I have gone over this with brother more than a few times. We have fun at lunch discussing various things and seeing if we can answer the questions that arise. If there are any AOPA members out there we are the sort that hunger for the monthly “Test Pilot” Q & A’s.
So what we have been hashing out lately is what keeps the envelope of a hot-air balloon inflated.
And I mean inflated firmly. Before y’all jump on this we’re not talking about the buoyancy of the balloon in general. We are the both of us fairly well versed in physics and math and understand the dynamics of lighter-than-air-craft. Our question is from whence the pressure differential in the envelope? Clearly the fabric of the envelope is in tension and that tension comes from a higher pressure from within the envelope. The trouble of the question comes from the fact that the bottom of the envelope is open to the atmosphere.
If a pressure differential exists sufficient to keep the envelope tightly inflated, how come it down run out da hole at da bottom?
And please, for the love of God, Don’t give any anthropomorphic explanations about air molecules and say “they just wanna rise!”
If you take a cup or glass, invert it and immerse it straight into water, water gets trapped in the cup, water gets trapped and creates buoyancy. At the mouth of the cup the pressure inside the cup must be the same as the surrounding water, because there is no barrier that is acting against a pressure difference. Yet at the top there is a pressure difference - air is pushing up more strongly than the air is pushing down. The reason is that the surrounding water is much more dense than the air inside the cup, so there is a larger pressure gradient. The water pressure at the mouth of the cup is much higher than the water pressure at the top, but inside, the pressure is more uniform.
I understand buoyancy but that is not really the nub of the question. For instance, we can take as our example a balloon that is just about to leave the ground. That is to say, it is at neutral buoyancy. So in this case there is no net force upward on the balloon, but there is still a some net pressure difference keeping the fabric of the envelope taut.
So again: how come no flow of air out of the envelope.
Sure there’s a net upward force on a balloon about to leave the ground. It’s just counteracted by the weight of the basket and rigging. The air in the balloon is a 15 psi, just like the air outside the balloon. It’s just warmer, so it takes less mass to maintain that pressure. The firmness of the fabric comes not from some excess in pressure, but from the fact that when you push on the surface you have to do work to compress the air inside to a higher pressure, or with an open balloon, force it out the bottom.
You can’t apply the net neutral buyancy of the overall system to apply to an isolated part. The envelope has an upward force equal to the weight of the basket and all the stuff in it.
I’d rather say the tension in the fabric. And there has to be a pressure differential from the inside to the outside to maintain that stress on the fabric. You fill up an envelope with STP air on an STP day and it goes thhhpppt!, regardless of whether or not you had to do work by pressing on the surface.
The envelope isn’t inflated like a rubber bladder balloon. Imagine a blob of warm air in a larger mass of cooler air. The wair air mass will be lese dense, therefore less heavy for the same volume so it will rise while the cooler air sinks around it. cover that warm air mass with a fabric envelope and it will still rise but have to lift the balloon with it.
Pressure differential will vary depending on where you measure it. If you measure at the mouth of the balloon near the bottom you’ll see little or no difference. If you measure at the top of the balloon you’ll see the maxium amount.
It’s not a pressure difference, however, the mass of buoyant air inside is restrained by the material at the top of the balloon. That’s where the lift comes from. The material on the sides is held taut by the the tension between the upward buoyant force, and the downward force provided by the weight of the gondola and fabric. Without the gondola, the sides of the balloon would go all flabby.
Squink, how can there not be a pressure difference? If the mass of warm air is pushing up on the top of the envelope there will certainly be a pressure difference between that and the ouside air.
Think outside the box for a minute. I think people are wrongly assuming that because the envelope isn’t closed there cannot be a pressure difference and that’s not true. If the ballon is lifting against the downward force of gravity on its mass there must be an upward force and the only surface to exert that force against is the inside surface of the top of the envelope.
Put another way I try the Wile E. Coyote stunt of trying to move my sailboat with an electric fan blowing against the sail. The sail billows forward and there is darn sure a pressure differential between the two sides.
Well why is it so hard to believe that there’s not a pressure difference? Think of a latex helium balloon (or even one inflated by breath). It’s clearly held taut without a pressure difference, because the balloon could expand or contract if there were one.
My WAG is that some of it does seep out around the edges of the hole at the bottom, but not very much. The hole isn’t really all that big and the pressure differential can be small. A differential of 0.05 psi will produce an outward force of over 7 lb. on a square foot of the envelope. I think that would certainly keep it inflated.
I would suppose that the air in contact with the envelope would cool and start to sink relative to the rising balloon. when it gets to the skirt it would expand out and if still hotter than the ambient would rise a little. So there is probably a continued leakage out the bottom which is what the bottled gas burner that supplies freshly heated air is for.
There is a pressure difference at the top. To prove this, poke a small hole at the top and notice that the hot air flows out of the balloon.
The OP’s question was why, if there’s a pressure differential sufficient to keep the balloon inflated, does the hot air not run out the bottom? The answer is that, because hot air is less dense than the surrounding air, a column of it of a height equal to the height of the balloon doesn’t have enough weight to force any out the bottom.
Because without a pressure difference, there is no force acting on the balloon and hence no lift. As Xema said, there is definitely a pressure difference at the top of the balloon. Because of the different density, the pressure gradient is larger outside the balloon than inside; therefore there is no pressure difference at the bottom (mouth) of the balloon.
I remember I had an argument with my high school chemistry teacher on whether the pressure inside a latex balloon is the same as outside. If it’s inflated by regular air, I still think there is a tiny pressure difference that is equal to the tension of the rubber. If it’s filled by helium then there is an additional pressure difference at the top which provides buoyancy.
I am sooo tickled. I was walking down to the local pub to throw darts and reduced the problem to differential volumes (much as that disgusts me). xema and** scr4** both hit the same nail on the same head I did.
It’s a different lapse rate of pressure with altitude, which in other terms is what the both of them said.
I was all ready to jump back in here with my insight, and here I find that you guys have already answered better than I might have given first chance.
This balloon is 90 ft in diameter and total weight is about 1000 lb. If we approximate it as a cylinder, the pressure difference at the top is about 1/1000 psi. It may seem insignificant but it adds up.
Incidentally, most of NASA’s high altitude helium balloons are also “zero-pressure balloons,” i.e. they’re open at the bottom. The skin is so thin that if you close the bottom, the night/day temperature difference is enough to burst the balloon. Unfortunately that means that multi-day flights are very difficult - the daily expansion/contraction cycle results in loss of helium, so after a couple of days there isn’t enough helium to stay aloft. One way to overcome this problem is to launch it in the arctic or antarctic summer where the balloon can be in constant sunlight. There’s also a big effort to make “superpressure balloons” using a stronger material. (“Superpressure” just means the pressure can be slightly higher than outside pressure to withstand the temperature change.) Check the “ULDB” section in the above link for more info.