The Stealth Bench: Visualisation · Signals from the Periphery

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THE RANGE

Subject

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Value

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State

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THE STEALTH BENCH
The B-2, the radar equation, and a Moscow paper
the shape is computable; so are its limits
every edge in two directions · four spikes, computed
the sphere is exact, and calibrates the whole bench
the fourth root: ten thousand times quieter buys ten times closer
walk the radar · change the wavelength · read the file

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Evidence

fact ⇄ what kind of claim · live

Physical optics over flat polygons: Gordon's edge sum, closed form

checked to machine precision against the plate formula 4πA²/λ²

EXACT

The conducting sphere: the one scattering problem with an exact answer

Mie series summed live; 3.65× resonance peak at ka ≈ 1.03 reproduced

EXACT

Straight edges as equivalent currents, calibrated to L²/π at broadside

the poor man's Ufimtsev; multi-bounce omitted, which favours the fighter

MODELLED

B-2: 52.4 m span, 33° sweep, 21 built, first flight 17 July 1989

published record; its actual RCS is classified and carried as a band

MEASURED

Detection range ∝ σ^¼: minus 40 dB of RCS buys one tenth the range

algebra on the radar equation; both halves of the stealth story

EXACT

A quarter-wave absorber is silent at 10 GHz and returns 91% at 1 GHz

exact transmission-line solution; real coatings detune the same way

EXACT

1999: an F-117 down, with a VHF P-18 in the kill chain

the only combat loss of a stealth aircraft, and it followed this arithmetic

REPORTED

Black triangles, the Belgian wave, and the 1992 charged-edge report

what the secrecy explains, what it cannot, and what nothing settles

READING

View

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The target

Sphere radius1.00 m

The calibration sphere, and the Bands view's subject. Slide it and watch the four band dots ride the exact Mie curve through three regimes.

The radar

Azimuth25.0°

Where the radar stands, measured off the nose. The wing's four spikes live at 33°, 147°, 213° and 327°, each a fraction of a degree wide.

Elevation2.0°

The radar's look-up angle. Ground radars live in the first few degrees; push toward 90° and meet the belly, a 536 m² mirror.

The ladder

Your target's σ0.0001 m²

Set any cross-section and the Ladder view prices it against a radar that sees 100 m² at 400 km. The fourth root does the rest.

Floor patternthe computed sweep, laid around the target

Edge highlighttwo colours = two directions

Rose overlaysthe other shapes, faint

Labels

Readout · live

This look returns

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Circle above 1 m²

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Median, full circle

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Wavelength

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Range it buys

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Sphere regime

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What is exact vs modelled here

Exact: the physical-optics integral over every flat facet (Gordon's closed-form edge sum, machine-checked against the plate formula), the full Mie series for the sphere, the Salisbury screen's reflection coefficient, and the fourth-root range law. Measured: the B-2's published dimensions, dates and fleet size, and the P-18 and S-125 identities in the 1999 loss. Modelled: the straight-edge term (equivalent currents calibrated so a broadside edge returns the textbook L²/π) and the baseline fighter itself, a generic conventional airframe. Multi-bounce returns (inlet cavities, corner reflectors) are not computed, and they would make the fighter worse, so the comparison is conservative. Reported: the reference RCS figures, the open B-2 estimates and the Vega 31 account. Reading: what the stealth era's secrecy does and does not explain in the sightings record.

The model, in full

Monostatic scattering is computed as physical optics plus an edge term. Each lit flat polygon contributes its exact phase integral by Gordon's method: the surface integral collapses to a sum over the polygon's edges, so a facet of any size costs its edge count. Each straight edge contributes an equivalent line current whose coefficient λ/2π is fixed by requiring the textbook broadside answer σ = L²/π, and whose sinc pattern falls out of the line integral. The sphere is the full Mie series with downward-recurrence Bessel functions, summed to machine precision. The absorber is the exact transmission-line solution of a 377 Ω sheet a quarter wave over metal. Detection range is R = R₀(σ/σ₀)^¼. Every anchor is checked in scripts/stealth-rcs-tune.mjs.

Where this instrument takes liberties

Physical optics is a high-frequency approximation: it is excellent in the optical regime the aircraft was designed in and degrades toward resonance, which is why the VHF story is carried by the exact sphere rather than by the wing model. The edge term is a calibrated stand-in for Ufimtsev's full theory. Travelling waves, surface joins, gaps and cavities are not modelled: on a real conventional aircraft those raise the return substantially, so every comparison here understates the wing's advantage rather than overstating it. The rendered bodies carry visual thickness and bulges the flat-facet model does not have. The baseline fighter is deliberately generic and stands for a class, not a type. The B-2's true RCS is classified: this bench never claims it, and carries the open estimate band instead. The 3D aircraft is "Lowpoly B2 Spirit bomber" (skfb.ly/pKVRV) by SIpriv, CC BY 4.0, modified: munitions removed, materials converted, scaled to true span.

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