I have a feeling this is an obviously dumb question, but here goes anyway.
A hypothetical experiment is set forth below.
First obtain a very lightweight yet very strong carbon fiber sphere, such that it resembles a large tough plastic balloon. Said sphere, is about, one meter in diameter and hermetically sealed except for one small valve. Said shut-off valve is used for the following two experiments:
A: The sphere is filled up with helium gas; the valve is then shut, whereupon the sphere acts like a big balloon, floating gently upward, as one might reasonably expect -yes?
B: Now the same sphere, having, of course, the remarkable property, that it can withstand pressure or high vacuum, with out altering its shape in any way, (the kind of balloon available on the planet Krypton) is now evacuated of air, this presumably would make the sphere or balloon lighter, as the air inside must weigh something. Would this newfangled vacuum balloon now act like the buoyant helium filled one described above-yes or no? I suspect not, but I don’t know, why please, enlighten me. Thanks in advance, I’ll hang up and listen to your answer.
Assuming that your “carbon fiber balloon” didn’t weigh enough to hold itself down (which you said it floats when filled with helium, so we can assume so), then yes, it would rise also. The density of the vacuum balloon would be less than the air around it. Heavy things fall down, lighter things go to the top. That’s about as non-scientific an answer you’re going to get on this board. Hope it helps.
Your balloon displaces a volume of air that weights aproximately 4.9 grams. It’s contents in helium weights approximately 0.68 grams. If the balloon plus helium weights less than 4.9 g it will float. Of course, the balloon with vacuum at it’s interior will weight 0.68 grams less than filled with helium and will float more easily.
Anything will float if it displaces its own mass or more of the medium it is in. Ships, helium balloons and evacuated carbon spheres will all float for the same reason.
You realize that if you go the vacuum method your sub-4.9 gram carbon fiber balloon will have to withstand more than 35 tons of pressure on its surface at sea level if it is completely evacuated. Interesting how filling it with 0.68 grams of helium will provide 35 tons of outward force to balance the atmosphere. I love physics.
While I know all this is true about what it takes to amke an object float, it is hard to picture what is the source of the buoyancy force? Maybe I am missing something basic, but if I drew a free body diagram (FBD) of a helium balloon, I would have a vector pointing straight down with a magnitude of m*g (the weight, pulling downward) and what greater vector pulling upwards??? (Plus, a small vector “f” downwards for air resistance.)
I was trained to think in terms of FBDs, but perhaps the hardest thing for me to picture when using a FBD here is that gravity makes it all work. And, we all know gravity pulls downwards, not up. If there could be a planet just like earth, but no gravity, helium balloons wouldn’t float upwards.
Yet, since when did volume ever enter into a force-balance problem (typically static, but not necessarily when trying to show all the forces acting on a body)? I just came to accept it, but it does bug me a bit. Maybe someone can share how they were taught to understand the fine print of buoyancy.
- Jinx
Thanks for the information, but why have we not seen a glut of
Newfangled vacuum balloons on the market?
Given new space age materials and so on, witness the gossamer condor
Human powered airplane etc. Could not a sufficiently large carbon fiber dodecahedron skeleton cleverly reinforced with titanium tubular struts placed inside and then covered with airtight Mylar sheeting, be able to withstand sufficient vacuum to float in air? As you suggest.
After all a vacuum is free whereas helium is rather costly.
Helium may be a tad pricy, but titanium and carbon fibre struts are far more so. Whereas for a helium balloon, all you need is a gastight membrane, latex or mylar or whatever. The pressure of the helium inside is all you need to keep it in shape.
As for a free-body diagram, it doesn’t directly depend on the volume. The FBD depends, of course, on the forces, but it just happens that in this case one of the forces depends on volume. One way to look at it is to put a little pressure force vector pushing in at every point of the balloon. The air pressure at the bottom of the balloon is a little higher, so those forces are stronger. Or you could just average out those vectors, and put one pressure vector on the bottom, and one on the top, with the bottom one a little bigger (you could also put pressure vectors around the sides, but these will all cancel out). Or you could just add all the pressure vectors together, which will give you the total buoyancy force on the balloon. This force would point up, and would be labelled as the buoyancy force on the balloon by the air.
Padeye, I am curious to know how you came up with these numbers. It is common for plastic tanks at chemical plants to support a full vacuum. This is 14.696 psia or about 30.0 mm abs. These tanks are made of FRP plastic and cylindrical in geometry. This vacuum balloon could, possibly, be made of FRP and spherical in geometry - which is stronger. (I used to run calcs to ensure atmospheric tanks, eps. plastic tanks, could not cave in should a pump, for example, try to pull a full vacuum.)
If it were 35 tons at sea level, wouldn’t we be squashed?
- Jinx
The vacuum balloon idea is not a new one, in any case. It may have been first proposed as long ago as 1670.
Oh come on. This is simple math. Calculate the surface area of a 1-meter (call it 39 inches) sphere in square inches (4 x pi x r^2), and multiply this by the sea-level air pressure (call it 14.7 psi). Voila! 35 tons (~70,000 pounds).
At ~15psia, to get 35 tons of pressure on the ballon you would need ~4667 square inches of ballon exposed. For a spherical ballon, that means a diameter of ~77 inches. Which is a bit big for a party balloon.
Should have previewed, and noticed Q.E.D.'s post beat me to it, and doesn’t have a math error. :smack: :smack:
Nope. A sphere of ~77 inches diameter would have a total force of about 137 tons on it. To get 35 tons you need a sphere about 39 inches across–which is close to the one-meter specified by the OP. This is using 14.7 psi atmospheric pressure.
A vacuum ballon is possible, but so far any material strong enough weighs more than its worth it.
At STP, 22.4 L of He massess ~4g
A 1 M diameter spere is .523 M^3 = 523l
523l = 22.3 moles ideal gas at STP
= 89.2g
Assuming air is 100% nitrogen, it masses 3.5 times as much as He
=312.2g
Is the bouyant force for a He balloon 312.2 - (89.2+mass of bag)?
on a vacuum balloon is it 312.2 - (mass of bag)?
on a H balloon is it 312.2 - (22.3 + mass of bag) (using 1 for atomic weight)?
Brian