126 THE DEVELOPMENT OF WEAPONS SYSTEM REQUIREMENTS 



perfect aiming would result. Practically, however, the measured and 

 computed quantities (Ro, Lm, Tc, Lc) are not correct for reasons previously 

 discussed. Thus the computed error eH,c differs from the actual aiming 

 error. The contribution of each source of error to this difference may be 

 expressed. 



Aen = (den,c/dx)Ax (2-65) 



where Aen = the steering error due to error in the quantity x 



den.c/dx = partial derivative of the steering error with respect to the 

 quantity x 



Ax = error in the measurement of the quantity x. 



As an example, the sensitivity of the steering error to an error in measured 

 lead angle may be derived from Equations 2-62 and 2-59 as: 



den.c/dLM = (deH.c/dLm) + {den ,c / dr ,c){dT .c / dLxj) 



[ Rn cos Lm 1 [" 

 F,T+Ro\[ 



r RmG ■ r 

 cos L\i : — sm Lm 



Rm 



(2-66) 



It should be noted that the sensitivity is a variable quantity during an 

 attack course; it also varies from one course to another. Consequently the 

 sensitivities must be examined for the range of attack courses. In this 

 discussion we will confine our attention to the two courses assumed (head-on 

 and 80° off the nose). 



The values of the input variables and their derivatives are shown in 

 Fig. 2-45. The error sensitivity factors for each of the assumed attack 

 courses are shown in Fig. 2-46. It will be noted that dynamic variations of 

 the input quantities are greatest for the attack which terminates near the 

 target's beam; thus, predictable bias errors arising from dynamic lags will 

 be greatest for this course. On the other hand, the effect of errors in angular 

 rate and lead angle is greatest for head-on attacks. This fact is particularly 

 significant because angular rate errors tend to be the most important source 

 of system errors. 



Using the foregoing error data, an error specification may be derived in 

 the following manner. For a head-on attack, the total system aiming error 

 must be held below 7° to ensure that the missile will hit a maneuvering 

 target (see Fig. 2-44). For purposes of deriving a tentative specification, 

 we may split this error among the various error sources by appropriate 

 manipulation of the following expression: 



Total system error = pilot requirement + 2(6e//,c/^>^i)Axi 



+ 2V2[(d6/,.c/a^,)<r.v,P (2-67) 



