440 REGULATORY CIRCUITS 



8-26 SEARCH PATTERN STABILIZATION 



The space reference for the search pattern control loops is derived from 

 a vertical gyro. The accuracy of the vertical gyro in maintaining a true 

 vertical need not be extremely good; available vertical gyros provide 

 sufficient accuracy for stabilizing the antenna search pattern during the 

 relatively short times that a particular target is being sought. The vertical 

 gyro used has two degrees of freedom and is provided with position detec- 

 tors that measure the aircraft pitch and roll angles with respect to the 

 vertical. Except for some missile applications, yaw angles are generally not 

 measured because the aircraft yaw motions are better controlled and the 

 search pattern is usually much wider in a horizontal direction (see Para- 

 graph 2-26). 



8-27 SEARCH STABILIZATION EQUATIONS 



Because the antenna motion of a two-gimbal antenna does not include 

 roll correction directly, the aircraft roll motion must be converted into the 

 proper azimuth or elevation commands for the two-antenna control loops. 



The exact transformation of aircraft motions to antenna commands is 

 rather complex as shown by the following formulae: 



sin Ea = sin As cos Es sine/) 



— (cos As cos Es sin 6 — sin Es cos 6) cos 4> (8-28) 



sin Aa cos Ea = sin As cos Es cos <^ 



-f (cos As cos Es sin 6 — sin Es cos 0) sin (8-29) 



where Ea is the elevation antenna angle command to move the antenna 

 with respect to the interceptor 



Aa is the azimuth antenna angle command to move the antenna 

 with respect to the interceptor 



Es is the elevation search angle with respect to space 



As is the azimuth search angle with respect to space 



</> is the aircraft roll angle in space 



d is the aircraft pitch angle in space. 



It is possible to mechanize these equations to within a few ininutes of arc^^ 

 by using several resolvers, as shown in Fig. 8-28; but to simplify the 

 mechanization, the transformation equations are often simplified. This 

 can be done in several different ways. One of the approximations which 



2^This inaccuracy is due to components, principally the resolvers. 



