Figure 30. Schematic showing the restriction on line-of-sight 

 by curvature of the Earth, h = height of radar, 

 r = Earth's radius, and d = range by line-of-sight. 



increasing height. The distance to the horizon for a radar experiencing 

 this refraction can be given as (Skolnik, 1962, pp. 506-509): 



d = v'Zkah (10) 



where a is the radius of the Earth. The term Ka is then an effective 

 radius of the Earth. For k = 4/3, equation (10) can be conveniently 

 written where d is measured in statute miles and h in feet as 



d (statute miles) = /2h(feet) (11) 



or 



h(feet) = (dfstatute miles]) 2 



where d is the distance to the horizon, and h the height of the radar; 

 for d = 5.28 kilometers (3 miles), then h = 1.4 meters (4.5 feet). 



For most radar installations, this antenna elevation is easily ob- 

 tained. However, further restrictions on the useful distance that radar 

 can view waves are imposed because the radar scatterers ride on the for- 

 ward face of the longer gravity waves. Thus, with an antenna at the 

 minimum required height as determined above, waves would not be seen out 

 to 5.28 kilometers because of shadowing of the radar scatterers by nearby 

 gravity waves. An example of the radar antenna at an elevation of 4.6 

 meters (15 feet) is shown in Figure 31 where two waves only 1.6 kilometers 

 (1 mile) from the radar with 1.5 meters (5 feet) in height are inspected. 

 Geometry shows that only the top 23 centimeters (0.75 foot) of the second 

 wave is seen by the radar. Unless strong winds were present, the return 

 from this small area of the wave would likely give a weak radar return. 

 Return from following waves farther from the radar would give an even 

 weaker return; therefore, the effective range for this installation is 

 about 1.6 kilometers. 



33 



