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The app calculates work above CP for every recorded second. When power stays above CP throughout an effort, total work above CP equals (average power − CP) × duration, even with uneven pacing. The full trace matters when power crosses below CP, when there are recoveries, and when accounting for earlier riding.

W′ is a modelled capacity for work above critical power, measured in kilojoules. Above CP, the balance falls by (power − CP) × time. Below CP, the expended portion recovers exponentially, with a time constant of W′ ÷ (CP − power). This is the differential W′ balance formulation, integrated exactly over each constant-power sample. The recovery multiplier changes that rate for sensitivity checks.

For each CP on a 1 W grid, we solve for W′ so the short effort ends with your chosen reserve. We then replay both rides and reject pairs that predict a negative balance at any point before the selected finishes. A 1 J numerical tolerance is used. The model never hides a negative balance by clamping it to zero.

One maximal effort describes a relationship between CP and W′. A longer, nonmaximal ride provides a constraint rather than a second exhaustion point. We show the surviving combinations without choosing one as the true value. The FTP and W′ references do not influence which pairs survive. A second well-paced maximal effort of a different duration, ideally with a third test for validation, would strengthen the estimate.

CP, W′ and recovery are assumed stable across both rides. Heat, fatigue, altitude, motivation and power-meter differences can break that assumption. W′ balance is an approximate performance model, not a direct measurement of an energy tank. A 38-minute climb is supporting context, not automatically a valid maximal CP test.

Uses standard FIT timestamp, power, heart-rate and altitude fields; automatically unpacks gzip exports, validates FIT checksums and reads normal/compressed timestamps, local definitions and developer-field lengths. GPS coordinates are not used. Valid zero power is retained. Recording intervals up to five seconds hold the previous power; longer intervals, invalid power and stopped timers remain unknown.

Unknown seconds hold the modelled depletion: they do not create recovery or expenditure. That is a missing-data assumption, not a physiological estimate. Missing power anywhere in the modelled span marks the results provisional. Review the warnings, especially gaps around hard efforts. Automatic effort detection requires at least 99% power coverage.

The recording’s elapsed time is retained, including pauses. Each displayed interval includes its start second and excludes its end second. Trace display may be reduced for screen drawing; calculations always use the full reconstructed one-second series. Files remain in memory only; refreshing the page clears the rides.

• Townsend et al. (2017) — differential and integral W′ balance models, equations 5–6.
• W′ reconstitution modelling during intermittent exercise performed to task failure — comparison of recovery assumptions.
• Garmin — FIT binary protocol, timestamps and checksums.