A shock reaches the ground only if the aircraft is faster than the speed of sound AT THE GROUND, not merely at its own altitude. At 11 km on a standard day that means above about Mach 1.15; slower than that, the boom bends back up before it lands.
Sound is faster in warm air, and the air near the ground is some 70 °C warmer than at the cruising altitude of a jet — 340 m/s against 295. Follow the shock down: its angle to the horizon is set by how much faster the aircraft is than the sound around it, and as the sound speeds up that margin shrinks, so the front flattens. If it reaches a height where the local speed of sound equals the aircraft’s own speed, it is running horizontally, and from there it turns back up. That is Mach cutoff, and it is why a jet at Mach 1.1 in the stratosphere can be supersonic and still silent on the ground — the whole basis of quiet supersonic flight over land. Mach 2 at 11 km lands its boom about half a minute after it passed overhead.
Wind moves the cutoff on its own — a tailwind at altitude effectively lowers the aircraft’s speed through the air below it, and a strong headwind the other way — and real days have temperature inversions that bend the shock in both directions. The rule is for still air in a standard atmosphere, and for the boom straight below the flight path; the carpet either side cuts off sooner.
Estimate with the rule, then check it against the calculator that models it properly.
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