Ship Resistance & Powering

How much power a ship needs. Learn resistance components (frictional, form, wave-making, air, appendages), Froude's hypothesis and model testing, the ITTC-1957 friction line, form factor, wave-making and the Froude number, effective power, the propulsive chain (hull, propeller, relative-rotative, shaft efficiencies), the Admiralty coefficient and cube law, slow steaming, fouling and hull coatings — with Python estimating resistance and brake power.

A ship's fuel bill — its largest operating cost — is set by hull resistance. Frictional resistance of the wetted hull dominates slow, full ships; wave-making dominates fast, fine ships. Designers minimise both with hull form, bulbous bows and smooth coatings.

Because power rises roughly with the cube of speed, slowing down is the most powerful fuel-saving lever — the reason 'slow steaming' became standard after 2008.

An analogy

Pushing a ship through water is like walking through a crowd: rubbing past people is friction, and the bigger your wake of disturbed people behind you, the harder it gets — at higher speeds you create a much bigger wake (waves).

Resistance components

Total resistance is split into:

Model testing and scaling

Models are towed in a towing tank at the same Froude number as the ship (so wave patterns match). The Reynolds number can't also be matched, so friction is scaled separately using the ITTC-1957 line and form factor (ITTC-1978 method). CFD increasingly supplements tank tests.

Propulsive efficiency

Hull efficiency η_H = (1 − t)/(1 − w) accounts for the propeller working in the hull's wake (w) and increasing resistance by suction (thrust deduction t); open-water efficiency η_O of the propeller; relative-rotative efficiency η_R; shaft/gear losses η_S. Quasi-propulsive coefficient η_D is typically 0.65–0.75.

Reducing power

Hull form optimisation, bulbous bows tuned to operating draught and speed, low-friction coatings (silicone foul-release), air lubrication, hull cleaning and propeller polishing, energy-saving devices (pre-swirl ducts, rudder bulbs), trim optimisation, weather routing, and slow steaming. These underpin IMO EEXI and CII compliance.

Formulas

Worked example: Friction coefficient

Given: Re = 1.09 × 10⁹

Find: C_F.

Answer: 0.00151

Worked example: Admiralty law

Given: 5000 kW at 14 kn

Find: Power at 16 kn.

Answer: 7464 kW (+49%)

Worked example: Hull efficiency

Given: w = 0.30, t = 0.20

Find: η_H.

Answer: 1.14 (the wake helps!)

Resistance and powering estimate

import math
# ITTC-1957 frictional resistance and effective power for the 180 m ship
L, V_kn, S = 180.0, 14.0, 7200.0             # length, speed, wetted surface m2
rho, nu = 1025.0, 1.19e-6
V = V_kn * 0.5144
Re = V * L / nu
Cf = 0.075 / (math.log10(Re) - 2) ** 2
k = 0.20                                       # form factor (1+k) = 1.20
Cw = 0.0003                                    # wave-making coefficient at this Fn (assumed)
Ct = (1 + k) * Cf + Cw + 0.0004                # + correlation allowance
Rt = 0.5 * rho * V**2 * S * Ct
PE = Rt * V
print(f"Re = {Re:.2e}, Cf = {Cf:.5f}, Ct = {Ct:.5f}")
print(f"total resistance {Rt/1000:.0f} kN, effective power {PE/1000:.0f} kW")
eta_D, eta_s = 0.70, 0.98
print(f"required brake power ~ {PE/eta_D/eta_s/1000:.0f} kW")
# Admiralty cube law: power at 12 knots
print(f"at 12 knots power ~ {PE/eta_D/eta_s/1000*(12/14)**3:.0f} kW (fuel per mile falls ~{(1-(12/14)**2)*100:.0f}%)")
# Re = 1.09e+09, Cf = 0.00151, Ct = 0.00252
# total resistance 482 kN, effective power 3469 kW
# required brake power ~ 5058 kW
# at 12 knots power ~ 3185 kW (fuel per mile falls ~27%)

Friction (with form factor) makes up ~72% of the resistance of this slow, full ship. Slowing from 14 to 12 knots cuts power by 37% and fuel per mile by ~27% (power ∝ V³, time per mile ∝ 1/V). In practice resistance also rises with fouling (a rough hull can add 10–40%).

Common mistakes

Applications

Key takeaways

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