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.

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, 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

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.