60 EXPERIMENTS IN AERODYNAMICS. 



The pressure on a plane moving normall)'- in the air is usually represented 

 by the equation 



k AV B 



P = 



1 + 0.00366 {t - 10°) 760 



where V is the velocity of the plane ; A is its area, B the atmospheric pressure 

 in millimeters, t the temperature in centigrade degrees, and k a coefficient whose 

 value for a standard temperature of 10° C. is determined by experiment. If the 

 pressure per unit area is diiferent for planes of different sizes and shapes, it will 

 be manifested by differences in the resulting values of k. Then, if k be given 

 its value for a plane of some fi.^ed size and shape, one or more additional factors 

 must be inserted in order that the formula shall give the pressure on a plane of 

 any other size and shape. Experiments show that the variations in k for planes 

 of diflFerent shapes and, within the range of experiment, for planes of diiFerent 

 sizes, are very small. 



Proceeding now to the case of inclined planes, and for our present purpose 

 neglecting the pressure and temperature, we may represent the resultant pressure 

 P„ on an inclined plane moved horizontally in the air at an angle a with the 

 horizon by the equation 



P^ = P,„F{a)=kA V'F{a), 



where F (a) is a function to be determined by experiment. From this equation 

 also we obtain directly the vertical component of pressure 



W= P„ cos a = k A V F (a) cos a 



and the horizontal component of pressure 



R = P^ sin a = k A V^ F (a) sin a. 



The point to which I wish now to direct especial attention is that, although shape 

 and aspect of plane have but slight effect on the pressure on normal planes, they 

 have a most important influence in determining the pressure on inclined planes. 

 Consequently, F (a) must be determined separately for planes of different size, 

 shape, and aspect. An empirical curve (Fig. 1) representing F (a) for a square 

 plane has been obtained from the experiments with the Resultant- Recorder. 



It is obvious that the above equation for W^ furnishes the basis for determin- 

 ing F (a) for variously shaped rectangles from the observations of soaring speed 

 obtained with the Component- Recorder, togetlier with experiments on normal 

 planes. The vertical component of pressure at soaring speed is the weight of 

 the plane, k is the fundamental constant of normal pressure derived from 

 experiments on the nornial plane, and Fis the soaring speed for the angle a. 



