CH. V] 



MECHANICAL RECREATIONS 



99 



long as its component normal to the sail is less than the 

 pressure of the -wind behind the sail and normal to it, the 

 resultant of the two will be a force behind the sail and normal 

 to it which tends to drive the boat forwards. But as the 

 velocity of the boat increases, a time will arrive when the 

 pressure of the wind is only just able to balance the resisting 

 force which is caused by the sail moving through the air. The 

 velocity of the boat will not increase beyond this, and the 

 motion will be then what mathematicians describe as "steady." 



In the accompanying figure, let BAR represent the keel 

 of a boat, B being the bow, and let SAL represent the sail. 

 Suppose that the wind is blowing in the direction WA with 

 a velocity u; and that this direction makes an angle with 

 the keel, i.e. angle WAR = 0. Suppose that the sail is set so 

 as to make an angle a with the keel, i.e. angle BAS=a, and 

 therefore angle WAL = + a. Suppose finally that v is the 

 velocity of the boat in the direction AB. 



I have already shown that the solution of the problem 

 depends on the relative directions and velocities of the wind 

 and the boat ; hence to find the result reduce the boat to rest 

 by impressing on it a velocity v in the direction BA, The 

 resultant velocity of v parallel to BA and of u parallel to WA 

 will be parallel to SL, if v sin a = u sin (0 + a) ; and in this case 

 the resultant pressure perpendicular to the sail vaoishes. 



Thus, for steady motion we have v sin a = u sin (0 + a). 

 Hence, whenever sin (0 + a) > sin a, we have v > u. Suppose, 



7—3 



