44 AEROPLANE PERFORMANCE CALCULATIONS 



Now from equations (4) and (2) we have 

 n 375PL _ 375? cos 



VW V 



Then from equations (i), (3), and (D) we have 



_ T = D + W sin 6 = J/J Y' ' + W sin ( 

 From this and equations (cos 0} and (sin 0) we have 

 375P P . 375P(i - 



/fi\ 

 This is a quadratic equation for x, i.e. for tan f-\ of which 



the solution is 



WV li WV 



- P^i I P 



p 



The angle of climb being now determined, we have, if C is 

 the rate of climb in feet per minute 



C = V sin 0*?*? = 88V sin 

 60 



wv l( wv 



l( 



+ P) - V| 



375(P P + P) 37 5(P P + 



Equations (C) and (x) are in a form convenient for tabular 

 treatment (see Chapter XII., page 122). 



The rate of climb at an altitude is obtained in an exactly 

 similar way, merely writing V, P p ', and P' for V, P p , and P. 



This concludes the investigation of rate of climb under the 

 assumptions of the Second Approximation. This approximation 

 does not differ materially from the First Approximation except 

 when the machine has a really high rate of climb. 



Third Approximation. The assumptions made in this case 

 are that the air download on the tail and the height of the pro- 

 peller axis may be disregarded, but the full power slip stream. 

 is taken account of. Any attempt at a frontal attack on the 



