1.
Osculating circle
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Its center lies on the inner normal line, and its curvature is the same as that of the given curve at that point. This circle, which is the one among all tangent circles at the point that approaches the curve most tightly, was named circulus osculans by Leibniz. The center and radius of the circle at a given point are called center of curvature. A geometric construction was described by Isaac Newton in his Principia, suddenly, at one point along the road, the steering wheel locks in its present position. Thereafter, the car moves in a circle that kisses the road at the point of locking, the curvature of the circle is equal to that of the road at that point. That circle is the circle of the road curve at that point. Let γ be a parametric plane curve, where s is the arc length. This determines the unit tangent vector T, the normal vector N, the signed curvature k. Suppose that P is a point on γ where k ≠0, the corresponding center of curvature is the point Q at distance R along N, in the same direction if k is positive and in the opposite direction if k is negative. The circle with center at Q and with radius R is called the circle to the curve γ at the point P. If C is a space curve then the osculating circle is defined in a similar way. It lies in the plane, the plane spanned by the tangent. The plane curve can also be given in a different regular parametrization γ = where regular means that γ ′ ≠0 for all t. This is entirely analogous to the construction of the tangent to a curve as a limit of the secant lines through pairs of points on C approaching P. The osculating circle S to a plane curve C at a regular point P can be characterized by the following properties, the circle S and the curve C have the common tangent line at P, and therefore the common normal line. Close to P, the distance between the points of the curve C and the circle S in the normal direction decays as the cube or a power of the distance to P in the tangential direction. If the derivative of the curvature with respect to s is nonzero at P then the osculating circle crosses the curve C at P, points P at which the derivative of the curvature is zero are called vertices. If P is a vertex then C and its osculating circle have contact of order at least four, if, moreover, the curvature has a non-zero local maximum or minimum at P then the osculating circle touches the curve C at P but does not cross it
2.
Ghent
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Ghent is a city and a municipality in the Flemish Region of Belgium. It is the capital and largest city of the East Flanders province and it is a port and university city. With 240,191 inhabitants in the beginning of 2009, Ghent is Belgiums second largest municipality by number of inhabitants, the current mayor of Ghent, Daniël Termont, leads a coalition of the Socialistische Partij Anders, Groen and Open VLD. The ten-day-long Ghent Festival is held every year and attended by about 1–1.5 million visitors, archaeological evidence shows human presence in the region of the confluence of Scheldt and Leie going back as far as the Stone Age and the Iron Age. Most historians believe that the name for Ghent, Ganda, is derived from the Celtic word ganda which means confluence. Other sources connect its name with a deity named Gontia. There are no records of the Roman period, but archaeological research confirms that the region of Ghent was further inhabited. When the Franks invaded the Roman territories from the end of the 4th century and well into the 5th century, they brought their language with them and Celtic, around 650, Saint Amand founded two abbeys in Ghent, St. Peters and Saint Bavos Abbey. The city grew from several nuclei, the abbeys and a commercial centre, around 800, Louis the Pious, son of Charlemagne, appointed Einhard, the biographer of Charlemagne, as abbot of both abbeys. In 851 and 879, the city was attacked and plundered twice by the Vikings. Within the protection of the County of Flanders, the city recovered and flourished from the 11th century, by the 13th century, Ghent was the biggest city in Europe north of the Alps after Paris, it was bigger than Cologne or Moscow. Within the city walls lived up to 65,000 people, the belfry and the towers of the Saint Bavo Cathedral and Saint Nicholas Church are just a few examples of the skyline of the period. The rivers flowed in an area where land was periodically flooded. These rich grass meersen were ideally suited for herding sheep, the wool of which was used for making cloth, during the Middle Ages Ghent was the leading city for cloth. The wool industry, originally established at Bruges, created the first European industrialized zone in Ghent in the High Middle Ages, the mercantile zone was so highly developed that wool had to be imported from Scotland and England. This was one of the reasons for Flanders good relationship with Scotland and England, Ghent was the birthplace of John of Gaunt, Duke of Lancaster. Trade with England suffered significantly during the Hundred Years War, the city recovered in the 15th century, when Flanders was united with neighbouring provinces under the Dukes of Burgundy. High taxes led to a rebellion and eventually the Battle of Gavere in 1453, around this time the centre of political and social importance in the Low Countries started to shift from Flanders to Brabant, although Ghent continued to play an important role
3.
Bruges
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Bruges is the capital and largest city of the province of West Flanders in the Flemish Region of Belgium, in the northwest of the country. The area of the whole city amounts to more than 13,840 hectares, including 1,075 hectares off the coast, the historic city centre is a prominent World Heritage Site of UNESCO. It is oval and about 430 hectares in size, the citys total population is 117,073, of whom around 20,000 live in the city centre. The metropolitan area, including the commuter zone, covers an area of 616 km2 and has a total of 255,844 inhabitants as of 1 January 2008. Along with a few other canal-based northern cities, such as Amsterdam and Stockholm, Bruges has a significant economic importance thanks to its port and was once one of the worlds chief commercial cities. Bruges is well known as the seat of the College of Europe, the name probably derives from the Old Dutch for bridge, brugga. Also compare Middle Dutch brucge, brugge, and modern Dutch bruggehoofd, the form brugghe would be a southern Dutch variant. The Dutch word and the English bridge both derive from Proto-Germanic *brugjō-, Bruges was a location of coastal settlement during prehistory. This Bronze Age and Iron Age settlement is unrelated to medieval city development, in the Bruges area, the first fortifications were built after Julius Caesars conquest of the Menapii in the first century BC, to protect the coastal area against pirates. The Franks took over the region from the Gallo-Romans around the 4th century. The Viking incursions of the century prompted Count Baldwin I of Flanders to reinforce the Roman fortifications, trade soon resumed with England. Bruges received its city charter on 27 July 1128, and new walls and canals were built, in 1089 Bruges became the capital of the County of Flanders. Since about 1050, gradual silting had caused the city to lose its access to the sea. A storm in 1134, however, re-established this access, through the creation of a channel at the Zwin. The new sea arm stretched all the way to Damme, a city became the commercial outpost for Bruges. Bruges had a location at the crossroads of the northern Hanseatic League trade. They developed, or borrowed from Italy, new forms of merchant capitalism, whereby several merchants would share the risks and profits and they employed new forms of economic exchange, including bills of exchange and letters of credit. The city eagerly welcomed foreign traders, most notably the Portuguese traders selling pepper and other spices, the citys entrepreneurs reached out to make economic colonies of England and Scotlands wool-producing districts
4.
Track (rail transport)
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The track on a railway or railroad, also known as the permanent way, is the structure consisting of the rails, fasteners, railroad ties and ballast, plus the underlying subgrade. It enables trains to move by providing a surface for their wheels to roll upon. For clarity it is referred to as railway track or railroad track. Tracks where electric trains or electric trams run are equipped with a system such as an overhead electrical power line or an additional electrified rail. The term permanent way also refers to the track in addition to structures such as fences etc. Most railroads with heavy traffic use continuously welded rails supported by sleepers attached via baseplates that spread the load, a plastic or rubber pad is usually placed between the rail and the tieplate where concrete sleepers are used. The rail is held down to the sleeper with resilient fastenings. For much of the 20th century, rail track used softwood timber sleepers and jointed rails, jointed rails were used at first because contemporary technology did not offer any alternative. The joints also needed to be lubricated, and wear at the mating surfaces needed to be rectified by shimming. For this reason jointed track is not financially appropriate for heavily operated railroads, timber sleepers are of many available timbers, and are often treated with creosote, copper-chrome-arsenic, or other wood preservative. Pre-stressed concrete sleepers are used where timber is scarce and where tonnage or speeds are high. Steel is used in some applications, the track ballast is customarily crushed stone, and the purpose of this is to support the sleepers and allow some adjustment of their position, while allowing free drainage. A disadvantage of traditional track structures is the demand for maintenance, particularly surfacing and lining to restore the desired track geometry. Weakness of the subgrade and drainage deficiencies also lead to maintenance costs. This can be overcome by using ballastless track, in its simplest form this consists of a continuous slab of concrete with the rails supported directly on its upper surface. There are a number of systems, and variations include a continuous reinforced concrete slab. Many permutations of design have been put forward, however, ballastless track has a high initial cost, and in the case of existing railroads the upgrade to such requires closure of the route for a long period. Its whole-life cost can be lower because of the reduction in maintenance, some rubber-tyred metros use ballastless tracks
5.
Centripetal acceleration
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Acceleration, in physics, is the rate of change of velocity of an object with respect to time. An objects acceleration is the net result of any and all forces acting on the object, the SI unit for acceleration is metre per second squared. Accelerations are vector quantities and add according to the parallelogram law, as a vector, the calculated net force is equal to the product of the objects mass and its acceleration. For example, when a car starts from a standstill and travels in a line at increasing speeds. If the car turns, there is an acceleration toward the new direction, in this example, we can call the forward acceleration of the car a linear acceleration, which passengers in the car might experience as a force pushing them back into their seats. When changing direction, we call this non-linear acceleration, which passengers might experience as a sideways force. If the speed of the car decreases, this is an acceleration in the direction from the direction of the vehicle. Passengers may experience deceleration as a force lifting them forwards, mathematically, there is no separate formula for deceleration, both are changes in velocity. Each of these accelerations might be felt by passengers until their velocity matches that of the car, an objects average acceleration over a period of time is its change in velocity divided by the duration of the period. Mathematically, a ¯ = Δ v Δ t, instantaneous acceleration, meanwhile, is the limit of the average acceleration over an infinitesimal interval of time. The SI unit of acceleration is the metre per second squared, or metre per second per second, as the velocity in metres per second changes by the acceleration value, every second. An object moving in a circular motion—such as a satellite orbiting the Earth—is accelerating due to the change of direction of motion, in this case it is said to be undergoing centripetal acceleration. Proper acceleration, the acceleration of a relative to a free-fall condition, is measured by an instrument called an accelerometer. As speeds approach the speed of light, relativistic effects become increasingly large and these components are called the tangential acceleration and the normal or radial acceleration. Geometrical analysis of space curves, which explains tangent, normal and binormal, is described by the Frenet–Serret formulas. Uniform or constant acceleration is a type of motion in which the velocity of an object changes by an amount in every equal time period. A frequently cited example of uniform acceleration is that of an object in free fall in a gravitational field. The acceleration of a body in the absence of resistances to motion is dependent only on the gravitational field strength g
6.
Cant (road/rail)
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The cant of a railway track or camber of a road is the rate of change in elevation between the two rails or edges. On railways, cant helps a train steer around a curve, keeping the wheel flanges from touching the rails, minimising friction and wear. However, it may be necessary to select a value at design time. Generally the aim is for trains to run without flange contact, allowance has to be made for the different speeds of trains. Slower trains will tend to make contact with the inner rail on curves, while faster trains will tend to ride outwards. Either contact causes wear and tear and may lead to derailment, many high-speed lines do not permit slower freight trains, particularly with heavier axle loads. In some cases, the impact is reduced by the use of flange lubrication, ideally, the track should have sleepers at a closer spacing and a greater depth of ballast to accommodate the increased forces exerted in the curve. At the ends of a curve, the amount of cant cannot change from zero to its maximum immediately and it must change gradually in a track transition curve. The length of the transition depends on the maximum allowable speed—the higher the speed, the greater length is required. For the United States standard maximum unbalanced superelevation of 75 mm, for high-speed railways in Europe, maximum cant is 180 mm. Track unbalanced superelevation in the United States is restricted to 75 mm, though 102 mm is permissible by waiver. The maximum value for European railways varies by country, some of which have curves with over 280 mm of unbalanced superelevation to permit high-speed transportation, the highest values are only for tilting trains, because it would be too uncomfortable for passengers. This follows simply from a balance weight, centrifugal force and normal force. In the approximation it is assumed that the cant is small compared to the gauge of the track. In a formula this becomes v m a x ≈ r g w = g d w with d =1 / r the curvature of the track, in the United States, maximum speed is subject to specific rules. In Australia, ARTC is increasing speed around curves sharper than an 800-metre radius by replacing wooden sleepers with concrete ones so that the cant can be increased, the rails themselves are now usually canted inwards by about 10 to 5 per cent. In 1925 about 15 of 36 major American railways had adopted this practice, in civil engineering, cant is often referred to as cross slope or camber. It helps rainwater drain from the road surface, along straight or gently curved sections, the middle of the road is normally higher than the edges. This is called normal crown and helps shed rainwater off the sides of the road, on more severe bends, the outside edge of the curve is raised, or superelevated, to help vehicles around the curve
7.
Tangent
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In geometry, the tangent line to a plane curve at a given point is the straight line that just touches the curve at that point. Leibniz defined it as the line through a pair of infinitely close points on the curve, a similar definition applies to space curves and curves in n-dimensional Euclidean space. Similarly, the tangent plane to a surface at a point is the plane that just touches the surface at that point. The concept of a tangent is one of the most fundamental notions in geometry and has been extensively generalized. The word tangent comes from the Latin tangere, to touch, euclid makes several references to the tangent to a circle in book III of the Elements. In Apollonius work Conics he defines a tangent as being a line such that no other straight line could fall between it and the curve, archimedes found the tangent to an Archimedean spiral by considering the path of a point moving along the curve. Independently Descartes used his method of normals based on the observation that the radius of a circle is always normal to the circle itself and these methods led to the development of differential calculus in the 17th century. Many people contributed, Roberval discovered a method of drawing tangents. René-François de Sluse and Johannes Hudde found algebraic algorithms for finding tangents, further developments included those of John Wallis and Isaac Barrow, leading to the theory of Isaac Newton and Gottfried Leibniz. An 1828 definition of a tangent was a line which touches a curve. This old definition prevents inflection points from having any tangent and it has been dismissed and the modern definitions are equivalent to those of Leibniz who defined the tangent line as the line through a pair of infinitely close points on the curve. The tangent at A is the limit when point B approximates or tends to A, the existence and uniqueness of the tangent line depends on a certain type of mathematical smoothness, known as differentiability. At most points, the tangent touches the curve without crossing it, a point where the tangent crosses the curve is called an inflection point. Circles, parabolas, hyperbolas and ellipses do not have any point, but more complicated curves do have, like the graph of a cubic function. Conversely, it may happen that the curve lies entirely on one side of a line passing through a point on it. This is the case, for example, for a passing through the vertex of a triangle. In convex geometry, such lines are called supporting lines, the geometrical idea of the tangent line as the limit of secant lines serves as the motivation for analytical methods that are used to find tangent lines explicitly. The question of finding the tangent line to a graph, or the tangent line problem, was one of the central questions leading to the development of calculus in the 17th century, suppose that a curve is given as the graph of a function, y = f
8.
History of rail transport
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Including systems with man or horse power, and tracks or guides made of stone or wood, the history of rail transport dates back as far as the ancient Greeks. Wagonways were relatively common in Europe from about 1500 through 1800, mechanised rail transport systems first appeared in England in the 1820s. These systems, which use of the steam locomotive, were critical to the Industrial Revolution. They have remained the form of long distance land transportation for many bulk materials such as coal, ore, grains, stone and sand. Reduction in friction was one of the reasons for the success of railroads compared to wagons. This was demonstrated on an iron plate-covered wooden tramway in 1805 at Croydon in England, “A good horse on an ordinary turnpike road can draw two thousand pounds, or one ton. A party of gentlemen were invited to look upon the experiment, twelve wagons were loaded with stones, till each wagon weighed three tons, and the wagons were fastened together. A horse was then attached, which drew the wagons with ease, six miles in two hours, having stopped four times, in order to show he had the power of starting, as well as drawing his great load. ”Wheeled vehicles pulled by men and animals ran in grooves in limestone, which provided the track element, preventing the wagons from leaving the intended route. The Diolkos was in use for over 650 years, until at least the 1st century AD, the first horse-drawn wagonways also appeared in ancient Greece, with others to be found on Malta and various parts of the Roman Empire, using cut-stone tracks. They fell into disuse as the Roman Empire collapsed, in 1515, Cardinal Matthäus Lang wrote a description of the Reisszug, a funicular railway at the Hohensalzburg Castle in Austria. The line originally used wooden rails and a hemp haulage rope, the line still exists, albeit in updated form, and is possibly the oldest wagonway still to operate. Wagonways are thought to have developed in Germany in the 1550s to facilitate the transport of ore tubs to and from mines, such an operation was illustrated in 1556 by Georgius Agricola. This used Hund carts with unflanged wheels running on wooden planks, such a transport system was used by German miners at Caldbeck, Cumbria, England, perhaps from the 1560s. An alternative explanation derives it from the Magyar hintó - a carriage, there are possible references to their use in central Europe in the 15th century. The first true railway is now suggested to have been a railway made at Broseley in Shropshire. This carried coal for James Clifford from his mines down to the river Severn to be loaded onto barges, though the first documentary record of this is later, its construction probably preceded the Wollaton Wagonway, completed in 1604, hitherto regarded as the earliest British installation. This ran from Strelley to Wollaton near Nottingham, another early wagonway is noted onwards. Huntingdon Beaumont, who was concerned with mining at Strelley, also laid down broad wooden rails near Newcastle upon Tyne, by the 18th century, such wagonways and tramways existed in a number of areas
9.
William John Macquorn Rankine
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William John Macquorn Rankine, FRSE FRS was a Scottish mechanical engineer who also contributed to civil engineering, physics and mathematics. He was a contributor, with Rudolf Clausius and William Thomson, to the science of thermodynamics. Rankine developed a theory of the steam engine and indeed of all heat engines. His manuals of engineering science and practice were used for decades after their publication in the 1850s and 1860s. He was an amateur singer, pianist and cellist who composed his own humorous songs. He was born in Edinburgh and died in Glasgow, a bachelor, born in Edinburgh to British Army lieutenant David Rankine and Barbara Grahame, of a prominent legal and banking family. Rankine was initially educated at home but he later attended Ayr Academy and, very briefly, in 1836, Rankine began to study a spectrum of scientific topics at the University of Edinburgh, including natural history under Robert Jameson and natural philosophy under James David Forbes. Under Forbes he was awarded prizes for essays on methods of physical inquiry, during vacations, he assisted his father who, from 1830, was manager and, later, effective treasurer and engineer of the Edinburgh and Dalkeith Railway which brought coal into the growing city. In fact, the technique was simultaneously in use by other engineers –, the year 1842 also marked Rankines first attempt to reduce the phenomena of heat to a mathematical form but he was frustrated by his lack of experimental data. At the time of Queen Victorias visit to Scotland, he organised a large bonfire situated on Arthurs Seat, the bonfire served as a beacon to initiate a chain of other bonfires across Scotland. Undaunted, he returned to his fascination with the mechanics of the heat engine. The following year, he used his theory to establish relationships between the temperature, pressure and density of gases, and expressions for the latent heat of evaporation of a liquid and he accurately predicted the surprising fact that the apparent specific heat of saturated steam would be negative. The work marked the first step on Rankines journey to develop a complete theory of heat. Rankine later recast the results of his theories in terms of a macroscopic account of energy. He defined and distinguished between actual energy which was lost in dynamic processes and potential energy by which it was replaced. He assumed the sum of the two energies to be constant, an idea already, although not for very long. From 1854, he made use of his thermodynamic function which he later realised was identical to the entropy of Clausius. By 1855, Rankine had formulated a science of energetics which gave an account of dynamics in terms of energy and its transformations rather than force, the theory was very influential in the 1890s
10.
Sine wave
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A sine wave or sinusoid is a mathematical curve that describes a smooth repetitive oscillation. It is named after the sine, of which it is the graph. It occurs often in pure and applied mathematics, as well as physics, engineering, signal processing and many other fields. Its most basic form as a function of time is, y = A sin = A sin where, A = the amplitude, F = the ordinary frequency, the number of oscillations that occur each second of time. ω = 2πf, the frequency, the rate of change of the function argument in units of radians per second φ = the phase. When φ is non-zero, the entire waveform appears to be shifted in time by the amount φ /ω seconds, a negative value represents a delay, and a positive value represents an advance. The sine wave is important in physics because it retains its shape when added to another sine wave of the same frequency and arbitrary phase. It is the only periodic waveform that has this property and this property leads to its importance in Fourier analysis and makes it acoustically unique. The wavenumber is related to the frequency by. K = ω v =2 π f v =2 π λ where λ is the wavelength, f is the frequency, and v is the linear speed. This equation gives a wave for a single dimension, thus the generalized equation given above gives the displacement of the wave at a position x at time t along a single line. This could, for example, be considered the value of a wave along a wire, in two or three spatial dimensions, the same equation describes a travelling plane wave if position x and wavenumber k are interpreted as vectors, and their product as a dot product. For more complex such as the height of a water wave in a pond after a stone has been dropped in. This wave pattern occurs often in nature, including wind waves, sound waves, a cosine wave is said to be sinusoidal, because cos = sin , which is also a sine wave with a phase-shift of π/2 radians. Because of this start, it is often said that the cosine function leads the sine function or the sine lags the cosine. The human ear can recognize single sine waves as sounding clear because sine waves are representations of a frequency with no harmonics. Presence of higher harmonics in addition to the fundamental causes variation in the timbre, on the other hand, if the sound contains aperiodic waves along with sine waves, then the sound will be perceived noisy as noise is characterized as being aperiodic or having a non-repetitive pattern. In 1822, French mathematician Joseph Fourier discovered that sinusoidal waves can be used as building blocks to describe and approximate any periodic waveform
11.
William Gravatt
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William Gravatt FRS, was a noted English civil engineer and scientific instrument maker. Whilst surveying the route for the South Eastern Railway to Dover, he devised the more transportable dumpy level and he then supervised the northern engineering team under Isambard Kingdom Brunel on the Bristol and Exeter Railway, where the deployment of his curve of sines theorem speeded construction. He died after being poisoned by an over dose of morphine by his nurse. Born in Gravesend, Kent on 14 July 1806, he was the son of Colonel William Gravatt, at age 15, his father negotiated an apprenticeship to mechanical engineer Bryan Donkin. During this period he met and became friends with John Smeaton, Edward Troughton, in 1832 he became a FelIow of the Royal Society, and a Fellow of the Royal Astronomical Society. Before he finished his apprenticeship, Gravatt successfully interviewed with Sir Marc Isambard Brunel, on 27 June 1827, after the tunnel flooded, Isambard Kingdom Brunel forbade anyone from entering the workings. However, company directors Robert Marten and Richard Harris insisted Gravatt take them in to inspect the damage, whist in the workings, Marten attempted to move forward in the dinghy, and after striking his head on the tunnel, tipped the boat over in 12 feet of water. Only Gravatt and miner Dowling could swim, and after rescuing Marten and Harris, joined by officials from the Humane Society, they eventually recovered the body with a drag-line. On 5 March 1828, silver medals were voted by the Royal Humane Society to Brunel, in 1832 during a break in work on the Thames Tunnel due to water ingress, Donkin recommended Gravatt as Engineer to the Calder and Hebble Navigation. Gravatt resultantly designed the arches for several bridges, using a solid iron-plate inverted arched chain above the platform, however, early in the start of construction Gravatt was dismissed on grounds of experience. He was replaced by William Bull, in 1834, he was employed by Brunel on a number of works. His major project was to survey the Taff Vale Railway, from Cardiff to Merthyr Tydfil and he was also asked to design several bridges for both the mainline and extensions to the Great Western Railway. In 1835, Brunel appointed Gravatt superintendent of the 75 miles of surveys for the Act of Parliament for the Bristol, Brunel himself was in charge of the design of White Ball Tunnel. In 1835, Brunel was appointed to improve navigation on the River Parrett from Westport to Langport and his Great Bow Bridge of 1840 at Langport still survives. With mixed instructions given to the contractors, bridges were sinking into the soft soil. Brunel wrote to Gravatt on 18 June 1841 stating that he had lost confidence in him, forcing his resignation, he was replaced by John Joseph Macdonnell. The Bristol to Bridgwater section of the B&ER was opened to traffic on 14 June 1841, Gravatt subsequently resurrected his reputation by designing and being appointed superintended for the St. Philips drawbridge, Bristol, which itself was replaced again in 1868. Returning to London, in 1850 Gravatt was selected by the Reverend John Craig to design, living in an apartment at 34 Parliament Street, his neighbours included the portrait photographer Richard Beard, who in 1852 came to take pictures of the instrument for the Illustrated London News
12.
William Froude
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William Froude was an English engineer, hydrodynamicist and naval architect. He was the first to formulate laws for the resistance that water offers to ships. His first employment was as a surveyor on the South Eastern Railway which, in 1837, led to Brunel giving him responsibility for the construction of a section of the Bristol and Exeter Railway. At Brunels invitation Froude turned his attention to the stability of ships in a seaway and his experiments were vindicated in full-scale trials conducted by the Admiralty and as a result the first ship test tank was built, at public expense, at his home in Torquay. Here he was able to combine mathematical expertise with practical experimentation to such effect that his methods are still followed today. In 1877, he was commissioned by the Admiralty to produce a capable of absorbing and measuring the power of large naval engines. He invented and built the worlds first water brake dynamometer, sometimes known as the hydraulic dynamometer and he died while on holiday in Simonstown, South Africa, and was buried there with full naval honours. He was the brother of James Anthony Froude, a historian, William was married to the former Catherine Henrietta Elizabeth Holdsworth, daughter of the Governor of Dartmouth Castle, mercantile magnate and member of Parliament Arthur Howe Holdsworth. Works by or about William Froude at Internet Archive Biography of William Froude Froude, second Torquay honour for Naval architect William Froude
13.
Elastica theory
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The elastica theory is a theory of mechanics of solid materials developed by Leonhard Euler that allows for very large scale elastic deflections of structures. Euler and Jakob Bernoulli developed the theory for elastic lines and studied buckling, certain situations can be solved exactly by elliptic functions. Later elastica theory was generalized by F. and E. Cosserat into a theory with intrinsic directions at each point. Elastica theory is an example of bifurcation theory, for most boundary conditions several solutions exist simultaneously. When small deflections of a structure are to be analyzed, elastica theory is not required, a modern treatise of the planar elastica with full account of bifurcation and instability has been recently presented by Bigoni. Finite strain theory A Treatise on the Mathematical Theory of Elasticity by Augustus Edward Hough Love Antman, web site of Gert van der Heijden. A PhD thesis on elastic rods by Geoff Goss, June 2003, the elastica, a mathematical history by Raph Levien
14.
Polynomial
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In mathematics, a polynomial is an expression consisting of variables and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents. An example of a polynomial of a single indeterminate x is x2 − 4x +7, an example in three variables is x3 + 2xyz2 − yz +1. Polynomials appear in a variety of areas of mathematics and science. In advanced mathematics, polynomials are used to construct polynomial rings and algebraic varieties, central concepts in algebra, the word polynomial joins two diverse roots, the Greek poly, meaning many, and the Latin nomen, or name. It was derived from the binomial by replacing the Latin root bi- with the Greek poly-. The word polynomial was first used in the 17th century, the x occurring in a polynomial is commonly called either a variable or an indeterminate. When the polynomial is considered as an expression, x is a symbol which does not have any value. It is thus correct to call it an indeterminate. However, when one considers the function defined by the polynomial, then x represents the argument of the function, many authors use these two words interchangeably. It is a convention to use uppercase letters for the indeterminates. However one may use it over any domain where addition and multiplication are defined, in particular, when a is the indeterminate x, then the image of x by this function is the polynomial P itself. This equality allows writing let P be a polynomial as a shorthand for let P be a polynomial in the indeterminate x. A polynomial is an expression that can be built from constants, the word indeterminate means that x represents no particular value, although any value may be substituted for it. The mapping that associates the result of substitution to the substituted value is a function. This can be expressed concisely by using summation notation, ∑ k =0 n a k x k That is. Each term consists of the product of a number—called the coefficient of the term—and a finite number of indeterminates, because x = x1, the degree of an indeterminate without a written exponent is one. A term and a polynomial with no indeterminates are called, respectively, a constant term, the degree of a constant term and of a nonzero constant polynomial is 0. The degree of the polynomial,0, is generally treated as not defined
15.
Leonhard Euler
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He also introduced much of the modern mathematical terminology and notation, particularly for mathematical analysis, such as the notion of a mathematical function. He is also known for his work in mechanics, fluid dynamics, optics, astronomy, Euler was one of the most eminent mathematicians of the 18th century, and is held to be one of the greatest in history. He is also considered to be the most prolific mathematician of all time. His collected works fill 60 to 80 quarto volumes, more than anybody in the field and he spent most of his adult life in Saint Petersburg, Russia, and in Berlin, then the capital of Prussia. A statement attributed to Pierre-Simon Laplace expresses Eulers influence on mathematics, Read Euler, read Euler, Leonhard Euler was born on 15 April 1707, in Basel, Switzerland to Paul III Euler, a pastor of the Reformed Church, and Marguerite née Brucker, a pastors daughter. He had two sisters, Anna Maria and Maria Magdalena, and a younger brother Johann Heinrich. Soon after the birth of Leonhard, the Eulers moved from Basel to the town of Riehen, Paul Euler was a friend of the Bernoulli family, Johann Bernoulli was then regarded as Europes foremost mathematician, and would eventually be the most important influence on young Leonhard. Eulers formal education started in Basel, where he was sent to live with his maternal grandmother. In 1720, aged thirteen, he enrolled at the University of Basel, during that time, he was receiving Saturday afternoon lessons from Johann Bernoulli, who quickly discovered his new pupils incredible talent for mathematics. In 1726, Euler completed a dissertation on the propagation of sound with the title De Sono, at that time, he was unsuccessfully attempting to obtain a position at the University of Basel. In 1727, he first entered the Paris Academy Prize Problem competition, Pierre Bouguer, who became known as the father of naval architecture, won and Euler took second place. Euler later won this annual prize twelve times, around this time Johann Bernoullis two sons, Daniel and Nicolaus, were working at the Imperial Russian Academy of Sciences in Saint Petersburg. In November 1726 Euler eagerly accepted the offer, but delayed making the trip to Saint Petersburg while he applied for a physics professorship at the University of Basel. Euler arrived in Saint Petersburg on 17 May 1727 and he was promoted from his junior post in the medical department of the academy to a position in the mathematics department. He lodged with Daniel Bernoulli with whom he worked in close collaboration. Euler mastered Russian and settled life in Saint Petersburg. He also took on a job as a medic in the Russian Navy. The Academy at Saint Petersburg, established by Peter the Great, was intended to improve education in Russia, as a result, it was made especially attractive to foreign scholars like Euler
16.
Clothoid
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An Euler spiral is a curve whose curvature changes linearly with its curve length. Euler spirals are commonly referred to as spiros, clothoids. Euler spirals have applications to diffraction computations and they are also widely used as transition curve in railroad engineering/highway engineering for connecting and transiting the geometry between a tangent and a circular curve. A similar application is found in photonic integrated circuits. Where the Euler spiral meets the circular curve, its curvature becomes equal to that of the latter, an object traveling on a circular path experiences a centripetal acceleration. On early railroads this instant application of force was not an issue since low speeds. As speeds of vehicles increased over the years, it became obvious that an easement is necessary so that the centripetal acceleration increases linearly with the traveled distance. Given the expression of centripetal acceleration V² / R, the solution is to provide an easement curve whose curvature,1 / R. This geometry is an Euler spiral, marie Alfred Cornu also solved the calculus of Euler spiral independently. Euler spirals are now used in rail and highway engineering for providing a transition or an easement between a tangent and a horizontal circular curve. The Cornu spiral can be used to describe a diffraction pattern, a pioneering and very elegant application of the Euler spiral to waveguides had been made as early as 1957, with a hollow metal waveguide for microwaves. There the idea was to exploit the fact that a straight metal waveguide can be bent to naturally take a gradual bend shape resembling an Euler spiral. Motorsport author Adam Brouillard has shown the Euler spirals use in optimizing the racing line during the corner portion of a turn. + ⋯ C = ∫0 L cos d s = ∫0 L d s = L − L55 ×2, + ⋯ Expand S according to power series expansion of sine, sin θ = θ − θ33. + ⋯ S = ∫0 L sin d s = ∫0 L d s = L33 − L77 ×3 and this thus confirms that the original and normalized Euler spirals are geometrically similar. The locus of the curve can be determined from Fresnel Integral. S4 i +14 i +1 |0 L = ∑ i =0 ∞ i, L4 i +14 i +1 y = ∑ i =0 ∞ i. S4 i +34 i +3 |0 L = ∑ i =0 ∞ i, the following SageMath code produces the second graph above
17.
Track geometry
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Track geometry is three-dimensional geometry of track layouts and associated measurements used in design, construction and maintenance of railroad tracks. The subject is used in the context of standards, speed limits and other regulations in the areas of track gauge, alignment, elevation, curvature and track surface. Although, the geometry of the tracks is three-dimensional by nature, horizontal layout is the track layout on the horizontal plane. This can be thought of as the view which is a view of a 3-dimensional track from the position above the track. In track geometry, the horizontal layout involves the layout of three main types, tangent track, curved track, and track transition curve which connects between a tangent and a curved track. In Australia, there is a definition for a bend which is a connection between two tangent tracks at almost 180 degrees without an intermediate curve. There is a set of speed limits for the bends separately from normal tangent track, vertical layout is the track layout on the vertical plane. This can be thought of as the view which is the side view of the track to show track elevation. In track geometry, the vertical layout involves concepts such as crosslevel, the reference rail is the base rail that is used as a reference point for the measurement. It can vary in different countries, most countries use one of the rails as the reference rail. For Swiss railroad, the rail for tangent track is the center line between two rails, but it is the outside rail for curved track. Track gauge or rail gauge is the distance between the sides of the heads of the two load bearing rails that make up a single railway line. Each country uses different gauges for different types of trains, however, the 1435 mm gauge was the basis of 60% of the worlds railways. Crosslevel is the measurement of the difference in elevation between the top surface of the two rails at any point of railroad track, the two points are measured at by the right angles to the reference rail. Since the rail can slightly move up and down, the measurement should be done under load and it is said to be zero crosslevel when there is no difference in elevation of both rails. It is said to be reverse crosslevel when the rail of curved track has lower elevation than the inside rail. Otherwise, the crosslevel is expressed in the unit of height, the speed limits are governed by the crosslevel of the track. In tangent track, it is desired to have zero crosslevel, however, the deviation from zero can take place
18.
Three-dimensional space
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Three-dimensional space is a geometric setting in which three values are required to determine the position of an element. This is the meaning of the term dimension. In physics and mathematics, a sequence of n numbers can be understood as a location in n-dimensional space, when n =3, the set of all such locations is called three-dimensional Euclidean space. It is commonly represented by the symbol ℝ3 and this serves as a three-parameter model of the physical universe in which all known matter exists. However, this space is one example of a large variety of spaces in three dimensions called 3-manifolds. Furthermore, in case, these three values can be labeled by any combination of three chosen from the terms width, height, depth, and breadth. In mathematics, analytic geometry describes every point in space by means of three coordinates. Three coordinate axes are given, each perpendicular to the two at the origin, the point at which they cross. They are usually labeled x, y, and z, below are images of the above-mentioned systems. Two distinct points determine a line. Three distinct points are either collinear or determine a unique plane, four distinct points can either be collinear, coplanar or determine the entire space. Two distinct lines can intersect, be parallel or be skew. Two parallel lines, or two intersecting lines, lie in a plane, so skew lines are lines that do not meet. Two distinct planes can either meet in a line or are parallel. Three distinct planes, no pair of which are parallel, can meet in a common line. In the last case, the three lines of intersection of each pair of planes are mutually parallel, a line can lie in a given plane, intersect that plane in a unique point or be parallel to the plane. In the last case, there will be lines in the plane that are parallel to the given line, a hyperplane is a subspace of one dimension less than the dimension of the full space. The hyperplanes of a space are the two-dimensional subspaces, that is
19.
Quadratic equation
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If a =0, then the equation is linear, not quadratic. The numbers a, b, and c are the coefficients of the equation, and may be distinguished by calling them, respectively, the coefficient, the linear coefficient. Because the quadratic equation involves only one unknown, it is called univariate, solutions to problems equivalent to the quadratic equation were known as early as 2000 BC. A quadratic equation with real or complex coefficients has two solutions, called roots and these two solutions may or may not be distinct, and they may or may not be real. It may be possible to express a quadratic equation ax2 + bx + c =0 as a product =0. In some cases, it is possible, by inspection, to determine values of p, q, r. If the quadratic equation is written in the form, then the Zero Factor Property states that the quadratic equation is satisfied if px + q =0 or rx + s =0. Solving these two linear equations provides the roots of the quadratic, for most students, factoring by inspection is the first method of solving quadratic equations to which they are exposed. As an example, x2 + 5x +6 factors as, the more general case where a does not equal 1 can require a considerable effort in trial and error guess-and-check, assuming that it can be factored at all by inspection. Except for special cases such as where b =0 or c =0 and this means that the great majority of quadratic equations that arise in practical applications cannot be solved by factoring by inspection. The process of completing the square makes use of the identity x 2 +2 h x + h 2 =2. Starting with an equation in standard form, ax2 + bx + c =0 Divide each side by a. Subtract the constant term c/a from both sides, add the square of one-half of b/a, the coefficient of x, to both sides. This completes the square, converting the left side into a perfect square, write the left side as a square and simplify the right side if necessary. Produce two linear equations by equating the square root of the side with the positive and negative square roots of the right side. Completing the square can be used to derive a formula for solving quadratic equations. The mathematical proof will now be briefly summarized and it can easily be seen, by polynomial expansion, that the following equation is equivalent to the quadratic equation,2 = b 2 −4 a c 4 a 2. Taking the square root of both sides, and isolating x, gives, x = − b ± b 2 −4 a c 2 a and these result in slightly different forms for the solution, but are otherwise equivalent
20.
Arc (geometry)
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In Euclidean geometry, an arc is a closed segment of a differentiable curve. A common example in the plane, is a segment of a circle called a circular arc, in space, if the arc is part of a great circle, it is called a great arc. Every pair of points on a circle determines two arcs. The length, L, of an arc of a circle with radius r and this is because L c i r c u m f e r e n c e = θ2 π. Substituting in the circumference L2 π r = θ2 π, and, with α being the angle measured in degrees, since θ = α/180π. For example, if the measure of the angle is 60 degrees and this is so because the circumference of a circle and the degrees of a circle, of which there are always 360, are directly proportional. The area of the sector formed by an arc and the center of a circle is A =12 r 2 θ. The area A has the proportion to the circle area as the angle θ to a full circle. We can cancel π on both sides, A r 2 = θ2, by multiplying both sides by r2, we get the final result, A =12 r 2 θ. Using the conversion described above, we find that the area of the sector for an angle measured in degrees is A = α360 π r 2. The area of the bounded by the arc and the straight line between its two end points is 12 r 2. To get the area of the arc segment, we need to subtract the area of the triangle, determined by the circles center and the two end points of the arc, from the area A. Using the intersecting chords theorem it is possible to calculate the radius r of a circle given the height H and its perpendicular bisector is another chord, which is a diameter of the circle. The length of the first chord is W, and it is divided by the bisector into two halves, each with length W/2. The total length of the diameter is 2r, and it is divided into two parts by the first chord, the length of one part is the sagitta of the arc, H, and the other part is the remainder of the diameter, with length 2r − H. Applying the intersecting chords theorem to these two chords produces H =2, whence 2 r − H = W24 H, so r = W28 H + H2
21.
Cartesian coordinates
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Each reference line is called a coordinate axis or just axis of the system, and the point where they meet is its origin, usually at ordered pair. The coordinates can also be defined as the positions of the projections of the point onto the two axis, expressed as signed distances from the origin. One can use the principle to specify the position of any point in three-dimensional space by three Cartesian coordinates, its signed distances to three mutually perpendicular planes. In general, n Cartesian coordinates specify the point in an n-dimensional Euclidean space for any dimension n and these coordinates are equal, up to sign, to distances from the point to n mutually perpendicular hyperplanes. The invention of Cartesian coordinates in the 17th century by René Descartes revolutionized mathematics by providing the first systematic link between Euclidean geometry and algebra. Using the Cartesian coordinate system, geometric shapes can be described by Cartesian equations, algebraic equations involving the coordinates of the points lying on the shape. For example, a circle of radius 2, centered at the origin of the plane, a familiar example is the concept of the graph of a function. Cartesian coordinates are also tools for most applied disciplines that deal with geometry, including astronomy, physics, engineering. They are the most common system used in computer graphics, computer-aided geometric design. Nicole Oresme, a French cleric and friend of the Dauphin of the 14th Century, used similar to Cartesian coordinates well before the time of Descartes. The adjective Cartesian refers to the French mathematician and philosopher René Descartes who published this idea in 1637 and it was independently discovered by Pierre de Fermat, who also worked in three dimensions, although Fermat did not publish the discovery. Both authors used a single axis in their treatments and have a length measured in reference to this axis. The concept of using a pair of axes was introduced later, after Descartes La Géométrie was translated into Latin in 1649 by Frans van Schooten and these commentators introduced several concepts while trying to clarify the ideas contained in Descartes work. Many other coordinate systems have developed since Descartes, such as the polar coordinates for the plane. The development of the Cartesian coordinate system would play a role in the development of the Calculus by Isaac Newton. The two-coordinate description of the plane was later generalized into the concept of vector spaces. Choosing a Cartesian coordinate system for a one-dimensional space – that is, for a straight line—involves choosing a point O of the line, a unit of length, and an orientation for the line. An orientation chooses which of the two half-lines determined by O is the positive, and which is negative, we say that the line is oriented from the negative half towards the positive half
22.
Fresnel integral
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Fresnel integrals, S and C, are two transcendental functions named after Augustin-Jean Fresnel that are used in optics, which are closely related to the error function. They arise in the description of near-field Fresnel diffraction phenomena and are defined through the following integral representations, the simultaneous parametric plot of S and C is the Euler spiral. Recently, they have used in the design of highways. The Fresnel integrals admit the following power series expansions that converge for all x, S = ∫0 x sin d t = ∑ n =0 ∞ n x 4 n +3. C = ∫0 x cos d t = ∑ n =0 ∞ n x 4 n +1, some authors, including Abramowitz and Stegun, use π2 t 2 for the argument of the integrals defining S and C. To get these functions, multiply the above integrals by 2 π, the Euler spiral, also known as Cornu spiral or clothoid, is the curve generated by a parametric plot of S against C. The Cornu spiral was created by Marie Alfred Cornu as a nomogram for diffraction computations in science and engineering. From the definitions of Fresnel integrals, the infinitesimals d x and d y are thus, d x = C ′ d t = cos d t, d y = S ′ d t = sin d t. Thus the length of the spiral measured from the origin can be expressed as L = ∫0 t 0 d x 2 + d y 2 = ∫0 t 0 d t = t 0. That is, the t is the curve length measured from the origin. The vector also expresses the unit tangent vector along the spiral, since t is the curve length, the curvature κ can be expressed as κ =1 R = d θ d t =2 t. And the rate of change of curvature with respect to the length is d κ d t = d 2 θ d t 2 =2. An Euler spiral has the property that its curvature at any point is proportional to the distance along the spiral and this property makes it useful as a transition curve in highway and railway engineering. If a vehicle follows the spiral at unit speed, the t in the above derivatives also represents the time. That is, a following the spiral at constant speed will have a constant rate of angular acceleration. Sections from Euler spirals are commonly incorporated into the shape of roller-coaster loops to make what are known as clothoid loops, C and S are odd functions of x. Asymptotics of the Fresnel integrals as x → ∞ are given by the formulas, using the power series expansions above, the Fresnel integrals can be extended to the domain of complex numbers, and they become analytic functions of a complex variable. The Fresnel integrals can be expressed using the function as follows
23.
Euler spiral
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An Euler spiral is a curve whose curvature changes linearly with its curve length. Euler spirals are commonly referred to as spiros, clothoids. Euler spirals have applications to diffraction computations and they are also widely used as transition curve in railroad engineering/highway engineering for connecting and transiting the geometry between a tangent and a circular curve. A similar application is found in photonic integrated circuits. Where the Euler spiral meets the circular curve, its curvature becomes equal to that of the latter, an object traveling on a circular path experiences a centripetal acceleration. On early railroads this instant application of force was not an issue since low speeds. As speeds of vehicles increased over the years, it became obvious that an easement is necessary so that the centripetal acceleration increases linearly with the traveled distance. Given the expression of centripetal acceleration V² / R, the solution is to provide an easement curve whose curvature,1 / R. This geometry is an Euler spiral, marie Alfred Cornu also solved the calculus of Euler spiral independently. Euler spirals are now used in rail and highway engineering for providing a transition or an easement between a tangent and a horizontal circular curve. The Cornu spiral can be used to describe a diffraction pattern, a pioneering and very elegant application of the Euler spiral to waveguides had been made as early as 1957, with a hollow metal waveguide for microwaves. There the idea was to exploit the fact that a straight metal waveguide can be bent to naturally take a gradual bend shape resembling an Euler spiral. Motorsport author Adam Brouillard has shown the Euler spirals use in optimizing the racing line during the corner portion of a turn. + ⋯ C = ∫0 L cos d s = ∫0 L d s = L − L55 ×2, + ⋯ Expand S according to power series expansion of sine, sin θ = θ − θ33. + ⋯ S = ∫0 L sin d s = ∫0 L d s = L33 − L77 ×3 and this thus confirms that the original and normalized Euler spirals are geometrically similar. The locus of the curve can be determined from Fresnel Integral. S4 i +14 i +1 |0 L = ∑ i =0 ∞ i, L4 i +14 i +1 y = ∑ i =0 ∞ i. S4 i +34 i +3 |0 L = ∑ i =0 ∞ i, the following SageMath code produces the second graph above
24.
Degree of curvature
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Degree of curve or degree of curvature is a measure of curvature of a circular arc used in civil engineering for its easy use in layout surveying. The degree of curvature is defined as the angle to the ends of an arc or chord of agreed length. Various lengths are used in different areas of practice. This angle is also the change in direction as that portion of the curve is traveled. Curvature is usually measured in radius of curvature, by this method curve setting can be easily done with the help of a transit or theodolite and a chain, tape or rope of a prescribed length. In an n-degree curve, the bearing changes by n degrees over the standard length of arc or chord. The usual distance in North American road work is 100 feet of arc, North American railroad work traditionally used 100 feet of chord and this may be used in other places for road work. Other lengths may be used—such as 30 metres or 100 metres where SI is favoured, or a shorter length for sharper curves. Where degree of curvature is based on 100 units of arc length, the conversion between degree of curvature and radius is Dr = 18000/π ≈5729.57795, where D is degree and r is radius. As an example, a curve with an arc length of 600 units that has a sweep of 6 degrees is a 1-degree curve, For every 100 feet of arc. The radius of such a curve is 5729.57795, if the chord definition is used each 100-unit chord length will sweep 1 degree with a radius of 5729.651 units, and the chord of the whole curve will be slightly shorter than 600 units. Since rail routes have very large radii, they are out in chords, as the difference to the arc is inconsequential. The 100 feet is called a station, used to define length along a road or other alignment, metric work may use similar notation, such as kilometers plus meters 1+000
25.
Minimum railway curve radius
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The minimum railway curve radius is the shortest allowable design radius for railway tracks under a particular set of conditions. It has an important bearing on costs and operating costs and, in combination with superelevation in the case of train tracks. Minimum radius of curve is one parameter in the design of vehicles as well as trams. Monorails and guideways are also subject to minimum radii, the first proper railway was the Liverpool and Manchester Railway which opened in 1830. Like the trams that had preceded it over a hundred years, among other reasons for the gentle curves were the lack of strength of the track, which might have overturned if the curves were too sharp causing derailments. There was no signalling at this time, so drivers had to be able to see ahead to avoid collisions with previous trains, the gentler the curves, the longer the visibility. The earliest rails were made in lengths of wrought iron. Minimum curve radii for railroads are governed by the speed operated, for handling of long freight trains, a minimum 717-foot radius is preferred. The sharpest curves tend to be on the narrowest of narrow gauge railways, as the need for more powerful locomotives grew, the need for more driving wheels on a longer, fixed wheelbase grew too. But long wheel bases are unfriendly to sharp curves, various types of articulated locomotives were devised to avoid having to operate multiple locomotives with multiple crews. More recent diesel and electric locomotives do not have a wheelbase problem and this is particularly true of the European buffer and chain couplers, where the buffers extend the profile of the railcar body. For a line with maximum speed 60 km/h, buffer-and-chain couplings reduce the radius to around 200 m. A long heavy freight train, especially those with wagons of mixed loading, may struggle on sharp curves, common solutions include, marshalling light and empty wagons at rear of train intermediate locomotives, including remotely controlled ones. Easing curves reduced speeds reduced cant, at the expense of fast passenger trains, equalizing wagon loading better driver training driving controls that display drawgear forces. And c2013 Electronically Controlled Pneumatic brakes, a similar problem occurs with harsh changes in gradients. To counter this, a cant is used, ideally the train should be tilted such that resultant force acts straight down through the bottom of the train, so the wheels, track, train and passengers feel little or no sideways force. Some trains are capable of tilting to enhance this effect for passenger comfort, because freight and passenger trains tend to move at different speeds and weigh dramatically different, a cant cannot be ideal for both types of rail traffic. The relationship between speed and tilt can be calculated mathematically, the values used when building high-speed railways vary, and depend on desired wear and safety levels
26.
International Standard Book Number
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The International Standard Book Number is a unique numeric commercial book identifier. An ISBN is assigned to each edition and variation of a book, for example, an e-book, a paperback and a hardcover edition of the same book would each have a different ISBN. The ISBN is 13 digits long if assigned on or after 1 January 2007, the method of assigning an ISBN is nation-based and varies from country to country, often depending on how large the publishing industry is within a country. The initial ISBN configuration of recognition was generated in 1967 based upon the 9-digit Standard Book Numbering created in 1966, the 10-digit ISBN format was developed by the International Organization for Standardization and was published in 1970 as international standard ISO2108. Occasionally, a book may appear without a printed ISBN if it is printed privately or the author does not follow the usual ISBN procedure, however, this can be rectified later. Another identifier, the International Standard Serial Number, identifies periodical publications such as magazines, the ISBN configuration of recognition was generated in 1967 in the United Kingdom by David Whitaker and in 1968 in the US by Emery Koltay. The 10-digit ISBN format was developed by the International Organization for Standardization and was published in 1970 as international standard ISO2108, the United Kingdom continued to use the 9-digit SBN code until 1974. The ISO on-line facility only refers back to 1978, an SBN may be converted to an ISBN by prefixing the digit 0. For example, the edition of Mr. J. G. Reeder Returns, published by Hodder in 1965, has SBN340013818 -340 indicating the publisher,01381 their serial number. This can be converted to ISBN 0-340-01381-8, the check digit does not need to be re-calculated, since 1 January 2007, ISBNs have contained 13 digits, a format that is compatible with Bookland European Article Number EAN-13s. An ISBN is assigned to each edition and variation of a book, for example, an ebook, a paperback, and a hardcover edition of the same book would each have a different ISBN. The ISBN is 13 digits long if assigned on or after 1 January 2007, a 13-digit ISBN can be separated into its parts, and when this is done it is customary to separate the parts with hyphens or spaces. Separating the parts of a 10-digit ISBN is also done with either hyphens or spaces, figuring out how to correctly separate a given ISBN number is complicated, because most of the parts do not use a fixed number of digits. ISBN issuance is country-specific, in that ISBNs are issued by the ISBN registration agency that is responsible for country or territory regardless of the publication language. Some ISBN registration agencies are based in national libraries or within ministries of culture, in other cases, the ISBN registration service is provided by organisations such as bibliographic data providers that are not government funded. In Canada, ISBNs are issued at no cost with the purpose of encouraging Canadian culture. In the United Kingdom, United States, and some countries, where the service is provided by non-government-funded organisations. Australia, ISBNs are issued by the library services agency Thorpe-Bowker
27.
Infrastructure
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Infrastructure refers to the fundamental facilities and systems serving a country, city, or area, including the services and facilities necessary for its economy to function. The word was imported from French, where it means subgrade, the word is a combination of the Latin prefix infra, meaning below, and structure. The military use of the term achieved currency in the United States after the formation of NATO in the 1940s and this crisis discussion contributed to an increase in infrastructure asset management and maintenance planning in the US. Public-policy discussions have been hampered by lack of a definition for infrastructure. A1987 US National Research Council panel adopted the public works infrastructure. The OECD also classifies communications as a part of infrastructure, the American Society of Civil Engineers has not defined the term, though issuing a US Infrastructure Report Card every 2-4 years. Hard infrastructure refers to the physical networks necessary for the functioning of an industrial nation. The term critical infrastructure distinguishes those infrastructure elements that, if damaged or destroyed. Similarly, a booking system might be critical infrastructure for an airline. These elements of infrastructure are the focus of efforts in the aftermath of natural disasters. The term infrastructure may be confused with the following overlapping or related concepts, service connections to municipal service and public utility networks would also be considered land improvements, not infrastructure. The term public works includes government-owned and operated infrastructure as well as buildings, such as schools. Public works generally refers to physical assets needed to deliver public services, public services include both infrastructure and services generally provided by government. Infrastructure may be owned and managed by governments or by private companies, generally, most roads, major ports and airports, water distribution systems and sewage networks are publicly owned, whereas most energy and telecommunications networks are privately owned. Publicly owned infrastructure may be paid for taxes, tolls, or metered user fees. Major investment projects are financed by the issuance of long-term bonds. Government owned and operated infrastructure may be developed and operated in the sector or in public-private partnerships. As of 2008 in the United States for example, public spending on infrastructure has varied between 2. 3% and 3. 6% of GDP since 1950, many financial institutions invest in infrastructure
28.
Permanent way (history)
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The permanent way is the elements of railway lines, generally the pairs of rails typically laid on the sleepers embedded in ballast, intended to carry the ordinary trains of a railway. The earliest tracks consisted of wooden rails on wooden sleepers. Various developments followed, with cast iron laid on top of the wooden rails. Rails were also fixed to rows of stone blocks, without any cross ties to maintain correct separation. This system also led to problems, as the blocks could individually move, developments in manufacturing technologies has led to changes to the design, manufacture and installation of rails, sleepers and the means of attachments. Cast iron rails,4 feet long, began to be used in the 1790s, the first steel rails were made in 1857 and standard rail lengths increased over time from 30 to 60 feet. Rails were typically specified by units of weight per linear length, Railway sleepers were traditionally made of Creosote-treated hardwoods and this continued through to modern times. Continuous welded rail was introduced into Britain in the mid 1960s, the earliest use of a railway track seems to have been in connection with mining in Germany in the 12th century. Mine passageways were usually wet and muddy, and moving barrows of ore along them was extremely difficult, improvements were made by laying timber planks so that wheeled containers could be dragged along by manpower. By the 16th century, the difficulty of keeping the running straight had been solved by having a pin going into a gap between the planks. Georg Agricola describes box-shaped carts, called dogs, about half as large again as a wheelbarrow, fitted with a blunt vertical pin and wooden rollers running on iron axles. An Elizabethan era example of this has been discovered at Silvergill in Cumbria, England and this, probably a rope-hauled incline plane, had existed long before 1605. This probably preceded the Wollaton Wagonway of 1604, which has hitherto been regarded as the first, in Shropshire, the gauge was usually narrow, to enable the wagons to be taken underground in drift mines. However, by far the greatest number of wagonways were near Newcastle upon Tyne and these took coal from the pithead down to a staithe, where the coal was loaded into river boats called keels. Wear of the rails was a problem. They could be renewed by turning them over, but had to be regularly replaced, sometimes, the rail was made in two parts, so that the top portion could easily be replaced when worn out. The rails were held together by wooden sleepers, covered with ballast to provide a surface for the horse to walk on. Cast iron strips could be laid on top of timber rails, and the use of such materials probably occurred in 1738, but there are claims that this technology went back to 1716
29.
Baulk road
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Brunel sought an improved design for the railway track needed for the Great Western Railway, authorised by Act of Parliament in 1835 to link London and Bristol. He refused to accept received wisdom without challenge, to achieve this he needed a wider track gauge and he settled on a 7 ft broad gauge but it was soon eased slightly to 7 ft 1⁄4 in. His original intention to have the wheels outside the width of the bodies was abandoned, early locomotive-powered railways had used short cast iron rails carried on stone blocks. A few were trying timber sleepers to support the rails and to maintain the gauge between them and these rails were brittle and broke easily, and they gave a rough ride due to the difficulty of maintaining a smooth line between the blocks or sleepers. Wrought iron rails were being manufactured but they were of poor quality due to the difficulty of cooling them evenly during manufacture, brunel decided to use a continuously supported wrought iron rail, a bridge rail with a smaller rail section that cooled more evenly. This was a section with wide flanges that could be bolted to the timber bearer. The longitudinal baulks, and therefore the rails, were kept to gauge by transoms – transverse timber spacers –, the transom kept the longitudinals from getting too close together, the tie rods stopped them spreading too far apart. In later years the tie rods were replaced by strap bolts and these were bolted to the transoms and passed through a hole drilled through the longitudinal to a nut on the outside. He cut the piles away from the transoms and this solved the problem, the bridge rail for this line weighed 43 lb/yd but this was soon increased, generally to 62 lb/yd. The longitudinal baulks were around 12 in. wide and 5 in, deep or 10 by 7 in, but the sizes varied depending on the timber available and the weight of traffic to be carried. Transoms were around 6 by 9 in and initially spaced at 15 feet intervals, the GWR also used conventional cross-sleepered track, especially on 4 ft 8 1⁄2 in standard gauge lines. Although its last broad gauge track was replaced by standard gauge in 1892, converting broad gauge baulk road to standard was done by cutting the transoms and slewing the longitudinal and its rail to its new position. Between 1852 and 1892 an ever-increasing length of the Great Western Railway had been laid as mixed gauge that could be used by trains of either gauge. For baulk road this meant laying an additional longitudinal between the two, but this significantly increased the cost and complexity of the track compared to cross-sleepers. Vignoles rail was a section that today would be classed as flat-bottomed rail. In its original form it was only about 4 inches deep and was used on baulk road interchangeably with bridge rail, william Henry Barlow’s Barlow rail was patented in 1849 as a purely metal road. Deep rails with an inverted, curved V section were designed to be directly into the ballast. The rails weighed 93 lb/yd but this was increased to 99 lb/yd
30.
Clip and scotch
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To clip and scotch a set of railway points uses two pieces of equipment to temporarily lock a set of points into a particular position. In this way the points are fixed in either the normal or reverse positions, for infrequently used points, this guards against mechanical failure of the points leaving them in a condition to derail trains. The clip and scotch method can also be used to deny access to the turnout or mainline. The block of wood set in the gap is known as the wedge and is functionally equivalent to a scotch. Requirements for the Design, Operation and Maintenance of Points, safety & Standards Directorate, Railtrack PLC, Evergreen House,160 Euston Road, London NW1 2DX. Archived from the original on October 6,2007, LUL RAILWAY SAFETY CASE VERSION3.24 GLOSSARY. Archived from the original on May 22,2005
31.
Datenail
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Datenails were tagging devices utilized by railroads to visually identify the age of a railroad tie. Different railroads used different sized nails with either alpha or numerical markings, an example would be a Southern Pacific Railroad nail with the marking 01 stamped on the head of the nail. The 01 would identify the nail as being hammered into a tie in the year 1901. Datenail use has dropped dramatically since the century and the advent of more modern maintenance of way equipment. Ties are no longer marked in this manner in North American practice, the Southern Railway never made use of datenails. Datenails are also found on utility poles, sometimes in conjunction with a showing the height of the pole in feet. The types of nails may have distinguishing characteristics, such as the datenail having raised digits, the pole height will be a multiple of five
32.
Fishplate
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In rail terminology, a fishplate, splice bar or joint bar is a metal bar that is bolted to the ends of two rails to join them together in a track. The name is derived from fish, a bar with a curved profile used to strengthen a ships mast. The top and bottom edges are tapered inwards so the device wedges itself between the top and bottom of the rail when it is bolted into place. In rail transport modelling, a fishplate is often a small copper or nickel silver plate that slips onto both rails to provide the functions of maintaining alignment and electrical continuity. The device was invented by William Bridges Adams in May 1842, because of his dissatisfaction with the scarf joints and he noted that to form the scarf joint the rail was halved in thickness at its ends, where the stress was greatest. It was first deployed on the Eastern Counties Railway in 1844, Adams and Robert Richardson patented the invention in 1847, but in 1849 James Samuel, the engineer of the ECR developed fishplates that could be bolted to the rails. The moving blades of a set of points can be connected to the rails by looser than normal fishplates. This is called a heeled switch, alternatively, the blade and stock rail can be a one piece heel-less switch, with a flexible thinned section to create the moving heel. Even though fishplates strengthen the weak points represented by rail joints, improvements can still be made, for example, the joints can be welded together using the thermite welding process. In 1967, at Hither Green on the Southern Region of British Railways, welded Rail installation was sped up due to this error, with strict procedures on Concrete and Wooden Sleepers. On 12 July 2013, the last four cars of an SNCF Paris-Limoges train left the track while entering the Brétigny-sur-Orge station, killing seven people and injuring 32. Under the weight of the train travelling at 137 km/h, the fishplate had pivoted around the first of four bolts meant to hold it in place, the most likely cause of the bolts coming loose, says BEA-TT, were stresses caused by cracking in the cast steel crossing. This had caused the head of the bolt to break off and the others to fail, one becoming unscrewed. Rail lengths Tie plate Fish Plate
33.
Ladder track
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This article is about the types of railway track technologies known as Ladder Track. For a description of the layout also known as ladder track. Ladder track is a type of track in which the track is laid on longitudinal supports with transverse connectors holding the two rails at the correct gauge distance. Modern ladder track can be considered a development of baulk road, Ladder type track has also be used historically on bridges lacking ballast, and in situations requiring good drainage or ease of maintenance such as stations. On the Hull and Selby Railway it was used in part as it was noted to produce smooth running, however the contact between rail and sleeper produced hydraulic pumping in wet conditions, which led to rolling stock becoming dirtied very quickly. The longitudinal track was also cause issue with wheel slip on inclines. No longitudinally laid track remained on the line after 1860, Research into longitudinal sleepers took place in Japan, Russia and France in the mid 20th century. In the late 20th century, interest in ladder type tracks increased due to its potential for lower cost and lower maintenance railways, as well as increased stability benefits over sleepered track. An additional benefit in ballasted ladder track is increased resistance to ballast wash out and other forms of ballast degradation due the addition longitudinal support, the same structural rigidity also adds to buckling resistance. Tubular Modular Track is a type of ladder track manufactured by Tubular Track Ltd. of South Africa first introduced in 1989. The track is modular and precast, rather than being cast in situ, the modular nature and controlled production of the track sections has the advantage of rapid installation and good quality control. The track has used mainly in southern Africa, including a section of the Gautrain line in South Africa. The system has also used in Saudi Arabia. The Railway Technical Research Institute of Japan has developed two types of track, ballasted and a floating un-ballasted type. Forms for axle load of 40 tonnes have been designed, the design can also incorporate ducts within the beams and can be converted to slab track by in-situ concrete pouring. The companys main market is mining applications, railroad tie Trackless train ラダー軌道 Ladder Track System, www. rtri. or
34.
Rail fastening system
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A rail fastening system is a means of fixing rails to railroad ties or sleepers. The terms rail anchors, tie plates, chairs and track fasteners are used to refer to parts or all of a rail fastening system, various types of fastening have been used over the years. The earliest wooden rails were fixed to wooden sleepers by pegs through holes in the rail, by the 18th century cast iron rails had come into use, and also had holes in the rail itself to allow them to be fixed to a support. The first chair for a rail is thought to have introduced in 1797 which attached to the rail on the vertical web via bolts. In North American practice the flanged T rail became the standard, elsewhere T rails were replaced by bull head rails of a rounded I or figure-8 appearance which still required a supporting chair. Eventually the flanged T rail became commonplace on all the worlds railways, a Golden Tie, also known as a Golden Spike or The Last Spike, may be used to symbolize the start or the completion of an endeavor. These are less often silver or another precious material, historically, a ceremonial Golden Spike driven by Leland Stanford connected the rails of the First Transcontinental Railroad across the United States. The valuable rail fastening spike represented the merge of the Central Pacific and Union Pacific railroads on May 10,1869, at Promontory Summit, since, railroad workers have been celebrated in popular culture, including in song and verse. Most recently, a Golden Spike marked the completion of the longest transportation tunnel in the world, the Gotthard Base Tunnel, full rail service began on 11 December 2016. Its functional length is 57.09 km and its the worlds deepest traffic tunnel, a rail spike is a large nail with an offset head that is used to secure rails and base plates to railroad ties in the track. Robert Livingston Stevens is credited with the invention of the railroad spike, in 1982, the spike was still the most common rail fastening in North America. Common sizes are from 9 to 10/16 inch square and ~5.5 to 6 inch long, a rail spike is roughly chisel-shaped and with a flat edged point, the spike is driven with the edge perpendicular to the grain, which gives greater resistance to loosening. The main function is to keep the rail in gauge, on smaller scale jobs spikes are still driven into wooden sleepers by hammering them with a spike maul. Though this manual work has largely replaced by hydraulic tools and machines. Splitting of the wood can be limited by pre-boring spike holes or adding steel bands around the wood, for use in the United States three basic standards are described in the ASTM A65 standard, for different carbon steel contents. A screw spike, rail screw or lag bolt is a metal screw used to fix a tie plate or to directly fasten a rail. Screw spikes are screwed into a hole bored in the sleeper, the screw spike was first introduced in 1860 in France and became common in continental Europe. A dog screw is a variant of the screw spike
35.
Rail profile
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The rail profile is the cross sectional shape of a railway rail, perpendicular to its length. Early rails were made of wood, cast iron or wrought iron, all modern rails are hot rolled steel with a cross section approximate to an I-beam, but asymmetric about a horizontal axis. The head is profiled to resist wear and to give a ride. Unlike some other uses of iron and steel, railway rails are subject to high stresses and are made of very high quality steel. It took many decades to improve the quality of the materials, minor flaws in the steel that may pose no problems in other applications can lead to broken rails and dangerous derailments when used on railway tracks. By and large, the heavier the rails and the rest of the trackwork, the rails represent a substantial fraction of the cost of a railway line. Only a small number of sizes are made by steelworks at one time. Worn, heavy rail from a mainline is often reclaimed and downgraded for re-use on a branchline, the weight of a rail per length is an important factor in determining rails strength and hence axleloads and speeds. Weights are measured in pounds per yard or kilograms per metre, rails in Canada, the United Kingdom and United States are described using imperial units. In Australia, metric units are used as in mainland Europe, commonly, in rail terminology Pound is a contraction of the expression pounds per yard and hence a 132–pound rail means a rail of 132 pounds per yard. Rails are made in a number of different sizes. Some common European rail sizes include, In the countries of former USSR65 kg/m rails and 75 kg/m rails are common, the American Society of Civil Engineers specified rail profiles in 1893 for 5-pound-per-yard increments from 40 to 100 lb/yd. Height of rail equaled width of foot for each ASCE tee-rail weight, ASCE90 lb/yd profile was adequate, but heavier weights were less satisfactory. In 1909, the American Railway Association specified standard profiles for 10 lb/yd increments from 60 to 100 lb/yd, the trend was to increase rail height/foot-width ratio and strengthen the web. Disadvantages of the foot were overcome through use of tie-plates. AREA recommendations reduced the weight of rail head down to 36%. Attention was also focused on improved fillet radii to reduce stress concentration at the web junction with the head, AREA recommended the ARA90 lb/yd profile. Old ASCE rails of lighter weight remained in use, and satisfied the demand for light rail for a few decades
36.
Railroad tie
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A railroad tie/railway tie/crosstie or railway sleeper is a rectangular support for the rails in railroad tracks. Generally laid perpendicular to the rails, ties transfer loads to the track ballast and subgrade, hold the rails upright, railroad ties are traditionally made of wood, but pre-stressed concrete is now also widely used, especially in Europe and Asia. Steel ties are common on secondary lines in the UK, plastic composite ties are also employed, as of January 2008, the approximate market share in North America for traditional and wood ties was 91. 5%, the remainder being concrete, steel, azobé and plastic composite. Approximately 3,520 wooden crossties are used per mile of railroad track in the US,2,640 per mile on main lines in the UK. The type of railroad tie used on the predecessors of the first true railway consisted of a pair of stone blocks laid into the ground, one advantage of this method of construction was that it allowed horses to tread the middle path without the risk of tripping. In railway use with heavier locomotives, it was found that it was hard to maintain the correct gauge. The stone blocks were in any case unsuitable on soft ground, such as at Chat Moss, bi-block ties with a tie rod are somewhat similar. Historically wooden rail ties were made by hewing with an axe, a variety of softwood and hardwoods timbers are used as ties, oak, jarrah and karri being popular hardwoods, although increasingly difficult to obtain, especially from sustainable sources. Sometimes non-toxic preservatives are used, such as copper azole or micronized copper, New boron-based wood preserving technology is being employed by major US railroads in a dual treatment process in order to extend the life of wood ties in wet areas. Some timbers are durable enough that they can be used untreated, problems with wooden ties include rot, splitting, insect infestation, plate-cutting, also known as chair shuffle in the UK and spike-pull. For more information on wooden ties the Railway Tie Association maintains a website devoted to wood tie research. Wooden ties can, of course, catch fire, as they age they develop cracks that allow sparks to lodge so that they catch fire more easily, concrete ties are cheaper and easier to obtain than timber and better able to carry higher axle-weights and sustain higher speeds. Their greater weight ensures improved retention of track geometry, especially when installed with continuous-welded rail, concrete ties have a longer service life and require less maintenance than timber due to their greater weight, which helps them remain in the correct position longer. Concrete ties need to be installed on a well-prepared subgrade with a depth on free-draining ballast to perform well. Concrete ties amplify wheel noise, so wooden ties are used in densely populated areas. On the highest categories of line in the UK, pre-stressed concrete ties are the only permitted by Network Rail standards. Steel ties are formed from pressed steel and are trough-shaped in section, the ends of the tie are shaped to form a spade which increases the lateral resistance of the tie. Housings to accommodate the system are welded to the upper surface of the tie
37.
Track ballast
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Track ballast forms the trackbed upon which railroad ties are laid. It is packed between, below, and around the ties and it is used to bear the load from the railroad ties, to facilitate drainage of water, and also to keep down vegetation that might interfere with the track structure. This also serves to hold the track in place as the roll by. It is typically made of crushed stone, although ballast has sometimes consisted of other, less suitable materials, the term ballast comes from a nautical term for the stones used to stabilize a ship. The appropriate thickness of a layer of track ballast depends on the size and spacing of the ties, the amount of traffic on the line, and various other factors. Track ballast should never be laid down less than 150 mm thick, an insufficient depth of ballast causes overloading of the underlying soil, and in unfavourable conditions overloading the soil causes the track to sink, usually unevenly. Ballast less than 300 mm thick can lead to vibrations that damage nearby structures, however, increasing the depth beyond 300 mm adds no extra benefit in reducing vibration. In turn, track ballast typically rests on a layer of crushed stones. The sub-ballast layer gives a solid support for the top ballast, sometimes an elastic mat is placed on the layer of sub-ballast and beneath the ballast, thereby significantly reducing vibration. The ballast shoulder always should be at least 150 mm wide, the shape of the ballast is also important. Stones must be cut, with sharp edges, so that they properly interlock and grip the ties in order to fully secure them against movement. In order to let the stones fully settle and interlock, speed limits are often lowered on sections of track for a period of time after new ballast has been laid. If ballast is badly fouled, the clogging will reduce its ability to drain properly, therefore, keeping the ballast clean is essential. Bioremediation can be used to clean ballast and it is not always necessary to replace the ballast if it is fouled, nor must all the ballast be removed if it is to be cleaned. Removing and cleaning the ballast from the shoulder is often sufficient, such machines can clean up to two kilometres of ballast in an hour. In such cases, it is necessary to replace the ballast altogether, the dump and jack method cannot of course be used through tunnels, under overbridges, and where there are platforms. Where the track is laid over a swamp, such as the Hexham swamp in Australia, the ballast continuously sinks, after 150 years of topping up, there appears to be 10 m of sunken ballast under the tracks. Chat Moss in the United Kingdom is similar, regular inspection of the ballast shoulder is important, as noted earlier, the lateral stability of the track depends upon the shoulder
38.
Balloon loop
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A balloon loop, turning loop or reversing loop allows a rail vehicle or train to reverse direction without having to shunt or even stop. Balloon loops can be useful for passenger trains and unit freight trains such as coal trains, Balloon loops are common on tram or streetcar systems. Balloon loops were first introduced on metro and tram lines, Balloon loops enable higher line capacity and also allow the use of single-ended trams which have several advantages, including lower cost and more seating when doors are on one side only. However, double-ended trams also benefit from the capacity advantage of balloon loops, initially the Sydney system was operated by single-ended steam trams and then, from the 1890s, by double-ended electric trams. The Sydney system was possibly the first major example of a tramway system. European systems were converted to looped operation in the early twentieth century. Looped operation with single-ended trams was also used on many North American streetcar systems, on a balloon loop, the station is on the balloon loop, and the platform may be curved or straight. Penfield - now closed and removed Outer Harbor - now closed and removed Olympic Park, Sydney, Australia, Beech Forrest, Victoria, Australia, single platform station on Victorian narrow gauge railway. These trains discharge and take on passengers at Brooklyn Bridge – City Hall, South Ferry was a two-track subway loop station in New York City, with a sharply curved side platform for each track. After the latter station was damaged in Hurricane Sandy, the station was reopened temporarily to provide service to the ferry terminal until the repairs to the latter station are complete. Bowdoin Station on the MBTA Blue Line in Boston has an island platform inside a balloon loop. The boarding platform is long enough for four cars. World Trade Center station on the PATH subway system linking New York, dungeness, Romney, Hythe and Dymchurch Railway, Kent, England, single track, single platform for both boarding and alighting. This evens the wear on the train wheels, central station in Newcastle upon Tyne is on a loop, allowing trains from the South to arrive via the King Edward VII Bridge and return using the High Level Bridge. Peasholm on the North Bay Railway in Scarborough, North Yorkshire has a balloon loop. The loop is used to allow the locomotive to run round the train, the first Wembley Stadium station in London was on a balloon loop, but the present station of that name is not. Barmouth Ferry station on the Fairbourne Railway, blackpool Tramway has a balloon loop at each end of the system and at two intermediate points. Kennington station, also on the Northern line, has a loop to the south of the station to allow terminating southbound trains to reach the northbound platforms to form a return service
39.
Classification yard
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A classification yard or marshalling yard is a railway yard found at some freight train stations, used to separate railway cars on to one of several tracks. First the cars are taken to a track, sometimes called a lead or a drill, from there the cars are sent through a series of switches called a ladder onto the classification tracks. Larger yards tend to put the lead on an artificially built hill called a hump to use the force of gravity to propel the cars through the ladder, freight trains that consist of isolated cars must be made into trains and divided according to their destinations. Thus the cars must be shunted several times along their route in contrast to a unit train and this shunting is done partly at the starting and final destinations and partly in classification yards. Flat yards are constructed on ground, or on a gentle slope. Freight cars are pushed by a locomotive and coast to their required location, hump yards are the largest and most effective classification yards, with the largest shunting capacity, often several thousand cars a day. The heart of these yards is the lead track on a small hill over which an engine pushes the cars. As concerns speed regulation, there are two types of hump yards—without or with mechanisation by retarders, in the old non-retarder yards braking was usually done in Europe by railroaders who laid skates onto the tracks. The skate or chock was manually placed on one or both of the rails so that the treadles or rims of the wheel or wheels caused frictional retardation, in the United States this braking was done by riders on the cars. In the modern retarder yards this work is done by mechanized rail brakes called retarders and they are operated either pneumatically or hydraulically. Pneumatic systems are prevalent in the United States, France, Belgium, Russia and China, while hydraulic systems are used in Germany, Italy and the Netherlands. In the United States, many classification bowls have more than 40 tracks—up to 72—which are often divided into six to ten tracks in each balloon loop. Bailey Yard in North Platte, Nebraska, United States, the worlds largest classification yard, is a hump yard, notably, in Europe, Russia and China, all major classification yards are hump yards. Europes largest hump yard is that of Maschen near Hamburg, Germany, the second largest is in the port of Antwerp, Belgium. According to the PRRT&HS PRR Chronology, the first hump yard in the United States was opened May 11,1903 as part of the Altoona Yards at Bells Mills. Other sources report the PRR yard at Youngwood, PA which opened in the 1880s to serve the Connellsville coke fields as the first U. S. hump yard. Gravity yards are operated similarly to hump yards but, in contrast to the latter, thus, only few gravity yards were ever built, sometimes requiring massive earthwork. Most gravity yards were built in Germany and Great Britain, a few also in some other European countries, in the USA, there were only very few old gravity yards, one of the few gravity yards in operation today is CSXs Readville Yard south of Boston, Massachusetts
40.
Coaling tower
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A coaling tower, coal stage or coaling station is a facility used to load coal as fuel into railway steam locomotives. Coaling towers were often sited at motive power depots or locomotive maintenance shops, coaling towers were constructed of wood, steel-reinforced concrete, or steel. The method of lifting the bulk coal into the storage bin varied, the coal usually was dropped from a hopper car into a pit below tracks adjacent to the tower. Some facilities lifted entire railway coal trucks or wagons, sanding pipes were often mounted on coaling towers to allow simultaneous replenishment of a locomotives sand box. As railroads transitioned from the use of locomotives to the use of diesel locomotives in the 1950s the need for coaling towers ended. Many reinforced concrete towers remain in place if they do not interfere with operations due to the high cost of demolition incurred with these massive structures, state, province, or county in which the coaling tower is located. Railroad for which the tower was originally built. Year in which the tower was built. Type of coaling station, tower or stage, chutes, dock, capacity in tons of coal which the coaling tower was built to store. Remarks, whether the tower is adjacent to tracks, name of the railroad yard, similar towers. Motive power depot Roundhouse Train Tower
41.
Junction (rail)
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A junction, in the context of rail transport, is a place at which two or more rail routes converge or diverge. This implies a connection between the tracks of the two routes, provided by points and signalling. In a simple case where two routes with one or two tracks each meet at a junction, a simple layout of tracks suffices to allow trains to transfer from one route to the other. More complicated junctions are needed to permit trains to travel in direction after joining the new route. In this latter case, the three points of the triangle may be different names, for example using points of the compass as well as the name of the overall place. Rail transport operations refer to stations that lie on or near a railway junction as a junction station, frequently, trains are built up and taken apart at such stations so that the same train can split up and go to multiple destinations. For goods trains, marshalling yards serve a similar purpose, the worlds first railway junction was Newton Junction near Newton-le-Willows, England where, in 1831, two railways merged. The capacity of the limits the capacity of a railway network more than the capacity of individual railway lines. This applies more as the density increases. Measures to improve junctions are often more useful than building new railway lines, the capacity of a railway junction can be increased with improved signalling measures, by building points suitable for higher speeds, or by turning level junctions into flying junctions. With more complicated junctions such construction can rapidly become very expensive, especially if space is restricted by tunnels, rail terminology Interlocking Railway town Double junction
42.
Gauntlet track
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Gauntlet track or interlaced track is an arrangement in which railway tracks run parallel on a single track bed and are interlaced such that only one pair of rails may be used at a time. Since this requires only slightly more width than a single track, trains run on the discrete pair of rails appropriate to their direction, track gauge or loading gauge. Gauntlet tracks can be used to provide clearance to a fixed obstruction adjacent to a track such as a cutting, bridge. Frog gauntlets are commonly used when a rail lines capacity is increased by the provision of an additional track. They are typically used for short stretches of track where it is cheaper to provide extra rails than to provide switches and this also eliminates the problem of switch failures. In a frog gauntlet, one crosses over a rail on the adjacent track. A frog is used to provide the flangeway for the crossing tracks, the train taking the gauntlet runs over the frog onto the parallel rails, passes through the gauntlet area, and passes over another frog to return to the original line. Since there are no points or other moving parts on a frog gauntlet track, because two trains cannot use the gauntlet at the same time, scheduling and signalling must allow for this restriction. In a point gauntlet track, the rails for the two tracks do not need to cross, so no frog is required. The train taking the gauntlet runs over a set of points onto the parallel rails, passes through the gauntlet area. This arrangement is used at the Roselle Park Station referenced below, at a small number of locations on single track lines in Britain, interlaced loops had been provided where sprung catch points were required because of the steep gradient. The points at either end of the loop were set according to the direction of travel. Trains running uphill were routed via the loop incorporating the sprung catch point, trains running downhill used the opposite loop, bypassing the catch point. Where tracks diverge, a section of track may be provided where the switches require to be located remote from the actual divergence. This arrangement is most commonly used on systems, to move the switches away from a heavily trafficked road. An arrangement similar to gauntlet track is used to allow trains of different gauges to use the same track. In that case, the two interlaced tracks will have different gauges, sometimes sharing one of the rails for a total of three rails, in Sydney, the Como bridge over the Georges River between Oatley and Como was built as single line in the 1880s. The line was duplicated soon after, except for that bridge, the bridge was fitted with gauntlet track, which needs no turnouts, and hence needs no signal box at the far end
43.
Passing loop
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A passing loop or passing siding is a place on a single line railway or tramway, often located at a station, where trains or trams travelling in opposite directions can pass each other. Trains/trams going in the direction can also overtake, providing that the signalling arrangement allows it. A passing loop is double ended and connected to the track at both ends, though a dead end siding known as a refuge siding, which is much less convenient. A similar arrangement is used on the track of cable railways and funiculars. Ideally, the loop should be longer than all trains needing to cross at that point, if one train is too long for the loop it must wait for the opposing train to enter the loop before proceeding, taking a few minutes. Ideally, the train should arrive first and leave second. If both trains are too long for the loop, time-consuming see-sawing operations are required for the trains to cross, the main line has straight track, while the loop line has low speed turnouts at either end. If the station has one platform, then it is usually located on the main line. If passenger trains are few in number, and the likelihood of two passenger trains crossing each other low, the platform on the loop line may be omitted. The through road has straight track, while the road has low speed turnouts at either end. A possible advantage of this layout is that trains scheduled to pass straight through the station can do so uninterrupted and this layout is mostly used at local stations where many passenger trains do not stop. Since there is one passenger platform, it is not convenient to cross two passenger trains if both stop. An example is Scone railway station, but the end was later rearranged to resemble a main. A disadvantage of the platform and through arrangement is the speed limits through the turnouts at each end, in the example layout shown, trains take the left-hand track in their direction of running. Low-speed turnouts restrict the speed in one direction, two platform faces are needed, and they can be provided either at a single island platform or two side platforms. Overtaking is not normally possible at this kind of up and down loop as some of the signals are absent. Crossing loops using up and down working are very common in British practice and it is possible to cross trains at stations equipped with only a siding. At Bombo, Australia, the loop had no platform
