The engine-out glide ring as a certified band

Everything here is decided on one pinned ADS-B trace: N412JS, a PC12 — a single-engine turboprop, which is why a glide ring is a live instrument and not a curiosity — cruising at 22,000 ft on 2026-08-26. Nothing happened on this flight. The question is what the panel would have been telling the crew if something had.

Four powered scenarios, same flight, same instant, drawn at one scale. Three of them are ordinary: the panel’s configured glide ratio sits inside the honest envelope, so its dashed line falls between the two boundaries and the picture is the familiar one — a solid core, a wide undecided annulus, nothing refuted. Watch the fourth.

The failure is not a bad number. It is an event the instrument cannot observe.

An unfeathered propeller is a large draggy disc, and it roughly halves what the aeroplane can reach. The ring on the glass does not move, because nothing in the system knows. Of the 1491 claims that line makes across the cruise, 425 — 29% — are now provably unreachable for every value in the envelope. The worst single row in that scenario: KN14, Flying W Airport, at 24,000 ft. The field is at least 113 km away, the line promises 115 km of reach, and the band ends at 93 km — not close, and not a judgement call.

Look again at the four ordinary scenarios. Not one of them contains a single refuted airfield, and that is not luck. While the panel’s assumed glide ratio, airspeed and wind sit anywhere inside the honest envelope, its line is mathematically guaranteed to fall between the two boundaries — this build asserts it across every such scenario and refuses to publish if it ever fails. So nothing inside that line can be proved unreachable.

The line is drawn from the very assumptions it would have to doubt. It cannot be caught being wrong — and it is never shown to be right either.

That is the whole case, and it is worth being precise about what it does and does not say. It does not say the ring is inaccurate. It says the ring is unfalsifiable: 54% of what it claims is undecided by the evidence it was drawn from, and it has no way to tell you which part. An instrument that cannot fail a test is not passing one.

What changed in the unfeathered case was not accuracy. The line became falsifiable, and was falsified. That is the difference between the two instruments, and it is why the undecided annulus is the product rather than a defect: a wider band is the same answer with its width shown. Narrow the inputs — real flight-test data, a propeller-state signal, a better wind — and the annulus shrinks. Its width is a measurement of what nobody knows yet.

Every verdict on this page is exact about a glide model. What it says about a real glide rests on that model’s premises, in the order a verdict travels through them, each with the rung its checking reached — validated (against the thing itself, held out), compared (against a model that keeps more), verified (the code against an exact solution of its own equations) or assumed (adopted; nothing here checked it):

1. assumed
   H4 · the envelopes are illustrative classes in stated configurations — not manufacturer data glide ratio and airspeed per class as typed in tools/build-report-glide-band.js, altitude ±250 ft about the ADS-B report, forecast wind speed ±25 % (+4 kt) and direction ±15°. No published performance figure for any aircraft is asserted anywhere here, and nothing claims what any product computes internally; what is compared is the point-estimate METHOD. Move the envelope and every percentage moves. The structural finding of §4 does not — it holds for any envelope wider than a point.
2. assumed
   H2 · steady wind through the descent and a steady-state glide no pushover transient, no shear or thermal structure, and no credit for trading cruise speed back into height. That last one can run either way for a verdict: height bought with the speed the aeroplane carries when the engine stops would add reach the model does not count, so REFUTED rests on H2 as much as REACHABLE does.
3. assumed
   H5 · the turn: height lost turning onto each field at standard rate from the actual ADS-B ground track progress during the turn counted as zero, and charged to both instruments equally. Conservative for REACHABLE; for REFUTED it runs the other way, since ground covered while turning would add reach the model does not count.
4. compared
   H3 · great circles on a sphere whose radius is enclosed by [6356.752, 6378.137] km compared at this build against the geodesic on the WGS84 ellipsoid (Vincenty’s inverse formula, first made to reproduce the textbook line Flinders Peak – Buninyong, 54,972.271 m, to the millimetre) at all 5,120 (cruise position, airfield) pairs decided here, latitudes 39.0° to 40.4° N. The sphere’s lower end holds at every pair, so REFUTED, which reads it, is untouched. Its upper end does not: east–west, the ellipsoid’s radius here is above the interval’s top, and the true distance exceeds the computed upper end at 2,168 pairs, by up to 0.141 %. Of the 21,748 REACHABLE verdicts across the 480 states, 13 do not survive the ellipsoid (9 of them inside the panel’s line, 1 in the headline scenario). They are not re-decided here: the verdicts are the kernel’s, and PROVED REACHABLE carries H3 as it carries H1.
5. assumed
   H1 · terrain is not modelled: the band is glide distance over ground at the field’s own elevation Asymmetric, and it runs the safe way. Rising ground can only REMOVE reach, so REFUTED is unaffected by it; PROVED REACHABLE means “reachable if the path is unobstructed”. A terrain layer moves green fields to undecided, never the reverse.
6. verified
   The band’s arithmetic outward-rounded intervals over the envelope; with a point envelope in still air the band collapses onto its exact solution h × L/D, and 4,000 random draws inside the envelope land inside the band (apps/glide-band/battery.js, 20 checks with 4 red controls, run at this build).

The arithmetic is verified and the geodesy compared; the weakest premise is assumed. Every verdict is exact given H1–H5, which is what the halo on the rings draws: the glide model’s own error has never been measured here, so it has no edge.

Terrain. H1 is the big one. A certified band with a terrain floor is the same arithmetic over a pinned elevation model — the next build, not a research problem.

Real performance data. The envelopes are stated, not measured. Flight-test data would replace H4 with something narrower and the annulus would shrink, which is exactly the point.

Design assurance. Nothing here is DO-178C evidence, and the distance between an exact enclosure and certifiable software is the real cost in avionics.

“We ran ten thousand sorties and saw no failure” has the same shape. It cannot be refuted by the evidence it rests on.

Which is the reason this is worth more than a display feature. The defect on this page is not really about glide rings — it is what happens whenever a point estimate is handed over as a decision boundary, and it is the same defect that makes a test campaign an unfalsifiable safety argument. The glide ring is simply the most legible instance of it: one line, one aeroplane, and a field you either reach or you do not.