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
Pretty useful stuff, levallon...but can't I just default to perpetual oceans/atmospheres based on existing gates to elemental planes?
ReplyDelete; )
Hmm..gates are a little beyond the scope here, but I did find this. https://www.physicsforums.com/threads/how-to-create-a-wormhole.470830/
ReplyDeleteThanks for commenting! :)
Great work!
ReplyDelete