Inherent errors in sonar range prediction

It is common practice to make sonar range predictions by solving the sonar equation for the range at which a predicted value of propagation loss is equal to the system-target Figure-of-Merit. The inherent limitations of this method are derived in this paper. It is shown that small errors in estimates of Figure-of-Merit can cause large errors in predicted range. Results are given for both passive and active sonar systems. For passive, low frequency systems, the relative range error approaches 23% per dB of uncertainty.