Emergency Manoeuvring

Ship Stopping — Crash Astern

Two-phase propulsion reversal · IMO stopping criterion

The crash-stop (or crash-astern) manoeuvre is the standard emergency procedure for halting a ship in the shortest possible distance. The engine is rapidly reduced from full ahead to full astern, generating a propulsive counter-force that decelerates the vessel against its own inertia and hydrodynamic resistance.

Thrust Schedule — Two Phases
$$ T_f(t) = \begin{cases} 1 - \dfrac{t}{t_{\text{red}}}, & t \leq t_{\text{red}} \quad \text{(linear reduction)} \\[8pt] T_{\text{rev}}, & t > t_{\text{red}} \quad \text{(constant astern)} \end{cases} $$

tred — thrust reduction time (engine response delay). Trev — dimensionless reverse thrust fraction (typically −0.3 to −0.5 of rated ahead thrust).

Equations of Motion

The simulation integrates the full 3-DOF Abkowitz maneuvering equations with a surge-direction propulsive term. Rudder angle is held at zero throughout (no steering), so any lateral drift and heading change arise purely from asymmetric hydrodynamic damping as forward speed decays.

Key Stopping Metrics (IMO)
$$ S_{\text{stop}},\quad t_{\text{stop}},\quad \Delta y_{\text{max}},\quad U_{\text{final}} $$

Sstop — head-reach (stopping distance along original track). tstop — time to reach near-zero speed. Δymax — maximum lateral deviation (track-keeping criterion). Ufinal — residual speed at end of run.

IMO Stopping Standard

The IMO MSC Circular 1053 requires that a ship's stopping distance (head-reach) shall not exceed 15 ship-lengths from full-ahead service speed. The lateral deviation criterion is secondary but important for traffic separation schemes.

Simulation Workflow

How the Visualiser Works

Single ship · two-phase thrust · deceleration trajectory

Phase 1 Thrust Reduction

Thrust ramps linearly from full ahead (1.0) to zero over the engine response time. Ship begins decelerating but still moves ahead. Trajectory drawn in amber.

Phase 2 Full Astern Thrust

Engine locks at the specified reverse fraction (Trev). The counter-thrust rapidly kills forward way. Trajectory drawn in coral / red.

Drift Lateral Deviation

With zero rudder, residual sway and yaw from the asymmetric flow around the stern produce lateral drift. The max deviation line is drawn in teal.

IMO Check Stopping Distance

Head-reach is compared to the 15L IMO limit. A green / amber / red verdict is rendered in the telemetry panel.

Operating Guide

Simulation Guide

1

Set Ship & Engine Parameters

Adjust initial speed, thrust reduction time, and reverse thrust fraction. All Abkowitz coefficients are editable in collapsible groups below.

2

Run the Solver

Click Run Simulation. The integrator advances until the simulation time T is reached or speed drops near zero.

3

Inspect Results

The 3D view animates the deceleration run. Analytical Plots shows speed decay, trajectory, thrust schedule, and heading drift. The IMO verdict is shown in the telemetry panel.

Manoeuvring · Emergency Stopping Trial

Ship Stopping Solver

Operational
Engine response delay — longer ⇒ more ahead distance before reversal kicks in
Fraction of rated thrust applied astern (negative). More negative ⇒ shorter stop.
Hull Mass & Inertia
Added Mass ▾
Linear Damping ▾
Cross-Coupling ▾
Nonlinear Damping ▾
Rudder Coefficients ▾
Bias Terms ▾
Manoeuvre Constants
Rudder during stop 0° (fixed)
IMO head-reach limit 15 L
Rudder held at zero throughout — lateral deviation is purely hydrodynamic. IMO MSC/Circ.1053 stopping standard applies.
Stopping Performance
Stopping Distance: — m
Distance in ship-lengths: —
Time to Stop: — s
Max Lateral Deviation: — m
Residual Speed Ufinal: — m/s
IMO Verdict: —
Samples: —
READY
U₀: — · Trev: —
Anim: 0.00 s · Phase: AHEAD
Start position
Phase 1 — thrust reducing
Phase 2 — full astern
Final position