122 THE DEVELOPMENT OF WEAPONS SYSTEM REQUIREMENTS 



Using Equations 2-52, 2-53, 2-56 to eliminate velocity terms in Equations 

 2-50 and 2-51 and rearranging terms, we obtain 



R -\- RT- RocosL = (2-57) 



sin L = {RT!Ro) d. (2-58) 



The fire-control system must solve two problems. It must provide (1) a 

 signal for automatically firing the missiles at the correct point, and (2) an 

 aiming error signal for the pilot or autopilot. 



The i\I radar measures range, range rate, lead angle, and space angular 

 velocity of the line of sight (R^f, Rm, L:,t, ^.i/)-'' Aircraft speed and altitude 



may be combined with known missile performance at the preset time of 

 flight to obtain Rq (see Equations 2-54 to 2-56). 



The measured target inputs and the computed missile characteristics 

 may be substituted into Equations 2-57 and 2-58 to obtain 



„ — Rm + Ro cos L^f ^ , . ... > ,-, -n\ 



Jc — -■ (computed time-to-go until nnpact) {^-^yj 



Rm 



sin Lc = I R.\[-^] 6m (computed correct lead angle). (2-60) 



Firing occurs when 



// (preset). (2-61) 



A steering error signal is obtained by taking the differences between the 

 sines of computed and measured lead angles and multiplying this difference 

 by a sensitivity factor (Ro cos L) /(Ro -\- VfT). This factor causes the 

 computed angular error signal to be a close approximation of the actual 

 angular aiming error. Thus, the computed steering error is 



tHc = [R^^ cos Lm\Ri^ + /VTc)][sin L, - sin L.m]. (2-62) 



Both the azimuth and elevation error signals are computed from an 

 expression of this form. 



Equations 2-59 to 2-62 define the fire-control and tracking problems that 

 are to be solved by the AI radar and fire-control system. The precision 

 required of this solution is determined by the angular aiming tolerances 

 corresponding to the selected value of preset time-of-flight. 



For the purpose of developing a representative set of accuracy specifi- 

 cations we shall select 10 seconds for the preset time of flight //, which 

 corresponds to a relative displacement at impact of Ro — 6800 ft. An 

 inspection of Fig. 2-42 shows this is a reasonable choice since firing will occur 

 near the center of the allowable launch zone for all angles off the nose at 



'-The subscript M denotes a measured quantity. 



