page_title: Track geometry
section_title: Curvature
hierarchical_section_title: Track geometry / Curvature
caption_attribution_description: English: A westbound SEPTA Paoli/Thorndale Line local on Track #4, westbound Amtrak Pennsylvanian (New York to Pittsburgh) on Track #3, and eastbound Amtrak Keystone Service (Harrisburg to New York) on Track #1 all meet at the curve on the four track Keystone Corridor in Rosemont, located about eleven miles west of Philadelphia. While normally pulled by GE Genesis P42DC diesel electric locomotive, on this run the "Pennsylvanian" was being powered by a AEM-7 electric locomotive (#924) as far as Harrisburg where it would have to change to diesel as the Norfolk Southern owned grade from Harrisburg to Pittsburgh is not electrified. The eastbound "Keystone Service" train is being pushed by a AEM-7 (#950) as well. Built, owned, and operated for more than a century by the Pennsylvania Railroad, since April 1, 1976, the grade (including all stations) between Philadelphia (30th Street Station) and Harrisburg (MP 105.2) has been owned and operated by Amtrak over which SEPTA also has operating rights for its Philadelphia regional rail commuter service between Zoo Interlocking (MP 1.9) and Cork Interlocking (MP 68.1) although by agreement between SEPTA and PennDOT, revenue service is prohibited west of Parkesburg (MP 44.2), the last station in Chester County. This portion of the grade was electrified by the PRR in 1915. Photograph by Bruce C. Cooper (original uploader)
context_page_description: 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, the standards are usually expressed in two separate layouts for horizontal and vertical.
context_section_description: In most countries, the measurement of curvature of curved track is expressed in radius. The shorter the radius, the sharper the curve is. For sharper curves, the speed limits are lower to prevent an outward horizontal centrifugal force to overturn the trains by directing its weight toward the outside rail. Cant may be used to allow higher speeds over the same curve.
  In the United States, the measurement of curvature is expressed in degree of curvature. This is done by having a chord of 100 feet (30.48 m) connecting to two points on an arc of the reference rail, then drawing radii from the center to each of the chord end points. The angle between the radii lines is the degree of curvature. The degree of curvature is inverse of radius. The larger the degree of curvature, the sharper the curve is. Expressing the curve in this way allows surveyors to use estimation and simpler tools in curve measurement. This can be done by using a 62-foot (18.90 m) string line to be a chord to connect the arc at the gage side of the reference rail. Then at the midpoint of the string line (at the 31st foot), a measurement is taken from the string line to the gauge of the reference rail. The number of inches in that measurement is approximated to be the number of degrees of curvature.
  Due to the limitation of how specific train equipment can make a turn at maximum speeds, there is a limitation of minimum curve radius to control the sharpness of all curves along a given route. Although most countries use radius for measurement of curvature, the term maximum degree of curvature is still used outside of the United States such as in India, but with the radius as the unit.
caption: Curve with superelevation of tracks on the Keystone Corridor near Rosemont, PA
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