354 THE CONQUEST OF THE AIR. 



extremely low, as a simple consideration will show. 



Let P = total force of all downward directed planes, 



V = the velocity. 



then the work to be done is P x V. 



and if P is in kg^s., V in metres 



P X V 

 H.P. = — y-~ horse power. 



P G 76 



As P = G weig:ht of planes, we gfet = = — , i.e.. by i 



H.P. H.P. V 



H.P. we can carry the more weight, the smaller we make the 

 velocity with which the planes are moved. 



76 

 Now in the present day aeroplanes — = 10 to 15, i.e. V must 



V 

 be 7.6 to 5 metres per second. 



The question is what must be the size of the planes? To find 

 this we must know the resistance of air. 



This resistance increases (i) proportionally with the area of 

 the opposing" surface, (2) the weight of air, (3) the square of the 

 velocity. If we double the latter, the resistance increases fourfold. 

 This may be explained as follows : — By doubling the velocity, the 

 particles of air are given double the velocity, but at the same 

 time the surface gets into contact with double the number of 

 particles. 



We may therefore express the resistance of air bv a formula. 

 P = o.6 FKV*, in which 

 F = resisting area, 



V = velocity. 



specific weight of air. 



K = constant = = 0. 125 



acceleration of gravity. 

 The factor 0.6 is an experimental constant and expresses the 

 efficiency. 



We obtain thus 

 p 



—_;- =0.6 X 0.125 Y^ =0.075 V^ 



For V = 7.5 metres per second. 



P o , 



— ^ =0.075 X 7.5- =4 kgs. square metre. 



I* 



In order to obtain such a machine which will carry 500 kgs., the 



area must be ^^ — = i2c: square metres. This area must always be 



4 

 available, so that — since the sustaining surface has to be moved 

 upwards in a collapsible state to make it available over and over 

 again — the necessary surface is really 250 square metres. For a 

 weight of 500 kilogrammes this surface would be too flimsy and 

 collapse at once. 



Fortunately better results are obtained with inclined surfaces 

 moved sideways. 



Experiments show that, if we move a plane surface horizon- 

 tally while it descends, the carrying capacity is increaiie'l mani- 



