Revised Whitham Theory for Enhanced Sonic Boom Prediction Without Equivalent Area Calculation

The classic Whitham theory approximates the sonic boom generated by a supersonic aircraft as equivalent to that of an axisymmetric body of revolution (BOR) with a matched equivalent area distribution. While capturing the fundamental supersonic flow physics, this approach oversimplifies the aircraft geometry, thereby restricting accuracy for complex configurations. To address this, we introduce a revised formulation of Whitham theory by i) replacing the BOR’s analytical solution with a supersonic panel method to compute the near-field linear overpressure distribution, preserving more geometric details, and ii) employing Whitham’s characteristic line correction to this linear overpressure, accounting for nonlinear effects of shock wave propagation. Notably, the revised method bypasses the equivalent area calculation, thereby simplifying implementation. To predict ground-level sonic booms, the near-field signature is propagated to the far field via the augmented Burgers equation, with perceived loudness calculated using Stevens’s Mark VII method. Validation against wind-tunnel test data (SEEB-ALR, 69 deg DWB, and unpowered Tu-144) demonstrates the accuracy of the method. Comparative assessments with the classic Whitham theory, using the AXIE and JAXA wing–body test cases, reveal two key improvements: i) marginally enhanced undertrack prediction accuracy and ii) dramatically improved off-track precision. Finally, the revised method is applied to the low-boom design of the AXIE model and a complex supersonic transport configuration. The optimum design, evaluated by a higher-fidelity method, achieves significant boom mitigation, demonstrating its engineering utility.