4-14] SOLUTIONS TO THE CLUTTER PROBLEM 225 



Since in search it is desirable to sweep out a large area, the problem is 

 concerned primarily with small depression angles. The variation of received 

 clutter power with range will then be of the form shown in Fig. 4-34, and 

 will be given by Equation 4-61 : 



UtYR' 



(4-72) 



In this we may insert the values of A and F given by Equations 4-60a and 

 4-62, respectively. The horizontal beamwidth <!> and the gain of the radar 

 antenna may be expressed by 



$ = y^ (4-73) 



G = ^^ (4-74) 



where Iw and 4 are the horizontal and vertical antenna apertures, respec- 

 tively, and ka and h are constants of the antenna design. If we adopt the 

 form of relation given in Equation 4-65 for a^, 



(T« = ^oA (4-75) 



then Equation 4-61 becomes for the received clutter power 



^c - (^,^3) (4-76) 



where kc = kah^h/i^T)' 



Fc = 6, R< Re 

 Fc-^6{Rc/R)\ R> Re 

 Re = 2hHiiio/\ = transition range for clutter 



as in Equations 4-62 and 4-64. kc is primarily a function of local wind speed, 

 while //i/io is dependent rather on wind history, but may be forecast with 

 reasonably good accuracy.^* 



Similarly, for the power Pt of the target echo, we have from Equation 4-1 



If the target is a surface target of uniform section and height Ht, then F^ is 

 to be replaced by F of Equation 4-62, with its transition range, Rt, given by 

 Equation 4-63 



Rt-^^-^ (4-78) 



A 



3^W. J. Pierson, Jr., G. Neumann, and R. W. James, Practical Methods for Observing and 

 Forecasting Ocean Waves, H. O. Pub. No. 603, U.S. Navy Hydrographic Office, 1955. 



