AIR PERFORMANCE 51 



a complete family of these curves on celluloid and keep it for use 

 when required. It is simply laid over the performance curves 

 with the axes corresponding, and then the intersection of any of 

 the " Throttling Curves," as these cubics are called, with the 

 P, P T , and P R curves, can be read off at once. Particulars of how 

 to make such a family of curves on celluloid are given in 

 Chapter XII., page 126. 



These throttling curves are only referred to here in order to 

 draw attention to a particularly useful property of the family. 



Let one of the curves be 



y = ax 3 



and suppose that it has been plotted on inch squared paper. 

 Then suppose that this curve is laid over a performance calcula- 

 tion which is plotted on millimetre squared paper, or in French 

 units, or with an open velocity scale and a close horse-power 

 scale, and let us consider what the meaning of the curve will be 

 when read off on the scale of the paper underneath it. 



A moment's consideration will show that the curve will 

 then be 



horse-power = ft (velocity) 3 , 



where ft is a new constant depending on the scales used in the 

 two directions. 



Since, however, ft is a constant, the curve is still of the form 

 y oc x* on the scale of the paper. 



Therefore, a set of such curves, once scribed on celluloid, can 

 be used on any kind of plotting of horse-power on a base of 

 speed, irrespective of the units used and the scales chosen, 



Consumption and Revolutions when Throttled. Aero 

 engines will not run indefinitely at full power without taking 

 harm, and for this reason it is desirable to know both the con- 

 sumption and the revolutions when flying horizontally, throttled 

 down to any speed.* 



Also it is preferred that a commercial machine should, for 

 reasons of economy, normally travel throttled : to investigate 

 this, again, we need to be able to calculate the consumption at 

 any speed and at any height. 



We will therefore find the revolutions and the indicated horse- 

 power when the machine is flying horizontally at a given speed 

 at a given height throttled of course. 



* As an example, the makers of one engine advise that if it is used when 

 cruising at not more than -7 of full consumption, and at not more than -9 of full 

 revolutions, its life will be practically indefinitely prolonged. 



