Rule Of Twelfths
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Rule Of Twelfths
The rule of twelfths is an approximation to a sine curve. It can be used as a rule of thumb for estimating a changing quantity where both the quantity and the steps are easily divisible by 12. Typical uses are predicting the height of the tide or the change in day length over the seasons. The rule The rule states that over the first period the quantity increases by 1/12. Then in the second period by 2/12, in the third by 3/12, in the fourth by 3/12, fifth by 2/12 and at the end of the sixth period reaches its maximum with an increase of 1/12. The steps are 1:2:3:3:2:1 giving a total change of 12/12. Over the next six intervals the quantity reduces in a similar manner by 1, 2, 3, 3, 2, 1 twelfths. Applications In many parts of the world the tides approximate to a semi-diurnal sine curve, that is there are two high- and two low- tides per day. As an estimate then each period equates to 1 hour, with the tide rising by 1, 2, 3, 3, 2, finally 1 twelfths of its total range in e ...
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Rule Of Twelfths
The rule of twelfths is an approximation to a sine curve. It can be used as a rule of thumb for estimating a changing quantity where both the quantity and the steps are easily divisible by 12. Typical uses are predicting the height of the tide or the change in day length over the seasons. The rule The rule states that over the first period the quantity increases by 1/12. Then in the second period by 2/12, in the third by 3/12, in the fourth by 3/12, fifth by 2/12 and at the end of the sixth period reaches its maximum with an increase of 1/12. The steps are 1:2:3:3:2:1 giving a total change of 12/12. Over the next six intervals the quantity reduces in a similar manner by 1, 2, 3, 3, 2, 1 twelfths. Applications In many parts of the world the tides approximate to a semi-diurnal sine curve, that is there are two high- and two low- tides per day. As an estimate then each period equates to 1 hour, with the tide rising by 1, 2, 3, 3, 2, finally 1 twelfths of its total range in e ...
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Sine Curve
A sine wave, sinusoidal wave, or just sinusoid is a mathematical curve defined in terms of the ''sine'' trigonometric function, of which it is the graph. It is a type of continuous wave and also a smooth periodic function. It occurs often in mathematics, as well as in physics, engineering, signal processing and many other fields. Formulation Its most basic form as a function of time (''t'') is: y(t) = A\sin(2 \pi f t + \varphi) = A\sin(\omega t + \varphi) where: * ''A'', ''amplitude'', the peak deviation of the function from zero. * ''f'', ''ordinary frequency'', the ''number'' of oscillations (cycles) that occur each second of time. * ''ω'' = 2''f'', ''angular frequency'', the rate of change of the function argument in units of radians per second. * \varphi, ''phase'', specifies (in radians) where in its cycle the oscillation is at ''t'' = 0. When \varphi is non-zero, the entire waveform appears to be shifted in time by the amount ''φ''/''ω'' seconds. A negative value repr ...
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Rule Of Thumb
In English, the phrase ''rule of thumb'' refers to an approximate method for doing something, based on practical experience rather than theory. This usage of the phrase can be traced back to the 17th century and has been associated with various trades where quantities were measured by comparison to the width or length of a thumb. A modern folk etymology holds that the phrase is derived from the maximum width of a stick allowed for wife-beating under English common law, but no such law ever existed. This belief may have originated in a rumored statement by 18th-century judge Sir Francis Buller that a man may beat his wife with a stick no wider than his thumb. The rumor produced numerous jokes and satirical cartoons at Buller's expense, but there is no record that he made such a statement. English jurist Sir William Blackstone wrote in his ''Commentaries on the Laws of England'' of an "old law" that once allowed "moderate" beatings by husbands, but he did not mention thumbs or any ...
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Boat
A boat is a watercraft of a large range of types and sizes, but generally smaller than a ship, which is distinguished by its larger size, shape, cargo or passenger capacity, or its ability to carry boats. Small boats are typically found on inland waterways such as rivers and lakes, or in protected coastal areas. However, some boats, such as the whaleboat, were intended for use in an offshore environment. In modern naval terms, a boat is a vessel small enough to be carried aboard a ship. Boats vary in proportion and construction methods with their intended purpose, available materials, or local traditions. Canoes have been used since prehistoric times and remain in use throughout the world for transportation, fishing, and sport. Fishing boats vary widely in style partly to match local conditions. Pleasure craft used in recreational boating include ski boats, pontoon boats, and sailboats. House boats may be used for vacationing or long-term residence. Lighters are used to convey ...
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Ship
A ship is a large watercraft that travels the world's oceans and other sufficiently deep waterways, carrying cargo or passengers, or in support of specialized missions, such as defense, research, and fishing. Ships are generally distinguished from boats, based on size, shape, load capacity, and purpose. Ships have supported exploration, trade, warfare, migration, colonization, and science. After the 15th century, new crops that had come from and to the Americas via the European seafarers significantly contributed to world population growth. Ship transport is responsible for the largest portion of world commerce. The word ''ship'' has meant, depending on the era and the context, either just a large vessel or specifically a ship-rigged sailing ship with three or more masts, each of which is square-rigged. As of 2016, there were more than 49,000 merchant ships, totaling almost 1.8 billion dead weight tons. Of these 28% were oil tankers, 43% were bulk carriers, and ...
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Slipway
A slipway, also known as boat ramp or launch or boat deployer, is a ramp on the shore by which ships or boats can be moved to and from the water. They are used for building and repairing ships and boats, and for launching and retrieving small boats on trailers towed by automobiles and flying boats on their undercarriage. The nautical terms ways and skids are alternative names for slipway. A ship undergoing construction in a shipyard is said to be ''on the ways''. If a ship is scrapped there, she is said to be ''broken up in the ways''. As the word "slip" implies, the ships or boats are moved over the ramp, by way of crane or fork lift. Prior to the move the vessel's hull is coated with grease, which then allows the ship or boat to "slip" off of the ramp and progress safely into the water. Slipways are used to launch (newly built) large ships, but can only dry-dock or repair smaller ships. Pulling large ships against the greased ramp would require too much force. Therefor ...
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Tide Table
Tide tables, sometimes called tide charts, are used for tidal prediction and show the daily times and levels of high and low tides, usually for a particular location. Tide heights at intermediate times (between high and low water) can be approximated by using the rule of twelfths or more accurately calculated by using a published tidal curve for the location. Tide levels are typically given relative to a low-water vertical datum, e.g. the mean lower low water (MLLW) datum in the US.Tidal Datums And Their Applications
NOAA Special Publication NOS CO-OPS 1, Silver Spring MD, June 2000.


Publication and scope

Tide tables are published in various forms, such as paper-based tables and tables available on the Internet. Most tide tables are calculated and published only for ...
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Chart Datum
A chart datum is the water level surface serving as origin of depths displayed on a nautical chart. A chart datum is generally derived from some tidal phase, in which case it is also known as a tidal datum. Common chart datums are ''lowest astronomical tide'' (LAT)Australian Bureau of MeteorologNational Tide Centre Glossary(retrieved 30 April 2013) and ''mean lower low water'' (MLLW). In non-tidal areas, e.g. the Baltic Sea, mean sea level (MSL) is used. A chart datum is a type of vertical datum and must not be confused with the horizontal datum for the chart. Definitions The following tidal phases are commonly used in the definition of chart datums. Lowest astronomical tide ''Lowest astronomical tide'' (LAT) is defined as the lowest tide level which can be predicted to occur under average meteorological conditions and under any combination of astronomical conditions. Many national charting agencies, including the United Kingdom Hydrographic Office and the Australian Hydrog ...
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Daytime
Daytime as observed on Earth is the period of the day during which a given location experiences natural illumination from direct sunlight. Daytime occurs when the Sun appears above the local horizon, that is, anywhere on the globe's hemisphere facing the Sun. In direct sunlight the movement of the sun can be recorded and observed using a sundial that casts a shadow that slowly moves during the day. Other planets and natural satellites that rotate relative to a luminous primary body, such as a local star, also experience daytime, but this article primarily discusses daytime on Earth. Characteristics Approximately half of Earth is illuminated at any time by the Sun. The area subjected to direct illumination is almost exactly half the planet; but because of atmospheric and other effects that extend the reach of indirect illumination, the area of the planet covered by either direct or indirect illumination amounts to slightly more than half the surface. The hemisphere of Eart ...
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Poole Harbour
Poole Harbour is a large natural harbour in Dorset, southern England, with the town of Poole on its shores. The harbour is a drowned valley (ria) formed at the end of the last ice age and is the estuary of several rivers, the largest being the Frome. The harbour has a long history of human settlement stretching to pre-Roman times. The harbour is extremely shallow (average depth ), with one main dredged channel through the harbour, from the mouth to Holes Bay. Poole Harbour has an area of approximately . It is one of several which lay claim to the title of "second largest natural harbour in the world" (after Port Jackson, Sydney). History In 1964 during harbour dredging, the waterlogged remains of a 2000-year-old Iron Age logboat were found off Brownsea Island. Dated at about 295 BC, the Poole Logboat is one of the largest vessels of its type from British waters. Its low freeboard would have limited its use to within Poole Harbour. Poole was used by the Romans as an invasi ...
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Solent
The Solent ( ) is a strait between the Isle of Wight and Great Britain. It is about long and varies in width between , although the Hurst Spit which projects into the Solent narrows the sea crossing between Hurst Castle and Colwell Bay to just over . The Solent is a major shipping lane for passenger, freight and military vessels. It is an important recreational area for water sports, particularly yachting, hosting the Cowes Week sailing event annually. It is sheltered by the Isle of Wight and has a complex tidal pattern, which has benefited Southampton's success as a port, providing a "double high tide" that extends the tidal window during which deep-draught ships can be handled. Portsmouth lies on its shores. Spithead, an area off Gilkicker Point near Gosport, is known as the place where the Royal Navy is traditionally reviewed by the monarch of the day. The area is of great ecological and landscape importance, particularly because of the coastal and estuarine habitats a ...
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Weymouth Bay
Weymouth Bay is a sheltered bay on the south coast of England, in Dorset. It is protected from erosion by Chesil Beach and the Isle of Portland, and includes several beaches, notably Weymouth Beach, a gently curving arc of golden sand which stretches from the resort of Weymouth. Weymouth Bay is situated approximately halfway along the UNESCO Jurassic Coast World Heritage Site. Boundary When Natural England looked at access to Weymouth Bay prior to the 2012 Olympic Games, they defined it as the stretch between Rufus Castle on the Isle of Portland and Lulworth Cove, an area which covers Portland Harbour, Weymouth Beach, and Ringstead Bay. Sailing The bay's waters are excellent for sailing — the best sailing waters in northern Europe, in part because the bay is sheltered from south-west winds. This means that Portland Bill can be accessed easily from anywhere on Weymouth Bay by sailing when the tide is turning as an eddy flows along Portland's eastern side. The bay is home to ...
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