98.NA October 2020 Q.7(b)

 When a propeller of 4.8m pitch turns at 110 rev/min, the apparent slip is found to be –s% and the real slip +1.5s%. If the wake speed is 25% of the ship speed, calculate the ship speed, the apparent slip and the real slip.

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Given

P = 4.8 m
N = 110
Apparent slip = -s % 
Real slip = +1.5s %

To find

1.Ship speed, V
2.Apparent slip
3.Real slip

Solution

Theoretical speed Vt = P x N x 60 / 1852
                                  = 4.8 x 110 x 60 / 1852
                                  = 17.11 knots

As given wake speed = 0.25 x Ship speed. The speed of the ship related to the wake is called speed of advance Va. That will be 75 % of the ship speed

Va = 0.75 V

Apparent slip = ((Vt - V) / Vt) x 100 %
                   -s = ((Vt - V) / Vt) x 100 %   ---------------------------------(1)

Real slip = ((Vt - Va) / Vt) x 100 %
   + 1.5 s =  ((Vt - Va) / Vt) x 100 %   --------------------------------------(2)

Substituting Va = 0.75 V in (2)

+ 1.5 s =  ((Vt - 0.75 V) / Vt) x 100 %  ------------------------------------(3)

Multiplying (1) with 1.5

-1.5 s = 1.5 x ((Vt - V) / Vt) x 100 % --------------------------------------(4)

Adding (3) and (4)

+1.5 s - 1.5 s = ((Vt - 0.75 V) / Vt) x 100 + 1.5 x ((Vt - V) / Vt) x 100
                   0 = (100 Vt - 75 V + 150 Vt - 150 V ) / Vt
                   0 = 250 Vt - 225 V
           225 V = 250 Vt
                      = 250 x 17.11
                      = 4277.5

1.Ship speed V = 4277.5 / 225
                      V = 19.01 knots

2.Apparent slip = ((Vt - V) / Vt) x 100
                         = ((17.11 - 19.01) / 17.11) x 100
   Apparent slip = - 11.10 %

3. Real slip =  + 1.5 x s
                   = 1.5 x 11.10
    Real slip = + 16.66 %