The sine wave equations don’t correspond to precise astronomical measurements; they’re just an approximation that gives you a good-enough graph.
Typical tide ranges around the coastline of Ceannis are 30-35 feet. If anyone wants to calculate what sizes and distances are most reasonable for the moons that create them, go for it. (If they’re narratively inconvenient, I can always come up with a magic-based excuse.)
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Thorn: Didn’t they teach you how the tides work in school?
Leif: I guess it’s not something we have any use for . . . Sønheim is effectively landlocked.
Sønheim:
Tundra/desert that nobody can go over
Mountains that are hard to go over
Polar ice sheets that nobody wants to go over
Thorn: Okay, so these two sine waves represent the orbits of the moons. Add them together. When they’re aligned so their combined pull is strongest, that’s HIGH TIDE.
The pull gets steadily lower until LOW TIDE.
Then the moons fall out of alignment. While they’re at odds, the tide levels off for a short period — that’s SHELF TIDE.
Moon = 2sin(x+90)
Moonlet = sin(2x-5)
It’s risky to build too close to the ocean . . . but important for sea travel. Usually we build out to the shelf tide line, and elevate. A boardwalk like this gives people something to stand on, even when the tide is highest.
Leif: Ohhh! So this is a “boardwalk” . . . and it’s elevated! I understand the meaning of one of your traditional ballads much better now.
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9 Comments
What about sun?
Same as in reality – it makes the high/low tides slightly more intense (spring tides) when it lines up with them, and moderates them (neap tides) when it’s at an angle.
The difference is minimal when compared to the overall force of the lunar tides, so most people don’t consider it, unless they’re doing detailed work/research involving the ocean.
Funny. I don’t do detailed work/research involving the ocean, I don’t even know how big the difference is, but I still know about the phenomena.
…see, that’s exactly what I mean. You don’t know the exact difference (and neither do I) between a spring high tide and a neap high tide. Unlike the difference between high tide and low tide, it’s not big enough that we ever need to take it into consideration.
At least on Earth, the sun’s gravitational effect on tides is almost negligible compared to the moon’s. I say almost, because spring tides are a thing.
So, Leif…are you hoping Thorn will bring you back here at low tide? ;D
“Under the boardwalk, out of the sun~”
I’ve got some very bad news for those equations. While they could describe the size of the tides on a given day, the actual tides are caused by rotation of the planet under the tidal bulges that you describe there. Well, unless the moonlet whips around twice a day(I assume not your intention) you still only get two high tides a day. When the moons are aligned(either together or directly opposite) you get extreme tides, but when they are 90 degrees off from each other, you’ll get those shelf tides.
So you’ll end up with Moon=2sin((360/T)x-offset) where T=.5*(1+1/month) days. Month in this case is just the time it takes the moon in question to return to the same place against the background stars. Schematically, that graph is still right(and the numbers used do look good for an explanation) but the periods being much closer in size mean that you get many more oscillations before they line up again for another very high tide.
As far as getting the size and range of the moons from the tides, it ends up depending on the size of your planet(both diameter and mass used separately) and the actual geography, since things like resonance end up affecting tides more than you would think(just look up the Bay of Fundee).
From the curves, the little moon is in 2:1 resonance with the big moon, making things rather neat.
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