158 



THE CALCULATION OF RADAR DETECTION PROBABILITY 



0.4 



0.6 



1.0 



1.2 



1.4 



1.6 



NORMALIZED RANGE, P=K4(R/Ro) 

 Fig. 3-9 Universal Curves of Average Cumulative Probability of Detection. 



maximum range. This is only part of the story, though. Normally, 

 AR and thus Ap would be made small by decreasing the scan time, which 

 in turn is obtained by speeding up the scan. With a higher scan speed, the 

 number of pulses returned on a scan over the target is reduced. This 

 reduces the factor K approximately through the relation in Equation 3-32. 

 The net result is to give an optimum value of scan speed or scan time which 

 maximizes the range at which a given value of cumulative detection 

 probability is obtained. With a slower scan than this optimum, the target 

 closes too much between scans and there will be too few chances to detect it. 

 With a faster scan, there are not enough hits per scan. The determination 

 of this optimum scan time will be illustrated as part of the following 

 example. 



To illustrate the use of the curves in Fig. 3-9, we shall continue with the 

 AI radar example which we have previously used in Paragraph 3-3 to 

 illustrate the calculation of the single-scan probability of detection for both 

 constant and fluctuating targets. We assume that the target closes on the 

 radar at 2000 ft /sec or about Mach 2. The scan time was assumed to be 

 3 seconds. The range decrement is 3 X 2000 = 6000 ft or 1.0 n.mi. The 

 value of K^''^ was previously determined to be 1.3 while the idealized range 

 is 20.4 n.mi. The normalized range decrement is thus 



Ap = 1.3 X 



1 

 20.4 



0.0635. 



(3-43) 



Referring to Fig. 3-9, the normalized range giving a cumulative proba- 

 bility of detection of 90 per cent for Ap = 0.0635 is p = 0.87. The equivalent 

 actual range is 



