More Options

Why We Are Unmoved as Oceans Ebb and Flow

Article

Paul Quincey

Volume 18.5, September / October 1994

If you think your body might be feeling the forces that cause the tides, think again.

“The moon moves the oceans, our bodies are 70 percent water — what must the moon be doing to our bodies?” This sort of question frequently crops up in the context of possible lunar influences,1 and it deserves a well-reasoned reply. The short answer, “Very little indeed,” is quite hard to justify in only a few words, and this can lead to dismissals that fudge the real issues. Apart from the sin of obscuring the truth, it is a shame to miss an opportunity to explain a piece of science of widespread interest.

A Brief History of Tides

The tides have had a rather special place in the history of science. On the purely practical side, the ability of seafaring people to predict times and heights of high tide is extremely valuable. Tide patterns can be complex, but prediction is always possible for any particular place just by carefully analyzing records of past tides. Such an analysis must have been an early instance of patient observation yielding useful knowledge about the physical world. Ancient civilizations undoubtedly noticed a link between tides and the moon, both its position in the sky and its age in the month.

From a more theoretical viewpoint, this astronomically connected movement of the sea begged for a scientific description, and some of the greatest names in science—Kepler, Galileo, Newton, Kelvin, Darwin (George Darwin, the son of Charles, the naturalist)—have applied their minds to the subject. Today, accurate tidal predictions are available in great annual tables for hundreds of coastal sites around the world, and it would seem that the tides have respectfully yielded all their secrets. Actually, these tables are still made by extrapolating from past records, and theory has only been able to add sophistication to the old method.

It is not yet possible to generate good tide tables starting from first principles, not because there are any fundamental problems with the theory, but because this would need extensive surveys of the seabed, together with truly formidable computing power. As perfectly good tables can already be made, this exercise has hardly been seen as one of the key problems of twentieth-century science. An unfortunate consequence of this state of affairs is that tidal theory has become something of a backwater, poorly understood by the general public and probably most scientists. Before we consider the effects of tidal forces on people, though, we need a decent understanding of why the seas respond as they do.

All You Need to Know About Tidal Forces

Fig1

Figure 1. The strength and direction of gravitational force on objects near a sphere, such as the sun. For clarity only one plane is illustrated.

Tidal forces, the basic cause of tides, were first outlined by Isaac Newton in his mighty work Principia. Their simplicity, as a natural consequence of Newtonian gravity, belies the complexity of the real tides that result from them. We can thus also admire Newton’s skill at picking convenient examples to illustrate his theory, while leaving a mass of inconvenient data for lesser mortals to explain.

The forces are best described with a few diagrams.

If we represent the strength and direction of gravitational force with arrows, Newton’s inverse square law means that the forces around a sphere, such as the sun, vary like those in Figure 1.

Fig2

Figure 2. The gravitational forces on the surface of a nearby sphere. The average force throughout the sphere is represented by the large central arrow.

If we place another sphere, such as the earth, some distance from the sun, the forces from the sun’s gravity must vary slightly throughout its volume. This is shown in Figure 2. In particular, the near-side forces are larger than the far-side forces, and the forces are not quite parallel to one another.

Now the earth responds to the sun’s gravity by orbiting around it; and because it moves as a solid body, the whole earth must move according to the average gravitational force involved. The average force, represented by the central arrow in Figure 2, is therefore what is required by every part of the earth to keep it moving in orbit. The earth’s motion exactly matches this average force in the same way that an orbiting astronaut’s motion matches the earth’s gravity, leaving him weightless.

If we now plot the differences between the average force and the actual force from point to point, we are left with much smaller residual forces that tend to distort the earth rather than move it. These residual forces are the tidal forces, and they form a sort of lemon-shaped pattern, like that in Figure 3.

Fig3

Figure 3. The pattern of tidal forces (the differences between the actual force and the average force) on a spherical body.

The same diagrams and reasoning apply to any two celestial objects, the size of the tidal forces on one body being determined simply by the mass and distance of the other. It turns out that the moon creates tidal forces on the earth roughly twice as large as those from the sun, while no other object ever causes tidal forces on the earth remotely as large as the moon’s or the sun’s. We can imagine, then, as the earth turns, one lemon shape aimed at the moon and a smaller one aimed at the sun. From the earth’s point of view, the larger one swings around every 24.8 hours and the smaller every 24 hours, but as the two ends of the lemon are very similar the cycles are effectively 12.4 and 12 hours long.2

The forces are best regarded as local variations to the earth’s gravity—everything’s weight varies slightly, and the vertical (as defined by a plumbline) swings a little to and fro. It is worth pointing out explicitly that water is neither more nor less subject to tidal forces than, say, apples or granite, and that there is no need for a more mysterious affinity to the moon than straightforward Newtonian gravity.

A Naive Theory of Tides

There is a tempting line of thought that runs like this. With tidal forces as they are, the earth will assume a slightly lemony shape. The solid earth will distort a little, but the oceans, being more mobile, will move much more. There will then be two bulges of water traveling westward around the earth with the moon, causing tides every 12.4 hours. The sun will produce smaller bulges, which reinforce the main tides at full moon and new moon (spring tides), but reduce them at half moon (neap tides).

This view is very satisfying, as it correctly describes the main features of real tides in many places. It is also profoundly wrong, for at least one obvious reason. Imagine one of the water bulges moving westward across the Atlantic Ocean. What would happen when it meets America? It would not travel overland to resume its journey in the Pacific; nor would it turn sideways, rushing along the coast to find a way through and keep to its westward schedule. It would do what any ripple in a pond would do: bounce back. So we suddenly have our bulge traveling the wrong way, ready to interfere with the next one coming along, and indeed the echoes from many earlier bulges. In short, the continents get in the way so much that the two-bulge picture is a nonstarter.

A More Realistic Theory of Tides

The bad news is that at this point we must abandon hope of an elegant description of real tides. The good news is that computers have been invented; therefore, when we ask “How would this ocean respond to these forces?” we can feed numbers and hydrodynamics equations into a computer and let it work out an answer. We also have a huge amount of information about tides at specific places, which, after all the theorizing, is what we need to compare with our answer to see if our idea is any good.

For the most elementary model, we can pretend that the tides repeat themselves exactly every 12.4 hours, which is not so far from the truth and makes the situation much more manageable. We then describe the shape and the depth of the earth’s oceans as closely as possible given the capacity of the computer. Depth is very important, as it determines the speed at which waves of tidal water tend to travel. We remember that the earth’s rotation will affect movements of water (via Coriolis effects).

Figure 4 shows one such result, taken from a paper by Parke and Hendershott (1980). You will notice that there are many “bulges” of water giving rise to local high tides and that they are moving in various directions. This is completely different from the naive version, but it does not change the recurrence of local tides in the same 12.4-hour interval. Moreover, the sun is still likely to increase the size of the tide around full moon and new moon when it reinforces the moon’s tidal force, so we still have spring and neap tides. But we can see that in general things will be complicated, as indeed they are.

Fig4

Figure 4. The calculated distribution of high water ridges in the oceans at one particular time during a 12.4-hour tidal cycle, taken from Parke and Hendershott 1980. The circle above the map shows the position of the notional moon.

Such a model can be checked against data for islands in mid-ocean, but mainland sites are more difficult because shallow water slows and alters the tide in a drastic way. This result, then, is rather crude, but it is at least a realistic approximation to tides in the oceans.

It is good enough to make an important observation. The pattern of the tides in the ocean is almost completely unlike the pattern of forces creating them, because the continents prevent the simple lemon-shaped response. The tidal forces may as well be banana- or pear-shaped, because the oceans never have the chance to move accordingly. For any confined object on the earth’s surface, and that could be an ocean or a person, the overall pattern of forces spanning the globe is largely irrelevant. From the object’s point of view, the relevant feature is how the local force changes in time. Oceans feel the tidal forces as a succession of regular nudges, and the tides arise from the set of standing and traveling waves that these create.

Tidal Forces on People

We have already seen that there is nothing special about water in tidal theory—everything feels the same tilting and weight change. We can easily put numbers to these forces: in the most extreme case, an object’s weight will be 0.000035 percent less when the moon is overhead than when the moon is on the horizon (Cook 1964: Chap. 6), and in the course of the tidal period the “vertical” will change by no more than 0.00001 degree (Darwin 1901: 100). That is all there is to it.3 When you consider the weight change we experience during a meal (about 1 percent), as we move from place to place on the earth’s surface (about 0.5 percent), or as the weather changes (about 0.03 percent), it is no wonder that we don’t notice the first aspect. It is perhaps even harder to contemplate a way for our bodies to notice the tilting—to somehow remember that we tended to lean over by a few millionths of a degree 6 hours ago, while constantly moving about in the meantime. It would be utterly implausible to expect a living creature, or any organ within one, to detect tidal forces directly.

Why Are Tides So Big?

At this point you may have a nagging thought: if the relevant forces are really that small, why is it that the oceans move so much? What makes the oceans so different from people if the changes in weight and the tilting are the same for both?

The obvious difference is simply size. This makes no difference to the weight change, but a big difference when it comes to tilting. If we tilt a teacup by a few degrees, the tea will rise up the side by a few millimeters, but if we could tilt the ocean by the same amount, the rise would be enormous. This is true, but it isn’t the whole answer. For a start, the maximum rise and fall would still be less than 1 meter (Proudman 1953: 276), and tides can be larger than that, even away from the complication of continental shelves. What is more, we have seen that the tides do not simply follow the tidal forces—if the oceans do not form two bulges they cannot be tilting backwards and forwards on cue. The fact that the oceans are not able to respond to the tidal forces in the most direct way suggests that their movement should be much less than 1 meter.

The real anwer lies in resonance—the situation where an object with a natural (or resonant) frequency is moved by a force that varies at a similar frequency. They may seem slow by human standards, but oceans have natural frequencies at which they will rock backwards and forwards, or swirl around (when the rotation of the earth introduces Coriolis forces), after they are disturbed. The frequency is fixed by the depth and “length” of the particular ocean. If we look at the two broad types of open sea, above and outside the continental shelf, the respective depths are roughly 100 and 4,000 meters. The length scale at which they resonate with a period of 12.4 hours is roughly 4,500 km in the deep ocean and 700 km on continental shelves.4

These distances are remarkable, in that they are moderately close to some real sizes of ocean and continental shelf, while there is no particular reason that this should be so. When the tidal forces resonate with an ocean’s natural frequency, we would expect a large response. In practice, some deep oceans are close enough to resonance with the tidal forces to produce large oceanic tides in some places. This can only be put down to coincidences linking sizes and depths of seas to the length of the day, and they are coincidences that give us the large and interesting tides that we have. The largest tides occur when coastal features are close to resonance with the oceanic tides and so greatly amplify them.

Back to Bodies

There remains one tantalizing loose end. If the oceans can have large tides because their resonant frequencies make them especially susceptible to tidal forces, maybe human bodies can resonate in some way. Unlike the ocean resonance this need not be fortuitous, as we could thank evolution for developing such a resonator if it brought suitable advantages to living creatures.

Well, what would this resonator need to be like? There is a simple test. To confirm that a bell resonates, you hit it and it rings. To confirm that the oceans resonate, you can wait for an earthquake and see if the disturbance dies down in oscillations. To see if any part of the body resonates with tidal forces, you give it a push and see if it wobbles with a period of 12.4 hours. There is no known organ, gland, or arrangement of parts in the human body that behaves remotely like this.

In any case, we have seen that tidal forces for people are swamped by other forces nearer to home and by our own movements, which makes the resonance idea inherently less feasible than in the oceans. To cap it all, the energy available to a resonator from tidal forces will depend on its mass. In the case of the tides, the resonators driven directly by tidal forces are the deep oceans—for a human being the energy involved is entirely negligible. And last but not least, there is no good evidence that people actually do respond in any way to tidal forces.

The Answer

Finally, then, a brief reply to the question “What does the moon do to our bodies?” Very little indeed. The force that moves the oceans is a minute but regular tilting of the vertical, no more than one hundred-thousandth of a degree. The moon emphatically does not “pull on water.” Oceans move because their size makes the tilting more noticeable, and because the repetition time (12.4 hours) is by chance quite similar to their natural resonant periods. People are too small, nothing about us likes to wobble that slowly, and our bodily fluids are free to carry on regardless.

Notes

  1. Strangely, lunar tidal forces are often invoked to explain monthly rhythms, when the tidal rhythms are essentially twice-daily and twice-monthly. The moon may well have established a monthly influence on nocturnally related activities, as illumination at night changes dramatically through the lunar month, but that does not concern us here.
  2. Some explanations state that only the near-side end of the lemon shape arises for gravitational reasons, while the far side is due to centrifugal force caused by the motion of orbiting. This idea is transparently false, but that has never been sufficient reason for an idea to fade away unassisted. As far as I know, the explanation was first put forward by Oliver Lodge (1893: 364) late in the last century.
  3. It is usual when discussing tidal forces on people to consider “direct” tidal effects, that is, distorting forces similar to the lemon-shaped ones on the earth, rather than weight changes and vertical changes. These “direct” forces are extremely small. For a person standing under a full moon they amount to a redistribution of weight roughly the equivalent of moving a single bacterium from the person’s head to his or her feet. We are subject to similar “distortions” from terrestrial objects that are 10 million times larger than this; we don’t notice them either, so it seems safe to ignore the subject.
  4. For the sake of illustration I have used the formula

    resonant length = v(gd/2f)

    in both cases. v(gd), where d is the depth and g is the acceleration due to gravity, gives the wave velocity, while f is the frequency. The resonant length is thus half a wavelength.

References

Paul Quincey

Paul Quincey is a physicist at the National Physical Laboratory, Hampton Road, Teddington, Middlesex, TW11 0LW, United Kingdom.