How much gas would I have to expel to achieve lift off?

25 July 2010

Question

How much gas would a 10 stone human have to expel (and with what force) in order to lift themselves 1 inch off the ground?

Answer

We put this question to Dr Mark Lewney, award-winning science communicator based in Cardiff...

Mark - If you weigh ten stone, or 63.5 kilograms, then the Earth pulls on you with a gravitational force of 622 Newton which you have to then overcome if you want to lift off for even a fraction of a second. You have to direct a force at least this strong towards the ground, which according to Newton's Second Law will be equal to the mass of the gas you expel multiplied by the acceleration given to it by your bowels. That means you could give an enormous amount of gas a small acceleration or give a tiny mass of gas a huge acceleration.

So how much does the average emission weigh? This is quite tricky to measure since methane is lighter than air. You actually weigh more after letting rip a ripe hum-dinger on boxing day due to a slight loss of buoyancy. Assuming that is that you don't also follow through with non-gaseous matter; an act commonly known as "sharting". Incidentally, pure methane is also completely odourless which proves that every real fart is actually a "shart" in disguise. Having asked Jeeves what the mass of the average human trump is, given the density of methane and the pressures and temperatures found in the bowel, he returned - admittedly with his nose turned up even higher than usual - with an answer of 0.037 grams or 0.000037 kilograms.

So, to generate the upward force required to oppose gravity, your bowel muscles must give this mass an acceleration of 622 divided by 0.000037, which equals 17 million metres per second per second, almost 2 million times the force of gravity. Assuming it's expelled in a 1 second toot, that yields a final exit velocity of 17,000 kilometres per second which is equal to 37.6 million miles an hour or 18% of the speed of light.

Anyone capable of achieving this feat is invited to contact the UK Space Agency with a view to highly profitable long term employment.

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