62 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 62 



§7. NEGLECTED COEFFICIENTS 



The changes in lateral force Y due to angular velocity of roll and 

 yaw, represented by the coefificients Yp and Yr, are neglected as un- 

 important. The surface of the aeroplane is fairly symmetrical about 

 the center of gravity and it is unlikely that any appreciable lateral 

 force could be created by any small angular velocity p or r. In the 

 calculations to follow Yp and Yr are made zero. 



The products of inertia are also neglected as not important and 

 difficult to estimate for an actual machine. 



§8. INDEPENDENCE OF THE LONGITUDINAL AND 

 LATERAL MOTION 



It is seen on figure 20 that the values of X, Z, and M are some- 

 what changed as the aeroplane yaws, and to this extent it is not strictly 

 correct to consider the lateral motion separately. We may imagine 

 that if there be set up a combined oscillation about the flight path in 

 roll, yaw, and side slip, the aeroplane will be influenced to take up an 

 oscillation in pitch of the nature of a forced oscillation. However, 

 any oscillation in pitch has already been shown to die out rapidly 

 (since the longitudinal motion is stable and strongly damped). We 

 may then consider the pitching induced by yawing, etc., as of the same 

 nature as that caused by any accidental disturbance of longitudinal 

 equilibrium, such as might result from gusty winds, shifting of 

 weights, or the firing of a gun. If the longitudinal motion be stable, 

 that stability should be quite independent of the nature of any dis- 

 turbing agent which gives the initial amplitude to the oscillation, pro- 

 vided the phenomenon of resonance is not present. That is, if the 

 natural period of the lateral motion, if oscillatory, happen by some 

 remote chance to be equal to the natural period of the longitudinal 

 oscillation, it may be possible for a machine which is unstable laterally 

 to seriously compromise its longitudinal stability. 



If the lateral motion be stable and, if oscillatory, damp out quickly, 

 it is difficult to see how any marked disturbance of the longitudinal 

 motion can be induced by the lateral motion. 



In circling flight, there is a constant angular velocity of yaw and 

 probably some side slip. In this case, the lateral and longitudinal 

 motions are interdependent, and the methods of calculation of this 

 paper will not apply. Indeed, we should have to combine the six 

 general equations of motion giving rise to a single equation of the 

 eighth order, which must then be solved for all the roots. In the 



