The Science of Fatigue at Sea — Research by Galvanic Works

New · Part 2 · Published April 2026

Multi-Day Fatigue at Sea

A two-state biomathematical model for recreational passage-making — how single-day fatigue compounds across multi-day passages, and why some watch rotations structurally protect recovery while others don’t.

The Swedish watch system — 4/4/5/6/5 — isn’t folklore. It’s the answer to a coprime number problem no one had written down.

Zucchelli & Smith · 2026 · doi.org/10.20944/preprints202604.1649.v2

Download Part 2 (PDF) Read on Preprints.org

Side-by-side pie charts — standard 4-on/4-off watch schedule vs the Swedish 4/4/5/6/5 rotation, showing how Swedish redistributes the 02:00 watch across the crew

Standard vs Swedish — the same hours, redistributed so every crew covers every hour exactly once.

Key findings from the papers

Three decades of research across chronobiology, sleep medicine, maritime safety, and biomathematical modelling — now extended with a two-state engine for multi-day offshore passages, and a coprime proof for short-handed watch rotations.

0.05%

17 hours awake = legally impaired

After 17 hours without sleep, cognitive performance drops to a level equivalent to the legal drink-drive limit in most countries. A normal first night watch on a two-crew passage.

Dawson & Reid (1997), Nature

The circadian trough at 3AM

Cognitive impairment at 3AM is roughly double that at 3PM for the same number of hours awake. The circadian rhythm creates a predictable danger window on every passage.

Folkard & Akerstedt, three-process model

78%

Sleep efficiency at sea

Polysomnographic studies aboard ships show sleep efficiency drops to 78% in moderate conditions and as low as 30% in heavy seas. Your bunk is not your bed at home.

Bernd et al. (2023), polysomnographic study at sea

0.10%

24 hours = double the legal limit

After 24 hours without sleep, impairment rises to approximately 0.10% BAC equivalent — well past the legal limit for driving in any jurisdiction.

Dawson & Reid (1997), independently replicated

14h

Commercial limits don't apply to you

The STCW mandates a maximum of 14 hours continuous wakefulness for professional mariners. A couple on a 120nm overnight passage will commonly exceed this before sighting their destination.

STCW Regulation VIII/1

Day 3

Cumulative sleep debt compounds

Multi-day passages create compounding sleep debt that persists even when sailors feel adapted. The model tracks how impairment accumulates across days — not just hours.

Van Dongen et al. (2003), Sleep

gcd = 1

Coprime watch schedules share the night

When cycle length and crew size share no common factor, every watch slot rotates through every crew. Swedish 4/4/5/6/5 on two crew: gcd(5, 2) = 1 — the 02:00 watch alternates. Standard 4-on/4-off on two crew: gcd(6, 2) = 2 — the same person draws 02:00 every single night.

Zucchelli & Smith (2026), Part 2 §6.4

4.4×

The same nap, less recovery

On a calm sea with consolidated rest, a two-hour nap restores about 33% of your fast fatigue state. In storm conditions with fragmented sleep, the same nap restores only 7.5% — a 4.4× reduction in per-hour recovery.

Zucchelli & Smith (2026), Part 2 §5

What's inside the papers

Part 1 The Science of Fatigue at Sea

1–2
The Problem & The BAC Equivalence
Why fatigue matters at sea, and the landmark research that equated hours awake to blood alcohol impairment.
3–4
Circadian Rhythm & Sleep Recovery
Why 3AM is not like 3PM, and why not all rest is equal — the science of sleep fragmentation and recovery.
5–6
Sea State & Cumulative Sleep Debt
How sea conditions degrade sleep quality, and why multi-day passages create compounding impairment that sailors don't feel.
7–8
The Integrated Model & Application
All the science combined into a single biomathematical framework — and how it's been implemented as a free calculator for sailors.
9–10
Regulatory Context & Practical Implications
What the professionals are required to do, and what recreational sailors can apply to their own passage planning.
11–12
Limitations & Conclusions
Known caveats of the model, areas for future research, and what this means for recreational sailing.

Part 2 Multi-Day Fatigue at Sea

1–2
Scope Extension from the Integrated Fatigue Model
Where the single-state accumulator of Part 1 reaches its validation horizon, and why pre-departure history, chronic restriction and debt-dependent recovery each require a state-structured treatment.
3–4
The McCauley–Ramakrishnan Two-State Engine
Fast homeostatic S, slow allostatic L, and a five-harmonic circadian term that places the nocturnal fatigue peak at 02:00 — calibrated back onto the Dawson–Reid BAC scale.
5
Maritime Parameter Tuning
Sea-state and sleep fragmentation combine multiplicatively on the sleep time constant — effective recovery from 4.9 h in calm consolidated rest to 25.5 h in storm-fragmented conditions.
6
Model-Derived Consequences
Per-crew trajectory divergence, pre-departure conditioning as an initial-value problem, the allostatic signature on multi-day passages, and the combinatorial justification of the Swedish watch system from gcd(K, N) = 1.
7–8
Modelling Boundaries & Conclusions
Off-watch activity, individual trait vulnerability, and caffeine are named as boundaries rather than encoded as parameters — and how the two papers fit together as one framework.

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Part 1 — The Science of Fatigue at Sea Part 2 — Multi-Day Fatigue at Sea

Also available at Preprints.org — Part 1 · Part 2