WEBSTER— DYNAMICAL ASPECTS. 



163 



sine law gives a much more rapid increase of force than the sine- 

 square, which is a very important point in practice. 



Beside the force at right angles to the plane the current tends 

 to turn the plane about a certain axis, as we see if we drop a card 

 with its long dimension horizontal. In falling it turns over and 

 over even if started with its surface horizontal. This turning 

 effect may be explained if we draw the stream-lines, which show 

 at each point the direction of flow of the air. It is a proposition 

 due to Bernoulli, that where the flow is fast the pressure is small, 

 and where it is slow the pressure is great. In Fig. 2 where the 



Fig. 2. 



stream lines are far apart the flow is slower than where they are 

 near together, just as a river flows most slowly where it is widest, 

 so that the pressure is large in such points as A, A, and small at 

 B, B, where the flow is rapid. Thus there is a tendency to turn the 

 body in the direction of the arrow. We may express this turning 

 property by saying that the effect of the air current on the plane is 

 represented by a single force R applied at a point P called the center 

 of pressure, not at the center of the plane, the position of P vary- 

 ing according to the angle of attack. 



Much mathematical skill has been expended to determine the 

 law of variation of the force with the angle, and the position of 

 the center of pressure. Curiously enough if the air acts hke a per- 

 fect fluid, and does not form vortices, it can be shown that there 

 would be no force on an obstacle, but merely a turning moment. 

 But if there are surfaces where the motion is discontinuous, on 

 crossing which we pass from fluid that is moving to fluid that is at 

 rest or moving less rapidly, the forces can be accounted for. Kirch- 

 hoft" many years ago treated such motions, and Sir George Green- 



