An automated solution for the wide band sonar equation

The Solution of the sonar equation for wideband echo-ranging systems requires the use of Urick´s generalized form of the sonar equation, and necessitates laborious computation of many frequency-dependent quantities in the equation. The solution has been automated using standard digital computer techniques, and results in a frequency-range contour map from which the echo-to-interference ratio can be seen. The fundamental use of the solution is to assess the effectiveness of proposed target strength experiments with a variety of source, receiver, and operational parameters. However, with the addition of detection thresholds, the solution can map out a frequency-range detection contour. Examples are presented to illustrate the (known) poor performance of omnidirectional sources and receivers, and begins with the use of a SUS explosive sound source. The example continues by demonstrating the improvements which may be achieved by the addition of receiving directivity, and concludes with the analysis of a measurement system using another impulsive sound source, Hydroshock(R). This system can effectively measure submarine target strength throughout the entire sonar and weapon frequency ranges in a single experiment. The paper alse reviews Urick´s generalized sonar equation, which equates the echo energy to the total interference energy both of which are received in a specific frequency and time window.