I started Gritmo out of a love for cycling and engineering, and a long-standing obsession with describing complex systems using as few variables as possible.
In Gritmo’s case, that system is the human body—something we still do not fully understand. Drawing on decades of research into effort and performance, we turn a small set of observable data into a model we can actually run. It can describe the rider, estimate what they may be able to do next, and guide their training.
CP and W′ were the smallest useful starting point. Unlike a single reference value such as FTP, the pair lets us represent a rider’s sustained-effort boundary and their capacity for work above it separately. In practice, that separation has proved essential to understanding how a rider responds to different efforts—and to using that understanding to analyze rides, plan effort across a course, and guide training.
01
Why CP and W′ are at the core
The two-parameter Critical Power model describes the relationship between power and tolerable duration. CP is the power asymptote of the model. W′ is its curvature constant, expressed in joules.
Physiologically, CP estimates the boundary above which oxygen uptake and metabolic disturbance cannot stabilize. W′ estimates the finite work that can be performed above that boundary.
Definitions
Critical power (CP)Critical power (CP)
The boundary above which fatigue cannot stabilize and modeled W′ begins to drain.
CP is not exactly FTP, 60-minute power, or a promise of indefinitely sustainable power.
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Above-CP work capacity (W′)
The finite amount of modeled work a rider can perform above CP.
W′ is not a literal tank, a single substrate store, or a purely anaerobic reserve.
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What that means
Imagine a hybrid car on a climb. At CP, the engine is working hard but remains steady. Push above CP and the electric boost joins in—but the battery is limited. In this picture, W′ represents its capacity: the total boost energy available above CP. It is a useful analogy, not literal physiology.
What this does not mean
W′ should not be interpreted as a purely anaerobic reservoir. Above CP, aerobic metabolism continues to contribute and oxygen uptake can rise toward VO₂max. In the model, W′ is a work constant that captures the combined limit of several physiological processes—not a single fuel tank inside the body.
Two-parameter model
P(t) = CP + W′ / tThe equation produces a modeled power-duration relationship. CP is its power asymptote, not a promise of indefinitely sustainable power.
02
Why one percentage is not enough
Percentage-based training places every rider on one relative scale. A target at 120% of FTP or CP tells us how far the target sits above a reference power. It does not tell us how much above-CP work the rider can perform.
Two riders can therefore receive the same target while taking on very different modeled costs.
What that means
A percentage describes the target. CP, W′, and duration estimate the dose for this rider.
Above-CP cost
(Target power − CP) × durationAt CP 300 W, three minutes at 360 W costs 10.8 kJ above CP. That is 90% of a 12 kJ W′, but only 45% of a 24 kJ W′.
| Rider A | Rider B | |
|---|---|---|
| CP | 300 W | 300 W |
| W′ | 12 kJ | 24 kJ |
| Target | 360 W | 360 W |
| 3 min above-CP cost | 90% of W′ | 45% of W′ |
03
How evidence becomes a model
Gritmo begins with observed power evidence. Three credible power bests across different durations are enough to fit an initial two-parameter model and check whether the observations are mutually coherent.
The observed efforts remain points. The continuous curve is modeled. Gritmo should not connect sparse observations and present the resulting line as something the rider actually performed.
A mathematically valid fit is not automatically a physiologically reliable model. Duration coverage, recency, maximality, residual error, and consistency all affect confidence.
Definitions
EvidenceEvidence
Observed information that supports or changes the rider model.
Evidence may come from rides, power bests, files, connected providers, or values entered by the rider.
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Power bests
The highest credible average power a rider has produced for a specific duration.
Power bests are evidence. They are not a separate rider model.
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Observed
A value directly supported by recorded or rider-provided evidence.
Observed efforts remain points; Gritmo does not connect sparse points and call the result observed.
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Modeled
An estimate produced by applying a defined relationship to the available evidence.
A modeled value is useful when its evidence, scope, and limits remain visible.
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Confidence
How strongly the available evidence supports an estimate.
Confidence describes the estimate, not the ability or value of the rider.
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What that means
The data gives Gritmo evidence. The curve is the simplest relationship currently used to explain that evidence together.
01
Observed power bests
02
CP and W′ fit
03
Rider model
04
Analysis and simulation
04
When time enters the rider model
CP and W′ describe the core power-duration relationship in a relatively fresh state. They do not fully describe what remains after accumulated work or what can be produced again after incomplete recovery.
Gritmo therefore keeps Durability and Repeatability separate from CP and W′. Each requires its own evidence and remains unknown until that evidence exists.
Definitions
DurabilityDurability
Ability to preserve performance after accumulated fatigue.
Without relevant late-Ride evidence, Durability is unknown—not weak.
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Repeatability
Ability to reproduce hard efforts.
A large W′ does not automatically imply strong Repeatability.
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What that means
CP and W′ show what a rider can do while fresh. Durability shows how well that ability holds up as fatigue builds. Repeatability shows how well they can go hard again before fully recovering.
Durability
Ability to preserve performance after accumulated fatigue. Without relevant late-Ride evidence, Durability is unknown—not weak.
Repeatability
Ability to reproduce hard efforts. A large W′ does not automatically imply strong Repeatability.
05
Where the model has limits
The CP/W′ model is strong because it is compact, interpretable, testable, and falsifiable. That does not make it universally accurate.
Its estimates depend on the durations and quality of the efforts used for fitting. W′ is generally more sensitive than CP to input error and model choice. Predictions also become less reliable outside the duration range supported by the evidence, particularly for very short or very long efforts.
Gritmo treats every output as an estimate. Confidence describes the support behind that estimate, not the ability or value of the rider.
What that means
A strong model is not always right. It makes useful predictions, exposes its errors, and can be corrected by better evidence.
06
Research notes
These sources support the physiological interpretation, field estimation, predictive use, and stated limits discussed above. Citing the research does not automatically validate every implementation choice inside Gritmo; those choices must also be tested against observed data.
Why I cite it: a rigorous synthesis of the physiological interpretation and practical utility of CP and W′.
Why I cite it: tests whether maximal field efforts can produce valid and repeatable CP estimates.
This Note is a working explanation of the current Gritmo model. I will revise it as the implementation changes, better evidence becomes available, or an interpretation no longer holds.
Model my physiology