Equation (4) is also valid for a nonspherical curved surface, in which case 

 r is the geometric mean of the two principal radii of curvature. These 

 shapes adhere to this direct relationship if the diameter of the shape per- 

 pendicular to the incident beam is greater than the incident wave length. 

 A direct relationship also exists between the disc at random orientation 

 and its radar cross section and it can be shown [5] that the average ef- 

 fective echoing area of simple shapes in random orientation is given by: 



<x=0.5A 



where A is the total physical cross-sectional area of the aggregate of 

 surfaces. It is not difficult to imagine the face of an iceberg as being 

 shaped similar to an aggregate of concave and convex curved surfaces of 

 diameter greater than 1.3 inches (X-band wave length); in fact, the 

 processes of melting leave an iceberg with a pocked-like micro morphology. 

 Based on these arguments an idealized iceberg model surface may be de- 

 fined as an aggregate of perfectly conducting surfaces larger than 1.3 

 inches in diameter. The reflection coefficient of these conducting shapes is 

 1 .0 and the ratio of effective echoing area to cross-sectional area is given by : 



f=0, (.3) 



These considerations lead to the computation of iceberg effective area 

 coefficient and reflection coefficient. At the maximum range of detection 

 the free space radar equation becomes : 



Pmia G-X-a 



= (u) 



Pt (47T) 3 /? 1 ,,,,, 



where P min is the minimum discernible signal. Substituting equation (1) 

 for R mRX and transposing we have the expression for the ratio of effective 

 echoing area to actual area : 



a P min (4,r) 3 K 



I = ~YmT (7) 



By substitution of the following average values for terms: 



Absolute Antenna Gain=10 3 

 Wave length =.032 meters 



P min =10- 12 watts 



P t =10+ 4 watts 



K =3.8Xl0 13 ydyft 2 



= 2.85X10 14 m 2 



t his expression becomes 



^ = 0.0.")ii. (8) 



. 1 



62 



