Directivity index of partially random sonobuoy arrays

The directivity index DI of the partially random sonobuoy array described in a previous paper [J. Acoust. Soc. Am. 64, S123(A) (1978)] is analyzed. The analysis is based on the definition of DI as the ratio in decibels of the power received by a single omnidirectional hydrophone of unity gain to the array power normalized to unity maximum gain. The array power is a random variable. Its expected value is used in the definition of DI to define the “nominal DI.” The variance of the array power provides a measure of the variability of the DI among the members of an ensemble. The type of partially random array analyzed consists of N elements arranged in vertical strings of M elements each. With N constant, the variance of the array power tends to increase as M is increased. The increase is the result of the increasingly large contribution to the array power of the side‐lobes at the main lobe elevation, which have a relatively large variance. The effects of the number of elements per string on the nominal DI an...