Solution Naval Numerical 2

Numerical 2: With respect to Ship Propulsion: (a). Explain the various efficiencies associated with propeller and shafting arrangement. (b). When a propeller of 4.8 m pitch turns at 110 rpm, the apparent slip is found to be —S and the real slip is 1.5 S. If the wake speed is 25% of the ship speed, calculate the ship speed, apparent slip and the real slip.

Solution: (a) 


 (b) Given, Pitch(P)=4.8 m

 RPM = 110 rpm, 
 Apparent slip(Sa) = - S
Real slip(Sr) = 1.5S.
Wake speed(V - Va) =  25 %of the ship speed (V); 
To, calculate the ship speed(V), apparent slip(S) and the real slip(Sr).

We know that the theoretical speed is given by;
Vt = Pitch x RPM x 60/1852 knots 
Vt = 4.8 x 110 x 60/1852 =17.11knots

V - Va=0.25XV 
Va= 0.75XV
Apparent slip, -S= (Vt-V)X100/Vt
Real Slip, 1.5S = (Vt-Va)X100/Vt
Dividing above equations
-1/1.5 = (Vt - V) / (Vt-Va)
Or, Vt-Va = 1.5(V-Vt)
Or, 2.5Vt = 1.5V + Va 
Replace Va with 0.75V and Vt with 17.11;
2.5 x 17.11 = 1.5V + 0.75V
V = 42.775/2.25
V = 19.01knots

Now, -S = (17.11 - 19.01) x 100/ 17.11
S= 11.1%
Thus Apparent slip = -S = -11.1%

And, Real slip (Sr) = 1.5 x S =  1.5 x 11.1 = 16.65%