84 



SCATTERING AND ABSORPTION OF MICROWAVES 



where «/i is the first order Bessel function of the first 

 kind. The maximum of a occurs for 6 = 0, when 

 equation (8) reduces to 



B' 2 H 



4ttV 

 X- 



(9) 



This sharp maximum of cr at 6 = is the phenom- 

 enon of specular reflection. The average value of 

 er over all values of 6 turns out to be 



1 , 

 -ira- 

 2 



(10) 



This result is independent of wavelength and suggests 

 that a large number of specularly reflecting surfaces 

 oriented at random will have a cross section inde- 

 pendent of X, or that a few surfaces of rapidly chang- 

 ing orientation may have this property. The lack 

 of dependence of wavelength of aircraft radar cross 

 sections might be understood on the basis of these 

 results. 



10.3 



SHIP TARGETS 



A ship being a collection of both complicated and 

 flat surfaces, a rigorous computation of the radar 

 cross section of any given ship of known design is 

 not feasible. Nevertheless, the Naval Research 

 Laboratory workers have been able to give a good 

 account of these problems. 37 " 76 ' 388 - 392 ' 417 - 421 



The path factor in the formula (6) raised to the 

 fourth power is 



sin S ' 



IJ = 6 [ 



1 



35 



(4 — cos So) 



(11) 



vhcre 



So = 



MhH 

 Xd 



hi = antenna height, 

 H = height of ship above water 

 including superstructure. 



The above result follows by integrating the received 

 power over the height H, assuming perfect reflection 

 from sea. 



It is seen in equation (11) that whether 5 < ir, 

 the region called the "far zone," or So > it, the "near 

 zone" (short ranges), materially affects the qualita- 

 tive behavior of the factor A%. In the latter region 



At ^ 6 . 

 The radar cross section of a ship which does not 

 exhibit marked specular reflection is given roughly by 



(12) 



where a = dimensionless constant dependent 



on ship design, 

 B = the breadth of the aspect under 



observation, 

 H = height of ship above water including 



superstructure. 



The approximate values of a to be used are indicated 

 in Table 3. 



Table 3. Ship targets. 



Type of ship 



Remarks 



In Tables 4 to 7, values of a computed from 

 equation (12) are called theoretical values. Experi- 

 mental values are computed from observations made 

 by the Naval Research Laboratory workers with 

 each quantity the mean of several observations. The 

 200-mc experimental result is unexpectedly low while 

 the values at the higher frequencies are a little 

 higher than would be anticipated. This points to the 

 existence of some specular reflection for this ship, 

 which would not be surprising in view of its great 

 size. Considering the uncertainty in the experimental 

 values, the agreement with the theoretical results is 

 not unsatisfactory and bears out the assumed 

 dependence on wavelength. 



The aircraft carrier shows pronounced specular 

 reflection at the direct broadside aspect, particularly 

 at the higher frequencies. These values of a are 



Table 4. Radar cross section of a battleship (BB-63), 

 broadside aspect, a = 0.1, B = 270 m, H = 24 m. 



