Sonic_boom - Wikiparency

# Sonic boom > [[PORTAL_Aviation|Aviation]] · [[PORTAL_Avionics|Avionics]] spine.  ## Microsims — three.js ### Sonic boom (three.js) <div class="microsim-player"> <iframe src="https://wikitube-3d-microsims.netlify.app/Sonic_boom.html" width="100%" height="620" frameborder="0" loading="lazy" sandbox="allow-scripts allow-same-origin" title="Sonic boom — three.js microsim"></iframe> </div> **Open it full-screen:** [Sonic_boom.html](https://wikitube-3d-microsims.netlify.app/Sonic_boom.html) · library `threejs` · route `microsim/threejs/` ### Related microsims Live sims on neighbouring articles: - [[Supersonic_transport]] - [[Concorde]] - [[Turbojet]] - [[Fixed-wing_aircraft]] - [[Aircraft_flight_dynamics]] - [[Noise_pollution]] *Sim hosted off-article; the article owns the reference, not the runtime (WIKI_RULES §10.4).*  ## Overview A **sonic boom** is the sound produced at a listener's position by the shock waves that a body travelling faster than the local speed of sound drags along behind it. It is the acoustic signature of a permanent feature of supersonic flight, not of a transition between flight regimes. That distinction is the most commonly mangled fact in the subject. In popular usage the boom is the sound of an aircraft "breaking the sound barrier", as though the aeroplane emitted one bang as its Machmeter passed 1.00 and then flew on in silence. It does not. The moment an aircraft becomes supersonic it acquires a conical shock system that trails it exactly as a boat acquires a wake, and it keeps that system for as long as it stays supersonic. Where the cone reaches the ground it cuts out a long, curved band called the **boom carpet**, typically several tens of kilometres wide, and that carpet slides across the landscape at the speed of the aircraft. Everybody the carpet passes over hears a boom — once, as the shock front sweeps across them, and not before. A supersonic aircraft crossing a continent therefore does not deliver one bang near its acceleration point. It lays down a strip of bangs a thousand kilometres long and eighty kilometres wide, one for each person under it, staggered in time. That is why supersonic flight over land has been restricted almost everywhere since the early 1970s, and it is what the microsim above exists to make unforgettable: the row of ground observers lights up one after another as the carpet reaches them, from the centreline outwards, while the observers beyond the carpet's lateral edge stream past in permanent silence. ## The physics ### Wavefronts, the Mach cone, and the angle μ Treat the aircraft as a point source emitting a spherical pressure pulse every instant. Each pulse, once released, belongs to the air, not to the aeroplane: its centre stays fixed in the airmass while its radius grows at the local speed of sound *a*. Meanwhile the source runs on at true airspeed *V*. After a time *t* a given wavefront has radius *at* and its centre lies a distance *Vt* behind the aircraft. Two rates, one ratio, and that ratio is the **Mach number** M = V/a. Three cases follow directly, and the microsim's "wavefront spheres" display shows all three: * **M < 1.** The spheres grow faster than they drift. Each new front lies wholly inside all the older ones, the aircraft sits inside every sphere it has ever emitted, and no two wavefronts ever cross. Sound bunches up ahead of the aircraft — which is the Doppler effect — but there is no shock and no boom. * **M = 1.** Drift and growth are equal. Every sphere is tangent to every other at a single point, the nose. The wavefronts pile up into a plane standing on the aircraft's nose, and the accumulated pressure disturbance is what the older literature called the "sound barrier". * **M > 1.** The spheres drift back faster than they grow. The aircraft leaves them behind, and their common tangent surface closes into a **Mach cone** trailing the apex. The half-angle of that cone, measured from the flight path, is the **Mach angle** $\mu = \arcsin\!\left(\frac{1}{M}\right)$ because the tangent from the current aircraft position to a wavefront of radius *at* whose centre is *Vt* away subtends an angle whose sine is *at/Vt* = *a/V* = 1/M. The time *t* cancels: every wavefront gives the same angle, which is precisely why they share a tangent surface at all. At M = 1.5 the cone half-angle is 41.8°, at M = 2 it is exactly 30.0°, and at M = 3 it is 19.5°. The cone gets narrower and sweeps further back as the aircraft goes faster, but it never disappears and never detaches. Ernst Mach and Peter Salcher photographed exactly this geometry around a supersonic bullet in 1887 using Toepler's schlieren method, which is why the angle and the number both carry Mach's name. ### From a cone of pressure to an N-wave A real aircraft is not a point. It is an extended body that pushes air aside at the nose, lets it expand over the fuselage and wing, and closes it again at the tail. Near the aircraft the pressure signature is a detailed record of that geometry: a bow shock, intermediate compressions and expansions from the canopy, inlets and wing, and a recompression shock at the tail. That detail does not survive the trip to the ground. Shock propagation is weakly nonlinear — the higher the local pressure, the faster the local propagation speed — so compressions steepen and overtake while expansions stretch. G. B. Whitham's 1952 slender-body analysis gives the machinery for tracking this, and over the tens of kilometres between a cruising aircraft and the ground the intermediate structure is absorbed. What arrives is the classic **far-field N-wave**: a near-instantaneous rise to a peak overpressure Δp, a straight-line expansion down through ambient to −Δp, and a second near-instantaneous recompression. The ear hears the two vertical edges, not the ramp between them. For a large aircraft they are about a quarter of a second apart, long enough to be perceived as two events — the characteristic "ba-BOOM". For a fighter the separation is nearer a tenth of a second and the two shocks fuse into a single crack. Whitham's theory, extended to lifting bodies by Walkden, yields a similarity rule for the peak overpressure. Collecting the exponents for the lift-dominated case gives $\Delta p \;\propto\; \frac{(M^{2}-1)^{3/8}}{M}\;\sqrt{W}\;\;l^{-1/4}\;h^{-3/4}$ with *W* the aircraft weight, *l* its length and *h* its altitude. Three features of that expression are worth dwelling on, because all three are visible on the sliders: 1. **Mach number barely matters** above about M 1.3. The function (M²−1)^(3/8)/M rises to a shallow maximum near M 2.2 and then declines. Flying faster does not make the boom appreciably louder; it makes the carpet wider. 2. **Weight matters, as its square root.** Lift is what displaces the air, so a heavier aircraft pushes harder. 3. **Length matters inversely, as l^(−1/4): longer is quieter.** Spreading the same weight over a longer body spreads the equivalent-area distribution, weakening the individual compressions and buying distance for them to fail to coalesce. This is the entire physical foundation of low-boom shaping. The microsim's overpressure model is this similarity law, anchored on a measured number rather than an assumed constant: Concorde in cruise produced a ground overpressure of about 1.94 lb/ft² (93 Pa) at roughly Mach 2 and 52,000 ft. Because that anchor is a *measured ground* value it already contains the ground reflection factor of roughly 1.9 by which a boom is amplified when the incident and reflected waves add at a listener standing on a hard surface. ### The carpet, and why it is finite Geometry alone would say the carpet has no edges. A cone hung under an aircraft at altitude *h* cuts a flat ground plane in a hyperbola, $x = -\sqrt{M^{2}-1}\;\sqrt{h^{2}+y^{2}}$ whose branches run away to infinite lateral distance. The vertex sits a distance *h*√(M²−1) behind the aircraft's ground position — 26 km at Mach 2 and 15 km altitude, which is why you do not look up and see the aeroplane that just banged you; you look up and find it already a long way past. The atmosphere stops the infinite branches. The speed of sound depends only on temperature, and in the standard atmosphere temperature falls from 288.15 K at sea level to 216.65 K at the tropopause, so *a* falls from 340.3 m/s at the ground to 295.1 m/s at 11 km and above. Sound therefore travels *faster* near the ground than at cruise altitude, and rays refract accordingly. The invariant along an acoustic ray in a stratified atmosphere is its **horizontal trace velocity** *c* = a(z)/cos θ, with θ the ray's dip below horizontal. A ray reaches the ground only if *c* exceeds the sea-level sound speed; if the local sound speed catches up with *c* first, the ray turns over and refracts back into the sky. Two consequences follow, and neither is obvious. **Lateral cutoff.** Rays leaving the Mach cone at azimuth φ around the flight axis have trace velocity c(φ) = V/√(1 + (M²−1)sin²φ), which falls as φ increases towards the horizontal. Setting c(φ) equal to the sea-level sound speed gives a cutoff azimuth beyond which no ray ever lands. That is the carpet's edge. At Mach 2 and 15.8 km the carpet comes out about 83 km wide, which matches the roughly 50-mile primary carpet reported for Concorde; the microsim computes the edge by integrating the refracted ray path rather than by assuming a number. **Mach cutoff.** The same condition applied on the centreline says something stronger: the boom reaches the ground only if the aircraft's *true airspeed* exceeds the *sea-level* speed of sound, not merely the speed of sound in the thin air it is flying through. At 15 km that threshold is $M_{\text{cutoff}} = \frac{340.3}{295.1} \approx 1.153$ Below it, an aircraft is genuinely supersonic, genuinely carries a Mach cone, and yet lays down no carpet at all: every ray refracts away before it lands. Set the microsim to Mach 1.14 at 15 km and the cone is plainly there while the carpet width reads zero. This is not a curiosity — "Mach cutoff cruise", flying just under the threshold so the boom never lands, is one of the live proposals for overland supersonic operations, and its weakness is equally visible: the margin is a few hundredths of a Mach number, and real atmospheric temperature and wind profiles move the threshold around. ### What the steady model leaves out A steady, level aircraft lays down a steady carpet; manoeuvre breaks that. When an aircraft accelerates, dives or turns, shocks emitted at different instants can converge on a **caustic**, and the superposition produces a locally amplified, U-shaped **focus boom** or "superboom", several times the steady overpressure in a limited zone. The focus associated with acceleration through the cutoff Mach number sits at a definite place on the ground, and it is almost certainly the origin of the folk belief that the boom happens "when the aircraft goes supersonic". The grain of truth is a specially loud patch near the acceleration point; the error is concluding that everyone else is spared. There is also a **secondary boom**: energy that refracted upward is turned back down by the warm layers of the stratosphere and thermosphere, returning as a low-frequency rumble a hundred kilometres or more from the track. Far too weak to break anything, and quite loud enough to generate complaints. ### Regulation, and why it exists The empirical case against overland supersonic flight was assembled quickly. In 1964 the United States ran a six-month test over Oklahoma City in which about 1,250 booms were deliberately laid on the city at roughly eight per day. It produced something like fifteen thousand complaints and several thousand damage claims, and the community-reaction study that followed made clear that habituation was not going to solve the problem. When Congress cancelled the Boeing 2707 supersonic transport in 1971 the political ground had already shifted, and in 1973 the FAA adopted 14 CFR § 91.817, prohibiting civil flight above Mach 1 over the United States and beyond its shores where the boom would reach US land. The rule is written as a **speed limit**, not a noise limit, and that is the crux of the modern argument. Concorde, in service from 1976, was consequently confined to supersonic cruise over water, and its economics never recovered from it. ICAO has never adopted a numerical sonic-boom standard, holding instead to the principle that boom should not cause unacceptable disturbance. Pressure to replace the blanket speed prohibition with a noise-based certification standard has grown since the late 2010s, and in 2025 the United States moved formally in that direction, directing the FAA to repeal the speed-based rule. The rulemaking that would give that direction legal effect was still in progress at the time of writing, and the number defining "quiet enough" had not been settled. ### Low-boom shaping and the X-59, honestly The possibility of an aircraft whose signature never fully coalesces into an N-wave goes back to Seebass and George's 1972 minimisation analysis and Darden's 1979 extension relaxing the nose-bluntness constraint. The idea is to tailor the equivalent-area distribution — cross-sectional area plus lift along the body — so that compressions arrive spread out rather than stacked, giving a shaped signature with a lower peak and, more importantly, a slower rise. Rise time governs high-frequency content, and high-frequency content is what makes a boom startling. Shaping has been demonstrated in flight once, at small scale. The Shaped Sonic Boom Demonstration flew a modified F-5E with a reprofiled nose and forebody in 2003 and showed that a deliberately shaped near-field signature can survive propagation to the ground rather than degenerating into an N-wave. A genuine and important result, and a narrow one: small aircraft, modest reshaping, limited envelope. NASA's **X-59**, built by Lockheed Martin Skunk Works for the Quesst mission, is the attempt to do it properly. It is about 30 m long, single-seat, powered by one F414 engine, and designed to cruise near Mach 1.4 at roughly 55,000 ft with a shaped ground signature whose perceived level is around 75 PLdB — a "thump" rather than a bang, of order a tenth of the peak pressure of Concorde's N-wave. It rolled out in January 2024 and flew for the first time in 2025. What has *not* been demonstrated deserves saying plainly, because this is a field with a long history of enthusiastic overstatement: * The 75 PLdB figure is a **design target**, not a measured community result. The point of the X-59 is to fly over real communities and collect the human-response data a regulator would need; until that dataset exists the acceptability question is open. * PLdB is a perceived-level metric developed for other kinds of impulsive noise. How well it ranks *shaped* booms for annoyance, as opposed to N-waves, is one of the things the campaign is meant to establish. * Atmospheric turbulence scatters booms, both amplifying and attenuating: measured peaks for nominally identical flights can differ by a factor of two. Shaping lowers the mean but does not abolish the tails, and turbulence tends to sharpen rise times — exactly the quantity shaping is trying to lengthen. * Shaping is a severe constraint on configuration. The X-59's fineness ratio, its long spike of a nose and its lack of forward windows are all consequences. Whether the approach scales to a fuselage holding fifty or a hundred passengers is unresolved. * None of this touches airport noise or fuel burn, independent obstacles for any supersonic transport. The honest summary: the physics of shaping is sound and has been demonstrated once at small scale; the aircraft that would demonstrate it at useful scale exists and has flown; and whether the resulting thump is acceptable to the people underneath is genuinely unanswered. ## Controls -> what each maps to | Control | Symbol | Range and units | What it drives | |---|---|---|---| | Mach number | *M* | 0.6 – 3.0, dimensionless | The ratio V/a at flight level. Sets the cone half-angle μ = arcsin(1/M), the shock lag *h*√(M²−1), the carpet width through the cutoff azimuth, and (weakly) the overpressure through (M²−1)^(3/8)/M. Below M = 1 no cone exists; at M = 1 exactly, μ = 90°. | | Altitude | *h* | 2 – 20 km | Sets the local temperature and hence the speed of sound *a* = √(γRT) from the ICAO standard atmosphere, so it changes the true airspeed for a given *M*. It also sets the ray path length, driving the carpet width, the shock lag, the N-wave duration (∝ h^(1/4)) and the overpressure (∝ h^(−3/4)). | | Aircraft length | *l* | 12 – 110 m | Length of the equivalent-area distribution. Overpressure falls as l^(−1/4) and the N-wave lengthens as l^(3/4). Longer really is quieter and slower-sounding. The drawn aircraft stretches with it, at 140× life size. | | Gross weight | *W* | 10 – 400 t | Stands in for the lift-induced part of the equivalent area. Overpressure rises as √W. It has no effect on the cone geometry at all: shock *shape* is kinematics, shock *strength* is aerodynamics. | | Wave display | — | spheres / cone / both | Switches between the expanding wavefront spheres (drawn as great circles plus their ground footprints) and the assembled Mach cone. The spheres show *why* the angle is arcsin(1/M); the cone shows *what* it does. | | N-wave plot | — | on / off | The live ground signature: bow-shock rise to +Δp, linear expansion to −Δp, tail-shock recovery, with the peak in both pascals and pounds per square foot. | | Pause / Reset | — | — | Freezes the ground scroll, or restores Concorde cruise (M 2.0, 15 km, 62 m, 150 t). | Live HUD readouts: Mach number and true airspeed; the equation μ = arcsin(1/M) evaluated at the current M; carpet width in km; peak overpressure in Pa and psf; and a running tally of how many ground observers have been boomed versus how many lie outside the carpet and never will be. Secondary readouts carry the local and sea-level sound speeds, the Mach cutoff number at the current altitude, the shock lag, the N-wave duration and the ambient pressures. ## Learning objective After using this simulation a reader should be able to state without hedging that a sonic boom is a continuous trailing phenomenon rather than a single event at the sound barrier, and to justify that geometrically: the Mach cone exists for every instant that M > 1, its ground intersection is a moving hyperbola, and the region that hyperbola sweeps is a carpet tens of kilometres wide travelling with the aircraft. They should be able to derive μ = arcsin(1/M) from the ratio of two speeds, see that the cone narrows but never vanishes as M rises, and explain why weight and length change a boom's loudness while changing nothing about its geometry. They should be able to say why the carpet has edges at all — refraction in a temperature-stratified atmosphere — and why an aircraft can be supersonic and still lay down no boom, which is the Mach cutoff. Finally, they should be able to place Concorde's roughly 2 psf N-wave and the X-59's roughly 0.3 psf design thump on one axis, and say which part of the low-boom claim has been demonstrated and which has not. ## Limits and connections The model in this microsim is deliberately transparent, and a reader should know exactly where it stops. **Steady, level, straight flight only.** No acceleration, turn, climb or dive, so no caustics and no focus booms. Real superbooms during transonic acceleration can be several times the steady overpressure over a limited ground patch, and this simulation cannot show them. **Horizontally stratified, windless atmosphere.** The ICAO standard atmosphere is used exactly, but real temperature profiles depart from it and there is no wind here at all. Wind shifts and skews the carpet by tens of kilometres and can widen it on one side while closing it on the other, because what matters to refraction is the *effective* sound speed along the ray, wind component included. **No turbulence.** Boundary-layer scattering produces most of the spread seen in measured boom data — routinely a factor of two either way in peak pressure — and also modifies rise times. None of that is here. **An N-wave is assumed,** with instantaneous shocks. Real rise times are a few milliseconds, not zero, and the whole point of low-boom shaping is a signature that is *not* an N-wave. This model therefore cannot represent the X-59; it can only say what an unshaped aircraft of the same size and weight would produce. **The overpressure law is a similarity scaling, not CFD.** Whitham/Walkden slender-body scaling anchored on one measured aircraft. It gets the trends right and lands within a few tens of per cent for conventional configurations at cruise; it should not be trusted to three significant figures. **Geometry simplifications.** The acoustic ground is a flat sea-level plane, so terrain reflection, diffraction and buildings are absent, and the ground reflection factor is folded into the calibration anchor rather than modelled. Secondary booms are not simulated. The wavefront spheres use a single sound speed, the one at flight level, because that is the picture in which sin μ = 1/M is exact; the carpet edge is computed from the properly refracted ray. For legibility the aircraft is drawn 140× life size and time runs 12× real, both stated on screen. The connections run outward. The cone geometry is the same construction that governs [[Supersonic_transport]] design and the wave drag that makes it expensive; [[Concorde]] is where nearly all the world's public boom-exposure data came from; sustained supersonic cruise depends on the afterburning [[Turbojet]]. The lift in the overpressure scaling is the lift treated in [[Fixed-wing_aircraft]] and [[Aircraft_flight_dynamics]], where the manoeuvres that cause focus booms belong. And the reason any of this is regulated belongs to [[Noise_pollution]], where the boom sits alongside airport noise as one of the two acoustic constraints that have shaped civil aviation more than any aerodynamic one. ## References - Mach, E., and Salcher, P. "Photographische Fixirung der durch Projectile in der Luft eingeleiteten Vorgänge." *Sitzungsberichte der Kaiserlichen Akademie der Wissenschaften in Wien*, vol. 95, 1887, pp. 764–780. The original schlieren photographs of the cone around a supersonic bullet. - Whitham, G. B. "The flow pattern of a supersonic projectile." *Communications on Pure and Applied Mathematics*, vol. 5, no. 3, 1952, pp. 301–348. The foundational theory of shock coalescence and the far-field N-wave. - Whitham, G. B. *Linear and Nonlinear Waves*. New York: Wiley, 1974. Chapter 9 gives the full nonlinear-propagation treatment. - Hayes, W. D., Haefeli, R. C., and Kulsrud, H. E. *Sonic Boom Propagation in a Stratified Atmosphere, with Computer Program*. NASA CR-1299, 1969. The standard ray-tracing formulation used for carpet and cutoff calculations. - Carlson, H. W. *Simplified Sonic-Boom Prediction*. NASA TP-1122, 1978. The engineering method behind most quick overpressure and lateral-cutoff estimates. - Borsky, P. N. *Community Reactions to Sonic Booms in the Oklahoma City Area*. AMRL-TR-65-37, Aerospace Medical Research Laboratories, Wright-Patterson AFB, 1965. The 1964 exposure programme and its social results. - Seebass, R., and George, A. R. "Sonic-Boom Minimization." *Journal of the Acoustical Society of America*, vol. 51, no. 2C, 1972, pp. 686–694. The theoretical basis of low-boom shaping. - Darden, C. M. *Sonic-Boom Minimization with Nose-Bluntness Relaxation*. NASA TP-1348, 1979. - Plotkin, K. J. "State of the art of sonic boom modeling." *Journal of the Acoustical Society of America*, vol. 111, no. 1, 2002, pp. 530–536. - Leatherwood, J. D., Sullivan, B. M., Shepherd, K. P., McCurdy, D. A., and Brown, S. A. "Summary of recent NASA studies of human response to sonic booms." *Journal of the Acoustical Society of America*, vol. 111, no. 1, 2002, pp. 586–598. On PLdB and the perception of booms. - Pawlowski, J. W., Graham, D. H., Boccadoro, C. H., Coen, P. G., and Maglieri, D. J. "Origins and Overview of the Shaped Sonic Boom Demonstration Program." AIAA 2005-5, 43rd AIAA Aerospace Sciences Meeting and Exhibit, 2005. The 2003 F-5E shaped-boom flight demonstration. - Maglieri, D. J., Bobbitt, P. J., Plotkin, K. J., Shepherd, K. P., Coen, P. G., and Richwine, D. M. *Sonic Boom: Six Decades of Research*. NASA SP-2014-622, NASA Langley Research Center, 2014. The definitive review, and the source of the Concorde overpressure and carpet-width figures used to calibrate this simulation. - Anderson, J. D. *Modern Compressible Flow: With Historical Perspective*. 3rd ed. New York: McGraw-Hill, 2003. ISBN 978-0-07-242443-0. Standard textbook treatment of Mach waves and the Mach angle. - International Civil Aviation Organization. *Manual of the ICAO Standard Atmosphere, extended to 80 kilometres*. Doc 7488/3, 3rd ed., 1993. Source of every temperature, pressure and sound-speed value in the simulation. - United States Federal Aviation Administration. 14 CFR § 91.817, "Civil aircraft sonic boom" (adopted 1973), and § 91.819, "Civil supersonic airplanes that do not comply with part 36." - NASA Aeronautics Research Mission Directorate. *Quesst Mission and the X-59*. NASA. The programme's own statements of the X-59's configuration, cruise condition and 75 PLdB design target; consult it directly for the current status of the community-response flight campaign, which is the part of the low-boom case that is still being gathered. **On the spine:** [[Aircraft]] · [[Aircraft_flight_dynamics]] · [[Fixed-wing_aircraft]] · [[Helicopter]] · [[Turbojet]] · [[Jet_engine]] · [[Sonic_boom]] · [[Contrail]] · [[Air_traffic_control]] · [[Avionics]] · [[Aviation]].  **Microsim — three.js (Wikitube framework):** *Sonic boom* <div class="wt-sim" data-src="https://wikitube-3d-microsims.netlify.app/acoustics/Sonic_boom.html" data-title="Sonic boom"></div> *Built from `MICROSIM_GUIDE/specs/acoustics/variants/Sonic_boom.json`; part of the [[PORTAL_Acoustics|Acoustics portal]] spine (section sims and See-also variants).*   **Part of the [[Aviation]] hub** — main article for section A11, *Faster than sound*. Related sections: Turbofan · Flight envelope.  ## Wikipedia : Wikitube **Strict pair:** [Wikipedia](https://en.wikipedia.org/wiki/Sonic_boom) : [Wikitube](https://en.wikitube.io/wiki/Sonic_boom) --- *PORTAL_Aviation three.js batch · 2026-08-05 · sim staged in `_3d_deploy_stage/`.*