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A correction to sonic boom theory

Published online by Cambridge University Press:  03 February 2016

T. Cain
T. Cain*
Affiliation:
tcain@gasdynamics.co.uk, Gas Dynamics Ltd, Farnborough, UK
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Abstract

Current sonic boom theory is based on linear midfield solutions coupled with acoustic propagation models. Approximate corrections are made within the theory to account for non-linearities, in particular for the coalescence of compression waves and the formation of weak shocks. A very large adjustment is made to account for the increasing acoustic impedance that the waves encounter as they propagate from the low density air at cruise altitude to the high density air at sea level. Typically this correction reduces the calculated over pressure levels by a factor of three. Here the method of characteristics (MOC) is used to prove that the density gradient within a hydrostatic atmosphere has no direct effect on the propagation or intensity of the wave. However gravity and ambient temperature both affect the wave propagation and the combined pressure level attenuation is not dissimilar to that previously attributed to acoustic impedance. Although the flawed acoustic theory has given reasonable predictions of measured sonic booms, the omission of gravity from the equation of motion and the inclusion of a false impedance modification, makes the model unreliable for prediction of future designs, particularly those focused on boom minimisation. As an aid to quiet supersonic aircraft design, Whitham’s theory is extended to include gravity and ambient temperature variation and shown to be in good agreement with a MOC solution for the real atmosphere.

Type
Research Article
Information
The Aeronautical Journal , Volume 113 , Issue 1149 , November 2009 , pp. 739 - 745
Copyright
Copyright © Royal Aeronautical Society 2009 

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