()^ SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 62 



It is seen that, for the particular aeroplane under consideration, 

 Routh's discriminant and the coefficients of the biquadratic are all 

 positive at high and intermediate speeds. The motion in these two 

 cases is, therefore, stable. 



At low speed, however, we observe that £o becomes negative, 

 indicating that the lateral motion is unstable. That is to say, one at 

 least of the roots of the biquadratic increases with time. In this case 

 Routh's discriminant continues to be positive, but is small compared 

 with its value at high speed. 



It is unfortunate that this lateral instability is associated with the 

 longitudinal instability which was found in Part I to be present at low 

 speed. 



§10. CHARACTER OF LATERAL MOTION 



Bairstow has shown that for the usual values of the coefficients of 

 the biquadratic equation for the lateral motion, the equation in ques- 

 tion mav be factored approximately, giving : 



provided £„ is small compared with B., or D.., and B^Do — Co is small 

 compared with C.,^. 



In our cases, the second condition is not satisfied luit the error made 

 is found by trial solutions to be unimportant. 



High Speed. 



Thus for the high-speed condition : 



First factor, D= — ^^ = —.0665. 



This is a subsidence which tends to reduce the amplitude of an initial 



disturbance to half value in t— ~ '^/ — 10.4 seconds. We may con- 



.0665 ^ 



sider this motion fairly stable. 



For the second factor we have another subsidence given by 



Z? = — -= ^- =—2^.2. 



A.B._ ^ ' 



which reduces to half value in /= ' ^ = ■O'i, second. Such motion 



23.2 



is so heavily damped that it would never be observed on the aeroplane. 



The third factor gives upon substitution : 



^'+ (r:-D:)^+B/-^:C =D= + .967D+..375 = o, 

 or 



D= — .484± 1.07/. 



