110 THE DEVELOPMENT OF WEAPONS SYSTEM REQUIREMENTS 

 The commanded heading differs from the correct heading by 



.c = £c + 0, - io = [l + P-'^] A«, + \^^^] ^H 

 I ^F COS Ld] L^fcosLdJ 



+ r^^i^lA^.. (2-44) 



l^F cos Ln] 



The error signal presented to the pilot is the difference between the 

 commanded heading and the actual heading, 



A^pF - ipFc - ^F. (2-45) 



It is assumed that the pilot follows the commanded heading with an error 

 whose standard deviation is 5°. 



The total heading error with respect to the correct heading is then 



\_RFf cos Ld] ll^F cos LdJ [^fcosLdJ 



(2-46) 



since the closing rate, R, may be expressed 



Cf.r 



-R = VtCosO -\- Vf cos Ld. (2-47) 



If the vectoring errors are assumed to be independent, we may write the 

 standard deviation of the collision course heading error as 



[V^^rrJ -^[FFCosLn""''') ^\Ff cos Ln''''') + "'H 



(2-48) 



where aa = iARa)/R. 



The evaluation of this expression for various values of lock-on range from 

 8 to 30 n.mi. is given in Fig. 2-32 for the estimates of measurement uncer- 

 tainty derived for the AEW system (Paragraph 2-21). The curves may be 

 interpreted in the following manner. For range to the target R and an 

 angle off the target's nose 6: if the proper collision-course lead angle for 

 this condition is Ld (Fig. 2-30) then the vectoring errors will cause the 

 interceptor lead angles to be normally distributed about the value Ld with 

 a standard deviation of cr^.r degrees. The magnitude of the heading error 

 increases very rapidly as the range decreases. This will be shown to have 

 detrimental effects on the AI radar gimbal angle requirements for short- 

 range lock-ons and on the ability to convert a short-range lock-on into 

 a successful attack. 



The large magnitude of the heading errors for forward-hemisphere 

 attacks is characteristic of any guidance system employing "prediction". 

 Collision vectoring is such a system; it attempts to guide the interceptor 

 towards a point in space where the target will be at some future time. 



