NO. 3 



LANGLI-n MEMOIB ON MECHANICAL ILIGHT 



43 



Eelation of Area to Weight and Poweb 



In order to get a more precise idea of the character of the alteration intro- 

 duced into these theoretical conditions by the variation of any of them, let us, 

 still confining ourselves to the use of the whirling-table, suppose that the plane 

 in question while possessing the same weight, shape, and angle of inclination, 

 were to have its area increased, and to fix our ideas, we will suppose that it be- 

 came 4 square feet instead of 1 as before. Then, from what has already been 

 said, V, the velocity, must vary inversely as the square root of the area; that is, 

 it must, under the given condition, become one-half of what it had been, for if 

 V did not alter, the impelling force continuing the same, the plane would rise 

 and its flight no longer be horizontal, unless the weight, now supposed to be con- 

 stant, were itself increased so as to restore horizontality. 



I have repeated Table XIII under the condition that the area be quadrupled, 

 while all the other conditions remain constant, except the soaring speed, which 

 must vary. 



W is the weight of the single plane; A is the area; R is the horizontal " drift." 

 of like planes which 1 H. P. will drive at velocity V. Work is RV. 



I. If Work is constant, R varies as :, V~i- II. If R is constant. Work varies as 



is constant while A varies, the weight which 1 H. P. will support varies as VA. 



Wt is the weight 



1 



v'-i 



III. If w 



The reader is reminded that these are simply deductions from the equations 

 given in " Aerodynamics," and that these deductions have not been verified by 

 direct trial, such as would show that no new conditions have in fact been intro- 

 duced in this new application. While, however, these deductions cannot convey 

 any confidence beyond what is warranted by the original experiments, in their 

 general trustworthiness as working formulae at this stage of the investigations, 

 we may, I think, feel confidence. 



I may, in view of its importance, repeat my remark that the relation of area 

 and weight which obtain in practice, will depend upon yet other than these theo- 

 retical considerations, for, as the Audit of the free aerodrome cannot be ex- 

 pected to be exactly horizontal nor maintained at any constant small angle, the 



