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Name: Dave C.
Status: other
Age: 40s
Location: N/A
Country: N/A
Date: 8/4/2004


Question:
Hydrogen balloons are more buoyant than helium balloons. Ignoring the practical problems (building it light enough and yet still strong enough to maintain its shape without internal pressure) would a balloon that is "filled" with vacuum be even more buoyant than hydrogen? How much?


Replies:
Dave,

What an intriguing question! I am a chemist, so take what I say accordingly. Nevertheless, I will put in two cents worth.

I think it would be more buoyant because buoyancy is related to the volume (weight) of air displaced relative to the weight of the load. Your theoretical vacuum-filled balloon made of all-but-weightless materials would offer displacement without the weight of the lifting gas itself. At this point, I think the balloon just disappeared in my mind. Now, lets see what NEWTON experts have to say to set me (us) straight. Thanks for asking the question.

Regards,
ProfHoff 897


Archimedes' principle is: A body is buoyed against the force of gravity by a force equal to the weight of the volume of displaced fluid. The practical problem of a "vacuum balloon" is finding a material that can maintain a significant volume against the compression force of the atmosphere: 1 atm = 101325 N/m^2 = 14.7 lb/ft^2

In the "experiment" you propose it is easier to visualize if instead of the atmosphere, consider the surrounding fluid to be water. Here submarines submerge/float by filling the ballast tanks with water/air. Here the buoyant force is controlled by changing the weight of the submarine, whose volume remains essentially fixed. So the buoyant force is either larger than, or less than, the weight of the submarine.

Vince Calder


Dave C.,

I do not have the numbers in front of me, but a "vacuum" balloon still maintaining its shape would be more buoyant. How buoyant something is in our atmosphere is actually a combination of two major forces: buoyancy, gravity. The buoyant force can be described quite easily: the weight of displaced fluid. For the balloon, this is the weight of displaced air. Gravity is the weight of the balloon and anything within, including any hydrogen or helium. Weight of a gas must be as measured in a vacuum, mass of the gas times gravitational acceleration (often expressed as "g"). The buoyant force is always upward, while gravity is always downward. The net effect is the difference between the two. If the buoyant force is greater than the weight, the object is "buoyant".

The balloon displaces the same amount of air whether filled with hydrogen or with nothing. The only requirement is that initial shape and size do not change. The empty balloon weighs a little less than the hydrogen balloon, and so has a greater net lift. The empty balloon will in fact be more buoyant by the weight of hydrogen within the hydrogen balloon.

Dr. Ken Mellendorf
Physics Instructor
Illinois Central College


The buoyancy you get from a balloon is the weight of the air that would replace the balloon minus the actual total weight of the balloon.

So if you have a very light gas and structure, the maximum buoyancy attainable depends on density of air (and strength of local gravity) more than on what's in the balloon.

If you build a perfectly weightless "vacuum balloon" you will get the maximum possible buoyancy for our air and gravity, which is about 1.3 kilograms per cubic meter of balloon-volume.

Then it is intuitively useful to think of any other balloon as offering some percentage of that maximum. The molecular weights of the gasses are good for figuring this percentage.
Nitrogen, N2,  28 grams/mole.
Oxygen, O2,     32 grams/mole
Air, 80% N2/20%O2, averages 28.8  grams/mole (I'll call it 29.)
Steam, H2O,    18 grams/mole
Helium, He,      4 grams/mole
Hydrogen, H2,  2 grams/mole
vacuum             0 grams/mole  (i.e., imagine the same number of 
particles as air would have, each with zero mass.)

( A mole of gas molecules fills a certain volume at a certain temperature, such as 22.4 Liter-atmospheres per mole at room temperature.)

If the buoyancy of vacuum is [air]-[vacuum] = (29)-(0) = 29 :: 29/29 = 100%, then the buoyancy of

hydrogen: [air] - [H2] = (29)-(2) = 27 :: 27/29 = 93%,
helium: [air] - [He] = (29)-(4)= 25 :: 25/29 = 86%,
steam: [air] - [H2O] = (29)-(18)= 11 :: 11/29 = 38%

(but then, steam must always be hotter than normal-temperature air, so it gets more like 50% buoyancy. )

You can see that vacuum offers only several percent more buoyancy than hydrogen. If helium were a bit cheaper it would do everything we could expect from a balloon.

The main advantage on Earth would be that a vacuum structure might be less flammable than hydrogen and cheaper than helium. The main advantage on Jupiter would be that the atmosphere there is mostly hydrogen, so we would need something lighter than hydrogen to have any positive buoyancy. For Jupiter I think we would do a "hot air balloon" sooner than a "vacuum balloon", but I cannot be sure.



Jim Swenson



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