The guy who designed the model used to post here all the time until he was put in timeout for being an argumentative and pompous ass.

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is the 2 point formula good enough ?

I am not smart so I keep it simple :-)

I cannot remember where I read it, but double the duration means dropping power by 5%. Sort of works, until it doesn’t. But I use it as a guide.

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Yes, the 5% work pretty well for durations between ca. 5 minutes and 2 hours.
If you want a formula: critical power=(duration in hours)^(-0.07)*FTP
Both above and below these durations, the drop getts larger.

What I've found with a small sample size:

<5 min: ~25% drop when doubling the duration
5-120 min: ~5%
120-240 min: ~10%
>240 min: ~15%

Obviously this can always only be a very rough guide.

I'd say it is more worth it to collect as many of those data points from real attempts as possible. People are different.

A Gaimon vs. a Sagan kind of thing if you will. The curves are different.

Best indicator of performance...................is...............

So that rule of thumb would give a power law, with P as power and t as duration, d log(P)/d log(t) = log(0.95)/log(2), or

P(t) = P_0 (t/t_0)^(-0.074)

where P_0 is a known reference power output at duration t_0.

This would be very similar to "Riegel's formula" in running, which says t_2 = t_1 (d_2/d_1)^b, where d_2 and d_1 are distances and t_2 and t_1 are the times required to run them, and the power b has been best fit by a value of about 1.06 (https://en.wikipedia.org/wiki/Peter_Riegel). This can be manipulated to:

v(t) = v_0 (t/t_0)^(1/b-1) = v_0 (t/t_0)^(-0.057)

where v_0 is the known running speed at duration t_0, and the exponent of -0.057 applies for b=1.06. This implies about a 3.9% decrease in running speed for every doubling of duration, which for a runner doing 8-minute miles, translates to 20 seconds slower per mile when the duration is doubled.

This sort of rule should apply over a wide "aerobic" range, for efforts from a few minutes to a few hours in duration.

Push the peddle harder + longer time = faster - getting tired = slower.

My math is easier

2 parameter model doesn't work as well as 3 parameter, but it only needs 66% as many parameters so for quick calcs I use 2 parameter too.

If two point is good enough....

You want to know your CP and W'

To get that

The power duration curve plots Power (y axis) against time (x axis)
You want to plot Energy (in Joules) against time and get the slope/intercept of that line which are CP and W'

So test1 is say 5min and 300 watts,
5min *60 s/min = 300s this is X1
300watts * 300s = 90,000Joules, this is Y1

Test2 is say 20min and 250 watts
20min * 60 s/min = 1200s this is X2
250watts * 1200s = 300,000joules, this is Y2

So calculate the slope (CP) and intercept of the line through these 2 points
Slope = CP = (Y2-Y1)/(X2-X1) = (300,000-90,000) / (1200-300) = 233w
Intercept = W’ = Y1 – CP*X1 = 20,000

You can now calculate Y for any X

Y = CP * X + W’

Example for 30min, or 1800s
Y = 233 * 1800 + 20000 = 439,400
This is in joules. Divide by duration
439400 / 1800 = 244 watts

So when you know your CP and W’ you can calculate Power for a given duration

told you it was simple

one reason I am asking this question is that if different people/ athlete types have different power curves then one would assume that there would be a different formula with slightly different math treatments for each. This in other words might be seen as a signature for that athlete type? Then knowing this what happens when you try to manipulate one of the factor points to the rest of the curve. What got me thinking about this is Xert has a 3 point model that you can plug in values and it will calculate the curve. I tried it and saw strange behaviours, when I increased 6 minute power with no other changes to the inputs the 60 minute duration number went down so it struck me funny and I was curious about the math behind what might generate this curve. It also make me wonder if you have a certain signature Climber vs sprinter for instance) then what durations you train may impact the outcomes? So one might say that it could help suggest training durations to focus on for certain kinds or focus for improvement? Mostly a thought experiment at the moment.

Index of resistance in running is double the distance and you will be 5% slower. I think as a basic starting point this is good for power durations of 20 minutes to 2 hours, longer than 2 hours and execution (nutritional inputs, pacing) have a larger contribution than all other factors combined.

So yeah as others have said, if you don’t know use 5% as a starting point and then test for clarity.

Maurice

Yours is a common question, and the answer is still not fully settled.

The quick version is that there may be phenotypes but they're not easy to spot just by looking at an ad hoc power profile table.

We know that it's possible to model the MMP or power duration curve -- the question is how many parameters and how do you put them together to get a fit that you're willing to live with.

There's a recent (very recent) paper: Puchowicz et al. "Development and field validation of an omni-domain power-duration model", https://www.tandfonline.com/...p;journalCode=rjsp20 that looks at modeling MMP.

Mike's also done some work on identifying a "relational" model of power duration based on the Golden Cheetah Open Data Project, based on data from ~2500 participating riders. Basically, there's a baseline power-duration that's kind of the average of all 2500 riders, then he models how each athlete differs from that baseline. It turns out that he gets a pretty good fit with only 3 additional principal components: one that moves the baseline up or down, one that tilts it from left to right, and one that twists it.

More than you probably wanted to know.

[Edited to add:] Or, you could just do what Marc suggested and go with two parameters (CP and W') that seem to work pretty well from maybe 4 or 5 minutes out to maybe an hour or so. For t seconds (where t ranges from maybe 240 or 300 seconds out to 3600 seconds), watts(t) = W'/t + CP. That will get you close, but it doesn't take into account the tilt or twist parameters.

  
More than you probably wanted to know.
thanks for this info Edit( Strangely enough I came across that very page this morning when I was bumping around looking for info, I have not yet had time to look into it or try to access the paper)

Actually that is really what I was wondering about. I have done some work in chemometrics which is multivariate approached to analytical chemistry and I always wondered why no one had tried modelling this sort of thing in human performance. It may have been the lack of a suitable data set? I think I will try to access that paper and see what I can glean from it. I usually have used specific program toolboxes that do all the heavy math lifting so that is my weakness but I sort of understand the concept of multivariate curve fitting and of course the inherent concern with over fitting so this is really exactly what I wondered but felt that it was unlikely that it had been explored so was thinking instead of the simpler option.

Check out Mike's page at veloclinic.com, especially the most recent entry, and those from November 2018 to January 2019.

thanks for this Robert.