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.




Friday, August 4, 2017

State of Energy Storage Methods

The crux of using intermittent renewable energy sources is how they integrate with flexible, conventional sources of energy to generate uninterrupted power. The link between both is the specific energy storage technology that is used. 

The state of storage technologies were reviewed by IEA 2014. Though it would be good to have an update, it is still a good resource to read as it reflects the current level of understanding of energy storage by mature countries in the IEA club.

An excellent database of storage plants around the world is maintained and updated by the U.S Department of Energy (Link). Engineers might want to head out there and learn the characteristics of some of these plants.






Friday, July 28, 2017

How Valid is Polar V800 HR to Measure HRV Metrics?

According to a 2015 paper by Giles et.al, the Polar V800 "improves" over previous generation Polar devices with narrower intra-class correlation coefficients, limits of agreement and effect sizes when compared to R-R readings obtained from a 3 lead Biopac ECG.

One of the key aspects of the paper is that it highlights the importance of understanding the effect of different softwares and their error correction routine on the R-R time series.  The paper references some earlier studies which flagged the concern that each system's individual HRV processing capability can potentially alter the HRV metrics in their own way making cross-comparability a big issue.

The paper discusses chiefly 7 errors that can be associated with the Polar V800 HRM signal. Potential factors leading to those errors are also stated. I'd like to borrow the learning and place them here :

Type of ErrorDescription of ErrorPotential Cause
T1Single interval of discrepancyNot stated
T2Long interval and short intervalNot stated
T3Short interval and long intervalNot stated
T4Too few intervals detectedDecrease or loss in contact between electrode-skin and resulting decrease in amplitude of the R wave
T5Too many intervals detectedNot stated
T6-aInterval(s) missed entirely, undetectableSoftware error due to time asynchronicity in the HRM and/or Loss of, or decrease in contact between electrode-skin.
T6-bInterval(s) missed entirely, detectableSame as T6-a

Although the causes of T1-T5 errors are not addressed in the paper, the authors state that all of them may be recognized and corrected without the use of a simultaneous ECG recording. However, they highlight the fact that the most appropriate technique for correction of R-R time series is still pending proper research and agreement.

The combined error rate of Polar V800 in standing and supine positions was 0.086% which is a marked improvement over previous research findings from the Polar S810 (0.40%) and Polar S810 (6.93%). The paper concludes that the device is a "valid" tool for the detection of RR intervals "at rest" and improves on previous HRM models with regard to comparability against ECG. 

The meat of the paper is it's tabulated summary of means, bias (LoA), ICC (95% CI) and effect size, which I'd like to reproduce here. These numbers are the justification for stating the validity of the V800. An interesting area to note is the level of discrepancy in HF power between V800 and ECG in the supine position. It is an order of magnitude different, whereas much more agreeable in the standing position. Is this a typo or the actual finding?


Saturday, July 22, 2017

Heart Rate to Power Ratio Metric for Running

Attached below are some squigglies of HR:Pw profiles from my own runs. Data indicates slope is very dependant on what the ambient conditions are. For instance, the body's challenge to cool is one fundamental driver of high HR. The body's ability to process oxygen at high altitudes is another. 

Long, slow, flat beachside run, hot and humid : First image is a long, slow controlled jog outdoors at 38 deg C, 50% humidity and medium wind for an effective temp index of 38. The squiggly goes straight up which is interesting. What this means is that under such hot conditions, prolonged exercise in low power still leads to gradual HR elevation or "drift". 



Treadmill run : Second image is from a 30 min easy run on a treadmill in an airconditioned gym. Power is limited to a tight range, run is well controlled and slope of squiggly is gentler than that of previous scenario.



Interval training, beachside, hot and humid : An example of 2 x 6 min, interspersed with 3 min slow running. 35 deg C, 50% humidity and medium wind for an effective temp index of 33. Key information - recovery jogs involved dousing self with water, on the head, down the back etc. During work segments, convection helps a bit to dissipate heat.



High altitude run : The last example is from a 40min run at high altitude, cool environment. Maximum elevation was around 11,800 ft and much of the running terrain was uphill, therefore power numbers are higher than equivalent runs done on flatland. This was the first run in such an environment, hence the body was coping with acclimitizing and effort can be classified oxygen limited.



The histograms on the x-y axes are another key piece of data. Skewness of the bars indicate frequency distribution at high and low ends of the heart rate or power spectrum.  

Altitude running when non-acclimatized is a case of high HR dominant running, where those bars are skewed to the higher numbers. For example, a predominantly dual peaked histogram for running power could point to an interval session, as the third image shows.

Another way to show the HR:Pw plot would be to express the numbers on the axis in terms of a percentage. This gives better visual cues on intensity, both to runner and a coach.

Apart from looking at slope, the area distribution of running data on a HR;Pw map might also be useful. At a conceptual level, the way datapoints can be arranged on a %HR:%Pw plot is depicted below by 3 types of colored dots. High HR:Pw runs in black and low HR:Pr runs in green. Red dots falling on the diagonal line might be an idealized scenario, where the increase in HR follows organically from an increase in running power.



Concluding Remarks

Heart rate to power ratio with frequency distribution information is one quick and easy way to classify the intensity of run. The advantage of the HR:Pw plot is that it captures whole body state of affairs (HR) and activity specific intensity (power). Ofcourse, the Hr:Pw profiles maybe slightly different for everyone, since everyone reacts a bit differently to temperature, humidity, altitude and stress. Looking at runs in this way also helps in controlling for ambient factors and in trying to compare apples to apples when analyzing performance across several runs.

Read more of my articles at Running Science.

Thursday, July 13, 2017

Harmonising VDOT Pace with Power Based Running : A Case Review

Note : If you're an elite athlete, please take the guidance of your coach. 

The VDOT based system of paces is a tried and tested system for run training designed by Jack Daniels and a colleague of his who worked for NASA. The system, described in JD's book "The Running Bible" appears to be sound at first glance - it is established from metabolic testing and the foundational idea that equally performing runners can be assigned equal aerobic profiles. 

JD has ofcourse outdone himself in both the national and international running stage so we can't argue whether he had his wits about him when he sat down to make VDOT.

I was interested to see how VDOT based paces, when converted to power, compares to the instruction in critical power based running zones. For this I pick an example runner, Tony. 


Converting VDOT Paces to Power

Let's assume that Tony recently raced 3km in 12 minutes for his season's best. Ambient conditions at the race were :

Temp = 95F
Altitude = Sea Level

This equates to a pace of 6:26/mile = 250 meters/min.VDOT is approximately 45 per the VDOT tables. 

The goal is to find an equivalent power for the VDOT pace so that he could implement power based training zones. Jim Vance has defined a simple factor tying speed and watts called Efficiency Index, EI, which is defined as the ratio of speed in meter per minute over watts, both continously captured over a 30 second rolling duration.

If Tony has knowledge that his short races in similar conditions in the past were done with an EI of 0.95 m/min/W, then knowing speed, corresponding power is : 

Equivalent Power for 3K = 250/0.95 = 263W

(According to the metric, as EI decreases, power to produce a given speed increases).

Given that 263W is an equivalent power estimated from race pace and an estimated EI, it must be checked whether this power value can be sustained when the powermeter is applied. 


VDOT Power Validation

1) As a first check, Tony can peer into his power duration (PD) curve in his favorite software of choice. If the PD curve looked something like the one below, which is a multiparameter exponental model fitted to all of Tony's runs 12 minutes and below, the chart seems to suggest a theoretical maximum of 220W for the 12 minute duration. 


Would it be correct to assume that Tony simply cannot sustain this wattage for this time? It might be fair to consider that the software generated PD curve in question just may not have race equivalent data. The model tries to make a trend around what is known, not what is unknown. If most of Tony's runs were from social runs in the park on weekends, the PD curve will underestimate his potential and would probably not be helpful. 

2)  The other bit of useful data from the VDOT system for this runner is the equivalency is terms of 5K, 10K, half and full marathon distances. For example, the equivalent 5K running time for the VDOT of 45 is 21:49 for the same ambient conditions. If you then used the Stryd's critical power model on their website, it suggests a critical power of 236W

By the old definition, critical power is the steady state rate of work output someone can theoretically sustain "indefinitely" although the notion of an indefinite time period is a bit corrupted - no one can exercise indefinitely! As now understood by the scientific community, it is a threshold below which VO2 and heart rate will not not see a rise and is also seen as the greatest point at which energy provision is still wholly oxidative (Poole, Burnley et.al).

Knowing that Tony's critical power is 236W, it seems "feasible" that he can pull off a short excursion into his anaerobic energy systems for 12 minutes at 263 Watts, which equates to 111% of his critical power. In this unsteady state, Tony will accumulate fatigue and have a rising heart rate and VO2.

3) Tony can validate this power (i.e know whether he can sustain it for 12 minutes or not) by performing a 3k at race pace in well rested conditions on similar terrain. Perhaps he chooses the same race the next time it's organized. If the average wattage generated by his powermeter is within 3% of 236W, he might be able to conclude that the conversion is roughly equivalent.  His pace to power conversion can also be adjusted by assuming a more generous Efficiency Index if prior data suggests that this is the case. It can also be adjusted by tuning the equivalent 10K pace resulting from the VDOT tables. 

While the VDOT-power conversion hasn't been perfect, it allows Tony to be able to go out and do a trial run or two and make necessary adjustments. Therefore, in so far as VDOTs are generated from race performances and the effect of ambient conditions on race paces are taken into account, I find no flaw with this procedure. 


Comparing VDOT Power Based Zones to Critical Power Based Zones

Under the VDOT guidance, Tony's training zones in terms of paces at a temperature of 95 F would have been  :


Based on a conservative EI estimate of 0.90, these training speeds can be converted to power values by the procedure noted in the earlier section. For example, the easy pace zone for the mile in terms of power would be 188-200Watts. The marathon pace for the mile would be 225W. And so on. 

The table below shows VDOT paces converted to power (watts) at two different EI estimates for the 1 mile distance. An EI = 0.9 for Tony would be conservative estimate for sluggish runs and sub-optimally executed fast races. An EI = 0.95 could be a theoretical maximum for optimal executed races. If evidence suggests the use of a more generous EI, I suppose that would be ok. 


The key question is how these VDOT pace based power zones compare to critical power based running zones prescribed by Stryd. 

Stryd's algorithm for power zones for a critical power of 236 is as follows :


Based on the comparison of the two zone tables, it seems that the choice of EI makes a key difference in interpretation. For example, for EI of 0.90, the VDOT marathon power of 225W would be considered to be threshold power under Stryd's model. For an EI of 0.95, the VDOT marathon power of 213W falls within the "moderate" power zone. But at the upper end, the VDOT repetition power of 261W comes conservative, whereas Stryd's power is a bit more aggressive at 10 extra watts. 


Conclusing Remarks

1) Equivalent running paces from VDOT tables, critical power and Efficiency Index (EI) appear to be key parameters affecting the conversion of VDOT paces to power. In the particular example, using Tony's equivalent 10K pace and an  EI estimate that corresponded to Tony's race data, the VDOT based powers bridge upto Stryd's power zones with minor differences. One might also make the assumption that training at two power values that are within 3-5% of each other elicits similar physiological responses.

2) A unique advantage of VDOT is that it accomodates pace derates for high temperature and altitude. Powermeter based running guidance has it's advantages, but it still has some catching up to do in terms of interpreting application for real world conditions - wind, temperature, humidity and altitude. The practicality of new, cookie cutter running programs based on power must be evaluated critically, particularly by runners living in hot, arid climates where the danger of heat stroke is real.

3) Because training zones are outputs from an algorithm that takes user input, they are estimations at best and it is a given that adjustments will need to be made to tally up RPE and overall whole body feeling to the prescribed guidance. Crucially, it is important that the zones are judged well before jumping straight into applying them in training. No one wants to waste time finding out they can't sustain a prescription. 

4) As far as my experience goes, both the VDOT system and the power based training systems are equally time consuming, although the fruit of added insight for advanced training is a plus. Both systems require frequent data diving, critical evaluation and adjustments. More so, the zones have to be re-evaluated at regular intervals to see how training and racing have modified them, for the better (or for worse!).

5) The interesting and larger implication of my writeup is that a traditional VDOT based system might be nearly equivalent to the power based running prescription, "if used correctly", which means a) it doesn't create a strong case for conversion from one system to the other and b) means that fundamentally both are sound in that they are calibrated to metabolic test data.

6) Additional research is needed to give empirical guidance on how truly different is training by VDOT vs powermeter for different classes of athletes. For example, in cycling research, it has already been established that there is "no empirical evidence" to suggest the superiority of either power based training or HR based training in the implementation of interval training. Both were roughly equivalent in terms of responses seen in recreational cyclists after a multi-week training cycle. 

Friday, July 7, 2017

Perspective : Why is There No Indian in the Tour de France?

Such was a recent question on Quora.

There’s little reason to pick the Tour de France if you want to inspect the absence of Indians in international professional cycling. It’s what goes on at a more fundamental level of international racing that counts.

A quick example to analyze the parity (or lack of) in Indian performance with respect to other competitors in order to understand why it’s challenging to move up :-

At the 2017 Asian Road Racing Championships held in Bahrain, India did seem to have “decent” amount of pedal power in terms of two national time trial winners representing at the ITT and a total of six talented roadies at the TTT. Even though numbers weren’t on their side, certainly it was commendable that these six got an invitation to represent the country.

However, it panned out that the Kazakhs, South Koreans and Japanese would go on to cream the competition. The best placed Indian at the ITT was a distant 5th place from last in a total field of 18.

For a flat TT course, it is instructive to look at absolute power outputs as they tend to be an objective marker of sustainable intensity. The following power duration chart is from a Kazakh rider, who was among the winners of the men’s TTT that week.


You can see that 30 min power is pushing 500W. I’ll leave digging up the Indian power duration chart as an exercise for you.

These Indian pros could better describe the intensity of racing at this level to you. But personally, I see a gap of over 100 Watts for this duration between a Kazakh and an Indian, which is a,,,, little PACIFIC OCEAN to bridge in cycling parlance.

Performance in any sport is multi-factorial. Sympathisers will tend to say that national poverty plays a big factor in setting back the sport. On the other hand, if national poverty were the only deciding factor, you shouldn’t even be seeing a war torn country like Iraq or even for that matter, Mongolia or Uzbekistan showing up to the races, let alone place well in contention for podium spot at these races.

I’ll explore some other points that I think are important.

Facts of Life :

1) Physiological : As long as there is no raw talent, you will always be trying to fit a square peg in a round hole. At a fundamental level, performance in cycling is determined by a high VO2max and the maximum velocity and/or power output you can sustain AT steady state lactate level in your bloodstream. You take two cyclists - A and B. If B has a higher VO2 engine and can process work at a higher fraction of that for a longer period of time without fatigue, B is atleast on paper the faster cyclist at the end of the day. Unfortunately, sports science research and papers in Indian cycling are lacking in the public domain so we can’t make comparisons of national level Indian cyclists against similar international competitors. I do suspect there is a big gap in prime physiological indicators that define success in cycling.

2) Winning : One of ways to get into the TdF is through wild card teams. To be noticed for selection, you have to simply perform. You can have all the talent and train like a madman all year, but if you’re not winning and arguably by big margins, it’s going to be difficult. Essentially, the meat of a pro’s career is done and dusted by age 35 and the rest will be sobering to watch. It’s in the younger years that you can do some crazy things in life. For example, when ex US pro George Hincapie was still in his tender years, he was entering crits and lapping the entire field. Young Alberto Contador would show up at races with a heavy iron bike and still fry the field. The infamous Lance Armstrong competed in traithlons as a teenager and gave older experienced competitors a serious run for their money. Answering when can you see an Indian at the Tour de France is similar to how Africans entered the Tour de France in 2005, or for that matter, how Columbians entered the Tour de France in the 1980’s. Fundamentally, you need talent yes, but you need to win some BIG races on the cycling calender and you need the likes of Mr. Eddy Merckx and Mr. Bernard Hinault to notice you and bless your move forward. The Columbians had over 3 decades to mature as a cycling nation, today they have several top cyclists posted in the Tour de France.

3) Cultural : Cycling is a relatively new professional sport in India. In western countries, cycling talent is identified at a tender age and nurtured through the teens. People give a damn about it, they appreciate it. In India, families like to see their girls and boys get a good job, marry before 30 and get settled in life. Loitering the streets on a bicycle comes with a stigma. Furthermore, the collective culture of bike racing, when compared to other national pasttimes such as cricket, is dismal. On this point alone, we can write a big essay. On the other hand, one can argue that India is talented in sports like cricket, badminton, hockey and wrestling. TV air time and press coverage going to something India is good at, cannot be really argued against. There can be some balance, however.

4) Financial : There aren’t many bike races and professional development programs in the country. A few are springing up in parts of India, but nothing at the level to show normal average joe Indians that there is a professional future in cycling. If you can’t put food on the table and feed your family, I don’t care what it is - lorry driving, or gold merchandising, you won’t be doing it. In this respect, Indians are like any others from any other nation - they have their priorities.

5) Environmental : What we describe as the ‘quality’ of cycling, whether recreational or sport, depends in large part on the quality of the surroundings. Prime among them : clean air and good, safe roads. I observe that several Indians in inner cities defy the odds to enjoy cycling during weekends. However, the amount of particulate pollution (PM10, PM2.5) in cities like Delhi and Bangalore are ridiculous and exercising in these conditions would arguably shorten life span. Those who ride motored 2 wheelers on these roads are found to wear face masks to block pollution. Cyclists, on the other hand, are completely exposed and elevated breathing rates mean a lot of crap is going in. Something of a sea shift needs to happen in the traffic and emissions scene in India to provide an environment conducive to performance. This is a long term change that I don’t see happening any time soon. Even legislating that drivers are not allowed to use certain roads at certain times of the day comes with massive uproar. Until these changes come about, cyclists have to ride long miles to get out into the country from places of inhabitation. (The nice thing about India is that it is a democracy and if you make enough noise, people responsible for change will listen….or something like that. So use that vote!)


Positive Signs of Change :

The sport does seem to be exploding in India which is a positive sign. Bike shops and cycling themed cafes are springing up. Several cycling clubs attract people to buy bicycles and take up recreational riding and racing.

Another positive sign is a strong Indian presence in the management circles of the Asian Cycling Federation since Mr. Onkar Singh took office as it’s Secretary General.

A third is, as I mentioned, the growth of junior cycling development programs which is identifying talent and taking them abroad to countries like Belgium. One example is the Indian Pro Cycling Project.

One hopes these developments bring in :

1) A fresh pool of genetically talented Indians into the sport, whether that is nationally or from overseas residing Indians.

2) Support for Indian cycling at the international platform. Such is happening currently at Asian level as I already mentioned.

3) Provides Indians an exposure to international racing and a glimpse of the true demands of a professional career.

4) Encourages businesses to notice cycling and support talents with sponsorships.

5) Encourages talented sports scientists to study indian cyclists and publish findings in international journals. What are the physiological gaps and what training methodologies can best bridge them?

As a summation, I would argue that a string in essential supply chain needs to pop up to support the upward movement of Indian cycling professionals. Good bicycle manufacturers, mechanics, scientists, coaches, sport directors, sport management consultants, aerodynamicists, nutritionists, business people, sponsorships and importantly, partnerships with international facilities and people. The list goes on and on. In a challenging sport like cycling, you really have to sit on the shoulders of giants.