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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