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.

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