Crack-to-Bang: Ranging, Not Localization

Crack-to-bang (also called crack-thump) is a published forensic-audio technique that is routinely over-read — including by people citing it to claim a precise shooter location. This page explains exactly what it establishes (a distance), why a distance is not a location, and where its assumptions inject error. The worked example is the publicly released correspondence between independent researcher Matt Kester and Dr. Robert Maher (Montana State University, author of Principles of Forensic Audio Analysis) about the shooting of Charlie Kirk at UVU.

A supersonic rifle bullet produces two separate sounds. First, the ballistic shock wave ("crack") — a cone trailing the bullet, like a miniature sonic boom. Second, the muzzle blast ("bang") — the explosion at the firearm, radiating from a fixed point. At a microphone, the crack arrives first and the bang second; the gap between them grows with distance.

For a microphone roughly on the bullet's line of flight, the gap relates to distance by a simple expression Dr. Maher states directly in his email:

distance = t_gap / ( (1/c) - (1/V) )

   t_gap = crack-to-bang time gap (s)
   c     = speed of sound  (~343 m/s)
   V     = bullet speed    (must be ASSUMED)

That is the whole engine. Feed it a measured gap, an assumed bullet speed, and a speed of sound, and it returns one number: a distance. Everything else — whether that distance means anything, and whether it can locate a shooter — follows from the geometry below.

From Maher's email — the crack-to-bang geometry (Mach angle θ_M, off-axis miss distance d), and a range recording at just 9 m showing how reflections tangle even a clean shot.

This is the crux. The formula returns a distance, call it D — the straight-line distance from the microphone to the firearm. A distance with no direction does not specify a point. It specifies every point that far away: the source lies somewhere on a sphere of radius D centered on the microphone (a circle, if you assume a ground plane).

To collapse that circle to a point you need information the single measurement does not contain:

• ▸An independent bearing (direction of arrival) — e.g. a directional/array sensor, or visual evidence of the muzzle flash/smoke.
• ▸A position established by other evidence and imported from outside the acoustics (e.g. a rooftop reported by authorities — a claim, not an acoustic measurement).
• ▸Multiple synchronized receivers — which is a different method entirely (TDOA), and the one this site uses.

This is exactly what Maher does: his acoustics give a range (~140 m) and no direction at all. The only bearing in play is the authorities' separately-reported rooftop east of the podium, which his range is then compared against — he notes the two "generally match." That is a consistency check against a claimed location, not an independent localization, and he is careful to frame it that way. No direction was ever recovered from the sound.

The clean formula assumes the microphone sits on the bullet's line of flight. Real cameras don't — they're scattered around the crowd, off to the side of the trajectory. Off-axis, the gap no longer depends on a single distance; it depends on where the mic sits relative to the bullet's path — its perpendicular miss distance and its position along the track — through the Mach-cone geometry (θ_M in Maher's diagram above).

Maher flags this himself, precisely:

The consequence is concrete and directional: for a given source distance an off-axis mic always yields a shorter gap (Maher's point above), so the on-axis formula reads that shorter gap as a nearer source — it underestimates the distance. The bias can't be corrected without the mic's position relative to the trajectory, which Maher didn't have. Combined with the reflection problem below (which pushes the other way), the "circle" from Section 2 is not just undirected but uncertain in radius.

Even setting the circle aside, the single distance number rests on a stack of assumptions, each carrying error:

To be clear up front: Dr. Maher's work here is competent and honest. He is a credentialed forensic-audio authority, his email is careful, and — crucially — he never claims more than the method can deliver. Reading it closely is the best possible illustration of crack-to-bang's true ceiling, because a leading expert applying it correctly still lands on a heavily-qualified "consistent with."

Maher's Oct 6 reply and his Sept 11 reporter analysis. Bottom: the ~0.241 s crack-to-bang gap on the one near-podium recording.

What he actually said, piece by piece:

• ▸Headline: "a single bullet, supersonic velocity, from about 140 meters away." Note that is a range, not a position.
• ▸Measurement: a ~240 ms (0.241 s) crack-to-bang gap on the one video "relatively close to the podium."
• ▸Calculation: 0.241 / ((1/343) − (1/800)) = 144.7 m, with the bullet speed assumed at ~800 m/s "since the exact trajectory of the bullet and the bullet's speed is not known."
• ▸Classification, not ID: consistent with a rifle such as a .308; "I do not think that the specific kind of rifle can be determined from the acoustical analysis."
• ▸No direction was recovered: the acoustics produced a distance only. Maher simply noted his ~140 m "generally matches" / "seems consistent" with the rooftop the authorities had already reported — a check against a claimed location, not a bearing derived from the sound.

Spectrogram, the ~140 m line on the aerial map, and the rooftop sightline.

A more distant recording "dominated by acoustic reflections," and the additional remarks deriving 144.7 m.

Independent researcher Matt Kester published this exchange. His goal, stated in his own Oct 2 message, was to fact-check the official narrative — he ran a 30-06 field test at a known 425 ft in Arizona, and used ChatGPT to help with the math (noting he was a Political Science major). He attached a "Bullet-to-Report Delay" table screening scenarios against the recordings.

Maher's signature (contact details redacted) and the start of Kester's Oct 2 inquiry.

Kester's request and the ChatGPT-assisted "Bullet-to-Report Delay" table.

Read honestly, the table can argue against a few specific alternatives but cannot locate anything:

• ▸Its only use is narrow, exclusionary, and conditional: if the ~0.216–0.227 s gaps are genuine direct-arrival measurements, they are too long for a close-range or subsonic shot (a subsonic .300 BLK at ~100 ft would produce no usable crack-bang separation, or the wrong sign), so the table could argue against those theories. But that "if" carries the whole claim: the audio is dominated by reflections and reverberation, and there is no onset validation that the gap was read between the direct crack and direct blast rather than an echo (see Section 4). A misidentified arrival makes the gap too long or too short — which would undercut even this exclusionary use. It also says nothing about direction or position, and rides entirely on the assumed velocities below.
• ✗It cannot localize: "Distance to Mic" is an input column (assumed/known) and "Velocity Used" is assumed, so the table only confirms that an assumed geometry is consistent with the observed gap — it does not solve for where the shooter was. It also leans on AI-generated arithmetic, inheriting every error in Section 4.

Plain-language explanation of evidentiary standards, not legal advice.