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PostPosted: Sun Jan 21, 2018 12:59 am 
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I plan to run my own roleplaying campaign and I also intend to do it within a world that is similar or identical to Eina-Afa AKA the can full of sky. Such things necessitate Godwalls to keep out the hurricanes, resulting in one general question and one specific question:

General: What's the function describing the ambient air pressure with respect to distance from the ground?

Specific: If it's 101.3 kPa at the ground, what's the air pressure 1000-1200km up? (I'm going to just assume that this answer is not altered by whether or not there is a Godwall nearby, which I now realise might be incorrect)

((Super specific: Can regular people, or people with wings, ascend a Godwall and colonise the top?))

Right now I'm neglecting any impact of drag, and assuming that the entire "mass" of air essentially keeps rotational pace with the outer wall (when in reality the higher layers will slip back).

I've tried tackling this myself and presenting the situation to other mathy people but we've all come to the conclusion that it's a a tricky problem. My best approach so far via integration is to model the system as a series of infinitely thin concentric rings (from the infinitely-small spindle to the ground) where each ring has its own pressure. Since air is compressible, weight-by-volume depends on local pressure; which depends on the total force exerted by the "weight" of the air above it; which depends on each ring's total mass and centrifugal force requirements for a circular path; and it can't drop to zero anywhere, otherwise there's nothing to keep the lower layers from being pushed upwards. Otherwise, I guess there's atmospheric flow simulations, which I've never done before.

So: if anyone happens to have the skills or knowledge to illuminate this problem, it would be very appreciated!


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PostPosted: Sun Jan 21, 2018 3:48 am 
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Try reading this article, then just assume that force due to centripetal accelleration is functionally equivalent to gravity.

If it makes you happy, you can break it down, and iterate 10 times or so over the radius of the of the can, changing gravity each time, as centripital accelleration changes based on radius.


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PostPosted: Sun Jan 21, 2018 4:05 am 
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Krennson wrote:
Try reading this article, then just assume that force due to centripetal accelleration is functionally equivalent to gravity.

If it makes you happy, you can break it down, and iterate 10 times or so over the radius of the of the can, changing gravity each time, as centripital accelleration changes based on radius.
You forgot your link.


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PostPosted: Sun Jan 21, 2018 11:25 am 
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Huh. did I forget to post the link?

https://en.wikipedia.org/wiki/Barometric_formula#Pressure_equations


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PostPosted: Sun Jan 21, 2018 1:27 pm 
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Can full of sky works best if you assume ground level is less than 1g and that the atmospheric pressure is more than Earth sea level. It also helps if you have a bunch of lighter molecules in the air mix. H2 is probably bad if you want a breathable Oxygen content, but He is fine. So rather than 79% N2, 20% O2, ~1% "Other"; go with five atmospheres at roughly 94% He, 5% O2, 1% "Other".

This makes flying a lot easier, gives a much higher scale height, is breathable for a good distance up, and generally just works better for everything except those natives who fly via H2 buoyancy, and they could have a tech assist.

I haven't bothered to figure if this will retain decent pressure to the center, I doubt it, but it might.


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PostPosted: Mon Jan 22, 2018 5:15 pm 
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Doug Lampert wrote:
Can full of sky works best if you assume ground level is less than 1g and that the atmospheric pressure is more than Earth sea level. It also helps if you have a bunch of lighter molecules in the air mix. H2 is probably bad if you want a breathable Oxygen content, but He is fine. So rather than 79% N2, 20% O2, ~1% "Other"; go with five atmospheres at roughly 94% He, 5% O2, 1% "Other".

This makes flying a lot easier, gives a much higher scale height, is breathable for a good distance up, and generally just works better for everything except those natives who fly via H2 buoyancy, and they could have a tech assist.

I haven't bothered to figure if this will retain decent pressure to the center, I doubt it, but it might.


Alright, I set up a quick formula for 1 km layers on a 4,000 km rotating station with an He/O2 mix at 300K (constant with altitude) and .1 g at the full radius.

No reasonable constant mix works, but if I assume that there's a system that adjusts the O2 fraction at different depths and keeps things breathable (16 kPa O2 partial pressure), then I get that 10 atmospheres at the bottom of the stackup gives a still breathable atmosphere at the top with some safety margin.

It takes tech-intervention or some really clever ducting or something to cause O2 concentrations to go UP as you rise given that 02 is much denser than He, but that's a lot easier than anything else about the system and should be fairly easily managed for anyone able to build a can full of sky in the first place.


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PostPosted: Mon Jan 22, 2018 11:41 pm 
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I don't think Eina-afa's "Spine" is necessarily surrounded by breathable atmosphere... I think the actual center is very-low-pressure.

Did you remember to model different gravities at different levels?

Doug Lampert wrote:
Doug Lampert wrote:
Can full of sky works best if you assume ground level is less than 1g and that the atmospheric pressure is more than Earth sea level. It also helps if you have a bunch of lighter molecules in the air mix. H2 is probably bad if you want a breathable Oxygen content, but He is fine. So rather than 79% N2, 20% O2, ~1% "Other"; go with five atmospheres at roughly 94% He, 5% O2, 1% "Other".

This makes flying a lot easier, gives a much higher scale height, is breathable for a good distance up, and generally just works better for everything except those natives who fly via H2 buoyancy, and they could have a tech assist.

I haven't bothered to figure if this will retain decent pressure to the center, I doubt it, but it might.


Alright, I set up a quick formula for 1 km layers on a 4,000 km rotating station with an He/O2 mix at 300K (constant with altitude) and .1 g at the full radius.

No reasonable constant mix works, but if I assume that there's a system that adjusts the O2 fraction at different depths and keeps things breathable (16 kPa O2 partial pressure), then I get that 10 atmospheres at the bottom of the stackup gives a still breathable atmosphere at the top with some safety margin.

It takes tech-intervention or some really clever ducting or something to cause O2 concentrations to go UP as you rise given that 02 is much denser than He, but that's a lot easier than anything else about the system and should be fairly easily managed for anyone able to build a can full of sky in the first place.


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PostPosted: Tue Jan 23, 2018 2:57 am 
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Krennson wrote:
I don't think Eina-afa's "Spine" is necessarily surrounded by breathable atmosphere... I think the actual center is very-low-pressure.


In the comic, the spine and upper reaches of the struts are shown to have no vegetation. Eina-Afa is old enough that something would of evolved to colonize that area if it could, so that means nothing can grow up there. Which probably means there isn't enough atmosphere to support life at that height.


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PostPosted: Tue Jan 23, 2018 9:54 am 
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Weren't they were running around on the spine, lifting a ton of weight, and otherwise having a good time?

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PostPosted: Tue Jan 23, 2018 10:07 am 
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keybounce wrote:
Weren't they were running around on the spine, lifting a ton of weight, and otherwise having a good time?

On a different ship, where normally the spine was the direction of gravity.

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PostPosted: Tue Jan 23, 2018 11:58 am 
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Krennson wrote:
I don't think Eina-afa's "Spine" is necessarily surrounded by breathable atmosphere... I think the actual center is very-low-pressure.

Did you remember to model different gravities at different levels?

Yes, without that it's completely hopeless. You get a slightly higher scale height than Earth from the reduced average molecular mass, and a factor of 10 from the gravity, but you need that fairly rapid drop-off in gravity for the center to be breathable.


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PostPosted: Wed Jan 24, 2018 7:06 am 
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keybounce wrote:
Weren't they were running around on the spine, lifting a ton of weight, and otherwise having a good time?


Didn't they have their helmets up? It's been a while, but I thought they had helmets on when they were along the spindle.


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PostPosted: Thu Jan 25, 2018 7:22 am 
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OK! I think I'm making some progress, though the numbers don't look good. I'd like a sanity check. Here's my work so far.

Basic principle: Like Doug, I'm modelling the system as a set of concentric 1km-deep layers which are individually homogenous. I set desired values for the lowest layer, then work out what the values of the layer immediately above must be, and so on recursively up to the hub. It hinges on the principle that the pressure seen by layer n must be equal to the pressure of layer n+1 plus the normal force due to layer n's own weight in the rotating system.

However, the current spreadsheet (at 50% scale, 50% gravity, 50% gas density, 3 atmospheres - 300kPa - at the hull) still has the death zone (calling that 40 kPa) starting a "mere" 70km up. It doesn't bode well for Godwall colonies, especially if you intend to use atmospheric flight to gain altitude. Mainly, that necessary normal force seems to be far too high; I'm losing 3% of my current pressure per kilometer. With that kind of drop, there couldn't possibly be any rolling storms of the comic's scale, removing the need for the godwalls entirely - which are one of the most important things I want to preserve when I use this world for a roleplay I'm planning.

I'm using the Ideal Gas Law, so I'm assuming constant gas mix and constant temperature throughout.

I'm almost considering returning to my first idea - an integration-based model to give a continuous curve of pressure according to height - but that felt like beating my head against a brick wall, so I'm hoping I can make this work with the approximation.


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PostPosted: Thu Jan 25, 2018 7:47 pm 
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OK, I've changed some values with potentially acceptable results.

The world is now 50% scale; 2000km radius, 500km godwalls. Gravity is at half strength - 5 m/s^2 at the hull. Air pressure at the hull is 300 kPa. Air density is at 10% normal, which I prefer to interpret as that this setting doesn't use "normal" gases and might actually use a different table of elements entirely. This in itself is OK, the system (Starfinder) doesn't really need to work with actual physics often if at all.

This makes it 40kPa at 500km altitude; if those godwalls create a high-pressure zone on the leading face and their borders where the wind slips past, then that should allow for a barely-habitable zone on the top edge if I completely ignore problems of partial pressure of oxygen, which I will.

I think I may commit to these values for my own use and move on unless I foresee significant problems coming up later.


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PostPosted: Fri Jan 26, 2018 3:26 am 
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Spekkio wrote:
OK, I've changed some values with potentially acceptable results.

The world is now 50% scale; 2000km radius, 500km godwalls. Gravity is at half strength - 5 m/s^2 at the hull. Air pressure at the hull is 300 kPa. Air density is at 10% normal, which I prefer to interpret as that this setting doesn't use "normal" gases and might actually use a different table of elements entirely. This in itself is OK, the system (Starfinder) doesn't really need to work with actual physics often if at all.

This makes it 40kPa at 500km altitude; if those godwalls create a high-pressure zone on the leading face and their borders where the wind slips past, then that should allow for a barely-habitable zone on the top edge if I completely ignore problems of partial pressure of oxygen, which I will.

I think I may commit to these values for my own use and move on unless I foresee significant problems coming up later.

I hate to throw a monkey wrench in your model when you are close to a happy spot, but have you considered the effect of gravity? In Eina-Afa, the spindle has a significant gravity well, which is probably why they get such a nice, high pressure atmosphere without crushing the stuff on the surface.


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PostPosted: Fri Jan 26, 2018 5:51 am 
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Motortiki wrote:
Spekkio wrote:
OK, I've changed some values with potentially acceptable results.

The world is now 50% scale; 2000km radius, 500km godwalls. Gravity is at half strength - 5 m/s^2 at the hull. Air pressure at the hull is 300 kPa. Air density is at 10% normal, which I prefer to interpret as that this setting doesn't use "normal" gases and might actually use a different table of elements entirely. This in itself is OK, the system (Starfinder) doesn't really need to work with actual physics often if at all.

This makes it 40kPa at 500km altitude; if those godwalls create a high-pressure zone on the leading face and their borders where the wind slips past, then that should allow for a barely-habitable zone on the top edge if I completely ignore problems of partial pressure of oxygen, which I will.

I think I may commit to these values for my own use and move on unless I foresee significant problems coming up later.

I hate to throw a monkey wrench in your model when you are close to a happy spot, but have you considered the effect of gravity? In Eina-Afa, the spindle has a significant gravity well, which is probably why they get such a nice, high pressure atmosphere without crushing the stuff on the surface.


Citing what? Are you thinking of the bit where they were teraported from inside the soulcrypt into one of the Oafan ships?

Anyway, I've been thinking on this further. I suspect that my pressure-dropoff problem would be mitigated by incorporating slippage between layers (less spin means less additional "weight" pushed onto lower layers) but I just have no idea how much drag there's going to be.


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PostPosted: Fri Jan 26, 2018 2:42 pm 
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Spekkio wrote:
Motortiki wrote:
Spekkio wrote:
OK, I've changed some values with potentially acceptable results.

The world is now 50% scale; 2000km radius, 500km godwalls. Gravity is at half strength - 5 m/s^2 at the hull. Air pressure at the hull is 300 kPa. Air density is at 10% normal, which I prefer to interpret as that this setting doesn't use "normal" gases and might actually use a different table of elements entirely. This in itself is OK, the system (Starfinder) doesn't really need to work with actual physics often if at all.

This makes it 40kPa at 500km altitude; if those godwalls create a high-pressure zone on the leading face and their borders where the wind slips past, then that should allow for a barely-habitable zone on the top edge if I completely ignore problems of partial pressure of oxygen, which I will.

I think I may commit to these values for my own use and move on unless I foresee significant problems coming up later.

I hate to throw a monkey wrench in your model when you are close to a happy spot, but have you considered the effect of gravity? In Eina-Afa, the spindle has a significant gravity well, which is probably why they get such a nice, high pressure atmosphere without crushing the stuff on the surface.


Citing what? Are you thinking of the bit where they were teraported from inside the soulcrypt into one of the Oafan ships?

Anyway, I've been thinking on this further. I suspect that my pressure-dropoff problem would be mitigated by incorporating slippage between layers (less spin means less additional "weight" pushed onto lower layers) but I just have no idea how much drag there's going to be.


100% drag up to near the top of your godwalls, and potentially very strong winds above. How much if any, I haven't the faintest idea.
Really, SHOULD there be "slippage". "Slippage" would be wind, but is there an outside force to make the wind "want" to stand still relative to a point outside the hull? If you spin a bucket of water on a rope, with a lid on it, does the water bunch up against the trailing edge of the bucket?


Unless that column down the middle has a mass on par with a planet, it shouldn't be enough to offset the spin gravity, and if it's enough, it just means the can has to spin that much faster to get the gravity back, so the high-mass column shouldn't matter in the least.

However, going back to partial pressures. What is the "death partial pressure" when you're living in an oxygen enriched environment at 3 atmospheres? I understand divers actually have to use hypoxic mixes for deep diving. At what point do you get too much oxygen at 3 atmospheres?


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PostPosted: Fri Jan 26, 2018 4:10 pm 
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Sean wrote:
However, going back to partial pressures. What is the "death partial pressure" when you're living in an oxygen enriched environment at 3 atmospheres? I understand divers actually have to use hypoxic mixes for deep diving. At what point do you get too much oxygen at 3 atmospheres?


There are two forms of oxygen toxicity - pulmonary (lungs) and CNS (central nervous system). Divers are concerned primarily with the CNS type, and rapid onset of symptoms (convulsions, etc) begins past 1.6 atmospheres. It's not an on/off switch - lower pressures are still toxic, they just take longer to take effect, but within the parameters of a typical dive, 1.6 bar PPO is considered to be the safe recreational limit. If you're spending more than a couple hours in the environment though, you'll be limited to significantly lower partial pressures, as pulmonary toxicity begins at PPO as low as 0.5 bar - it just takes significantly longer (days) to get there, but in a habitat, you have those days and then some.

A while ago we had a long discussion on Eina-Afa atmosphere here, and I think the only way it can work is with the habitat systems using active gravitics to stop the atmosphere from settling on perimeter walls.


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PostPosted: Fri Jan 26, 2018 5:17 pm 
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Did you account for the fact that the atmosphere and everything in it will induce gravity? The upper atmospheres will be pulled towards the spindle and not the outside, putting far less pressure on the lower atmospheres while the middle atmospheres are relatively neutral but still ahve some pressure from the top/bottom of the other atmospheres pressing against it.

It's theoretically possible to have a torus shaped planet due to high rotation speeds, so having a self stable athmosphere that is torus shaped should be plausible, especially if it is bounded.

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Last edited by grahamf on Sat Jan 27, 2018 7:08 am, edited 1 time in total.

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PostPosted: Sat Jan 27, 2018 12:52 am 
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IIRC, there's also something about that while centrifugal effect somewhat imitates gravity, it isn't quite the same, and the difference can be significant in this situation.

Don't ask details, that's all I remember.

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PostPosted: Sat Jan 27, 2018 1:49 pm 
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FreeFlier wrote:
IIRC, there's also something about that while centrifugal effect somewhat imitates gravity, it isn't quite the same, and the difference can be significant in this situation.

Don't ask details, that's all I remember.

--FreeFlier


Wind speed and direction changes local observed acceleration. Prevailing winds at the outer rim will tend to be against the spin, which will (slightly) reduce the downward pressure from that gas.

I ignored this (and actual gravity) in my calculations on the basis that both are "in the noise" and that I had a solution involving not excessively high pressure at the outside and breathable atmosphere at the center, which was my goal (I may have mishandled acceleration drop-off toward the center though, if I remember I'll recheck when I'm on the correct computer).

The problem is non-trivial. On Earth the atmosphere at 8 km is unbreathable. A cylinder is better, but we're still looking at trying for breathable air 500 times that high up.


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PostPosted: Sun Jan 28, 2018 6:08 am 
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Sean wrote:
Spekkio wrote:
Motortiki wrote:
I hate to throw a monkey wrench in your model when you are close to a happy spot, but have you considered the effect of gravity? In Eina-Afa, the spindle has a significant gravity well, which is probably why they get such a nice, high pressure atmosphere without crushing the stuff on the surface.


Citing what? Are you thinking of the bit where they were teraported from inside the soulcrypt into one of the Oafan ships?

Anyway, I've been thinking on this further. I suspect that my pressure-dropoff problem would be mitigated by incorporating slippage between layers (less spin means less additional "weight" pushed onto lower layers) but I just have no idea how much drag there's going to be.


100% drag up to near the top of your godwalls, and potentially very strong winds above. How much if any, I haven't the faintest idea.
Really, SHOULD there be "slippage". "Slippage" would be wind, but is there an outside force to make the wind "want" to stand still relative to a point outside the hull? If you spin a bucket of water on a rope, with a lid on it, does the water bunch up against the trailing edge of the bucket?


Unless that column down the middle has a mass on par with a planet, it shouldn't be enough to offset the spin gravity, and if it's enough, it just means the can has to spin that much faster to get the gravity back, so the high-mass column shouldn't matter in the least.

However, going back to partial pressures. What is the "death partial pressure" when you're living in an oxygen enriched environment at 3 atmospheres? I understand divers actually have to use hypoxic mixes for deep diving. At what point do you get too much oxygen at 3 atmospheres?


There absolutely must be slippage! If there was no relative movement between air of different altitudes, there would be no rolling storms appearing, and no need for the godwalls at all. There's still slippage with godwalls installed, that's why Eina-Afa clouds are regularly drawn with curly bits on them. 1 2 3 4

Compare with this vortex dome. It's not quite the same but you can see some of the same structures appearing.

Furthermore, it's known that each godwall produces a huge high-pressure zone on the windward face and a low-pressure zone on the back; that wouldn't be true unless the air was constantly falling behind the hull's pace, even at low altitudes. I interpret that to mean that people on the ground will experience regular (thought probably not constant) prevailing winds.

I don't like to appeal to authority, but after so many headaches I eventually just emailed Howard to ask if he had any notes on this - he's busy, but Sandra told me that with altitude the air eventually loses all its tangential velocity and much of the interior air mass will be essentially quite still.

So, I just made up a flat 5% tangential speed loss per km and plugged that into my spreadsheet, and now everything works with near-earthlike attributes; 200 kPa at the hull dropping gradually to 66 kPa throughout the vast majority of the interior space. I think I'll call that good enough unless I get a player that really knows their meteorology.

Oh. Also, I did gravity calculations for the mass of the atmosphere itself ages ago and it's tiny. Air has mass, but not nearly as much as solid rock - this thing's approximately as big as Earth but the inside doesn't have remotely the same mass.


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