Low Gravity & High Atmo Density Question

[hypervelocity]

Hey guys! Hope everyone is great today!

I have a simple question regarding gravity and atmospheric density that maybe any of you would like to answer.

What would be a combination of low gravity and high atmospheric density that would enable a 100 kg object (shape it the way you want - a flat panel will do) to remain buoyant above a planetary surface, floating in the dense atmosphere?

I will specially appreciate equations showing the equilibrium of forces.

Let me know if I am missing something that would hinder my assumptions.

Many thanks in advance!

[tseitsei89]

Depends on the volume of the said object

[Green Baron]

Static buoyancy (Archimedes) is what you're looking for. If you have the densities then a volume or gravity is not needed as long as both exist (there is an "up" and a "down"). Object density / atmo density > 1 means object sinks, = 1 stays there, < 1 object rises.

You can complicate things if you like with temperature, varying atmo density, surface tension, hollow objects or those consisting of different densities/materials.

In short: a 100kg object will level off in an altitude where it displaces 100kg of atmosphere.

Edited January 6, 2018 by Green Baron

[tseitsei89]

Okay now I have more time so I'll try to write a proper explenation.

 

The hardest part is first so feel free to skip over it if you don't understand it.

Buoyancy is actually caused by the pressure difference on the top and bottom part of the object. And there is a pressure difference since the equation for calculating the hydrostatic pressure caused by a fluid is p(fluid) = roo(fluid)*g*z, where roo(fluid) is the density of the fluid, g is the local g and z is the height of the fluid on top of the point where we want to calculate the pressure for. So the z will be different for the top and bottom parts of the object.

Now, to get the actual force caused by this pressure difference we need to calculate how quickly the pressure is changing in different points. And we can do this by simply taking a gradient of the pressure. So grad(p) = roo(fluid)*g*grad(z) = roo(fluid)*g.

And now finally we have to integrate this pressure gradient over the whole volume of the object: integral[ grad(p)*dV] = integral[roo(fluid)*g*dV] = roo(fluid)*g*integral[dV] = roo(fluid)*g*V.

 

HARDER PART ENDS HERE. The rest should be quite simple.

 

As we calculated above the upwards force caused by buoyancy in Newtons is F(up) = m(atm)*g = roo(atm)*g*V where g is the local g.

The object is floating when upwards force equals downwards force (aka gravity) so F(up) = F(down) --> roo(atm)*g*V = m(object)*g --> roo(atm)*V = m(object).

Now we also know that m(object) = roo(object)*V, therefore roo(atm)*V = roo(object)*V ---> roo(atm) = roo(object).

And this obviously means that the object will float stationary if its density is equal to the density of the atmospheres density. The magnitude of gravity nor the shape or volume of the object do not play any role in this.

[Starman4308]

Low gravity doesn't help you, because now your vessel displaces less weight of air. High density would help, but you're still looking at either a substantial rigid balloon to resist exterior pressure, or an inflatable with a low molecular weight lifting gas.

[Snark]

On 1/5/2018 at 3:15 PM, hypervelocity said:

What would be a combination of low gravity and high atmospheric density that would enable a 100 kg object (shape it the way you want - a flat panel will do) to remain buoyant above a planetary surface, floating in the dense atmosphere?

There are a few misconceptions layered into this... let's unpack it a bit. 

• Gravity is completely irrelevant.  An object floats if it's less dense than the surrounding medium, and sinks if it's more dense.  Gravity is completely irrelevant to this, as long as there is some.  Suppose you have an object floating in a pond, and you get a pencil and draw where the waterline is on the object based on how high it floats in the water.  You could make gravity 1000x stronger, or 1000x weaker, and it wouldn't move the waterline relative to your pencil mark even one millimeter.
• Object weight is not the important thing.  What matters is the object's density, not its weight.  When you look up in the sky and see the Goodyear blimp floating overhead?  It weighs many tons.  So saying "a 100 kg object" is completely irrelevant to the question-- is it 100 kg of styrofoam, or 100 kg of tungsten?
• Object shape is completely irrelevant.  Styrofoam floats in water.  Doesn't matter if it's a sphere or a cube or a rod or a flat sheet.  Again, it's just the relative density that matters.

So what you're really asking is this:

"What would be the necessary atmospheric conditions to allow a solid object made of <material> to float above the surface?"

That highlighted bit is both necessary and sufficient to answer the question-- it completely matters what the material is (i.e. what's its density).  If its density is low enough, it will float whether the gravity is 1% or 10000% Earths, and whether it's a milligram or a megaton, regardless of shape.  If its density is high enough, it won't.

So... we need to know the density you have in mind.  What kind of material is the object?

[radonek]

Given the inputs, I guess underlying question is really about flying on Titan.

[wumpus]

52 minutes ago, Snark said:

There are a few misconceptions layered into this... let's unpack it a bit. 

[absolutely critical stuff the OP probably needs to re-read]

So... we need to know the density you have in mind.  What kind of material is the object?

How do you float 100kg in a dense atmosphere?  As long as object density > atmospheric density, if floats.

Every [manned] hot air balloon ever made has had more mass than 100kg.  So you don't need an atmosphere any more dense than Earth.

A complementary question (that you appear to be asking, but it is lost in ignoring the basics of buoyancy is where you might find a high-density atmosphere with low gravity.  Neptune and Uranus appear to qualify with near 1g gravity (at surface) but escape velocities twice Earth's (so gasses have a much harder time escaping).  While I don't know much about either planet's atmosphere, it appears they could easily hold an atmosphere considerably more dense than Earth's [I'm equally unsure how the surface is defined in a gas giant].  So you presumably want a massive but low density planet (low g but high escape velocity) to hold a dense atmosphere.

[Green Baron]

4 minutes ago, wumpus said:

... object density > atmospheric density, if floats.

Typo: < or <=

:-)

[Snark]

1 hour ago, radonek said:

Given the inputs, I guess underlying question is really about flying on Titan.

That wasn't my impression.

Simply flying isn't hard.  You can fly with a heavier-than-air powered craft, such as an airplane or helicopter.  You can fly with a big bag of buoyant gas, like a helium or hot-air balloon.  Presumably the OP is aware of both of these.

It sounded to me as though what the OP was really after isn't a practical question of "I want to fly in location X, how do I do that"-- but rather, the really interesting question "what would it take for a solid object to float in a gaseous medium?"  We're so used to a world in which "solid things always sink in a gas" that it's fascinating to imagine a situation in which the opposite might hold true (and wonder whether/how such a thing would be possible).

Or such is my impression, don't want to put words in @hypervelocity's mouth. 

1 hour ago, wumpus said:

A complementary question (that you appear to be asking, but it is lost in ignoring the basics of buoyancy is where you might find a high-density atmosphere with low gravity.  Neptune and Uranus appear to qualify with near 1g gravity (at surface) but escape velocities twice Earth's (so gasses have a much harder time escaping).  While I don't know much about either planet's atmosphere, it appears they could easily hold an atmosphere considerably more dense than Earth's

Weelllllll... not necessarily.  Their atmosphere is mostly hydrogen, and what's not hydrogen is mostly helium (with a small amount of methane and such left over).  Hydrogen is literally the worst possible stuff to try to float in, precisely because it's so light.

Yes, if you go deep enough in the atmosphere you'll start to compress it enough to get a lot denser than up above... but even liquid hydrogen is only about a tenth as dense as water, IIRC.  So you're going to be hard-pressed to float anything in it passively.  (With a power source, perhaps you could have a hot-air balloon, i.e. float a bubble of warm hydrogen in the surrounding colder hydrogen... but that's not what the OP was asking.)

So, the atmospheric composition (i.e. what gases are in it) will matter, a lot.  Some gases simply can't be made all that dense regardless of how much you compress them.   You'd want an atmosphere with the highest possible molecular mass.  But again, we'd need to know what object density the OP had in mind, i.e. what material, before we can start talking meaningfully about what conditions would be required to float it.

(Unless of course you're talking about delving so deep into a gas giant that you start getting exotic hyper-compressed states of matter like metallic hydrogen, but by then calling it a "gas" seems a bit of a stretch, IMHO.) 

[YNM]

If you're a fish, water is the "atmosphere", so...

[wumpus]

21 minutes ago, Snark said:

Weelllllll... not necessarily.  Their atmosphere is mostly hydrogen, and what's not hydrogen is mostly helium (with a small amount of methane and such left over).  Hydrogen is literally the worst possible stuff to try to float in, precisely because it's so light.

My point was that high density/low gravity appeared possible, but I'm less sure how you could find/construct a planet that would have such an atmosphere (all the dense gasses in a gas giant will be "surface or below", probably leaving a hydrogen and other less dense gas "atmosphere").  But the limit on gas density should be the escape velocity of the planet which can be a lot higher than Earth's without increasing the surface acceleration (the "gravity" you feel on the surface).  Perhaps a planet made of soapstone, talc or similar low density rock.

- of course, that "surface acceleration" doesn't affect buoyancy at all.  It just sounds like the OP would prefer a feeling of low gravity.

[Green Baron]

Volcanic rocks with high fluid (i.e. gaseous) contents float in and on water under earthly conditions (1g, salty ocean, magma temp. and composition), so there is that.

While all of that is correct imo, an "atmosphere" of molten rock or metal isn't really hard to imagine, it would be called and is being called a magma ocean (one can debate if lava is the better word here :-)). Almost everything imaginable will float in it until it melts. Including the one ring.

A very dense atmosphere like that on Venus with a high CO2 percentage or a lot of water vapour would be somewhere between an ocean and an atmosphere, maybe, if close to the switching point of condensation/vapourisation, both at the same time, but still an atmosphere.

And the core of a gas giant is not exactly its atmosphere ;-) Maybe a white dwarf's shell with similar conditions ... but that is all rather hypothetical and maybe far fetched, idk.

If something material shall float in equilibrium conditions it must be in sort of a gaseous or liquid atmosphere. Floating in Hydrogen otoh. would only be possible with less hydrogen, aka depressurized vessel. Would be a really big blimp though to generate only little static lift ...

 

[radonek]

 

[Snark]

1 hour ago, wumpus said:

My point was that high density/low gravity appeared possible, but I'm less sure how you could find/construct a planet that would have such an atmosphere

First of all... I don't think that the OP actually cares about low gravity, or that it's actually a requirement for what he was asking about.  I think he just said "low gravity" because he (mistakenly) thought that that would make things "easier", i.e. he was thinking "I want stuff to float, and that's easier if gravity is lower."  Which is not the case.  So I don't think "low gravity" is particularly a requirement.

That said, though... even if you do stipulate it, I think low gravity is easy, here:  you just do it with a small planet rather than with a gas giant.  Yes, that means the planet will have a relatively low escape velocity.  But remember, we're trying to optimize the atmosphere for maximum density, here.  That means we want a gas with the highest possible molecular mass (since that boosts the density).  And gases with very high molecular masses have very low molecular speeds, which means it's a lot easier for a small planet to hang on to them.  It's okay for the escape velocity to be relatively low.

And gets even easier if we stipulate that the temperature is fairly low, which both reduces the molecular speed and increases the average density for a given pressure, both of which we want.  Of course... we've also stipulated that the medium has to be a gas, not a liquid, which means we can't lower the temperature or raise the pressure too much.  And gases with very high molecular masses also tend to have fairly high boiling points, meaning you can't chill/compress them much without turning them into a liquid.

For example, tungsten hexafluoride is 11 times denser than air under standard conditions (25 C, one atmosphere) ... but its boiling point at that pressure is 17 C, so if the planet was even a little chillier than room temperature, it would be an ocean rather than an atmosphere. 

 

[hypervelocity]

It is amazing the number of misconceptions I included in my OP - @Snark's post brought back everything I learnt in high school physics, so very very grateful for that. You also correctly observed the below:

20 hours ago, Snark said:

First of all... I don't think that the OP actually cares about low gravity, or that it's actually a requirement for what he was asking about.  I think he just said "low gravity" because he (mistakenly) thought that that would make things "easier", i.e. he was thinking "I want stuff to float, and that's easier if gravity is lower."  Which is not the case.  So I don't think "low gravity" is particularly a requirement.

@YNM's comment made me laugh, and I liked @radonek's conjecture. 

I'm also amazed by the willingness people around here have to teach things, and to clarify misconceptions like the ones I had - you guys actually had to dig through all the nonsense I wrote in order to find the underlying question, so thanks for that!

In reality, this was all about trying to imagine floating structures in high atmospheric density worlds, say Venus for instance (I know there was a NASA concept going around lately, HAVOC was it?)

Now onto brass tacks, how do we do it on KSP + RSS + Realism Overhaul?  I am now filling a huge procedural tank with air and dropping it at Venus - will it float? (KSP/RO now models atmo pressure right? will it get crushed before floating?)

Edited January 11, 2018 by hypervelocity

[PB666]

21 hours ago, Snark said:

First of all... I don't think that the OP actually cares about low gravity, or that it's actually a requirement for what he was asking about.  I think he just said "low gravity" because he (mistakenly) thought that that would make things "easier", i.e. he was thinking "I want stuff to float, and that's easier if gravity is lower."  Which is not the case.  So I don't think "low gravity" is particularly a requirement.

That said, though... even if you do stipulate it, I think low gravity is easy, here:  you just do it with a small planet rather than with a gas giant.  Yes, that means the planet will have a relatively low escape velocity.  But remember, we're trying to optimize the atmosphere for maximum density, here.  That means we want a gas with the highest possible molecular mass (since that boosts the density).  And gases with very high molecular masses have very low molecular speeds, which means it's a lot easier for a small planet to hang on to them.  It's okay for the escape velocity to be relatively low.

And gets even easier if we stipulate that the temperature is fairly low, which both reduces the molecular speed and increases the average density for a given pressure, both of which we want.  Of course... we've also stipulated that the medium has to be a gas, not a liquid, which means we can't lower the temperature or raise the pressure too much.  And gases with very high molecular masses also tend to have fairly high boiling points, meaning you can't chill/compress them much without turning them into a liquid.

For example, tungsten hexafluoride is 11 times denser than air under standard conditions (25 C, one atmosphere) ... but its boiling point at that pressure is 17 C, so if the planet was even a little chillier than room temperature, it would be an ocean rather than an atmosphere. 

 

But there is nonetheless a missing component to the system. In order to be lighter than air there has to be a set of tensors that bound the object being evaluated. If you wanted something, like a drop of water to be lighter than air, you can compress the air, but you are also compressing the water. Likewise if you want to take air and make it lighter than air by compressing the air outside, you have to resist the effect of that air on the air. So its more important to define the context than to define the context in which that comparison metric is true.

Tungsten hexaflouride could be used to displace an airship, but only if the parameters of the airship are defined.

Therefore if I had 100kg and atmosphere is 22.4 liters per mole of N2/O2 which we can basically has a molecular weight 29.2 grams (=0.0292 kg) per mole, the you need not fancy scenarios. Since the mass of gas per liter is 1.3 grams/liter since there is 1000 liters in a M³ and 1000 grams in a kg that converts to 1.3 kg per meter. We can also look at this from pressure. PV = nRT

R = 8.3144598
V = Meter cubed = 1
P = 101300 Pa
n = number of moles
T = 293
101300 = 293 * 8.314 * n

n = 41.3

41.3 moles x 0.0292 kg/mole = 1.214 kg per meter cubed.

Thus without any stipulation of gravity, escape velocity . . . . . . . we have any ship that has a volume 82.34 cubic meters and a mass of 100 kg can float in Earths lower atmosphere. Its not the density of material comprising the ship that matters per say but the ability of that material to resist the (tension) on its exterior surface. If you took the ship to the top of mount Everest it would have to increase its volume by (101,300/38,210). The postulate is easier if you are using a material whose innate properties are relatively bouyant. For example a very light payload helium balloon in a completely elastic container will continue to rise as long as the the molar ratio of hydrogen to N2/O2 11.6:1, however even in this situation the physical constraints on the system (the more elastic a material the more it weighs, the less elastic the more its likely to break under its own pressure). So in both situations the ability to resist a force, either exterior or interior is missing from the original argument.

 

 

[Snark]

2 hours ago, hypervelocity said:

In reality, this was all about trying to imagine floating structures in high atmospheric density worlds, say Venus for instance (I know there was a NASA concept going around lately, HAVOC was it?)

Ohhh, is that what you were driving at?  Well, heck, that's easy, then. 

You just do it the same way that we do it on Earth:  with a balloon.

Specifically, a balloon that's filled with a gas whose molecular mass is significantly lower than the molecular mass of the surrounding atmosphere.  On Venus, this is pretty easy.  (Well, "easy" in terms of "have a gas that's significantly buoyant."  The physics is simple.  The engineering of building a craft that can survive the temperatures, the presence of corrosive sulfuric acid, etc. is another matter entirely, but that's not what we're talking about here.)

Why is it easy on Venus?  It's easy because the atmosphere is mostly CO₂, which has a nicely high molecular mass (44).  So all you need to do is to fill your balloon with something that's significantly lighter than that, and Bob's your uncle.

There are a variety of gases you could choose from, but in terms of convenience, I would think that good old-fashioned water would be a reasonable choice.  At Venusian temperatures, it's a gas, with a molecular mass of 18.  That puts it 26 below the atmosphere's molecular mass, meaning that a water-vapor-filled balloon on Venus would have slightly better relative buoyancy than a helium-filled balloon on Earth, which is plenty enough to lift a good-sized vehicle.

Using actual helium would be even more buoyant, of course, but water seems more practical from an engineering standpoint.  It's easier to transport to Venus in the first place-- you can store it as a liquid or solid, without needing a heavily-pressurized container.  And, after you've inflated your balloon, it's less prone to leakage than helium is (helium, with its small monatomic particles and high mean velocity, is a notorious escape artist that tends to leak through things easily-- given time it'll even diffuse through glass).

But anyway, you could fill your balloon with basically any gas that's significantly lighter than CO₂ and which doesn't chemically break down at Venusian temperatures, which leaves the field fairly wide open.

[wumpus]

23 hours ago, Snark said:

First of all... I don't think that the OP actually cares about low gravity, or that it's actually a requirement for what he was asking about.  I think he just said "low gravity" because he (mistakenly) thought that that would make things "easier", i.e. he was thinking "I want stuff to float, and that's easier if gravity is lower."  Which is not the case.  So I don't think "low gravity" is particularly a requirement.

 

On 1/10/2018 at 12:39 PM, wumpus said:

My point was that high density/low gravity appeared possible, but I'm less sure how you could find/construct a planet that would have such an atmosphere (all the dense gasses in a gas giant will be "surface or below", probably leaving a hydrogen and other less dense gas "atmosphere").  But the limit on gas density should be the escape velocity of the planet which can be a lot higher than Earth's without increasing the surface acceleration (the "gravity" you feel on the surface).  Perhaps a planet made of soapstone, talc or similar low density rock.

Oops.  I kept saying "density" when all the things I talked about were "pressure".  While increasing pressure should [usually] increase density (for gasses), as Snark points out you could simply introduce more dense gasses.  Still, increasing the escape velocity allows to increase the pressure and thus the density [regardless of the gas] at equal surface gravity (increasing the surface gravity also allows for higher pressure, but appears less preferred).

50 minutes ago, Snark said:

Specifically, a balloon that's filled with a gas whose molecular mass is significantly lower than the molecular mass of the surrounding atmosphere.  On Venus, this is pretty easy.  (Well, "easy" in terms of "have a gas that's significantly buoyant."  The physics is simple.  The engineering of building a craft that can survive the temperatures, the presence of corrosive sulfuric acid, etc. is another matter entirely, but that's not what we're talking about here.)

Could you make the fine print any finer?  Also don't forget the winds of Venus: they go beyond "hurricane force" well into tornado speeds and probably off that chart as well (370kmh), although I don't know if they violently change direction.

 

Edited January 11, 2018 by wumpus
needed to snark at snark

[Snark]

29 minutes ago, wumpus said:

Could you make the fine print any finer?

Yes. 

30 minutes ago, wumpus said:

Also don't forget the winds of Venus: they go beyond "hurricane force" well into tornado speeds and probably off that chart as well (370kmh), although I don't know if they violently change direction.

Which, like my fine-print parenthetical comment, is also off-topic for this thread, since this is simply about buoyancy and not a general topic about the engineering challenges of Venus exploration.  Perhaps a topic better taken up elsewhere.

[Green Baron]

If the winds are uniform they aren't really a problem for a hypothetical theoretical balloon, it'll just be drifting with them and conditions will be still in the balloon. What ARE problems are windshear and convection, both are hypothetically theoretically not a big issue in the upper venus atmosphere as long as the balloon stays above the convection zones. These are assumed hypothethesized to be limited to the hadley cells.

Should the hypothetical theoretical balloon sink too low it'll be transported to the equator poles where the elevator is going down ... hypothetcally.

:-)

Edit: sorry, yes, off topic. As usual.

Edited January 11, 2018 by Green Baron

[PB666]

48 minutes ago, Snark said:

Ohhh, is that what you were driving at?  Well, heck, that's easy, then. 

You just do it the same way that we do it on Earth:  with a balloon.

Specifically, a balloon that's filled with a gas whose molecular mass is significantly lower than the molecular mass of the surrounding atmosphere.  On Venus, this is pretty easy.  (Well, "easy" in terms of "have a gas that's significantly buoyant."  The physics is simple.  The engineering of building a craft that can survive the temperatures, the presence of corrosive sulfuric acid, etc. is another matter entirely, but that's not what we're talking about here.)

Why is it easy on Venus?  It's easy because the atmosphere is mostly CO₂, which has a nicely high molecular mass (44).  So all you need to do is to fill your balloon with something that's significantly lighter than that, and Bob's your uncle.

 

Again I would point out that the structure is context dependent. The atmosphere of Venus at atmospheric pressure is :

50000     75c      1.066bar (107985 Pa)

55000     27c         0.5314bar

75'C is (273+75)k = 348K

CO2 is 44 and N2/O2 is 29.3 so the advantage is not as great as you think the gas density at 50000 is only 26% (1.45 kg/m3) higher than earth, thus instead of needed a tensor volume of 60 cubic meters to support 100 kg. The problem with this it the current types of materials one might use are not stable to the heat and/or the temperature. At 55000 feet the temperature is more agreeable but you would need to create a tension barrier on 110 cubic meters.

Again I believe that a situation where standing outside temperature is untenable, since the energy gain, would be less over the volume when weight of the cooling sytem is factored in. For all intents an purposes nuclear is a non-starter because you are trying to dissipate heat in a high heat environment, so that the only source of power is solar. Solar may be a non-starter because of the vulnerability of solar to sulferic acid.

At 55000 meters the survival metric is higher but the volume is also greater.
So lets say you have a perfect sphere of volume 110 made of carbon fiber of d=1.4 1400kg/m3. r = 2.97 meters. surface area is 35.3 meters. Again we are conceiving that the volume is a vacuum, to use hydrogen add another meter and for helium add another couple of meters. Lets say the barrier was 0.010 mm thick, then the mass would be 1400 kg * 35.3 * 0.01 = 494.2 kg. So basically at this mass the thickness would have to be less than 2 mm in thickness. Again this is credible, So lets then argue our payload is 50 kg, that means the thickness would be 1mm in thickness.
There is some improvement if you decide to go to say 1000kg, the surface area to volume goes down but the stress on the binding points go up.

The next problem is that you have create a lighter than air ship, you are at the bottom facing Venus and the ship is above you reflecting both sunlight (which you need) and heat back at you which your don't. This both makes nuclear a non-starter and solar difficult.

We could talk about experiences with H2SO4 but the only know substance that I have worked with in the laboratory that is stable to the substance is certain types of glass. While the vapor pressure of H2S04 is low, the problem is that H2S04 has the lowest pKa of any acid for its first proton and secondarily H2S04 is an oxidant and at that pH is a very strong oxidant and exposure to sunlight and UV would only increase its oxidation potential. CO2 is the most oxidized state of carbon and although it can form carbonic gas transiently in strong acid its not likely to buffer its effects. When we talk about the stability of metals, i don't believe there is one that is stable over time, carbon is best described as a semimetal it can take on the role as an oxidant and reductant. However in a highly acidic environment it more than likely adopt a role as a reductant, it will want to deliver electrons to sulfuric acid. https://en.wikipedia.org/wiki/Aromatic_sulfonation  https://en.wikipedia.org/wiki/Nitration. And you can surmise its effects on Carbon fiber. 

 

[Snark]

21 minutes ago, PB666 said:

Again I would point out that the structure is context dependent.

I think you're vastly, vastly overcomplicating things for what the OP is asking.  All he wants to know is "what does it take to be able to float on Venus".  And that's a really simple question, in terms of buoyancy physics.

Here's a pretty reasonable set of basic assumptions:

Spoiler

• You're using a balloon.
• The balloon is engineered to not rely on structural strength; it's just a flaccid sack whose internal pressure basically equals the exterior pressure.
• The craft is made out of materials that are incompressible (other than the gas in the balloon, of course).
• "Incompressible" defined as "sane numbers".  We're not talking about insane extreme physics conditions like the heart of Jupiter or something, where "solid" materials actually compress by amounts that would significantly affect their buoyancy.  Any actual compression of the solid materials of the craft is so tiny that it's insignificant, relative to the overall buoyancy of the craft.
• The volume of the gas in the balloon is far larger than the volume of the solid materials that the balloon is constructed of.

With that in mind, it's really simple.

M_ship = V_b * (1 - m_b/m_a) * ρ_a

where:

• M_ship is the total mass of the solid components of the ship that can be lifted
• V_b is the volume of the gas in the balloon, at a particular location
• m_b is the average molecular mass of the gas in the balloon
• m_a is the average molecular mass of the atmosphere
• ρ_a is the density of the atmosphere, at that location.

It's that simple.

Yes, this is an approximation.  It ignores that solid things can, in fact, compress by a microscopic amount.  It ignores the buoyancy of the solid components themselves, by assuming their volume is negligible compared with the balloon gas.  But it's a pretty darn good approximation, and getting it much more accurate than that will vastly complicate the math, and I expect what the OP here wants is a fairly simple answer.

[PB666]

35 minutes ago, Snark said:

I think you're vastly, vastly overcomplicating things for what the OP is asking.  All he wants to know is "what does it take to be able to float on Venus".  And that's a really simple question, in terms of buoyancy physics.

Here's a pretty reasonable set of basic assumptions:

  Reveal hidden contents

• You're using a balloon.
• The balloon is engineered to not rely on structural strength; it's just a flaccid sack whose internal pressure basically equals the exterior pressure.
• The craft is made out of materials that are incompressible (other than the gas in the balloon, of course).
• "Incompressible" defined as "sane numbers".  We're not talking about insane extreme physics conditions like the heart of Jupiter or something, where "solid" materials actually compress by amounts that would significantly affect their buoyancy.  Any actual compression of the solid materials of the craft is so tiny that it's insignificant, relative to the overall buoyancy of the craft.
• The volume of the gas in the balloon is far larger than the volume of the solid materials that the balloon is constructed of.

With that in mind, it's really simple.

M_ship = V_b * (1 - m_b/m_a) * ρ_a

where:

• M_ship is the total mass of the solid components of the ship that can be lifted
• V_b is the volume of the gas in the balloon, at a particular location
• m_b is the average molecular mass of the gas in the balloon
• m_a is the average molecular mass of the atmosphere
• ρ_a is the density of the atmosphere, at that location.

It's that simple.

Yes, this is an approximation.  It ignores that solid things can, in fact, compress by a microscopic amount.  It ignores the buoyancy of the solid components themselves, by assuming their volume is negligible compared with the balloon gas.  But it's a pretty darn good approximation, and getting it much more accurate than that will vastly complicate the math, and I expect what the OP here wants is a fairly simple answer.

Im adding the complications on the front side, I gsve a volume under several circumstances. Sure one could create a balloon out of lead despite th fact it would never work. 

[hypervelocity]

2 hours ago, Snark said:

I think you're vastly, vastly overcomplicating things for what the OP is asking.  All he wants to know is "what does it take to be able to float on Venus".  And that's a really simple question, in terms of buoyancy physics.

I don't mind the conversation and I think you pretty much explained the basics that I was looking for, so happy for you guys to delve deeper

4 hours ago, Snark said:

Ohhh, is *that* what you were driving at?  

What other fun challenges did you have in mind? I would love to take this further!