Emergency Manoeuvring

Williamson Turn — Precise MOB Recovery

Three-phase track-retracing manoeuvre · IMO emergency procedure

The Williamson Turn is the most accurate of the three IMO-recommended man-overboard manoeuvres. Unlike the faster Anderson Turn, the Williamson does not loop back — instead, it physically retraces the ship's original track in reverse. This makes it the manoeuvre of choice when the casualty has fallen overboard but cannot be kept in sight (e.g. at night, in fog, or after delayed detection).

Three-Phase Rudder Schedule
$$ \delta_{cmd}(t) = \begin{cases} +35°, & \psi < +60° \quad \text{(Phase 1: hard one way)} \\ -35°, & \psi \geq +60°, \, \psi > -130° \quad \text{(Phase 2: counter rudder)} \\ \;\;0°, & \psi \leq -130° \quad \text{(Phase 3: centred, retrace)} \end{cases} $$

The +60° / −130° thresholds are calibrated so Phase 3 begins with the ship on the reciprocal heading aligned with the original track, sliding back along it toward the casualty.

Anderson vs Williamson — When Each Wins

The Anderson Turn is fastest but only useful when the casualty remains visible — its tight 250° loop offsets the recovery from the original track. The Williamson Turn sacrifices roughly a minute of recovery time in exchange for putting the ship squarely back on the inbound course, allowing reacquisition even when the MOB is no longer in sight.

Performance Metrics

Five quantities summarise a Williamson Turn run:

Recovery Quality Indices
$$ t_1, \quad t_2, \quad t_{opp}, \quad \Delta y, \quad \Delta\psi $$

t₁ — time at end of Phase 1 (ψ = +60°). t₂ — time at end of Phase 2 (ψ = −130°). topp — time at which the ship's heading reaches 180° (reciprocal). Δy — cross-track error at topp. Δψ — heading error from the reciprocal target at topp.

Rudder Rate Limit

Real rudder machinery cannot snap instantaneously between ±35°. The model enforces a slew-rate limit on the commanded angle. The visible gap between the commanded square wave and the actual rate-limited rudder signal is shown in the Rudder plot.

Simulation Workflow

How the Visualiser Works

Single ship · three-phase trajectory · MOB beacon

Phase 1 Hard Rudder Initial Turn

Ship turns one way with hard rudder until heading reaches +60°. Trajectory drawn in amber.

Phase 2 Counter Rudder Reversal

At ψ = +60° the rudder flips to the opposite hard angle, swinging the ship across to ψ = −130°. Trajectory drawn in coral.

Phase 3 Rudder Centred — Retrace

At ψ = −130° the rudder is centred. The ship coasts back along the reciprocal of its original track until ψ ≈ 180°. Trajectory drawn in teal.

MOB Beacon Casualty Marker

A red beacon at the origin marks where the casualty entered the water. A dashed line at the end of the run shows the final cross-track error.

Operating Guide

Simulation Guide

1

Set Ship & Conditions

Pre-loaded with Mariner-class defaults. All Abkowitz coefficients are editable in collapsible groups.

2

Run the Solver

Click Run Simulation. The integrator runs through all three phases and stops when ψ reaches 175°.

3

Inspect Results

The 3D view animates the full S-shaped track. Analytical Plots shows the trajectory in 3 colors, heading-vs-time with all three target lines, and the commanded-vs-actual rudder signal.

Manoeuvring · MOB Recovery Trial

Williamson Turn Solver

Operational
Real machinery limit — slower rate ⇒ larger lag at every phase change
Hull Mass & Inertia
Added Mass ▾
Linear Damping ▾
Cross-Coupling ▾
Nonlinear Damping ▾
Rudder Coefficients ▾
Bias Terms ▾
Manoeuvre Constants
Phase 1 rudder +35°
Phase 2 rudder −35°
Phase 3 rudder 0°
P1→P2 at ψ +60°
P2→P3 at ψ −130°
Target ψ +180°
Williamson Turn convention — fixed by the manoeuvre definition.
Recovery Performance
t₁ (ψ = +60°): — s
t₂ (ψ = −130°): — s
topp (ψ = 180°): — s
Cross-track Error |Δy|: — m
Cross-track in ship-lengths: —
Heading Error |Δψ|: — °
Recovery Quality: —
Samples: —
READY
U₀: — · Slew: —
Anim: 0.00 s · Phase: PHASE 1
MOB casualty (origin)
Phase 1 — +35° rudder
Phase 2 — −35° counter
Phase 3 — centred / retrace
Phase transitions
Final position (ψ ≈ 180°)