How is the value of CP calculated in the Critical Power plot¶

Basically the CP model is that there is a fixed supply of anaerobic work, which can be fully spent over any duration, and a sustainable aerobic power, which can be sustained indefinitely. Obviously very simplistic....

Most CP calculators ask for two fixed time durations: for example 5 minutes and 20 minutes. But the problem is you then need to have totally nailed an effort at both of those exact times. More common with me is you go hard up a hill of a given length, and the time it takes is variable. Maybe you had a super power for 4:30, but your 5:00 power isn't so hot, or you did a super 30 minute effort but your 20 minute effort wasn't your best. So what the code does is iteratively pick pairs of time points which generate the "best" CP curve for your data.

The issue with it is it uses all of your history, while physiology is constantly changing. We talked about putting in a time limit that it would use data only from the previous N days for some N. But unfortunately other tasks got in the way of me contributing further.

I like the CP curve because at least within the duration of around 2 minutes to around 30 minutes it gives me an idea if a "PR" over a given time duration is actually a quality result or not. For example, if all I do are 5 minute and 20 minute intervals, then I go out and PR a 7 minute interval, is that really the result of superior fitness, or just the result of doing an interval duration I'd previously neglected? The guide for this is if the 7 minute effort "pushes up" the CP curve. If it does, it really represents a new level of performance. If not, it might just be a "gap fill" effort.

Thanks to Dan Connely for the code and description