Examination of the Variances in Sonic Boom Waveforms Recorded During Flight Tests

Abstract

Maglieri et al. (NASA TN D-5040) have previously reported on the variability in F-104 sonic-boom signatures measured at 42 separate microphones spaced along an 8000-ft linear array. The present paper, based on the same data, is concerned with the time variation of the variances in the waveforms. Each waveform recorded during a given overflight is assigned a time origin corresponding to that when the overpressure first reached 13 of its peak value. The average signature p̄(t) = 〈p(t)〉 and the variance 〈(p−p̄)2〉 are derived from the data as functions of time t. Our interpretation of the theory of S. C. Crow [J. Fluid Mech. 37, 529 (1969)] is that a log-log plot of variance versus time should give nearly a straight line over intermediate times with a slope of −7/6. The experimentally derived plots tend to be concave downwards with a slope −α varying between −0.1 and −1.5 over the time interval during which the assumptions of Crow's theory would appear to correspond. A typical segment of the curve gives 〈(p−p̄)2〉/(Δp0〉2 = (t/tc)−α, where tc varies between 0.1 and 2.0 msec. A discussion is given of the choice of time origin in the analysis and of the possible errors due to the limited number of samples.