Question

With reference to the wake of a vessel:

(a) Explain Wake fraction and Quasi Propulsive co-efficient(OPC).

(b) A ship travelling at 15.5 knots has a propeller of 5.5 m pitch turning at 95 rev/min. The thrust of the propeller is 380 KN and the delivered power 3540 KW. If the real slip is 20% and the thrust deduction factor 0.198, calculate the Quasi Propulsive Coefficient (QPC) and the wake fraction.

Answer 1

Part (a)

Wake fraction and Quasi Propulsive Coefficient (QPC).

Wake fraction (w):

When a ship moves through the water, the water in the wake region behind the hull is carried forward with the ship. This is the wake.
The wake fraction is the ratio of the speed of the wake (the water carried forward) to the ship's speed. It is defined as w = (V - Va)/V, where V is the ship speed and Va is the speed of advance of the propeller relative to the water.
The wake is made up of frictional wake (water dragged along by the hull), potential wake (due to the pressure field around the hull) and wave wake.
The wake fraction is beneficial because it reduces the effective speed of the water entering the propeller, reducing the power required.

Quasi Propulsive Coefficient (QPC):

The QPC is the ratio of the effective power (the power required to tow the hull, i.e. the useful work done in propelling the ship) to the delivered power (the power delivered to the propeller).
QPC = Effective Power / Delivered Power.
It is a measure of the overall efficiency of the propulsion system, combining the hull efficiency, the propeller (open water) efficiency and the relative rotative efficiency.
QPC = hull efficiency x propeller efficiency x relative rotative efficiency.
The hull efficiency = (1 - t)/(1 - w), where t is the thrust deduction factor and w is the wake fraction.

Part (b)

Calculation.

Ship speed V = 15.5 knots = 15.5 x 1852/3600 = 7.968 m/s.

Propeller pitch P = 5.5 m, rev/min = 95, so rev/s = 95/60 = 1.5833 rev/s.

Pitch speed (theoretical speed of advance) = P x rev/s = 5.5 x 1.5833 = 8.708 m/s.

Real slip = 20% = 0.20.

Real slip = (Pitch speed - Va)/Pitch speed, so Va = Pitch speed x (1 - real slip) = 8.708 x 0.80 = 6.966 m/s.

Wake fraction w = (V - Va)/V = (7.968 - 6.966)/7.968 = 1.002/7.968 = 0.1258.

Answer: Wake fraction = 0.126 (12.6%).

Thrust T = 380 kN = 380000 N.

Thrust power = T x Va = 380000 x 6.966 = 2647080 W = 2647 kW.

Delivered power PD = 3540 kW.

Propeller efficiency (open water) = Thrust power/Delivered power = 2647/3540 = 0.7477.

Thrust deduction factor t = 0.198.

Hull efficiency = (1 - t)/(1 - w) = (1 - 0.198)/(1 - 0.1258) = 0.802/0.8742 = 0.9174.

QPC = hull efficiency x propeller efficiency = 0.9174 x 0.7477 = 0.686.

Answer: QPC = 0.686.

(Note: QPC can also be found as QPC = (T x V)/(PD) x (1-t) ... but the standard method above gives QPC = 0.686.)

✓ Verified Model Answer (Text Solution)

Wake fraction and Quasi Propulsive Coefficient (QPC).

Wake fraction (w):

Quasi Propulsive Coefficient (QPC):

Calculation.