Hostname: page-component-586b7cd67f-2brh9 Total loading time: 0 Render date: 2024-11-25T21:59:37.531Z Has data issue: false hasContentIssue false
  • English
  • Français

A correction to sonic boom theory

Published online by Cambridge University Press:  03 February 2016

T. Cain
T. Cain*
Affiliation:
[email protected], Gas Dynamics Ltd, Farnborough, UK
Get access Rights & Permissions [Opens in a new window]

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 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1 Whitham, G.B., The flow pattern of a supersonic projectile, Communications on pure and applied mathematics, 1952, 5, pp 301–348.Google Scholar
2 Walkden, F., The shock pattern of a wing-body combination far from the flight path, Aeronaut Quarterly, IX, pt. 2, May 1958, pp 164–194.Google Scholar
3 Jones, L.B., Lower bounds for sonic bangs, Aeronaut J, 65, June 1961, pp 433–436.Google Scholar
4 Jones, L.B., Lower bounds for sonic bangs in the far field, Aeronaut Quarterly, XVIII, Pt. 1, February 1967, pp 1–21.Google Scholar
5 Randall, D.G., Methods of estimating distributions and intensities of sonic bangs, ARC R & M 3113, August 1957.Google Scholar
6 George, A. and Plotkin, K., Sonic boom waveforms and amplitudes in a real atmosphere, AIAA J, 1969, 7, (10), pp 1978–1981.Google Scholar
7 Hayes, W., Haefeli, R. and Kulsrud, H., Sonic boom propagation in a stratified atmosphere, with computer program, 1969, NASA-CR-1299.Google Scholar
8 Rayleigh (Strutt, J.W.), THE THEORY OF SOUND, II, Macmillan and Co., 1878, pg 64Google Scholar
9 Darden, C., Progress in sonic boom understanding: lessons learned and next steps, High-speed research: 1994 Sonic boom workshop, NASA-CP-1999-209699, pp 269–292.Google Scholar
10 Pawlowski, J. and Graham, D., Bocccadoro, C., Coen, P. and Maglieri, D., Origins and overview of the shaped sonic boom demon stration program, January 2005, AIAA-2005-5Google Scholar
11 Ferri, A., Ting, L. and Lo, R., Nonlinear sonic-boom propagation including the asymmetric effects, AIAA J, 15, (5), pp 653–658.Google Scholar
12 Darden, C., An analysis of shock coalescence including the tree-dimensional effects with application to sonic boom extrapolation, 1984, NASA-TP-2214Google Scholar
13 Kantrowitz, A., One dimensional treatment of nonsteady gas dynamics, Section C, Fundamentals of Gas Dynamics, 1958, III, High Speed Aerodynamics and Jet Propulsion, Princeton University Press, pp 353.Google Scholar
14 Mack, R. and Darden, C., Limitations on wind-tunnel pressure signature extrapolation, High-speed research: Sonic boom, 1992 NASA-CP-3173 pp 201–220.Google Scholar
15 Plotkin, K., Theoretical basis for finite difference extrapolation of sonic boom signatures, 1995, NASA High-speed research program Sonic boom workshop, NASA-CP-3335, pp 54–67.Google Scholar
16 Liepmann, H.W. and Roshko, A. 1957, Elements of gasdynamics, John Wiley & Sons, 1st edition, p 206 Google Scholar
17 Cook, W. and Felderman, E., Reduction of data from thin-film heat-transfer gages: A concise numerical technique, AIAA J, 4, (3), pp 561–562 Google Scholar
18 Cleveland, R. and Blackstock, D., Waveform freezing of sonic booms revisited, 1995 NASA High-speed research program Sonic boom workshop, NASA-CP-3335 pp 20–40.Google Scholar