This is my take on the generation of vapour trails. It's rather long, so ignore it if it's not of interest to you. (Sorry also to Wayne, who has asked us to be brief.)
It's in two parts. The volume of vapour involved and the mechanism of trail formation.
Taking Fluffy..'s data on a 747 allows you to calculate the first part. I've assumed it's flying at 35,000 feet. The numbers vary a bit for other altitudes, but 35,000 seems about average for commercial jets.
A 747 produces 15 tonnes/hour of water in the exhaust gas of its four engines. The volume of water vapour this creates can be calculated using Avogadro's Law and the Combined Gas Law (Boyle's + Charles' Laws).
Avogadro says that the vapour created from one gram mole of any substance occupies 22.4 litres at N.T.P. (Normal Temperature and Pressure) which is 0C(273K) and 760mmHg.
A gram mole of water is 18 grams, so every hour the 747 creates:
15,000,000/18 g.moles
= 833,333 g.moles
The volume of this at NTP = 833,333 x 22.4 litres
= 18,670,000 litres
To convert this to 35,000 feet requires the Combined Gas Law: P1.V1/T1 = P2.V2/T2
At 35,000 feet the atmospheric pressure is 179 mmHg and the temperature is -65.6F(-54C/219K). These data are available
HERE and
HERE.
So: 760 x 18,670,000/273 = 179 x V/219
Therefore: V = 63,590,000 litres/hour
= 17,700 litres/second
Blimey, I hope somebody will confirm these figures!
The second part is what happens to this invisible vapour?
The atmosphere will support a certain water vapour content. Its capacity to do so is directly proportional to temperature and pressure. Hot air holds more than cold. High pressure more than low.
Under specific conditions, water vapour will condense into liquid droplets (fog). These conditions occur at the
Dew Point of the air. If the Dew Point is below 0C, the fog may freeze into ice crystals, so it's called the
Frost Point.
Ice formation usually requires a nucleator such as dust, soot, pollen, bacteria, etc. around which the crystals form. Without this, water drops can go down to -40C without freezing.
If the atmosphere is at or near the Dew Point, any excess water vapour added to it will condense into fog/ice crystals. This is when vapour trails are produced. Wing tip/vortex precipitation produces transient trails because no extra water is involved. This fog re-evaporates very quickly.
If the atmosphere is very dry, it will be well above its Dew Point and the extra vapour introduced remains in the gaseous phase. So no vapour trail is produced.
In 1998, NASA flew a jet in circles until its vapour trail created a Cirrus cloud covering 1,400 square miles! See
HERE.
Does anybody fancy checking the numbers? All the required data are available where indicated.
Cheers,
JaX
