PROPULSION OF SHIPS 401 



the ends of a horizontal lever with an adjustable fulcrum, the position 

 of this fulcrum may be readily adjusted until the lever floats in its mid 

 position, and the relative resistances of the two models are then in the 

 ratio of the lengths of the arms of the lever. Let resistance of model (2) 

 be n times that of model (1). 



Let E represent wave-making and eddy resistances ; E = skin friction. 



Thus resistance of model (2) = m # 2 + m F* = n m E l + Hl Fi 



But m E 2=s 



V ( J* V , f F ( Zl 



. r&a I -j- ) = n s^i ( r 1 



V s/2 / \ gtl ' 



.'. Total resistance of new ship is given by 



S JR 2 = S E, + S F* - S F* + ( j* ) [n { .Ex (^)" + w Fi ] - TO F a ] 



Of the terms in this expression S F 2 , m Fi, and m .F a can be readily calcu- 

 lated, while s Ei being equal to .,/?i 8 F\ 9 can also be obtained, since the 

 total resistance s Ri of ship (1) is known, while its frictional resistance 

 s Fi can be readily calculated. 



AET. 115. THE PROPULSION OF SHIPS. 



Of the many systems of mechanical propulsion which have from time 

 to time been devised, only three have attained any measure of success. 

 These respectively use the paddle wheel, the screw propeller, and the 

 hydraulic jet as their propelling agents. 



The principle underlying all these systems is the same, the propeller 

 being devised so as to create a sternwards current of water, and the 

 corresponding reaction on the propeller providing the propelling force on 

 the ship. Thus, whatever system be adopted, if a mass of water of 

 weight C Ibs. per second have its sternward velocity increased by v feet 

 per second by the action of the propeller, the change of momentum per 



second in this direction = - -foot-pound units, and the thrust on the 



t7 



propeller is of the same magnitude, Ibs., and in the opposite direction. 



Since the thrust varies as the product of C and v, any one of these 

 factors may be changed without affecting the thrust if the other factor 

 suffer a corresponding change, so that a given thrust may be obtained by 

 the comparatively slow movement of a large mass of water, or by the 

 quick movement of a smaller mass. Other things being equal, then, an 



H.A. D D 



