[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.

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'.

Re: [Space] Mapping Large Flat Areas
 

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.

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.

Re: [Space] Mapping Large Flat Areas
 

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.

Re: [Space] Mapping Large Flat Areas
 

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?

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.

Re: [Space] Mapping Large Flat Areas
 

Ah. In that case, your question isn't actually answerable. There are no mappings of 3d space to 2d space that preserve adjacency.

Re: [Space] Mapping Large Flat Areas
 

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.

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?