Horseshoe curve

A horseshoe curve is a reversing curve through a single tight curve in a railway or a road, through an angle of about 180 degrees or more. The U shape, or even slight balloon shape, of such a curve resembles a horseshoe, hence the name. On roads such curves, if tight enough, are typically called hairpin turns.

A horseshoe curve is a means to lengthen an ascending or descending grade and thereby reduce the maximum gradient. If the straight route between two points would be too steep to climb, a more circuitous route will increase the distance travelled, allowing the difference in altitude to be averaged over a longer track (or road) length. This is similar to the function of a spiral. However, a horseshoe curve does not involve the track crossing over itself, and the full horseshoe involves both relatively straight and tightly curved sections, while a spiral generally has a more uniform curvature. Obviously, a horseshoe also gives rise to a severe change in direction, while a spiral generally does not.

Curve

In mathematics, a curve (also called a curved line in older texts) is, generally speaking, an object similar to a line but that need not be straight. Thus, a line is a special case of curve null curvature.

Various disciplines within mathematics have given the term different meanings depending on the area of study, so the precise meaning depends on context. However, many of these meanings are special instances of the definition which follows. A curve is a topological space which is locally homeomorphic to a line. In everyday language, this means that a curve is a set of points which, near each of its points, looks like a line, up to a deformation. A simple example of a curve is the parabola, shown to the right. A large number of other curves have been studied in multiple mathematical fields.

A closed curve is a curve that forms a path whose starting point is also its ending point—that is, a path from any of its points to the same point.

Closely related meanings include the graph of a function (as in Phillips curve) and a two-dimensional graph.

Horseshoe

A horseshoe is a fabricated product, normally made of metal, although sometimes made partially or wholly of modern synthetic materials, designed to protect a horse's hoof from wear. Shoes are attached on the palmar surface of the hooves, usually nailed through the insensitive hoof wall that is anatomically akin to the human toenail, although much larger and thicker. However, there are many cases where shoes are glued.

The fitting of horseshoes is a professional occupation, conducted by a farrier, who specializes in the preparation of feet, assessing potential lameness issues, and fitting appropriate shoes, including remedial features where required. In some countries, such as the United Kingdom, horseshoeing is legally restricted to only people with specific qualifications and experience. In others, such as the United States, where professional licensing is not legally required, professional organizations provide certification programs that publicly identify qualified individuals.

Norfolk Southern Railway

The Norfolk Southern Railway (reporting mark NS), (also known as Norfolk Southern Railway Company or simply Norfolk Southern) is a Class I railroad in the United States, owned by the Norfolk Southern Corporation. With headquarters in Norfolk, Virginia, the company operates over 22,000 route miles in 22 eastern states, the District of Columbia, and has rights in Canada from Buffalo to Toronto and over the Albany to Montreal route. The most common commodity hauled on the railroad is coal from mines in Indiana, Kentucky, Pennsylvania, Tennessee, Virginia, and West Virginia. The railroad also offers the most extensive intermodal network in eastern North America.

The Norfolk Southern Railway was founded in 1894 as the Southern Railway, making it the fourth oldest Class I railroad in North America (just behind Union Pacific Railroad, Canadian Pacific Railway and Kansas City Southern Railway). The railroad was renamed from "Southern Railway" to its current name "Norfolk Southern Railway" on December 31, 1990 to reflect its parent company, making the railroad the third business entity to use the "Norfolk Southern" name. Its holding company was the second business entity to use the "Norfolk Southern" name starting in 1982 and the holding company was named in honor of the original Norfolk Southern Railway that existed from 1942 to 1982.

Altoona, Pennsylvania

Altoona is a city in central Pennsylvania Blair County, Pennsylvania, United States. It is the principal city of the Altoona Metropolitan Statistical Area (MSA). The population was 46,320 at the time of the 2010 Census, making it the tenth most populous city in Pennsylvania. The Altoona MSA includes all of Blair County and was recorded as having a population of 127,089 at the 2010 Census, around 100,000 of which live within a 5-mile (8.0 km) radius of the Altoona city center according to U.S. Census zip code population data. This includes the adjacent boroughs of Hollidaysburg and Duncansville, adjacent townships of Logan, Allegheny, Blair, Frankstown, Antis, and Tyrone, as well as nearby boroughs of Bellwood and Newry.

Having grown around the railroad industry, the city is currently working to recover from industrial decline and urban decentralization experienced in recent decades. The city is home to the Altoona Curve baseball team of the Double A Eastern League, which is the Double A affiliate of the Major League Baseball team Pittsburgh Pirates. It also houses the 75+ year-old Altoona Symphony Orchestra, under the direction of Teresa Cheung. Prominent landmarks include the Horseshoe Curve, the Railroaders Memorial Museum, the Juniata Shops of the Altoona Works, the Mishler Theatre, the Cathedral of the Blessed Sacrament, and the Jaffa Shrine Center.