i6 Raylekui, TJic MccJianicixl Principles of Flight. 



the relative i^ressures at the smaller angles, the results 

 appear to be at least as accurate as those obtained on a 

 larger scale with the whirling machine ; but the reference 

 to the pressure operative at 90 '^ is probably less accurate. 

 The principal conclusion that at small angles the pressure 

 is proportional to sin a, and by no means to sin "a, is abun- 

 dantly established. 



In applying these results, the first problem which sug- 

 gests itself for solution is that of the gliding motion of an 

 aeroplane. It was first successfully treated by Penaud,* 

 and it may be taken under slightly different forms. We may 

 begin by supposing the motion to be strictl}' horizontal, 

 the velocit}' being V and the inclination <jf the plane to 

 the horizon being a. Under these circumstances a pro- 

 pelling force F'\'~, required, which we suppose to act horizon- 

 tally. The mean pressure upon the plane we \\\\\ denote 

 by lc^^■-s^n«, the assumption of proportionality to sina 

 being amply sufficient for the case of small angles, with 

 which alone we are practically concerned. If .S be the 

 area (jf the plane, the whole normal force is kS ['-sina. In 

 view of the smallness of «, we ma\' equate this to the 

 weight (/F) supported. Thus 



]V=KSV'^\X\a (9), 



also 



F= KSV'~%\\Va (10). 



If F he independent of / ', as approximatcl}- in the 

 method of rocket propulsion, these equations show at once 

 that there is no limit to the weight that may be supported 

 by a given F. It is only necessary to make a small 

 enough, and to take V large enough to satisfy (9). 



In other methods of j)ropulsion we should have to 



* Sociile Philomatliiqite de Paris, 1876 ; J\eport of Aeronautical Society, 

 1876. See also W. Froude, Glasgow Proceedings, vol. xviii., p. 65, 1891. 



