The Speed and Power of Ships; Text (Paperback)

This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1911 Excerpt: ...without setting up any special theory of propeller action, has pointed out the limit of propeller efficiency beyond which we cannot go. Suppose we have a frictionless propelling apparatus discharging a column of water of A square feet area directly aft with an absolute velocity u, while the speed of the ship is v, both v and u being measured in feet per second. Then if w denote the weight per cubic foot of the water, the weight acted on per second is wA (v + u) and the mass is-A (v + u). S IV The reaction or thrust T----A (v + u) u being equal to the S sternward momentum generated per second. IV Useful work =-A (v + u) vu. S There being no friction, the lost work is simply the kinetic energy in the water discharged. Hence we have Lost work =--A (v + u)--. g 2 IV IV 14? Gross work =-A (v + u) vu H--A (v + -)--g g 2. Useful work v Efficiency e =----= Gross work, u v +-2 Also solving for u in the equation for thrust T, we get /s, gT v u = V +a V 4 wA 2 Substituting in the expression for efficiency, we have 4 tion that the water is discharged without increase of pressure. The effect of an increase of pressure would be to decrease the efficiency, since work done against pressure would be done with v efficiency Hence we conclude that the value of e above v + u is the maximum that could be attained by a perfect propeller. Suppose, applying this to a screw propeller, we write--for A, 4 where d is the diameter of the propeller in feet. Now if U denote useful horse-power delivered by the propeller and P denote gross horse-power, or horse-power delivered to the propeller, we have eP = U =--, whence T = e. Also v = V, where V 550 v 3 600 is speed of advance in knots. And g = 32.16, w = 64 for sea water. Substituting and reducing, we have finally P 1 16--24 e + 8 c...