copyright 2001-2002 by Linda "Sweetwind" Tam
Contents:I once promised to discuss Abode's tides (way back in Sendings #9). Today, after much procrastination, I'll finally start to make good on that promise!
Let's start out with the basics about tides. First off, as you probably already know, tides are caused by the massive bodies near the planet in question - on Earth, primarily the Moon, and to a lesser degree the Sun. On Abode, tides are due primarily to the two moons and the Daystar.
I want you to understand exactly how these bodies cause the tides, to help you understand how the tides on Abode will be different from Earth's. So let me start with the two forces involved, and work my way towards the tides themselves. Here goes: First, imagine grabbing someone else's hands in yours and swinging yourselves around as fast as you can, like a fast "ring-around-the-rosies" dance. Your hair streams backwards behind you as you whirl around; at least it does if you have nice long hair. We call that force pushing your hair backwards centrifugal force. Centrifugal force operates on the Earth and the Moon also, as they do their celestial dance together.
While you spin around with your partner, you can feel the centrifugal force trying to tear you apart from each other. So hold on tight! Centrifugal force also tries to tear the Earth and the Moon apart, but they don't have linked hands. What holds them together? The answer is what we call gravitational force. As was discovered by Isaac Newton in 1675, there will be a force between two masses that depends on how massive each body is, and how far apart they are. For the Earth and the Moon, or for any two bodies in stable orbit, the gravitational force exactly cancels out the centrifugal force, and they spin around each other in an unchanging path.
At least, the forces exactly cancel out at the center of each body. The centrifugal force is constant throughout each body. However, since the gravitational force depends upon the distance between the masses, the gravitational force is different in different parts of the body. In the case of the Earth, the gravitational force is stronger than the centrifugal force on the surface of the Earth facing the Moon, while the centrifugal force is stronger on the surface of the Earth facing away from the Moon. If the Earth had hair that was free to flow, it would whip out on the side away from the Moon! It doesn't, but it does have something else on its surface that flows: water. Any water farther from the Moon than the center of the Earth is flung by centrifugal force in the direction away from the Moon. This results in tidal currents that actually cause water to drain away from the Moon.
On the other hand, any water closer to the Moon than is the center of the Earth will be attracted, gravitationally, to the Moon more strongly than the Earth as a whole. It will flow towards the Moon. For my Figure 1 I'll drag out the standard diagram shown in every textbook discussion of the tides, which shows the two tidal bulges that occur as water flows in response to these competing forces.
Since tidal currents are responsible for the changing water level you see at the shore, tides don't affect small bodies of water. You will not see the level of beer in your glass rise and fall due to tidal action, unless you've already drained the glass too many times <g>. Tides occur only when the body of water spreads far enough around the Earth - or whatever planet - to be affected differently by gravitational and centrifugal forces at widely different points on its surface. Also, the tidal currents have to be able to flow freely. The ancient Greeks did not have a word for "tides" - they lived on the Mediterranean Sea, which is mostly landlocked. Tidal currents do try to flow through the Straits of Gibraltar from the Atlantic, but not enough water makes it through to form a perceptible tide on the shores of Greece. Tides on Abode, therefore (consulting Plate 13 of the revised Wolfrider's Guide, which shows a map of the planet), would not affect the Muchcold Water, which is a great lake or a small landlocked sea. However, tides should be present in all the other seas and oceans: the Vastdeep Water, the Idyl Water, Stormsea, Skyglass, and the Redmist Ocean. Of course, the tides at any particular shore are dependent on local geography. The long peninsula that guards the bay at the city of Outset, on the continent of Hearthstone, probably diminishes the tides experienced there by presenting an obstacle to the free flow of tidal currents. On the opposite side of Hearthstone, meanwhile, the city of Anvil probably experiences large water level changes, since it faces the open ocean. (As an aside - we are told the legendary explorer Cam Triompe is from Hearthstone, but his port of origin is never mentioned. Dare I speculate that Outset, being sheltered so nicely by that peninsula from weather as well as tides, would be a great port town, like Earth's San Francisco, and an excellent candidate for Cam's hometown?)
The usual way to predict the tides is to use harmonic analysis, in which the actual tide experienced at a location is broken up into all the parts, or constituents, that come together to cause it. Let me take this process backwards and start with the major constituents to build some tide charts. As you can see from Figure 1, the height of the tide at any given place on Earth depends primarily on where the Moon is - rising, overhead, and so on. So, what is called the Principal Lunar Semidiurnal Constituent is shown in Figure 2. Semidiurnal means twice a day, since there are two high tides a day - one corresponding to each tidal bulge. Figure 2 shows about two days' worth of tides, starting at low tide: there are two high tides the first day, then two high tides the second day.
The next major constituent in a tide chart is the Principal Solar Semidiurnal Constituent - due to whether the Sun is rising, overhead, and so on. The Sun generates a pair of tidal bulges on the Earth just as the Moon does. The bulges are smaller than the ones the Moon causes, not quite half as high; these are shown in Figure 3.
Combining those two constituents together, you would expect that when they are in synch with each other
(when the Moon is new or full), the Sun's bulges will reinforce the Moon's bulges and you'll get a really
high tide pattern (Figure 4).
When they're out of synch (when the Moon is in its first quarter or last quarter),
the Sun's bulges will partially cancel out the Moon's bulges (Figure 5).
Piece of cake, right? So let's look at
the actual first-quarter tides from a city on Earth chosen totally at random - let's say ... Poughkeepsie (see Figure 6).
(Of course, Poughkeepsie is on the
Hudson River,
not the Atlantic Ocean. But tidal currents do backwash up major
rivers and cause tides near their mouths.)
It looks like that smooth sine wave we were expecting, except, if you look closely, you'll see that the second
high tide each day is a little bit higher than the first... why is that? This is due to the third primary component
of Earthly tides, which is called the Lunisolar Diurnal Constituent. (Don't blame me, I didn't make these names up!
See Figure 7.)
Diurnal means it happens once a day, and lunisolar means it is caused by both the Sun and the Moon.
This constituent accounts for the declination of the Moon and the Sun.
That is, since the Earth's axis of rotation
is tilted with respect to the way the Moon orbits the Earth and the Earth orbits the Sun, you may see a different
part of each bulge as the Earth spins. Figure 8 illustrates this effect for the Moon's declination.
This constituent will be larger or smaller depending on where you are on the Earth's surface.
Adding a Lunisolar Diurnal Constituent to the theoretical tide chart of Figure 5 gives us Figure 9, which looks
a lot like what we saw in Poughkeepsie.
The diurnal constituent shows up much more strongly in the tide chart
for my home port of Long Beach, California (Figure 10).
And now I have rattled on too long for this time, but at least I've summarized the three main components of an Earthly tide chart. There are actually at least 37 constituents that need to be used to predict the tides, so we've only scratched the surface here. But you can see that we get reasonable-looking charts with only these three - just don't try to sail your boat by them. However, on Abode we'll need FOUR main components to draw up a tide chart. Yes, instead of a Principal Lunar Semidiurnal Constituent, we'll need both a Principal Maternal Semidiurnal Constituent and a Principal Filial Semidiurnal Constituent. Join me when I continue with part 2 in the next issue of Sendings and, meanwhile, you are invited to figure out how I coined the names of those two new constituents.
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© 2002 linda_tam@alumni.hmc.eduLast updated on January 5, 2003
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