9-13] RANGE TRACKING DESIGN EXAMPLE 



9-13 RANGE TRACKING DESIGN EXAMPLE 



As an example of going from the 

 tactical to the practical in prelimi- 

 nary servo-system design^^ consider 

 a bombing aircraft on a constant- 

 velocity straight and level flight that 

 is radar range tracking a fixed 

 surface target as depicted in Fig. 9- 

 18 for which 



/ = time in seconds (/ = 

 at minimum range or 

 crossover) 



V 



505 



o 



Fig. 9-1 



Pass-Course Range-Tracking 

 Problem. 



aircraft horizontal speed in knots 

 H = aircraft altitude 

 Ri = range to target in yards 

 /?o = slant range to target at crossover 

 = fixed ground surface target. 

 The aircraft radar range tracking time function becomes 



Ri = {R^ + {KVtYYi'^ 



yd hr 



(9-6) 



where K = 0.5626 



n.mi. sec 



Equation 9-6 may be normalized to the form 



r[-(-;)T 



(9-7) 



where T = R^IKV. 



As was suggested earlier, an asymptotic-segment representation of the 

 upper bound of the excitation function transformed to the frequency 

 domain that is reasonably accurately located provides the amount of detail 

 useful in the engineering design of a servo system transfer function. Since 

 our objective is to determine the upper bound of the magnitude on a log- 

 magnitude log-frequency plot, with any errors resulting from approximation 

 methods such that a servo-system transfer function based upon the analysis 

 will be conservatively designed, the tedious details associated with close 



2''Pass-course angle tracking is treated in a comparable manner in C. F. White, Tactical to 

 Practical in Preliminary Servo-System Design, NRL Report 4879, February 1957. 



