Critical power, W′ and the power–duration curve

A real boundary, not a percentage

Critical power is the highest work rate you can hold with your physiology in steady state. Below it, oxygen uptake, blood lactate and muscle metabolites settle at an elevated but stable level. Cross it and nothing settles: lactate climbs, oxygen uptake drifts up toward maximum, and the effort ends in exhaustion at a time you can predict ¹.

This makes CP a physiological line rather than an arbitrary fraction of some other number. Two riders with the same 20-minute power can have different critical powers, and the boundary sits where each one's response stops stabilising ¹.

W′ is what you spend above the line

The relationship between power and how long you can hold it is hyperbolic, and the curve has two parameters: the asymptote (critical power) and the curvature constant, W′ ². W′ is a finite quantity of work, measured in joules, that is available only above CP. Spend it and the effort stops.

W′ refills when you drop below CP, on an exponential time course rather than instantly, and the further below CP you go the faster it comes back ³. That is why the recovery valleys in an interval session matter as much as the intervals, and why a set of hard efforts with soft-pedalling in between behaves differently from the same efforts separated by tempo.

Fitting the curve from real efforts

CP and W′ are estimated, not measured directly. The standard approach is a set of maximal efforts of different durations, fitted to the power–duration relationship; from the fitted parameters you can then predict time to exhaustion at any power above CP ⁴.

The duration window matters. The hyperbolic model describes efforts of roughly two to twenty minutes well, and efforts outside that range distort the fit. Very short sprints are limited by things the model does not represent, and very long efforts fall short of what it predicts ⁴ ¹.

Efforts need to be genuinely maximal for their duration. A paced 12-minute test inflates CP and shrinks W′.
Two efforts can produce a fit; three or more spread across the window produce a more stable one.
Estimates from ride data rather than dedicated tests are only as good as the hard efforts in that data.

FTP: trackable, but not the boundary

Functional threshold power is conventionally the highest power you could hold for about an hour, usually estimated from a shorter test, commonly 95% of a 20-minute best ⁵. It is easy to test, easy to re-test, and it anchors training zones and load scoring across the whole app.

What it is not is a direct read on the maximal metabolic steady state. When FTP has been compared against laboratory measures of that boundary, agreement has been poor: FTP can sit above or below it, and the direction and size of the gap differ between individuals ⁶.

Both facts can hold at once. FTP works as a trend line for your own fitness and as a scaling factor for load, and it should not be read as the physiological threshold that critical power describes.

Where the model stops helping

A two-parameter curve fitted from fresh maximal efforts says nothing about what happens four hours into a ride. Neither CP nor W′ is assumed to be constant across a long day, and the literature treats change in these parameters under accumulated fatigue as its own question ¹.

Modelled W′ balance also depends on the recovery time constant used, which varies between athletes and with how the work is arranged ³. Treat a live W′ number as a good estimate of how much is left, not a fuel gauge.

References

Numbered in order of first appearance. Every link goes to the original work.