2-27] 



ANALYSIS OF THE CONVERSION PROBLEM 



121 



target's nose. In a lead-collision system, missile launching occurs auto- 

 matically at such a range that the missile time of flight to the impact point 

 equals a preset constant. The value of this constant may be chosen to 

 utilize the best characteristics within the allowable launching zones. For 

 a given angle off the target, the lead angles required in a lead-collision 

 system correspond closely to the collision vectoring lead angles — a fact 

 which is helpful in solving the conversion problem. 



Lead-collision geometry is shown in Fig. 2-43. Solution of the fire-control 

 triangle yields 



Relative Range at Impact 



V^iT-t,) 



Missile Average Velocity 



Relative to interceptor 



During Time of Flight, ff AV Interceptor 



T = Time to Go Until Impact 



Fig. 2-43 Lead-Collision Geometry: Two-Dimensional. 



R^ y^T cos 6+ VtT cos L^- V^tf cos L (2-50) 



VtT sin d = {V,^T+ V^tf) sin L. (2-51) 



The component of relative velocity along the line-of-sight is 



R ^ -Frcosd - Ff cos L. (2-52) 



The component of relative velocity perpendicular to the line-of-sight is 



Rd = Ft sin d - Fp sin L. (2-53) 



By definition of a lead collision course 



// = a preset constant. (2-54) 



From the definition of missile characteristics for straight-line flight 

 (Fig. 2-6) 



F^ =/(Ff, altitude,//). (2-55) 



Thus, for a fixed time of flight and known speed and altitude conditions 



FrJf = Ro = constant. (2-56) 



