AIR PERFORMANCE 47 



P + R W - L * ~ L 



" 



The procedure to be adopted therefore is to find 2 V and 2 P 

 by a tabular process from the above (see Chapter XII. , page 123), 

 plot the modified machine performance curve so obtained, and 

 apply to it either the method of the First Approximation or the 

 Second Approximation. 



Comparison of the Results of the Three Approximations. A 

 reference to examples (6), (7), and (8), Chapter XIX., page 169, 

 shows that the rates of climb in feet per minute in standard 

 density air for a particular machine come out as 758, 744, and 

 707, while the corresponding speeds in miles per hour are 71, 

 74, and 70 respectively. 



We see therefore that, except in unusual cases, the method 

 of the First Approximation, though optimistic, is not far off the 

 mark. This is the method ordinarily used, and it is advisable to 

 retain the other methods for special cases only. 



Times to Altitudes. General Method. In the general case 

 we must first determine C', the rate of climb in feet per minute 

 at a series of altitudes, from the ground* up to the "ceiling," 

 that is to say, the altitude at which the rate of climb is zero. 



Let / be the time in minutes from leaving the ground, and 

 let x^ be the height of the ground in feet* 



Let x be any altitude in feet on the same basis, then 



P, dx 

 = ~dt 



*L 1 



'' ~dx C 



* - 



Hence the time to any required altitude is readily obtained 

 by plotting ~, on a base of standard altitude and then integrating 



V-X 



graphically. 



* The ground is not the altitude at which or is zero : two corrections are neces- 

 sary, one for climate and the other for the height of the ground above sea level. 

 Thus, for instance, for a place at sea level in England under normal conditions the 

 ground level may be taken as zero, but the value of cr is not I but 1*025 ( see curve 

 of page 104), while for the same place in the summer, the ground level must be 

 taken as 2350 and consequently the value of a- as -952 (see footnote, page 117). 



