How high can an airship rise?

[Baluncore]

There are some changes that need to happen, to take the thought experiment towards a real experiment.

a hypothetical envelope of volume V and mass M that is perfectly rigid and thus maintains constant volume.

Using a sphere of the lightest weight film would weigh less and still limit the volume. Also, the top of the envelope needs thicker film to withstand greater differential pressure and surface tension, than at the bottom, where thinner film can be used. That film mass distribution will tend to capsize the balloon, unless there is a suspended payload that defines the base of the envelope.

Fill this vehicle with one atm. of helium at sea level, and turn it loose.

A film envelope will lift with only about 10% hydrogen or helium. Why waste the limited helium resource, by 100% filling a rigid envelope, when a spherical film envelope is easier to transport and costs 90% less to partially fill?

As it rises, the external pressure drops. Releasing helium will indeed reduce the mass of the vehicle, and reduce its density, allowing it to rise higher.

As it rises, a film envelope will expand with the lift gas, until finally, the base of the film envelope becomes spherical. Then the mode of operation changes. I would put a one-way flap valve at the base to release the excess lift gas, so there is zero differential pressure pushing the base of the envelope downwards from inside.

Scientific high-altitude balloons will get to this height before bursting, where V is the mechanical limit on the volume of the envelope.

Bursting is used to aid recovery of the payload, and to clear the controlled airspace. By continuously venting excess lift gas from an opening in the base, a greater height than the burst height would be reached.

 

[Baluncore]

You could get a bit higher if you evacuated this (extremely) theoretical envelope, leaving a high vacuum, before releasing the vehicle.

Consider a rigid spherical envelope, that you want to fly as a vacuum balloon, to a height where the external air pressure is; Pa.

Initially, on the ground, the envelope is manufactured, filled with air at one bar.
Start pumping out air, until the internal pressure is Pa below local atmospheric.
The balloon will then start to lift, with only a partial vacuum.
The envelope then only needs to withstand an external crush of Pa.
The internal depression of Pa, reduces the density of the internal air.
No special, rare or expensive lifting gas is needed.

As the balloon rises, pump out more air, maintaining a differential pressure of Pa.
When the balloon has reached an altitude where the external air pressure is Pa, the envelope will contain a true vacuum.

At no time during the flight was the external crush greater than Pa.
The (solar powered) pump never needed to develop a pressure difference greater than Pa.

The big mistake with vacuum balloons, is attempting to design them to withstand the crush of a high vacuum at sea level.

 

[askingask]

Consider a rigid spherical envelope, that you want to fly as a vacuum balloon, to a height where the external air pressure is; Pa.

Initially, on the ground, the envelope is manufactured, filled with air at one bar.
Start pumping out air, until the internal pressure is Pa below local atmospheric.
The balloon will then start to lift, with only a partial vacuum.
The envelope then only needs to withstand an external crush of Pa.
The internal depression of Pa, reduces the density of the internal air.
No special, rare or expensive lifting gas is needed.

As the balloon rises, pump out more air, maintaining a differential pressure of Pa.
When the balloon has reached an altitude where the external air pressure is Pa, the envelope will contain a true vacuum.

At no time during the flight was the external crush greater than Pa.
The (solar powered) pump never needed to develop a pressure difference greater than Pa.

The big mistake with vacuum balloons, is attempting to design them to withstand the crush of a high vacuum at sea level.

That is genius, never thought about that, but based on our discussion here, it makes absolutely sense. The only problem here is that to keep the envelop lightweight the pressure difference has to be small. But if the pressure difference is small net buoyancy will also be very small. Question is where is the optimal point, if one exists even, where the weight of the envelop is small enough and the pressure difference is big enough to ensure the density difference.

 

[askingask]

Consider a rigid spherical envelope, that you want to fly as a vacuum balloon, to a height where the external air pressure is; Pa.

Initially, on the ground, the envelope is manufactured, filled with air at one bar.
Start pumping out air, until the internal pressure is Pa below local atmospheric.
The balloon will then start to lift, with only a partial vacuum.
The envelope then only needs to withstand an external crush of Pa.
The internal depression of Pa, reduces the density of the internal air.
No special, rare or expensive lifting gas is needed.

As the balloon rises, pump out more air, maintaining a differential pressure of Pa.
When the balloon has reached an altitude where the external air pressure is Pa, the envelope will contain a true vacuum.

At no time during the flight was the external crush greater than Pa.
The (solar powered) pump never needed to develop a pressure difference greater than Pa.

The big mistake with vacuum balloons, is attempting to design them to withstand the crush of a high vacuum at sea level.

Perhaps this could be especially useful for missions on mars.

 

[Baluncore]

The only problem here is that to keep the envelop lightweight the pressure difference has to be small. But if the pressure difference is small net buoyancy will also be very small.

A functional vacuum balloon does not yet exist, because a sufficiently low-mass, crush-surviving envelope, has still not been engineered. But, I expect it will happen.

 

[askingask]

A functional vacuum balloon does not yet exist, because a sufficiently low-mass, crush-surviving envelope, has still not been engineered. But, I expect it will happen.

Honestly hydrogen is pretty good already and people over estimate its danger. No need for expensive helium.

 

[Baluncore]

Honestly hydrogen is pretty good already and people over estimate its danger.

If you use hydrogen, the cost of insurance will be greater for historical reasons.
Hydrogen molecules are small, fast, and pass through many envelope materials. Helium diffuses at a lower rate.

 

[askingask]

for historical reasons.

Lol

 

[akhmeteli]

The big mistake with vacuum balloons, is attempting to design them to withstand the crush of a high vacuum at sea level.

I respectfully disagree. If the pressure difference between exterior and interior of the vacuum balloon is small, the shell needs to be very light to provide buoyancy, so it would be more difficult to prevent the balloon failure, in spite of the lesser pressure difference. According to our calculations/computations, it is easier to design a vacuum balloon for sea level and low interior pressure / high pressure difference than, say, for sea level and low pressure difference, or for higher altitudes.

We offered a design of a sea level and high pressure difference vacuum balloon at Eng 2021, 2(4), 480-491

 

[Baluncore]

According to our calculations/computations, it is easier to design a vacuum balloon for sea level and low interior pressure / high pressure difference than, say, for sea level and low pressure difference, or for higher altitudes.

That is true, but to rise to any altitude where the air pressure is Pa, the balloon must also be neutrally buoyant, with a differential envelope pressure of Pa, at sea level. I ask why a high vacuum would be needed at sea level, if that design will later fly at an external pressure of Pa.

A demonstration system, capable of neutral buoyancy at sea level with high vacuum, would be unable to rise above sea level.

That challenge has the same design and material constraints, as if you halve the mass of the carcass, at half an atmosphere differential pressure, with half the crush, and the balloon could rise from sea level to half an atmosphere = 5470 metres.

The limiting factor is the composite materials needed, and the composite structures required for both tension and compression, to prevent the crush.

I predict the first partial-vacuum balloon to fly will be in a hot and dry atmosphere. There should be a few drops of water inside the balloon, so the RH of the internal air, remains close to 100%, or would that be cheating?

 

[akhmeteli]

That is true, but to rise to any altitude where the air pressure is Pa, the balloon must also be neutrally buoyant, with a differential envelope pressure of Pa, at sea level. I ask why a high vacuum would be needed at sea level, if that design will later fly at an external pressure of Pa.

But vacuum balloons can have some applications at sea level as well, so I don't understand why designing vacuum balloons for sea level would be a "big mistake".

A demonstration system, capable of neutral buoyancy at sea level with high vacuum, would be unable to rise above sea level.

Technically, yes, but, for example, at the altitude of 150 m, the air density is just 1.8% less than that at sea level (and the pressure is about 1.8% less), so a system designed for a range from 0 m to 150 m will not be much different from a purely sea level system. On the other hand, the distance of direct vision at the altitude of 150 m is about 44 km, so this altitude may be of interest, say, for antenna applications.

I predict the first partial-vacuum balloon to fly will be in a hot and dry atmosphere. There should be a few drops of water inside the balloon, so the RH of the internal air, remains close to 100%, or would that be cheating?

I have not thought about "dry", but cold air is better for a vacuum balloon. The pressure being equal, the buoyancy force is higher for cold air as air density is higher.

 

[Baluncore]

The pressure being equal, the buoyancy force is higher for cold air as air density is higher.

The temperature of a partial-vacuum balloon will equilibrate with the environment. The saturated air, inside the balloon, will have a lower density than the dry air outside. That is significantly enhanced at higher temperatures.

 

[akhmeteli]

The temperature of a partial-vacuum balloon will equilibrate with the environment. The saturated air, inside the balloon, will have a lower density than the dry air outside. That is significantly enhanced at higher temperatures.

At high altitudes, there cannot be "hot atmosphere" (unless one considers altitudes unreasonable for balloons). As for sea level, let us compare temperatures of 0 deg C and 50 deg C. The pressure of saturated vapor pressure at 50C is about 12% of the atmospheric pressure, but the air density and, therefore, the buoyancy force is about 15% less at 50C than at 0C (for the same atmospheric pressure).

 

[Baluncore]

On the other hand, the distance of direct vision at the altitude of 150 m is about 44 km, so this altitude may be of interest, say, for antenna applications.

At 150 metres you could use a fixed tower, or a tethered helium balloon. I have flown gyro kites well above 150 m, and they generate their own power.

At high altitudes, there cannot be "hot atmosphere" (unless one considers altitudes unreasonable for balloons).

A high-vacuum balloon at sea level is a demonstration package, of less practical use than a stepladder. It will hover best below sea level, on a cold and dry night, during an anticyclone. Think the Dead Sea, Death Valley, or deep underground in a mine. The problem with mines is that they get hotter with depth, and have RH=100%.

Only a partial-vacuum balloon can benefit from internal saturation, RH=100%. At the depressed boiling point of water, the lift gas remaining would be steam from the air, being a clear cloud chamber.

 

[akhmeteli]

At 150 metres you could use a fixed tower, or a tethered helium balloon. I have flown gyro kites well above 150 m, and they generate their own power.

Fixed towers of this height are (very?) expensive, they require some land to own or rent, they require lighting for aircraft safety, which creates serious maintenance problems.

As for helium balloons, they have their own set of issues (don't get me started:-) ). Furthermore, helium balloons are competitors to stratospheric vacuum balloons too.

I don't know much about gyro kites, but I believe they are wind-dependent.

And tethered balloons require some real estate, and their altitude is wind-dependent

A high-vacuum balloon at sea level is a demonstration package, of less practical use than a stepladder. It will hover best below sea level, on a cold and dry night, during an anticyclone. Think the Dead Sea, Death Valley, or deep underground in a mine. The problem with mines is that they get hotter with depth, and have RH=100%.

So you don't think there is any application for low-altitude vacuum balloons. I believe there are some important applications, such as antennas, freight transportation in remote areas, etc., so let us agree to disagree.

And let us not forget that, while making a sea-level balloon is really hard, making a stratospheric balloon is significantly harder.

Only a partial-vacuum balloon can benefit from internal saturation, RH=100%. At the depressed boiling point of water, the lift gas remaining would be steam from the air, being a clear cloud chamber.

So again, internal saturation does not seem important at low altitudes, and temperature and water vapor content are low at high altitudes.

 

[Baluncore]

As for helium balloons, they have their own set of issues (don't get me started:-) ). Furthermore, helium balloons are competitors to stratospheric vacuum balloons too.

Only one competitor wins each race. I will bet on the favourite, helium. Vacuum balloons have so many issues, they DNS.

I don't know much about gyro kites, but I believe they are wind-dependent.

They can be flown from a slow moving vehicle or a ship. The vehicle can stop when there is some wind.

And tethered balloons require some real estate, and their altitude is wind-dependent

Untethered balloons do not stay where you release them. Their position is wind dependent, unless they are dirigible.

So you don't think there is any application for low-altitude vacuum balloons. I believe there are some important applications, such as antennas, freight transportation in remote areas, etc., so let us agree to disagree.

We have not needed vacuum balloons for those applications before. Instead, we have used lifting gas balloons, that are more available and less fragile than vacuum balloons. I have no problem disagreeing with you on the existence of applications for vacuum balloons. Vacuum balloons will be a novelty, with no application that cannot be met by a helium balloon.

And let us not forget that, while making a sea-level balloon is really hard, making a stratospheric balloon is significantly harder.

There are several companies making and flying stratospheric balloons now, so how hard can hard be? I believe it is hard to make a vacuum balloon, even for sea level.

So again, internal saturation does not seem important at low altitudes, and temperature and water vapor content are low at high altitudes.

Internal saturation is important at low altitudes. The molecular weight of dry air is 29 g/mole, while that of water is 18 g/mole. That becomes important at low altitudes and high temperatures. When low RH increases the density of the external air, the presence of saturated air inside the balloon, becomes an advantage. That is obviously not possible with a vacuum balloon.

 

[russ_watters]

Now let us say we have some form of non elastic gasbag filled with hydrogen. Just for simplicity sake. I'm not asking for the material weight of that bag or whatever. All I'm asking for, is that if the bag rises to an altitude where it can't go any higher. Would venting the gas of the bag to equalize pressure, compared to the atmosphere at that altitude, cause the bag to gain altitude again?

I was away for the weekend and only skimmed the rest of the posts...

The gas bags of most balloons are already non-elastic. Do you mean fixed volume? Rigid? Or having more gas than needed for the volume and lift? If the last, then yes. In other words, the balloon gains altitude until fully inflated and keeps gaining altitude until the outside air density is low enough that the balloon can't rise any further(or it pops). If the internal pressure at that point is above atmospheric then it can vent lifting gas and rise a little further. But not as much as if it had a larger envelope.

...I don't know what you're actually looking for here though.

 

[Baluncore]

If the internal pressure at that point is above atmospheric then it can vent lifting gas and rise a little further.

And that lift-gas venting, should be done from the lowest point of the envelope, where the optimum differential pressure is zero.

 

[russ_watters]

And that lift-gas venting, should be done from the lowest point of the envelope, where the optimum differential pressure is zero.

Deleted a prior reply...I'm not sure I care to get into these intricacies without knowing which scenario the OP is after. There's a lot of nuance here that I don't think matters to OP, and answers that are scenario-dependent.

 

[akhmeteli]

Only one competitor wins each race. I will bet on the favourite, helium. Vacuum balloons have so many issues, they DNS.

There is a difference between "helium is the winner of the race" and "low-altitude vacuum balloons do not have applications"

They can be flown from a slow moving vehicle or a ship. The vehicle can stop when there is some wind.

That makes them an exotic solution even in the best-case scenario.

Untethered balloons do not stay where you release them. Their position is wind dependent, unless they are dirigible.

I agree, but this is true both for low- and high-altitude vacuum balloons (and for helium balloons).

We have not needed vacuum balloons for those applications before. Instead, we have used lifting gas balloons, that are more available and less fragile than vacuum balloons. I have no problem disagreeing with you on the existence of applications for vacuum balloons. Vacuum balloons will be a novelty, with no application that cannot be met by a helium balloon.

Note that helium balloons have difficulty with altitude control. For example, if they are used for freight transportation, they need to get some ballast onboard after unloading to get rid of excessive buoyancy (or require helium compression). Vacuum balloons can just bleed in some air.

There are several companies making and flying stratospheric balloons now, so how hard can hard be? I believe it is hard to make a vacuum balloon, even for sea level.

Sorry, I meant to say "And let us not forget that, while making a sea-level vacuum balloon is really hard, making a stratospheric vacuum balloon is significantly harder."

Internal saturation is important at low altitudes. The molecular weight of dry air is 29 g/mole, while that of water is 18 g/mole. That becomes important at low altitudes and high temperatures. When low RH increases the density of the external air, the presence of saturated air inside the balloon, becomes an advantage. That is obviously not possible with a vacuum balloon.

I am not sure about that. My understanding is water vapor can exist in vacuum as well, depending on the wall temperature.

 

[Baluncore]

There is a difference between "helium is the winner of the race" and "low-altitude vacuum balloons do not have applications"

That there is a difference is a truism, and both statements are true.

That makes them an exotic solution even in the best-case scenario.

Gyro kites have filled some observation and antenna applications since the 1940s.
https://en.wikipedia.org/wiki/Rotor_kite
Any balloon has drag, so is pulled down in a wind, or when towed by a vehicle. Kites fly higher than balloons in a wind, gyro kites fly higher than traditional kites. Gyro kites are practical, and certainly not as exotic as vacuum balloons.

Note that helium balloons have difficulty with altitude control. For example, if they are used for freight transportation, they need to get some ballast onboard after unloading to get rid of excessive buoyancy (or require helium compression). Vacuum balloons can just bleed in some air.

I have more difficulty with understanding, how a load can possibly be attached to the envelope of a vacuum balloon, without catastrophically destroying the symmetry of balanced forces.
Where a payload is delivered, a prepared ballast load can be collected.

"And let us not forget that, while making a sea-level vacuum balloon is really hard, making a stratospheric vacuum balloon is significantly harder."

How do you support a sea level vacuum balloon during construction and liftoff?
A partial vacuum balloon for high altitude flight can move through the entire process.

I am not sure about that. My understanding is water vapor can exist in vacuum as well, depending on the wall temperature.

In a partial vacuum, yes, but not in a true or full vacuum. Water molecules may stick chemically to the cold wall of a vacuum chamber, but not in sufficient numbers to create lift.

 

[askingask]

Deleted a prior reply...I'm not sure I care to get into these intricacies without knowing which scenario the OP is after. There's a lot of nuance here that I don't think matters to OP, and answers that are scenario-dependent.

It has been answered by James Demers already. But thank you.

 

[akhmeteli]

That there is a difference is a truism, and both statements are true.

At least the second statement is just your opinion.

Gyro kites have filled some observation and antenna applications since the 1940s.
https://en.wikipedia.org/wiki/Rotor_kite
Any balloon has drag, so is pulled down in a wind, or when towed by a vehicle. Kites fly higher than balloons in a wind, gyro kites fly higher than traditional kites. Gyro kites are practical, and certainly not as exotic as vacuum balloons.

I used "exotic" for versions towed by vehicles, which require vehicles, roads, and what not.

I have more difficulty with understanding, how a load can possibly be attached to the envelope of a vacuum balloon, without catastrophically destroying the symmetry of balanced forces.
Where a payload is delivered, a prepared ballast load can be collected.

Let us consider a numerical example. Let us assume that the vacuum balloon has the radius of $R=2.5$ m, the air density is $\rho=1.29$ kg/m3. The maximum lift it can create (if we neglect the mass of the shell:-) ) is $(4/3)\pi R^3\rho\approx 84$ kg, whereas the force of atmospheric pressure acting on 1 square meter of the surfaced of the balloon is about 10 tons, i.e., more than a hundred times greater. So I don't see the load "catastrophically destroying the symmetry of balanced forces". As for attaching a load to a vacuum balloon, one can use a thin film enveloping the balloon and attach the load to this film under the balloon (the film will have a shape of a pear with the thinner end at the bottom).

How do you support a sea level vacuum balloon during construction and liftoff?
A partial vacuum balloon for high altitude flight can move through the entire process.

For example, using a light plastic foam support concave at the top or a similar inflated support.

In a partial vacuum, yes, but not in a true or full vacuum. Water molecules may stick chemically to the cold wall of a vacuum chamber, but not in sufficient numbers to create lift.

I don't understand that. Water molecules stuck to the cold wall of a vacuum chamber do not create lift or internal pressure.

 

[Baluncore]

My understanding is water vapor can exist in vacuum as well, depending on the wall temperature.

Obviously, if there is water vapour present, then it is not a true vacuum. To be a true vacuum, any water molecules present would have to chemically bond to the cold wall of the chamber, increasing the mass of the envelope.

I don't understand that. Water molecules stuck to the cold wall of a vacuum chamber do not create lift or internal pressure.

I did not say that they did. You hypothesised a belief in a contradiction, where there was a true vacuum containing free water vapour. You have now gone off on a tangent.

Water boils at lower temperatures, at lower pressures. A partial-vacuum balloon can contain cold steam, without other air molecules being present.
In a partial-vacuum balloon, where the air is replaced by water vapour, the balloon has greater buoyancy than with the same internal pressure of dry air.
The advantage of water vapour over dry air is; 29 / 18 = 1.6
Obviously, that advantage is not available with a full-vacuum balloon.

 

[akhmeteli]

Obviously, if there is water vapour present, then it is not a true vacuum. To be a true vacuum, any water molecules present would have to chemically bond to the cold wall of the chamber, increasing the mass of the envelope.

Technically, yes, but there is such thing as Torricellian vacuum. There can be water vapor and nothing else in a container.

I did not say that they did. You hypothesised a belief in a contradiction, where there was a true vacuum containing free water vapour. You have now gone off on a tangent.

Again, there can be water vapor and nothing else in a container. But I'd say you went off on a tangent when you started to talk about humidity. Condensation makes water vapor impractical as lighter-than-air gas for Earth atmosphere.

Water boils at lower temperatures, at lower pressures. A partial-vacuum balloon can contain cold steam, without other air molecules being present.
In a partial-vacuum balloon, where the air is replaced by water vapour, the balloon has greater buoyancy than with the same internal pressure of dry air.
The advantage of water vapour over dry air is; 29 / 18 = 1.6
Obviously, that advantage is not available with a full-vacuum balloon.

Again, technically, yes, but if "the air is replaced by water vapour", it is Torricellian vacuum. And again, I don't think water vapor can be practical as a lighter-than-air gas in Earth atmosphere due to condensation at reasonable temperatures.

 

[akhmeteli]

Where a payload is delivered, a prepared ballast load can be collected.

Still, this is pain in the neck. It is one of the problems with helium ballons, besides helium being pretty expensive, nonrenewable, penetrating through pretty much any envelope. So I believe there can be at least some niche applications for low-altitude vacuum balloons.

 

[Baluncore]

Condensation makes water vapor impractical as lighter-than-air gas for Earth atmosphere.

Except in a partial vacuum balloon.

And again, I don't think water vapor can be practical as a lighter-than-air gas in Earth atmosphere due to condensation at reasonable temperatures.

Your fear of condensation prevents you from researching the diverse possibilities available.

Consider what would happen if you assembled, or fabricated, a rigid envelope underwater. Gradually, as the water is pumped out, the envelope rises through the surface, before it finally lifts off. It will then contain water vapour without air, so has the 61% advantage while it is a partial vacuum balloon.

Any condensate that forms as it rises will be pumped out from the bottom of the envelope. Indeed, a cold condenser would be one way to remove water vapour from inside the envelope.

As it approaches maximum altitude, it begins to approach a full vacuum, the cold steam does not need to be pumped out, as the vapour will condense and be removed as a liquid by the more efficient positive displacement pump.

 

[akhmeteli]

Except in a partial vacuum balloon.

Your fear of condensation prevents you from researching the diverse possibilities available.

Consider what would happen if you assembled, or fabricated, a rigid envelope underwater. Gradually, as the water is pumped out, the envelope rises through the surface, before it finally lifts off. It will then contain water vapour without air, so has the 61% advantage while it is a partial vacuum balloon.

Any condensate that forms as it rises will be pumped out from the bottom of the envelope. Indeed, a cold condenser would be one way to remove water vapour from inside the envelope.

As it approaches maximum altitude, it begins to approach a full vacuum, the cold steam does not need to be pumped out, as the vapour will condense and be removed as a liquid by the more efficient positive displacement pump.

So you seem to consider water vapor just as a means to prevent failure of the vacuum balloon on its way from the Earth's surface to its (high) design altitude. However, condensation strongly limits the water vapor pressure. If I am not mistaken, unless we have some exotic conditions, saturated water vapor is pretty much the same if there is air and if there isn't, so even at 50 deg Celsius it is only about 12% of the atmospheric pressure. Not an attractive design. Your shell would need to be very light to be buoyant at high altitude and very strong to withstand 88% of atmospheric pressure near the Earth's surface.

 

[Baluncore]

Your shell would need to be very light to be buoyant at high altitude and very strong to withstand 88% of atmospheric pressure near the Earth's surface.

Meanwhile, you write about flying vacuum balloons, as having a place transporting loads, then flooding the vacuum with air, to re-ballast the balloon.
Verily. "Your shell would need to be very light to be buoyant at sea level and very strong to withstand 100% of atmospheric pressure near the Earth's surface."

I am prepared to compromise, to reduce the stress where stress is unnecessary. You are insisting on an ideal, a total vacuum balloon at sea level. Perfection is the enemy of progress.

I cannot understand why you believe the laws of physics are so different for you than they are for me.

 

[akhmeteli]

Meanwhile, you write about flying vacuum balloons, as having a place transporting loads, then flooding the vacuum with air, to re-ballast the balloon.
Verily. "Your shell would need to be very light to be buoyant at sea level and very strong to withstand 100% of atmospheric pressure near the Earth's surface."

I don't know, maybe I completely misunderstand what you have in mind, but this is how it looks to me at the moment.

Your design is supposed to withstand 88% of atmospheric pressure at sea level and also to be buoyant at high altitude, where air density is, say, one tenth of that at sea level, so your envelope weighs only one tenth of what would provide minimum buoyancy at sea level.

My design is supposed to withstand 100% of atmospheric pressure at sea level and to be buoyant at sea level, so the envelope can weigh much more than in your design.

It seems obvious to me that it is much easier (although still difficult) to implement my design than yours as a heavier envelope has a much better chance to withstand air pressure comparable to that at sea level.

What do I miss?

I am prepared to compromise, to reduce the stress where stress is unnecessary. You are insisting on an ideal, a total vacuum balloon at sea level. Perfection is the enemy of progress.

I cannot understand why you believe the laws of physics are so different for you than they are for me.

I don't know what laws of physics you use, but I use very standard laws of physics. My design (described in our article cited earlier) uses commercially available materials and is viable according to both (semi)analytical formulas and finite-element analysis.

 

[Baluncore]

My design (described in our article cited earlier) uses commercially available materials and is viable according to both (semi)analytical formulas and finite-element analysis.

Then, as a proof of your analysis, build it.

 

[akhmeteli]

Then, as a proof of your analysis, build it.

And I am trying to do that, but it takes (a lot of) time. Making a vacuum balloon is hard: the idea is 350+ years old, but it has not been realized yet.

As for our design, one of the challenges is making thin boron carbide plates (say, 0.1-0.2 mm thick). I cannot disclose what has been done in that direction, but note that there are commercially available thin plates made of a different ceramic (alumina) . Some of them are 0.127 mm (0.005") thick.

 

[Baluncore]

You appear to be engineering at one extreme, a smooth thin shell, under 2D hoop compression.

I am looking at an hierarchical internal truss structure, that transmits external air pressure forces radially, with a slack external film envelope. Think of a dandelion seed head, without the internal payload of seed.

 

[akhmeteli]

You appear to be engineering at one extreme, a smooth thin shell, under 2D hoop compression.

I am looking at an hierarchical internal truss structure, that transmits external air pressure forces radially, with a slack external film envelope. Think of a dandelion seed head, without the internal payload of seed.

Maybe your approach is better than mine, maybe it's worse, who knows. Are any details publicly available? I guess buckling is critical to your approach too.

 

[Baluncore]

Maybe your approach is better than mine, maybe it's worse, who knows. Are any details publicly available? I guess buckling is critical to your approach too.

Each to their own. You go your way. If I thought your solution was best, I would still take a contrary way, to explore a different valley.

No published analysis. Too many threads yet to pull together, too many still to reject.

Buckling is critical to any chamber subjected to a net positive external pressure. You are concerned with the buckling of a shell. I am concerned with column stability, of structures that spread the load, with sufficient redundancy to allow for some failure.

My envelope is interesting, because it must be lightweight, so it should not be under great tension. By allowing it to flex inwards, the tension can be minimised. The skin then takes on a deeply dimpled surface, so looks a bit like an exaggerated golf ball, or a starved horse.