Friday, January 11, 2019

Worldbuilding, Part Two




Previously, I outlined method for deriving planetary parameters based on your world map. I will now continue with this.
I. Surface gravity: Though we have already covered escape velocity, surface gravity is different. I have not found a calculator to do this, but it is not difficult. The formula is g = G * M / r2. G here is the gravitational constant. Multiply your planet’s mass by 6.67 * 10-11. Note the negative integer. Take the resulting value and divide it by your planet’s radius (in meters) squared. The result is in meters/second2. You can find calculators on the internet that will convert this to feet/second2 if you wish.
II. Axial tilt. The Earth is tilted 23.25°. This tilt changes over the course of thousands of years, and the Earth is currently at about the midpoint of its range. This, like rotation, is determined at planet formation and influenced by bombardment of comets and asteroids and other bodies. You can set it at any value that you wish. Greater tilt means more severe seasons, and less tilt more mild seasons. Reddit and Stack Exchange are full of discussion of radical axial tilt. What seems different is actually commonplace. Planetary mean temperature is a function of the distance to the star and the axial tilt, but there is really no need to go into this unless you are really interested. And bored. Axial tilt does have an impact on climate and weather, which will be discussed.
III. Atmospheric Circulation. This is how all of this got started. I asked a question: Given Earth-like conditions and the geography that I have decided exists, will the weather be what I want it to be? And what can I do to make it what I want?
The answers and what I learned to get them will have a major impact on your planet’s climate. Around the equator and stretching 300 to 600 miles in width is the Inter Tropical Convergence Zone (ITCZ). The ITCZ is where the sun is overhead during the equinoxes (roughly the equator), and it heats the ocean resulting in evaporation. Warm air rises and flows toward the poles, creating the Hadley cells. This creates low pressure and surface air flows in to replace it. The air descends at about 30°. This air is dry, having dropped most of it’s moisture to create the rain in the tropics. Most of the world’s deserts occur around 30° latitude. Coastal areas, particularly east coasts, typically avoid being deserts due to ocean currents.
On Earth, there are three cells per hemisphere, but rather than flow straight north and south, the Coriolis Effect causes the air flow of the Hadley Cells to drift eastward. The Temperate cell flows toward the Hadley Cell. The Hadley Cell transports warm air towards the poles and the Polar Cell and Temperate cell facilitate the return trip. If you know where the boundaries of these cells are, you have an approximate location of the jet streams (Jet Stream, Temperate Jet, Polar Jet) which are strong determiners of weather. The references below include more detailed descriptions of this.
Here’s where it gets complicated. The whole damn thing moves. The Tropic of Cancer is the latitude where the sun appears overhead on the summer solstice, and the Tropic of Capricorn is where it appears overhead on the winter solstice. The ITCZ follows the sun and shifts the atmospheric cells. The size of the cells can also fluctuate, but that is beyond the scope here. For our purposes, it is enough to know that depending on where you are on your planet and when, winds can shift depending on season. If your axial tilt is only ten degrees, that means that during the winter, the sun will barely rise above the horizon.
     All of this is absurdly simplified, but giving some consideration to this will help you establish wind direction and basic weather patterns. See the references for more, but be prepared to do your own research. I found the cengage.com link very clear, though it does involve some reading (don’t worry there are clear illustrations, too).
IV. Orbital Resonance: Orbital resonance refers to the regular gravitational influence that planetary bodies exert upon each each other, typically involving low number ratios. In other words, the influence of other planets helps keep your planet in its orbit. This is pretty complicated stuff, but Wikipedia has a nice animation demonstrating the idea. I have not chosen to explore this much, even in addressing the moons of Kemen. A handwave seems appropriate here. I have ruled that there are two inner and at least two outer planets in the Kemen system to keep everything on track. If you wish to include other planets in your campaign, orbital resonance may be interesting to you.
Underground fireballs are dangerous,
Levallon
Posted by at No comments:

Friday, January 4, 2019

Worldbuilding, part one


Greetings!

     Here is another infrequent installment of a series of posts describing things I do in my campaign that you might interested in doing yourself.
     What I am talking about is called “worldbuilding,” but is more like world modeling. I am going to show you how to create a model world with a minimum of math, that you can use to give justification to your world and create opportunities for new adventures.
     (Wait! Why would I care? D&D is about dungeons! First, many adventures can occur on the surface. The Three Musketeers, Robin Hood, and many other adventures occurred above ground. Even stories like The Lord of the Rings were mostly above ground.
    (Second, just how many times do you think that you’re going to be able to convince your paladin that going into a dark, dirty dungeon, where his armor does not shine and his banner (and hair) does not flow in the wind of his steed, so you can steal gold and magic from the dead, is not too ignoble an endeavor for one of his station? Now, stop interrupting!)

Step One: Make it an alternate Earth. Okay, you’re done!


You’re still reading. That means you either find this entertaining, or you want to know how to model a world with parameters different from the ones of Earth. You’re sure you want do to this? Okay…

I. As a DM, you most likely have maps of your world. Some of these show the area around encounter areas, others perhaps cities in relation to each other, etc. The point is that you have maps of different scales. Perhaps you’ve mapped your whole world, or maybe, like me, only a portion and you’re saving the rest for future expansion.
    Pull out your largest scale map. If this map has lines of latitude, great. If not, you will need to add some. The only ones you really need are two major ones. It might be the Equator and the Tropic of Cancer, it might the from the north pole to 45°. Any two will do, but it is important for you to be able to determine the number of degrees between the two. For example, from the Equator to the northern boundary of the Tropic of Cancer is typically 30° (there are conditions where it’s not, but let’s not get into that just yet).
    Using the scale of your map, determine the distance (in miles, kms, dragon lengths, whatever) between these two lines. Yes, I know that maps are flat and planets are not, just do it.

II. Covert the number of degrees between your two latitude lines to radians. Here’s how: http://www.1728.org/radians.htm . For example, 45° = .79 radians. On the linked page, you will see an equation, S= r*Θ. You can use this equation or scroll down and use the calculator. S= arc length, or the measure of the distance because the two latitude lines in step I. Enter the central angle in radians (remember the decimal point!), and press calculate. The answer is the radius of your planet. Write this down where you won’t lose it.

Change this number to kilometers, and keep all your measurements in metric! It’s easy to convert them later in to miles, leagues, mille passus, cubits, or whatever unit you prefer. For calculations, do it in metric.

III. You have the radius. Multiply it by two. Now you have the planet’s diameter. Use the calculator on your computer or online to cube your radius, (raise the number to the third power) and multiply that number by 4.188. V= 4/3π*r3. Your answer should be in cubic meters (m3). Now you have radius, diameter and volume of your planet.

IV. At this point, I’ll introduce some more sites. The first is useful for doing computations without having to constantly convert back and forth out of scientific notation.

The next site is important to the next step.

This calculator will return any of three values as long as you have the other two. Volume you have already figured out. For now, assume that the density of your planet is equal to that of Earth, 5514 kg/m3. Enter the volume and density values for your planet into the calculator. Make sure the units are m3 and kg/m3, respectively. Use the dropdown boxes to change the units. Press calculate. The answer is your planet’s mass. You now know the radius, diameter, volume, density and mass.

V. Go to https://www.calculatorsoup.com/calculators/math/scientificnotation.php . In the top box enter your planet’s mass. In the bottom box, enter 5.97 *10^24. Go to the little box on the left and change the operator to divide, and press calculate. You will get a number in scientific notation. If it has a negative exponent, move the decimal point to the left as many places as the exponent. For example, 3.3 × 10-1 = .33, and 1.3350251256281 × 100 =1.33. Whatever your number is, go to https://www.omnicalculator.com/physics/escape-velocity and enter it next to where it says “Earths.” This is your planet measured in Earth masses. Next enter your radius in km, and verify the units. Now look at the escape velocity. Write down this number.

VI. So now you have a number of parameters for your planet. Don’t go applying to NASA just yet. Click this link https://en.wikipedia.org/wiki/Atmosphere#/media/File:Solar_system_escape_velocity_vs_surface_temperature.svg
Is your planet’s escape velocity above 7 km/sec? If so, it will be fairly Earthlike. If not, it will not have oceans and will likely be very dry, like Mars, because it will be incapable of preventing water vapor from escaping to space. (Having an uh-oh moment? Keep reading...)

VII. Dig out your radius, multiply it by 6.28. This is the circumference of your planet. (Note, I generally round everything to two decimal places to keep everything simple, but you don’t have to).
    Now we have what I call a fudge factor. How long do you want your planet’s day to be? Divide your circumference by the number of (Earth) hours in your planet’s day. Now you have the equatorial rotation speed. For comparison, for Earth, the speed is about 1,000 mph. (460 meters/sec).
    Just like we did with mass, we want to convert our parameters of radius and rotation to units where Earth = 1. So divide the radius of your planet by 6378 km. Do the same with your rotation: divide the hours of your planet’s full rotation by 24. Now multiply them together and compare the result here:


This will tell you how many circulation cells your planet’s atmosphere has. Earth has 3 per hemisphere. Venus and Titan have 1. Rotation is very important to all this. Rotation creates creates the Coriolis effect, and this is turn has a pretty big impact on our climate and weather. If your rotation is slow, your day will be longer but it will also make it more likely that your planet will only have one cell per hemisphere. If your planet is closer to its star and has a slow rotation, it is possible for it to be habitable. In fact, if it is closer to the star it can only be habitable if it has a slow rotation. Rotation also has an impact on the generation of magnetic fields which deflect the solar wind. If your rotation is too fast, you won’t have as much sunlight because your day will be shorter and that will affect sleep and growth cycles.
    All of this world building material is based on what we know, and there is a lot that we don’t know. Also, this material has been greatly simplified to make it easy to create plausible worlds. If you want to get more exact, see the reference list.

VIII. Crap! My planet is broken!
Relax. Kemen had to be reworked several times. Here’s what you can do.
If you want a wet world and your planet’s escape velocity is below 7, you have to makes some changes. There are some “fudge factors” in all this. The first is density. Planetary density is an average of the substances that make up the planet. Earth has iron-nickel core surrounded by a mantle of silicates and metals. There are higher density elements in the Earth, though they are not present in the same high quantity as iron and nickel, and of course the oceans and atmosphere are less dense. Thus, we need an average.
    In the process above, we used 5514 kg/m3 for the density figure. This is the density of Earth. Earth is the most dense object known in the solar system, but doesn’t mean that it is automatically at the end of the scale. Higher densities could be achieved with greater concentrations of metals, but I’d be careful not to go above 6500-7000 kg/m3. I’m not sure what those higher density values mean. In the case of Kemen, I have ruled that there are higher concentrations of heavy metals, and further, that the oceans are not as deep as Earth’s so there is less water to average.
    So you can increase the density and see if that changes your numbers. If you’re close to seven, it may do the trick. If not, about the only fix (short of a handwave or magic) is to increase the mass. The way I did it was to plug small increases into the calculator https://www.omnicalculator.com/physics/escape-velocity and backtracking the math so if I could live with it. For example, instead of .28 Earths, I’d bump it up to .30 or .32 to see what escape velocity I got. When I one I was happy with (close to 8), I reversed the equations and calculators. I entered the mass and density and calculated for volume, divided by 4.188, and took the cube root (raise to 1/3 on a calculator) of the remaining number to get the radius. It changed some distances, but only by about 100 miles or so, and I decided I could live with it.
   This has gotten longer than I intended. Here are some references and useful sites for learning more, especially about atmospheric circulation. Next week, I will talk about some other parameters, such as surface gravity, atmospheric circulation and weather, and orbital resonance.

Listen at doors!
Levallon

 References
 












USEFUL SITES









Posted by at 3 comments:
Subscribe to: Posts (Atom)