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Propelling Power and Speed-Resistance due to Frictional Eddies-Computation of Augmented Surface-Computation of Probable Resistance-Computation of Engine Power required at a Given Speed-Computation of Probable Speed-Example of Calculation of Probable Speed of H. M. S. Warrior.
THE resistance to the motion of a ship due to the production of frictional eddies by a given portion of her skin is the product of the following factors :-
I. The area of the portion of the ship's skin in question;
II. The cube of the ratio which the velocity of gliding of the particles of water over that area bears to the speed of the ship, being a quantity depending on the figure of the ship and the position of the part of her skin under consideration;
III. The height due to the ship's speed; that is (in feet)
(speed in feet per second)2, or (speed in knots)2 :
IV. The heaviness (or weight of an unit of volume) of the water (64 lbs. per cubic foot of sea-water); and
V. A factor called the coefficient of friction, depending on the material with which the ship's skin is coated, and its condition as to roughness or smoothness.
The sum of the products of the factors I. and II. for the whole skin of the ship, has of late been called her Augmented Surface; and the Eddy-Resistance of the whole ship may therefore be expressed as the product of her Augmented Surface; by the factors III., IV., and V., above mentioned.
[In algebraical symbols, let ds denote the area of a small portion of the ship's skin, q the ratio which the velocity of gliding of the water over that portion bears to the speed of the ship, c the speed of the ship, g gravity, w the heaviness of the water, ƒ the coefficient of friction: then,