Resistance, Propulsion, and Powering
Resistance
Resistance components
Total resistance is split into viscous (friction plus form) and wave-making parts, plus air and appendage resistance. Model tests follow Froude similarity: speeds scale as √λ and wave resistance as λ³, while viscous resistance is handled by Reynolds similarity using the ITTC-57 line Cf = 0.075/(log₁₀Re − 2)². A form factor (1+k) multiplies the frictional coefficient, and a correlation allowance bridges model and full scale. Hull-form parameters - block coefficient C_B, prismatic coefficient C_P, LCB position, bulbous bow and transom immersion - strongly affect wave resistance.
Traps
Do not scale total resistance directly by λ³; only the wave component follows that law. Use waterline length for Froude number and the correct viscosity and length for Reynolds number. Shallow water, restricted channels and fouling raise resistance sharply. A bulbous bow helps near the design Froude number but can be detrimental off-design. Watch whether the question asks for effective power P_E = R_T·V or for brake power.
Worked example
A 100 m ship at 12 kn: V = 12 × 0.5144 = 6.17 m/s; Fr = V/√(gL) = 6.17/√981 = 0.197. Wave resistance is moderate here but rises steeply toward Fr ≈ 0.25–0.35, where it dominates. Rule of thumb: Cf ≈ 1.5 × 10⁻³ near Re = 10⁹, so frictional resistance is often the largest single component for slow, full-form ships.
Propulsion and Powering
Propeller fundamentals
Propeller behaviour is described by the advance coefficient J = V_A/(nD), thrust coefficient K_T, torque coefficient K_Q and open-water efficiency η_O = J·K_T/(2π·K_Q). Advance speed is V_A = V(1 − w), where w is the wake fraction; thrust deduction t links thrust and resistance through R = T(1 − t). Hull efficiency is η_H = (1 − t)/(1 − w), relative rotative efficiency η_R accounts for non-uniform wake, and the quasi-propulsive coefficient is η_D = η_O·η_H·η_R. Shafting and gearbox losses give the overall propulsive coefficient, and the required brake power follows from P_E and the various efficiencies.
Traps
Never use ship speed in J when a wake fraction is given; a positive w reduces V_A. Thrust deduction is usually positive, so hull efficiency can exceed unity. The propeller law P ∝ n³ applies in calm water at fixed pitch with an unchanged advance ratio. Cavitation depends on blade area ratio, immersion and thrust loading, not rpm alone.
Worked example
V = 10 kn = 5.14 m/s, w = 0.25, n = 2.0 rev/s, D = 2.0 m. V_A = 5.14 × 0.75 = 3.86 m/s; J = 3.86/(2.0 × 2.0) = 0.964. With K_T = 0.15 and K_Q = 0.030, η_O = 0.964 × 0.15/(2π × 0.030) = 0.77. Rule of thumb: from the propeller law, a 10% rpm reduction cuts power demand to about 0.9³ = 73% of the original.