Time and Tide, Part One
Let’s take a look at the physics behind our tides using an iron barbell to demonstrate some of the principles that affect them. The better we understand these concepts, the better chance we have of correctly estimating our local tides during a voyage, should we need to.
Imagine, for a moment, that I have a barbell—two iron balls of equal mass held together by a steel bar. If I want to balance this barbell on a fulcrum, I have to place the fulcrum at the center of the mass between the two iron balls. Now, if I am able to throw this barbell so that it tumbles end over end, the point around which the balls will pivot is the same point on which I had positioned my fulcrum ( Figure 1). This point on my steel bar is called the barycenter, which is simply the center of gravity of the two balls of the barbell. The centers of mass of the individual balls describe a circle around the barycenter as the barbell tumbles through the air.
Now, if I make one of the iron balls smaller, in order to balance the barbell, I must move the fulcrum closer to the larger of the iron balls. And if I again throw the barbell so that it tumbles end over end, the point around which the two balls pivot is the again same place that we placed our fulcrum. Because our barycenter is now closer to the larger ball, the center of mass of the larger ball will inscribe a small circle around the barycenter, while the center of mass of the smaller ball will inscribe a much larger circle around the barycenter.
Now, if I make one of the iron balls really small, say onequarter of the diameter of the larger ball, then in order to balance the barbell, I would actually need to move the fulcrum inside the larger ball, if that were possible. But if I were able to do that and once again throw the barbell so that it tumbled, the smaller ball would make a very large circle around the barycenter. And because the barycenter would actually be somewhat inside the larger ball, the center of gravity of the larger ball would wobble around the barycenter, in the direction opposite the smaller ball ( Figure 2).
If you’re wondering how all this relates to tides, let’s call the larger iron ball “earth” and the smaller one “moon.” We’ll call the steel bar “gravity” (and make it invisible). Just like before, the smaller ball (the moon) travels in a large circle around the barycenter of the two balls, and the larger ball (earth) wobbles around the barycenter, which happens to be just a little bit inside the larger ball. Now in this case, the larger ball (earth) is mostly covered in water. The moon’s gravity pulls the earth’s
water toward it, and so a standing wave of water forms under the moon. As the earth wobbles away from the moon around the earth-moon barycenter, an equal and opposite standing wave of water forms on the part of the earth facing away from the moon as well ( Figure 3).
From the perspective of a person standing on the earth’s surface, as the earth rotates on its own axis under these two standing waves, the water gets higher, then lower, then higher, then lower, every time the earth rotates under the moon. This is an idealized model; in fact, the shape of the different ocean basins change this standard wave-form profoundly, but let’s stay with it for just a bit more.
While the gravitational balance between the earth and the moon is the single most important factor affecting our tides, it is not the only one. Our sun also plays a critical role. The sun is much larger than the moon, but it is also much, much farther away, so it has a smaller effect on our tides than the moon does, but it is nonetheless significant.
When the earth, moon, and sun are in line, whether at the new moon or at the full moon, the sun’s gravity works in concert with the moon’s, and the earth’s tides experience the highest highs and the lowest lows of the month ( Figure 4). This is called a “spring tide.” The name can be misleading as it suggests that it is a seasonal effect, but it’s “spring” as in a fountain of water, not the season. These tides occur twice each month all throughout the year.
When the moon and sun are at right angles to each other as seen from earth (at the quarter moons), the sun’s gravity partly cancels out the moon’s, so we see lower high tides and higher low tides. Called “neap tides,” these also occur twice each month throughout the year ( Figure 5).
So, based on all of this, we can begin to make some assumptions about the times of high and low tides in relation to where the moon (and to a lesser extent, the sun) is in our sky. When the moon is low on the horizon, whether rising or setting, we would expect the tide to be low; when the moon crosses our meridian, whether to the south or to the north, we would expect the tide to be high. However, this is only true in some parts of the world.
Here we see Seattle ( right), on the day of the new moon, when the sun and moon are close enough to each other in the sky (as seen from the earth) to be gravitationally considered a single object.
Immediately we notice that the high tides occur about an hour before sunrise and sunset. The higher low tide occurs about an hour before the moon and the sun cross our meridian; the lower low tide occurs about an hour before
they cross the opposite side of the world from us. All of this is basically opposite of what we should expect, based on what we know of tides so far.
So what is happening? Imagine a washtub half filled with water. Now imagine sloshing that water around in a circle. Around the edge of the washtub, the level of the water will rise and fall as the water sloshes around. But at some point in the middle of the washtub, the level of the water will remain the same while the rest of the water rotates around it. This place where the water stays the same level is called an amphidromic point; the sloshing around the washtub is called amphidromic rotation. “Amphidromic” means, roughly, “water running around in a circle.” We see this most frequently in places (like the West Coast of the U.S.) that have very steep continental shelves relatively close to shore, as the tidal standing waves fill and empty the large ocean basins.
In the world’s oceans there are specific amphidromic points around which the ocean tides rotate. The amphidromic point driving Seattle’s tides happens to be off the Oregon coast.
How can we know if amphidromic rotation is strong enough to significantly
influence a local tidal cycle? As a very general rule, if our local tidal wave-form is a “standard” semidiurnal high-low-high-low, the altitude of the moon will likely yield a good estimate of the tidal height at a given moment. If you are in a place with either diurnal or mixed-semidiurnal tides, however, more information is probably necessary.
Every body of water, from oceans to lakes to cups of coffee to our own bodies, experience tides. The amplitude of the tide is largely determined by the volume of water in that body. As a very general rule, the farther away you are from the equator (within a given ocean basin), the greater the amplitude of the tides. An exception to this is the Arctic Ocean, which has a very small range of tides. However, this makes sense as the Arctic Ocean it is at the “hub” around which the global standing tidal waves rotate. In addition, the Arctic is a rather small ocean basin that is largely covered by ice for most of the year.
In our next installment we will dive into a few very specific examples of how tides are calculated and how they can be applied to a coastal and open-ocean voyage. Until then, good watch!
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