PRACTICAL DESIGN CONSIDERATIONS 



509 



1 slope in the 



9-14] 



general, the presence of an asymptotic segment with 

 vicinity of unity gain. 



The foregoing material, then, pro- 

 vides the reasons for the nature of 

 the "typical" airborne radar range 

 transfer function shown in Fig. 9-22. 



In the detailed consideration in 

 Chapter 2 of an airborne radar sys- 

 tem, the dynamic variation of lead 

 collision fire-control parameters was 

 depicted in Fig. 2-45. Range and 

 range-rate plots as functions of time- 

 to-go were given there; when com- 

 pared with the pass-course range 

 function considered here, these are 

 seen to be remarkably comparable 

 in all aspects important to choice of 

 range tracking servo system transfer 

 function. Thus the pass course is 

 seen to qualify equally well for air- 

 function. Thus the pass course 



is seen to qualify equally well for air-to-air interceptor-target range track- 

 ing system considerations. 



If we make a straight-line approximation of the range rate curve of 

 Fig. 2-45 by a zero slope at the — 1266-ft/sec ordinate value to 3.3-sec 

 time-to-go followed by a straight line with a slope of 80 ft /sec^ through the 

 — 1000-ft/sec ordinate value at zero time-to-go (and assume a comparable 

 positive-time function to avoid transients extraneous to the real range 

 tracking problem), the equation comparable to Equation 9-10 becomes 



R^*(s) — ' tJt-. 80(-f-^"3-3 + ^+^"3.3). (9_17) 



s-^jc^ (;oo) 3 



Then, 



1160 sin 3.3 col 



Fig. 9-22 General Shape of Typical 



Airborne Radar Range Tracking Servo 



System Transfer Function. 



R^*is) 



The 



^52.8 

 ^ 160 



•2, —3 corner (see Fig. 9-21) becomes 

 52.8 160 160 



160 



..,3 ' 



CO, 



52. 



3 rad/sec. 



(9-18) 

 (9-19) 

 (9-20) 



(9-21) 



