The day

The same aircraft trails nothing on one day and a cirrus sheet on the next. Two numbers of the day decide which.

Cold enough: does it form?Copy Anchor Link

The exhaust is hot and wet. As it mixes with the air round it, both its heat and its water are diluted by the same air, so it cools and dries along a straight line. A contrail forms if that line crosses water saturation on the way: the air must be colder than the threshold the Schmidt–Appleman criterion gives for the day's pressure, humidity and the engines.

On a standard day, for the default fighter on kerosene in dry air:

Humid air lifts the threshold a little, and a warmer day (temperatureOffsetK) eats into the margin under it. The engines matter too: the more of the fuel's heat goes into pushing the aircraft, the less is left to warm the plume, so an efficient airliner trails in air a degree warmer than a fighter.

state.visible says whether it forms, and state.criterion gives the threshold and the mixing line's slope.

Wet enough: does it last?Copy Anchor Link

Once formed and frozen, the trail is ice. What happens to it next is the air's humidity over ice:

• Under 100 %, the ice evaporates as the trail mixes with the dry air round it. It lasts seconds: under ten at 50 %.
• Over 100 %, the air is supersaturated over ice. The crystals take up the excess vapour as they mix into it and grow: the trail persists, and spreads into a sheet of cirrus as long as the air stays that way.

state.iceHumidity and state.persistent say which.

Humidity over water, humidity over iceCopy Anchor Link

air.relativeHumidity is over water, as @aeronautic/core and a Flight take it. At contrail temperatures ice saturates at far less vapour than water: at -56.5 °C, 59 % over water is 100 % over ice. Turn one into the other with the helpers:

import { moist_air } from "@aeronautic/core";
import {
  humidity_over_water,
  ice_humidity,
} from "@aeronautic/contrails/physics";

const temperature_k = moist_air(11_000, 0, 0).temperatureK;

// 112 % over ice, the default day: 66 % over water
const relativeHumidity = humidity_over_water(1.12, temperature_k);

// And back
ice_humidity(moist_air(11_000, relativeHumidity, 0)); // 1.12

A day from the providerCopy Anchor Link

Inside a <FlightProvider>, the altitude, temperature offset and humidity come from its flight and win over air, so every package on the aircraft flies the same day.