- Shaft (transmission) efficiency: the ratio of the delivered power at the propeller to the brake power of the engine, accounting for the losses in the shaft bearings, stern tube and any gearing. It is typically 0.97-0.99.
- Propeller (open-water) efficiency: the ratio of the thrust power (T x Va) to the delivered power (2 pi n Q). It represents the efficiency of the propeller itself in converting the delivered power into thrust power.
- Hull efficiency: the ratio of the effective power to the thrust power, = (1 - t)/(1 - w), where t is the thrust deduction factor and w the wake fraction. It accounts for the interaction between the hull and the propeller.
- Quasi-propulsive coefficient (QPC): the ratio of the effective power to the delivered power, = hull efficiency x propeller efficiency. It is the overall efficiency of the propulsion system in converting the delivered power into effective (towing) power.
- Overall (propulsive) efficiency: the ratio of the effective power to the brake power, = QPC x shaft efficiency. It is the overall efficiency of the engine-to-propeller-to-hull system.
A propeller of 4.8 m pitch turns at 110 rev/min. The apparent slip is -S% and the real slip is +1.5S%. The wake speed is 25% of the ship speed. Calculate the ship speed, the apparent slip and the real slip.
Pitch speed = pitch x rev/s = 4.8 x 110/60 = 8.8 m/s.
Let the ship speed be V (m/s). The speed of advance Va = V x (1 - 0.25) = 0.75 V.
Apparent slip = (pitch speed - V)/pitch speed = -S/100.
Real slip = (pitch speed - Va)/pitch speed = 1.5 S/100.
From the apparent slip: (8.8 - V)/8.8 = -S/100, so V = 8.8(1 + S/100).
From the real slip: (8.8 - 0.75 V)/8.8 = 1.5 S/100, so 8.8 - 0.75 V = 0.132 S.
Substitute V = 8.8(1 + S/100): 8.8 - 6.6(1 + S/100) = 0.132 S.
8.8 - 6.6 - 0.066 S = 0.132 S, so 2.2 = 0.198 S, S = 11.11.
Apparent slip = -11.11%; real slip = 1.5 x 11.11 = 16.67%.
Ship speed V = 8.8(1 + 0.1111) = 9.78 m/s = 9.78 x 1.944 = 19.0 knots.
Answer: ship speed about 19.0 knots; apparent slip -11.1%; real slip +16.7%.