Exponential Functions Permit Estimation of Anaerobic Work Capacity and Critical Power from Less than 2 Min All-Out Test
Why this work is in the frame
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Bibliographic record
Abstract
The Critical Power Model (CPM) is key for assessing athletes’ aerobic and anaerobic energy systems but typically involves lengthy, exhausting protocols. The 3 min all-out test (3MT) simplifies CPM assessment, yet its duration remains demanding. Exponential decay models, specifically mono- and bi-exponential functions, offer a more efficient alternative by accurately capturing the nonlinear energy dynamics in high-intensity efforts. This study explores shortening the 3MT using these functions to reduce athlete strain while preserving the accuracy of critical power (CP) and work capacity (W′) estimates. Seventy-six competitive cyclists and triathletes completed a 3MT on a cycle ergometer, with CP and W′ calculated at shorter intervals. Results showed that a 90 s test using the bi-exponential model yielded CP and W′ values similar to those of the full 3MT. Meanwhile, the mono-exponential model required at least 135 s. Bland–Altman and linear regression analyses confirmed that a 120 s test with the mono-exponential model reliably estimated CP and W′ with minimal physical strain. These findings support a shortened, less-demanding 3MT as a valid alternative for CPM assessment.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it