162 



SYMPOSIUM ON AERONAUTICS. 



plane the air is at rest and the object- in motion in the direction 

 opposite to that of the preceding case. We also notice that in both 

 cases three forces are involved, first, the weight of the object, second, 

 the action of the wind on the plane, and third, the pull of the kite- 

 string or the thrust of the propeller. I may also say that it makes 

 no difference whether the propeller pushes from behind, as in the 

 first aeroplanes, or pulls from in front, as is now usually the case. 

 Since the time of Newton it has been known that the force of 

 the wind on the plane is proportional to the square of the relative 

 velocity, since it is proportional to the momentum destroyed in a 

 given time, and this is proportional, for a given mass, to its velocity, 

 while the mass arriving is again proportional to the velocity, so 

 that the square is accounted for. Finally the influence of the angle 

 made by the wind with the surface of the plane, the so-called angle 

 of attack, must be known. We may assume that wind blowing 

 tangent to a surface will slide along without exerting any force on 

 it, although the action of the wind in supporting a flag shows that 

 this is not so. But the wing of an aeroplane is made so smooth that 

 for practical purposes we may neglect the tangential drag, and as- 

 sume that the force is at right angles or normal to the plane. Ac- 

 cording to Newton, who treated the air like a stream of particles 

 impinging on the plane, the force would have been proportional to 



90" 



Fig. I. 



the square of the sine of the angle of attack, but we now know 

 through the many series of experiments that have been made by 

 Langley and others, that this law is not correct, and that it is much 

 more nearly proportional to the first power of the sine. The dif- 

 ference is made apparent in Fig. i, in which the vertical height of 

 a point denotes the force, the horizontal distance the angle of at- 

 tack of the ])lane, for both laws. We see that for small angles the 



