Hallade Method
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Hallade Method
The Hallade method, devised by Frenchman Emile Hallade, is a method used in track geometry for surveying, designing and setting out curves in railway track. It involves measuring the offset of a string line from the outside of a curve at the central point of a chord. In reality, string is too thick to provide a clear reading and breaks easily under the tension needed to minimise movement due to wind. A reel of wire may be used instead, with special holders (Hallade forks) employed to hold the wire at a fixed distance from the rail. The measurement is taken with a Hallade rule, a specialist ruler whose zero point matches the offset of the forks, thus cancelling it out. The purpose of the offset is to allow small negative measurements. Without this, surveyors would frequently have to read from both sides of the rail to determine the correct values on straight sections of track which typically feature a mix of small positive and negative versines. A standard chord length is used: in ...
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Versine
The versine or versed sine is a trigonometric function found in some of the earliest (Sanskrit Āryabhaṭa's sine table , ''Aryabhatia'',The Āryabhaṭīya by Āryabhaṭa
Section I) trigonometric tables. The versine of an angle is 1 minus its cosine. There are several related functions, most notably the coversine and haversine. The latter, half a versine, is of particular importance in the haversine formula of navigation.


Overview

The versine or versed sine is a trigonometric function already appearing in some of ...
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Track Geometry
Track geometry is concerned with the properties and relations of points, lines, curves, and surfaces in the three-dimensional positioning of railroad track. The term is also applied to measurements used in design, construction and maintenance of track. Track geometry involves standards, speed limits and other regulations in the areas of track gauge, alignment, elevation, curvature and track surface. Standards are usually separately expressed for horizontal and vertical layouts although track geometry is three-dimensional. Layout Horizontal layout Horizontal layout is the track layout on the horizontal plane. This can be thought of as the plan 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 track types: tangent track (straight line), curved track, and track transition curve (also called transition spiral or spiral) which connects between a tangent and a curved track. Curved ...
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Surveying
Surveying or land surveying is the technique, profession, art, and science of determining the terrestrial two-dimensional or three-dimensional positions of points and the distances and angles between them. A land surveying professional is called a land surveyor. These points are usually on the surface of the Earth, and they are often used to establish maps and boundaries for ownership, locations, such as the designed positions of structural components for construction or the surface location of subsurface features, or other purposes required by government or civil law, such as property sales. Surveyors work with elements of geodesy, geometry, trigonometry, regression analysis, physics, engineering, metrology, programming languages, and the law. They use equipment, such as total stations, robotic total stations, theodolites, GNSS receivers, retroreflectors, 3D scanners, LiDAR sensors, radios, inclinometer, handheld tablets, optical and digital levels, subsurface locators, d ...
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Rail Transport
Rail transport (also known as train transport) is a means of transport that transfers passengers and goods on wheeled vehicles running on rails, which are incorporated in tracks. In contrast to road transport, where the vehicles run on a prepared flat surface, rail vehicles ( rolling stock) are directionally guided by the tracks on which they run. Tracks usually consist of steel rails, installed on sleepers (ties) set in ballast, on which the rolling stock, usually fitted with metal wheels, moves. Other variations are also possible, such as "slab track", in which the rails are fastened to a concrete foundation resting on a prepared subsurface. Rolling stock in a rail transport system generally encounters lower frictional resistance than rubber-tyred road vehicles, so passenger and freight cars (carriages and wagons) can be coupled into longer trains. The operation is carried out by a railway company, providing transport between train stations or freight customer ...
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Chord (geometry)
A chord of a circle is a straight line segment whose endpoints both lie on a circular arc. The infinite line extension of a chord is a secant line, or just ''secant''. More generally, a chord is a line segment joining two points on any curve, for instance, an ellipse. A chord that passes through a circle's center point is the circle's diameter. The word ''chord'' is from the Latin ''chorda'' meaning '' bowstring''. In circles Among properties of chords of a circle are the following: # Chords are equidistant from the center if and only if their lengths are equal. # Equal chords are subtended by equal angles from the center of the circle. # A chord that passes through the center of a circle is called a diameter and is the longest chord of that specific circle. # If the line extensions (secant lines) of chords AB and CD intersect at a point P, then their lengths satisfy AP·PB = CP·PD (power of a point theorem). In conics The midpoints of a set of parallel chords of a coni ...
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Versine
The versine or versed sine is a trigonometric function found in some of the earliest (Sanskrit Āryabhaṭa's sine table , ''Aryabhatia'',The Āryabhaṭīya by Āryabhaṭa
Section I) trigonometric tables. The versine of an angle is 1 minus its cosine. There are several related functions, most notably the coversine and haversine. The latter, half a versine, is of particular importance in the haversine formula of navigation.


Overview

The versine or versed sine is a trigonometric function already appearing in some of ...
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Pythagorean Theorem
In mathematics, the Pythagorean theorem or Pythagoras' theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle. It states that the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares on the other two sides. This theorem can be written as an equation relating the lengths of the sides ''a'', ''b'' and the hypotenuse ''c'', often called the Pythagorean equation: :a^2 + b^2 = c^2 , The theorem is named for the Greek philosopher Pythagoras, born around 570 BC. The theorem has been proven numerous times by many different methods – possibly the most for any mathematical theorem. The proofs are diverse, including both geometric proofs and algebraic proofs, with some dating back thousands of years. When Euclidean space is represented by a Cartesian coordinate system in analytic geometry, Euclidean distance satisfies the Pythagorean relation: the squared dist ...
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Cess (rail Transport)
This article contains a list of jargon used to varying degrees by railfans, trainspotters, and railway employees in the United Kingdom, including nicknames for various locomotives and multiple units. Although not exhaustive, many of the entries in this list appear from time to time in specialist, rail-related publications. There may be significant regional variation in usage. A ; Absolute block signalling : A British signalling scheme designed to ensure the safe operation of a railway by allowing only one train to occupy a defined section of track (block) at a time ; Aspect : The indication displayed by a colour-light signal (e.g. a yellow aspect) ; Autocoach : A passenger coach fitted with a driving cab and controls for use in an autotrain ; Automatic warning system (AWS) : The specific form of limited cab signalling introduced in 1948 in the United Kingdom to help train drivers observe and obey warning signals B ; Baby Deltic : D5900 class Bo-Bo diesel-electric loc ...
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Cant (rail)
The cant of a railway track or camber of a road (also referred to as superelevation, cross slope or cross fall) is the rate of change in elevation (height) between the two rails or edges. This is normally greater where the railway or road is curved; raising the outer rail or the outer edge of the road creates a banked turn, thus allowing vehicles to maneuver through the curve at higher speeds than would otherwise be possible were the surface flat or level. Rail On railways, cant helps a train steer around a curve, keeping the wheel flanges from touching the rails, minimizing friction, wear and rail squeal. The main functions of cant are the following: * Improve distribution of the load across both rails * Reduce wear on rails and wheels * Neutralize the effect of lateral forces * Improve passenger comfort The necessary cant in a curve depends on the expected speed of the trains and the radius. However, it may be necessary to select a compromise value at design time, for ...
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Ballast Tamper
Ballast is material that is used to provide stability to a vehicle or structure. Ballast, other than cargo, may be placed in a vehicle, often a ship or the gondola of a balloon or airship, to provide stability. A compartment within a boat, ship, submarine, or other floating structure that holds water is called a ballast tank. Water should move in and out from the ballast tank to balance the ship. In a vessel that travels on the water, the ballast will remain below the water level, to counteract the effects of weight above the water level. The ballast may be redistributed in the vessel or disposed of altogether to change its effects on the movement of the vessel. History The basic concept behind the ballast tank can be seen in many forms of aquatic life, such as the blowfish or members of the argonaut group of octopus. The concept has been invented and reinvented many times by humans to serve a variety of purposes. In the fifteenth and sixteenth century, the ballast "did not consi ...
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Track Geometry
Track geometry is concerned with the properties and relations of points, lines, curves, and surfaces in the three-dimensional positioning of railroad track. The term is also applied to measurements used in design, construction and maintenance of track. Track geometry involves standards, speed limits and other regulations in the areas of track gauge, alignment, elevation, curvature and track surface. Standards are usually separately expressed for horizontal and vertical layouts although track geometry is three-dimensional. Layout Horizontal layout Horizontal layout is the track layout on the horizontal plane. This can be thought of as the plan 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 track types: tangent track (straight line), curved track, and track transition curve (also called transition spiral or spiral) which connects between a tangent and a curved track. Curved ...
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