Friday, July 1, 2016

Possibly onto something

Trying to streamline the determination of swell in a given area of the game world's ocean.  Every other part of this wave project so far was fairly straightforward, each piece following on the last naturally, and merely requiring hours of patient number crunching and typing out into tabular form to produce.  Turning a whole world's worth of weather into a table takes a little more thought, and a little effort into making it elegant and easy to use.  More so than just rounding off heights to whole numbers, anyway.

At first, I was thinking that I would simply use the icosahedral world map template that came with the AD&D 2nd Edition World Builder's Guidebook (now available on; I've never regretted buying the print version, and I highly recommend the PDF for anyone interested in world building). For an Earth-sized world, that comes out to 600 miles per hex.  I'm making the call that weather systems generally run about that size (Wikipedia says storms are in the vicinity of 60-1250 miles diameter, so not far off).  For my purposes here,  a weather check (determined through whatever method, but here mostly concerning wind speed), covers a 600 mile hex, at least over the ocean where terrain doesn't break it up.

Next, starting with the 2d6 wind speed roll used in the D&D Expert rules, I figured the probabilities of high winds across multiple 600 miles hexes.  Swell is produced by high winds, so when looking at multiple hexes, you really only need to worry about the highest wind among them.  I did the math by hand to figure out the new probability curves for a 2 hex region, but somehow couldn't get it to work out for more than that.  I still don't know what I was doing wrong.  Luckily, the Troll Dice Roller and Probability Calculator was there, and didn't take too long to figure out.  Thanks, Torben Mogensen; Troll was invaluable.

My idea at this point was to look at all the ocean in a straight line out from a given point in all directions and use that number of hexes to figure out what swell was hitting that point, thus taking into account every direction it could come from and the fetch in those directions.  This way, an island or a point on the tip of a peninsula is more likely to have a large swell than a point in a protected bay or inland sea. 

I decided to look at the Hawaiian Islands to see how well this system maps out to the real world.  The Hawaiian Island chain fits pretty much into a single 600 mile hex, at least the main islands do.  There are six hexes of ocean surrounding that, and 12 more surrounding those, so I worked out the probability curve for winds across 19 hexes.  And that's where the problem came in.  With 19 hexes, there's an 80% chance of winds of Beaufort number 11 or 12, and since it's only three hexes out, the waves have little time to dwindle down.  Hawaii is a surfer's paradise, but swells over 20 feet (growing higher as they start running inshore) are not an everyday thing.  I distinctly remember, when I was stationed there, going to the beach and not being swept away or pounded by massive plunging waves (I did see some some frighteningly large ones, though, on occasion).  And those 19 hexes aren't even all of the ocean hexes that could possibly be the source of a Hawaiian swell.

But, I think using a larger hex might work.  A 1200 mile hex would mean fewer chances of a really high wind result, and also double the average distance the swell would travel, giving it time to diminish to a more reasonable (from my perspective) level.  I'm going to work some numbers for a few different real-world areas at 1200 miles per hex and see where that takes me.

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