The Reflection Bench: Visualisation · Signals from the Periphery

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THE SKY

Subject

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Value

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State

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THE REFLECTION BENCH
U-2, OXCART, and the CIA's own UFO claim
the mechanism can be computed; the share must be counted
2.18° of extra daylight, and refraction cancels
a glint to magnitude -10, calibrated on Iridium
4,294 sightings demanded, and no tally ever shown
run the evening · sweep the roughness · read the table

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Evidence

fact ⇄ what kind of claim · live

CIA-UAP-003: the sun had set for the airliner, not for the U-2 above it

the document's own mechanism, stated in physical terms

REPORTED

dip(70,000 ft) − dip(20,000 ft) = 2.177°, and refraction cancels

arccos(R/(R+h)) · about 11 minutes at 40° N, twice a day

EXACT

Iridium's 1.9 m² antenna at 780 km flared near magnitude −8

this bench's glint model returns −8.3 before it may describe a U-2

MEASURED

The beam grazes the air, so it arrives red and several magnitudes down

computed here · which is why the reports say fiery, not silver

MODELLED

CIA to Sea Blue mid-1958; USAF bare to 1962; all Black Velvet from late 1965

the finish the mechanism needs was gone before the window closed

MEASURED

Blue Book: 12,618 reports, 701 unidentified; largest year 1,501 in 1952

the biggest year in the record predates the U-2's first flight by three

MEASURED

Blue Book's own chief saw no appreciable rise after the U-2 began flying

Robert Friend 1997; Maccabee's ten-months-either-side test agrees

REPORTED

"More than one-half" is a summary judgement with no figures attached

the flight-log comparisons the history describes were never published

READING

View

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The moment

Solar depression3.20°

Degrees below the horizon. The physics cares about this, not the clock: how many minutes it buys depends entirely on latitude and date.

Latitude37.0° N

The sun falls at a quarter of a degree per minute at the equator and far more slowly toward the poles. 25° to 49° covers the contiguous United States.

Who is looking, and at what

Range60 km

Ground range from the observer. Line of sight from 20,000 ft to 70,000 ft reaches about 800 km, so the whole dial is geometrically available.

Bearing from the sun28°

0° puts the aircraft toward the sunset, 180° puts it opposite. Bearing decides the phase angle, and with it how much of the reflection comes your way.

The surface

Surface roughness1.00°

The half-width of the specular lobe: the one quantity nobody published. The shaded band in the Glint view sweeps it, and the conclusion does not move.

The count

US sorties per year1,000

Never published, so it is a dial rather than a number. Whatever you assume, the readout prices the claim in reports per flight.

The Earth's shadowsolved per azimuth

Starsfade in as the sky gives up

Naked-eye gatehide what the sky would swallow

Labels

Readout · live

Dip: target / observer

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Window, this date

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Open, per year

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Apparent magnitude

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This sky reaches

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Reports per sortie

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What is exact vs modelled here

Exact: the horizon dip, the sunlit test at every point, the window in minutes, the annual open fraction, the Earth's shadow on the sky, and the great-circle placement of every mark. Nothing in that list is fitted. Measured: Blue Book's year table in full, the published dimensions and ceilings, the paint history, the flight counts that were published, and the Iridium flare the glint model is calibrated on. Modelled: the two brightness channels, the atmospheric reddening, the twilight limiting magnitude, and the sky colour. Reported: the CIA passage itself, and the objections from Friend, Maccabee, Friedman and Hastings. Reading: whether a mechanism that works explains a share nobody has ever counted.

The model, in full

An altitude h holds the sun until the sun's true elevation reaches −(arccos(R/(R+h)) + 0.833°), the second term being refraction plus the solar semidiameter. Since it is identical at both ends it cancels in the difference, so the window's width is refraction-free. Solar position is the standard low-precision reduction, run in local apparent solar time. Brightness has two channels: a convex Lambertian body calibrated on the diffuse sphere law, and a specular facet with a Gaussian lobe whose peak is capped by the sun's own angular size, which is what makes it reproduce a measured Iridium flare at −8.3. The incoming beam is attenuated along its tangent path by Rayleigh scattering with the standard sqrt(2πR/H) enhancement, three bands, which supplies both the dimming and the colour. All anchors in scripts/u2-tune.mjs.

Where this instrument takes liberties

The sky colour is the Preetham analytic model on an exposure ramp; below about five degrees of depression it is held and dimmed rather than solved, and the starfield is a deterministic scatter rather than a catalogue. The twilight limiting magnitude is an empirical stand-in curve, not a measurement, and the bonus for an observer above most of the air is a rounded estimate; it is the least certain number here and everything gated by it is marked. The airframes' side and frontal silhouettes are estimated from the three published dimensions with a fill factor, the wing areas are published, and a factor of two in either is 0.75 magnitudes. Ozone's Chappuis band is not modelled and would redden the beam further. The claimed window is dated 1956 to 1968 because the document does not date it, and that is the widest reading its wording supports. The Geometry view stretches the vertical axis and prints the factor.

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