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Old 05-28-2019, 12:45 PM   #1
RustedKitsune
 
Join Date: Oct 2018
Default [Space] Mapping Large Flat Areas

When using an FTL model that isn’t based on real space distance, and isn’t limited in destinations per star (such as Traveller’s jump drive, or a flat hyperspace model), what is the formula for average distance between neighbouring systems? So if I have area A, measured in arbitrary FTL distances, and interesting planets N, is 1.12*(sqrt(A/N)), backhacked from the 3D formula a reasonable approximation? Is sqrt(A/N) the better formula? Will I have to force learning calculus on people?
Stack Exchange just keeps recommending calculus courses, so I’m hoping someone here has figured this out.
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Old 05-28-2019, 12:58 PM   #2
Anthony
 
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Default Re: [Space] Mapping Large Flat Areas

I think you have to explain what you mean a bit more. If you're using an FTL model that isn't based on real space distance, you're going to have to start by defining what you mean by 'neighboring' and 'distance'.
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Old 05-28-2019, 01:06 PM   #3
RustedKitsune
 
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Default Re: [Space] Mapping Large Flat Areas

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Originally Posted by Anthony View Post
I think you have to explain what you mean a bit more. If you're using an FTL model that isn't based on real space distance, you're going to have to start by defining what you mean by 'neighboring' and 'distance'.
Distance is parsec equivalent, or the distance travelled by an FTL-1 drive over the GM defined unit of time. Neighbouring is the ones nearby each other, given a random distribution in the area.
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Old 05-28-2019, 02:18 PM   #4
hal
 
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Default Re: [Space] Mapping Large Flat Areas

I'm just curious - why aren't you using real space for 3D distance measurements where you can simply use X, Y, Z coordinates, and get true distance values?

Astrosynthesis will let you as a GM, track where stars are, where planets are relative to their stars, and even track where the planets are in their orbits at any given time based on information that is generated using GURPS SPACE.

Even if you didn't have Astrosysnthesis, you can simply use real world locations of stars that are freely available at:

http://www.projectrho.com/

Having a spreadsheet to track things as a GM as a database function works well enough. Printing out the spreadsheet such that you have the X/Y/Z coordinates works well enough, and a simple calculator in which you know your current location's X/Y/Z and your destination's X/Y/Z will permit a person with a calculator to simply use the ((X1-X2)^2 + (Y1-Y2)^2 + (Z1-Z2)^2)^.5 formula to determine actual distance.

Just about any FTL rule you want to create for how long it takes to travel that distance can be invoked. You can create FTL mechanisms such as the STUTTERWARP easily enough, or you can create your own JUMP DRIVE or heck, you could probably even recreate the FTL 2448 game universe well enough. You can also find FULL THRUST by Ground Zero in PDF format (free) which has its own campaign rules of sorts for ship battles. Star Trek warp drive can be emulated well enough.

So - the question of having to bring calculus into this seems a bit odd to my way of thinking. Sometimes keeping it relatively simple is the best way to go.
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Old 05-28-2019, 02:23 PM   #5
Gumby Bush
 
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Default Re: [Space] Mapping Large Flat Areas

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Originally Posted by RustedKitsune View Post
Distance is ... the distance travelled by an FTL-1 drive over the GM defined unit of time.
I don't understand how this "isn't based on real space distance." Or, if it is a different sort of space distance, it should act the same as if it were, just plotted in hyperspace instead of real space.

Edit: Ninjaed by hal.
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Old 05-28-2019, 02:56 PM   #6
Anthony
 
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Default Re: [Space] Mapping Large Flat Areas

Quote:
Originally Posted by RustedKitsune View Post
Distance is parsec equivalent, or the distance travelled by an FTL-1 drive over the GM defined unit of time. Neighbouring is the ones nearby each other, given a random distribution in the area.
That's based on real space distance, so you can use normal solutions for real space distance. However, you'll still have to define neighbor, because there are several ways of defining the term. Finally, you'll want to define what you mean by average.

Given a random distribution, the median distance to the nearest star is equal to the radius of a sphere that has a 50% chance of containing a star. I don't immediately recall the mean, it should be near to but not identical to that number.

Separately, what do you want this information for?
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Old 05-28-2019, 03:27 PM   #7
RustedKitsune
 
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Default Re: [Space] Mapping Large Flat Areas

Let me clarify: this is for hyperspace variants where hyperspace is TWO DIMENSIONAL and the positions of stars in Hyperspace is NOT based on their real space positions. In short, there is not a Z-Coordinate, just X and Y, and I’m trying to find the average distance between stars near each other given any area and any number of stars.
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Old 05-28-2019, 03:34 PM   #8
Anthony
 
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Default Re: [Space] Mapping Large Flat Areas

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Originally Posted by RustedKitsune View Post
Let me clarify: this is for hyperspace variants where hyperspace is TWO DIMENSIONAL and the positions of stars in Hyperspace is NOT based on their real space positions. In short, there is not a Z-Coordinate, just X and Y, and I’m trying to find the average distance between stars near each other given any area and any number of stars.
Ah. In that case, your question isn't actually answerable. There are no mappings of 3d space to 2d space that preserve adjacency.
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Old 05-28-2019, 03:38 PM   #9
RustedKitsune
 
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Default Re: [Space] Mapping Large Flat Areas

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Originally Posted by Anthony View Post
Ah. In that case, your question isn't actually answerable. There are no mappings of 3d space to 2d space that preserve adjacency.
In this model, it is presumed that real space distance does not translate into FTL distance. There is no need to account for real space being 3D.
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Old 05-28-2019, 03:56 PM   #10
RustedKitsune
 
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Default Re: [Space] Mapping Large Flat Areas

Or should I just presume that the 2d ftl space has an effective height of 1 and then use the equations for a 3D space?
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