8 ELEMENTS OF AIRBORNE RADAR SYSTEMS DESIGN PROBLEM 



platform. This capability is essential to the solution of the fire-control 

 problem. 



An analysis of the two-dimensional fire-control problem (Fig. 1-4) 

 illustrates the basic principles. If an aircraft is armed with a weapon 

 which is fired along the aircraft flight line, the weapon position relative 

 to the interceptor // seconds after firing can be expressed 



Rf^ = V,tf (1-5) 



L=Lead Angle 

 = Line of sight Angular Rate 



Fig. 1-4 Air-to-Air Fighter-Bomber Duel Fire-Control Problem in Two-Dimen- 

 sional Coordinates Relative to the Weapon Firing Aircraft. 



where Rfw = future relative weapon position 



Vq = average velocity of weapon relative to fighter velocity 

 // = weapon time of flight (i.e. time elapsed after weapon firing). 



The fire-control problem is solved when the future relative range of the 

 weapon coincides with the future relative range of the target Rft, i.e. Rfw 

 = Rft (at some value of //). 



The predicted future relative target range may be expressed in terms 

 of its components relative to the line of sight 



Rft^ = R- VTRvtf = R- Rtf (1-6) 



Rftn = VTRjf = R4>tf (1-7) 



Similarly, relative weapon range may be expressed 



