How much do we float in atmosphere?

The atmosphere is a fluid and we have volume, therefore we displace some of it and some buoyancy force must exist. How strong is it? How much does it affect gravitational acceleration on the surface of Earth? And considering only buoyancy (no drag), how much difference would make falling in atmosphere and a vacuum?

• One quick way to look at it: Humans are mostly water, water is about 1000 times denser than air so your apparent mass is reduced through air buoyancy by about 1/1000 Feb 11, 2015 at 13:40

Average human body volume = 0.0664 $m^3$ (seems low to me, but that's according to Wolfram Alpha: http://www.wolframalpha.com/input/?i=volume+human+body). Density of air depends on temperature and pressure, but is about 1.2 or 1.3 $kg/m^3$. That means we displace, on average, about 80 g of air, giving us a buoyancy of about 0.8 N (about 1/6 lb).

The acceleration due to gravity and buoyancy would be $a = g - \frac{F_\text{buoy}}{m}$. To take round numbers, use $m = 80 kg$. Then the second term is $-0.01 m/s^2$, reducing the acceleration by about one part in 1000. (The effect of drag becomes much bigger pretty quickly as you fall.)

• The human body volume seems accurate. The average human does not float in water and assuming a mass of 80kg it's volume must not be larger than 80l. Therefore i think wolfram is correct with the 66l it is saying. Feb 11, 2015 at 8:56
• @SpaceTrucker: "The average human does not float in water" -- well, that critically depends on whether you count the lung capacity as inside or outside the human (most people just about float if they keep their mouths shut, drowned bodies not so much). Fortunately, for the purpose of buoyancy in air it doesn't really matter which you choose :-) Feb 11, 2015 at 10:33
• You have the acceleration delta in Newtons... Feb 11, 2015 at 10:59
• $= 87.6 \text{ Indian chungas} = 166 \text{ Hessian Schoppen}$ ;-) Feb 11, 2015 at 14:28
• @A.Donda -- resisting the temptation to edit all questions so volume is expressed in kilochungas and microschoppen...
– Joe
Feb 11, 2015 at 18:42

You will displace air equal to your volume. If your volume is $v$,you will displace air of volume $v$, If the density of air is $d$, then the mass of the air displaced will be equal to the product of volume and density. and thus force on you according to Archimedes ' principle =$vdg$,

'g' is the acceleration due to gravity.

Archimedes' principle indicates that the upward buoyant force that is exerted on a body immersed in a fluid, whether fully or partially submerged, is equal to the weight of the fluid that the body displaces. http://en.m.wikipedia.org/wiki/Archimedes%27_principle

• For some scale, assuming a human has a density approximately equal to that of water, we weigh .12% less in air than we would in a vacuum.
– k_g
Feb 11, 2015 at 3:31

Not much. By Archimedes principle the buoyant force is equal to the weight of the volume of fluid displaced, which would be the volume of your body. And the fluid is air. So you would only be slightly heavier than you are now if there was a vacuum at the earth's surface.