WILSON— AEROPLANE ENCOUNTERING GUSTS. 235 



velocity of yaw without much bank, but for the divergent motion the 

 bank is a serious matter for even moderate side-slip. 



35. The initial conditions (/>=/) = 2; = r = o give 



0= .02436C1 — 8.542C00 — .3268C03 + 1.215C, + 1\„ 

 o = — 8.326C01 4- 3-797^2 + 1041C23 + 564-8Co4 + h-o, 



0= .2571C01 + .OO5897C0 — 6.37lC,3 + IO.56C,, + Iro. 



These equations must be solved for the four constants C. 

 Qi = — -9839^*0 — -I i48/'^o + .000740A.0 — .02797! ro, 

 C22 = — .000149/^0 4- -I I70^'«o — .0000342/1.0 — .01 163/ro, 

 C3 = — .01595/^0 — -002 153/'^ — -0007067,0 + -0396/ro, 

 Co4=. 01468/^0 + .ooi466/'^o — •00045377,0 — .07201/ro. 



36. The equations from which the particular solutions are ob- 

 tained are (since Yp = Np=^Yr = o) : 



Av= (7)8,, — A) V, + Lph,,p, + (LrSo, -f A^r83i)^i, 



Acf> = D8,,v,+Lp8,,p,-\-{LrB,o-{-Nr8s2)r^, (14) 



Ar = DB,,v, -f LpS,,p^ + (L^S^s + Nrh3)r^, 

 or 



Az'=(— 6407)3 — 95227)- — 346ior> -1-854)2/1 -f (7134^ 



-t- 2732)/^, — ( 1 125607)- + 1 1047007)) r„ 

 A<^=(— 59-55^ — 26.55)^^^'! +(—221507)- — 139707) 



— 34510)/', -I- (3895^' + 9707) -f 3062)^,, 

 Ar= (—32.847) — 280.7 )7)-z/, + (— 9030)/'! 



4- (—9927)3 — 87247)- — 21037) -f854)r„ 

 with 



A = 25927)* 4- 237807)3 4- i8ooo7}- 4- 346107) — 854. 



Motion in Lateral Gusts. 



37. We shall take as before the type /(i — e-''^) for that of a 

 single gust. 



