Subject: MYSTARA-L Digest - 8 Nov 2001 to 9 Nov 2001 (#2001-308)
From: Automatic digest processor
Date: 10/11/2001, 19:00
To: Recipients of MYSTARA-L digests
Reply-to: Mystara RPG Discussion
There are 5 messages totalling 202 lines in this issue.
Topics of the day:
1. Anybody got a clue on hexes? (4)
2. Green orcish blood?
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Date: Fri, 9 Nov 2001 00:15:41 +0000
From: Mike Harvey
Subject: Re: Anybody got a clue on hexes?
la Volpe wrote:
> A question mainly for the mappers:
> is there anybody who knows what the area for a 8-miles hex should be?
> I know how to calculate an area for an hexagon, but the problem is to
> decide
> what "8 miles" mean. Is it a side? Is it from one point to the opposite?
I interpret it as from one side to another, thus:
_______
/ \ ^
/ \ |
/ \ |
\ / |
\ / |
\_______/ v
(you'll need to use a fixed-width font to see that correctly)
As far as the area, I've worked a general formula:
A = (3 x^2) / (4 sin 60)
Bizzarely, 3 / (4 sin 60) = sin 60, at least as far as I've been
able to determine. I happened on that by accident and I can't figure
out why it's true. So the simplified formula is
A = x^2 sin 60
So the area of hexagon:
1 mile ..... 554 acres (sin 60 x 640 acres)
8 miles .... 55 square miles
24 miles ... 499 square miles
72 miles ... 4489 square miles
an 8 mile hexagon is 8 x 8 x 0.8660 = 55.42
square miles.
If anyone wants the proof of the formula:
______ _____________
/ /|\ ^ | /| /
/ / | \ | | / | /
/ / | \ |x | / | /
\ / | / | | / | /
\ / | / | | / | /
\/_____|/ v |/_____|/
A B
You can break figure A up into 12 smaller identical 30-60-90
triangles, and rearrange them into figure B. Figure B is composed of
three identical 30-60-90 triangles of height X. Each triangle in
figure B is
height = x
hypotenuse = x / sin60
base = (sin 30) (x/sin60) = x / (2 sin60)
The area of each triangle is (1/2)(base)(height), which is
A = (1/2)(x/(2sin60))(x) = (x^2) / (4 sin 60)
The area of figure B then is
A = (3) (x^2) / (4 sin 60) = x^2 sin 60
Mike
----------------------------------------------------------------------
Mike Harvey
gm@dsl-only.net (formerly bing@iccom.com)
http://members.dsl-only.net/~bing/
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Date: Fri, 9 Nov 2001 12:00:17 -0700
From: Angelo Bertolli
Subject: Re: Anybody got a clue on hexes?
I think it's from the center of one hex to the center of the next.
----- Original Message -----
From: "la Volpe"
Sent: Thursday, November 08, 2001 1:07 PM
Subject: Anybody got a clue on hexes?
> A question mainly for the mappers:
> is there anybody who knows what the area for a 8-miles hex should be?
> I know how to calculate an area for an hexagon, but the problem is to
> decide
> what "8 miles" mean. Is it a side? Is it from one point to the opposite?
>
> Any clue?
>
> Iulius Sergius Scaevola
> Captain of the XXth Cohort
> Port Lucinius, Thyatis
>
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Date: Fri, 9 Nov 2001 17:38:49 -0500
From: Geoff Gander
Subject: Re: Anybody got a clue on hexes?
>
> It is the distance across the hex, from one flat face to the one across from
> it. The area for a 24 mile hex is 480-500 sq. miles, I forget the exact
> number.
>
> What's the formula for calculated the area?
IIRC, Bruce Heard posted the formula here, or on the old MMB. It was as
follows:
.866 * d squared, where d is the diameter of the hex. Therefore, an
8-mile hex would be:
.866 * 64 (8 squared)
He said this was the formula TSR used to calculate the areas of the nations.
Geoff
--
Geoff Gander, BA 97
Cartographer/Game Designer/Government Peon
Carnifex Loremaster
au998@freenet.carleton.ca : www.geocities.com/TimesSquare/Realm/2091
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Date: Fri, 9 Nov 2001 21:12:25 -0500
From: Dan Eustace
Subject: Re: Anybody got a clue on hexes?
So the simplified formula is
>
> A = x^2 sin 60
>
> So the area of hexagon:
>
> 1 mile ..... 554 acres (sin 60 x 640 acres)
> 8 miles .... 55 square miles
> 24 miles ... 499 square miles
> 72 miles ... 4489 square miles
>
> an 8 mile hexagon is 8 x 8 x 0.8660 = 55.42
> square miles.
Wow, you guys are good! This matches with Bruce Heard's 0.866x2, as noted
by Geoff (since sin60=0.866). I knew the 24 mile hex was around 500 sq.
miles! This also matches with the areas in the PWAs, so I think you guys
have proved how hex size is determined. Using Brendan's formula (.5 *
apothem * length of the side * the number of sides.
The apothem being the length from the center of the hexagon to the center of
the side (or in other words, 1/2 hex size)), and solving for the length of
the side, we get 499/36=13.86 miles/side for a 24 mile hex. When I drew out
24 mile map hexes on graph paper I used 14 miles/side, which gives a hex
with 504 sq. mile area. Not bad for winging it!
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Date: Fri, 9 Nov 2001 18:50:18 -0800
From: The Stalker
Subject: Green orcish blood?
Do orcs have green blood??
I wouldn't think so. I always had all blood red IMC, but reading the
beginning of the "Dark Knight of Karameikos" novel, it clearly states that
orcs have green blood. Hmmmm...
Does this mean orcs have green blood in general? Or do they just have green
blood on Mystara? Or do they only have green blood in bad stories? ;)
[Note: I'm not saying the novel is, since I haven't actually read - just
that green orcish blood might be a reason for saying so]
- The Stalker
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End of MYSTARA-L Digest - 8 Nov 2001 to 9 Nov 2001 (#2001-308)
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