Piecewise Wathan 1RM & RIR-Based RPE Load Prescription
Linear 1RM formulas break down above 8 repetitions and fail completely on weighted pull-ups and dips. Here is the exact piecewise Wathan equation and RIR inversion running in the Struggl Prescriptive Load & Implicit RPE Subsystems.
- Exponential Wathan Equation: e1RM = 100 * W / (48.8 + 53.8 * exp(-0.075 * reps)), validated by LeSuer et al. (1997, DOI: 10.1519/00124278-199711000-00001) across Squat, Bench Press, and Deadlift.
- RIR-Based RPE Scale: Zourdos et al. (2016, DOI: 10.1519/JSC.0000000000001049) and Helms et al. (2016, DOI: 10.1519/SSC.0000000000000218) anchor RPE to Repetitions in Reserve (RIR = 10 - RPE).
- Total System Load for Weighted Calisthenics: `total_load = bodyweight_kg * bodyweight_factor + added_kg`, ensuring a +20 kg pull-up for an 80 kg athlete is evaluated as a 100 kg system load.
| Component | Deterministic Specification & Literature Benchmark |
|---|---|
| Rule / Benchmark 01 | Exponential Wathan Equation: e1RM = 100 * W / (48.8 + 53.8 * exp(-0.075 * reps)), validated by LeSuer et al. (1997, DOI: 10.1519/00124278-199711000-00001) across Squat, Bench Press, and Deadlift. |
| Rule / Benchmark 02 | RIR-Based RPE Scale: Zourdos et al. (2016, DOI: 10.1519/JSC.0000000000001049) and Helms et al. (2016, DOI: 10.1519/SSC.0000000000000218) anchor RPE to Repetitions in Reserve (RIR = 10 - RPE). |
| Rule / Benchmark 03 | Total System Load for Weighted Calisthenics: `total_load = bodyweight_kg * bodyweight_factor + added_kg`, ensuring a +20 kg pull-up for an 80 kg athlete is evaluated as a 100 kg system load. |
Verified Scientific DOIs: 10.1519/00124278-199711000-00001, 10.1519/JSC.0000000000001049, 10.1519/SSC.0000000000000218, 10.3389/fphys.2018.00247