AIR PERFORMANCE 43 



With these assumptions then, let be the inclination of the 

 path to the horizontal, let P be (as usual) the machine horse- 

 power required for horizontal flight, let P p be the propeller horse- 

 power available at the speed in question (then P p equals P T or P R , 

 whichever is the least at the speed in question), and let V be the 

 speed in miles per hour along the path. 



Further, let W be (as usual) the total weight of the machine 

 in pounds, let T be the thrust of the propeller in pounds, let L 

 be the actual air lift at right angles to the path of flight in pounds, 

 and let D be the actual total air resistance of the machine along 

 the flight path in pounds. 



Then by resolving along and perpendicular to the flight path 

 we have the equations 



T = D + W sin B . . . (i) 

 and L = W cos (2) 



Also of course 



TV 



(3) 



375 



p - 



DV/W\ 



375(1:) 



The term ( _ \ in the last equation is due to the fact that on 



climb L is not the same as W, while it is, at least very approxi- 

 mately, in horizontal flight, to which P refers by the definition we 

 have given it. 



/fi\ 

 Now let x = tan (-J 







.'. COS 6 = COS 2( - 



cos 2 * - sin 2 A I - tan 2 * 



2 (} 



\2j 



*\ + sin 2 A I + tan 2 f-\ 



2j \2j \2j 



.... (cos*) 



I + X" 



2 sin f-\ cos f-\ 2 tan (- 



and sin 6 = sin 2(-~ ) = 



