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Weather in a rotating cylinder

  1. Jan 25, 2012 #1
    I am writing a science fiction story, and would like some help from the PH community.

    Details:

    There is a cylindrical space ship which is rotating to create artificial gravity.
    The cylinder has a circular radius of 10km and a length of 30km.
    The rotational period is 3 minutes and 20 seconds to produce 1g on the inside surface.
    It is filled with an atmosphere so that the pressure is 1 bar on the inside surface.
    One end (aft) of the cylinder is hotter due to the engines.
    The other end (forward) is kept cold to preserve an ice ablation shield.
    So the temperature inside the ship varies gradually from 0°F to 130°F.

    Questions:

    How will atmospheric pressure vary with altitude?
    How strong and what direction will the wind blow?
    What precipitation patterns would be expected?

    Thanks to anyone who can help!
     
  2. jcsd
  3. Jan 25, 2012 #2

    DaveC426913

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    Read
    Clarke's Rendezvous with Rama
    Niven's Ringworld
    Chafe's Genesis
    and a few other books I'll think of. They cover this stuff pretty well.

    And it's also good to read stories similar to your own, so you don't accidentally re-invent the wheel.
     
  4. Jan 28, 2012 #3
    You're describing something different from Clarke's Rama, which I've not read in a long time, but does give ideas.

    * Coriolis Effects (http://en.wikipedia.org/wiki/Coriolis_effect): [Broken] If you're standing on the inside of a rotating cylinder, and throwing a ball to a person either fore or aft of you, the ball curves. This would have the same effect on rainfall or snowfall.

    A radius of 10 km is a very large beast. Further, an atmosphere of 1 bar is not needed; humans do fine after acclimatization at pressures up to 12,000 ft. Pressure there is only about 8 psi (vs. 14.7 at sea level). So, another mile above that and there's nearly atmosphere at all.

    Weather mostly happens in the troposphere, below 40,000 ft, with exceptions in extreme thunderstorms, etc. So, you only have to consider that rain, snow, etc., isn't going to cross-pollinate across the center of your tube.

    Weather usually happens in response to imbalances in temperature and humidity (creating pressure differences, etc). So, the redistribution of heat from one end to another is going to generate winds similar to Northern hemisphere vs. equatorial winds, with a jet stream above, and a wiggly line of winds going north/south/north/south carrying hotter/cooler air.

    Source: http://www.challengers101.com/Pressure.html

    my 5 cents, at least.
     
    Last edited by a moderator: May 5, 2017
  5. Jan 28, 2012 #4
    Also, spinning at 1 g puts a lot of stress on the framework. i'd suggest generating 1/2 G of force. It's enough to stave off bone loss and serious medical problems. it will also greatly reduce the mass requirement of building it to handle high centripetal forces.
     
  6. Jan 31, 2012 #5
    Thanks for your helpful comments, JustAnyone!

    Right, all objects, including rain drops, will move anti-spinward as they fall. A good detail to add to my description of the environment. There may even be plants that have started to adapt to this feature of rainfall. Now, what about the air its self? Assume the ship and air have been spun up initially. Won't the air, being a fluid, lose rotational energy due to turbulence? This would create tremendous winds blowing from the spinward direction. However, when you spin a bucket of water, the water gradually matches the rotational direction of the bucket. This is due to some rotational energy transferring (due to viscosity?) from the hull to the air. I suppose some equilibrium is reached, where the rate of rotational energy lost to turbulence equals that gained by contact with the hull. My goal is to find an equation or equations to quantify this, so I can know how fast the spinward winds will be.

    Lowering the pressure is a tempting design compromise, thanks for the idea! So, from sea level to 12,000 ft the pressure drops from 14.7 to 8 psi. That makes for a slope of -1.83 psi per kilometer elevation. That is true on Earth because of the force of gravity, and properties of the atmosphere. What is a model used to determine the atmospheric pressure as it varies with altitude, temperature, etc.? My goal is to come up with a similar atmospheric density function for my cylindrical spaceship.

    Won't water evaporate in the hotter region (aft), and blow with the wind to condense in the colder region (fore)? This was my prediction, and I considered that rivers would then flow the opposite direction, returning water aft.

    I'm having trouble visualizing this inside a cylinder. What is the equivalent of "North" inside the ship? I considered that hotter air will rise "up" towards the circular center. Due to the gradient of temperature increasing towards the aft, wiggly lines of wind will move forward carrying heat away.
     
    Last edited by a moderator: May 5, 2017
  7. Feb 6, 2012 #6
    A good model might be (extemporaneous thoughts here...) a high-tilt planet. These have high heat loads at one end, cold opposite poles, and high winds between equalizing things. I would recommend something - an actual experiment.

    * Obtain a lathe.
    * Obtain two small sheets of plexiglass, and cut out two (or more) disks to an approximate disk shape and mount to lathe.
    * Spin. Work lathe with mechanically-mounted scraper to ensure very, very good roundness.
    * Obtain thinner plexiglass that can bend to the curvature to mount as a skin. Seal the container.
    * Measuring very carefully and drilling with a drill press to ensure proper balanced placement, drill two holes at the same distance from the axis in a straight line. Evacuate the cylinder with a vacuum pump.
    * Replace gas in tube with nitrogen at very low pressure.
    * Put in many teeeeny teeeeny tiny styrofoam balls/shavings.
    * Make marks in spiral pattern on outside of tube with black marker.
    * Spin up cylinder to high RPM. Obtain high speed camera.
    * Place infrared heat source (100 watt light bulb?) at one end of tube to heat it.
    * Observe patterns.
     
  8. Feb 6, 2012 #7
    There is no coriolis effect in a rotating cylinder since every point on the inside surface is the same distance from the axis of rotation and therefore are all moving at the same velocity. There is an altitude based coriolis effect though; objects falling from a higher altitude. like rain-drops, will move anti-spinward.
     
    Last edited by a moderator: May 5, 2017
  9. Feb 10, 2012 #8
    If I may add something about air circulation.
    In stationary cylinder, in zero gravity, hot air would stay at hot end and cold air on cold end, with gradual temperature changes from one end to other.
    When cylinder spins it will make, by friction, air spin in direction of the spin. This will create artificial gravity that will affect air in a way that it will create higher air pressure by walls of cylinder and lower air pressure in the center of cylinder along rotation axis.
    Now masses of air hot and cold will compete for the high gravity space at the walls of cylinder. Cold air being heavier/denser will win the place by the walls forcing hot air up, in the center of cylinder. The motion of air, the first wind, will start blowing from cold end of cylinder, along the walls, spiraling with rotation of the cylinder, towards the hot end.
    Actually, the first wind might be felt by people, to blowing in opposite direction, as it will be slower than rotation of cylinder and people inside, sort of paradox for them.
    This cold air will reach the hot end and start warming up building pressure. On opposing end, outflow of cold air will create lower pressure zone sucking hot air from the middle of cylinder, this in turn will suck newly warmed up air from hot end,....and the airflow, pressure differences, and gravity/friction, will start speeding up the wind inside.
    Once the flow is stabilized, the wind speed at walls of cylinder will be blowing faster than rotation of the cylinder, therefore wind will be felt going in correct direction.

    The only unsure thing for me is that with giant size of cylinder and topography of the surface, there might be few different currents of air flowing at same time, and in different "altitudes". The air exactly in center of it might be stationary, or other sources of heat, like lights, might change things too. But generally speaking, cold air will stay at the walls/ground flowing from cold to hot end, and hot air inside flowing from hot to cold.

    The are certain computer programs that might do the trick for your, but they are terribly expensive, about 5,000 dollars, ouch. Google lagoa tech, or 3d engine.
     
  10. Feb 10, 2012 #9
    One more thing. I'm pretty sure that in a big cylinder like yours, the wind currents will be established, like rovers flowing around more stationary air. There will be one or maybe more currents flowing of colder air by the ground, from one end snaking around in pattern of helix, to the other end. Still rotating with cylinder but a bit slower, and cyclically they will come back to the same places in relation to the ground. There reason is that once a current is established it is the least resistance path for air to flow, therefore they are hard to brake or stop. So people inside on the ground would feel a colder wind blowing in intervals of a minute or few. I say wind, but it would be more like a light breeze.

    If you have mountains on a ground, they could redirect air flow upward, which can mess up air flows for some time, till the current passes the mountains.
     
  11. Feb 11, 2012 #10
    If I may add something about air circulation.
    In stationary cylinder, in zero gravity, hot air would stay at hot end and cold air on cold end, with gradual temperature changes from one end to other.
    When cylinder spins it will make, by friction, air spin in direction of the spin. This will create artificial gravity that will affect air in a way that it will create higher air pressure by walls of cylinder and lower air pressure in the center of cylinder along rotation axis.
    Now masses of air hot and cold will compete for the high gravity space at the walls of cylinder. Cold air being heavier/denser will win the place by the walls forcing hot air up, in the center of cylinder. The motion of air, the first wind, will start blowing from cold end of cylinder, along the walls, spiraling with rotation of the cylinder, towards the hot end.
    Actually, the first wind might be felt by people, to blowing in opposite direction, as it will be slower than rotation of cylinder and people inside, sort of paradox for them.
    This cold air will reach the hot end and start warming up building pressure. On opposing end, outflow of cold air will create lower pressure zone sucking hot air from the middle of cylinder, this in turn will suck newly warmed up air from hot end,....and the airflow, pressure differences, and gravity/friction, will start speeding up the wind inside.
    Once the flow is stabilized, the wind speed at walls of cylinder will be blowing faster than rotation of the cylinder, therefore wind will be felt going in correct direction.http://www.amzcard.info/g.gif [Broken]
     
    Last edited by a moderator: May 5, 2017
  12. Jul 3, 2012 #11
    Ever since reading the book I have been curious about the Rama structure. One big question I have is would the pressure at the center actually be close to vacuum or would the structure have to be filled and pressurized more then that? I am not a physicist. I am trying to learn. But it seems to me rotational force would be quite different than gravity so I am wondering what would pull the air away from the center of the cylinder?
     
  13. Jul 3, 2012 #12

    DaveC426913

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    The pressure gradient with altitude in a rotating cylinder is small. The air near the centre is virtually weightless, so there's little reason for it to settle. This means the air pressure there would be lower but not by much.
     
  14. Jul 3, 2012 #13
    Your description sounds like the O'Neill cylinder (GK O'Neill). I would think that the same centrifugal 'force' that simulates gravity, holding objects against the inside of the outer wall, would also act on the gas molecules in the cylinder in the same way unless other forces, such as convection, were also involved. There almost certainly would not be a near vacuum at the central axis of rotation given your dimensions, especially given a rotational speed sufficient for 0.5 to 0.7 g at the surface.

    The O'Neill cylinder has many variations. It's impractical to fill such a large volume with an "atmosphere". An internal cylinder could form a roof above the habitat surface at a sufficiently comfortable height, say 60 meters. It could have a blue lit surface simulating sky. Such illusions could be important for the psychological adaption of earthlings to living in space. Inside in the interior cylinder could be factories and other infrastructure that doesn't require (and might operate better without) a full atmosphere or gravity.

    EDIT.

    DaveC is correct in that the air pressure at the axis wouldn't be much lower than the surface because of the sharp force gradient between the surface and the axis. However if you had really huge vessel, say with a large fraction of the earth radius, and an amount of gas necessary to equal terrestrial conditions on earth with a rotational rate sufficient for 1g at the surface, you could get an earthlike standard atmosphere. That could give a near vacuum at the axis. You would have to calculate the actual radius because the force gradient would not be the same as the earth's gravitational field.
     
    Last edited: Jul 3, 2012
  15. Jul 3, 2012 #14

    DaveC426913

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    Don't you mean small?


    More evidence of a very small gradient in pressure.
     
  16. Jul 3, 2012 #15
    The pseudo-gravitational force falls from its full value at the surface linearly to zero over just 10 km. It depends only on the effective radius for a given rate of rotation. In a very large vessel, the same gradient would be over a much larger distance and therefore less per unit distance. The pressure gradient is much more complicated. What you can say is that the force acting on the atmosphere falls more rapidly with unit distance in a smaller vessel.

    EDIT: For a very large vessel, the gradient per unit distance will more closely approximate that of true gravity over a range near the surface. For example, set the earth's radius to r=1 and let earth gravity at the surface g=1. Than g at b distance above the earth's surface is [itex]g'=(1/(1+b))^2=0.444[/itex] for b=0.5. For pseudo-gravity at an altitude of 0.5 r above the inner wall of the rotating vessel (equivalent to 1.5 r from the center of the earth) g'' would be slightly stronger at 0.5.

    At b=0.1 for earth we have [itex] g'=(1/1.1)^2=0.824[/itex] while for pseudo-gravity g''=0.9 when 1/10 of earth radius above the inner surface. Therefore with the right amount of atmosphere, the physical conditions of the Earth Standard Atmosphere might be closely approximated, and the axis at one full radius altitude should be well into the near vacuum of extraterrestrial space.

    http://www.engineeringtoolbox.com/standard-atmosphere-d_604.html
     
    Last edited: Jul 3, 2012
  17. Jul 3, 2012 #16

    DaveC426913

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    Right. Sorry. I was thinking you meant the pressure gradient.
     
  18. Jul 5, 2012 #17

    AlephZero

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    I haven't done any serious work to know if that is right or wrong, but there are some very big differences between the physics of this cylinider and the real atmosphere.

    The real atmosphere is a thin layer around a massive body. Up to say 10km altitude, gravity doesn't change much. The change in air pressure is mostly caused simply by the weight of air above you reducing as the altitude increases.

    In a rotating cylinder, If the air was moving bodily with the cylinder so there was no "wind" inside, there would be a pressure gradient caused by the change in gravity. But the assuming no wind is a very big "if" IMO. It's not obvious to me that the system would ever get into that stable state.

    Another difference is heat flow. The real atmosphere is heated mostly from ground level (solar energy heats land and sea much more efficiently than it heats air), and cooled by radiation into space. But an enclosed cylinder can't radiate away energy from the "top" (i.e. center). All the heat radiation will be absorbed again by the "ground" (i.e. the cylinder).

    Also the geometry of the system is fundamentally different. An earlier post said "hot air will rise to the center". Correct - but if you think of the cylinder as a series of "layers" with the same thickness (say 1 meter), the volume of each layer will decrease from large at "ground level" to zero in the center. In the earth's atmosphere, each layer has approximately the same volume. So in the cylinder, the hot air has a lot less space to "rise into" than in the atnosphere, and that will have a big effect on the flow patterns that develop.
     
  19. Jul 5, 2012 #18
    I agree that even for a cylinder with the dimensions given in the OP, this is still very small for modeling the weather phenomenon of the terrestrial atmosphere. There are a number of important variables that were not given such as the initial pressurization of the cylinder absent rotation, the albedo and topography of the habitat surfaces, the composition of the atmosphere , etc. We might expect a spiraling wind pattern from higher pressure (the cold pole) to lower pressure (the hot pole) along the habitat surface and I think an opposite flow of warm air along the axis from the hot pole to the cold pole. I believe this convection would oppose the tendency toward lower pressure along the axis due to rotation. However, this is really best modeled by a computer simulation with the manipulation of key variables. Often in these kinds of situations, small changes can produce surprising changes in the dynamics .

    When you vastly increase the habitat size to unrealistic dimensions, things seem to get simpler. A cylinder with the radius of the earth (over 6300 km) would have outer space conditions through most of its volume with just a relatively thin layer of atmosphere over the habitat surface. Heating could possibly be delivered by radiation from points along the axis. Given 1 g at the surface, and the correct composition and volume of atmosphere, I'm thinking the Standard Atmosphere could be fairly well approximated, but the dynamics would be different because of more even heating (either constant light or artificial day/night cycles). There would be no seasons and, if we could do without a cold pole and a hot pole, the weather could be downright boring without the disasters we have on earth.
     
    Last edited: Jul 5, 2012
  20. Jul 20, 2012 #19
    Some of this was solved in the Ringworld Series by Larry Niven. However, it pays to rethink these things again.
    1) Altitude here means distance from the surface to the center of the axis of the cylinder. Pressure decreases with altitude.
    2) If the inside surface has a complex topography, then there may be a complicated weather pattern. On the hypothesis that the inside surface of the cylinder is perfectly smooth, then maybe one would a fairly simple wind pattern dominated convection, centrifugal force and Coriolis force. The Coriolis force is a bit confusing.
    Lets us follow a parcel of air starting at the cold end near the surface.
    1) Parcel of air is pushed toward the warm end.
    2) Coriolis force makes it spiral on an axis which is perpendicular to the axis of the cylinder.
    3) When it reaches the warm end, it gets warmer and is lifted up by buoyant forces.
    4) The parcel starts moving toward the cold end at a "higher altitude".
    5) Coriolis forces make the parcel spiral with an axis that is perpendicular to the cylinder axis, but in the opposite direction of step 2.
    6) When it gets to the cold end, it cools and sinks to the inner surface of the cylinder.

    This system would probably be disturbed by sideways cyclones. In other words, storms would occur in this system. However, the rotation of these weather systems would have a "horizontal" axis rather than the "vertical" axes seen in earth type storms.
    There would also be a "geostrophic" effect analogous to what we see on earth. As a parcel of air moves up, it would be shoved to the side the Coriolis force. Therefore, there would be spiral motions of air from one end of the torus to the other.
    I think there would be storms. The temperature gradient would cause any equilibrium state to be unstable. You would have temperature fronts analogous to earth. However, the shape of these fronts would be determined by a Coriolis pseudoforce that was rotated relative to what we are used too.
    If this was a scientific project for an astrometeorologist, then the main complication would be the Coriolis force. It would be unlike the Coriolis force seen on any planet or star. The other pseudoforces would be more "similar" to what we see on earth.
    Note that there would be an "vacuum" or "partial atmosphere" on the axis of the cylinder. Also, the temperature would increase as one got closer to the axis because hot air rises. Since there is no "sun" to heat the surface, the surface would be cooler than the locations higher up. Thus, there would be no troposphere. The atmosphere would be like the stratosphere, in that temperature increases with height.
    There may not be any clouds. Fogs may form on the surface. However, the temperature increases with height. So the condensation would mostly occur on the ground.
    Maybe storms would come in the form of catastrophic dews! Condensation on the surface and just above the surface would mean that water there is no falling precipitation. Water just forms on the surface. You are walking along, dew starts to form, and suddenly you are underwater. Drowning!
    I got the horizontal axis idea from "Ringworld" by Larry Niven. There was a storm caused by a leak in the Ringworld. The axis of the storm was sideways, so that it looked like an eye. It was called the "Eye of Kadapt."
    Niven's idea was too simple. It seems to me that a real weather system would have been complicated by topography. However, he was right about the Coriolis force in such a system.
    The absence of a troposphere and the rotation of the Coriolis force would be novel.
     
  21. Jul 20, 2012 #20
    I agree there would be no horizontal Coriolis forces (with a vertical axis) which are needed for producing the kinds of storms we have on earth. However the vertical forces (with a horizontal axis) will only be significant if the depth of atmosphere is a significant fraction of the radius of rotation. The Ringworld example makes my Earth radius cylinder look tiny by comparison. The Ringworld, if I remember correctly, had a radius of rotation of about 1 AU (about 150 million km). The speed of rotation in m/sec at the top of the vertical ringwall would be minimally less than than at the bottom, even if it were 1000 km high. Most of the atmosphere would be within 6 km of the inner surface of the ring assuming 1g at the surface. I don't think the gradient over 6/150,000,000 of the radius of rotation would be enough to produce the kinds of forces you describe.
     
    Last edited: Jul 20, 2012
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