Extrapolating power curve

[new to intervals.icu. I am NOT an athlete, but a senior who is into touring. I want to keep track of my “range” as in car range estimates that tell you how many miles/kilometers you can expect based on the amount of fuel in the tank, and the driving conditions]

On the Power tab, the power curve displays actual values for duration of up to 2 hrs (the longest amount of time I spent on my indoor trainer) and the power profile settings allow to display comparative power for duration up to 4 hrs. I assume that this is via extrapolation of the power curve.

  1. Is it possible to extend the horizon to 8 hrs?
  2. Is it possible to concoct a “range” statistics that would be something like how many kilometers (or miles) one can expect to be able to ride day after day (i.e. within reasonable fatigue)?

Sorry if the questions are trivial and/or poorly formulated.

No, the power curve displays what you have done/achieved.
It shows your best performance over that time range.

Thanks.

My understanding is that the CSV file that can be downloaded from the POWER page is the modeled curve (eFTP) and not the best, or average, power observed at some duration, right?

Is it possible to download the raw data (i.e. best effort and/or average power at various duration)

You can select a few options:

  • best power
  • this season
  • last season
  • indoor
  • outdoor
  • race

Here’s an example of the various power curves, along with the model curve for each one.

You can get the curves for different periods and also the ‘fitted’ curve which is used to calculate eFTP. But you can’t use that last one to predict what you would be able to do over 8 hours or something. It’s a mathematically fitted curve to describe power/duration relation for durations typically to 1 hour. Anything longer then 2 hours will be very dependent on hydration and food intake. The mathematical curve would go on to infinity, and is totally unable to predict any kind of performance over durations you’ve never done before.

If you use a Garmin edge 40 series or the 1050, a parameter called Stamina may be what you are looking for. It measures the amount of “fuel” you still have available.

Garmin’s documentation indicates that both a power meter and a heart rate monitor are needed for it to work.

Edit: link to the edge 1040 manual.

https://www8.garmin.com/manuals/webhelp/GUID-0083D0A0-EA6E-41F0-8207-3F1498875E61/EN-US/GUID-7AF5563D-FD32-4DB6-94CE-9631E044E3CD.html

Unlike a car the body has 3 types of fueling: LO7 of Unit 1 - Energy systems and their relation to exercise (2021) - PT Institute - for your endurance/touring question you are most interested in your aerobic power, and as mentioned above is also dependent on adequate refuelling.
In some ways you are already covered by things like the FTP calculations as that covers your aerobic power too. Also your TTE and VO2Max.

In theory, the distance you could cover could be reverse engineered by figuring out the elevation provided, and the power required/desired, which can then be compared to your FTP to produce a Load figure. But then all you’ve done is provided a rather complicated way of replicating your Fitness figure, as there’s some evidence to suggest that your chronic training load is a good predictor: Volume vs Intensity | Alan Couzens

There’s another person here who is using Machine Learning to estimate: I would like to get your opinions on the FTP model I developed (now see ::::: Riduck.com :::::)

Just wanted to thank you all for your time.

For context – while I am not training to qualify as a pro, I have several months-long tours under my belt, typically averaging 100kms/day which, depending on the course profile and weather, may go upwards of 200kms.

I became interested in indoor training because I am getting older and read somewhere that performance (stamina) sometimes declines quite fast — so I now have an eye on my FTP and am happy to report that it as low is it was years ago, but not lower :slight_smile:

I am also familiar with Javascript and Python, and therefore very happy to discover that this is geek heaven.


To the original questions

  1. I now understand that the downloaded CSV contains the data used to generate the plot.
  2. I’ll try to model my power curve using a different model. For now, the fit is rather poor. (not sure that the pic will show in this post

If you have your history with activities, you can import it and create wider date ranges. That will show the curve for earlier date ranges and can give you a better idea of how you’re doing on longer activities.
Some rules of thumb that I use to prepare for long and ultra events:

  • The ten weeks before a major event, should have approximately a weekly average training time close or upwards of the estimated time to finish the event
  • The long training ride should during those 10 weeks build up to at least 80% of the estimated finishing time
  • On the shorter training rides, do something specific to the goal event. Climbs, similar in duration for example if the event has sustained climbs.

Use training time, not distance. On the event you will probably cruise a lot of the time in a sheltered group at higher speeds compared to your solotraining.

This is for event durations of up to ~9-10 hours.
For ultra’s with even longer duration, I first build to the expected duration as a weekly goal. Then I start compounding the same number of hours on less consecutive days.

  • First build to 16 hours a week (with one rest day)
  • Then 16 hours on 5 days, 4 days…
  • The last stage, I do 16 hours over 2 days (which comes down to doing them in around 30-36 hours.

During these ‘compounding’ stages, rehurse refuelling strategy!
I finished, more or less comfortably, events of 17-19 hours by preparing like that.

It’s not really all that different of the fit for my model curve. It’s tricky as has been pointed out that people tend not to actually produce power according to the curve anyway during the same ride.

Joe Friel wrote a lot of books about training, including one perhaps you might find interesting as a self described senior: What It Takes to be Fast After 50 - Joe Friel

My understanding is that the eFTP model is designed to estimate FTP (max power sustained for 1hr). Which would explain why it lands at eFTP and remains essentially flat afterwards. (Actually, the developers may want to truncate the model line at the 1hr mark)

I am looking for a model that would allow reasonable extrapolation for up to 8hrs (or more) based on observations culled from shorter workouts (I certainly can’t spend 8hrs/day day after day, during winter time).

I’ll try to get a couple of 3-hour long z2 sessions on record and then put the numbers through fine model… Will get back to this thread once I get results. 2 weeks or so.

You might want to watch this webinar for WKO5, as the principles are similar when using a model to estimate power.

Critical Power is possibly a better option, as it’s formula based, and also using maximal efforts

I’ll add more later, including the formula and a working example (in Excel).

You might want to watch this webinar for WKO5, as the principles are similar when using a model to estimate power.

Critical Power is possibly a better option [edit: to extrapolate beyond your longest distance], as it’s formula based, and also using maximal efforts

  • P = Power
  • W’ = W-Prime, aka Anaerobic Work Capacity
  • T = Time
  • CP = Critical Power

Formulae:

  • P = W’(1/T)+CP

  • CP = INTERCEPT(Known Ys , Known Xs)

  • W’ = SLOPE(Known Ys , Known Xs)

  • Known Ys is a list of average power for known durations

  • Known Xs is a list of known durations, eg. 5s, 60s, 5m, 12m, 60m, etc.

Many CP models are hyperbolic in shape and will always produce a poor fit as time increases and the curve flattens. That’s why some folks have added a decay parameter in the modeled power beyond critical power (WKO’s model, Golden Cheetah’s Extended CP, Omni-duration PD model, etc). Other models like Perronet and Thibault’s model start decaying just after 7 minutes (assumed VO2max duration) but can also be used to fid data over longer durations.

I don’t think any hyperbolic model will work for estimating long durations - like 2 or 3 parameter. You’d have to use a model like Extended CP or OMPD to try to model out that far (see the circled part of the curve).

Here are your curve fits based on the screen clip you posted.

Very interesting. (If you have a source that would give the details of the various models, I’d love to read it)

On the “technical” side of model specification: I did run a quick piece-wise-linear-fit model that settled, IIRC, on 9 segments resulting in an almost perfect (over) fit.

I would rather use some form of modified exponential decay (i.e. constant or duration varying rate of reduction).

One thing that concerns me is that the raw power curve data is a function of physiological aspects, that the model should capture, conflated with psychological factors (I am willing to suffer for duration x because it’ll improve my FTP) and by the idiosyncrasies of the workout schedule (I schedule an hour-long tempo ride twice a week, and longer z2 endurance rides. Unsurprisingly my power curve exhibits a sudden downward shift at the 1-hour mark.)

A reasonable estimate of LRP (Long Run Power :wink: should probably be solely based on endurance rides. Or is it tautological…

A CP curve, would but a fractional power curve fits pretty damn well. I’ve done that with my observed peak power up to 4 hours and it was able to predict to within 10-20 watts my real world power average at 14 hours.

May I ask what was the model specification?