100 THE DEVELOPMENT OF WEAPONS SYSTEM REQUIREMENTS 



similar computation may be made using scan number 2 and scan number 12. 

 If the errors for the two computations are independent, we may improve the 

 heading approximation by ^2 by sim.ply averaging the two computations to 

 yield for a straight-line target: 



a^T = 14.5 /V2= 10.2°. (2-31) 



Such improvement is obtained at the expense of increased dynamic lags 

 when the target maneuvers. 



Many other smoothing schemes could be used. However, for present 

 purposes, it is reasonable to assume that the hypothetical AEW system can 

 provide heading information with an accuracy of the order of 10° (standard 

 deviation). The suitability of this figure will depend upon the sensitivity 

 of interceptor performance to this figure. 



From the foregoing analysis, the accuracies of the AEW radar system 

 with which the interceptor system must be compatible are approximately 



Position Error: or = 2 n. mi. radial error, rms (2-32) 



Velocity Measureynent Error: avr = 50 knots rms (2-33) 



Heading Measurefnent Error: g^t = 10° rms (2-34) 



For the vectoring problem we are interested in the relative position 

 inaccuracy between the interceptor and the target. The total relative 

 radial position error, <trt, between two objects is 



(TRT = ^^ (TT = 2.8 n. mi. (2-35) 



As will be shown later (Paragraph 2-25) it is convenient to express the 

 total relative position error in terms of two components: (1) a component 

 (TRR along the line of sight between target and interceptor and (2) a com- 

 ponent, (TRa^ normal to the target sight-line, 



where (trr = aRT/yjl = 2 n.mi. (2-36) 



aRa = cTRT/^I2 = 2 n.ml (2-37) 



The position, velocity, and heading information is employed to vector 

 interceptors on a collision course with assigned targets (Paragraph 2-11 and 

 Equation 2-4). 



2-22 INTERCEPTOR SYSTEM STUDY MODEL 



The design goal for the kill probability of a single interceptor has been 

 derived as 0.5. We shall now study the problem of specifying the require- 

 ments of an airborne intercept (AI) radar and fire-control system that will 

 allow the interceptor to achieve this goal within the limitations imposed by 

 other system elements and the operational environment (Step 3, Fig. 2-2). 



