1910] on the Dynamics of a Golf Ball. 803 



increase tlie velocity of the blast on this side, and if the velocity of 

 the ball is less than that of the blast, though it will diminish the 

 velocity of the air, it will not do so to so great an extent as on 

 the other side of the ball. Thus the increase in pressure of the air 

 at the top of the ball over that at P, if it exists at all, will be less 

 than the increase in pressure at the bottom of the ball. Thus the 

 pressure at the bottom of the bnll will be greater than that at the 

 top, so that the ball will be acted on by a force tending to make it 

 move upwards. 



We have supposed here that the golf ball is at rest, and the air 

 rushing 23ast it from riglit to left ; the forces are just the same as if 

 the air were at rest, and the golf ball rushing through it from left to 

 right. As- in Fig. 13, such a ball rotating in the direction shown in 

 the figure will move upwards, i.e., it will follow its nose. 



It may perhaps make the explanation of this difference of pressure 

 easier if we take a some\\hat commonplace example of a similar 

 effect. Instead of a golf ball, let us consider the case of an Atlantic 

 liner, and, to imitate the rotation of the ball, let us suppose that the 

 passengers are taking their morning walk on the promenade deck, 

 aU circulating round the same way. When they are on one side of 

 the boat they have to face the wind, on the other side they have the 

 wind 'At their backs. Xow when they face the wind, the pressure of 

 the wind against them is greater than if they were at rest, and this 

 increased pressure is exerted in all directions, and so acts against the 

 part of the ship adjacent to the deck; when they are moving with their 

 backs to the wind, the pressure against their backs is not so great as 

 when they were still, so the pressure acting against this side of the ship 

 will not be so great. Thus the rotation of the passengers will increase 

 the pressure on the side of the ship when they are facing the wind, 

 and diminish it on the other side. This case is quite analogous to 

 that of the golf ball. 



The difference between the pi'essures on the two sides of the golf 

 ball is proportional to the velocity of the ball multiplied by the velo- 

 city of spin. As the spin imparted to the ball by a club with a given 

 loft is proportional to the velocity with which the ball leaves the club ; 

 the difference of pressure when the ball starts is proportional to the 

 square of its initial velocity. The difference between the average 

 pressures on the two sides of the ball need only be about one-iifth of 

 one per cent, of the atmospheric pressure to produce a force on the ball 

 greater than its weight. The ball leaves the club in a good drive with 

 a velocity sufficient to produce far greater pressures than this. The 

 consequence is that when the ball starts from the tee spinning in the 

 direction shown in Fig. 14, this is often called underspin, the 

 upward force due to the spin is greater than its weight, thus the re- 

 sultant force is upwards, and the ball is repelled from the earth 

 instead of being attracted to it. The consequence is that the path 

 of the ball curves upward as in the curve A, instead of downwards as 



