Limitations of linear theory for sonic boom calculations

Abstract

Current sonic boom minimization theories have been reviewed to emphasize the capabilities and flexibilities of the methods. Preliminary comparisons of sonic booms predicted for two Mach 3 concepts illustrate the benefits of shaping. Finally, for very simple bodies of revolution, sonic boom predictions were made using two method— a modified linear theory method and a nonlinear method—for both far-Held N-waves and midfield signature shapes. Preliminary analysis on these simple bodies verified that current modified linear theory prediction methods become inadequate for predicting midfield signatures for Mach numbers above three. The importance of impulse in sonic boom response and the importance of three-dimensional effects which could not be simulated with the bodies of revolution will determine the validity of current modified linear theory methods in predicting midfield signatures at lower Mach numbers. ENEWED interest in the possible development of a high- speed civil transport (HSCT) in this country has resulted in an assessment of the technology needs and environmental concerns surrounding such a vehicle. One environmental con- cern which could have significant impact on the economic viability of a HSCT is the sonic boom created by supersonic overland flight. Commercial overland supersonic flight is pro- hibited by law in the United States. In order to examine the possibility of modifying this law, technologists must first es- tablish an acceptability criteria and then demonstrate that this criteria can be met with an economically viable vehicle design concept. Even if overland supersonic flight does not become a reality, methods of predicting primary boom footprints, caustic levels and locations, and a statistical variability of waveforms due to atmospheric effects must be available so that any effects of sonic boom could be predicted. Most currently used prediction methods are based on the- ories developed by Whitham1 for a supersonic projectile, and by Walkden2 who extended the analysis to include lifting bod- ies. These theories combined with the supersonic area rule theory developed by Hayes 3 led to the generally accepted prediction methods described in some detail in Ref. 4. Orig- inally, it was felt that all sonic boom pressure signatures would have attained the standard TV-wave shape when they inter- sected the ground. Work by McLean5 indicated that this was not so for airplanes with extensive lifting surfaces. The freez- ing effects of the real atmosphere pointed out by Hayes 6 reinforced the idea that the signature may still retain midfield effects when it intersects the ground. A midfield signature retains effects of the airplane shape and, thus, offers shaping as a possible avenue of minimizing the sonic boom.