A propeller has a pitch ratio of 0.95. When turning at 120 rev/min the real slip is 30%, the wake fraction 0.28 & the ship speed 16 knots. The thrust is found to be 400 kN, the torque 270 kNm & the QPC 0.67.Calculate:
a) The propeller diameter
b) The shaft power
c) The propeller efficiency
d) The thrust deduction factor
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Given
p = 0.95
N = 120
s = 0.3
w = 0.28
V = 16
T = 400
Torque = 270
QPC = 0.67
To find
a) The propeller diameter
b) The shaft power
c) The propeller efficiency
d) The thrust deduction factor
Solution
We know that wake fraction, w = (V - Va) / V
0.28 = (16 - Va) / 16
4.48 = 16 - Va
Speed of advance, Va = 16 - 4.48
= 11.52 knots
We know that real slip, s = (Vt - Va) / Vt
0.3 = (Vt - 11.52) / Vt
0.3 Vt = Vt - 11.52
Vt - 0.3 Vt = 11.52
0.7 Vt = 11.52
Theoretical speed, Vt = 16.457 knots
We know that theoretical speed, Vt = (P x N x 60) / 1852
16.457 = (P x 120 x 60) / 1852
30478.36 = 7200 x P
Pitch, P = 4.23 m
a) We know that pitch ratio, p = P/D
0.95 = 4.23 / D
0.95 D = 4.23
Propeller diameter, D = 4.45 m
b) We know that delivered power dp = 2π n x Torque
And shaft power = dp / transmission efficiency
In question nothing mentioned about transmission efficiency. So it considered as negligible.
So shaft power, sp = 2π n x Torque {n = rev per sec
= 2π x (120/60) x 270
= 3391.2 kW
c) We know that thrust power, tp = Thrust x Speed of advance
= 400 x 11.52 x (1852/3600)
= 2370.56 kW
Also thrust power, tp = dp x propeller efficiency
So propeller efficiency = tp /dp
= 2370.56 / 3391.2
= 69.90 %
d) We know that effective power, ep = dp x QPC
= 3391.2 x 0.67
= 2272.10 kW
Also ep = Rt x V
The total resistance, Rt = ep / V
= [2272.10 / 16] x [3600 / 1852]
= 276.03 kN
Also Rt = T (1 - t)
276.03 = 400 (1 - t)
1- t = 0.69
Thrust reduction factor, t = 1- 0.69
= 0.31
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