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Critical Power

Two all-out efforts define your entire power-duration curve — CP is the ceiling, W′ is the battery above it.

Critical power is the highest power you can sustain without draining your anaerobic reserves; W′ (W-prime) is the size of those reserves in kilojoules. Together they form the two-parameter model that predicts your maximum power for ANY duration — the framework behind modern cycling pacing, verified against physiology since Monod and Scherrer in 1965. Two genuinely all-out time trials (~3 minutes and ~10–12 minutes) are all it takes. No lab, no 20-minute FTP test with its arbitrary 95% fudge.

Why people use this

Cyclists and triathletes use it to turn two all-out time trials into the whole power-duration curve — CP as the aerobic ceiling, W′ as the anaerobic battery — with time-to-exhaustion at any pace, replacing the arbitrary 95%-of-20-minutes FTP estimate.

How it works

1. Each effort is work = power × time. The model fits W = CP×t + W′: CP is the slope, W′ the intercept of the work-time line.
2. Predicted max power for any duration: P(t) = CP + W′/t. Time to exhaustion above CP: t = W′/(P − CP).
3. Example: 3 min at 450 W and 12 min at 380 W → CP 357 W, W′ 16.8 kJ; 20-minute max ≈ 371 W; 400 W lasts ~6.5 minutes.
4. Valid range is roughly 2–30 minutes: below that, maximal power is mechanically capped; beyond it, glycogen and heat break the model.

Common questions

How is critical power different from FTP?

FTP is defined as ~60-minute power and estimated as 95% of a 20-minute test — an arbitrary correction. Critical power is a physiological threshold fitted from two all-out efforts, and it typically sits a few percent ABOVE FTP. The practical difference: CP comes with W′, which tells you not just your ceiling but exactly how long you can sit above it — 400 W for ~6.5 minutes when your CP is 357 W and W′ is 16.8 kJ, for example.

What do my two test efforts need to be?

Short enough to be VO₂max-limited and long enough to separate the parameters: the standard pair is ~3 minutes and ~10–12 minutes, on separate days or fully recovered. Both must be truly all-out — a paced tempo effort poisons the fit. If the longer effort averages MORE power than the short one, the model refuses (you will see the invalid-model note), which is itself a pacing-quality check.

Can I use this for running or rowing?

Yes — the same hyperbolic law holds for running (critical speed in m/s, with D′ in meters instead of W′) and rowing erg watts. Enter pace-derived power or speed consistently for both efforts. Just respect the valid window: roughly 2–30 minutes, since sprint mechanics cap short efforts and endurance economy dominates long ones.

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