2-27] ANALYSIS OF THE CONVERSION PROBLEM 125 



and computed quantities in this expression were correct and if the pilot flew 

 the aircraft in such a manner as to reduce the computed error to zero, then 



Random errors arise from several main sources. First of all are the 

 measurement uncertainties caused by the basic limitations of the measuring 

 device. The angular measuring accuracy of a radar, for example, is limited 

 by beamwidth as was indicated in the discussion of AEW radar require- 

 ments.'^ Mechanical and electrical component tolerances also contribute 

 to errors of this type. 



The system noise sources also contribute to random errors. For example, 

 the finite dimensions of a radar target introduce time-dependent uncer- 

 tainties into the measurements of range and angle (see Paragraph 4-8). 

 Similarly the vagaries of airflow past the aircraft may introduce random 

 noise errors into flight data measurements. These latter would aff^ect the 

 computation of Rq- 



Random aiming errors also are caused by the pilot's inability to guide 

 the aircraft on exactly the course indicated by the displayed error infor- 

 mation. Paragraph 12-7 will discuss this problem in some detail. Generally 

 speaking, however, if the pilot is presented with an error signal which is 

 band-limited to about 0.25 rad sec'^ and if the error signal, is contaminated 

 by random noise which is bandlimited to about 1 rad /sec, then the pilot can 

 steer the aircraft with a random error which has a standard deviation 

 approximately equal to the standard deviation of the noise. Thus the pilot's 

 contribution to the total aiming error may be written: 



(Tpf = (tn (2-64) 



where cpf = standard deviation of the pilot's flyability error 



o-iv = rms value of the noise on the error signal display. 



To illustrate how the error specification might be developed we shall 

 consider two cases: (1) a head-on attack and (2) an attack which begins at 

 an angle oflF the target's nose at launch of 80°. 



The method for attacking the problem can be outlined as follows. As 

 already mentioned. Equation 2-62 is designed to provide a reasonable 

 approximation of the actual heading error. In fact, if all of the measured 



i^Actually, as will be indicated in Chapter 5, the problem is a good deal more complicated 

 than is indicated by this statement. Signal-to-noise ratio and observation time also strongly 

 affect the angular accuracy. However, for fixed values of these latter parameters, the state- 

 ment is substantially correct. 



'^The bandwidth of the error signal depends upon the type of attack trajectory flown. A 

 lead-collision course is a straight line; hence the effective bandwidth of the input guidance 

 signals is very low. Curved-course trajectories such as lead-pursuit have higher effective 

 guidance signal bandwidths. Chap. 12 of the "Guidance" volume of this series presents an 

 excellent discussion of the concept of treating a guidance trajectory in terms of its frequency 

 spectrum. 



