Comments on W'bal and tau

[Steve Windisch]

After some experimentation, it seems that the integral version of the W' chart just does not make sense. Using it to view the W'bal from a criterium shows me going far into negative territory for my estimated W' (19kJ). If I make major modifications to FTP, W', or both, I can force the chart to make sense. Using those same parameters to then view a training ride where I went just as hard at certain points but took it easy for most of the time, the W'bal chart indicates that I barely tried. I think this highlights a critical mistake in the model and upon examination of the formulas involved, it becomes fairly clear that a ride dependent tau is to blame. By definition, it is the half-life of recovery time and I see no reason this should vary so extremely from one ride to the next and it definitely shouldn't be affected by my decision to ride easy back home after doing some hard hill repeats. I know actual clinical tests would have to be done to verify this, but I think tau should be only mildly variable (like FTP or W').

Of course there is the differential model which has none of these problems, but the way it is currently coded it has a constant tau (tau = W'/CP). I'd like to propose a minor change to the implementation of the differential model to include the configured tau from the options:

Instead of recovering with formula: W = W + (CP-smoothed.value(t))*(WPRIME-W)/WPRIME;

I propose recovering with formula: W = W + (CP-smoothed.value(t))/CP*(WPRIME-W)/TAU;

This gives the same model if tau is configured to be equal to W'/CP, but allows people with slower (or faster) recovery time to use the more consistent differential model.

The only question this raises is how to determine one's personal tau value. The most obvious answer to me is to use the established formula, but use information from the mean maximal cp chart instead. Again, this would have to be verified by some actual clinical testing.

Let the debate begin

[Henrik Johansson]

I'm afraid that I not capable to debate the need of personalized recovery ability based on any facts or personal experience since I am just starting to dig into the W' and tau stuff.

But in general being able to tweak things do appeal to people who feel the need to tweak, but also adds a new parameter for "everyone" to learn how to use.
So it is essential that one select an appearance of the new parameter that is easy to grasp for most users.

In this case I think one should avoid yet another tau. It is confusing enough already with the static tau (the one in the options) for the "integral" implementation (or?) and the automatically and dynamically calculated one for the "differential" implementations. And then it is the tau that is presented in the Activities:Stress chart that I have no clue on where it is from, but probably is some kind of average over the activity duration.

It is also confusing to use the "tau" name for something that is not a timeconstant for an exponential function, which is the normal association.

Instead one might consider introduction of an unitless scaling factor in % (for the "differential" model) to speed up or slow down recovery and call it something like "differential model tau scaling factor". And put the reciprocal of this factor in front of the 1s delta/change of W'.

W = W + 1/TAUSCALINGFACTOR * (CP-smoothed.value(t))*(WPRIME-W)/WPRIME;

Default should of course be 100%. Slow recovery athletes would use values above 100% and fast ones, values below.

But if this really is needed or not I don't know.

rgs
Henrik
 

[Mark Liversedge]

Hi,

TAU is used in multiple places to mean exactly the same thing

The recovery time constant for W' in the W'bal formula from 2012 

In options it is set in advance for calculating W'bal in train view, because we can't calculate it on the fly.

In the Activity > Stress chart it is as calculated for the ride being shown.

In the CP/W' Solver it is solved value.

We do not use it to mean anything else anywhere.

See:

http://www.ncbi.nlm.nih.gov/pubmed/22382171

http://www.ncbi.nlm.nih.gov/pubmed/24509723

http://www.ncbi.nlm.nih.gov/pubmed/24492634

And for a layman description and implementation specifics

http://markliversedge.blogspot.co.uk/2014/07/wbal-its-implementation-and-optimisation.html

Cheers,

Mark

[Henrik Johansson]

Mark,

I agree that the usage of the (original) tau when calculating the W'bal should always be the same.

But the difference that I was trying to discuss is how you get the value(s) for tau.
Not always easy to be crystal clear...
This far I have seen quite a number of different ways to calculate a value for tau.

Thanks for stating the background of the tau values in GC.

rgs
Henrik

[Henrik Johansson]

Regarding literature it is also possible to download Skiba's dissertation:

https://ore.exeter.ac.uk/repository/handle/10871/15727

And I just realized that he is discussing this very subject in section 8.2 (especially pp. 153-158).

His name of the model with an extra "personalized" constant is W'BAL-KODE.
And the W'BAL-ODE name for the one without the constant K (in GC vocabulary "differential").
Unfortuanately no firm conclusions on its viability, just stating the question.

Do want to set the record straight on the expressions for these two models' "inherent" taus.

W'BAL-ODE : tau(t) = W'(0)/DCP(t)

W'BAL-KODE : tau(t) = K*W'(0)/DCP(t)

where DCP(t)=CP-P(t)

Didn't find any references to Fronconi & Clarke's work when searching with the standard tools or reading papers etc.
Anyone know of anything?

Also couldn't get hold of the "Validation of a novel intermittent w' model for cycling using field data" article (24509723).
Any suggestions on how to obtain it?

rgs
Henrik