Question of the Week

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

Sun, 25th Jul 2010

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Matthew asked:

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?


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. Shuttle Launch

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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Could use all your waste to produce biogas, which is mostly methane,
then burn the methane to power a hot air balloon to lift you off the ground.  RD, Sun, 18th Jul 2010

If we are talking about a reaction engine (a jet of sorts) it's not so much the mass of gas as how much you can accelerate it.

If you had one pound of gas, I think you would have to accelerate it by 140 times g (32 ft/sec^2) to achieve "lift off" if you weigh 140 pounds (10 stone) and you are standing on the Earth.

That comes to roughly 4,480 ft/sec^2 Geezer, Mon, 19th Jul 2010

Your guts would explode : a pound of methane would take up over 60 litres at STP.

High pressure gas in your bowel is hazardous ...

BTW as Vlad the impaler would tell you, your intestines will not support your body weight.
RD, Mon, 19th Jul 2010

Your guts would explode : a pound of methane would take up over 60 litres at STP.

High pressure gas in your bowel is hazardous ...

BTW as Vlad the impaler would tell you, your intestines will not support your body weight.

Well, yes. There are a few minor practicalities to consider.

Another slight problem would be cooling. Assuming the gas had been stored under sufficient pressure to achieve lift off prior to being released, the rapid expansion when it returned to atmospheric pressure would have a rather extreme cooling effect.

I think it might, quite literally, freeze the subject's a*s off. Geezer, Mon, 19th Jul 2010

Maybe store the gas in a robust CO2 type gas cylinder ...

See this youtube video from 2:44 onwards
RD, Tue, 20th Jul 2010

There is a fairly simple equation to figure out how much thrust you need to accelerate a given mass to a given "delta V" (change in velocity..."velocity" is a vector, speed and direction).

The simplest answer neglects the mass change due to the burn, and just derives thrust F from velocity change dv, time t and mass m. Acceleration a = dv/t = 0.6 m/s^2. F = ma = 12000 N.

You'll need to know the mass of whatever is being used to create the thrust. Human flatulence is usually (if you're in good health) composed mostly by normal air Nitrogen: 20–90% Hydrogen: 0–50% Carbon dioxide: 10–30% Oxygen: 0–10% Methane: 0–10%. There are tiny amounts of other gasses which are responsible for the smell.

To lift off the Earth you need a delta V greater than 1G or 32 feet per second. This is quite a lot of thrust for the average sized human. It'd think the pressures required would cause a rupture in the holding tank which I imagine would be extremely painful and quite likely fatal (considering the "tank" is your guts).
mountaineirc1969, Thu, 22nd Jul 2010

or power a VW "dung" beetle ...

*What's that in "miles per turd" ?  RD, Sun, 8th Aug 2010

The fart-lift-off-phenomenon relies on Newton's lesser-known "turd" law... chris, Mon, 9th Aug 2010

That would alter the math quite a bit. If the "object" had sufficient mass and it was accelerated quite a bit, in a low gravity situation, liftoff might actually be possible.  If they ever build a base on the Moon, they might want to consider installing seat belts on the cans. Geezer, Tue, 10th Aug 2010

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