56 AEROPLANE PERFORMANCE CALCULATIONS 



The results obtained by this investigation can, of course, be 

 applied to ordinary journeys and should make it easier to main- 

 tain good economy : their real application, however, is to such a 

 problem as " Against how fast a head wind will the machine in 

 question cross the Atlantic?" 



We will suppose the flight to take place at constant altitude, 

 so that cr is constant. 



Also we will disregard head winds at first, and allow for 

 them at the end. 



We have from page 5 5 



V 



V ' 



T V K 



Also we will take the following definitions : 



x is the distance in miles covered from the start up to -the 

 moment under consideration. 



/ is the time in hours from the start. 



W is the total weight of the machine at time t. Note that 

 W is a variable, owing to the consumption of fuel. 



8 is the total pounds per hour of fuel being expended at the 

 moment under consideration. Note this includes petrol, oil, and, 

 in the case of water-cooled engines, that part of the total water 

 supply that is evaporated. 



N' is the revolutions (as usual). 



N is the full revolutions (as usual). 



A is the full consumption in standard density air. 



Suffix o refers to the commencement of the cruise. 



We now assume that the pilot reduces speed as the machine 

 gets lighter so as to always fly at the same value of X (as a 

 matter of fact all he has to do is to leave the elevator setting 

 alone) : of course, he will also have to throttle down progressively 

 in order to avoid climbing above the constant altitude. 



Since X is constant, the " gliding angle " is constant, and of 

 course we have 



)'-J .;.,.,..<(.) 



?L wv 



P' /V 



.. P', V is always on the same " Throttling Curve" ; 

 but V T ' and V R ' are on the same "Throttling Curve" as V, 



