226 SCIENCE PROGRESS 



Asymmetrical Derivatives for Two Transverse Planes 



Let a lf a 2 be the angles of attack, and l u I 2 the moments of 

 inertia of the planes respectively. 



Let (I, 2a) be the vector sum of (I„ 2a x ) and (I 2 , 2a 2 ). 



Then Z w = Z y = Z q = L w = M w = o for the planes with 

 values as above added for fins. 



Take K the same for both planes. We find for such planes 

 and fins as above that 



L p - KUIcos'a + KU{Ty» + M, + \{h + L - I)} 



L q =- 2KUIcosasina -KU{Txy+P} 



M p = - KUIcosasina -KU{Txy + P} 



M q = 2KUIsin 3 a + KU{Tx 2 + M 2 + A(h + U- 0} 



[Note that, from page 225, 

 L w = KTUy, M w = - KTUx, Z w = -- KTU, Z p = + KTUy, Z q = - KTUx 



are due to the fins.] 



Ii + I 2 — I may be proved to be positive. Prof. Bryan points 

 out that M 2 increases stability, and therefore the additions — 

 |(Ii + I2 — I) — to it will also do so. Two transverse planes with 

 fins will give stability in steady motion. Frictional resistances, 

 etc., will again effect the above values. The wash from the 

 front plane to the back may be overcome by placing the back 

 planes on a slightly higher level. 



See pp. 150-164, Stability in Aviation, for /3 =}= °- From these 

 pages we may conclude that bent-up planes are equivalent to 

 the planes /3 = o with fins, and therefore give stability. 



