Persistent Spreading Contrail

How long can a persistent spreading contrail last? Can there be a contrail shadow with a spreading contrail?

Contrails are basically just clouds.. so they can last as long as the conditions allow them to. Sometimes thats just a few minutes, sometimes its several hours.. there's no way to really put a number on it because it all really depends on the weather conditions at the altitude the contrails are at. Things like how fast the air is moving, the humidity at altitude, the temp, etc.. just like with regular clouds.
 
How long can a persistent spreading contrail last? Can there be a contrail shadow with a spreading contrail?
And yes, spreading contrails can cast shadows. They are just clouds: there is nothing special about contrails. Anything a cirrus cloud can do, so can a contrail.

As to how long they can last, one study which deliberately created distinctive contrails by flying in circles found the cloud they formed was still visible 18 hours later: http://www.met.reading.ac.uk/~sgs02rpa/PAPERS/Haywood09JGR.pdf
 
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