*This article is about tides in the ocean. For the laundry detergent, see Tide (detergent).* The Bay of Fundy at high tide The same location at low tide The **tide** is the regular rising and falling of the ocean's surface caused by changes in gravitational forces external to the Earth. The primary changing gravitational field is due to the Moon while the secondary field is caused by the Sun. ## Types of tides
The maximum water level is called **high tide**; the minimum level is **low tide**. At any given point on the ocean, there are normally two high tides and two low tides each day. On average, high tides occur 12 hours 24 minutes apart. The 12 hours is due to the Earth's rotation, and the 24 minutes to the Moon's orbit. The 12 hours is half of a solar day and the 24 minutes is half of a lunar extension, which is 1/(29-day lunar cycle). The height of the high and low tides (relative to mean sea level) also varies. Around new and full Moon, the tidal forces due to the Sun reinforce those of the Moon. The tide's range is then at its maximum: this is called the **spring tide**, or just **springs**. When the Moon is at first quarter or third quarter, the forces due to the Sun partially cancel out those of the Moon. At these points in the Lunar cycle, the tide's range is at its minimum: this is called the **neap tide**, or **neaps**. The relative distance of the Moon from the Earth also affects tide heights: When the Moon is at perigee the range increases, and when it is at apogee the range is reduced. Every 7½ lunations, perigee and (alternately) either a new or full Moon coincide; at these times the range of tide heights is greatest of all, and if a storm happens to be moving onshore at this time, the consequences (in the form of property damage, etc.) can be especially severe (surfers are aware of this, and will often intentionally go out to sea during these times, as the waves are more spectacular than ever). In most places there is a delay between the phases of the Moon and its effect on the tide. Springs and neaps in the North Sea, for example, are two days behind the new/full moon and first/third quarter, respectively. The reason for this is that the tide originates in the southern oceans, the only place on the globe where a circumventing wave (as caused by the tidal force of the Moon) can travel unimpeded by land. The resulting effect on the amplitude, or height, of the tide travels across the oceans. It is known that it travels as a standing wave northwards over the Atlantic. This causes relatively low tidal ranges in some locations (knots) and high ones in other places. This is not to be confused with tidal ranges caused by local geography, as can be found in Nova Scotia, Bristol, the Channel Islands, and the English Channel. In these places tidal ranges can be over 10 metres. The Atlantic tidal wave arrives after approximately a day in the English Channel area of the European coast and needs another day to go around the British islands in order to be effective in the North Sea. Peaks and lows of the Channel wave and North Sea wave meet in Dover Strait / Pas de Calais at about the same time but generally favour a current in the direction of the North Sea. The exact time and height of the tide at a particular coastal point is also greatly influenced by the local topography. There are some extreme cases: the Bay of Fundy, on the east coast of Canada, features the largest tidal range in the world, 16 metres (53 feet), because of the shape of the bay. Southampton in the United Kingdom has a double high tide caused by the flow of water around the Isle of Wight, and Weymouth, Dorset has a double low tide because of the Isle of Portland. Also there is only a slight tide in the Mediterranean due to the narrow connection with the ocean.
## Tidal physics If we ignore external forces, the ocean's surface defines a geopotential surface or geoid, where the gravitational force is directly downward and there is no net lateral force and hence no flow of water. Now add external, massive objects such as the moon and sun, which move relative to the earth. These massive objects have strong gravitational fields and the relative movement results in strong changing gravitational fields. It is these changing fields that drive the tides. Gravitational forces follow the inverse-square law (force is inversely proportional to the square of the distance), but tidal forces are proportional to the cube of the distance. The much greater distance of the Sun makes its tidal forces on the Earth much smaller than the Moon's (about 40% as strong). It is easy to understand the mechanism of tides by considering that the gravitational pull exerted by the moon (or sun) on the centre of mass of the solid earth is different from the pull on the body of water at the surface. Towards the moon (or sun) the water is closer than the solid earth so it is pulled more and rises. On the opposite side of the earth, facing away, the water is farther than the solid earth, so it is pulled less and moves away from earth, rising as well. On the lateral sides water and earth are pulled equally, but water is drawn away by the rise on the sides towards and away from the moon (or sun). Since the distance between centre and surface of the earth is equal towards and away from the moon, the forces creating both high tides are approximately equal. Since the moon rotates around the earth in one lunar day (24 hours, 48 minutes) each of the two bulges travel around at that speed, leading to one high tide every 12 hours 24 minutes. The theoretical amplitude of **oceanic tides** is about 1 metre at the equator, but the real value differs considerably, not only because of global topography as explained above, but also because the natural period of the oceans is rather large: about 30 hours (by comparison, the natural period of the Earth's crust is about 57 minutes). This means that, if the Moon suddenly vanished, the level of the oceans would oscillate with a period of 30 hours with a slowly decreasing amplitude until the stored energy dissipated completely (this 30 h value is a simple function of terrestrial gravity and the average depth of the oceans). Because the Moon's tidal forces drive the oceans with a period of about 12.42 hours (half of the Earth's synodic period of rotation), complex resonance phenomena take place; the main outcome of which being that the average tidal lag is six hours (which means low tide occurs when the Moon is at its zenith or its nadir, a result that goes against common intuition). Tidal lag and the transfer of momentum between sea and land causes the Earth's rotation to slow down and the Moon to be moved further away in a process known as tidal acceleration.
## Tides and navigation Tidal flows are of profound importance in navigation and very significant errors in position will occur if tides are not taken into account. Tidal heights are also very important; for example many rivers and harbours have a shallow "bar" at the entrance which will prevent boats with significant draught from entering at certain states of the tide. Tidal flow can be found by looking at a "tidal chart" for the area of interest. Tidal Charts come in sets, each one of the set covering a single hour between one high tide and another (they ignore the extra 24 minutes) and give the average tidal flow for that one hour. An arrow on the tidal chart indicates direction and two numbers are given: average flow (usually in knots) for spring tides and neap tides respectively. If a tidal chart is not available, most nautical charts have "tidal diamonds" which relate specific points on the chart to a table of data giving direction and speed of tidal flow. Standard procedure is to calculate a "Dead Reckoning" position (or DR) from distance and direction of travel and mark this on the chart (with a vertical cross like a plus sign) and then draw in a line from the DR in the direction of the tide. Measuring the distance the tide will have moved the boat along this line then gives an "Estimated Position" or EP (traditionally marked with a dot in a triangle). All nautical charts have depth markings on them which give the depth of water at that point during the lowest possible astronomical tide (tides may be lower or higher for meteorological reasons). Heights and times of low and high tide on each day are available in "tide tables". The actual depth of water at the given points at these times can then be calculated by adding the figures given to the depth given on the chart. Depths for intervening times can be calculated from tidal curves (each port has its own). If an accurate curve is not available, the rule of twelths can be used. This approximation works on the basis that the increase in depth in the six hours between low and high tide will follow this simple rule: first hour - 1/12, second - 2/12, third - 3/12, fourth - 3/12, fifth - 2/12, sixth - 1/12. (N.B. It would be foolish to attempt navigation without some training and the "Rule of Twelths" in particular should be used with caution)
## Other tides In addition to oceanic tides, there are **atmospheric tides** as well as **terrestrial tides** (**land tides**), affecting the rocky mass of the Earth. Atmospheric tides are negligible, drowned by the much more important effects of weather and the solar thermal tides. The Earth's crust, on the other hand, rises and falls imperceptibly in response to the Moon's sollicitation. The amplitude of terrestrial tides is about 1.5 metres at the equator, and they are nearly in phase with the Moon (the tidal lag is about two hours only) - which means that they reinforce the apparent oceanic tides. The first mathematical explanation of tidal forces was given in 1687 by Isaac Newton in the *Philosophiae Naturalis Principia Mathematica*. Tsunami, the large waves that occur after earthquakes, are often called *tidal waves*, but have nothing to do with the tides. Other phenomena unrelated to tides but using the word *tide* are rip tide, storm tide, and hurricane tide. For some reason *tidal wave* has been singled out for replacement in recent years.
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