438 REGULATORY CIRCUITS 



Aircraft Transfer Functions. The aircraft cannot maneuver with 

 large amplitudes at high frequencies. This can be shown from simplified 

 transfer functions of the aircraft relating control surface motion to aircraft 

 motion. The transfer functions can be obtained from transforms of the 

 differential equations which describe aircraft motion. When simplified, to 

 eliminate the short term yawing oscillation term, the transfer function 

 relating aircraft heading to control surface position reduces to the form 

 K/S(l + Ts).^^ K and T depend upon the particular aircraft charac- 

 teristics, and a frequency plot of this function should resemble the plotted 

 data described in the preceding paragraph. 



The general form of the space isolation required by the radar antenna 

 should be the reciprocal of the aircraft response transfer function. The 

 equivalent gain factor of the isolation transfer function ultimately depends 

 upon the amount of isolation needed, the equivalent gain of the aircraft, 

 pilot or autopilot, course computer, and the error presentation as discussed 

 in Paragraph 8-32. 



Gust Disturbances. As an aircraft flies an attack course, it is sub- 

 jected to winds and turbulence or velocity fluctuations in the surrounding 

 air. Turbulence disturbs the aircraft in a random manner, and its general 

 effect is referred to as a gust disturbance. 



Because of their random nature, gust disturbances are best determined 

 by measurement and then described by power density spectra. The data 

 of typical measurements and the associated normalized power density 

 spectra are presented in the following documents: 



{a) An Investigation oj the Power Spectral Density oj Atmospheric Turbu- 

 lence by G. C. Clementson, Report No. 6445-T-31, Instrumentation 

 Laboratory, M.I.T., May 1951. 



[b) A Statistical Description of Large-Scale Atmospheric Turbulence by 

 R. A. Summers, Report No. T-55, Instrumentation Laboratory, 

 M.I.T., May 1954. 



The normalized power density spectra may be applied to a specific 

 aircraft by scaling both abscissa and ordinate. The effect on the tracking 

 loop antenna position and rate may be then found by multiplying the gust 

 power density spectrum by the square of the transfer function magnitude 

 relating the disturbance to the antenna position rate in the channel corre- 

 sponding to the direction that the gust disturbances were measured. The 

 square root of the integral of this product is the rms value of the antenna 

 motion or rate. For most tactical situations the effect of gust disturbances 

 is negligible when compared with other factors and it will not be considered 

 further in this text. For high-speed, low-altitude flights, however, gusts 



i^Actually, the transfer function varies in roll, pitch', and yaw. The most useful transfer 

 functions are those which transform aircraft motion to antenna motion. 



