SFRPG

Hi Guys,
In trying to work with T5 on a project for my own world building (One player wants to play a High Noble (someone with a land grant per T5), I ran into an oddity...

Some time back, I ran into a quick and dirty formula for calculating the area of a hex. Simply put, if you measured from side to side of a hex (ie, a line drawn from the center of one side, through the center of the hexagon, and to the other side at the center of the line), you could estimate the area of the hex as follows:

Find the width from face to face, and multiply that by 0.866, then multiply the two together to get your area.

For example, if your hex is nominally 25 miles wide from face to face, its area will be 25 * (25 * 0.86 = 21.5) = 537.5 square miles.

In digging deeper, I had to get the formula other than the one given above as:

Area of a hexagon is (3*(3^.5))/2 * length of Sides^2

An apothem (the line from the center of the hexagon making a perpendicular line bisecting the side of a hexagon) is = Sides/2tan(180/N) where N is number of sides in polygon (6 for a hexagon).

When you don't know the LENGTH of the sides of your hexagon, but the length of the Apothem, then the formula becomes:

Length of Sides = 2 * Tan(30) * Apothem length

Final formula then becomes:

3*(3^.5))/2 * (apothem*2*tan(30))^2

(note: if using excel, you have to use (tan(radians(degrees)) to get the proper tangent value in degrees.)

So, why all this background?

Page 693 of Traveller 5th edition has this to say about fief hexes:

"Outright Ownership of one Local Hex (approximately 65 square km= 6500 hectares= 16,000 acres)."

Elsewhere, it has this to say about local hex on page 459...

"Mapped In Hexes. The Traveller Mapping System defines a hierarchy of mapping hexes: the 1000 km World Hex; the 100 km Terrain Hex; the 10 km Local Hex; and the 1 km Single Hex."

This on page 421:

"Hex Size. Hex size (or hex diameter) reflects the distance from the center of a hex to the center of an adjacent similarly sized hex. Hexes are universally even decimal multiples of meters (100 meters, 1,000 meters, 10 kilometers, and 1 km)."

This is the way to determine what the Apothum is - which would be half the distance between center of hex to center of hex (or the line that separates them from each other).

So why all this attention to detail? Per Marc Miller, each "Local Hex" is a 10 km hex, which makes it a 5 km Apothem, which in turn makes the area of a 10 km hex equal to 86.60254038 square km, or 8660.254038 hectares, or 21,399.9537766255 acres - not the approximately 65 sq km or 16,000 acres.

Can someone verify this information. I'm thinking that I'm the one who had to have messed up. But when I used the simple formula for determining the area of a hexagon, it didn't match Marc's information, so I dug deeper to find the formula that I outlined above, and that matched the quick and dirty value, but still didn't match Marc's information.

Help?

Having gone through four alternative methods for calculating the area of a hex, I now believe that the formulas I used were accurate. It is a minor issue overall, where Marc's original figures are about 25% off the mark. It won't break any campaigns, and if I hadn't had my reasons for looking closely at the area of a local hex, I would never have spotted it. On the scale of 1 to 10 importance wise, 1 being who cares, to 10 - stop the presses! - I largely suspect this rates at best, a .1 on the overall grand scheme of things. ; )

I mean we're talking Traveller here (and T5 at that), it's not unknown for them to get calculations wrong...

_________________
SFRPG Owner/Admin
This post (or any other post I made here) may not be quoted or copied beyond the SF RPG boards without my explicit permission.
evildrganymede.net - visit the The Worldbuilding Hub
Check out my Youtube channel for all my streamed gaming videos!

keyboard kill. Double points because I'm guessing it wasn't intended as one. And if it were, well, double points bonus. That's twice in one day someone commented on T5 in that manner.

*wry chuckle*

I was going to make a snarky comment about the quality of T5 and the prevalent opinion of it on this board, but I figured I´d wait for the pros who had actually read it.

_________________
Space isn't remote at all. It's only an hour's drive away if your car could go straight upwards. Sir Frederick Hoyle
Earth is the cradle of humanity, but one cannot live in a cradle forever. Konstantin Tsiolkovsky
Man has earned the right to hold this planet against all comers, by virtue of occasionally producing someone completely bat**** insane. xkcd #556
Just like people, stars can be very important without being terribly bright. Phil Plait, "Bad Astronomy"

Have they even got T5 to a playable, generally accessible state yet? Or done a new version written by people who know how to write and edit RPGs? Last I heard they were 'fixing' things in it but I lost track of anything to do with Traveller years ago.

_________________
SFRPG Owner/Admin
This post (or any other post I made here) may not be quoted or copied beyond the SF RPG boards without my explicit permission.
evildrganymede.net - visit the The Worldbuilding Hub
Check out my Youtube channel for all my streamed gaming videos!

I have no idea. Whatever curiousity I had about T5 died in the fires in which the initial version was roasted here. For all I care, CE is the T5 that should have been.

_________________
Space isn't remote at all. It's only an hour's drive away if your car could go straight upwards. Sir Frederick Hoyle
Earth is the cradle of humanity, but one cannot live in a cradle forever. Konstantin Tsiolkovsky
Man has earned the right to hold this planet against all comers, by virtue of occasionally producing someone completely bat**** insane. xkcd #556
Just like people, stars can be very important without being terribly bright. Phil Plait, "Bad Astronomy"

There was talk of players guides that weren't 1000 page tomes, I guess nothing came of that either.

_________________
SFRPG Owner/Admin
This post (or any other post I made here) may not be quoted or copied beyond the SF RPG boards without my explicit permission.
evildrganymede.net - visit the The Worldbuilding Hub
Check out my Youtube channel for all my streamed gaming videos!

I always hated the idea of a fixed number of hexes per world surface and vary the size of the hexes to fit the map.

Personally, I would rather see a fixed Hex size of 1000km and vary the number of hexes to match the surface area (related to the SIZE code in the UWP). SO Much easier, just make a map for each world size, but once you get to the world hex level, everything below that perfectly matches the 1000/100/10/1 system...

_________________
My friends call me Richard. You can call me Sir.
www.XmasDragon.com