36 



SMITHSONIAN MISCELLANEOUS COLLECTIONS 



VOL. 62 



V miles per hour 

 U feet per sec. . 

 Normal incidence 

 Xj, 



Am; 



z„ 



^ w 



M.. 



M, 



A 



B, 



C, 



D^ 



£1 •■•■• 



Routh's discr. . . 



m 



Long period, sec. 

 Time to damp, 50;; 

 Time to double. 

 Character 



+ 



76.9 

 112. 5 

 0° 

 .158 

 •356 



•57 

 5.62 



3-2 



192.0 



21 .6 



317.0 



1492.0 



266.0 



59-2 



+ 117X 10" 



50 



34-7 

 8.1 



Stable 



53 



78 



3 



- 3 



+ 3 



-123 



21 



207 



804 



128 



106 



44 



65 



6 



12 



249 



823 



77 



99 



o' 



+ 



+ 



6 

 o 

 o 



3 



o 



16.4X lO'' 



50 



17.6 



II .0 

 Stable 



6 

 3 



1 194 

 245 

 985 

 92 



25 



7 



6 



3 

 o 

 6 



4 

 3.2X 10" 



50 

 15.8 



13-1 

 Stable 



93 

 21 



T59 



444 



72 



36.9 



- 54-0 

 12° 



- . 162 

 o 



- 1. 19 



- 1 .0 

 + 1 .41 



- 60.5 

 21 .6 

 85.1 ■ 



1 50 . o 

 22. 1 

 54 -o 



- . I2X 10'' 



50 

 10.56 



24.7 



Unstable 



The coefficients of the biquadratic computed from the formulae of 

 §9 give for high speed 



21.62D* + 31 7-oZ)'' + 1492.0D- + 266.0!) + 59.2 = o. 

 Each coefficient is positive and Routh's discriminant 



is also positive and equal to 117x10''. The motion is, therefore, 

 stable. The aeroplane if set pitching will return in time to its normal 

 attitude. 



Bairstow has shown that, considering the usual values of the 

 coefficients of the Ijiquadratic, it may be factored approximately, 

 giving : 



The first factor reduces to : 



Z)-+ 14.75/^ + 69.0 = 0, 



D— -~/.s8±T,.8si where i=\''~^. 



This is the well-known condition for a simple damped oscillation of 



period, 



' ^ 27r ^ , 



p= —ry- =1.64 seconds, 



3-83 





' By interpolation. 



