$$F=kAV^2N$$

Where,

• k = Constant
• A = Area of rudder in m2
• V = Ship's speed in m/s

The constant is dependent on size of rudder, rudder angle and density of water.

Variables affecting force on rudder:

• Rudder angle
• Density of water
• Ship speed

These are the three variables, while all other are constant parameters i.e.

• Area of rudder
• Size of rudder.

(b) Given:

$$\Delta=15000t$$

$$Shaft\:Power\:\left(SP\right)=420$$

$$Transmission\:Efficiency=83\%$$

$$Shaft\:losses=6\%$$

$$Propeller\:Efficiency=65\%$$

$$QPC=0.71$$

$$Thrust\:Power=2550kW$$

$$\left(\imaginaryI\right)\:Delivered\:Power\:\left(DP\right)=\frac{Thrust\:Power\:\left(TP\right)}{Propeller\:Efficiency\:\left(\eta P\right)}$$

$$DP=\frac{2550}{0.65}$$

$$DP=3923.07kW$$

$$\left(ii\right)\:Shaft\:Power=\frac{Delivered\:Power\:\left(DP\right)}{Transmission\:Efficiency\:\left(\eta T\right)}\:$$

$$SP=\frac{3923.07}{0.83}$$

$$SP=4726.59kW$$

$$\left(iii\right)\:Indicated\:Power=\frac{Shaft\:Power\:\left(SP\right)}{Mechanical\:Efficiency\:\left(\eta m\right)}$$

$$IP=\frac{4276.59}{0.83}$$

$$IP=5694.68kW$$

$$\left(iv\right)\:Effective\:Power=DP\times QPC$$

$$EP=3923.07\times0.71$$

$$EP=2785.3797kW$$

$$\left(v\right)\:Shaft\:Power=\frac{\Delta^{\frac23}\times V^3}{Admiralty\:Co-efficient}$$

$$4726.59=\frac{15000^{\frac23}\times V^3}{420}$$

$$V=14.83\:knots$$