Sunday, July 8, 2012

Pi, Bursts, and Cones

About two Pi Days ago, I celebrated in the most appropriate way I could think of: I actually did some calculations involving pi.

See, at some point I had seen Paizo's Steel Sqwire templates. I judged them unnecessarily expensive, because I knew I could make some that were just as good myself.

So I went and I found some wire...

...and did some calculations.

I decided that all the fiddly little right angles and squarenesses in the RAW templates for cones and bursts were unnecessary, because I was making templates to represent actual cone and burst shapes. I decided my cones would be quarter-circles and my spheres would be circles! So that involved some math.

As everyone should know from elementary school, the circumference of a circle is 2πr. And, obviously, the perimeter of a quarter-circle is 2πr divided by 4, plus 2r, or r(π/2+2). And 1 inch for a mini equals 5 feet in-character, so we divide all our answers by 5.

radius (ft.) cone (in.) burst (in.)
10 7.1 12.6
15 10.7 18.8
20 14.3 25.1
30 21.4 37.7
40 28.6 50.3
50 35.7 62.8
60 42.8 75.4
70 50.0 88.0
(If you do this yourself, you might consider yourself well-advised to double-check my math before cutting.)

I elected to make a 20' burst and a 30' cone, because those are the biggest that would fit in my D&D stuff carrying folder, and anything smaller is easy enough to figure out on the fly.

So I cut my wire to length and affixed it to itself with a connector and...
This dragon's breath weapon is 10' too short for its size. Oops.
This changeling is casting darkness. Or fireball. Or obscuring mist. Or fog cloud. Or stinking cloud. Or cloudkill. Or solid fog. Or dispel magic. Or zone of truth. Or something. This is a useful size template to have, is what I'm saying.


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