Pocketbook of Useful Formulæ and Memoranda
for Civil and Mechanical Engineers

563 OF ENGINEERING FORMULÆ. Relation between Pitch, Slip, and Efficiency— continued. In these calculations the motion of water in the ship’s wake has been disregarded, the action being assumed as if in undisturbed water. .... The area which will drive a ship with a given “ slip ratio Is directly as the vessel’s resistance, and inversely as the square of the speed ; and since at moderate speeds a ship's resistance Is proportional to the square of the speed, the same area of propeller will at moderate speeds drive a given ship with the same slip ratio ; and areas directly as the squares of the respective dimensions of two similar ships will drive with the sartie slip ratio, since the wetted surface measures the resistance in each case. At the higher speeds the slip ratio will increase with the given propelling area. The maximum of efficiency is not produced by extending the area of the propelling plane so as to minimize the slip, but the slip angle that gives the maximum efficiency is moderate. If friction did not exist, the obliquity with which the pro- peller acts on the water would cause no loss in efficiency. The value of 3, which gives the maximum efficiency, is the same whatever be the value of <J>. Although the slip angle ought to have the same value whatever be the pitch angle, the slip ratio will be greater for large pitch angles than for email. If the slip angle be that which gives the maximum efficiency, then to produce the maximum efficiency the pro- pelling plane ought to stand at an angle of 45° with the line of ship’s motion, whatever be the coefficient of surface friction or of normal pressure. If the slip angle exceed that which gives the maximum efficiency, the pitch angle must al.-o be increased; if the excess be small, the pitch angle must be increased by the same amount; if the excess be large, the increment of pitch angle must be still greater. The calculations point to the conclusion that a very much longer pitch than has commonly been adopted is favourable to efficiency; and that instead of its being correct to regard a large amount of slip as a proof of waste of power, the opposite conclusion is the true one. To assert that a screw works with unusually little slip, is to prove that it works with large waste of power. 2 o 2