436 REGULATORY CIRCUITS 



Under these conditions a major portion of the aircraft motions took place 

 at several relatively well defined frequencies. Rolling motions predomi- 

 nated; these took place at frequencies between 0.5 and 3.0 rad/sec, with 

 maximum rolling rate amplitudes in the range of to 20 deg/sec. Also 

 evident is a yawing oscillation at a frequency of 0.5 rad /sec, and a maximum 

 yawing rate amplitude of 1.2 °/sec, and a small pitching oscillation at a 

 frequency of 6 rad/sec and a maximum pitching amplitude of 2° /sec. 



Sinusoidal Representation of Disturbances. This method is more 

 useful in determining the stabilization control loop specifications. Specifi- 

 cally, this information may be obtained from actual time responses of a 

 simulated aircraft on an analog computer as was shown in the preceding 

 discussion. Portions of the time responses may be approximated by sine 

 waves, and the amplitudes and frequencies of the sine waves can be recorded 

 for various aircraft motions from several different courses. 



To study the effect of aircraft motion on tracking-line stabilization, the 

 aircraft motions are converted into motion with respect to the axes of the 

 antenna gimbals. Usually, the antenna has two gimbals. ^^ The azimuth 

 gimbal allows the antenna to rotate about an axis parallel to the aircraft's 

 vertical axis; the elevation gimbal permits the antenna to nod up or down. 

 The basic angle and angular rate relationships for such a two-gimbal 

 system are shown in Fig. 8-27. 



Aircraft 

 Fore -and -Aft 



Dire 



action 



Aircraft Roll, Pitch, Yaw Rates 

 l^= Azimuth Gimbal Angle 

 dp = Elevation Gimbal Angle 



Transformations 



Antenna Rates Due to Aircraft Angular Rates: 



Azimuth coa = oJ;< cos 6^ sin 8,+ co^ sin d^ sin d, + co, cos e, 



Elevation w^ = - co^ sin 0^ + o>y cos Q^ 



Fig. 8-27 Angle and Angular Rate Relationships for a Two-Gimbal Radar 



Antenna. 



When the antenna tracking lead angle is large, the aircraft rolling 

 motions appear as azimuth and elevation disturbances as is demonstrated 

 by the cox terms in the transformation relationships in Fig. 8-27. This fact 



"In some missile applications it is necessary to provide a third gimbal to space-stabilize the 

 antenna in roll. This is not considered here. 



