minimum size for foil balloon to float?September 29, 2009 12:40 AM   Subscribe

How small can a helium filled foil balloon be...and still float?

If I created a foil balloon about the size of a coffee cup and filled it with helium would it still float? Or is there a minimum size to become airborne? I don't want to waste my time if its impossible.
posted by swiffa to Science & Nature (9 answers total) 1 user marked this as a favorite

Best answer: ((Density of Air)*(Volume of Coffee Cup) - ((Density of Helium Gas) *(Volume of Coffee Cup)) - (Mass of Aluminum Foil)

Density of air: 1.19 g/L.
Density of He: 0.1786 g/L
Volume of coffee mug: ~ 0.4L
Mass of Aluminum foil needed: This is up to you

If the result is negative, it floats.
posted by pseudonick at 12:51 AM on September 29, 2009 [2 favorites]

Anecdote: a florist near me sells bunches of "silver dollar" foil balloons. They're cheating a bit on that description, but not much: I'd guess the diameter is about two inches, with the usual lemon-shaped profile.
posted by rokusan at 1:04 AM on September 29, 2009 [1 favorite]

pseudonick has the answer. Just plug in the values, and you can find out if any random thing will float. Substitute the density of air with the density of water (1000 g/L), and you can reuse the formula for all your nautical engineering, too.

One thing you might keep in mind for your math is that a "foil balloon" is not made of aluminum foil. It's a nylon sheet with an atom-thick layer of aluminum vapor-deposited over it (protip: it's actually not Mylar, which has a different plastic base).

Just pointing this out in case you'd intended to use pseudonick's formula and regular kitchen aluminum foil--which is about a thousand times too thick and heavy.
posted by Netzapper at 1:12 AM on September 29, 2009

Best answer: Remember that air is a fluid just like water. To make something float, you have to make it weigh less than the fluid that it is in. A boat is full of (mostly) air. The weight of the boat pushes down on the water, and the density of the water pushes up on the boat. If the boat is heavier than the amount of water it can displace, it will sink. I believe Mythbusters once made a foil boat, and then filled it with a very heavy gas, and it sank.

(exactly as pseudonick writes) A coffee mug displaces 0.4 L of air, and that air weighs ~0.48 grams. If a 0.4L balloon was filled with helium, that helium would weigh 0.07 grams. So your balloon can't weigh more than .40 grams or so.
posted by gjc at 3:58 AM on September 29, 2009

If you further assume a sphere, then you can calculate the minimum radius as a function of the density of the foil: R = 3 * (mass of foil per unit area) / (difference between density of air and density of helium.)
posted by Rhomboid at 4:09 AM on September 29, 2009

I believe pseudonick means, "If the result is positive, it floats."
posted by dsword at 5:49 AM on September 29, 2009

Just a bit of anecdotal data: here is the Mythbusters episode where they build a balloon out of regular aluminum foil first, and then one out of lead foil (to see if a "lead balloon" could really float). Skip to 5:07 for the first flying aluminum balloon.
As they explained in this episode, bigger is better - the mass to be lifted (foil) grows with the surface area of the balloon (2nd power), the lifting power (helium) grows with the volume of the balloon (3rd power).
posted by PontifexPrimus at 5:55 AM on September 29, 2009 [1 favorite]

Don't forget to compensate for altitude, temperature and humidity...
posted by cosmac at 8:02 AM on September 29, 2009

A while ago I was working on an installation that involved copper foil balloons. At two thousandths of an inch thickness, I calculated that the balloon would have to have a volume of just about a cubic meter (in the shape of a cube) if the seams were wasteless and weightless.

If you really mean Mylar (or similar) then I should think it can be pretty small.
posted by cmoj at 8:53 AM on September 29, 2009 [1 favorite]

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