Introduction
Wind is the second-largest weather effect on a ship's speed after waves. Speed trials and performance monitoring remove it with the method of ISO 15016 Annex C: a wind resistance coefficient that depends on the relative wind direction and the ship's above-water shape, applied to the transverse projected area and the relative wind speed, minus the still-air resistance that the calm-water baseline already contains. This calculator uses the Fujiwara regression of the standard, ported from and pinned to the atlas-back production code, or coefficients from wind-tunnel tests.
It is for performance analysts correcting trials and noon reports, naval architects estimating weather margins, and anyone checking a wind correction.
Formulas
Resistance increase (C.1): R_AA = ½ ρ_A C_AA(ψ) A_XV V_WR² − ½ ρ_A C_AA(0) A_XV V_G²
Air density (C.2): ρ_A = p_A / (2.8705 (t_A + 273.15)), p_A in hPa
Fujiwara (C.12): C_AA(ψ) = C_LF cos ψ + C_XLI (sin ψ − ½ sin ψ cos²ψ) sin ψ cos ψ + C_ALF sin ψ cos³ψ
Head-wind branch: C_LF, C_XLI, C_ALF from A_LV/(L_OA B), C_MC/L_OA, A_LV/(L_OA H_BR), A_XV/(B H_BR), A_OD/A_LV, B/L_OA
Following branch: from B/L_OA, H_C/L_OA, A_OD/L_OA², A_XV/B², A_LV/(L_OA H_BR), A_XV/A_LV, A_XV/(B H_BR), A_OD/A_LV
Beam wind (C.19): C_AA(90°) = ½ [C_AA(80°) + C_AA(100°)]
Added power: P = R_AA V_G / η_D- V_WR, ψ — relative wind speed and direction at 10 m; V_G — speed over ground; A_XV, A_LV — transverse and lateral projected areas above the waterline; A_OD — lateral area of superstructures; C_MC — centre of A_LV from amidships; H_BR — height of the top of the superstructure; H_C — height of the centre of A_LV.
Assumptions and limitations
- Relative wind at the 10 m reference height; correct anemometer readings first.
- The Fujiwara regression represents conventional merchant ships; wind-tunnel data for the type are better when available.
- The value at exactly 90° follows formula C.19 and stands apart from its neighbours.
- Drift, rudder and gust effects are not included.
Worked example
A 200 m ship with a 32 m beam, A_XV 600 m², A_LV 1200 m² and A_OD 800 m² makes 14 kn over the ground into a 30 kn relative wind from 20° on the starboard bow, at 15 °C and 1013.25 hPa.
- Air density 1.225 kg/m³.
- The Fujiwara coefficients give C_AA(20°) = 0.943 and C_AA(0°) = 0.769.
- Wind force ½ × 1.225 × 0.943 × 600 × (15.43 m/s)² = 82.6 kN; still-air resistance ½ × 1.225 × 0.769 × 600 × (7.20 m/s)² = 14.7 kN.
- R_AA = 67.9 kN; with η_D = 0.7 the added power is 699 kW.
FAQ
Why subtract the still-air term?
The calm-water resistance from tank tests or trials already includes the air resistance at the ship's own speed with no wind. Only the difference is the weather effect.
Why is C_AA larger at 20–30° than head-on?
For many hull and superstructure forms the longitudinal force peaks with the wind slightly off the bow, where the flow over the superstructure gives a large drag component.
Can the wind help?
Yes. With a following wind stronger than the ship's own speed, C_AA is negative and R_AA becomes an assistance.
Which areas do I need?
Transverse and lateral projected areas above the waterline, including deck cargo and superstructures, from the general arrangement or the ship's wind area drawing at the actual draft.
Why speed over ground?
ISO 15016 defines the relative wind with the speed over ground, and ISO 19030 uses the same speed for the wind power correction.
Related calculators
- True wind from apparent wind — the relative wind at 10 m from the anemometer.
- STAwave-1 added wave resistance — the wave part of the weather correction.
- Water temperature correction — the temperature and density part of ISO 15016.
- Shallow water speed — the depth correction.