Contrails vs Chemtrails

A few years ago I got involved in a conversation with my brother in law who has, shall we say, conspiracy theorist leanings.  He was terribly upset whenever he looked up and saw what he described as "chemtrails" in the sky.  Apparently, the illuminati - or whoever - are controlling our thoughts by spraying mind altering chemicals from jumbo jets. The main argument he made was that they didn't look like what you would expect to come out of an engine.

A few days later I was mulling over this while cycling to work.  What, I thought, should it look like?  I realized that it should be really easy to work out and by the time I arrived at work, I'd figured it all out, bar some missing constants that I then looked up.  I quickly knocked up an email which I then sent ... to myself.  Because responding to conspiracy theorists with arithmetic is like poking bears with sticks.

I took special care when researching online not to use any search terms that refer to either contrails or chemtrails so that I didn't end up with values that could possibly have been chosen for the sake of winning this argument.  I was quite proud of the end result, which is that contrails ought to look roughly how those lines in the sky do look.

Here's the email

Subject: Contrails - my own research

Been looking up some numbers.

According to http://wiki.answers.com/Q/What_is_the_fuel_consumption_of_a_Boeing_747 a 747 burns 12 litres per km

Burning 1 gram of hydrocarbon produces approximately 1 gram of water (and 3 grams of CO2) so let's say that a 747 produces 12 litres of water per km.

Now according to http://wiki.answers.com/Q/What_is_the_ambient_temperature_at_30000_feet the temperature at 30000 feet is -50 degC.

And according to http://web.gccaz.edu/~lnewman/gph111/topic_units/Labs_all/Water%20Vapor%20Capacity%20of%20Air.pdf the water vapour capacity of air at -40 degC (which is close enough to -50) is 0.1 g/kg. This means that every km a 747 saturates 120000 kg of air.

Now according to http://www.electronics-cooling.com/1998/09/cooling-electronics-at-high-altitudes-made-easy/ the air density at 30000 feet (about 10km) is about 0.5 kg/m3.  This means that every km a 747 saturates 240000 m3 of air. This is equivalent to two cylinders each with a cross sectional area of 120 m2.

Therefore, you would expect the water vapour produced by the ordinary combustion of fuel to produce two trail shape clouds about 12m in diameter each.

POSTSCRIPT

Just saw two protesters in Amsterdam and took this snap