Sonic Boom Simulator: Shock Wave Propagation & Ground Overpressure

simulator intermediate ~10 min
Loading simulation...
ΔP ≈ 1.0 psf — Mach 1.6 at 15 km altitude

A Mach 1.6 aircraft at 15 km altitude with 800 kN weight produces roughly 1.0 psf (48 Pa) ground overpressure with a Mach cone half-angle of 38.7° and a boom carpet about 45 km wide.

Formula

μ = arcsin(1/M) (Mach cone half-angle)
ΔP ∝ (M²−1)^(1/8)·W^(3/4) / h^(3/4) (Whitham theory)
T_N-wave ≈ L·√(h·√(M²−1)) / (V·c₀)

Breaking the Sound Barrier

When an aircraft exceeds the local speed of sound, it outruns the pressure waves it generates. These waves pile up into shock waves — extremely thin regions (a few micrometers) where pressure, density, and temperature jump discontinuously. The conical shock system that envelops the aircraft sweeps across the ground, and observers within the 'boom carpet' hear a startling double bang — the sonic boom. Chuck Yeager first experienced this crossing Mach 1 in the Bell X-1 on October 14, 1947.

The N-Wave

The ground-level pressure signature of a conventional sonic boom resembles the letter N: a sudden overpressure (bow shock), followed by a gradual pressure decrease through the aircraft's flow field, ending with a sudden underpressure (tail shock). The peak overpressure depends on Mach number, altitude, aircraft weight and length, and atmospheric conditions. Typical values range from 0.5 psf for a high-altitude fighter to 2+ psf for Concorde — enough to rattle windows and startle people.

Boom Carpet and Propagation

The Mach cone intersects the ground in a hyperbolic strip — the boom carpet — whose width is approximately 2h·tan(arcsin(1/M)). For a Mach 1.6 aircraft at 15 km, this carpet is about 45 km wide. Atmospheric refraction bends shock rays away from the surface at the carpet edges, creating a sharp cutoff. Temperature gradients, wind, and turbulence cause focusing and defocusing that produces significant overpressure variations along the carpet.

Low-Boom Design

NASA's X-59 QueSST program and private ventures like Boom Supersonic are pioneering shaped sonic boom technology. By carefully distributing the aircraft's volume and lift along its length, designers can prevent the bow and tail shocks from coalescing into a sharp N-wave. Instead, the pressure disturbance arrives as a series of weak shocks perceived as a quiet thump — potentially opening the door to overland supersonic commercial flight for the first time since Concorde's retirement.

FAQ

What causes a sonic boom?

A sonic boom occurs when an object travels faster than the speed of sound. The pressure disturbances cannot propagate ahead of the object and accumulate into a shock wave — a thin region of abrupt pressure, temperature, and density increase. The conical shock wave sweeps along the ground, perceived as a sudden double bang (the N-wave).

What is the Mach cone?

The Mach cone is the conical shock surface generated by a supersonic object. Its half-angle is μ = arcsin(1/M). At Mach 1, the cone is flat (90°); at Mach 2, it narrows to 30°. All observers within the cone's intersection with the ground — the 'boom carpet' — hear the sonic boom.

Can sonic booms be eliminated?

Not eliminated entirely, but significantly reduced. NASA's X-59 QueSST aircraft uses shaped fuselage and wing design to prevent shock waves from coalescing into a sharp N-wave, instead producing a distributed pressure rise perceived as a quiet thump rather than a boom.

Why is supersonic flight banned over land?

The FAA banned civil supersonic overland flight in 1973 after public outcry over sonic boom disturbance during SST development. Concorde was restricted to transoceanic routes. Current research aims to demonstrate that low-boom designs can achieve acceptable community noise levels.

Sources

Embed

<iframe src="https://homo-deus.com/lab/aeroacoustics/sonic-boom/embed" width="100%" height="400" frameborder="0"></iframe>
View source on GitHub