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How Does a Hot Air Balloon Produce Lift?

06/02/2012 8:26 PM

This may seem like a simple question, but I don't believe there will be found a simple answer people can agree on.

Consider, the bottom of the balloon is open. Thus Pi=Po

Vi does not equal Vo, the shell of the balloon provides a bound condition, but an open bound condition, given the hole at the bottom.

Ti > To So, the heat is the only recognized energy source for the lift.

Thus, the heat must decrease mass/density without increasing total pressure significantly or increasing the contained volume beyond the flexible bound condition.

Heat = buoyancy implies mass reduction

Heat = lift implies anti-gravity.

Either choice, or both make me slightly uncomfortable.

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#1

Re: How does a hot air balloon produce lift?

06/02/2012 8:31 PM
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#2

Re: How does a hot air balloon produce lift?

06/02/2012 8:44 PM

The less dense hot air weighs a certain amount. The more dense cold air that was replaced weighed a greater amount. The difference is the force that lifts the balloon. Sheesh.

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#3

Re: How does a hot air balloon produce lift?

06/02/2012 9:04 PM

It's the same principle as a water vapor bubble under water rising to the top, molecular density + gravity force = buoyancy of less dense bubble....

"Air Pressure + Gravity = Buoyancy

All air particles in the atmosphere are drawn by the downward force of gravity. But the pressure in the air creates an upward force working opposite gravity's pull. Air density builds to whatever level balances the force of gravity, because at this point gravity isn't strong enough to pull down a greater number of particles.

This pressure level is highest right at the surface of the Earth because the air at this level is supporting the weight of all the air above it -- more weight above means a greater downward gravitational force. As you move up through levels of the atmosphere, the air has less air mass above it, and so the balancing pressure decreases. This is why pressure drops as you rise in altitude.

This difference in air pressure causes an upward buoyant force in the air all around us. Essentially, the air pressure is greater below things than it is above things, so air pushes up more than it pushes down. But this buoyant force is weak compared to the force of gravity -- it is only as strong as the weight of the air displaced by an object. Obviously, most any solid object is going to be heavier than the air it displaces, so buoyant force doesn't move it at all. The buoyant force can only move things that are lighter than the air around them.

For buoyancy to push something up in the air, the thing has to be lighter than an equal volume of the air around it. The most obvious thing that is lighter than air is nothing at all. A vacuum can have volume but does not have mass, and so, it would seem, a balloon with a vacuum inside should be lifted by the buoyancy of the air around it. This doesn't work, however, because of the force of surrounding air pressure. Air pressure doesn't crush an inflated balloon, because the air inside the balloon pushes out with the same force as the outside air pushing in. A vacuum, on the other hand, doesn't have any outward pressure, since it has no particles bouncing against anything. Without equal pressure balancing it out, the outside air pressure will easily crush the balloon. And any container strong enough to hold up to the air pressure at the earth's surface will be much too heavy to be lifted by the buoyant force.

Another option would be to fill the balloon with air that is less dense than the surrounding air. Because the air in the balloon has less mass per unit of volume than the air in the atmosphere, it would be lighter than the air it was displacing, so the buoyant force would lift the balloon up. But again, fewer air particles per volume means lower air pressure, so the surrounding air pressure would squeeze the balloon until the air density inside was equal to the air density outside.

There are fewer air particles per unit of volume inside the balloon, but because those particles are moving faster, the inside and outside air pressure are the same.

All of this is assuming that the air in the balloon and the air outside the balloon exist under exactly the same conditions. If we change the conditions of the air inside the balloon, we can decrease density, while keeping air pressure the same. As we saw in the last section, the force of air pressure on an object depends on how often air particles collide with that object, as well as the force of each collision. We saw that we can increase overall pressure in two ways:

• Increase the number of air particles so there is a greater number of particle impacts over a given surface area.
• Increase the speed of the particles so that the particles hit an area more often and each particle collides with greater force.

So, to lower air density in a balloon without losing air pressure, you simply need to increase the speed of the air particles. You can do this very easily by heating the air. The air particles absorb the heat energy and become more excited. This makes them move faster, which means they collide with a surface more often, and with greater force.

For this reason, hot air exerts greater air pressure per particle than cold air, so you don't need as many air particles to build to the same pressure level. So a hot air balloon rises because it is filled with hot, less dense air and is surrounded by colder, more dense air."

http://science.howstuffworks.com/transport/flight/modern/hot-air-balloon6.htm

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#4

Re: How does a hot air balloon produce lift?

06/02/2012 9:30 PM

You're correct on many key aspects but are not following through with the complete analysis. The pressure and densities of a hot air balloon are in the range that the ideal gas law applies.

PV=nRT

The bold symbols are the only values that will change. Since the number of moles (n) can be expressed by n=m/M with M being the average molar mass of the gas (air). Then a little simple algebra gives :

d-1=V/m=(PM)-1RT

So as the gas gets warm it gets less dense and rises.

Now if you have trouble understanding that anything in a fluid will rise if it is less dense than the fluid around it, just look at that ice cube in your drink.

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#8

Re: How does a hot air balloon produce lift?

06/03/2012 10:02 AM

Beginning with

d-1=V/m=(PM)-1RT

focusing on d^-1=V/m, given V is the basically fixed Volume of the balloon, then m the mass of the air atoms changed.

Buoyancy = variable molecular mass.

Being more realistic. What changes is V_m/m_n. The volume required for a single atomic mass. The molecular density. So, vacuum energy causes buoyancy?

However, the molecular bond lengths don't change, nor does the atomic radius change with changing T, so, how does V_m the molecular volume increase with increasing T?

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#9

Re: How does a hot air balloon produce lift?

06/03/2012 10:47 AM

"However, the molecular bond lengths don't change, nor does the atomic radius change with changing T, so, how does V_m the molecular volume increase with increasing T?"

I don't think that's true. All molecules are in motion within themselves having vibrational and rotational modes (plus of course the translational mode).There are 2 vibrational modes - "stretching" and "scissors." Both of these increase in amplitude with temperature. So an increasing amplitude stretching bond would effectively increase the average size of the molecule in the case of a diatomic molecule.

Is this relevant? Not sure.

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#19

Re: How does a hot air balloon produce lift?

06/03/2012 4:35 PM

"However, the molecular bond lengths don't change, nor does the atomic radius change with changing T, so, how does V_m the molecular volume increase with increasing T?"

All molecules are in motion within themselves having vibrational and rotational modes (plus of course the translational mode). There are 2 vibrational modes - "stretching" and "scissors." Both of these increase in amplitude with temperature.

YES

O2 and N2 are both linear diatomic so except for water vapor, scissors doesn't really apply. Amplitude does increase, but very very slightly. Mean bond length doesn't change.

The external kinetic energy per molecule does change. There is a documented change in the skew of the Boltzman curve with T.

The final question then is, how does heat accelerate ideal gas molecules?

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#11

Re: How does a hot air balloon produce lift?

06/03/2012 11:10 AM

The space between molecules changes, but I don't think the space changes between the atoms within each molecules. Even if it did, it wouldn't make much difference.

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#12

Re: How does a hot air balloon produce lift?

06/03/2012 11:21 AM

Here we have the confusion!

With a gas the volume of individual molecules and their bond length has nothing to do with the average volume occupied by each molecule. The molecules of a gas are free to travel through space and do travel that space for considerable distances (compared to the size of the molecule) before confronting another molecule. In a liquid the molecules are free to move but there space to move is limited because the molecules are effectively touching each other. This combination of attributes is pivotal for hydraulics to work. Then there are solids where the molecules are not free to travel and as such the molecules are effectively touching each other.

This relationship of the number of molecules a gas will contain in a volume of space is how the molecular mass of aromatic compounds are measured. An arbitrary volume of the liquid is poured into a flask with a known total volume. The flask has a small opening to atmosphere (usually foil with a slit) and a thermometer inside the flask. The flask is slowly heated until all of the fluid vaporizes. At the moment of complete vaporization the temperature of the gas is recorded. The flask is now quickly chilled (ice bath commonly) so that the known volume of vapour condenses back to a liquid. The mass of the liquid is found by weight. A little simple mathematics follows and bingo. The average molar mass of the remaining liquid has been found.

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#5

Re: How Does a Hot Air Balloon Produce Lift?

06/03/2012 3:04 AM

Air expands as it is heated.
Hot air has the same mass as it had when it was cold, but it now occupies a larger volume as it has expanded. Thus it is less dense thus it rises.
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#6

Re: How Does a Hot Air Balloon Produce Lift?

06/03/2012 4:04 AM

Spam: This post was deleted because it contained advertising outside the Commercial Space forum. Please review Section 14 of the CR4 Site FAQ about advertising.

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#10

Re: How Does a Hot Air Balloon Produce Lift?

06/03/2012 10:54 AM

SPAMSPAMSPAMSPAMSPAMSPAMSPAMSPAMSPAMSPAMSPAMSPAMSPAMSPAM

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#7

Re: How Does a Hot Air Balloon Produce Lift?

06/03/2012 8:00 AM

Wow. You're way ahead of me. I'm still trying to figure out why the balloon floats on water and doesn't sink?

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#13

Re: How Does a Hot Air Balloon Produce Lift?

06/03/2012 11:48 AM

There are times when ignorance is bliss. This is one for me.

I'm not sure why one would insist that everything must have a mathematical explanation.

How do you model the behaviour of a helium filled balloon in a closed car?

Why is there no light diffusion in a vacuum, mathematically?

Are we there yet?

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#14

Re: How Does a Hot Air Balloon Produce Lift?

06/03/2012 12:19 PM

The energy source for the lift is gravitational potential energy, not heat (or only indirectly heat).

If things can move, the heaviest stuff goes to the bottom, as this minimizes the total gravitational potential energy of the system. (Same reason that water flows down.) The decrease of overall energy provides the lifting energy for the lighter stuff.

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#32

Re: How Does a Hot Air Balloon Produce Lift?

06/06/2012 12:37 PM

Is this, " gravitational potential energy" what keeps boats afloat, too?

Gravitational Potential Energy

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#33

Re: How Does a Hot Air Balloon Produce Lift?

06/06/2012 4:30 PM

Yes.

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#15

Re: How Does a Hot Air Balloon Produce Lift?

06/03/2012 1:58 PM

Score 1 for Off Topic
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#16

Re: How Does a Hot Air Balloon Produce Lift?

06/03/2012 2:00 PM

I agree. Let's "float" the idea and see where it goes.

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#18

Re: How Does a Hot Air Balloon Produce Lift?

06/03/2012 2:35 PM

I'm good...

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#17

Re: How Does a Hot Air Balloon Produce Lift?

06/03/2012 2:16 PM

If people don't know how air works, can we call them airheads?

ξ

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#20

Re: How Does a Hot Air Balloon Produce Lift?

06/03/2012 10:46 PM

Medically speaking they would be pneumocephalads, and (in order to NOT be off topic), since the cranial bones cannot expand to allow enough cold air to be displaced by the expanded heated air to 'offset' the weight of the patient, they will never get airborne.

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#21

Re: How Does a Hot Air Balloon Produce Lift?

06/04/2012 6:10 AM

The hot air has less mass per unit volume than the outside colder air. The balloon floats up, exchanging places with the colder air above, converting gravitational potential energy into kinetic energy.

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#22

Re: How Does a Hot Air Balloon Produce Lift?

06/04/2012 6:27 AM

Hot air up the middle cooler air out down the side thus the hot air occupies has the same voulume but is much less dense. There is your lift.

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#23

Re: How Does a Hot Air Balloon Produce Lift?

06/04/2012 7:49 AM

OK, all the above is but an oversimplified model of yours, because obviously some of the air is replaced by a mixture of CO2 + H20 from burned propane, some of the water vapor will condense and drop, and some will diffuse thru the envelope, and CO2 is denser than air but will be partially absorbed by algae on the inner surface (depending on envelope color, of course), and...

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#24

Re: How Does a Hot Air Balloon Produce Lift?

06/04/2012 8:57 AM

I suspect one can learn much about hot air balloon physics by turning the balloon upside down and noting differences in operation.

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#25

Re: How Does a Hot Air Balloon Produce Lift?

06/04/2012 7:44 PM

"Heat = buoyancy implies mass reduction"

This is whats happening - the mass reduction occurs because of the opening in the bottom of the balloon. As the air mass is heated its pressure rises. The opening allows a portion of the heated air mass to be forced out of the bounds of the balloon, thus reducing the mass by expelling a portion of the heated air mass.

If the ballon were to be made non-expandable and completely sealed, the pressure inside would simply rise and the balloon's mass would remain the same. Because it's size also remains the same, there is no change in buoyancy.

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#26

Re: How Does a Hot Air Balloon Produce Lift?

06/05/2012 10:00 AM

Nah...solar balloons retain their mass and are non-expandable (to a point) working solely on the principle of hot air rising.

There is no loss of the heated air mass...

I think we are nuking this

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#28

Re: How Does a Hot Air Balloon Produce Lift?

06/05/2012 12:27 PM

The solar balloon is not initially fully inflated. That allows the air mass to expand thus changing its displacement.

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#29

Re: How Does a Hot Air Balloon Produce Lift?

06/05/2012 7:12 PM

Yeah, but none of this nonsense:

"...thus reducing the mass by expelling a portion of the heated air mass."

whatever...

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#31

Re: How Does a Hot Air Balloon Produce Lift?

06/05/2012 7:24 PM

The damn thing floats because the volume of air that the balloon displaces is LIGHTER than the volume of air that the balloon displaces.

The hot air around here seems to be escaping from you!

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#34

Re: How Does a Hot Air Balloon Produce Lift?

06/06/2012 8:38 PM

"The damn thing floats because the volume of air that the balloon displaces is LIGHTER than the volume of air that the balloon displaces."

Well, DUH. In the solar balloon, the initial air mass is signifigantly smaller than the fully inflated size of the balloon. As it heats up and expands, it displaces a larger volume of air - its mass never changes only its volume.

HOWEVER - in a conventional hot air balloon *once its fully inflated* the trapped air mass can and DOES change its total mass as the opening in the bottom allows a portion of the air mass to escape as further heating causes the pressure to rise. This reduction in the total air mass (by further heating) is what allows the balloon to rise further after it has reached equilibrium. THAT is what I was referring to in my original post.

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#35

Re: How Does a Hot Air Balloon Produce Lift?

06/06/2012 9:25 PM

What makes the difference is that the baloon is open on the bottom and allows air voulume to escape and leave a less dense hot air in the baloon creating the lift.

If the ballon can not expand and is closed and you heat it up nothing will happen.

Cheers IS

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#36

Re: How Does a Hot Air Balloon Produce Lift?

06/06/2012 9:39 PM

Well, it may explode.

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#38

Re: How Does a Hot Air Balloon Produce Lift?

06/10/2012 8:12 AM

You say it! All hot air!

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#27

Re: How Does a Hot Air Balloon Produce Lift?

06/05/2012 10:18 AM

How could I've overlooked this for so long. You're the wizard and you still don't know how it works.

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#30

Re: How Does a Hot Air Balloon Produce Lift?

06/05/2012 7:13 PM

After all of the mish-mash mumbo-jumbo and math...

Next thing you know someone will say that bumble-bees can't fly because the math doesn't work...yeah, okay

yikes.

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#37

Re: How Does a Hot Air Balloon Produce Lift?

06/07/2012 9:20 AM

Heat rises. The balloon traps the hot air. A pocket of hot air surrounded by cold air will rise.

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