48 AEROPLANE PERFORMANCE CALCULATIONS 



The Particular Case where the Rate of Climb is a Linear 

 Function of the Altitude. It often happens that when C' is plotted 

 on x the curve is, at least very approximately, a straight line. 

 In this case let any altitude from ground level in feet be a (then 

 x = a + ;tr ). Then C' is a linear function of a. 



Let the value of C' at a = o be c and let the value of a at 

 C' = o be a Then 



Also we have, much as before 

 da _ ~/ 

 'dt ~ 



,. t - fe 



-r 



= f a^da = _ cti f d(g^ - a) 

 J (i - ) c } (*i - ) 



= - [log. (a, - a) - log, a, 



Therefore, in this special case (which is of fairly frequent 

 occurrence) we can dispense with the graphical integration and 

 use the above formula instead. 



Ceiling. There is really a "ceiling," i.e. a height at which 

 the climb is zero, corresponding to each point on the machine 

 performance curve. Ordinarily the word "ceiling" is applied 

 only to the best of these values, or " maximum ceiling ". In what 

 follows, however, we shall refer to a ceiling for each point on the 

 machine performance curve. 



Consider a point on the machine performance curve at an 

 altitude which is the ceiling for this point : then the climb is 

 zero, therefore P T ' = P' * at this altitude and at this speed V. 



Now the point P', V was obtained from a particular point 

 P, V on the machine performance curve for standard density air, 



* If the propeller were designed with an excessively small value of V , the 

 criterion would be P R ' = P', but such a case never occurs in practice, as it would 

 indicate a propeller design which always sacrificed a lot of the available horse-power. 



