Ship turning calculator
What this calculates: steady turn radius, advance, transfer, and tactical diameter from a first-order Nomoto yaw model (K, T indices), for a container ship, tanker, bulk carrier, or naval frigate.
What it assumes: a constant-speed, step rudder deflection driving a linear first-order yaw response — the standard textbook Nomoto simplification, not a full manoeuvring (MMG) model.
What it ignores: speed loss in the turn, drift angle and sway, roll during the turn, and rudder ramp time.
Vessel
Fine hull form, moderately responsive.
Nomoto indices (K′, T′)
Higher K′ means a more agile ship; higher T′ means a slower yaw response and a wider turn. These are converted to dimensional K = K′·V/L and T = T′·L/V for the simulation.
Use this turn radius and speed in the stability tool →Turning circle figures
| Quantity | Value | In ship lengths |
|---|---|---|
| K (dimensional gain) | 4.527e-2 /s per rad | |
| T (dimensional time constant) | 26.5 s | |
| Steady yaw rate | 1.58 °/s | |
| Steady turn radius | 409 m | |
| Advance (90° heading change) | 670 m | 2.23 L |
| Transfer (90° heading change) | 480 m | 1.60 L |
| Tactical diameter (180° heading change) | 899 m | 3.00 L |
Honest limits
• This is a tier-1 Nomoto first-order model (K, T indices only) - it has no drift angle, sway, roll, or speed loss during the turn
• The vessel-type K′/T′ presets are illustrative, reflecting known qualitative trends (agile vs. sluggish hull forms), not measured sea-trial or captive-model data for a named ship
• IMO Res. MSC.137(76) turning-circle criteria (advance ≤ 4.5L, tactical diameter ≤ 5L) are shown as a reference only - real compliance is judged from full-scale sea trials at design draught and max ahead service speed
• Vessel-type K′/T′ presets are pedagogical, not tuned to pass IMO limits - the tanker preset, for instance, lands outside the tactical-diameter criterion here even though real VLCCs generally comply
• Rudder deflection is treated as an instantaneous step, not a realistic ramp rate
• Speed is held constant through the turn - real ships lose 20-40% of speed in a hard turn
How it works
The Nomoto model treats yaw rate as a first-order response to rudder angle: T·dr/dt + r = K·δ. K and T are estimated from non-dimensional K′ and T′ indices, scaled by ship length and speed. Solving that response in closed form gives the heading over time, which is then integrated to trace the ship's trajectory; advance, transfer, and tactical diameter are read off that trajectory at 90° and 180° of heading change. The turn radius and speed can be handed off to the stability calculator to see the resulting heel angle in a steady turn.