1904;] The Longitudinal Stability of Aerial Gliders. 113 



Substituting these values in the expressions for A, B, etc., assuming 

 that k 2 = a 2 , we have 



A = a 2 , B = 273-^, C 



D = 917y 5 E = 120000 — , H 



This will be positive if V" 2 > 1040«. This condition will also make 

 C positive, and is therefore the condition of stability. 



Ex. 7. — Let us now suppose the small plane to be placed behind the 

 other 



— - — s y 



being inclined to it at an angle of 5°, the direction of motion again 

 making an angle of 10° with the large plane and k 2 being = a 2 , as 

 in Ex. 6. 



In this case we have 



f(a) = 0-3, /'(*) = 1-6, ' <f>(a) = 0"49, = 0-59, 



f(af) = 0'17, /'(a') = 1-8, <f> (a') = 0'55, </>' (a') = 0'6. 



If the distance between the centres of the planes be 3a, the condi- 

 tions of equilibrium give 



r; = -0-35a, m = -2'65«. 



Substituting, we obtain 



mX u 



mX 



.-. A = a 2 , 

 1) = 1780 ~, 

 H will l)e positive if V L> > 250a. 



The condition of stability is therefore that V > s /(250a). 



[7. Effect of Moment of Inertia on Stability. 



It will be seen from (5) that the radius of gyration, k 2 , occurs only 

 in the expressions for A, B, the first two coefficients of the deter- 

 minantal equation. We have A = k 2 , B = k' 2 (X ( , + Y v ) + Ge. In all 

 the cases considered X. u + Y v and G<? are positive, and therefore these 

 two coefficients are positive for all values of k 2 . 



VOL. LXXIII. I 



- 50-8rt- 15050 y 2 , 



= 118. 10 5 ^- 123. 10* ^ 



= 1-9KSVA, 

 = 0-41 KSVa, 

 - 0-65 KSVtf, 



mG u = 0-33KSVa, 

 mG v = 0-056 KSVa, 

 mGre = 1-32KSW. 



B = 233 



V' 



E = 80000 



Y 2 



C = 34-8^-2400 



V 2 



H - 12. 10°^ 2 -3. 10 y a 



V 4 



