8-24] AIRCRAFT MOTIONS 437 



is important because the rolling rates can be quite large relative to the 

 yawing and pitching rates (see Fig. 8-26). 



When the sinusoids representing aircraft motions are transformed into 

 equivalent motions in antenna coordinates, results like those shown in 

 Table 8-3 are obtained.^^ These results are typical of what might be 



Table 8-3 ANTENNA DISTURBANCE FROM 

 AIRCRAFT MOTION OF FREQUENCY c^d 



obtained for lead angles of 45 deg from a large sample of the type of 

 simulation data displayed in Fig. 8-26. It is assumed that the magnitude 

 of this motion could disturb either channel of the tracking control loops 

 at any time without further attenuation. 



It should be emphasized that in a missile system or in an autopilot- 

 controlled aircraft, these motions can be calculated by considering the 

 equations of aircraft motion in three dimensions as it follows a prescribed 

 course, assuming that the aircraft and autopilot design are known well 

 enough to be described mathematically. The resulting data can also be 

 approximated by calculating the aircraft frequency response from its design 

 equations; this is often done. Although the computations may be simplified 

 through the use of matrix notation and block diagram representation, the 

 cross-coupling between the control loops is complex and nonlinear because 

 of trigonometric functions involved, and it is difficult to interpret except for 

 simple cases which are discussed in the next section. The task becomes 

 more difficult, if not impossible, when a human pilot is involved because the 

 human transfer function is not defined to a usable degree of accuracy or 

 with sufficient reliability necessary for realistic results. Therefore, when 

 available, analogue simulation is the most propitious method of obtaining 

 information about aircraft motion in space with or without autopilot 

 control. 



i^In practice many more values should be used because the nature of these disturbances is 

 essentially random and a large sample should be made to obtain representative data. Note, 

 for example, that a single frequency may have different amplitudes at different times. 



