32 AEROPLANE PERFORMANCE CALCULATIONS 



component of thrust, and that the propeller slip stream meets the 

 wings at the same angle as the undisturbed air would do. 



Unfortunately, the approximation cannot be carried any 

 farther than has been done in the Third Method, if a complete 

 and easily workable solution is desired. 



The outstanding error due to this cause is not serious unless 

 the propeller shaft is mounted in the machine at an unusual angle 

 to the chord of the wing. This, however, is often done in 

 machines designed to fly off the decks of ships, in order to obtain 

 the advantage which can be got in this way. 



The whole question of the effect on the performance of an 

 inclined propeller shaft is therefore postponed to Chapter VI. 



Non-Horizontal Flight. The consideration of the problem 

 when the line of flight is not horizontal belongs to the question 

 of the rate of climb of the machine: it is therefore appropriate 

 to postpone it to Chapter V., page 42. 



Flight at an Altitude. For the purposes of aeroplane per- 

 formance calculations flight at an altitude is distinguished from 

 flight in standard density air solely by the fact that o-, the ratro 

 of the air density at the altitude to the standard air density, is 

 not unity. We will now consider the influence of cr on the cal- 

 culations of the machine performance curve. 



As an example of the conversion process we will follow the 

 proof of the Fourth Method, page 28. 



The dimensions and weight of the machine will be the same 

 at the altitude, also the values of X, L/D and k ltnax : hence also 

 the quantities a, b\ c, d',6 y <f>, and ty will be the same at the al- 

 titude, remembering that Rj and R 2 are not the resistances at 

 the altitude, but in standard density air. 



Let V, P, T, L, w, D lt D 2 , and b refer to standard density 

 air, but let the corresponding quantities at the altitude be 

 V, P', T', L', w', IV, D,', and b'. 



Then, analogously to the proof of the Fourth Method we 

 shall have, for flight at the altitude, the equations 



r = ,[(: 



L' = a- x -00237/yS - S' + (i + ') 2 S'](i-467V') 2 . (3) 

 also U(ck c -/+/) + D 1 'A 1 + D 2 '^ 2 = w'l 



w = L' - W 



