GURPS Magic "Hex Radius" to "Hex Area" Conversion

by Eric Funk


It happened one day that I had some GURPS books while on a bus on the way to an airport, and whilst comparing the areas of effect of Regular and Area spells. While pondering the tiny chart on the sidebar of p. M 10 and p. B 150, a mathematical pattern lept out at me.

Here is what I found:

n
1 = 1
2 = 1 + 6
3 = 1 + 6 + 12
4 = 1 + 6 + 12 + 18
Using a piece of grid paper, I then verified the above and was pleased to find the following result:
5 = 1 + 6 + 12 + 18 + 24

avg = m(m+1)/2


Substituting:
6 (n-1)(n)/2 + 1
3n(n-1) + 1

3n*n -3n + 1

(The formula for Area spells is 3*n*n-3*n +1 where n is the "radius")

Since the "Height" of a magic hex is defined as 12', we know that each hex contains 3x3x12 = ~100cf, calculated exactly as 85cf (see p. TM37). Reverse engineered, one gets 7.08sf/hex.
Combine this with a table of densities, and now one has a dangerous combination.

e.g.: Create Earth, 10 hex radius: 3×10×10 - 3×10 + 1 => 300-30+1 => 271 hexes.
271 hexes × 85cf/hex = 23,035cf.
23,035cf × 100lbs/cf (dry sand) = 2,303,500lbs -> ~1,120 tons (great fun indoors!
A subsequent casting of Earth to Stone would double its mass (similar to concrete)...



What other use is this?
To tell how many hexes one has to play with as per the GURPS FAQ.


Another use:
http://www.krommnotes.org/krommmag.html
"Q: Can the shape of the area be changed for Area spells? That is if you cast a 2 hex area spell can you stretch it to 1 by 7 hexes? (a)"

The answer was yes!


"Hex Radius" <= => "Hex Area"




A hex grid of the above
(based on public domain hex grid found here)