Optimum data analysis procedures for Titan 4 and Space Shuttle payload acoustic measurements during lift-off

Analytical expressions have been derived to describe the mean square error in the estimation of the maximum rms value computed from a step-wise (or running) time average of a nonstationary random signal. These analytical expressions have been applied to the problem of selecting the optimum averaging times that will minimize the total mean square errors in estimates of the maximum sound pressure levels measured inside the Titan IV payload fairing (PLF) and the Space Shuttle payload bay (PLB) during lift-off. Based on evaluations of typical Titan IV and Space Shuttle launch data, it has been determined that the optimum averaging times for computing the maximum levels are (1) T (sub o) = 1.14 sec for the maximum overall level, and T(sub oi) = 4.88 f (sub i) (exp -0.2) sec for the maximum 1/3 octave band levels inside the Titan IV PLF, and (2) T (sub o) = 1.65 sec for the maximum overall level, and T (sub oi) = 7.10 f (sub i) (exp -0.2) sec for the maximum 1/3 octave band levels inside the Space Shuttle PLB, where f (sub i) is the 1/3 octave band center frequency. However, the results for both vehicles indicate that the total rms error in the maximum level estimates will be within 25 percent the minimum error for all averaging times within plus or minus 50 percent of the optimum averaging time, so a precise selection of the exact optimum averaging time is not critical. Based on these results, linear averaging times (T) are recommended for computing the maximum sound pressure level during lift-off.