Tuesday, September 19, 2017

New Fatigue Factors for Running : Men's Road and Track Racing

Zersenay Tadese during the unbroken world record half marathon at Lisbon in 2010.

Readers will recall that in a recent post, I did an exercise to calculate Riegel fatigue factors from updated world record performance times for women's road and track racing. I then ran some numbers on a near-world class local female runner aged almost 40 to predict her half marathon time from her most recent 10K time. The Riegel model predicted the closest times to her actual finishing time compared to several other models widely available on the internet. 

In this post, I attempt the same thing for men's road and track racing.


I. Fatigue Factors for Men's Road Racing

I constructed a table with the latest road racing world record times for men. The following ln-ln plot of time to distance results in a slope of -0.0497 (R2  = 0.8101). When corrected into the fatigue factor form, it results in a number 1.0497. This is a bit different to Riegel's estimation of 1.07732 back in the day, a percentage decrease of 2.5%. 

Fig 1 :  ln-ln graph of men's world class road racing bests

Fig 2 : Table showing the data behind the updated Riegel model for world class men's road racing.
Apart from Stanley Biwott's 1:27:13 30K, no major recent records have been set in other distances. This shows the strength of Kimetto and Tedese's placings in the long and mid-distance categories. These records haven't been broken for several years although EliUd Kipchoge seems very hungry in 2017. A world record attempt at the marathon may mean taking out the half marathon world record in the process. 


II. Fatigue Factors for Men's Track Racing

The following ln-ln plot of time to distance for men's track results in a slope of -0.0777 (R2= 0.9901). When corrected into the fatigue factor form, it results in a number 1.0777. 

There are two interesting aspects to this number. First, the linear fit is very close to actual results. Secondly, this number is very close to Riegel's estimation of 1.07732 back in the late 1970's.

Fig 3 :  ln-ln graph of men's world class track racing bests

Fig 4 : Table showing the data behind the updated Riegel model for world class men's track racing.

No recent upheavals have happened in men's track racing, with the last record in the 25k and 30K distance being established in 2011. El Guerrouj, Bekele and Gebrselassie's records meanwhile have stood the test of time proving the remarkable forms they were in when they competed.


III. Application to a World Class Local Male Runner Y

I applied the Riegel fatigue factor for young male world class road racing to a 30 year old long distance runner Y to see how off the predictions are when using his 10K time to predict half marathon time. Both the races were held in the U.A.E and just a couple of months apart. 

Runner Y is a local running celebrity of sorts, having established record times in everything from your weekend park run predictor to the RAK half marathon. 

The math behind the following predictions were already explained in the past post

Riegel fatigue factor = 1.0497
Individual : Y, local male sponsored athlete
Age Bracket : 30-35
Actual 10K time (T1) = 31:40
Predicted 21.1K time (T2) = 1:09:21
Actual 21.1K time  = 1:06:10

Outcome : The prediction was under-estimated by 3 minutes 11 seconds. Runner Y finished in 1st place at the half marathon. The 2nd placed male runner finished in 1:15:06. For that difference in outcome between first and second place, the Riegel method still predicts the podium. So in a corrupted yet logical way, it appears that the difference of 00:03:11 is something we can live with. 



IV. Comparison of Riegel Predictions to Other Time Prediction Models for Runner Y

The following table compares Y's actual performance with old and new Riegel models and several other running predictors easily available on the internet. Please keep in mind that the case study was to predict half marathon time using 10K time.


Fig 5 : Comparison of updated Riegel prediction for men's road racing against 10 other models widely available on the internet. The error in prediction in also calculated and shown.

As shown in the table, the updated Riegel method performs the best prediction among several other models. In the women's case as well, it performed the best half marathon prediction

Please note that the Runner's World predictor tool did not work. The times entered were outside the "limits" of the tool, which perhaps is something deliberately programmed by them to prevent application for elite athletes. 


V. Conclusion

In this writeup, I updated the fatigue factor or what people term the Riegel exponent to include road racing and track racing data for men. The updated fatigue factor for world class road racing = 1.0497 and that for world class track racing = 1.0777. 

As opposed to women's racing, what is remarkable is that several of the men's records in both track and road have stood the test of time. Very few records have been broken in recent years. This further re-inforces the fact that there is more news to cover in women's racing, it's alive and kicking and these are exciting times. 

Men have some catching up to do. 

I used the updated Riegel model for men's road racing to predict the half marathon performance of a 30-35 age bracket world class road runner living in the U.A.E. The Riegel model appears to give the best prediction when compared to 10 other models. Further, the updated Riegel fatigue factor gives a better prediction in the case study that the number from Riegel's original paper. 


When considering both the men's and women's prediction I wrote about, the Riegel method appears to be a simple and reliable method that anyone could easily program. The fatigue factor can also be tweaked to fit the data of specific runners.

Since world records are being broken year after year, it seems justified that running prediction calculators for world class runners should update their fatigue factors as new data comes in.

Coaches are advised to guide with application and interpretation issues for recreational runners especially those above the age categories that the model was made from. As shown in this post, prediction tools are only a guideline. 


Therefore, two words of caution :

A. The understanding is that specific data for a runner takes precedence over estimations done using data for world class athletes, the latter which can detrimentally over-estimate race time if mis-applied.

B. Specific data involving similarities in race course and weather conditions takes precedence over distributed data containing a variety of different races courses and weather. In general, it is better to avoid exceptionally tough courses and/or conditions involving generous amounts of assistors, such as a tailwind or rabbits, from the dataset.


References

Riegel, Peter S. “Athletic Records and Human Endurance: A Time-vs.-Distance Equation Describing World-Record Performances May Be Used to Compare the Relative Endurance Capabilities of Various Groups of People.” American Scientist, vol. 69, no. 3, 1981, pp. 285–290. Link to paper.

Prediction Models :

Runner's World Predictor : Link.
Daniel's Equivalence Predictor : Link.
McMillian Race Predictor : Link.
Godwin Race Predictor : Link.
Purdy, Cameron & VO2 Max Predictors : Link.

Saturday, September 9, 2017

Alberto Contador On His Final Angliru : Climbing Speed & Power to Weight Ratio



This post is modeled on the calculation method shown in a past post where I calculated Contador's VAM and power to weight ratio on the Angliru during the 2008 Vuelta a'Espana.

Today, Contador won the final mountain stage of the Vuelta, and again on the Alto d'Angliru.

My preliminary calculation suggests that Contador climbed 950 height meters in a time of roughly 35 minutes. I clocked his climbing time from the 9.3K to go mark.

The estimation is therefore :


The Ferrari method to estimate power to watt ratio is therefore :


His VAM today is less than my estimation for his 2008 VAM (done for the last 4K and quite high due to road steepness in the last sections), his power to weight ratio is also less than my estimation for his 2008 power to weight ratio. 

However, reductions seem reasonable for a man at the twilight of his career and do not make room for suspicion. The power to weight ratio displayed at the end of a grand tour is remarkable nevertheless.

This is a clean performance unless further data instructed otherwise. 

The calculations are based on the following raw data.



Friday, September 8, 2017

New Fatigue Factors for Running : Women's Road and Track Racing

I. Introduction 

Peter Riegel, an American mechanical engineer and competitive runner, developed a simple computer implementable formula in the 1980's.

A research engineer by profession, he first became curious of the relationship between distance and world record times in various sports. 

For example, when he plotted running times vs running distances on a log-log plot, he found a straight line fit for all distances that spanned from the mile to the marathon. 

In fact, he found that the straight line fit existed for any endurance sport he examined with the caveat that the range of validity was from any effort greater than 3.5 minutes upto 3:50:00.  Anything outside this range and the straight line fit did not hold true.

I'm not sure how he quantified the error threshold at which to abandon straight line representation. I imagine this threshold would have had to be different for short distance racing compared to long distance racing, since a deviation of even a handful of seconds during a 200m event can mean the difference between first place and last place. The same is not necessarily true for long events.

In a publication in the American Scientist (1981), he wrote that deviation outside of a straight line fit were found in two domains :

Short distance events : Short, high intensity transient phenomena were not represented well by simple equations. This must mean anerorobic performance cannot be fit to linear equation. 

Long distance events : Increased fatigue on body, lack of world-class competition data in very long distance events and introduction of multi-day events with rest were also not represented well by simple linear equation. 


II. Predicting Race Times With Fatigue Factor

When the natural logarithm of speed and distance is plotted from world best running times for distances spanning 5K to the marathon, we can define the slope of the line as a positive number :


The fatigue factor is used in a simple exponential equation to predict an unknown distance performance from a known distance performance. This results in a simple race time predictor which can yield surprisingly close predictions if used for the same class of runner, gender and possibly age.

This is the math behind the predictor formula used in a number of running websites. The originator is therefore Riegel, the engineer.

Fig 1: The Riegel time predictor formula.

where :

T2 = Unknown performance time for distance D2
T1 = Known performance time for distance D1, where D1 < D2
fatigue factor =  Amount a runner's speed (or velocity) decreases as race distance increases. Calulated as the slope of ln speed vs ln distance plot, negated and added to 1.

Riegel calculated fatigue factors for several classes of runners according to the best available data of the late 70's. I've marked them in the red circle below. 

Figure 2 : Table showing Peter Riegel's original fatigue factors based on data from the 1970's.


III. Fatigue Factors for Women's Road Racing

I decided to plot ln-ln slopes for world class runners of both genders using latest available data of 2017. I started with women's road races.

The following ln-ln plot of time to distance results in a slope of -0.0397 (R2  = 0.7283). 

Fig 3 : ln-ln graph of women's world class road racing bests.

When corrected into the fatigue factor form, it results in a number 1.0397. This is appreciably different to Riegel's estimation of 1.08 back in the day, a percentage decrease of 3.9%. 

It sends a little shock through your system. The decrease in the fatigue factor shows that the world records are not just tumbling in women's racing, they are being destroyed.  The other obvious implication is that slope appears to be straightening out, meaning that women are seemingly able to maintain faster speeds for longer distances. 

The woman mainly responsible for this phenomena on the road this year is the young Kenyan superstar Joyciline Jepkosgei, who smashed 3 WR's on her way to the women's half marathon world record. Whether she had a tailwind at her back in Prague, I do not know but her run that day yields a Daniel's VDOT of 74.4.

At the other end of the spectrum is the marathon WR of Paula Radcliffe, who is in her 14th straight year of the unchallenged record while she enjoys retirement.  The 2003 WR yields a Daniel's VDOT of 74.7, stunning when compared to Jepkosgei's WR in the half this year. Though not totally uncontroversial, it goes onto show what an absolute phenomenon she was!

Now the fun part. Using the fatigue factor of 1.0397, the Riegel prediction for Joyciline Jepkosgei if she had a go at the marathon is 2:13:21. Her coach, whoever they are, should be really interested in this bit of news, although I think they already know and if they knew they would also consider the R2  = 0.7283.  

For reference, the graph used the following data. You are welcome to correct me if I got any of the numbers wrong. 

Fig 4 : Table showing the data behind the updated Riegel model for world class women's road racing.


IV. Fatigue Factors for Women's Track Racing

In similar fashion, I plotted the ln-ln plot of speed vs distance incorporating the latest IAAF world records from 2017. The fatigue factor comes out at 1.1228 (R2  = 0.8381). Compared to Riegel's estimate of 1.08 for women from the 1970's, this constitutes a 13.7% increase. I would tend to doubt if Riegel actually examined women's track records separately so I'm not sure if this comparison is valid.

Fig 5 :  ln-ln graph of women's world class track racing.

The database behind the curve is as follows :

Fig 6 : Table showing the data behind the updated Riegel model for world class women's track racing.

The biggest eye popper in the WR list is Olympic gold medalist Almaz Ayana's 10K performance at the IAAF Worlds in London. I followed Ayana's kilometer splits that night, live. It was incredible. With a Daniel's VDOT of 74.9, she left a world class field consisting even of Tirunesh Dibaba in the dust and managed to lap the lagging runners atleast once around the track.

Fig 7 : Graph of splits at the Women's 10,000m track finals at IAAF London 2017

V. Application to World Class Female Runner X

I applied the Riegel fatigue factor for young female world class road racing to a 40 year old long distance runner X to see how off the predictions are when using her 10K time to predict half marathon time. Both the races were held in the U.A.E and just a month apart. Runner X is a retired world class European runner and currently an entrepreneur. Even in retirement, she performs within 80% or more of absolute world class runners.

Riegel fatigue factor = 1.0397
Individual : X, retired world class runner
Age Bracket : 35-40
Actual 10K time (T1) = 34:42
Predicted 21.1K time (T2) = 1:15:25
Actual 21.1K time  = 1:12:27

Outcome : Interestingly, the prediction was under-estimated by 2 minutes 58 seconds. Runner X finished in 16th place at the half marathon. The 17th place runner finished in 1:17:57. Would you consider this an error we can live with in the absense of any other data? You decide.


VI. Comparison of Riegel Predictions to Other Time Prediction Models for Runner X

The following table compares X's actual performance with old and new Riegel models and several other running predictors easily available on the internet. As (luck) would have it, my updated Riegel model specifically for women's road racing performs better than any of the others. Again, please keep in mind that the case study was to predict half marathon time using 10K time.

Fig 8 : Comparison of updated Riegel prediction for women's road racing against 10 other models widely available on the internet. The error in prediction in also calculated and shown.


VII. Conclusion

In this writeup, I updated the fatigue factor or what people term the Riegel exponent to include road racing and track racing data from 2017 for women. The new fatigue factor for world class road racing = 1.0397 and that for world class track racing = 1.1228.

The results, atleast on the road racing side are startling. The reduced fatigue factors suggest that women's road racing is alive and kicking, with women seemingly able to race faster for longer distances.

Track racing records have also been broken this year but other than the women's 10K, records in other distances within the validity range of Riegel equation have not seen a major shakeup.

Due to the complexity of the topic, any discussion of physiological factors or training interventions responsible for the faster times are excluded in this post.

I used the updated Riegel model for women's road racing to predict the half marathon performance of a 30-39 age bracket world class road runner living in the U.A.E. The model appears to give the best predicton when compared to 10 other models.

Since world records are being broken year after year, it seems justified that running prediction calculators for world class runners should update their fatigue factors as new data comes in.

Coaches are advised to guide with application and interpretation issues for recreational runners especially those above the age categories that the model was made from. Therefore, two words of caution :

A. The understanding is that specific data for a runner takes precedence over estimations done using data for world class athletes, the latter which can detrimentally over-estimate race time if mis-applied.

B. Specific data involving similarities in race course and weather conditions takes precedence over distributed data containing a variety of different races courses and weather. In general, it is better to avoid exceptionally tough courses and/or conditions involving generous amounts of assistors, such as a tailwind or rabbits, from the dataset.

See part 2 for Riegel fatigue factors for men's racing.


Reference

Riegel, Peter S. “Athletic Records and Human Endurance: A Time-vs.-Distance Equation Describing World-Record Performances May Be Used to Compare the Relative Endurance Capabilities of Various Groups of People.” American Scientist, vol. 69, no. 3, 1981, pp. 285–290. Link to paper.

Friday, August 25, 2017

Dr. Chester Kyle : Pioneer in Human Powered Vehicle Aerodynamics

Chester Kyle, PhD is a pioneer in cycling science and the aerodynamics of human powered locomotion. Now retired, he served as an adjunct professor of mechanical engineering at the U of California at Long Beach for several years. He also served a stint at Nike designing aerodynamic clothing. 

When you read the breadth and scope of his work, you really will be surprised how much of aerodynamic design and technology that has infiltrated cycling, whether real or gimmick, had been already explored by him and his students. From drivetrain efficiency to the aerodynamic drag of a shaved vs unshaved cadaver, there was practically little he didn't explore and write on.

Several ideas introduced by him and his peers at the US Olympic committee and human powered vehicle circles went onto win international cycling championships and setting speed records. At the height of his career, the UCI was hot on the chase of these "ideas", banning several of the improvements broguht to the UCI sanctioned cycling races. As Dr. Kyle likes to joke, 'the minute they saw them [plop], they became illegal'.

Dr. Kyle's investigations into technical aspects of cycling through simple experiments driven by a sense of economics and curiosity for the science should serve as an example for any investigator today. The most important aspect of these investigations was that he helped produce a body of empirical data that let other researchers and designers go about their business.

On 13th May 2010, he was invited to a seminar for the students of MAE297.  The following is the video from that lecture. An amazing little talk, and made no worse by Dr. Kyle's upbeat attitude and quirky sense of humor. 

Credits :
Film by the UC Davis Engineering distance learning program, 2010.



Sunday, August 20, 2017

How the Paris Agreement Will Impact EU Climate and Energy Policies

A broad topic but a good discussion panel organized by Bruegel.

There appears to be the view that emissions targets and ETS will have to revised. More importantly, innovation in new technologies and renewables and how to integrate it with the existing infrastructure will be key in setting up planned targets for 2050. Natural gas will have a bridging role in the energy transition.

Apart from the EU Commissioner for Energy and Climate Action Miguel Arias CaƱete, the panel also has a GE representative Hendrik Bourgeois who provides the investment requirements and investment risks coming along the way to low carbon. 

In short, despite the optimism from some circles, the engineering, economical and social challenges for a low carbon economy makes implementing the Paris Agreement an extremely complex task. Below is just the EU viewpoint. 

The EU's Roadmap for a competitive low carbon economy in 2050 can be read here.



Saturday, August 19, 2017

Laws of Thermodynamics (In Simple English)

First Law: It is impossible to obtain something from nothing, but one may break even

Second Law: One may break even but only at the lowest possible temperature

Third Law: One cannot reach the lowest possible temperature

Implication: It is impossible to obtain something from nothing, so one must optimize resources


This was obtained from one of my thermodynamics reference books from college days. I'm amused at the plain language in the three maxims. A lot of new discussion surrounding energy systems can be cut short if you invoked any of these maxims in it's simplest form and then thought again. 


Citation :
Advanced Thermodynamics Engineering, by K. Annamalai and I. K. Puri, CRC Press.

Wednesday, August 9, 2017

An Equation for Running Stress Score (RSS)

On Stryd's website, there is a narrative about their proprietery scoring system based on power called Running Stress Score (RSS).

The key statement is how RSS is defined using a 'co-efficient' K.


Someone who would like to reverse engineer this formula would wonder if co-efficient 'K' is a constant or does it vary depending on the intensity.

One clue to help in finding K is a table of examples in which Stryd states an expected value of RSS.


Infact, from the equation of RSS, the value of K is defined as :

K = [ Natural log (RSS/min) - Natural log (100)] / Natural log (Power/CP)
where CP = critical power

One finds from this calculation that there is not a single value of K that can be fitted to the running examples in the table above. So either this is a small mystery or K is not constant.

Might there be an easier model to explain the change of RSS/min with intensity? As a first goto, a simple exponential model would reflect rapidly increasing stress scores for higher intensities.

So I took the data and tried to force fit an exponential line through. The result gave 98.7% fit based on the data fed to it.


Based on this exercise :

RSS/min = A x exp(B x Power/Cp)
where parameter A = 0.0758
and     parameter B =  3.1297

How does this equation fit with a real run and it's corresponding RSS from Stryd's powercenter? I took a recent run from the running database and threw it into the model.

I found that the modeled RSS/min is within 3% of the actual value, which says that the fit is alright but more importantly, I can produce a better match by decreasing assumed CP to around 193.5 W.