4 AEROPLANE PERFORMANCE CALCULATIONS 



Further, it has been established that the function of /V 

 referred to consists of the sum of a constant and terms whose 

 importance is relatively small. If we neglect these terms entirely 

 we have the V 2 law, which, as has been stated above, is a general 

 approximation to the facts. 



It is necessary, however, to consider more closely the 

 quantity K. As has been stated, K is a function of /V and can 

 therefore be plotted on /V as a base if enough experiments are 

 available. This has been done for a great variety of objects of 

 different kinds and the following results have been obtained : 



(1) For bodies of the high resistance class, such as round 

 wires and cables, K may be taken as practically constant from 

 the values of /V attained in wind tunnel tests up to the values 

 of /V corresponding to machines in flight, so that we may use 

 the formula 



resistance = (a constant) x / 2 V 2 . 



(2) For bodies of the friction class, such as well stream-lined 

 fuselages, K decreases as /V increases over the above range to 

 such an extent that the best approximation for the resistance is 

 found to be the formula 



resistance = (a constant) x (/V) 1 ' 85 . 



(3) We may safely assume that bodies of an intermediate 

 class, such as stream-lined struts, can be dealt with by a formula 

 of an intermediate type. 



We will now consider Case (2) in some detail. Suppose that 

 we have to find the resistance of the hull of a flying boat which 

 is anticipated to have minimum and maximum flying speeds of 

 roughly 40 and 120 miles per hour respectively, and that we 

 have to work from a wind tunnel test on a model made to a 

 linear scale of T V full size, carried out at a wind speed of 27 miles 

 per hour conditions that are quite usual. 



Let L be the value of / for the case of the actual hull, and 

 let X be the constant in the equation of Case (2) above, then 



X/ 2 V 2 X/ 2 V 2 



resistance = X(/V) 1>85 



//VV 15 ' 



L "<r) 



//vy 15 



The values of (j-J are readily found by logarithms in given 

 numerical cases, so that we can obtain the following table : 



