Ship Resistance and Propulsion
Ship Resistance and Propulsion covers the components of resistance, model–ship scaling, propeller action and the chain of efficiencies from effective power to brake power. GATE NM expects you to know which scaling law applies and to keep model and full-scale quantities separate.
Core rules
- Total resistance R_T = R_F + R_W + R_Form + R_A; at model scale, wave resistance is scaled by Froude similarity.
- Froude scaling: V_m/V_s = 1/√λ and R_s/R_m = λ³ for geometrically similar bodies in the same fluid, with λ the length ratio.
- ITTC-57 friction line: C_F = 0.075/(log10 Re − 2)². Reynolds number Re = VL/ν.
- Propeller advance ratio J = V_A/(nD); open-water efficiency η_O = (T V_A)/(2πnQ).
- Hull efficiency η_H = (1 − t)/(1 − w), where t is thrust deduction and w is wake fraction.
- Effective power P_E = R_T V; delivered power P_D = P_E/η_D; brake power P_B = P_D/η_S.
Worked example
A ship has R_T = 240 kN at V = 10 m/s. Effective power P_E = 240 × 10 = 2400 kW. If the quasi-propulsive coefficient η_D = 0.60, delivered power P_D = 2400/0.60 = 4000 kW. If shafting efficiency η_S = 0.95, brake power P_B = 4000/0.95 ≈ 4211 kW. The reasoning is a chain: resistance times speed gives effective power; divide by each efficiency in turn to move back to engine output.
Traps
Do not scale model resistance by λ² or λ; wave resistance follows λ³ under Froude scaling. Do not mix knots and m/s. Model tests are usually in freshwater, so apply a density correction. Thrust deduction reduces thrust available, while wake fraction reduces the inflow velocity; they act in opposite directions in η_H. Propeller curves are usually given at constant pitch; off-design points need the advance ratio.