Rain in the real world and GURPS MAGIC

[hal]

Hello Folks,
I thought I'd mention this just in case anyone wants to do the math or what have you...

"Rainfall rate is generally described as light, moderate or heavy. Light rainfall is considered less than 0.10 inches of rain per hour. Moderate rainfall measures 0.10 to 0.30 inches of rain per hour. Heavy rainfall is more than 0.30 inches of rain per hour. Rainfall amount is described as the depth of water reaching the ground, typically in inches or millimeters (25 mm equals one inch). An inch of rain is exactly that, water that is one inch deep. One inch of rainfall equals 4.7 gallons of water per square yard or 22,650 gallons of water per acre!"

Just thought someone would find it useful for their game worlds when they try and use the Rain spell and figure out just how much water they're producing with the spell itself.

For instance, a 3 hex radius spell is really 2.5 yards in radius (measuring from the center of a hex as 1 hex radius, etc). Area is equal to Pi *r^2 or 19.6 square yards. This works out to 92.2842841992 gallons of water for a mere 1 fatigue (remember, base cost is 1/10 per hex radius, minimum of 1. You could go to a 10 hex radius for 1 energy and produce 1332.5851 gallons.

Compare/contrast this with Create Water at 2 energy per gallon created.

Now put this into motion with a magic circle of mages who start the spell up with 3 people. Each person then has to reinforce the spell every hour on the hour. That produces roughly 32,000 gallons of water per day - swapping out 1 mage every 8 hours just to keep the circle going.

Now place that constant rainfall over a pan that collects water and sends it to an overshot mill wheel. That is a fair amount of water that can be created from just 1 fatigue over a period of time.

[whswhs]

The area of a single hex is 0.87 square yards. I usually take "one hex radius" to mean that single hex plus the hexes adjacent to each of its six sides, which is seven hexes or 6.09 square yards; two hex radius adds 12 more hexes, for 19 hexes or 16.53 square yards; three hex radius adds 18 hexes, for 37 hexes or 32.19 square yards. The formula for radius N is N(N+1)/2 + 1 hexes.

[Agemegos]

Originally Posted by whswhs

The area of a single hex is 0.87 square yards. I usually take "one hex radius" to mean that single hex plus the hexes adjacent to each of its six sides, which is seven hexes or 6.09 square yards; two hex radius adds 12 more hexes, for 19 hexes or 16.53 square yards; three hex radius adds 18 hexes, for 37 hexes or 32.19 square yards. The formula for radius N is N(N+1)/2 + 1 hexes.

2, 4, 7, 11, 16, 22, 29, …


Try 3N(N+1) + 1

[whswhs]

Originally Posted by Agemegos

2, 4, 7, 11, 16, 22, 29, …


Try 3N(N+1) + 1

Damn. Forgot to multiply by 6. Thanks.

[Tyneras]

Impressive return on energy investment! Though Create Water does have the advantage of being instant, in a container or other form of your choosing and working consistently anywhere. Nice set of trade offs.

Mages constantly casting rain over a cistern or reservoir would be a handy way of building up their magical muscles and being useful at the same time. I'm imagining a wizard tower built into a hydroelectric damn constantly keeping it topped up.

[maximara]

Originally Posted by whswhs

The area of a single hex is 0.87 square yards. I usually take "one hex radius" to mean that single hex plus the hexes adjacent to each of its six sides, which is seven hexes or 6.09 square yards; two hex radius adds 12 more hexes, for 19 hexes or 16.53 square yards; three hex radius adds 18 hexes, for 37 hexes or 32.19 square yards. The formula for radius N is N(N+1)/2 + 1 hexes.

That differs from how Basic Set explains it on pg 239. Per the diagram the formula for hexes is 3r^2 - 3r + 1 or 3N(N-1) +1

It all depends on how the circle is placed on the hexagon. It is either a(√3)/2 for circle inside hexagon or ((3*√3)/2)*a^2 for hexagon inside circle.

If the area of a hex is exactly 1 yd then we have √(1/2.598) or 0.6204 for the circumradius

[whswhs]

Originally Posted by maximara

That differs from how Basic Set explains it on pg 239. Per the diagram the formula for hexes is 3r^2 - 3r + 1 or 3N(N-1) +1

It all depends on how the circle is placed on the hexagon. It is either a(√3)/2 for circle inside hexagon or ((3*√3)/2)*a^2 for hexagon inside circle.

If the area of a hex is exactly 1 yd then we have √(1/2.598) or 0.6204 for the circumradius

If you break the hex up into twelve triangles you can determine that its area is approximately 0.87 times the square of the distance between adjacent hex centers.

[maximara]

Originally Posted by whswhs

If you break the hex up into twelve triangles you can determine that its area is approximately 0.87 times the square of the distance between adjacent hex centers.

So basically the circle is inside the hexagon ie A= 2 * √(3) * R^2

[Polydamas]

I would introduce consequences if someone tried to keep a weather spell going for months at a time. Two relatively tame ones would be the local mana becoming Aspected to the opposite element or the cost of the spell steadily increasing.

Originally Posted by maximara

That differs from how Basic Set explains it on pg 239. Per the diagram the formula for hexes is 3r^2 - 3r + 1 or 3N(N-1) +1

It all depends on how the circle is placed on the hexagon. It is either a(√3)/2 for circle inside hexagon or ((3*√3)/2)*a^2 for hexagon inside circle.

If the area of a hex is exactly 1 yd then we have √(1/2.598) or 0.6204 for the circumradius

I was going to cite p. B239 as well, but now I am thinking ... could it be that a two-yard radius is represented on the battle map as seven hexes but actually fills another ring of half-hexes? It does seem like "a two-yard radius is a circle four yards across" is the natural meaning.

[Pursuivant]

The Snow spell is another hack for getting lots of water cheap if you can defer instant gratification.

Each point of energy yields 1 inch of snow over a 15 yard radius, providing 916,088 cubic inches or 3965.761 gallons of snow. Assuming a snow ratio of 10" snow = 1" water, that gives you a bit more than 396 gallons of water per point of energy.

The drawbacks are that you need to cast Snow when the temperature is below 32 *F, it takes an hour for the snow to fall, it falls over a large area, and it must then be heated to convert it to water. Even so, a great deal for weather mages in drought-prone regions where the seasonal temperatures drop below freezing.

Either cast Snow on the fields each winter and let natural percolation during the spring runoff top up the local aquifers, or build special cone-shaped structures which use gravity to channel the snow to a central point where it is heated, pipes or enchantments below the melting chamber transport the meltwater to where it is needed.

If the GM is indulgent about allowing snow to have its realistic physical effects, mass castings of Snow are also useful for collapsing buildings, triggering avalanches, and blocking or burying things.