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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 (rail transport), 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 plane, horizontal and Vertical direction, 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 Multiview orthographic projection#Plan, 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 transit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Railroad
Rail transport (also known as train transport) is a means of transport using wheeled vehicles running in railway track, tracks, which usually consist of two parallel steel railway track, rails. Rail transport is one of the two primary means of land transport, next to road transport. It is used for about 8% of passenger and rail freight transport, freight transport globally, thanks to its Energy efficiency in transport, energy efficiency and potentially high-speed rail, high speed.Rolling stock on rails generally encounters lower friction, frictional resistance than rubber-tyred road vehicles, allowing rail cars to be coupled into longer trains. Power is usually provided by Diesel locomotive, diesel or Electric locomotive, electric locomotives. While railway transport is capital intensity, capital-intensive and less flexible than road transport, it can carry heavy loads of passengers and cargo with greater energy efficiency and safety. Precursors of railways driven by human or an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Derailment
In rail transport, a derailment is a type of train wreck that occurs when a rail vehicle such as a train comes off its rails. Although many derailments are minor, all result in temporary disruption of the proper operation of the railway system and they are a potentially serious hazard. A derailment of a train can be caused by a collision with another object, an operational error (such as excessive speed through a curve), the mechanical failure of tracks (such as broken rails), or the mechanical failure of the wheels, among other causes. In emergency situations, deliberate derailment with derails or catch points is sometimes used to prevent a more serious accident. History The first recorded train derailment in history is known as the Hightstown rail accident in New Jersey that occurred on 8 November 1833. The train was traveling between Hightstown and Spotswood, New Jersey, and derailed after an axle broke on one of the carriages as a result of a journal box catching fir ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Banked Turn
A banked turn (or banking turn) is a turn or change of direction in which the vehicle banks or inclines, usually towards the inside of the turn. For a road or railroad this is usually due to the roadbed having a transverse down-slope towards the inside of the curve. The bank angle is the angle at which the vehicle is inclined about its longitudinal axis with respect to the horizontal. Turn on flat surfaces If the bank angle is zero, the surface is flat and the normal force is vertically upward. The only force keeping the vehicle turning on its path is friction, or traction. This must be large enough to provide the centripetal force, a relationship that can be expressed as an inequality, assuming the car is driving in a circle of radius r: :\mu mg > . The expression on the right hand side is the centripetal acceleration multiplied by mass, the force required to turn the vehicle. The left hand side is the maximum frictional force, which equals the coefficient of friction ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
5 Inch Track Superelevation
5 (five) is a number, numeral and digit. It is the natural number, and cardinal number, following 4 and preceding 6, and is a prime number. Humans, and many other animals, have 5 digits on their limbs. Mathematics 5 is a Fermat prime, a Mersenne prime exponent, as well as a Fibonacci number. 5 is the first congruent number, as well as the length of the hypotenuse of the smallest integer-sided right triangle, making part of the smallest Pythagorean triple ( 3, 4, 5). 5 is the first safe prime and the first good prime. 11 forms the first pair of sexy primes with 5. 5 is the second Fermat prime, of a total of five known Fermat primes. 5 is also the first of three known Wilson primes (5, 13, 563). Geometry A shape with five sides is called a pentagon. The pentagon is the first regular polygon that does not tile the plane with copies of itself. It is the largest face any of the five regular three-dimensional regular Platonic solid can have. A conic is determine ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Minimum Railway Curve Radius
The minimum railway curve radius is the shortest allowable design radius for the centerline of railway tracks under a particular set of conditions. It has an important bearing on construction costs and operating costs and, in combination with superelevation (difference in elevation of the two rails) in the case of train tracks, determines the maximum safe speed of a curve. The minimum radius of a curve is one parameter in the design of railway vehicles as well as trams; monorails and automated guideways are also subject to a minimum radius. History The first proper railway was the Liverpool and Manchester Railway, which opened in 1830. Like the tram roads that had preceded it over a hundred years, the L&M had gentle curves and gradients. Reasons for these gentle curves include the lack of strength of the track, which might have overturned if the curves were too sharp causing derailments. The gentler the curves, the greater the visibility, thus boosting safety via increa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Inverse Function
In mathematics, the inverse function of a function (also called the inverse of ) is a function that undoes the operation of . The inverse of exists if and only if is bijective, and if it exists, is denoted by f^ . For a function f\colon X\to Y, its inverse f^\colon Y\to X admits an explicit description: it sends each element y\in Y to the unique element x\in X such that . As an example, consider the real-valued function of a real variable given by . One can think of as the function which multiplies its input by 5 then subtracts 7 from the result. To undo this, one adds 7 to the input, then divides the result by 5. Therefore, the inverse of is the function f^\colon \R\to\R defined by f^(y) = \frac . Definitions Let be a function whose domain is the set , and whose codomain is the set . Then is ''invertible'' if there exists a function from to such that g(f(x))=x for all x\in X and f(g(y))=y for all y\in Y. If is invertible, then there is exactly one functi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chord (geometry)
A chord (from the Latin ''chorda'', meaning " bowstring") of a circle is a straight line segment whose endpoints both lie on a circular arc. If a chord were to be extended infinitely on both directions into a line, the object is a ''secant line''. The perpendicular line passing through the chord's midpoint is called '' sagitta'' (Latin for "arrow"). More generally, a chord is a line segment joining two points on any curve, for instance, on an ellipse. A chord that passes through a circle's center point is the circle's ''diameter''. 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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Degree Of Curvature
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. Definition The Degree (angle), degree of curvature is defined as the central angle to the ends of an agreed length of either an Arc (curvature), arc or a Chord (geometry), chord; various lengths are commonly used in different areas of practice. This angle is also the Body relative direction, change in forward direction as that portion of the curve is traveled. In an ''n''-degree curve, the forward Bearing (angle), bearing changes by ''n'' degree (angle), degrees over the standard length of arc or chord. Usage Curvature is usually measured in radius of curvature. A small circle can be easily laid out by just using radius of curvature, but degree of curvature is more convenient for calculating and laying out the curve if the radius is as large as a kilometer or mile, as is needed for large scale works like roads and railroads. By using ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Euler Spiral
An Euler spiral is a curve whose curvature changes linearly with its curve length (the curvature of a circular curve is equal to the reciprocal of the radius). This curve is also referred to as a clothoid or Cornu spiral.Levien, Raph"The Euler spiral: a mathematical history."Rapp. tech (2008). The behavior of Fresnel integrals can be illustrated by an Euler spiral, a connection first made by Marie Alfred Cornu in 1874. Euler's spiral is a type of superspiral that has the property of a monotonic curvature function. The Euler spiral has applications to diffraction computations. They are also widely used in railway engineering, railway and highway engineering to design transition curves between straight and curved sections of railways or roads. A similar application is also found in photonic integrated circuits. The principle of linear variation of the curvature of the transition curve between a tangent and a circular curve defines the geometry of the Euler spiral: *Its curvature be ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Centrifugal Force
Centrifugal force is a fictitious force in Newtonian mechanics (also called an "inertial" or "pseudo" force) that appears to act on all objects when viewed in a rotating frame of reference. It appears to be directed radially away from the axis of rotation of the frame. The magnitude of the centrifugal force ''F'' on an object of mass ''m'' at the perpendicular distance ''ρ'' from the axis of a rotating frame of reference with angular velocity is F = m\omega^2 \rho. This fictitious force is often applied to rotating devices, such as centrifuges, centrifugal pumps, centrifugal governors, and centrifugal clutches, and in centrifugal railways, planetary orbits and banked curves, when they are analyzed in a non–inertial reference frame such as a rotating coordinate system. The term has sometimes also been used for the '' reactive centrifugal force'', a real frame-independent Newtonian force that exists as a reaction to a centripetal force in some scenarios. History F ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Radius
In classical geometry, a radius (: radii or radiuses) of a circle or sphere is any of the line segments from its Centre (geometry), center to its perimeter, and in more modern usage, it is also their length. The radius of a regular polygon is the line segment or distance from its center to any of its Vertex (geometry), vertices. The name comes from the Latin ''radius'', meaning ray but also the spoke of a chariot wheel.Definition of Radius at dictionary.reference.com. Accessed on 2009-08-08. The typical abbreviation and mathematical symbol for radius is ''R'' or ''r''. By extension, the diameter ''D'' is defined as twice the radius:Definition of radius at mathwords.com. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Amtrak Keystone Corridor Rosemont Curve
The National Railroad Passenger Corporation, doing business as Amtrak (; ), is the national passenger railroad company of the United States. It operates intercity rail service in 46 of the 48 contiguous U.S. states and three Canadian provinces. ''Amtrak'' is a portmanteau of the words ''America'' and ''track.'' Founded in 1971 as a quasi-public corporation to operate many U.S. passenger rail routes, Amtrak receives a combination of state and federal subsidies but is managed as a for-profit organization. The company's headquarters is located one block west of Union Station in Washington, D.C. Amtrak is headed by a Board of Directors, two of whom are the secretary of transportation and chief executive officer (CEO) of Amtrak, while the other eight members are nominated to serve a term of five years. Amtrak's network includes over 500 stations along of track. It directly owns approximately of this track and operates an additional of track; the remaining mileage is over ra ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
