The smoke
What the flame burns to, laid along each flare's path, spreading and lit.
The flame burns to a white smoke: magnesium oxide and fluoride, and the Teflon's carbon. It is laid along the flare's path through the air, where it stays as the aircraft flies on.
How much
The Teflon's fluorine takes the magnesium it can to MgF₂ and leaves its
carbon as soot; the rest of the magnesium burns in the air to MgO. A
kilogram of MTV, 500 g of magnesium and 450 g of Teflon, leaves 561 g of
MgF₂, 108 g of carbon and 466 g of MgO: 1.13 kg of smoke, smokeYield, its
50 g of Viton left aside.
Along its path it holds what the grain burnt there: ṁ Y / v a metre, the grain's mass rate times the yield over its speed through the air. A flare that is fast leaves it thin, one that has slowed leaves it thick:
| at | smoke a metre | through its middle, as laid |
|---|---|---|
| 250 m/s, released | 0.64 g | τ 2.7 |
| 60 m/s, after 1 s | 2.7 g | τ 11 |
| 30 m/s, falling | 5.4 g | τ 22 |
How it spreads
Across its path the air's turbulence spreads it, as Richardson's law spreads
two points apart: σ² = σ₀² + ½ ε t³, from the flame's own width. ε is the
air's dissipation rate, turbulenceM2PerS3 on air: 10⁻³ m²/s³, the top
of a mixed layer, by default, an estimate of a typical day. It stays a
few metres wide for half a minute, then grows fast: 10 m at a minute, 30 m
at two.
Its optical depth through its middle is κ λ / (√(2π) σ), its cross-section a Gaussian's. It is let go once that falls below 0.02, or the air has carried it past the day's visibility from the aircraft: at 250 m/s, about a minute and a half.
How it is lit
It scatters what falls on it, once, by Henyey and Greenstein's phase: the
sun's light and the sky's, given on look as the contrails' are, and the
flares'. Each burning flare lights the smoke near it as I / (d² + σ²),
brightest by far where it has just passed. A trail shows that light times
1 − e^-τ over what is behind it, and hides that much of it.
What a white oxide smoke stops and scatters is not measured for an MTV
flare's. Its particles are a fraction of a micron; 2 m² a gram
(smokeExtinctionM2PerKg), 0.8 of it scattered, the soot taking the rest
(smokeAlbedo), and a g of 0.6 (smokeAsymmetry) are estimates.
Left out
- The wind: the smoke drifts with the air the flares are laid in. A wind moves that air, the aircraft and its smoke alike.
- Its own shadow: the sunlight reaching a point of it has not crossed the rest of it. A thick young trail is as lit on its far side.
- Light scattered more than once: in a thick trail more of it reaches the eye than once-scattered light gives.