The Science of Fatigue at Sea: A Biomathematical Model for Recreational Sailing

Fatigue is a leading contributor to maritime accidents, yet recreational sailors lack the regulatory frameworks and fatigue management tools available to commercial mariners. Peer-reviewed research published in Nature demonstrates that after 17 hours of sustained wakefulness, cognitive performance degrades to a level equivalent to a blood alcohol concentration of 0.05% — the legal driving limit in most countries (Dawson & Reid, 1997). After 24 hours, this rises to 0.10%, well past the threshold for legal intoxication. These findings have been independently replicated (Williamson & Feyer, 2000) and confirmed in field studies aboard racing yachts (Hurdiel et al., 2014). This paper synthesises more than three decades of peer-reviewed research spanning chronobiology, sleep medicine, occupational health, and maritime safety into a biomathematical fatigue model calibrated specifically for pleasure boat passage-making. The model integrates sleep-wake homeostasis, circadian rhythm modulation, sleep fragmentation effects, environmental sleep degradation from sea state, and cumulative multi-day sleep debt into a single framework that outputs impairment as a BAC (blood alcohol concentration) equivalence — an intuitive metric that any sailor can understand. Critically, the model is not merely theoretical. It has been implemented as a freely available, open-access passage fatigue calculator for mobile and web platforms, making it accessible to the widest possible population of recreational mariners. The application faithfully reproduces every formula, constant, and coefficient described in this paper, allowing sailors to simulate any passage plan — varying crew size, watch schedule, departure time, pre-departure sleep, and sea state — and see the predicted fatigue trajectory hour by hour. The purpose is to bridge the gap between laboratory science and practical seamanship: to give pleasure boat crews the same evidence-based fatigue awareness that professional mariners receive through regulation.