148 



ANNUAL EEPORT SMITHSONIAN INSTITUTION, 1908. 



ELEMENTARY THP^ORY OF AVIATION. 



(After M. Armengaud, jr.) 



R 



F. Direotion 



\ V. Pressure 

 of Wind 



vRNi 



P 



Fig. 1. 



E = resistance of air per square meter. 



S = sustaining surface. 



V = speed, assuming horizontal displacement in calm air. 



i = angle of attack. 



P = weight to be sustained and driven forward. 



/ = horizontal component of the resistance or the force opposed to horizontal motion. 



P^ = vertical component, or reaction making up the sustaining force, and equal 



to P. 

 T = elementary work in the case of a plane. 

 'cB = total work. 

 K = coefficient of resistance of the air. 



LAW OP VAKIATIONS OF THE RESISTANCE OF THE AIB FOLLOWING THE ANGLE OF 



ATTACK. 



Nj —Resistance of the inclined plane making the angle i. 

 Ngo= Resistance of the perpendicular plane to advancement. 



sin- i (Newton and Euler). 



sin i (Marey). 



2 n sin i 





4+7r sin i 

 (4-f 7r) sin i 



4+7!: sin i 

 2 sin i 



(Rayleigh). 



(Gerlach). 



(Duchemin). 



l+sm^ I 



sin i [a— {a— I) sin^ i] (Renard). 



In the case of a narrow plane. 



R=KSV^ (plane perpendicular to V). 

 Rj=KSV2 sin i (inclined on V). 



