Athlete summary
Critical Power (CP) is the highest power you can sustain without continually drawing down your anaerobic reserve. W′ (pronounced “W-prime”) is that reserve in joules — the finite work you can do above CP.
Together they describe the power–duration curve for hard efforts (~2–20 minutes):
P(t) ≈ CP + W′ / t
So a 3-minute max is much higher than a 12-minute max, but both should land on the same CP/W′ line when the efforts were truly maximal and well spaced.
Koyaro stores CP and W′ as physiology measurements. They feed W′bal charts, race effort budgets, polarized hard-boundary fallback, CP intensity domains, and severe-interval design. After prior work, fatigued CP/W′ (Fatigued Critical Power and W′ after prior work) replace fresh CP as the late-ride heavy↔severe boundary when known.
Prefer CP over a single FTP conversion
When you already have several well-spaced maximal efforts, fit CP/W′ (with accepted QC) and use that ecosystem (domains, W′bal, severe targets) rather than multiplying one bout by 0.95 / 0.90 / 0.75. Single-effort FTP tests remain useful for a quick zone refresh — see FTP field tests — 20-min, 8-min, and ramp conversions.
Fit quality (do not apply bad fits)
A fit always returns diagnostics. Only accepted fits may update athlete anchors (eFTP-from-CP follows the same rule).
| Check | Why |
|---|---|
| R² ≥ 0.95 | Points must hug the model |
| Residuals | Max |predicted − observed| ≤ ~8% of mean power |
| Spacing | Longest/shortest duration ≥ 2× and ≥ ~3 min span |
| Maximality | Mean power must fall as duration rises (otherwise an effort looks submaximal) |
| Physiology | Fitted CP and W′ must be positive |
Rejected fits still expose parameters for coaching review — they are never applied silently.
Optional 3-parameter model
When you have ≥ 3 well-spaced maximal efforts, the engine can fit the Morton/Whipp form:
P(t) = CP + W′ / (t − k)
The extra time asymptote k (often slightly negative) improves short-duration curvature and yields an implied Pmax when k < 0. Prefer 2-param for routine field testing; use 3-param when the 2-param residuals systematically bend at short t.
CP-anchored domains & severe targets
With CP set, intensity domains are:
| Domain | Boundary |
|---|---|
| Moderate | below lab VT1/LT1 when logged and below the hard boundary; else ~0.80×hard |
| Heavy | up to CP when set; else lab P_LT2 (MLSS neighbourhood) |
| Severe | above the hard boundary, up to lab MAP (power at V̇O2max) when MAP > hard; else ~1.20×hard |
| Extreme | above MAP / the 1.20×hard proxy |
Severe work for a bout of duration t uses a fraction of W′ spend (default ~40% per interval — v1 authoring heuristic, / not a Skiba/Jones optimum), not the single-bout hyperbolic maximum — so repeats remain recoverable under W′bal.
Literature
- Jones & Vanhatalo — Critical Power / W′ as the heavy–severe boundary and power–duration framework.
- Morton — three-parameter critical power model (time asymptote / Pmax).
- Field practice — multi-duration maximal efforts (~3–12+ min) for stable fits.