TAKING OFF OF AEROPLANES. 



237 



The following' calculations are based on figures of 

 reduction of horse power Avith density used in dealing with 

 I)erforiuance tests during- the war. I understand that these 

 tigures are considered to be too optimistic, but, as it is my 

 object to g'ive a lower limit to the effect sought, the 

 values are in the rig-ht direction, and at any rate are not 

 exaggerations. 



It is often stated that the tenuity of the atmosphere 

 makes Hying dithcult, because the air is " too thin to hold up 

 the machine." This is erroneous in the sens© usually 

 intended. The thinness of the air also diminishes the resist- 

 ance to the forward motion of the machine, and the greater 

 air speed thereby obtained compensates for the loss of lifting- 

 power at a. given speed. By far the most important effect 

 is that of reducing the engine power. 



The density of the air can be calculated when the 

 pressure and temperature are known. In the following "work 

 the conditions are taken at 8, 000, 4,000, 5,000 and (i.OOO feet 

 altitude, and temperatures 50, GO, 70, 80, 90, 100 degrees 

 Fahrenheit. The altitudes are what are called " isothermal 

 heights," /.r., heights as given by an ordinary aneroid or 

 altimeter. 



The curves of Fig. 1 show the engine factor f (d) M-hich 

 must be used to nudtiply the horse i:)ower at sea-level for the 

 same number of revolutions per minute to get the horse power 

 actually obtained. ^/=the density of air compared Avith that 

 at sea-level under standard conditions i/.c, 1,222 grammes 

 per cubic metre). 



The greatest possible varieties of machines with diftVrent 

 loadings and in air of dift'erent densities have performances 

 which fit into the tAvo cui'A'es giA'en in Figs. 2 and 3 faiil\^ 

 well. _ ' 



In Fig. 2 the abscissa is J'J„\/ d f (d) ^/7/w, and the 

 ordinate V^/d\/l/w. 



In Fig. 3 th e abscissa is E„\/ d f (d) \/7/w, and the 

 ordinate vsj ds/t Irv. 



Where 



£'„ = engine horse power per 1,000 lbs. of load. 

 d = density relative to air at sea-level. 

 w = wing-loading in lbs. per square foot. 



V = level speed (air sjDeed) in miles per hour. 



V =rate of climb in feet per niiniite. 



It is from these- figures that the following Avork is 

 calculated. The AAay in Avhich the density and loading come 

 into the aboA^e quantities is the result of elementary 

 a erodynamical theory . * 



The points shown in Figs. 2 and 3 are calculated from 

 actual tests on Yickers-Vimy bombers and D.II.9 machines. 



* L. Bairstow, " Applied Aerodynamics." 



