Multi-Day Fatigue at Sea: A Two-State Biomathematical Model for Recreational Passage-Making

Zucchelli and Smith [1] described a biomathematical fatigue model for recreational passage-making — the Integrated Fatigue Model (IFM) — with output expressed as a blood-alcohol-concentration (BAC) equivalence anchored on Dawson and Reid [2]. The IFM reproduces the dose-response using simpler linear extrapolations for multi-day fatigue accumulation and a simpler pre-departure accounting; Zucchelli and Smith marked 48 hours as the primary validation horizon. This paper extends the scientific treatment to multi-day offshore passage-making: transits of 48 hours and longer, non-rested departures, and short-handed watch-rotation choices. The engine is rebuilt on the McCauley–Ramakrishnan unified model [3-5] — a two-state framework with fast homeostatic S and slow allostatic L — and recalibrated against the Dawson–Reid 17 h / 24 h anchors so the BAC output of Zucchelli and Smith [1] is preserved. Maritime tuning combines sea-state [6] and fragmentation [7] effects multiplicatively on the sleep time constant, yielding effective τs from 4.9 h (calm + deep at sea) to 25.5 h (storm + fragmented); the 4.2 h shore-laboratory baseline is not reachable at sea in the current calibration. A combinatorial consequence — the circadian-burden-distribution property of crew-rotation cycles whose length is coprime with the crew size — formalises the effectiveness of the Swedish watch system.