. Airborne radar. Airplanes; Guided missiles. 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 and rad/sec, with maximum rolling rate amplitudes in the range of 0 to 20 deg/sec. Also evident is a yawing oscillation at a frequency of rad /sec, and a maximum yawing rate amplitude of °/sec, and a small pitching oscillation at a frequency of 6 rad/sec and a maximum pitching amplitude of 2°/sec. Sinusoidal Representa
. Airborne radar. Airplanes; Guided missiles. 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 and rad/sec, with maximum rolling rate amplitudes in the range of 0 to 20 deg/sec. Also evident is a yawing oscillation at a frequency of rad /sec, and a maximum yawing rate amplitude of °/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;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 transf
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