308 OF STEAM NAVIGATION. [SECT. x. 



640. The size of the wheels depends chiefly on the mode of giving them 

 motion from the engine ; they must be so large as to have the proper speed at the 

 circumference, and where large wheels can be admitted, they have some ad- 

 vantages : they must necessarily be narrower, and they strike the fluid in a 

 favourable direction, and also quit it better ; the paddles having more direct action 

 on the water, they splash it about much less ; the weight of the wheel also renders 

 it more effective, as a regulator of the forces acting upon it. On the other hand, 

 there are some strong practical objections to very large wheels for sea vessels ; 

 they give the momentum of the waves a greater hold on the machinery, they are 

 cumbersome and unsightly, and they raise the point of action too high above the 

 water line. 



641. When the wheels are on the first motion, the radius is determined by 

 the velocity of the engine. Let that velocity be n strokes per minute, then 3' 1 41 6 

 x 2 r = the circumference of the wheel ; r being its radius, and its velocity per 

 minute is 3*1416 x 2 r n : but this is to the velocity of the boat nearly as 

 3 to 2 ; * hence, 



3-1416 x 2 r n = ^ x 3 ". 



B 



or : - = , the number of strokes per minute, when v = the miles per hour. 



Also fixing the number of strokes we have, 



21 v 



= r, the radius of the wheel. 



n 



This therefore reduces to this simple rule : 



RULE. The velocity of the vessel per hour multiplied by 21 is equal to the 

 number of strokes per minute, multiplied by the radius of the wheel. 



From this exceedingly simple rule it can be known at once whether the wheel 

 becomes too large or not, when the simple crank motion is used ; it ought to be 

 used in preference to a second motion, in all cases where it does not involve some 

 other difficulties than merely the size of the wheel. 



For further information on the subject of paddle wheels, the reader is referred 

 to the Appendix. 



MoDIF'CATIONS OF PADDLE WHEELS. 



642. Several methods have been tried or projected for getting rid of certain 

 supposed defects of the paddle wheels. The quantity of force lost by oblique action 



1 This ratio is obtained from art. 630. 



