The chaff

A chaff cartridge holds millions of aluminised glass fibres, each cut to half a radar's wavelength. The airstream tears the packet into a cloud, which stays where it formed as the aircraft flies on. To the eye it is a faint grey puff.

fire({ payload: "chaff" }) lets a program of it go, from the same dispensers as the flares.

The payloadCopy Anchor Link

CHAFF.rr178, an RR-178 class cartridge, holds 88,775 m of dipole (Dalkıran, Bilkent University), a mil thick, 25.4 µm, the usual. Glass is 2540 kg/m³ and aluminium 2700: at 2600 for the two it throws 117 g, a little under the third of a pound US patent 4,653,403 gives.

Its cuts span 2 to 20 GHz, 7.5 to 75 mm. Taken at their geometric mean, 24 mm, that is about 3.7 million dipoles.

The bloomCopy Anchor Link

The airstream tears the packet apart layer by layer: in a fifth of a second it is a cloud 1.5 to 2 m across and 10 to 12 m long, at about 800 ft/s (US patent 4,653,403). Those are taken as ±2σ of a Gaussian, bloomWidthM 1.75 and bloomLengthM 11 at bloomAtMPerS 244. The length is laid along its path, so it goes with the speed it was thrown at; it is never shorter than the cloud is wide.

It grows as 1 − (1 − t/T)², fast at first and less as the packet slows. The throw is taken as the flare's, 30 m/s from the same impulse cartridge: an estimate.

The fallCopy Anchor Link

A fibre that thin is stopped by the air within a metre, so the cloud stays where it formed, in the air. It then falls broadside. Its Reynolds number across it is a few tenths: the air's wake reaches only a few of its diameters, far short of its length, so Stokes's drag over the whole rod does not hold. Each length of it is a cylinder in Oseen's flow, with Lamb's drag 4πμU / (½ − γ − ln(Re/8)) a metre, against its weight:

U = ρ g d² (½ − γ − ln(Re/8)) / (16 μ)

solved in a few steps, the drag going with the speed only through the logarithm. μ is Sutherland's. Thinner air falls it faster higher up:

One-mil chaff is measured to fall at 0.6 to 1 ft/s, 0.18 to 0.3 m/s, at sea level, about twice that at 40,000 ft (Stine, 1980). US patent 5,212,488 gives 0.3 m/s.

How it spreadsCopy Anchor Link

After the bloom the air's turbulence spreads it as it does the smoke, Richardson's law from its bloomed size. It is let go once even seen end on its depth falls below 0.02, or the air has carried it past the day's visibility: at the default 10⁻³ m²/s³, about half a minute.

How it is litCopy Anchor Link

The fibres stop light with their shadow: a quarter of their surface over every orientation, as any convex body's, π d L / 4, 1.77 m² for the cartridge. Spread over the cloud's Gaussian, that is its optical depth: about 1.5 through its middle as it blooms, seen end on, 0.23 side on.

Aluminium reflects 0.91 of visible light. A convex mirror turned every way scatters the same in every direction, so the cloud is lit with an isotropic phase, 1/4π: the sun's light and the sky's from look, and each burning flare's, I / (d² + σ²). At night only the flares show it.

The glintsCopy Anchor Link

That isotropic light is the mean. Each fibre is a mirror cylinder: it sends a source's light on a cone round its axis, and the eye is on that cone only when the axis is square to h, half way between the source and the eye. A source of angular radius α allows |a · h| < α / |s + v|, and for axes turned every way that bound is the share of fibres glinting: a quarter of a percent for the sun behind the eye, every fibre looking into it.

Those few carry all of the light. Over a frame each fibre sweeps through more of them as it turns: the air's eddies its own size tumble it at (ε / L²)^⅓ (Parsa et al., 2012), 1.2 rad/s at the default turbulence, its order-one constant taken as 1, an estimate; and the view turning turns h half as fast. So each pixel holds a mean count of glints, its dipoles there times that share, and draws a Poisson count of them: where the cloud is dense, hundreds and a smooth grey; where it thins, a few or none, and it glitters. The sky lights it from everywhere and does not glint.

The flashCopy Anchor Link

Once the airstream lets them go, the fibres fall level: a rod falling broadside is turned back to it by the flow's own torque, as ρ U² / (μ ln(L/d)) (Khayat and Cox, 1989), while the eddies tumble it at (ε / L²)^⅓. Their balance leaves it a tilt σ = √(tumble / (2 righting)), about 2.5° at sea level: the scaling is Khayat and Cox's, its constant taken as 1 and used past where they derived it, an estimate, kept under 0.2 rad.

A cloud of mirror facets sends ρ E D(h) / 4 towards the eye, D the share of its mirror facing h. For fibres turned every way that gives back the isotropic light above; level, their axes lie within σ of the horizontal and D goes as e^(−z) I₀(z) / (σ √(2π) |h_y|), z = cot²η / (4σ²), η the elevation of h. Far from the vertical that is 1 / (π cos η), the fibres facing up lighting it less and sideways more; at the vertical, where the sun's reflection would be, it is 1 / (σ √(2π)): seen from above, the sun overhead, the cloud flashes about eighteen times brighter than turned every way, within a few degrees. Over every h it sends out the same light, to within a tenth of a percent. More of its fibres catch the sun there, so the flash is smoother than its glitter.

Level, a fibre also shows more of itself from above than edge on: its shadow is 4/π of the mean seen from straight above, 8/π² from the side.

Left outCopy Anchor Link

• Bent fibres: cut fibres are a little bent, and flutter as they fall; they are taken as straight.
• The wind: the cloud drifts with the air, as the smoke does.
• The radar: what the cloud returns to a radar is not drawn, only what the eye sees.