Ask A Scientist Physics Archive

          
name         Dave C.
status       other
age          40s

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?
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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
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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
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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
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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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