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Why No Predictions for Theoretical Tides?
by Duane Dunkerson

Why? There is the vagabond Moon, constant Sun, far Jupiter, and an inconstant Earth.

The earthly and astronomical effects on the tides are so complex that a theoretical finality is impossible. Meanwhile, periods of tidal oscillations are predictable. At least the oscillations could benefit the business interests. Seagoing commerce had to have some approach to prediction for the tides.

The first tide predicting machine was designed by Lord Kelvin. It went into operation in 1873. By 1910 the US Coast and Geodetic Survey had the Coast and Geodetic Survey Tide-Predicting Machine No.2. It was eleven feet long, two feet wide, and six feet high with a weight of 2,500 pounds. Thirty-seven elements bearing on tidal prediction were represented by components of the machine. This machine was used to attempt to predict the tides. Accompanying the tides are currents. Finding the velocities of these currents was also attempted by Machine No. 2. These velocities are a sum of a series of harmonics of periodic elements of the tides.

By 1965 the Table of Tides was still typed by hand. Then in 1973 predictions were attempted by computer. This involved two walk-in closets of punch cards. In 1979 was inaugurated an interactive phone dial-up prediction service. PCs got into the act by 1987. Now the seven volumes of the Tide and Current Prediction Tables are on one CD.

The most recent water levels, within 6 minutes, can be obtained by phone. One can also get the information via satellite. A tidal gauge that finds unusual water heights will automatically send such notice to the satellite for retransmission to various ground stations.

This is as close as it gets to knowing the tides. Michelson in 1913 got microscopically close to tidal action. He used pipes, one set N-S, another set W-E, to measure tides through a microscope. He saw changes as little as a variance in water level of 1/1000 of an inch. These water heights were about 69% of what theory would have predicted.

Michelson observed the usual decreases in water levels, the ebb tides, and the increases in water levels, the flood tides. There are two tides per day, two high, two low. Between a high and a low there is usually six hours. The average interval between the same high tide is about 24 hours and 51 minutes. This corresponds to two successive southern passages of the Moon. One tide comes ahead of the Moon on the earthly side towards the Moon. Another tidal outward bulge of water is to be found on the opposite side of the Earth.

The Moon pulls on the Earth. The water can freely flow and does so, to and from the sublunar point. Because the earth rotates, the bulges of water move in waves. The bulge moves ahead of the Moon because of friction. That is, the Earth rotates faster than the Moon revolves. From high tide to high tide is called the establishment of port. For New York, the e of p is on average at 8 hours and 13 minutes.

Even with a locale pinned down, the water heights of tides varies since the Moon in its orbit is inclined to the ecliptic. Because of this, for half a month the Moon is north of the Earth's equator and for the other half, it is south of the equator. There is then a smallish second tide. Twice a month, as the Moon appears to cross the equator, the second tide is not observed.

There are also brief periods when the water isn't going anywhere. There is not ebbing or flooding during what is called slack water. This doesn't mean that the Moon has stopped working gravitationally. In any event the Moon does not lift the water toward it. It can't do such lifting when its lunar force is nine million times weaker than the force of Earth's gravity at the Earth's surface. The tides are produced by a component of the tidal force of the Moon which draws water along the earth's surface toward sublunar and antipodal points.

If the Earth's surfaces were completely submerged by an ocean of unvarying depth and if the Earth were to face the Moon at all times, there would be tides two feet high. But, of course, the oceans are of varying depth. Shallow water slows wave travel. Times for high water of two ports 2/10 of a mile apart may differ if one has shallower water than the other. Bigger tides arise in water that is more shallow. The Bay of Fundy has tides of 50 feet. Other high tides have been found on the east coast of Patagonia, the Bristol Channel, the coast of Normandy and in the Hudson Strait. In New Brunswick at St. John, the river, also called St. John, flows upstream during flood tide.

In addition to rivers, lakes are also affected by the lunar tide action. These are effects usually easier to detail. Lake high tides are opposite the Moon when the Moon is below the horizon. If the Moon is up, the water of the lake follows the Moon around the shore. Low tide goes along the opposing shore. Lake Michigan, for example, has a tidal difference of 1and 3/4 inches.

It is not only the Moon that rises above the lakes of Earth. The Sun plays a role in the tides too. At new or full moon there are higher tides as Sun and Moon act along the same line. At first and third quarter (quadrature) of the Moon, there are neap ("neap" - from the Greek for "scanty") tides.

Neaped or not, the Moon comes in closer at perigee. It is 10 per cent closer and then the tides can be 20% greater. Now, by this time this should be enough to show that the tides don't allow for prediction. Overcome these various factors and then there is Jupiter. Yes, Jupiter causes tides. They are tiny. Nevertheless we are speaking of tides. Tides are tides. Jovian tides are 10,000,000 less effective than the familiar lunar causation. The solar contribution, by the way, is 5/11 of the lunar one. The Moon, Sun, Jupiter, and other contributors to celestial mechanics for accurately locating all the generating forces are simply not enough. You need to conduct observations per locale for at least more than 18 years.

In some matters the past provides a comfort zone of predictability. We know sometimes what happened first then what came next. Unfortunately the lack of prediction involving tides reaches back to ancient times. Actually it is a subsidiary effect of the tides that has thrown off the calculations for the occurrences of ancient eclipses. The eclipses happen later than we would suppose. This is because the earth's rotation is slowing due to tidal friction. At the same time(s) the Moon is increasing in speed in its orbit. The tidal drag is two billion horsepower.

For more uncertainty as to the when or what tides were or could do, one can go much, much further back in time as Asimov did in his speculation that the tides played the key role in the evolution of life. The tides challenged some of sea life by tossing then up onto land twice daily. To change you need change - like no credit extended unless you have credit. The agents of change became changed. With the Moon closer such a long time ago, the tides were more pronounced. Asimov speculated that perhaps one needs a sea and Moon and tides. Without these in existence, evolution like ours could not come about.

It is like us, contrarily, to look ahead and not so far behind. One can attempt to predict when there will be a new moon by gathering your own tidal data. During new and full moon high tides get higher and low tides get lower. Measurement of your local tides can lead to a prediction as to when the next new moon should appear. If you could stick with the measurement for around 18 years, you could become fairly accurate in those predictions.


   

 

   
 

 

 
 
 
 
 
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