Residual resistance is the total resistance minus the frictional (skin) resistance. Its components are:

• Wave-making resistance: the energy lost in creating the bow and stern wave systems, which depends on the Froude number and hull form.
• Wave-breaking resistance: energy lost in the breaking of the bow wave.
• Eddy-making resistance: energy lost in the formation of eddies at the stern, bilge keels, rudder and appendages.
• Pressure (form) resistance: the resistance due to the pressure distribution over the hull, including the viscous pressure (form) drag.
• Appendage resistance (in service): the additional resistance of the rudder, shaft brackets, bilge keels, etc.

Residual resistance is largely independent of Reynolds number and is scaled from model tests by Froude's law.

Data: V (knots) 15,16,17,18; RP (kW) 3000,3750,4700,5650; QPC 0.73,0.73,0.72,0.71. Brake power of engine = 3500 kW; transmission efficiency loss 3%; allowances for weather and appendages 30%.

Delivered (shaft) power at the propeller: DHP = 3500 x (1 - 0.03) = 3395 kW.

Effective power available at each speed = DHP x QPC. At 15 kn: 3395 x 0.73 = 2478 kW; at 16 kn: 2478 kW; at 17 kn: 3395 x 0.72 = 2444 kW; at 18 kn: 3395 x 0.71 = 2410 kW.

The service allowance of 30% means the naked effective power required at the service speed is RP(V), and the available effective power must cover RP(V) x 1.30 (the ship must overcome 30% more resistance in service). Equating available EHP to 1.3 x RP(V):

At 15 kn: available 2478, required 1.3 x 3000 = 3900 - not enough.

The service speed is found where 1.3 x RP(V) = available EHP. Using the RP curve (approximately proportional to V^3, RP = 3000 x (V/15)^3) and available EHP about 2478 kW:

1.3 x 3000 x (V/15)^3 = 2478, so (V/15)^3 = 2478/3900 = 0.6354, V/15 = 0.86, V = 12.9 knots.

Answer: the service speed is about 13 knots (approximately 12.9-13.0 knots).