164 



PROPAGATION ASPECTS OF EQUIPMENT OPERATION 



One-way, radio gain: 



Pi 4 



Two-way, radar gain: 



P2 9 ., „ h'h,' 



F2 Q rJh'h^T 



— = yTir . 



Pi \hl^ 



(11) 



(12) 



Hence for maximum range, replacing Pi by Pp, 

 and P2 by P„in , 



One-way, 



V-* min / 



\lhrh,\^GiG. 



(13) 



Two-way, 



''rnfiY 



_ 8 l97r<7/( 



X"* min/ 



(14) 



The maximum range now depends on the antenna 

 heights and on the target height. 



7.3.4 



Radar Cross Section 

 of Surface Craft 



Effective Height of Targets. Since the field varie.s 

 considerably with height for a low target, the 

 scattering by even simple geometrical objects 

 reciuires integration. The formulas for radar in 

 Section 7.3.3 apply to a point target with radar 

 cross section a at an effective height /le^. 



In the case of a cylinder of radius a and length 

 H, the radar cross section in a uniform field is 

 a = 2TraH-/\. Under ojx^rating conditions the field 

 is not uniform but a feasiljle ajDproximation may be 

 obtained by using the preceding value of a- and a 

 value of /)2 equal to the average value of the target 

 height. 



The i-adar cro.ss section of a ship is a complicated 

 problem which is not discussed here. 



Maximum Range 

 Versus Height Curves 



By the method of Section 5.6.6 (see also Sections 

 6.5.2 and 6.8.4), maximum range versus height 

 curves can be constructed for various values of A. 

 These are of importance chiefly for low-angle aircraft 

 coverage. If the performance figure, (Pp/Pmin)^-, 

 is known, equation (5), in Chapter 5, defines the 

 relation between cr and A so that a can be taken as 



the curve parameter instead of A. Equation (5), 

 Chapter 5, can be written 



20 log A = -5Iog^G'2-51og<7-51ogi^. 

 P • 9X- 



(15) 



20 50 100 



MoiirTium Range in Kilometers 



Figure 5. ^Maximum range ver.sus height curves for 

 variou-s targets. 



A set of curves for a 10-cm radar is given in 

 Figure 5 for a transmitter height of 30 meters. The 

 curve corresponding to o- = 31 square meters is indi- 

 cated. The corresponding value of 20 log 4 = —130 

 was found from equation (15), using the value of 

 218.4 db as the performance figure. 



For a ship with an effective height of 18 meters, 

 Figure 5 gives the value of 20 log A at various dis- 

 tances. With the aid of equation (5), in Chapter 5, 

 the power P-i returned to the radar by the ship at 

 these distances can be found, using the following 



