Progress
What the model tells us
- Altitude is the lever. Over a year of real soundings (6 US stations, 4,283 launches), the any-direction boomless Mach has a median of 1.067 at FL350 but 1.147 at FL550. With a 0.03 safety margin a usable corridor (≥ M1.05) exists 38% of the time at FL350, 85% at FL500 and 93% at FL550.
- Winter and the north are the weak spots; the tropics are the best. At FL500 the corridor is usable 69% of the time in winter against 99% in summer. International Falls (48.6°N) manages 57% at FL500; San Juan is usable essentially always from FL500 up.
- The limit is really a ground-speed limit. The boom stays up when the aircraft moves over the ground slower than sound travels in the air below it. Into the wind you can fly a higher Mach because the wind slows you down, which is why the best-direction arrows point upwind. With the wind behind you the allowed Mach is lower, but you still cover more ground: in strong winds at FL400 the median is M1.25 and 635 kt over the ground into the wind, against M1.05 and 681 kt with it. The tailwind aircraft is faster at 94% of those points.
- The margin sets the boom risk, and the ensemble knows where to spend it. GFS misses the boomless Mach by about ±0.013 a day ahead (4,004 balloon launches over a year). Over a year of hindcasts with that error, a single 0.05 margin still lets 1.2% of flights put more than 20 nm of boom on the ground. The 31-member GEFS ensemble spreads out where the forecast goes wrong: the error is three to four times larger in the most uncertain tenth of points than in the calmest. A margin scaled to that spread holds boom flights to 0.5% and saves 27.7 minutes at FL550 (23.5 at FL450), 1.1–2.4 minutes more than one margin for the whole world.
- Corridors only matter over land and coasts. Over open ocean full design Mach is already allowed, so routes ignore bright areas at sea. Where a route can stay over water longer, for example through the Mediterranean, it does.
- Corridors save time but don't fix the economics. For a Boom Overture-type aircraft they save about 25 minutes per flight against today's overland ban where an airline would actually use them (about 45 minutes if every corridor were flown, but slow corridors cost more fuel than the time is worth). A seat still costs about $2,300 more than on a 787-9, and the aircraft burns about 11× the fuel per passenger at today's $1.47/kg, so it pays off only if an hour is worth more than about $1,250 to the passenger.
- The white on the map is direction-specific. A bright corridor in "Best" mode is usually for flying into the wind. The same air, flown the other way, often allows only M1.02–1.08. Plan a route and the map offers to switch to that route's heading.
- Water beats corridors. Over open sea a supersonic aircraft flies its full design Mach (M1.7–2.0), against M1.1–1.3 in a corridor. A route will detour over water (e.g. through the Mediterranean) before it uses a white corridor over land.
- How loud is it just below the turning point? About 0.11 psf at 1.1 Haglund heights, then it dies fast. Below the turning point every pitch fades, the high ones first (Airy decay). The model reproduces NASA FaINT's F-18 measurements (0.03–0.09 psf with the turning point 1–2 Haglund heights up). For a 61 m airliner the rule's 0.11 psf is reached about 1.3 km below the turning point, 0.05 psf at 1.7 km. The planner keeps that cushion for each aircraft. With the forecast margin the model gives well under 0.01 psf, but FaINT still measured up to 0.10 psf far below the turning point (turbulence, background noise), so the planner shows 0.10 psf as the upper value: under the 0.11 limit, with little room.
- Supersonic over land without a corridor is 15× too loud. An Overture-class aircraft at M1.7 and FL550 puts about 1.7 psf on the ground (Carlson's method; Concorde measured 1.94 psf at M2). The proposed limit is 0.11 psf, so overland speed comes from Mach cutoff or not at all.
Findings 1, 2 and 4 come from the validation against soundings and a year of GFS hindcasts (validation/, study/). Finding 4 also uses 53 weeks of GEFS. Findings 9 and 10 use NASA FaINT and TP-1122. The rest come from the live forecast and the Economics tab.
How the map is made
Sound travels faster in warm air. A boom created high up, in cold air, bends upward as it descends into warmer layers. If a layer under the aircraft carries sound faster than the aircraft moves over it, the boom turns around before it reaches the ground. This is Mach cutoff.
The calculation
Mα = ( maxzf ≤ z < za [ c + w·eα ] − wa·eα ) / ( ca cos α ), M = min over rays α
For every 1° column of the forecast, seven flight levels (FL300 to FL600) and 36 directions of travel, the map finds the largest Mach for which every boom ray, straight down and to the sides, turns at least 1 km above the highest terrain under the boom footprint. The forecast is the mean of NOAA GFS and ECMWF IFS (the IFS run may be up to 12 h older; GFS alone when IFS is not available), which cuts the error against weather balloons by about 10% (Method §6.2). The speed of sound includes humidity and the wind along each ray is included. A forecast-error margin is subtracted: one number from the slider, or Auto. Auto is k·√(s² + e² + 0.005²) per point and direction, where s is the spread of the 31-member GEFS ensemble for that hour, e = 0.012 is the error no model run sees (0.015 over high terrain) and 0.005 allows for the aircraft's air data; k (4.0 at FL350 and FL550, 4.25 at FL450) holds flights with more than 0.11 psf on the ground to about 0.3% at FL550 in a year of hindcasts, including the router's choice of path (95% upper bound 0.47%). Without a fresh ensemble, Auto falls back to a fixed map of the local forecast error. The map opens on Auto; turning it off gives one margin for the whole world (0.05 by default).
Routes
Routes come from a time-dependent search on a 1° grid in 16 directions, refined continuously from two independent starting routes. The aircraft meets the forecast for the time it gets there, and ground speed comes from the wind triangle. Climb and descent are subsonic, acceleration and deceleration take time and fuel, and boomless legs are flown in constant-Mach blocks of at least 300 nm.
Where it applies
Mach cutoff unlocks speed only where the rule is written about the boom reaching the ground. Elsewhere the test is the aircraft's Mach number. The map treats every territory as restricted until its rule says otherwise.
Limits
- Research prototype, not for flight planning, and not affiliated with Boom, NASA or the FAA.
- Loudness is v0: the primary boom from Carlson's simplified method (NASA TP-1122, within about 15% of flight data), cutoff legs from a linear caustic (Airy) model checked against FaINT; nonlinear focusing at the turning point itself is not modelled. Secondary booms: where the stratosphere would bring them down is checked on every supersonic leg over water, and legs that would put one on land are slowed to the cutoff Mach; their loudness is only estimated, from Concorde measurements scaled to the aircraft. Not a compliance determination under the proposed rule.
- The cushion under the turning point is checked against FaINT's F-18 measurements, not yet against an airliner-size boom (XB-1 data requested, #21).
- Climb or descent angle is not modelled (a −3° descent costs about 0.03 Mach). Each column is treated as uniform along the 40–90 km ray path; 3D ray tracing through the forecast changes the limit by 0.0022 Mach (standard deviation, no bias, 95% within 0.0045), well inside the margin.
- Regulated zone: under 14 CFR 91.817(b) a sonic boom may not reach the surface within the United States, which includes the 12 nm territorial sea and the Great Lakes. Routes treat every country's territory (Natural Earth 10 m land, islands and lakes) plus 12 nm of territorial sea plus a 24 nm boom-carpet half-width, measured as great-circle distance on a 0.1° grid, as a zone where the aircraft must be boomless or subsonic. Full supersonic speed is used only beyond that line.
- The FAA proposal (docket FAA-2026-6935) covers the United States. Other countries keep overland bans, so the global map shows physics only.
Sanity check
A standard atmosphere with no wind gives M 1.15 at FL400 without the buffer and M 1.14 with it, within the range Boom's XB-1 flew without an audible boom in 2025 (M 1.12–1.18). This is a sanity check, not validation.
Data: NOAA GFS and GEFS via AWS Open Data, checked hourly and rebuilt within an hour of each new GFS run; ECMWF IFS open data (© ECMWF, CC BY 4.0). Satellite and night-lights images: we acknowledge the use of imagery provided by services from NASA's Global Imagery Browse Services (GIBS), part of NASA's Earth Science Data and Information System (ESDIS). Terrain: GFS orography and AWS Terrain Tiles (SRTM, GMTED2010, ETOPO1). Coastlines: Natural Earth. Code, red-team review and sources: github.com/FernandoVazq/mach-corridor. Privacy.