Rockets, air and propellant

Rockets, and what the presets changeCopy Anchor Link

A rocket plume is the same field with different physics leaning on it. A preset (src/presets.ts) is nothing but numbers: the per-nozzle params, and the batch's profile.

• There is no burner. burnerThreshold is 0, and dryTemperatureK equals exitTemperatureK.
• The exit is faster and the gas lighter. Exit Mach 3 to 4.5, a molar mass of 13 to 23, so the exhaust leaves at two to four kilometres a second against a jet's one. The potential core is short, the mixing layer is supersonic (its growth falls with the convective Mach number), and the shock spacing is longer.
• The propellant decides the colour and the opacity. Kerolox is sooty: dense and yellow-orange, with an opaque tail that trails smoke. Hydrolox exhaust is water vapour: nearly invisible but for the Mach disks and the haze. Methalox sits between, a violet band glow and a little soot. A solid booster's exhaust is alumina, white and scattering, lit by skyLight and sunLight.

Lengths come from nozzleRadiusM, so a preset resized stays the same plume at a different size. Speeds do not scale, because the gas does not go faster out of a bigger nozzle.

The world scale of a nozzle's matrix also scales the plume without changing its look. Lengths are multiplied by it and densities divided by it, so scale={2} on the group draws the same flame twice the size rather than a thicker one.

Sunlight on the smokeCopy Anchor Link

Sky light comes from everywhere, so it lights smoke evenly. The sun comes from one way, and sunLight, aimed by sunDirection (toward the sun, in world space), adds three things to the particles' scattering:

• Forward scattering. A Henyey-Greenstein phase with g = 0.6: smoke seen against the sun glows, and seen with the sun behind the camera it is dull.
• Self-shadowing. The light reaching a point has crossed the plume between it and the sun. That depth is not marched. The plume's particles fall off across the axis as a Gaussian, so the depth along a straight ray through it is closed form, an erfc of how far the point is past the axis toward the sun. One evaluation a sample, and the side away from the sun goes dark.
• Light that got there anyway. Smoke this dense scatters many times. A share of the light (30%) is let through a shadow thinned to a quarter, so the shadowed side is dim rather than black.

It is zero by default, which is night or a plume lit by the sky alone, and the solid_booster preset turns it on. Give it the direction of the scene's directional light, and keep it in the units skyLight and exposure share.

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The air, and what altitude does to a plumeCopy Anchor Link

altitudeM, temperatureOffsetK and airspeedMPerS replace the old ambient_temperature_k. standard_atmosphere is the 1976 ISA to 86 km, with its eight layers, and isothermal above. atmosphere(profile) adds three things. The day's offset warms the air at the same pressure, so a hot day is a thinner one. Then the speed of sound, and the ram an inlet recovers: isentropic, less the MIL-E-5007 loss once supersonic. Each params pressureRatio is now at sea level, standing still. The plume works out its own from there:

Which one an engine is comes out of its own numbers. breathes is smoothstep(0, 0.2, 1 - dry/exit). An engine whose dry and wet exhausts are the same temperature has no burner, so it is not breathing air.

Six things follow from the ratio and the air.

• Expansion. The jet expands to the ambient pressure. The fully expanded area grows with the ratio, and the gas thins by u_exit / (expanded_area * u_jet). The area is clamped to 0.25–36 of the exit, enough for a booster at 30 km. Near the lip, before the first disk, the gas has not expanded yet. expanding blends the core's temperature from the jet's back to the exit's, and its density from thinned back to one, so the plume does not start already dilute.
• Compression. Behind a Mach disk the normal shock recompresses the gas, by its density ratio scaled to the train's strength. dense is the product of the two, capped at one, and it multiplies the soot, the particles and the band emission alike. That is why a high-altitude disk is the brightest thing in a plume that is otherwise thin.
• The swing is multiplicative. The shock train heats the gas behind each disk and cools it in the fan between them. It used to add a fixed number of kelvin, which at 30 km swung a ballooning plume's fans below absolute zero and made it vanish. It is now T_a + (T - T_a) * (1 + swing)^cell, which never crosses the ambient.
• Quench. The fuel left in the exhaust burns only where there is air to burn it in: quench = ρ(1 + c) / (ρ + c) with c = 0.03. It multiplies afterburningK, so the bright sheath of a kerosene rocket fades as it climbs. It also scales soot burnout: high up there is no oxygen to burn the soot, so all of it survives.
• Soot formation, and why a reheat flame turns blue up high. A hydrocarbon flame's soot grows as about the pressure it burns at to a power of one to two. An afterburner burns at roughly the ambient pressure times its inlet's ram, so a jet's sootPerM is scaled by (pressure * ram)^PLUME_SOOT_PRESSURE_EXPONENT (1.5, capped at 3), blended in by breathes. A rocket's chamber sets its own pressure, so its soot stays. The yellow-orange of a reheat flame on the runway is nearly all soot glowing. Its blue band emission does not depend on the soot. At 9 km, standing, the soot is down to about a sixth, and at 250 m/s the ram brings it back to about a quarter. The flame turns violet-blue, and its diamonds stay. At sea level, standing, the factor is exactly one, so no preset's look there has changed. The altitude sweep example flies it up and back down.
• Haze. The refraction is multiplied by the air's density (Gladstone–Dale), so heat shimmer fades with altitude too.

Airspeed is coflow. Air already moving with the jet shears it less. The velocity ratio λ = U_air / U_jet, capped at 0.85, scales the mixing layer's spread by (1 - λ)/(1 + λ) and divides the core length by the same. The convective Mach number uses the difference of the two speeds. A fighter in cruise therefore draws a longer, tighter plume than the same engine on the stand.

Reach had to change for altitude as well. High up, the first disk stands tens of metres down a ballooning plume, past where the thermal length would have cut the plume off. The shortest a plume is now drawn reaches the first disk plus a cell and a half behind it: max(8r, (firstDisk + 1.5) * spacing).

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Propellant, and why the colour depends on the mixCopy Anchor Link

A rocket runs fuel-rich on purpose: lighter exhaust is faster exhaust, and a cooler chamber is one that survives. The mix is the mass ratio of oxidiser to fuel (O/F), and it decides most of what the plume looks like. propellant.ts turns { fuel, mixtureRatio } into the params that carry it, through the equivalence ratio φ = stoichiometric / OF. Above one is rich.

• sootSurvival = clamp(0.15 + 1.36 (φ - 1.11), 0, 0.95). The richer the mix, the less oxygen the mixing layer has left to burn the soot with.
• The chamber is hottest a little rich of even, at φ = 1.05, and cooler on either side: share = max(1 - 0.45 (φ - 1.05)², 0.4).

propellant_params(propellant, reference) scales a known engine's own values, temperatures included, by how far its mix has moved. A preset therefore comes back exactly at its own mix: kerolox at 2.36, methalox at 3.6, hydrolox at 6. Without a reference, the soot and afterburning come straight from the laws and the temperatures are left alone. resolve_afterburner_params takes propellant as one more input. It is applied before any explicit param, so an explicit param still wins.

What this draws: a kerolox engine run at O/F 1.6 is dark and smoky, and all of its leftover fuel burns in the sheath. At 3.3 it is clean, with a violet band glow and the diamonds showing through. Altitude then compounds it. The thinner the air, the less of the leftover fuel and soot it can burn, so a rich engine high up trails more smoke and less fire.