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Why do contrails form?
Short answer
Contrails form when hot, humid exhaust from jet engines meets air that is cold enough, typically below about −40 °C at cruise altitude, for the water vapour to condense on soot particles and freeze into ice crystals. Whether they linger or vanish within seconds depends on how close the surrounding air already is to ice saturation.

Exhaust meets cold air
Burning one kilogram of kerosene releases roughly 1.25 kg of water vapour along with carbon dioxide, soot and sulphur compounds. It leaves the exhaust nozzle at several hundred degrees Celsius, far too hot to condense. Within a fraction of a second, however, the plume mixes with ambient air that, at typical cruise altitudes of 10 to 12 km, sits between −40 °C and −60 °C. Mixing lowers the temperature far faster than it lowers the water content, so for a brief moment the mixture becomes supersaturated. Water vapour then condenses on the soot particles and, at those temperatures, freezes almost immediately into ice crystals. A contrail, short for condensation trail, is a line of tiny ice crystals, physically the same thing as a cirrus cloud.
The Schmidt–Appleman criterion
Whether a trail forms at all is governed by a relationship worked out in the 1940s and 1950s by Ernst Schmidt and Herbert Appleman. It combines the ratio of water to heat in the exhaust with the ambient pressure and temperature. Below a threshold temperature, typically around −40 °C but varying with altitude, humidity and engine efficiency, the mixing line crosses water saturation and a contrail appears. Above it, nothing visible forms. Modern high-bypass engines are more efficient, so they leave more of the fuel's energy as thrust and less as heat in the exhaust; counterintuitively, that makes contrails slightly more likely, because the plume cools with relatively more water in it.
Why some persist and others vanish
The lifetime of a contrail depends on the surrounding air. If it is dry relative to ice, the crystals sublimate within seconds and the trail is a short white dash behind the aircraft. If the air is already supersaturated with respect to ice, which happens frequently in the upper troposphere, the crystals keep growing by taking up ambient moisture and the trail can spread over hours into a sheet of contrail cirrus several kilometres wide. These persistent trails matter for climate: they trap outgoing infrared radiation, and studies by DLR and others suggest their warming effect is comparable to, or larger than, that of aviation's carbon dioxide. Rerouting flights around ice-supersaturated regions is currently being tested as a way to reduce it.
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