Model-Test Powering Prediction and Margin Stacking
A 180 m, 21.3 kn feeder container ship is being powered from a 1:30 scale model test. At the corresponding ship speed of 10.95 m/s, the 2.0 m model has a wetted area of 3.50 m² and a measured total resistance of 38.0 N in fresh water. The prediction follows ITTC-1978: model Cf = 0.00320, ship Cf = 0.00195, form factor (1+k) = 1.18, and roughness allowance ΔCf = 0.00040. Sea water density is 1025 kg/m³. The yard's estimated quasi-propulsive efficiency is 0.62. The specification requires a 15% sea margin and a 10% engine margin, so the selected engine must be able to deliver the service power at 90% MCR. Catalogue MCR ratings are 18,500 kW, 21,000 kW and 24,000 kW. The owner has read that a silicone foul-release coating can save 8% power and asks whether the sea margin can therefore be deleted to allow the smallest engine. No sea trials or coating performance data are available yet.
1. Compute the wave resistance coefficient, ship total resistance and effective power at 10.95 m/s.
Read the worked answer
Model total resistance coefficient: Ct_m = R_Tm / (0.5 ρ_m S_m V_m²) = 38.0 / (0.5 × 1000 × 3.50 × 2.0²) = 38.0 / 7,000 = 0.005429.
Strip out model friction and form effect: Cw = Ct_m − (1+k)Cf_m = 0.005429 − 1.18 × 0.00320 = 0.005429 − 0.003776 = 0.001653.
Build the ship coefficient with ship friction, the same form factor and roughness allowance: Ct_s = (1+k)Cf_s + Cw + ΔCf = 1.18 × 0.00195 + 0.001653 + 0.00040 = 0.004354.
Ship wetted area scales as λ²: S_s = 3.50 × 30² = 3,150 m². R_Ts = 0.5 × 1025 × 3,150 × 10.95² × 0.004354 ≈ 843 kN. Effective power EHP = R_Ts × V_s = 843 × 10.95 ≈ 9,230 kW.
The calculation assumes the form factor is unchanged between model and ship, which is the normal ITTC-1978 assumption but should be questioned if the model test lacked a turbulence stimulator.
2. Determine the required MCR and select an engine from the catalogue. Show how the sea margin and engine margin are applied.
Read the worked answer
Delivered power at the propeller is DHP = EHP / ηD = 9,230 / 0.62 ≈ 14,890 kW.
The 15% sea margin is applied to the service power to cover added resistance in weather, fouling and ageing: service power = 14,890 × 1.15 ≈ 17,120 kW.
The 10% engine margin means the service power must not exceed 90% MCR: required MCR = 17,120 / 0.90 ≈ 19,020 kW.
Catalogue check:
- 18,500 kW: 90% MCR = 16,650 kW, below the required 17,120 kW, so insufficient.
- 21,000 kW: 90% MCR = 18,900 kW, sufficient.
- 24,000 kW: sufficient but unnecessarily large.
Select the 21,000 kW engine. The two margins are not the same thing: the sea margin is added resistance, while the engine margin keeps the engine below 100% MCR so it has reserve for manoeuvring, load changes and degradation. They act at different points and should not be combined into one arbitrary percentage.
3. Evaluate the owner's proposal to delete the 15% sea margin on the basis of an expected 8% coating benefit. What would you recommend?
Read the worked answer
If the sea margin is deleted, required MCR = 14,890 / 0.90 ≈ 16,540 kW. Applying an assumed 8% coating benefit gives 14,890 × 0.92 / 0.90 ≈ 15,220 kW, which would appear to make the 18,500 kW engine acceptable.
That conclusion is not defensible yet. The 8% figure is a vendor claim, not a measured sea-trial result, and it applies mainly to calm-water frictional resistance. The sea margin covers wind, waves, current, hull and propeller fouling, and ageing, none of which the coating removes. With no sea margin, a 15% increase in resistance would take the engine to 100% MCR, leaving nothing for manoeuvring or adverse weather. The engine margin is not a substitute because it is intended to keep normal service power at 90% MCR, not to absorb weather.
Recommendation: retain the 15% sea margin and treat the coating as a fuel-saving measure. If the owner insists on a reduced margin, require a validated sea trial and a revised powering prediction, and retain at least a 10% reserve. Selecting the 18,500 kW engine on an unproven 8% claim is a commercial risk, not an engineering justification.