Toroidal Worlds: Have You Ever Used One?

[RickAllison]

What are the community's experiences with toroidal (donut) worlds in campaigns? Did they get into physics with it, or was it just a quirk of the setting?

I ask because I'm gearing up to DM a campaign on one that will be as accurate as I can. Things like higher gravity near the poles combined with mountains making for nigh-impassable barriers, faster day and nights, and the moon actually passing through the center of the torus. I want it to be a very surrealistic setting, so I am making the world at a 45 degree tilt so the players get such strange scenarios as the weather actually getting really warm at the poles, while the normal polar weather is at places like Canada. I want my players to be explorers, high-level adventurers exploring a frontier that no one has returned from (so the majority of the world doesn't even know what shape they are!), so any tips are appreciated!

[Segev]

If your toroidal world is otherwise behaving like a spherical one - in that it revolves around a sun and rotates on an axis for a day/night cycle - then the "poles" as they probably think of them will actually be based on nearness to the axis of rotation. The reason we think of the "poles" of a toroidal world as being "where the map wraps around at the top and bottom" is that game-worlds that are technically toroidal are trying to emulate Mercator projections (I may have misspelled that) while being "round."

Genuine toroids in 3D would be even weirder, with what you're probably thinking of as the "equator" being shorter than what you're probably thinking of as the "pole line." Or, another way to think of it, there is an "inner equator" and an "outer equator."

Also, if it's rotating about an axis and revolving along a planet-like path around a sun, the day/night would be somewhat normal for those on the exterior, who are closer to the "outer equator," compared to our own experience on Earth. But those on the inner surface of the torus would see the other side overhead, and they would see its shadow pass over them daily at around the mid-point of the day as the far side of the world blocked out the sun.


If it is, instead, a ring-around-the-sun sort of deal, there wouldn't be a day/night cycle: the inner surface would be in perpetual day, and the outer surface in perpetual night. So I think the former is more interesting, especially if you want it weird and alien.

[Lord Torath]

An orbit that takes your moon through the center of the torus would be inherently unstable, and probably wouldn't last more than one pass. If you want to go with Spelljammer physics though (orbital mechanics are stable, regardless of orbit, just because), feel free.

Gravity on the inside of the torus would be less than gravity on the outside, as the other half of the torus would tend to pull you away from the half you're standing on. I would expect gravity to be strongest on the "Outer" equator, and weakest on the "Inner" equator.

[Squibsallotl]

Sigil immediately comes to mind. I've run a campaign there before, and to be honest my players didn't seem to care much about the setting's physical peculiarities.

So we can look up and see the roofs of buildings above our heads, big deal. What really matters is that we're in a food queue behind a pit fiend :P

[RickAllison]

An orbit that takes your moon through the center of the torus would be inherently unstable, and probably wouldn't last more than one pass. If you want to go with Spelljammer physics though (orbital mechanics are stable, regardless of orbit, just because), feel free.

Not necessarily true. It creates an odd orbit that traces figure-8s around the torus and actually creates a secondary torus. Depending on the size of the satellite, it could even be made to take on a vase-like orbit inside the torus, though that would be even stranger.

Gravity on the inside of the torus would be less than gravity on the outside, as the other half of the torus would tend to pull you away from the half you're standing on. I would expect gravity to be strongest on the "Outer" equator, and weakest on the "Inner" equator.

Actually, from what I've read of theoretical toroidal worlds it is the opposite. The "poles", best defined as being the circles on the top and bottom of the torus, have the highest degree of gravity (almost twice as much as at the outer equator for small-hole worlds, while about 1.5 times as much as the outer equator for larger, hoop-like worlds), then the interior equator having a slightly-higher apparent gravity (about 1.08X) due to the rotation of the planet. Essentially, the centripetal force that is counteracted by gravity on the outside functions WITH gravity on the inside, actually raising the effective gravity above that of the exterior equator despite having competing (but farther away) gravity fields.

So in the ultimate sense of un-intuitiveness, the exterior equator is actually the band on the theoretical planet with the lowest gravity!

Also, I should note that part of the assumptions that make toroidal planets stable (though unlikely to be naturally-made) is that they would be spinning faster than a pseudo-spherical planet. This faster revolution stabilizes the tendency to collapse, but also has a significant effect on the apparent gravity when a motionless analysis would lean otherwise.

[Lord Torath]

Oops. Yes, I completely ignored the centrifugal force's effects on apparent gravity. Interesting. So how long is a sidereal day on this world?

[RickAllison]

Oops. Yes, I completely ignored the centrifugal force's effects on apparent gravity. Interesting. So how long is a sidereal day on this world?

I had originally supposed it would be a 12-hour cycle just for ease of use, but turning it up to 3X Earth speed (so 8-hour cycles) would be great for the extended rest variant rules I'm using. Resting becomes an identifiable time from when the sun is at a point and when it is there again!

[MrStabby]

To step back a little...

1) What aspect of this will make the world more fun for your players?
2) How do you expect them to interact with the differences between this and a "normal" world?
3) For those players not into orbital mechanics (fools!), how do you keep them interested in the world?

My worry is that for most players, if the most interesting thing about a world is its shape not its contents then it might be a bit boring. If the contents are more interesting than the shape then they will focus on the contents and you won't need that much detail on the shape. I play the game with a group average of 0.8 science PhDs per player and even they won't really care that much.

On the other hand they may metagame it and think that if that much attention is paid to the shape of the world then the shape of the world must be central to the plot.

[Segev]

On the other hand they may metagame it and think that if that much attention is paid to the shape of the world then the shape of the world must be central to the plot.

But, given the shape, the center is a hole. So central to the plot is a plot hole! Oh no!




More seriously, I had not thought about the need for it to spin around its central axis to avoid collapse. Technically, with a strong and rigid enough construction, "archway" physics would also prevent collapse, but that's definitely getting into a constructed world, not one that occurred even vaguely naturally.

[RickAllison]

To step back a little...

1) What aspect of this will make the world more fun for your players?
2) How do you expect them to interact with the differences between this and a "normal" world?
3) For those players not into orbital mechanics (fools!), how do you keep them interested in the world?

My worry is that for most players, if the most interesting thing about a world is its shape not its contents then it might be a bit boring. If the contents are more interesting than the shape then they will focus on the contents and you won't need that much detail on the shape. I play the game with a group average of 0.8 science PhDs per player and even they won't really care that much.

On the other hand they may metagame it and think that if that much attention is paid to the shape of the world then the shape of the world must be central to the plot.

The basic plot of the storyline actually revolves around it being a torus . The effects of it being a torus have created barriers such that no records exist of anyone travelling beyond the the icy wastelands and living to tell the tale. When a mysterious plague starts draining the life from countless people throughout all the world with the only clue being streaks of light travelling from the deceased to thee polar regions, an expedition is mounted (including the PCs) to figure out why people are dying.

Thus, I'm trying to imagine how the physics of the toroidal world will affect the different regions in the cross-section because it is those sections that the players will be travelling through. I'm using the theoretical physics of such a world to design the contents. I'm leaning towards having an eldritch abomination or other such bad thing that is in the Lagrange point in the center of the torus. The PCs become the first known explorers to find out what lies over the icy wastes, then find the thing that is killing everyone. Then they try to figure out how to kill that thing, I suppose .

EDIT: Segev, I never said it was a natural world, I said it was stable . I'm thinking something along the lines of the world basically being a weapon or a portal. It was created by the thing imprisoned here so it can escape. Maybe the party will find out that once you get past the first layers of bedrock, the planet is a giant machine or other such abomination.

[Lord Torath]

More seriously, I had not thought about the need for it to spin around its central axis to avoid collapse. Technically, with a strong and rigid enough construction, "archway" physics would also prevent collapse, but that's definitely getting into a constructed world, not one that occurred even vaguely naturally.

I suspect this is where RickAllison got most of his information: http://www.aleph.se/andart/archives/...orusearth.html Interesting stuff.

One of the key points is that "rocky" planets are basically balls of liquid with no surface tension. We don't have any materials strong enough (that I'm aware off) to create the archway required to maintain a torus of planetary mass. Both the torus worlds explored in that article needed days about 3 hours long (just under 3 hours for earth-massed "Donut", and about 3 1/2 hours for 6x earth-massed "Hoop") to maintain their shape. RickAllison has decided to ignore that bit to have his stable with an 8-12 hour day.

[RickAllison]

I suspect this is where RickAllison got most of his information: http://www.aleph.se/andart/archives/...orusearth.html Interesting stuff.

One of the key points is that "rocky" planets are basically balls of liquid with no surface tension. We don't have any materials strong enough (that I'm aware off) to create the archway required to maintain a torus of planetary mass. Both the torus worlds explored in that article needed days about 3 hours long (just under 3 hours for earth-massed "Donut", and about 3 1/2 hours for 6x earth-massed "Hoop") to maintain their shape. RickAllison has decided to ignore that bit to have his stable with an 8-12 hour day.

Yup! Much as I am trying to model my world accurately, my sanity comes first . I'll just handwave my canon as being stable at a lower angular velocity since it is an artificial creation and so the underlying structure is more rigid than a traditional planetary core.

[Segev]

Segev, I never said it was a natural world, I said it was stable . I'm thinking something along the lines of the world basically being a weapon or a portal. It was created by the thing imprisoned here so it can escape. Maybe the party will find out that once you get past the first layers of bedrock, the planet is a giant machine or other such abomination.

Fair enough! Then I will point out that you need not assume it is rotating about its "donut hole" axis at all, nor at any particular speed, to maintain structural integrity. It can be, of course! That's entirely up to you and how you want to arrange it. But don't feel constrained to it; the choice does influence how the apparent gravity of the world works, after all!

As an example, it could be spinning on an axis that passes through the ring itself. Like if you took a finger-ring and spun it on the table like a top. Or spinning a quarter in a similar fashion.

Advantage of that orientation is that day/night is easier to maintain for the inner side as well as the outer side. Though as long as the axis of rotation (and the slant of the ring) is not in the same plane as the direct line to the sun, the inner surface would get day/night fairly normally from the "donut hole" axis spin, too, now that I think about it.

Mostly, I encourage you to imagine different axes for the rotation and different orientations of that axis with the plane of its revolution about the sun to see which generate the most fun (and least problematic) gravitic and other effects.

[RickAllison]

Fair enough! Then I will point out that you need not assume it is rotating about its "donut hole" axis at all, nor at any particular speed, to maintain structural integrity. It can be, of course! That's entirely up to you and how you want to arrange it. But don't feel constrained to it; the choice does influence how the apparent gravity of the world works, after all!

As an example, it could be spinning on an axis that passes through the ring itself. Like if you took a finger-ring and spun it on the table like a top. Or spinning a quarter in a similar fashion.

Advantage of that orientation is that day/night is easier to maintain for the inner side as well as the outer side. Though as long as the axis of rotation (and the slant of the ring) is not in the same plane as the direct line to the sun, the inner surface would get day/night fairly normally from the "donut hole" axis spin, too, now that I think about it.

Mostly, I encourage you to imagine different axes for the rotation and different orientations of that axis with the plane of its revolution about the sun to see which generate the most fun (and least problematic) gravitic and other effects.

And now I feel sick. I'm imagining a donut-shaped Earth spinning around like a quarter and it is quite nauseating.

The way I actually have it set up is on a 45 degree tilt with respect to its star! It creates the rather unique situation where the warmest spots are either equator (always shining there) and the polar rings (no exposure in winter, but the most direct exposure in summer). So the glacial activity occurs at places like the northern USA and southern Canada, while the northernmost places are rather temperate when they aren't inhospitable (hibernation is big, I think). Allows for much more varied climates!

[Chimera245]

A "spinning quarter" world's inner ring would have and *almost* normal day/night cycle. Don't forget it would have a brief solar eclipse from the other side of the torus everyday at noon.

[Thrudd]

Have you read "Integral Trees" by Larry Niven? It takes place in a gas torus surrounding a neutron star, and describes the physics of that environment quite well. Of course, this is different because there is no ground, living things exist in free fall, constantly orbiting the central star within the zone of habitable atmosphere.

[Kane0]

Did someone say Sigil?

[Âmesang]

"A doughnut on top of an infinite pizza."

Honestly that reminds me that there are some peculiar worlds in Greyspace; Ginsel, a crescent-shaped planet, and the Spectre, a flat-disk world, orbiting like a flipped coin.

So we can look up and see the roofs of buildings above our heads, big deal. What really matters is that we're in a food queue behind a pit fiend :P

I'd be more worried about being behind a black knight with telekinesis and a brilliant energy sword.

"Give me Penne all'Arrabbiata or you shall die! And you and everyone in this canteen! Death by tray it shall be!"

[Jay R]

I would assume that universal gravity doesn't work like it does in this world, and ignore the scientific instability.

I haven't played on a toroidal world since playing Black Hole in the 1970s.

It had a black hole at the center of the doughnut hole.

[Winter_Wolf]

The only toroidal world I know of is Mystara/the Hollow World, and the cutaway view is just weird. You have to really suspend disbelief if you're at all interested in geology/planetology. Everyone in the Hollow World is apparently insane because there's no night in the Land of the Etenal Sun, and how is it that the core/sun doesn't at least once in a while jostle against the inner surface? The writers straight up ignore or are completely ignorant of science, or resorted ye olde "because magic" rationale.

[Âmesang]

I was just thinking about Mystara the other day and wondering what the air-pressure would be like in a "Hollow World" since you have all of that mass (solid, liquid, and gas) pushing down on you from all directions.

[MesiDoomstalker]

Actually, I had an idea for a Toridial World and trying to puzzle out a simple way to explain the pecularities of a world to players who aren't super Physics savvy told me it wasn't the greatest idea. Instead, I came up with a loose cosmological concept where the Prime is a planetoid sized cylinder and the other planes are also cylinder's, all revolving around a Star-Like-Thing (TM) and at one point the various planes were all one Torus world but A Cataclysm (TM) broke up the Torus and created the current cosmological configuration.