THE PROBLEM 
Evolve sonar array designs to optimize beam formation with 
various types of conventional or novel arrays, with plane 
and curved wavefronts; and derive directivity functions for 
general arrays which may be very large in terms of wave- 
lengths, and may have an arbitrary distribution of elements. 
The elements may be arranged discretely or continuously; 
the arrays may be one-, two-, ar three-dimensional. 
RESULTS 
Expressions are presented which allow the determination of 
directivity patterns for any kind of array, conventional or 
novel. 
RECOMMENDATIONS 
1. Employ the general directivity function to find array 
directivity patterns not now available. 
2. Program the general directivity function for an electronic 
computer. 
ADMINISTRATIVE INFORMATION 
Work was performed by the author, a member of the Special 
Research Division, under AS 02101, S-F001 03 04, Task 
8051, NEL L3-2, as a portion of the sonar techniques pro- 
gram. The report covers work performed mostly between 
June and September 1960, and was approved for publication 
28 November 1961. 
The author wishes to thank Dr. C. J. Krieger for his val- 
uable suggestions, many of which have been incorporated 
into the report. 
0 (HU MN 
0301 0040553 
