Solution Naval Numerical 5

Numerical 5: With reference to fixed pitch propellers: 

(a). Explain Propeller Slip and Propeller Thrust 

(b). The shaft power of a ship is 3000 KW, the ship speed V is 13.2 knot Propeller rps is 1.27. Propeller pitch is 5.5m and the speed of advance is 11 Knots. Find: 

(i). Real Slip 

(ii). Wake fraction 

(iii). Propeller thrust, when its efficiency, η = 70 %.

Answer: (a).
(b) Given shaft power(sp) = 3000KW
Ship’s speed (V) = 13.2 knots
Rotation speed of propeller = 1.27 rps
Propeller pitch (P) = 5.5m
Speed of advance (va) = 11knot.
To find, 

(i) real slip 

(ii) Wake fraction 

(iii) propeller thrust at η = 70% 

(i) Real slip, 
$real\ slip =\frac{Theoritical\ speed (V_{t})-Speed\ of\ advance(V_{a})}{Theoritical\ speed (V_{t})}\times 100$ 

Theoretical speed $V_{t}=\frac{P\times RPS\times3600}{1852} Knots$ 

$V_{t}=\frac{5.5\times 1.27\times3600}{1852}= 13.58 Knots$ 

$Real\ slip =\frac{13.58-11}{13.58}=.189\ or\ 18.9$ %


(ii) wake fraction
$wake\ fraction = \frac{Ship\ speed(V)-Speed\ of\ advance(V_{a})}{Ship\ speed(V)}$ 

$wake\ fraction = \frac{13.2-11)}{13.2}=0.167\ or\ 16.7$ %

(iii) Propeller Thrust, at η =70%

 Thrust power = 3000 x 0.7

$t_{p}=2100$  kW 

Also,  Thrust Power $t_{p} = T\times V_{a}$ 

Where $V_{a}$ in m/s

Thus 11 x 1852/ 3600 = 5.6588

T = 2100/ 5.6588,

Thrust, T = 371.1 kN