# Vertical cyclones in a rotating space habitat

A common, matter-efficient, science-fiction habitat is a hollow cylinder or ring in space that is spun to simulate the pull of gravity on its interior surface. While for most purposes this artificial gravity acts just like what we are used to on Earth there will be observable differences between the Coriolis effects in the two rotating systems.

The Coriolis effects on the Earth deflect matter moving towards a pole (ascending) to the East (spinward) and matter moving towards the equator (descending) to the West (anti-spinward). One of the most notable consequences of this effect is the formation of cyclones. The Coriolis effect deflects winds into a circle around a low-pressure zone resulting in incredibly powerful storm systems.

On a rotating habitat, the largest Coriolis effects would be observed vertically (from the perspective of someone in the habitat). On Earth, this vertical component of the Coriolis effect is called the Eotvos effect but isn’t strong enough to overcome other vertical forces such as gravity and pressure. In our rotating habitat, the vertical Coriolis effect or Eotvos effect should be noticeably stronger and will also deflect moving air into cycles. Air moving spinward is deflected down. Air moving down is deflected anti-spinward. Air moving anti-spinward is deflected up. Air moving up is deflected spinward. This could create a wind cycle just like the ones on Earth that result in cyclones except these cyclones would be turned to stand on their edge. These vertical cyclones would spin in the opposite direction that the habitat spins.

I want to know whether it is possible for such vertical cyclones to form in a rotating habitat.

There are several distinct differences between our Earthly cyclones and these proposed vertical cyclones that jeopardize their existence in my mind. The main problem I see is that a vertical cycle will go through significant changes in pressure between high altitude and low altitude. Will this disrupt the cycle?

What other factors might make these vertical cyclones unrealistic?

Assuming the feasibility is dependent on the specific dimensions of the habitat here are the relevant characteristics of a torus that I have in mind:

Dimensions:

Distance from the center of the tube to the center of the ring: 10,000 km

Radius of the tube: 200 km

Spin:

Angular Velocity: ~0.005 rotations/minute

Tangential Velocity: ~5500 m/s

Centripetal Acceleration: ~3 m/s^2

Assume any other aspects of the world such as atmospheric pressure or composition are close to Earth's.

Other important innformation about the habitat, summarised from a previous question: A self eclipsing orbital ring:

The habitat orbits around a sun with the axis of rotation of the ring being perpendicular to its orbital plane. The upper half of the ring is transparent so it is fully naturally lit. The ring maintains the same absolute orientation during its year which causes interesting seasons as well as 2 eclipses every year where one side of the ring eclipses the other.

• The differences in pressure will have the greatest effect of changing temperature. Expect cloud formations and condensation to follow predictable patterns; especially if the habitat is tightly climate controlled. The most effective (and cheapest) way to disrupt the vortices is to construct baffles -- tall walls that radiate from the hab's center. As a bonus, the baffles can double as structurally significant spokes, reducing stress on the outer hull. Jun 6, 2019 at 20:14
• I'd like you to consider removing the "hard science" tag. Whilst it is justified, the problem you're asking about is hideously difficult to reason about and does not appear to have been well researched. Have a quick peek at this Space Exploration answer to see what you're up against. Jun 6, 2019 at 20:23
• As example of this in modern fiction, schlockmercenary.com/2013-03-30. This is the beginning of Book 14: Broken Wind — Part II: Can Full of Sky. This section introduces a monstrously large rotating habitat that deals with this subject. Jun 6, 2019 at 22:43
• @MikeNichols, FYI, the hard-science tag is actually ruthless. It is intended to force respondents to absolutely prove their case with citations, references, and mathematics. It produces a higher-quality answer as the expense of quantity - and if no one on the site has the background to provide those details, you get nothing. "Well-reasoned" doesn't qualify for the hard-science tag, and it was meant to be that way. Though others have disagreed, IMO the hard-science tag guarantees your question can't be closed as POB - because answers must prove themselves (no opinions). Jun 7, 2019 at 0:26
• That info belongs into the question.
– Karl
Jun 7, 2019 at 6:17

## 4 Answers

I think there is a very serious problem with the practicality of your environment. If I understand your description, you have a torus with major radius 10,000 km and minor radius 200 km, spinning fast enough to produce approximately 1/3g centrifugal 'gravity' within the volume of the torus.

But then you want approximately 1 atmosphere pressure inside the torus. The atmosphere will be driven to the outer radius of the torus in the in the same way as our atmosphere is attracted to the surface by earth's gravity. This will result in a pressure differential with height similar to that seen on our atmosphere.

Using the barometric formula for a surface pressure of 100 kPa (1 atmosphere), a gravitational constant of g/3, and a thermally equilibrated temperature of 290 Kelvin (23 C or 73 F), the approximate pressure as a function of altitude will be P(h) ~ 100,000*exp(-0.000035h) kPa. As a result, your atmospheric pressure will drop to about half an atmosphere at an altitude of ~20 km, and will be lower than that at the top of Everest by the time you are about 30 km up.

This means that most of your toroidal volume will be empty unlivable vacuum. See picture below for scale.

The 'good' news is that over the practical depth of the atmosphere, the variation in radial velocity is only around 15-20 m/s. That should be sufficient to produce some weather and wind resulting from Coriolis forces acting on convective motion of air within the atmosphere, but probably not enough to produce deadly storms etc.

• You should perhaps read the space exploration question linked in the comments on the OP. Artificial gravity in a rotating habitat isn't quit ethe same as an actual gravitational field, and the scale height of the atmosphere is not likely to be the same as on a planet. Jun 20, 2019 at 6:12
• In a torus (Rmaj=10,000 km, Rmin=200 km) as described in the question, the variation in artificial gravity between inner and outer surfaces of the torus is 4%. But over the ~20 km depth of viable atmosphere the variation is only 0.2% - coincidentally almost identical to the variation in g through the 6 km depth of earth's viable atmosphere (0.196%). The barometric formula is only an approximation - variations in temperature, atmospheric constituents and radiative flux (amongst other effects) will have a vastly greater effect on pressure versus altitude than the very minor variation in local g. Jun 23, 2019 at 1:04

As pointed out by @Ash in a comment the Hadley Cells are air circulation effect that needs to be in mind and take a huge part in cyclons and hurricanes.

Basically hurricanes are formed by differences in pressure and temperature between different air flows. I don't see how in your scenario the air flow can be heated differently to form a cyclon.

Sure if the air moves inside your hollow cylinder it would be forced by the coriolis and the eotvos effect to change direction but why would it move in the first place?

tl;dr; No such thing as hurricanes inside the tube if it's heated evenly

• To turn your last question around, what makes you think that ~8 billion cubic kilometers of air in a rotating habitat in space will remain totally unpeturbed and neatly co-rotating in perpetuity? It would seem that there's a potential feedback loop that could amplify small effects; I don't think you can just handwave that away. Jun 17, 2019 at 11:10
• Also, speaking of tl;dr, the OP is about a habitat, things which aren't known for being static and conveniently isotropic. I assume you (and others) have missed the important comment the OP left about the nature of the habitat involved, so I've moved it into the main body of the question itself. Jun 17, 2019 at 11:18
• @JJCV, The Coriolis effect does act on already existing wind forces, but it accelerates them a lot. This link has a diagram of the Coriolis effect on a ball. Imagine the ball moving hardly at all (the air currents in the torus would be slight), but the disc rotating many times faster. As the ball approaches the edge of the disc, it moves faster and faster relative to the disc. In the same way, the Coriolis here would be mostly circular without much of a spiral shape. Jun 17, 2019 at 23:42
• Edit: I should've said "initial air currents will be slight." Once, the Coriolis gets going, air currents will no longer be slight. Jun 17, 2019 at 23:50

This site provides a great explanation of the Coriolis Effect. It is primarily caused by a difference in the distance from the surface to the axis of the earth between the equator and the latitudes to the north and south.

Time to do some math. The air in the top of the torus would be moving at $$\dfrac{\pi DR}{m}$$, or $$\pi(10200)0.005$$ kilometers per minute. The result is about $$160$$ kilometers per minute.

The air in the outside of the torus would be moving at $$\pi(9800)0.005$$ kilometers per minute. This result is $$154$$ kilometers per minute.

You will have a pretty powerful Coriolis effect. The difference in the velocity of the air in the top/bottom of the torus and the outer edge would be $$6$$ kilometers per minute. Translated into hours, this is $$360$$ kilometers per hour.

The cyclones will be the inverse of a hurricane, with high wind speeds on the outside and low wind speeds on the inside. The Coriolis cyclones will be "seasonal". This means the following: They will not be permanent, but will slowly spin up to $$360$$ kilometers per hour, and then the resistance caused by the other cyclones will cause the cyclones to wind down to little or no wind speed. This means that they have little friction with each other, and will be able to spin back up to $$360$$ kilometers per hour. Here is a diagram to help clarify what the cyclones will look like inside the torus:

$$360$$ kilometers per hour is $$223.694$$ miles per hour. According to Wikipedia, the people on the edges of the cyclone would experience the following.

Incredible damage. Strong-framed, well-built houses leveled off foundations and swept away; steel-reinforced concrete structures are critically damaged; tall buildings collapse or have severe structural deformations; cars, trucks, and trains can be thrown approximately $$1$$ mile ($$1.6$$ km).

• The effect of the coriolis force on the atmosphere of a rotating planet is very different from the effect on the contents of a rotating torus; the comparison is not particularly helpful. You're also assuming that the difference in tangential velocities of regions 200km apart is going to be the same as the resulting windspeeds they experience, which is somewhat dubious, to say the least. Jun 17, 2019 at 8:35
• The Coriolis would be different on a planet, because the planets' Hadley cells would break the cyclones up. However, without the Hadley cells, the Coriolis cyclone will merge into one big tornado destroying everything in its path. Jun 17, 2019 at 20:13
• You haven't demonstrated that, though. The two points where you're measuring windspeed are 200km apart, and windspeed will vary smoothly across that region, not sharply. You also cannot form "one big tornado" that somehow causes the entire air mass in the torus to counter-rotate. Breaking up the air mass in the tube into multiple tornadoes also does not seem stable; tornadoes rotating in the same direction cannot butt up against each other after all, and counter-rotating ones will be slowed by the coriolis force. Jun 19, 2019 at 19:48
• I added a paragraph of description and a diagram of the habitat. I hope it helps clear things up. Jun 19, 2019 at 21:13
• Your diagram isn't entirely helpful; it shows the axes of the vortices to be either tangential or circumferential at the left, they're rotating in the opposite direction at the right and their axes appear to be radial in the middle. A vortex driven by the coriolis force in a rotating habitat should probably have its axis parallel to the axis of rotation. You probably need two diagrams, a circular slice through the tube and a doughnut shaped slice through the whole ring. Jun 20, 2019 at 19:46

I do not think so. Earth has an open atmosphere where gases are exposed to space, and your torus would have all the atmosphere contained. Additionally, if the temperature were stable between the center and the edge of the tube, then there would be no natural places where air pressure builds.
The Coriolis Effect on earth is caused by the sun heating the air at the equator more than the air north and south of the equator. The hot air rises and expands, traveling north and south. As it cools, it descends, completing the circuit back to the surface of earth. Since the temperature inside the torus is presumably constant, these areas of high/low pressure air would not form, meaning that the Coriolis Effect would not happen.

• The centrifugal force acts just like a real force in a rotating reference frame, so if the tube has a radius of 200 km (presumably referring the radius of a cross-section of the tube, since the ring itself is said to have a radius of 10,000 km) that should large enough to create a measurable pressure differential between "top' and "bottom" according to the discussion at quora.com/Why-is-pressure-due-to-gravity-low-in-gas-container about gas pressure within sealed containers in gravitational fields Jun 7, 2019 at 21:22
• The effective gravity of the ring habitat is about a third Earth-normal, giving a scale height of about 25 km. The tube is 16 scale heights tall, so the top will be in an effective vacuum. It may not be technically exposed to space, but there's no practical difference.
– Mark
Jun 8, 2019 at 2:51
• Um that's very much not how the Coriolis Effect works, it is a product of the Earth's rotation not solar heating. You have however neatly described Hadley Cells a completely different beast.
– Ash
Jun 16, 2019 at 15:29