# Tidal Movement

Apart from the water cycle there are other major movements of water. The sea levels, for example, are continually rising and lowering. A tide is a cycle of sea level changes characterized by a several hour water rise, up to its highest level called slack tide. This is followed by a several hour lowering of the sea level until the ebb tide is reached and the cycle starts again. The ranges between low and hide tide can reach extremes of a 12 to 16 meter difference as is the case in Nova Scotia on the east coast of Canada.

The normal surface level of the ocean is defined by the gravitational force of the Earth. Ignoring external forces, the gravitational force is directed towards the centre of the Earth, without any net lateral forces — and as a result no flow of water. However there *is* flow of water and this is due to gravitational forces from outside the Earth. The Earth is affected by the gravitational pulls of massive external bodies like the Moon and Sun. These massive bodies have strong gravitational fields that diminish with distance in space. The Sun's gravitational pull on Earth is 179 times stronger than the Moon's, but because of its much greater distance from the Earth, the Sun's tidal effect is lesser than that of the Moon's only about 46% as strong. The difference between the forces at the Earth's centre and surface determines the effective tidal force. For simplicity, the next few sections use the word "Moon" where "Sun" may also be understood.

**Tidal forces-** Since the tidal force is caused by gravitational pull of the Moon it is obvious that the sea level will rise on the spot closest to the Moon, while the water level decreases on spots further away from the Moon. However the Earth itself is also subject to the gravitational pull of the Moon. Thus three different forces occur. The strongest gravitational pull is experienced by the surface water on the Moon side- as a result the sea level rises on that side. The second strongest gravitational pull is experienced by the Earth itself. The weakest gravitational pull is experienced by the surface water on the opposite side of the Earth, the spot furthest away from the Moon. As a result the water level on the opposite side of the Earth is higher as well- since it has less gravitational pull from the Moon than the solid Earth. As the water level rises on two sides of the Earth, it will decrease in-between to make up for the difference. As a result the sea surface will show two bulges, one on each side of the Earth.

**Tidal amplitude and cycle time-** The rotation of the Earth relative to the Moon is one lunar day (24 hours and 48 minutes). Accordingly, each of the two bulges travels around at that speed, leading to one high tide every 12 hours and 24 minutes. The theoretical amplitude of oceanic tides due to the Moon is about 54 cm at the highest point. This is the amplitude that would be reached if the ocean were uniform and if the Earth were not rotating. The Sun similarly causes tides, of which the theoretical (average?) amplitude is about 25 cm (46 % of that of the Moon) and the cycle time is 12 hours. At spring tide the two effects add to each other to a theoretical level of 79 cm, while at neap tide the theoretical level is reduced to 29 cm. The distances between the Earth and the Moon and Sun vary, because the orbits are not circular but elliptical. This causes a variation in the tidal force and theoretical amplitude of about ±18% for the Moon and ±5% for the Sun. If both were aligned and in the closest possible position, the theoretical amplitude would reach 93 cm. Real amplitudes differ considerably due to discrepancies in latitude (influences distance to Sun and Moon), the shape and geometry of the coastline, and storms (that can also move large quantities of water).

**Tidal lag-** Because the Moon's tidal forces drive the oceans’ currents with a period of about 12.42 hours (half of the Earth's synodic period of rotation), which is considerably less than the natural period of the oceans, complex resonance phenomena take place. The lag between the Moon's passage and the tidal response varies between two hours in the southern oceans to two days in the North Sea. The global average tidal lag is six hours (which means that low tide occurs when the Moon is at its zenith, or its nadir, a result that challenges common intuition).

**Tides and Navigation-** Tidal flows are of utmost importance in navigation: indeed, very significant and potentially dangerous errors in the calculation of a ship’s position can and will occur if tidal activity is not taken into account. Tidal heights are also very important; for example, many rivers and harbors have a shallow "bar" at the entrance which will prevent boats with significant keel from entering and result in a boat’s interim grounding at low tides. Predicted tidal flows can be found by easily accessible tidal charts concerning a given area of interest. (link)

Tidal charts come in sets, each chart 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 particular 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 data table 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 a line from the DR in the direction of the tide. Measuring the distance the tide will have moved the boat along this line will give 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 these 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 twelfths 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: 1st hour - 1/12; 2nd - 2/12; 3rd - 3/12; 4th - 3/12; 5th - 2/12; 6th - 1/12.