Disc World (3): The Almanac

In the last few posts, we’ve discussed various disc worlds, ending with one where the sun orbits just outside the body of the disc with a daily orbit in a plane that starts parallel to the disc and then rotates over the course of a year so that at the quarter points, it is perpendicular to the disc. What would that mean to folks living on the disc?

The pic below shows the sun over the horizon for two different places at two different times of the year. The mountains are gray with darker gray meaning closer. The scale on the left and right shows the inclination of the sun from the horizon in degrees (it only goes halfway up the sky). The sun itself is sized as it would appear at that point on the disc and time of day. When the sun is lower in the sky, it is traversing more air and therefore is more red. The numbers by each sun indicate the hour for the sun position.

The first image shows a spring day about 1000 miles north of the center of the world.  Note that the sun is rising in the north and is larger in the morning, growing smaller as it passes to the south.

Now for something widely different: a spring day near the edge of the world, only a few hundred miles from the edge. Now the Rim Mountains at the edge of the world loom fantastically high on the horizon (at 45 to -45 degrees). The mountains around 135 degrees are some mountains close to this point but not on the rim. The distant rim mountains are the light gray between the two. Just as impressive as mountains reaching high above the horizon is the size of the sun. In the morning when the sun is passing near this spot on the disc world, it is enormous, over 10 degrees in arc (the full moon and sun are about half a degree by comparison). As the day passes the sun swiftly grows smaller and colder.

What does that mean for the temperature? As we discussed in the last post, when the sun is closer, it is larger and hotter. In the case the last day and place, it would be scorching, 200 degrees F or more. When it is distant or below the Rim Mountains, it would be frigid. The next plots quantify that by showing for the entire disc various yearly metrics.

First on the left we have the yearly peak power for the disc. The power units  are arbitrary; the scale is logarithmic. This plot shows that the maximum power (or heat) a place receives is just a function of distance from the edge of the world. It doesn’t mean every spot near the edge is just as warm during the year, however. Some places just have a few days of high power; others many days. The plot on the right shows the yearly peak temperature in degrees and as would be expected is similar to the power chart (although this time the scale is linear).

The next two plots indicate what the temperature over the course of a year is like. The left shows the number of days of the year where the temperature is over 60F, picked as a cool day but one that could still grow crops. In this disc world, the center is always cold (there are also mountains in the center which increase the altitude) and the east-west band is noticeably chillier most of the year than the north-south axis. On the right is another view of temperature, this time showing the median temperature, i.e., the temperature in the middle. Interestingly, even though as shown above the edges of the world are scorching hot at times, most of the times the edges are frigid except as you approach the poles where the sun always rises and sets.

What would the weather be like? It would be interesting to run a finite-element analysis of it but that is more than I want to sign up to program. Suffice it to say that with such extreme and rapid temperature changes, the winds should be fierce and storms impressive. The Rim Mountains would be mostly arctic-cold with a few weeks a year of days in the 100s or more. It would be a land of extremes and a perfect setting for a Norse-themed D&D campaign, book or game.

Why this exercise? Well, aside from a setting a book and a D&D campaign in this sort of world, this is an example of what you can do if you build on a relatively simple premise and explore the consequences. E.ven if you don’t use a disc world yourself, hopefully the exercise is of use. For any uber-geeks out there, the program I used to create these images of the world and more on the setting can be found at Affliction.

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The Disc World (2): a land of extremes

Last time we looked at a vanilla disc world; this time we’ll take a look at something more exotic: a world where the sun is noticeably larger in the morning than the afternoon, where the edge of the world is a place of deep, bitter cold except for brief times where it rains molten rock, a world worthy of a high fantasy setting.

We still start with a world that is a disc, as in the Norse myths. Instead of a disc orbiting a sun at an Earth-like distance, let’s go to a more cozy world, something more along the scale of what the ancient Greeks imagined to be celestial distances.

For this world, let’s take the same 6000 mile disc and let’s add Rim Mountains 200 miles high. Yes, that is quite an impressive height for mountains but it is no more (or less) implausible than a 6000 mile wide slab of rock. How is that physically possible? I don’t know; this is a fantasy exercise, let’s take that as a given.

To that, let’s add a sun only 200 miles across but orbiting at a radius of 3200 miles so that the edge of the sun is only 100 miles from the edge of the disc. As a minor note, there is also a mountain range along the east-west axis about the height of the Rim Mountains. (That doesn’t affect things much but explains why there are perturbations in some of the energy plots for this world that I’ll share in the next post).

In the system, the disc is fixed in the center of the universe. The sun orbits the disc once per day. The plane of the solar orbit at start of year is parallel to the plane of the disc. Over the course of the year, the solar plane rotates along the disc’s north-south axis. This means that at New Year’s the sun is just below the Rim Mountains. As the year progresses the sun rises higher and higher over the mountains until at the quarter of the year, the sun rises highest over the world passing exactly over the north-south line. Then it starts taking a lower path in the sky until at the half of the year, it is once more just below the Rim Mountains. For the second half of the year, the sun progresses as in the first half however this time it traverses the sky in reverse (since the plane of the sun is “flipped” over).

Let’s assume that the sun rotates clockwise in the plane as looking down at New Year’s. This means for the first half of the year the sun rises in the north and sets in the south. For the second half of the year, the sun does the opposite: it rises in the south and sets in the north. Day and night are essentially equal except for the effect of the Rim Mountains. When the sun is very low in the sky around New Year’s and half way through the year, the mountains block the sun much of the day and the days are therefore shorter.

Okay, that’s quite a bit of a set up but what does that get us?

For starters, with the sun orbiting just beyond the radius of the world disc, the apparent size of the sun depends a great deal on where you are on the world and where the sun is in its orbit. How much? Well if you are on in the Rim Mountains themselves the effect is huge: the sun could take 45 degrees of sky (for comparison, the moon and sun on Earth are very close to half of a degree. At its farthest distance when the sun is rising on the far side of the disc, the apparent size would be less than half a degree. For some at the north pole, at sun rise, the sun would extend from horizon to halfway to overhead. That’s immense.

Moreover, when the sun is close it would be scorching hot. In the world of Calyx, it would be hot enough to melt rock, sending rivers of lava off the edge of the world to circulate back onto the Rim Mountains as a rain of lava and ash. When the sun is distant, it would be frigid in the mountains, a land of ice. The Rim Mountains, at least in the east and west (the north and south are different as we will see) would be briefly hot beyond anything on earth then ice-locked the rest of the year. You would have a half a year of hard ice ended by a brief rain of fire. How’s that for an exotic land of fire and ice? Kind of reminds you of the land of frost and fire giants of Norse myth, doesn’t it?

The north and south poles are different at the edge of the world because the sun always rises and sets at these poles. Therefore the sun blisters the Rim Mountains at the North and South Pole every single day. Instead of mostly frigid days and a few days of melting rock, you would have molten rock and lava every day of the year: a land of lava flows.

Partway between east and north on the Rim Mountains, it grades from one extreme to the other. For those looking for a setting, this provides a nice continuum to plop your characters into.

At the center of the world, things are much more stable. For one thing, the sun is always 3200 miles away. Around New Years it is very low in the sky and warms the land little, as the season progresses it rises higher until the sun is directly overhead and hottest at quarter year and so on through the rest of the year. Hottest is still relative: with the sun 3200 mile overhead, it is still distant and cool. The only change is that the sunlight beats straight down onto the land rather than glancing. This makes for a chilly place.

Moving from the center, things become stranger. Go north along the north-south axis from center and you find the sun closer and therefore larger in the sky and hotter in the morning (at year start) and dimmer, colder and smaller in the afternoon; the closer you are to the rim, the larger the effect. In the second half of the year, it all reverses: large sun in morning, smaller one in afternoon.

Move east from the center along the east-west axis and the sun will be same size in morning and afternoon. But now in the first quarter of the year, the sun is charting a path over the eastern half of the disc and it is very warm (how warm depends how close you are to the rim but remember as we get very close to the rim it is hot enough to melt rock). In the second quarter of the year, the sun is tracing a path over the western portion of the disc and the sun is distant and cold.

So: along north-south, warmth and size of sun varies over the course of the day. Along the east-west, warmth and size of the sun varies over the course of the seasons. Of course, if you are in between true north and true east, you get a mixture of the two effects.

One might ask how I can speak so authoritatively. Well, some of it is just a mental exercise but in the end it does get quite tricky and it is one thing to mentally figure out the general flavor of things, another thing to really quantify how things would behave. Therefore, being the uber-geek that I am, I wrote a C++ program to produce all sorts of cool pictures and images to help visualize what life on this disc world might be like. A taste of these images are in the post.

More in the next post….

The Disc World

Campaign Cartographer
Campaign Cartographer

You may remember a disc world from Terry Practchett‘s Discworld series but disc worlds go way back in human history: many cultures imagined the world as a disc, including my favorite, the Norse. It’s hard to imagine how a disc world could exist in our universe but that’s the beauty of fantasy: we’re allowed some suspension of disbelief. So, the world is a disc: what would it be like on this world?

As one might imagine, there are a lot of variables. Let’s posit a disc 6000 miles across with mountains on the edge of the disc to form a rim (why? I like the aesthetic of something to hold the air in but one could certainly do without them; this is a fantasy exercise afterall). Finally, for heat and light nothing says you can’t have a light on top of a tall tree something like Tolkien’s early world but let’s go with a classic sun.

What would days and seasons be like? Well, it depends entirely on the relationship between the sun and disc. If the disc orbited the sun with a period of hundreds of days, you would have your year, much like Earth. But what about days and seasons?

First let’s image the disc always pointed the same way in space, regardless of where it is in its yearly orbit (just like the Earth maintains the same axis giving us seasons). If we start off with the disc facing the sun at the New Year, then half way through the year the disc is facing away from the sun. A quarter of the way through the year, the sun strikes the disc in parallel. This would mean that half the year there was no light on one side of the disc and the other half of the year you went from dim to very bright and back to dim. Plus there would be no day/night variation (or put another way, a day is the same as a year).

That might make for a very different place of long winters and long days, something like the Polar Regions on earth but for the entire disc world, not just the planetary extremes. Certainly a very different setting for your project.

I like days, though, so what if we spin the work around an axis through the disc? Let’s start with the disc again facing the sun at New Year’s and the axis of rotation perpendicular to the orbit of the sun. On New Year’s day you would have day and night, something like a tropical day on Earth. In fact, as the year progressed, nothing would change. You would always have a day and night, the noon would always have the sun straight up. Now you have a world of days and nights but no seasons. Could be an interesting place for a desert or Arabian type world.

One point about this arrangement: half way through the year, the disc world’s day starts a half-day later then it does at the start of the year: each day the sun rises and sets a little later (or a little earlier depending on which way the disc spins relative to the orbit around the sun). If yearly orbit is an exact multiple of daily disc rotation , the disc-worldians see one more or one less days per year than you might otherwise expect. A minor nit but if a day is 24 hours and a year is 24 * 360 hours, the disc world would have 359 or 361 sunrises per year depending on whether which way the disc spin with respect to the orbit around the sun.

Instead, let’s keep the spinning disc but tilt the axis. So now the world faces the sun at New Year’s but it is tipped forward. What does this do? At the start of the year, you have a day where the sun is not directly overhead but a quarter way through the year sun is directly overhead (repeating for the second half of the year). Now you have seasons. The amount of season would be determined by the degree of tilt.  With a little tilt you would vary from a sun a little off vertical at noon in the winter; 90 degrees of title and mid-winter would be a day of twilight.

Now you have days and seasons similar to earth but there are differences:

  • Seasons are identical everywhere on the surface of the disc unlike Earth where it is winter in the north when it is summer in the south and the equatorial regions have no seasons at all.
  • Day and night are always equal length (except for the 90 degree tilt case where twice a year the day is all twilight)
  • There are two progressions of a seasons in a year: from winter at New Year’s to summer at the quarter year back to winter at the half year then summer at the three-quarter point.

So, that’s a basic disc world but can you do more with it? Most certainly, stay tuned for the next post when we imagine a fixed disc and a sun that orbits around it just outside the edge of the disc. Now our disc world will stop being something Earth-like and start looking very different…