mainly on running power. LSS, ground contact time, VO, ground reaction force, swing angle etc are all biomechanical ingrediants of what makes power. Power is an input to create propulsive speed. 

Many weeks ago, one of the questions I had on my mind was whether pacing by a powermeter is a valid approach. In cycling time trials, it is common for athletes to pace by a known power as a percentage of critical power (CP). Could running adopt that strategy?

To test this, I ran what is billed as the "World's Fastest Half Marathon", the RAK Half in Ras al Khaimah, U.A.E on February 2017. Being a flat out race with little undulating terrain, it was a perfect ground to inspect running power. I completed the half in a net time of 1:50:49, the reasons for which are below. 

Prior to this run, I had no idea of the correct value of my CP since I hadn't bothered to do any of the track based tests that Stryd advised. However, I had an idea of estimated CP from a multicomponent exponential model fitted to all the past runs with power since January 1, 2017. 

CP from the model in the immediate week before the RAK half was approximately 207 Watts.

To test whether pacing by power was a valid approach, I had to run at what I call "suicide pace", which is an unsustainable power output greater than the estimated CP. This had to be mostly by feel or RPE (rate of perceived exertion). 

The test protocol is below and deceptively simple. 

Test Protocol

1. I chose my "suicide pace" as around 230 Watts average.

230 ÷ 207 = 1.11 Intensity Factor.

2. I switched the watch to power mode and ran by knowledge of power alone. No speed, no heart rate, no duration,

3. I ran till certain 'death', i.e complete fatigue. I then limped to finish line, plugged the computer to post process the data.

The intelligence I gained from this exercise is, as in previous posts, summarized in blue italics.

Pacing By Power Insights

The following plot shows power and speed as a function of duration.

Fig.1 : Time dependant running power (black) and speed (yellow) for the RAK half.

The following are the insights I gain from the data :

1. Power tracked running speed remarkably well. Ups and downs in power followed ups and downs in speed, except for data regions showing spikes in speed.

2. A regression analysis on speed vs power from my RAK run suggests that an increase of 1 Watt translates to an increase in running speed of 0.0134 m/s = 0.03 mph. In other words, a 1 mph increase in speed demands a 33 Watt increase in power. 

3. About 57 minutes into the race, another tracker of effort - heart rate - crossed into my anaerobic zone, inviting fatigue due to lactate metabolites accumulating in the body. Plot overlayed with HR data is below, showing the exact point at which HR crossed into my red zone.

Fig.2 : Power and speed overlayed with heart rate for the duration of the race.

4. For the next 27 minutes, I was in pure purgatory. Pace kept decreasing steadily. At precisely 1:23:00 which I call Point of Exhaustion, I had to drastically decrease my pace to gear down HR. Essentially my test was over and from hereon it just an effort to get across the finish line. 

Stats for the first 57 minutes were as follows :

Duration = 57:00
Distance = 7.6 miles, 12.23 km
Pace = 07:28  min/mile, 4:39 min/km
Work = 804 kJ
Average Power = 235 Watts
Average Heart Rate = 195 bpm (Spot on at Threshold)
Average IF = 1.121
GOVSS = 66
Gradient = 0.1%
Average Step Rate = 185 SPM.

5. After feeding the data into the post processor, the time distribution of watts pins down the power target I should have honed into for the Half.  This is shown in Fig. 3. Had I geared down wattage to a range between 205-210 Watts, I'm led to believe that with current fitness level, I could have run the distance without issues. 

Fig. 3 : Time distribution of power readings. Zones established from Jim Vance methodology.

6. I believe running power helps quantify the demands of training and racing. It makes it possible to analyze and score training data based on Intensity Factor and Normalized Power, a 30 second rolling average algorithm introduced by Andrew Coggan and supported by Annan (2006) . 

7. Since power is Joules over second, it also accurately pinpoints the energy expenditure of a running race, giving clues as to why a runner 'bonked' for example. Power can be overlayed onto a course map by GIS techniques and used to pinpoint energy expenditute and power intensity on a specific stretch of the course. An example shown below in Fig.4, giving me some great data for one of the defining stretches of the RAK Half Marathon. 

Fig.4 : Segment of RAK Half course highlighted in red shows the power and energy requirements of running the 9 mile stretch of road, which happens to be a deciding point in the race.  

8. Running with power may also allow the study of how biomechanical adjustments translate to improvements in running. For example, it is possible to inspect if one style of running leads to better running effectiveness than another. I would want to look into these in future posts. Running effectivess is discussed below.

Anaerobic Work Capacity Insights (W prime)

By plugging the last one month's worth of running power data into a 3 parameter model, my critical power is estimated to be 235W.  Being 5W conservative, I took it to be 230W.  The figure below shows a composite plot with power, pace, heart rate and anaerobic work capacity (AWC or W prime, kilojoules). 

Fig.5 : Expenditure and reconstitution of work capacity above critical power (AWC). Such a plot is also called W' balance analysis. (Further reading : Skiba, 2012)

1. Comparing time constant of depletion of AWC against exertion through power and heart rate, a clearer story emerges of how much anaerobic work I did. I find that AWC crosses 0 at where my heart rate went into the red zone. From 17 minutes to 1:10:00, I'm largely anaerobic which again speaks to how wrong this pacing was with respect to speed and power. 

2. Again, this is only a preliminary look at AWC and W' balance. I would not trust it 100% just yet. I would like to give it much further thought as I get more 'good data', i.e data that correctly captures my maximum running power, critical power and W' through running to failure tests. 

3. This sort of analysis has the potential to help design power based workouts for this target race duration. For example, the analysis above tells me I need to do further tempo work but at a lower power level wrt to CP (Perhaps 80-90% would be a good start. 90% of 230W = 207W. Trial and error will decide what the actual number is). 

Running Effectiveness (RE) Insights

With running power data, one can analyze the ratio of speed (m/s) to power/weight ratio (watts/kg), effectively defining an achievable amount of speed for a given unit of power to weight ratio. RE is a surrogate for "efficiency" or "economy". Folks are also finding from track runs that finishing times among young runners correlate very strongly with RE. 

In the old days, you could take a ratio of speed to HR and come up with a running index. RE is a similar index idea, except what's at the numerator is speed and denominator is wattage, therefore if you could increase speed with the same or perhaps even lesser amount of watts, your HR goes up. 

I calculated RE for the RAK half and the following are insights I gain from the RE data. (Please note I assumed that my weight was a constant 65kg for the duration of the race).

1. My average running effectiveness for the entire duration of the RAK Half was 1.00194  m/s/W/kg. The plot of RE and speed vs duration is shown below, displaying that even though speed dropped off, the trend of RE was more or less constant. 

Fig.6 : Power and speed data overlaid with calculated RE for the duration of the race.

2. The Spearman ranked correlation co-efficient between speed and RE is +0.334. A linear regression between just the raw values of speed vs RE from the run suggests that an increase of 1 kph in speed demands an increase in RE of 1.25 m/s/W/kg. 

3. One interesting technique of analysis is to linearize power, speed and running effectiveness. This is done by expressing each as a ratio of their respective averages for the duration of the race and multplying by 100 for a percentage. The linear trend lines of these 3 curves are shown in the plot below. 

Fig. 6 : Linear trend lines for relative speed, relative power and relative RE vs time. 

The plot shows linear trends for relative power and relative speed dropping off from start to end of race, perhaps suggesting the effect of fatigue.  However, linear trend for relative RE stays constant. From this, I gather that for the duration of a half marathon, the amount of speed you can produce for a set amount of watt/kg stays more or less constant. It is possible, however, that a longer duration race, such as a marathon or an ultramarathon, shows a more clearer drop in RE with time. In other words, fatigue may be more pronouned during long races that it also shows up in the RE data. This is something I will continue to look at in future.

Your comments welcome!

NOTE: My half marathon PB when I was younger is 1:40:51, done on hilly terrain. Link for results.

Saturday, February 11, 2017

Actionable Intelligence for Running Part 3 : Leg Spring Stiffness & Speed-Time Relationships

LSS is a theoretical concept under the linear spring mass model of running, which has proven to remarkably explain several characteristics of running. Mathematical models teach first principles. If most of what you want to know can be explained by a simple model, the additional time spent on increasing the complexity of modeling is not justified.

In Part 2 of this series, I found that change in Ground Contact Time (GCT) is a better explainer of change in Leg Spring Stiffness (LSS) than is change in cadence (step frequency or SF). 

In this post, I continue looking into LSS variation with running speed for both treadmill runs and outdoor runs on predominatly asphalt. Running subject is me again. The "intelligence" gained from this post is summarized in blue italics. Please visit Part 2 for abbreviations used in the writeup.

LSS and Speed Relationship for Treadmill Runs

Around 12,527 datapoints were collected over strictly controlled treadmill runs executed on a Cybex 770T from January 1 - February 9, 2017. The data was cleaned by eliminating null values of LSS; my Stryd footpod is expected to give such data from time to time, mostly during the start of runs. The LSS vs running speed plot is shown below.

Fig.1 : Scatter plot of Stryd measured LSS vs running speed for treadmill running. Sample frequency = 0.5 Hz.

The question is whether the data suggests the relationship is linear or not. The Excel based R^2 value of 0.7902 did not inform me correctly. A better method was to use a correlation test. 

A Ryan Joiner test to test the null hypothesis that the data was a random sample from a normal distribution. The probability plot of LSS from this dataset is shown below. Since the probability line is not straight, the RJ value < 1 and p-value was  .001

Fig.2 : Supplementary plot showing non-normality in LSS data collected during treadmill runs.

Next, a Spearman's rank order correlation test for non-normal data was done. The correlation coefficient was 0.104, p value = 0. This told me that the data has a monotonically increasing relation and that the probability of seeing the observed relationship was 0 if the relationship was anything other. The fact that the sample is large may show that Spearman's rank order correlation of 0.104 has high power. 

Fig. 1 also shows presence of outliers - datapoints of high LSS for the same magnitude of runs as the majority of parent data. What's going on here? When I peer into just these points, I find evidence that high LSS values (13kN/m or greater) can belong in either a high cadence region or a low cadence region. 

The low cadence region 1 consists of high vertical oscillation (VO) and high GCT. The high cadence region 2 consists of low VO and low GCT. After inspecting these subsets of data individually, region 1 was found to correspond with low speed strides I did on the treadmill (for want of some variation in a long run). Region 2 corresponded with high speed, high cadence running. These two regions are shown below in Fig.3.

Fig.3 : Plot showing two regimes where LSS data was found to be greater than 13 kN/m. Region 1 is low SF region with high VO and GCT, while region 2 is high SF region with low VO and GCT.

The fact that leg stiffness is high at high stride frequencies is consistent with literature. I didn't find confirmatory evidence in research for high values of leg stiffness at low step frequencies and high GCT. However, it logically makes sense that one would have to neuromechanically adjust leg stiffness to cushion a higher degree of fall from greater VO. I'll keep looking in future for data within region 1.

LSS and Speed Relationship for Outdoor Runs

I also looked for the relationship of LSS with speed for outdoor runs executed on predominantly paved surfaces. 10,164 datapoints were inspected from the period January 1 - February 9, 2017 and found to show a near monotonic relationship between speed and LSS. The Ryan Joiner test on this dataset rejected the null hypothesis that the data was a random drawing from a normal distribution (.001

Fig.4 : Scatter plot of Stryd measured LSS vs running speed for outdoor runs. Sample frequency = 0.5 Hz. This dataset includes a run done at -4 deg C ambient temperature when the running surface author encountered was covered with thin ice.

A negative correlation co-efficient was somewhat puzzling to me. I have to point out that 2,347 of these datapoints in the sample corresponded to a run done in the UK when ambient temperature was minus 4 degree C. There was still icy frost on the ground. During this run, I was trying consciously to stay upright and not slip on an unlit running path besides the Thames river at 6 in the morning. Neuromechanically, this might mean I could have changed leg stiffness to maintain center of gravity. That leg stiffnesses are adjusted by human runners based on type of running surface was shown by Farley  

Following that theory, I eliminated these 2,347 datapoints from the dataset and followed through with the rank ordered Spearman test on the rest of the 7,736 datapoints. The correlation coefficient was 0.022, p-value = 0.057. This told me LSS was typically monotonically increasing with running speed and within this dataset, the probability that it is a chance event is small. 

The takeaway : Given a more or less fixed step rate, leg spring stiffness is correlated with speed. The data shows that leg spring stiffness monotonically increases with speed. Majority of LSS values can be in a tight window, for example for all my runs they were typically between 10-12 kN/m. 

A cautionary note is that higher than typical LSS values may be exhibited during periods of slow speed, low step rate running where vertical oscillation is high (such as during strides). It may also be exhibited during periods of high speed, high step rate running where vertical oscillation is small. It is important to survey the behavior of these connected parameters when trying to assess why LSS numbers are higher than your typical values. When such data are accounted for in outdoor runs and indoor runs (running motion oddities due to the effect of "slippery" icy surfaces for example), the relationship between LSS and running speed is appreciably monotonic positive. 

LSS vs Speed and Time In Endurance Runs Greater than 1 Hour

I've not done too many distance runs greater than 1 hour 20 minutes. That said, there are two runs of between 1:20:00 - 1:40:00 which I thought could be inspected to see if long duration running and it's accompanying fatiguing aspects could translate to decreases in leg spring stiffness. The two runs with speed and LSS are displayed in Figs. 5 & 6. Plot captions indicate the conditions under which they were done. 

Fig.5 : 1 hz data from endurance run #1 executed in Abu Dhabi on February 3, 2017 under 17 deg C ambient temperature and 21 kph winds (around Beufort Scale 6). Number of sample points = 2,962. Plot shows LSS, GCT and speed variation with time. Mean LSS = 10.233 kN/m, mean speed = 3 m/s, mean GCT = 247.22 ms. 

Fig.6 : 1 hz data from endurance run #2 executed in Staines-on-Thames on January 23, 2017 under -4 deg C ambient temperature and low winds (around Beufort Scale 6). Number of sample points = 2,448. Plot shows LSS, GCT and speed variation with time. Mean LSS = 10.54 kN/m, mean speed = 2.67 m/s, mean GCT = 262.83 ms.

In Fig.5, the Spearman rank ordered correlation between duration and LSS showed a correlation coefficient of -0.337, p value = 0. In Fig.6, the Spearman rank ordered correlation between duration and LSS showed a correlation coefficient of only -0.094, p value = 0. The relationships in both these runs between duration and LSS was mildly monotonic decreasing.

What is interesting is that the faster, warmer, longer duration run in windier conditions shows a stronger negative correlation between LSS and duration than does the somewhat shorter, colder and slower run in cold temperature.

A contour plot of LSS, speed and duration for the run from Fig.5 is shown below. It indicates that there is a cluster of low LSS values in the range 5.0-7.5 kN/m corresponding to high speed and high duration. This is interesting and I need to concentrate on these instances both within the data and in reality to understand what is going on. For example, it hasn't been uncommon for my left feet to exhibit fatigue from long duration running.

Fig.7 : Contour plot of LSS vs Speed and Time in a long run on a windy day in Abu Dhabi on January 23, 2017

However, due to the lack of further long runs and lack of high intensity data, I cannot fully elaborate on fatigue and it's effects on LSS. It will be something I will keep a watch on. Perhaps introducing power and form power into these metrics will form a clearer picture.

The takeaway : A preliminary analysis of two long duration runs suggest there is a monotonic decreasing relationship between duration of run and LSS. It perhaps is likely that changes in running form and/or fatigue can influence LSS as evidenced by the contour plot. This aspect needs a much more comprehensive treatment with other markers of performance. 

In the next post, I will move to power based metrics and see how indoor and outdoor runs compare. I will also inspect my power data from the recent RAK half marathon and see how power based pacing helps in duration specific stamina and how that methodology compares to speed based pacing. Stay tuned.

Saturday, January 21, 2017

Actionable Intelligence for Running Part 2 : Effect of Step frequency on Leg Spring Characteristics for Treadmill Running

In Part 1, I reviewed research literature on the relationship of inverse ground contact time, 1/tc, to the metabolic cost of running. Further, because the leg stores and reuses elastic energy, spring mass models have been used quite extensively since the 1960's to describe it's spring characteristics. 

In this installment, I will investigate the relationships between leg spring characteristics against variable step frequency and variable ground contact time in two tests. I will use two wearable electronics - a Polar V800 and a Stryd gen 2 footpod - along with a treadmill and an Android phone. Force plates, kinematic arms or 3D motion capture systems were not used.   

A point to note is that the human leg is not a pure linear spring due to various muscoskeletal complexities, therefore the estimated stiffness variables will be preceded with the word "effective" in this writeup while device native metrics are called as is. 

Lastly, as the test was done on myself, there could be an effect of human error and testing inexperience shown in this study. When possible, I've tried to introduce randomization in the test protocol to equalize the effect of external factors not accounted for in the experimental design. You are free to mail me pointing out any flaws in understanding.

Commentary to the findings (or the "intelligence") is highlighted in blue. 

Abbreviations Used

Calculations Used

Read Part 1. Or ask.

Subject and Equipment Used

Test Protocol

1. 5 min warmup at 2.8 m/s pace.
2. 2 min run at 3.3 m/s pace to determine fcSF. 
3. Calculate 6 test SF values from 30% reduction to 30% increase in 10% increments : 0.7fcSF, 0.8fcSF, 0.9fcSF, +1.1fcSF, +1.2fcSF, +1.3fcSF.
They also also called SF-30% ,SF-20% , SF-10% ,SF10% ,SF20% & SF30%
4. Part A (Variable GCT - Variable SF test) : Randomize the order of the above and complete 6 trials of 2 min each at 3.33 m/s. 2 min recovery in between. 
5. Practice a running motion for self-imposing short GCT and long GCT. 
6. Part B (Variable GCT - Fixed SF test) : Complete 2 x 3 min randomized trials strictly at fcSF and at a pace of 3.33 m/s, one with short GCT and one with long GCT.
7. Consolidate data for post processing within a statistical computer package.

Note : 3.33 m/s corresponds to 12 kph on the treadmill and 8 min/mile. A cadence of 180 SPM corresponds to 3 Hz. 

I. Results of Test Part A 

The fcSF during the initial 2 min trial run was 177 SPM which is 2.95 Hz. 
Corresponding GCT was 235.5 ms. 
LSS at fcSF = 10.2 kN/m.

Calculated values of SF for the 6 trial runs were as follows :

626 data points were consolidated from this test. 

Data is plotted below.

Fig.1 ; Spread in data for Part A for each of the 6 SFs.

FIG 1 : Box plots of FT and GCT at the 6 different SF's are shown relative to fcSF (marked with a dotted reference line). 

The data corresponding to 2.065 Hz or
SF-30% has a large spread because I had difficulty trying to main such a low cadence, having to hold the sides of the treadmill for support at times. This plot has been made after cleaning up a lot of null values within the SF-30% dataset. Inspite of this, there still is great spread relative to data at other SFs.

The general takeaway is that ground contact times fall steadily with increase in step rate and rises with decrease in step rate. One would expect aerial times to be high in the low cadence region, but the data seems to show an inflection point at fcSF of 2.95Hz. In the increasing cadence region, FT tends to decrease.  

Fig.2 : Scatter plot showing % change in LSS vs % change in GCT during 
the variable GCT - variable SF test.

Fig.3 : Scatter plot showing % change in LSS vs % change in SF during 
the variable GCT - variable SF test.

FIGS 2 & 3 :  Decreasing changes in GCT obtained from the variable SF test correspond to positive changes in LSS. A simple linear regression shows R^2 value is 0.79. The Pearson correlation test of both yields -0.889 (P < 0.05).  

Problematic, however, is the fit of SF variation with LSS. Some of the noise in the left hand side is most likely due to the improperly executed low cadence test at SF-30%. If you consider just the right hand side of Fig 3, there seems to be a +ve to +ve relationship between higher SFs (SF10%, SF20% ,SF30% ) and LSS. The Pearson correlation between SF and LSS yields -0.421 (P < 0.05). 

Takeaway here is that GCT maybe a better predictor of LSS. Test Part B will prove if this is correct.

II. Results of Test Part B 

With some time given to practice, I was able to achieve a short and long GCT as follows :

Short GCT   226.6 ms
Long GCT   246 ms

The short GCT was obtained by conscious fore foot landing close to vertical line passing through COM and quick leg swings. The long GCT resulted from an exaggerated rolling motion of the feet, almost to the point of heel first first landing. Point of contact was farther away from the vertical line passing through COM. 

326 datapoints were consolidated from this test. 

Plots of data are presented below. 

Fig 4. Scatter plot showing % change LSS vs % change GCT during 
the variable GCT - fixed SF test.

Fig 4 :   Almost 96% of the variation in LSS was explained by variation in GCT. Further, the Pearson correlation between variable GCT and variable LSS was 0.98 (P < 0.05). The plot shows that variations in GCT in a variable GCT test - fixed SF test are more strongly related to LSS than in a variable GCT - variable SF test. This plot shows the LSS - SF relationship for both tests A and B making it clear the stronger regression in Test B (orange markers).

Takeaway is that lesser ground contact times are correlated with higher leg stiffnesses. (whether one causes is the other cannot be proved here. Also, that there maybe an injury limited stiffness value beyond which it is futile to stiffen the leg is also impossible to show here, since both tests rarely exceeded 12 kph. Theoretically, it seems possible that to generate high leg stiffnesses, the body may have to exaggerate dorsiflexion in the feet. But stiffness could also be a function of knee and hip torques so I refrain from digressing.)

III. Other Investigations

A. Variation of Estimated Ground Reaction Force with Change in SF

Fig 5. Scatter plot showing peak nGRF expressed as N/kg with % variation in SF.

Fig 5 An expression for GRF was obtained from sinusoidal approximations given in Blum and verified with an older paper by Morin et. al. Using temporal variables measured by Stryd, the calculated GRF was then normalized by my body weight. This is shown in Fig.5.

The takeaway here is that nGRF decreases with increased SF, seemingly stabilizing between 
SF20%. and SF30%. Above the preferred step frequency, peak ground force decreases. This finding agrees with literature. The behavior at lower SFs could be a product of high COM elevation or aerial time. It tends to agree with certain reality that drastically reducing cadence at the same high running speed makes loud landing sounds in the gym. High force = high loading = high noise! This observation points to a flaw in the finding in Fig 1 that aerial time reduces with decreasing step frequency, infact I believe it should be the opposite. 

B. Variation of Rate of Force Production with Change in SF

Having seen in Part 1 that metabolic cost is directly linked to the inverse of GCT, it's interesting to inspect the behavior of this variable from the variable SF test data from Part A.

Fig 6. Scatter plot showing rate of force production vs % change in SF.

Fig 6 : There seems to be a distinct bow to the shape of this curve corresponding to the line of fcSF. Below and above this line at SF-30% ,SF-20% ,SF-10% ,SF10% ,SF20% & SF30% , inverse GCT shows increase. 

While data is limited to 626 samples and there is still some noisy data at the extreme low cadence, this graph generally agrees with literature. The surrogate data here suggests that there is a global minimum in metabolic cost at my freely chosen cadence of 177 SPM at 3.33 m/s pace. Intuitively, faster cadence means lesser GCTs. Muscle firing must be fast to produce ground force. Faster muscle firing has an oxygen penalty. Lesser cadence than preferred cadence at the same running speed also doesn't look optimal, as leg loading increases (Fig 5).

C. Vertical and Leg Spring Stiffness

One of Stryd's developers told me recently that they had not decided to release the math used to calculate leg spring stiffness (LSS) just yet. Curious as I am, I investigated how my own estimated values of ELS and Δy(COM) compare with Stryd's LSS and VO. 

EVS is the ratio of peak GRF and the vertical change in COM. ELS is the ratio of peak GRF and change in resting leg length. Both can be estimated from temporal variables and some high school math. 

C.1  Variation of Stryd Reported ELS vs % Change in SF

Fig 7. Scatter plot showing change in Stryd reported LSS and estimated VO with % change in SF.

Fig 7 : For lack of a metric to compare Stryd's LSS, I plotted it against the measured VO. The data suggests there's a curvilinear relation in both the variables with variable SF. LSS appears convex shaped against SF. The lowest VO corresponds to the highest SF's (and vice versa) whereas in leg spring stiffness, there appears to be a global minima between fcSF and SF10%.

The takeaway is that oscillation of a fixed point on my COM decreases with increasing step frequency. This agrees with the decreasing trend of FT and GCT at high SF's from Fig 1. Spring stiffness also increases with step frequencies. Both these findings tend to agree with literature.

C.2  Variation of estimated EVS vs % Change in SF

Fig 8. Scatter plot showing change in estimated EVS and estimated Δy(COM) with % change in SF.

Fig 8 : The change in estimated EVS is convex shaped with % change in SF whereas that of Δy(COM) is concave shaped. The data seems to suggest that global minima in EVS is somewhere between fcSF and SF10% and much higher in both directions from this point. Global minima in Δy(COM) is closer to the highest SFs and maxima is clustered around the lowest SFs. The magnitude of estimated EVS seems smaller than I expected compared against literature reported values.

The estimated value of vertical stiffness agrees with Stryd's LSS trend (Fig. 7) - both are convex shaped in SF and there appears to be a global minima between preferred cadence and SF10%

Variation of estimated ELS vs % Change in SF

Fig 9. Scatter plot showing change in estimated ELS and estimated ΔL with % change in SF. Note that ELS calculation corrects for the translation in point of foot contact, therefore it is a POFT corrected spring stiffness, yielding higher magnitudes than those calculated without POFT correction. 

The change in estimated ELS is convex shaped with % change in SF whereas that of ΔL is concave shaped. The data seems to suggest that global minima in ELS is somewhere around SF10% and much higher in both directions from this point. Global minima in ΔL is hard to tell, there seems to be two local minimas instead at the lowest and highest SFs each. The magnitude of estimated ELS also seems smaller than I expected compared against literature reported values. 

Comparing Figs. 8 and 9, the increase in effective vertical stiffness is more pronounced than effective leg spring stiffness at higher SFs. The magnitude of effective vertical stiffness is also higher than that of effective leg spring stiffness. This is in direct agreement with observed trends in literature (duh, most are using the same mathematics!)

Estimated ELS Compared to Stryd's Leg Spring Stiffness

Fig. 10.  Scatter and median value of bias magnitude between estimated Δy (COM) and VO reported by Stryd. Bias =  [Δy (COM) - VO ].

Fig 11. Scatter and median value of bias between estimated ELS and Stryd reported LSS.  
Bias =  ELS - LSS.

Figs. 10 & 11 : The last two plots show the difference in Stryd's metrics of VO and LSS vs estimated Δy(COM) and ELS respectively. 

The bias in estimated Δy(COM) and VO each is lowest around SF-30% and SF-20% and progressively increases with increasing SF. At SF10% and beyond, there is an average of 0.1m of difference.   

The bias (or delta) in estimated ELS is approximately 5 KN/m less than Stryd's LSS between SF-20%  and SF20%. At lower and higher SF's, the bias seems to get larger, with the highest bias of 10 kN/m at SF-30%

ELS was calulcated using a POFT relation to model change in leg length and maximum ground reaction force was modeled using temporal parameters such as duty factor (obtained from Styrd data) and body mass.  I'm not able to fully justify the difference of 5kN/m between ELS and LSS, especially since ELS was estimated from Stryd's GCT and forward speed. 

The one possibility is that Stryd's algorithm for LSS uses half of leg swept angle in it's calculation of change in leg length. When this angle is introduced, change in leg length is smaller than that calculated from a simple spring model with POFT. Because change in leg length is smaller using the angle, for the same ground reaction force, estimated leg stiffness will be higher. Therefore, difference in applied models could very well explain the difference in obtained spring stiffnesses. Which model is "more correct" in leg stiffness calculation is a topic of debate.

In the next installment, I'll be continuing to stick with leg spring characteristics but with a changes in running speed. I will also hope to compare treadmill running with outdoor running to see what real world conditions impose on the metrics.


1. The nature of the "curve" : Ground Reaction Force versus time during different step frequencies of running. Fast walking (or slow running) has two peaks corresponding to the lesser peak of heel touch and the greater peak before toe off. As running gets faster (and also in mid-foot or fore-foot based running), the curve F(t) assumes just one peak, making estimations of GRF easier with sinusoidal expressions which is essentially what researchers have done. 

2. The planar spring mass model for running forwards : The shape of the vertical displacement, vertical force and horizontal force curves.

3. How vertical oscillation is defined : It is the total peak to peak displacement of the center of mass during the gait cycle, not to be confused with "change in vertical position of COM" which would only be a half of this peak to peak value. 

4. How an accelerometer can detect ground contact time from acceleration signals. From Strohrmann, IEEE 2012.

5. Consequences of POFT : The distance d of POFT as the anterioposterior difference in the position of the point of force application at ground contact and lift-off. This is due to real human running motion where individuals roll the feet from point of intial contact to toe off. This modifies the planar linear spring model as below. 

For the same peak vertical GRF, contact time and contact length, POFT d lowers the horizontal GRF and enables humans to do less external mechanical work per step. Also, with POFT accounted for, leg stiffness required to achieve certain running mechanics will increase as POFT increases. This would decrease leg shortening, and therefore reduce metabolic cost by reducing knee flexion. Without consideration of POFT, horizontal GRF and mechanical work can be overestimated.
For the same leg stiffness, increasing POFT d will reduce the peak vertical force and increase contact time and VO. Despite the higher VO, the external mechanical work was shown to be lower due to the lower peak horizontal GRF. (Bullimore, 2005

6. Duty factor : 

Duty Factor = Ground Contact Time / (Ground Contact Time + Flight Time). Lesser duty factors correspond to faster running but also higher peak vertical forces. It is not possible for humans to sustain high peak forces.  This is the physics based reason why GCT cannot be decreased for human beings below a certain limit.