1.
Gladstone railway station, South Australia
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Gladstone railway station is located on the Crystal Brook-Broken Hill line in Gladstone, South Australia. Gladstone station opened in 1876 when a line opened from Port Pirie in the west, it was extended east to Peterborough. In 1888, a line was built north to Laura and ultimately Wilmington, when a line from Balaklava in the south reached Gladstone in 1894, it became a four-way junction station. All were built as narrow gauge lines, in 1927, the line from the south was converted to broad gauge, making Gladstone a break of gauge station. As part of the project, the line between Port Augusta and Broken Hill was converted to standard gauge in 1969, thus Gladstone became a junction for three gauges. By 1993, the lines to the north and south had closed, the only passenger rail service which stops at the station is Great Southern Rails weekly Indian Pacific service operating between Sydney and Perth. Media related to Gladstone railway station at Wikimedia Commons Flickr gallery Johnnys Pages gallery
2.
Peterborough railway station, South Australia
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Peterborough railway station is located on the Crystal Brook-Broken Hill line in Peterborough, South Australia. Peterborough originally opened in January 1880 as Petersburg when a narrow gauge line opened from Port Pirie to the west, in November 1881, a line arrived from Terowie and the south, in 1882 it was extended north to Quorn. In 1888, a line was built eastwards to Broken Hill, thus Petersburg became a four-way junction station and the town was the headquarters for the South Australian Railways narrow gauge network, with an extensive locomotive depot. A roundhouse was added in 1927, the roundhouse and turntable are listed on the South Australian Heritage Register. The station along with the town, was renamed Peterborough in 1917, as part of the standardisation project, the line between Port Augusta and Broken Hill was converted to standard gauge in 1970, thus Peterborough became a break of gauge station. Following the conversion of the Adelaide to Crystal Brook line to standard gauge in 1982, by 1988, both the narrow gauge line to the north and broad gauge line to the south had closed. Today the former roundhouse is home to the Steamtown Heritage Rail Centre, the only passenger rail service which stops at the station is Great Southern Rails weekly Indian Pacific service operating between Sydney and Perth. Media related to Peterborough railway station at Wikimedia Commons Flickr gallery Johnnys Pages gallery Johnnys Pages gallery
3.
South Australia
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South Australia is a state in the southern central part of Australia. It covers some of the most arid parts of the country, with a total land area of 983,482 square kilometres, it is the fourth-largest of Australias states and territories. Other population centres in the state are relatively small, the state comprises less than 8 percent of the Australian population and ranks fifth in population among the six states and two territories. The majority of its people reside in Adelaide, most of the remainder are settled in fertile areas along the south-eastern coast and River Murray. The states colonial origins are unique in Australia as a settled, planned British province. Official settlement began on 28 December 1836, when the colony was proclaimed at the Old Gum Tree by Governor John Hindmarsh, as with the rest of the continent, the region had been long occupied by Aboriginal peoples, who were organised into numerous tribes and languages. The first British settlement to be established was Kingscote, Kangaroo Island, on 26 July 1836, the guiding principle behind settlement was that of systematic colonisation, a theory espoused by Edward Gibbon Wakefield that was later employed by the New Zealand Company. The goal was to establish the province as a centre of civilisation for free immigrants, promising civil liberties, although its history is marked by economic hardship, South Australia has remained politically innovative and culturally vibrant. Today, it is known for its wine and numerous cultural festivals. The states economy is dominated by the agricultural, manufacturing and mining industries, the state has an increasingly significant finance sector as well. Evidence of human activity in South Australia dates back as far as 20,000 years, with flint mining activity, in addition wooden spears and tools were made in an area now covered in peat bog in the South East. Kangaroo Island was inhabited long before the island was cut off by rising sea levels, thijssen named his discovery Pieter Nuyts Land, after the highest ranking individual on board. The complete coastline of South Australia was first mapped by Matthew Flinders, the land which now forms the state of South Australia was claimed for Britain in 1788 as part of the colony of New South Wales. Although the new colony included almost two-thirds of the continent, early settlements were all on the eastern coast and it took more than forty years before any serious proposal to establish settlements in the south-western portion of New South Wales were put forward. In 1834, the British Parliament passed the South Australia Act 1834, the act stated that 802,511 square kilometres would be allotted to the colony and it would be convict-free. In contrast to the rest of Australia, terra nullius did not apply to the new province, although the patent guaranteed land rights under force of law for the indigenous inhabitants it was ignored by the South Australian Company authorities and squatters. Settlement of seven vessels and 636 people was made at Kingscote on Kangaroo Island. The first immigrants arrived at Holdfast Bay in November 1836, the Colonisation Commissioners intended to establish a police service as soon as misconduct within the increasing population warranted it
4.
Track gauge
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In rail transport, track gauge is the spacing of the rails on a railway track and is measured between the inner faces of the load-bearing rails. All vehicles on a network must have running gear that is compatible with the track gauge, as the dominant parameter determining interoperability, it is still frequently used as a descriptor of a route or network. There is a distinction between the gauge and actual gauge at some locality, due to divergence of track components from the nominal. Railway engineers use a device, like a caliper, to measure the actual gauge, the nominal track gauge is the distance between the inner faces of the rails. In current practice, it is specified at a distance below the rail head as the inner faces of the rail head are not necessarily vertical. In some cases in the earliest days of railways, the company saw itself as an infrastructure provider only. Colloquially the wagons might be referred to as four-foot gauge wagons, say and this nominal value does not equate to the flange spacing, as some freedom is allowed for. An infrastructure manager might specify new or replacement track components at a variation from the nominal gauge for pragmatic reasons. Track is defined in old Imperial units or in universally accepted metric units or SI units, Imperial units were established in United Kingdom by The Weights and Measures Act of 1824. In addition, there are constraints, such as the load-carrying capacity of axles. Narrow gauge railways usually cost less to build because they are lighter in construction, using smaller cars and locomotives, as well as smaller bridges, smaller tunnels. Narrow gauge is often used in mountainous terrain, where the savings in civil engineering work can be substantial. Broader gauge railways are generally expensive to build and require wider curves. There is no single perfect gauge, because different environments and economic considerations come into play, a narrow gauge is superior if ones main considerations are economy and tight curvature. For direct, unimpeded routes with high traffic, a broad gauge may be preferable, the Standard, Russian, and 46 gauges are designed to strike a reasonable balance between these factors. In addition to the general trade-off, another important factor is standardization, once a standard has been chosen, and equipment, infrastructure, and training calibrated to that standard, conversion becomes difficult and expensive. This also makes it easier to adopt an existing standard than to invent a new one and this is true of many technologies, including railroad gauges. The reduced cost, greater efficiency, and greater economic opportunity offered by the use of a common standard explains why a number of gauges predominate worldwide
5.
Rapid transit track gauge
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Rapid transit track gauge is often 1,435 mm standard gauge, but also 1,000 mm,1,067 mm,1,524 mm, and 1,676 mm, among others. Standard gauge railways and rapid transit systems are dominant in Europe, North America, West Asia, North Africa, some of the largest and oldest subway systems in the world use standard gauge in agreement with the country wide dominant usage for track gauge, e. g. The following list contains rapid transit systems that are either non-standard gauge, or are standard gauge, for references for the figures, see each systems page. List of track gauges List of tram track gauges
6.
Narrow-gauge railway
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A narrow-gauge railway is a railway with a track gauge narrower than the 1,435 mm of standard gauge railways. Most existing narrow-gauge railways are between 600 mm and 1,067 mm, narrow-gauge railways also have specialized use in mines and other environments where a very small structure gauge makes a very small loading gauge necessary. Narrow-gauge railways also have general applications. Many narrow-gauge street tramways are used, particularly in Europe, where 1,000 mm metre gauge tramways are common, the earliest recorded railway is shown in the De re metallica of 1556, which shows a mine in Bohemia with a railway of about 2 ft gauge. During the 16th century, railways were mainly restricted to hand-pushed narrow-gauge lines in mines throughout Europe, during the 17th century, mine railways were extended to provide transportation above ground. These lines were industrial, connecting mines with nearby transportation points and these railways were usually built to the same narrow gauge as the mine railways from which they developed. The worlds first steam locomotive on rails, built in 1802 by Richard Trevithick for the Coalbrookdale Company, during the 1820s and 1830s, a number of industrial narrow-gauge railways in the United Kingdom used steam locomotives. In 1842, the first narrow-gauge steam locomotive outside the UK was built for the 1,100 mm gauge Antwerp-Ghent Railway in Belgium, historically, many narrow-gauge railways were built as part of specific industrial enterprises and were primarily industrial railways rather than general carriers. Some common uses for these industrial narrow-gauge railways were mining, logging, construction, tunnelling, quarrying, extensive narrow-gauge networks were constructed in many parts of the world for these purposes. For example, mountain logging operations in the 19th century often used narrow-gauge railways to transport logs from mill sites to market, significant sugarcane railways still operate in Cuba, Fiji, Java, the Philippines, and Queensland. Narrow-gauge railway equipment remains in use for the construction of tunnels. Extensive narrow-gauge railway systems served the front-line trenches of both sides in World War I and they were a short-lived military application, and after the end of the war, the surplus equipment from these created a small boom in narrow gauge railway building in Europe. Narrow-gauge railways usually cost less to build because they are lighter in construction, using smaller cars and locomotives, as well as smaller bridges, smaller tunnels. Narrow gauge is often used in mountainous terrain, where the savings in civil engineering work can be substantial. It is also used in populated areas where the potential demand is too low for broader gauge railways to be economically viable. This is the case in some of Australia and most of Southern Africa, the use of such railways has almost vanished due to the capabilities of modern trucks. In many countries, narrow gauge railways were built as feeder or branch lines to feed traffic to more important standard gauge lines, the choice was often not between a narrow-gauge railway and a standard gauge one, but between a narrow-gauge railway and none at all. Some bulk commodities, such as coal, ore, and gravel, can be transshipped, but this still incurs time penalties
7.
Bosnian-gauge railways
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Bosnian gauge is a railway track gauge of 760 mm. It was used extensively in the former Austro-Hungarian Empire as a form of narrow gauge. The name is used for lines of the same gauge outside Bosnia. Similar track gauges are the 2 ft 6 in and 750 mm gauge and it was completed in 1879, using the 760 mm temporary tracks and rolling stock used during the construction of the recently finished Temesvár-Orsova line. The Brod - Zenica - Sarajevo Bosna Bahn provided the basis for the narrow gauge railway network which was established in Bosnia-Herzegovina. In barely two decades a national 760 mm network was built, by the 1890s this stretched through Mostar to the Dalmatian border at Metkovic, and to Gruž, a suburb of Dubrovnik, on the coast of the Adriatic Sea. This narrow gauge main line carried much heavier traffic than many of the standard gauge main lines across the Austro-Hungarian Empire. It was the success of the Bosnian narrow gauge net which gave impetus after the turn of the century to the building of 760 mm gauge lines across all other territories of the Monarchy. The technical solutions pioneered there were used later on all the narrow railways of Austria-Hungary. List of town tramway systems in Croatia List of track gauges Sarajevo Tramway History of Bosnian railways
8.
Swedish three foot gauge railways
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Swedish three-foot gauge railways are railways with the gauge 891 mm, or 3 Swedish feet in the old Swedish measurement system. Railways with this gauge have only existed in Sweden and this was the most common narrow gauge in Sweden. Sweden once had some fairly extensive networks, but most narrow gauge railways are now closed. Some were converted to standard gauge and some remain as heritage railways, the only commercial Swedish three foot gauge railway still in use is the suburban railway Roslagsbanan in north-eastern Stockholm. The Nordmark-Klarälvens Järnväg was a 175 km network issued from different lines built from 1873 and it was electrified in 1920, with 15 AEG-locomotives. A new class of 5 locomotives went in 1961, the network was dismantled in 1990. 70 km between Hultsfred and Västervik as well as the sections between Virserum-Hjortöström and Åseda-Hultanäs are served by tourist trains in the summer, including 4 km of dual gauge track. The Vadstena - Fågelsta narrow gauge railway was part of a network in Östergötland
9.
900 mm gauge railways
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900 mm narrow gauge railways are generally found in Europe. This gauge is used for light urban rail networks, industrial and agricultural railways. In Sweden there has been a network of railways with 891 mm gauge. This is so close to 900 mm that they are more or less compatible, and some sales of rolling stock between the gauges have taken place
10.
3 ft 6 in gauge railways
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Railways with a track gauge of 3 ft 6 in/1,067 mm were first constructed as horse-drawn wagonways. From the mid-nineteenth century, the 3 ft 6 in gauge became widespread in the British Empire, there are approximately 112,000 kilometres of 1,067 mm gauge track in the world. 1795 One of the first railways to use 3 ft 6 in gauge was the Little Eaton Gangway in England, other 3 ft 6 in gauge wagonways in England and Wales were also built in the early nineteenth century. 1862 In 1862 the Norwegian engineer Carl Abraham Pihl constructed the first 3 ft 6 in gauge railway in Norway,1865 In 1865 the Queensland Railways were constructed. Its 3 ft 6 in gauge was promoted by the Irish engineer Abraham Fitzgibbon,1868 In 1868 Charles Fox asks civil engineer Edmund Wragge to survey a 3 ft 6 in railway in Costa Rica. 1871 In 1871 the Canadian Toronto, Grey and Bruce Railway,1872 In January 1872 Robert Fairlie advocated the use of 3 ft 6 in gauge in his book Railways Or No Railways, Narrow Gauge, Economy with Efficiency v. Broad Gauge, Costliness with Extravagance. 1872 also saw the opening of the first 3 ft 6 in gauge railway in Japan,1873 On 1 January 1873, the first 3 ft 6 in gauge railway was opened in New Zealand, constructed by the British firm John Brogden and Sons. Earlier built 4 ft 8 1⁄2 in and broad gauge railways were converted to the narrower gauge. Also in 1873 the Cape Colony adopted the 3 ft 6 in gauge, after conducting several studies in southern Europe, the Molteno Government selected the gauge as being the most economically suited for traversing steep mountain ranges. Beginning in 1873, under supervision of Railway engineer of the Colony William Brounger, the Cape Government Railways rapidly expanded and the gauge became the standard for southern Africa. 1876 Natal also converted its short 10 kilometres long Durban network from 4 ft 8 1⁄2 in broad gauge prior to commencing with construction of a network across the colony in 1876. Other new railways in Southern Africa, notably Mozambique, Bechuanaland, after 1876 In the late nineteenth and early twentieth century numerous 3 ft 6 in gauge tram systems were built in the United Kingdom and the Netherlands. In Sweden, the gauge was nicknamed Blekinge gauge, as most of the railways in the province of Blekinge had this gauge. An alternate name for this gauge, Cape gauge, is named after the Cape Colony in what is now South Africa, the term Cape Gauge is used in other languages, such as the Dutch kaapspoor, German Kapspur, Norwegian kappspor and French voie cape. After metrication in the 1960s, the gauge was referred to in official South African Railways publications as 1065 mm instead of 1067 mm, the gauge is sometimes referred to as CAP gauge, after C. A. The gauge name Colonial Gauge was used in New Zealand, in Australia the imperial term 3 foot 6 inch is used. In some Australian publications the term medium gauge is also used, in Japan 1,067 mm gauge is referred to as kyōki, which directly translates as narrow gauge. It is defined in metric units, Cape Government Railways Heritage railway List of track gauges Norwegian gauge controversy South African Trains – A Pictorial Encyclopaedia Why Did Japan Choose the 36 Narrow Gauge
11.
4 ft 6 in gauge railway
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The 4 ft 6 in track gauge, also called the Scotch gauge, was adopted by early 19th century railways mainly in the Lanarkshire area of Scotland. It differed from the gauge of 4 ft 8 in that was used on some lines in England. In the early 1840s standard gauge lines began to be constructed in Scotland, the gauge was outlawed in Great Britain by law in 1846. From 1903, tram lines of Tokyo adopted this gauge, a small number of early to mid-19th century passenger railways were built to 4 ft 6 in Scotch gauge including, Ardrossan and Johnstone Railway. Authorised on 20 July 1806 and opened on 6 November 1810, authorised on 17 May 1824 and opened on 1 October 1826. Incorporated on 19 May 1826 and opened on 8 August 1828, authorised on 26 May 1826 and opened in part on 4 July 1831. Incorporated on 26 May 1826 and ceremonially opened on 27 September 1831 for both passengers and goods, the engineers were Thomas Grainger and John Miller from Edinburgh. Incorporated on 21 June 1829 and partially opened on 21 March 1834, the engineers were Thomas Grainger and John Miller from Edinburgh. Incorporated on 3 July 1835 and opened on 31 August 1840, authorised on 21 July 1835 and opened on 3 April 1837 for both passengers and goods. Interestingly Robert Stephenson and Company built a Scotch gauge locomotive, the St. Rollox, for the Garnkirk and Glasgow Railway, all the lines were later relaid in standard gauge. In addition to the lines, there were three railways, authorised between 1822 and 1835, that were built in the Dundee area, to a gauge of 4 ft 6 1⁄2 in. They were, The Dundee and Newtyle Railway, the Newtyle and Coupar Angus Railway. Grainger and Miller built another two lines in the same area to a gauge of 5 ft 6 in. Thomas Grainger is said to have chosen this gauge, since he regarded 4 ft 8 1⁄2 in standard gauge as being too narrow and they were, The Dundee and Arbroath Railway. Incorporated on 19 May 1836 and opened in part in October 1838, incorporated on 19 May 1836 and opened in part on 24 November 1838. A few remnants of old lines remain, but are non functional with the exception of one example of the St Michaels Mount Tramway at St Michaels Mount in Cornwall and it is a partial underground railway that used to bring luggage up to the castle. It occasionally operates, but only for reasons and is not open to the general public. It is therefore believed to be Britains last functionally operational Scotch gauge railway, after the end of Scotch gauge in Britain, the gauge was revived in Japan
12.
Broad-gauge railway
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Broad-gauge railways use a track gauge greater than the 1,435 mm standard gauge. In Britain the Great Western Railway, designed by Isambard Kingdom Brunel, pioneered broad gauge in 1838 with a gauge of 7 ft 1⁄4 in, some harbours also used railways of this gauge for construction and maintenance. These included Portland Harbour and Holyhead Breakwater, which used a locomotive for working sidings, as it was not connected to the national network, this broad-gauge operation continued until the locomotive wore out in 1913. The gauge initially proposed by Brunel was 7 ft exactly but this was increased by 1⁄4 in to accommodate clearance problems identified during early testing. It became apparent that standardization on a gauge throughout a rail transport system was advantageous. Rolling stock did not need to match the gauge exactly, a difference of a few millimetres could be coped with, the value of interoperability was initially not obvious to the industry. The standardization movement was gradual, over time the value of a proprietary gauge diminished, being replaced by the idea of charging money for equipment used on other railway lines. Ireland, using the criteria, was allocated a different standard gauge. Broad-gauge lines in Britain were gradually converted to dual gauge or standard gauge from 1864, Ireland and some states in Australia and Brazil have a gauge of 5 ft 3 in, but Luas, the Dublin light rail system, is built to standard gauge. Russia and the other former Soviet Republics use a 1,520 mm gauge while Finland continues to use the 5 ft gauge inherited from Imperial Russia, in 1839 the Netherlands started its railway system with two broad-gauge railways. But the neighbouring countries Prussia and Belgium already used standard gauge, in 1855, NRS regauged its line and shortly afterwards connected to the Prussian railways. There are replicas of one broad-gauge 2-2-2 locomotive and three carriages in the Dutch Railway Museum in Utrecht and these replicas were built for the 100th anniversary of the Dutch Railways in 1938–39. Portugal and the Spanish Renfe system use a gauge of 1,668 mm called Ancho Ibérico in Spanish or Bitola Ibérica in Portuguese, in India, Pakistan and Bangladesh, a gauge of 5 ft 6 in is widespread. This is also used by the Bay Area Rapid Transit system of the San Francisco Bay Area. In Toronto, Canada the gauge for TTC subways and streetcars was chosen in 1861, years after the establishment of gauge in Britain. In 1861, the province was supplying subsidies only to broad gauge railways. The use of a non-standard gauge precludes interoperability of rolling stock on railway networks. On the 5 ft 3 in and 5 ft 6 in gauges, the extra width allowed bigger inside cylinders and greater power, in the event, the most powerful engines on standard gauge in North America and Scandinavia far exceeded the power of any broad-gauge locomotive
13.
5 ft and 1520 mm gauge railways
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Railways with a railway track gauge of 5 ft/1,524 mm were first constructed in the United Kingdom and the United States. This gauge is commonly called Russian gauge because this gauge was later chosen as the common track gauge for the Russian Empire. The gauge was redefined by Russian Railways to be 1520 mm, the primary region where Russian gauge is used is the former Soviet Union, Mongolia and Finland, with about 225,000 km of track. Russian gauge is the second most common gauge in the world, in 1748, the Wylam waggonway was built to a 5 ft gauge for the shipment of coal from Wylam to Lemington down the River Tyne. In 1839, the Eastern Counties Railway was constructed, and in 1840, in 1844, both lines were converted to 1,435 mm standard gauge. In 1903, the East Hill Cliff Railway, a funicular, was opened. In 1827, Horatio Allen, the engineer of the South Carolina Canal and Rail Road Company, prescribed the usage of 5 ft gauge. The presence of several distinct gauges was a disadvantage to the Confederate States of America during the American Civil War. In 1886, when around 11,500 miles of 5 ft gauge track existed in the United States, while of almost no practical importance the railway did demonstrate that this gauge was viable. The second railway in the Russian Empire was the Warsaw–Vienna railway which was built to 1,435 mm, for the building of Russias first major railway, the Moscow – Saint Petersburg Railway, engineer Pavel Melnikov hired as consultant George Washington Whistler, a prominent American railway engineer. Melnikov, of the Construction Commission overseeing the railway, recommended 6 ft following the example of the first railway and his study of US Railways. Following a report sent by Whistler the head of the Main Administration of Transport and Buildings recommended 5 ft and it was approved for the railway by Tsar Nicholas I on February 14,1843. The next lines built were also approved with this gauge but it was not until March 1860 that a Government decree stated all major railways in Russia would be 5 ft gauge. It is widely and incorrectly believed that Imperial Russia chose a gauge broader than standard gauge for military reasons, in 1841 a Russian army engineer wrote a paper stating that such a danger did not exist since railways could be made dysfunctional by retreating forces. Finally for the Moscow - Saint Petersburg Railway, which became the benchmark, despite this the difference in gauge did play a role in hindering invading armies, especially in World War II, it was just not selected with that in mind. The 5-foot gauge became the standard in the whole Russian Empire and that includes the Baltic states, Ukraine, Belarus, the Caucasian and Central Asian republics, Finland, and in the once Soviet-influenced Mongolia. This formed a break of gauge between Changchun and Kuancheng, until the rest of the former Chinese Eastern Railway was converted to standard gauge, unlike in South Manchuria, the Soviet Unions reconquest of southern Sakhalin from Japan did not result in regauging of the railway system. Southern Sakhalin has continued with the original Japanese 1,067 mm gauge simultaneously with the Russian gauge railway, constructed in the northern part of the island in 1930-1932
14.
5 ft 3 in gauge railways
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Railways with track gauge of 5 ft 3 in are broad gauge railways, currently in use in Australia, Brazil and Ireland. 600 BCE The Diolkos across the Isthmus of Corinth in Greece – a grooved paved trackway – was constructed with a gauge of 5 ft 3 in. 1840 The Grand Duchy of Baden State Railway was constructed to 5 ft 3 in gauge,1843 The Board of Trade of the United Kingdom recommended the use of 5 ft 3 in in Ireland, after investigating a dispute caused by diverse gauges in Ireland. 1846 The Regulating the Gauge of Railways Act 1846 made this gauge mandatory throughout all of Ireland,1847 The Swiss Northern Railway was opened, converted to standard gauge in 1854. 1854 The first Australian 5 ft 3 in line was opened,1858 The first Brazilian 5 ft 3 in railway was opened, the Companhia de Estrada de Ferro Dom Pedro II. 1863 The Canterbury Provincial Railways in New Zealand was built in 5 ft 3 in until gauge conversion to 3 ft 6 in in 1876 In Ireland this gauge is known as Irish gauge, in Australia this gauge is known as Victorian Broad Gauge. In Brazil this gauge is known as Bitola larga. The Pennsylvania trolley gauges of 5 ft 2 1⁄2 in and 5 ft 2 1⁄4 in are similar to Irish gauge, there is also 5 ft 2 in gauge, which is similar as well. One of the advantages of the broader 1,600 mm Irish gauge. In practice, Ireland does not have any heavily-loaded or steeply-graded lines that would require especially powerful locomotives. The most powerful locomotives on systems of this gauge were. By comparison a non-articulated standard gauge locomotive in the country was
15.
5 ft 6 in gauge railway
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5 ft 6 in/1,676 mm gauge is a broad track gauge commonly used in India, Pakistan, Sri Lanka, Argentina and Chile, but is also used on BART, in the San Francisco Bay Area, United States. It is historically known as Broad gauge in South Asia or Provincial gauge and it is the widest gauge in regular use anywhere in the world. See 5 ft 6 in gauge in Scotland This gauge was first used in Scotland for two short, isolated lines, the Dundee and Arbroath Railway and the Arbroath and Forfar Railway. However, soon there were disagreements with Lord Dalhousie favoring a 6 ft gauge and Mr. Simms, the consulting engineer favoring five feet and six inches gauge. The debate was settled in favor of the five and half feet gauge, called the broad gauge in 1850s. In the late 20th century, India adopted Project Unigauge, Gauge conversion towards Indian gauge is underway, replacing several narrow gauges and metre gauges. Pakistan uses primarily broad gauge, but also has a mix of metre gauge, the Bangladesh Railways uses a mix of broad gauge and metre gauge. The broad gauge network is located to the west of the Jamuna River. The Jamuna Bridge is a mixed use bridge that contains a gauge connection across the river linking both networks. Sri Lanka previously had a mix of broad gauge and other narrow gauges, however, all services currently operate on broad gauge as the other lines have either been closed or converted. In the 1850s it was first used in Canada, and was used in other British colonies. It was known as the Provincial gauge in Canada, the earliest railways in Canada, including the 1836 Champlain and St. Lawrence,1839 Albion Colliery tramway and 1847 Montreal and Lachine Railway were all built to standard gauge. The Grand Trunk Railway which operated in several Canadian provinces and American states used it, the Grand Trunk Railway was operated from headquarters in Montreal, Quebec, but corporate headquarters were in London, England. The St. Lawrence and Atlantic Railroad which operated in Quebec, Vermont, New Hampshire, there is a longstanding rumour that the Provincial gauge was selected specifically to create a break-of-gauge with US railways, the War of 1812 still being a fresh memory. However, there is supporting evidence for this, and this story appears to be traced to a single claim from the late 1800s. The Bay Area Rapid Transit system is the operating railroad in the United State to use Indian gauge. The original engineers for the system had background in aerospace and intended to make a system for other municipalities to emulate. The use of Indian gauge rails was one of many design elements included in its design
16.
Track gauge in the United States
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Originally, various gauges were used in the United States. Some railways, primarily in the northeast, used standard gauge, as a general rule, southern railroads were built to one or another broad gauge, mostly 5 ft, while northern railroads that were not standard-gauge tended to be narrow-gauge. Notable exceptions were the 6 ft railroads that predominated in the first part of the 19th Century in New York State, problems began as soon as lines began to meet and in much of the north-eastern United States, standard gauge was adopted. Non-standard gauges remain in use for municipal and regional mass transit systems not requiring interchange of equipment. The New York and Erie Railroad was originally 6 ft gauge,6 ft gauge was also cited for improved stability, and the New York and Erie eventually had rolling stock with 11 feet wide loading gauge. Major cities including Rochester, Syracuse, Utica, and Albany all were connected by six foot gauged railroads extending from Elmira and Binghamton on the New York and these lines included the Avon, Genesee & Mt. Other 6 ft gauge lines included the Syracuse, Binghamton & New York, the Walkill Valley railroad, the Portland Company was formed to build locomotives of this gauge for use on the local rail system. The New England railways were similarly standard-gauged in the 1870s, in the 1960s, the gauge was selected for use in the Bay Area Rapid Transit system, serving the San Francisco Bay Area, it is the only place in America where this gauge is in use. The rapid transit segment of the system covers 104 miles of track in revenue service. 5 ft 2 1⁄4 in and 5 ft 2 1⁄2 in are commonly known as Pennsylvania trolley gauge because it was used by railroad lines in the state of Pennsylvania. This configuration allowed for rolling stock that could more efficiently accommodate cotton bales. In the U. S. this gauge was changed to 4 ft 9 in in 1886, most of the original track in Ohio was built in 4 ft 10 in gauge, the Ohio Gauge. The Washington Metro system in the D. C. metropolitan area was built to 4 ft 8 1⁄4 in narrow gauge. 3 ft gauge railways became the dominant narrow gauge throughout the United States from the Boston, Revere Beach, the gauge was also used by the Oahu Railway and Land Company of Hawaii and the White Pass and Yukon Route of Alaska. Heritage railroads operate portions of the formerly extensive Colorado system as the Durango and Silverton Narrow Gauge Railroad and Cumbres, the Angels Flight and Court Flight funicular railways of Los Angeles used 2 ft 6 in. This became a popular gauge for railways in California, Florida, Hawaii, Minnesota, Montana, Nebraska, Oregon. Several Maine railroads used 2 ft gauge following demonstration on the Billerica, several railroads in Maine used it, including the Sandy River & Rangly Lakes, the Waterville Wisscassett & Farmington, the Kennebec Central, the Monson, and the Saco Biddford & Harrison. When these railroads ceased operation in the 1940s, their equipment was transferred to the Edaville Railroad, the gauge was also used by the Mount Gretna Narrow Gauge Railway, and by some mining railways of the Rocky Mountains
17.
Isambard Kingdom Brunel
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Brunel built dockyards, the Great Western Railway, a series of steamships including the first propeller-driven transatlantic steamship, and numerous important bridges and tunnels. His designs revolutionised public transport and modern engineering, though Brunels projects were not always successful, they often contained innovative solutions to long-standing engineering problems. Brunel set the standard for a railway, using careful surveys to minimise grades and curves. This necessitated expensive construction techniques, new bridges, new viaducts, one controversial feature was the wide gauge, a broad gauge of 7 ft 1⁄4 in, instead of what was later to be known as standard gauge of 4 ft 8 1⁄2 in. Brunel astonished Britain by proposing to extend the Great Western Railway westward to North America by building steam-powered iron-hulled ships and he designed and built three ships that revolutionised naval engineering, the Great Western, the Great Britain, and the Great Eastern. In 2002, Brunel was placed second in a BBC public poll to determine the 100 Greatest Britons, in 2006, the bicentenary of his birth, a major programme of events celebrated his life and work under the name Brunel 200. Brunels name is an amalgamation of his parents names and he inherited the family name of his father, and his middle name is his mothers surname. Brunels first name, Isambard, comes from his fathers middle name, Isambard is a Norman name of Germanic origin, meaning iron-bright. A cognate name is the German surname Eisenbarth, which can still be found today among Bavarians and German-Americans and he had two older sisters, Sophia and Emma, and the whole family moved to London in 1808 for his fathers work. Brunel had a childhood, despite the familys constant money worries. His father taught him drawing and observational techniques from the age of four, during this time he also learned fluent French and the basic principles of engineering. He was encouraged to draw interesting buildings and identify any faults in their structure, when Brunel was eight he was sent to Dr Morrells boarding school in Hove, where he learned the classics. When Brunel was 15, his father Marc, who had accumulated debts of over £5,000, was sent to a debtors prison. After three months went by with no prospect of release, Marc let it be known that he was considering an offer from the Tsar of Russia. In August 1821, facing the prospect of losing a prominent engineer, Brunel subsequently studied under the prominent master clockmaker and horologist Abraham-Louis Breguet, who praised Brunels potential in letters to his father. In late 1822, having completed his apprenticeship, Brunel returned to England, Brunels father, Marc, was the chief engineer, and the project was funded by the Thames Tunnel Company. The composition of the riverbed at Rotherhithe was often more than waterlogged sediment. The latter incident, in 1828, killed the two most senior miners, and Brunel himself narrowly escaped death and he was seriously injured, and spent six months recuperating
18.
Break of gauge
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With railways, a break-of-gauge occurs where a line of one gauge meets a line of a different gauge. Trains and rolling stock cannot run through some form of conversion between gauges, and freight and passengers must otherwise be transhipped. A break-of-gauge adds delays, cost, and inconvenience, narrow gauges tend to be associated with smaller loading gauges and sharper curves, which tend to reduce initial capital costs. This offsets the costs of any affected by the break-of-gauge. Historically narrow gauge railways were built on marginal lines, mostly through hilly and mountainous terrain to cut costs. Associated disadvantages were not recognized as much as rail lines were operated independent of potentially connecting lines regardless of gauge as competing companies built. Only the building of union stations or the nationalization of railroads changed this, an advantage is that invading armies may be severely hampered. Another advantage might be if the different gauges have different loading gauges. Similarly, if the larger and smaller gauges use different couplers or brakes, for passenger trains the inconvenience is less, especially at major stations where many passengers change trains or end their journeys anyway. Therefore, some railways have been built with gauges otherwise not used in the concerned countries. For example, the railways in Japan and Spain use 1,435 mm while their respective mainline railroad systems use 1,067 mm and 1,668 mm. For night trains, which are common in places like Russia. For these, often the bogies are replaced, even if it takes more time than having passengers change trains. If local government has influence over the construction of railways, some may see it as desirable for trains to stop in rather than pass through their town. Transhipping freight from cars of one gauge to cars of another is very labour- and time-intensive, if the capacity of the freight cars on both systems does not match, additional inefficiencies can arise. If the frequency is low, trains might need to wait a time for its counterpart to arrive before transshipping. This is avoided by storing the goods, but that is also an inconvenience, technical solutions to avoid transhipping include variable gauge axles, replacing the bogies of cars, and using transporter cars that can carry a car of a different gauge. Talgo and CAF have developed dual-gauge axles which permit through running between broad gauge and standard gauge, in Japan the Gauge Change Train, built on Talgo patents, runs on standard and narrow 1,067 mm gauge
19.
Dual gauge
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A dual-gauge railway is a line of track that provides for trains of two separate track gauges. A mixed-gauge railway provides for more than two gauges, but is also a term sometimes used to denote dual-gauge. A dual-gauge track configuration usually consists of three rails, two rails, one for each gauge, plus a common rail--although at times, commonality is not possible. In an ordinary three-rail dual-gauge configuration, the two adjacent outer rails give provide each of the gauges, while the outer rail is common to trains of both gauges operating over it. This configuration is not to be confused with the electric current traction rail or a check or guard rail, in railways, the most important specification is that of rail gauge, the distance between the inner surfaces of the heads of the travel rails. A problem arises when different gauges outside of this tolerance meet one another, in allowing railway tracks of different gauges to share the same alignment, costs can be reduced, and infrastructure shared, e. g. platforms, bridges and tunnels etc. Dual gauge can replace two separate tracks by sharing one common running rail and one of the two outer rails which determine the gauge. However, there are complications and costs involved that may offset the savings. One issue is that points are more complex, and therefore more expensive, arrangements are necessary to ensure trains of both gauges can be safely signalled, track circuits and mechanical interlocking where provided must be operated through the common rail. Also, the rail will have an increased wear and tear over the other separate gauge rails. The following pairs of gauges can be dual-gauged without problem, standard gauge and 1,676 mm,3 ft and 3 ft 6 in, and 5 ft and 6 ft. Standard gauge and 1,600 mm can also be dual-gauged, albeit with lighter, narrow-footed rails and this last combination is of particular historical interest, as it was of strategic significance during World War II. If three-rail dual gauge is impossible, four-rail gauntlet track dual-gauge has to be used, the complications and difficulties outlined illustrate the benefits of standardised railway gauges, where possible. Alternatively the rails may be too light for the loads imposed by broader-gauge railcars, such potential problems can rule out dual-gauge as a feasible option, unless heavier rails are installed. Dual-gauge lines in Java were regauged from 4 ft 8 1⁄2 in to 3 ft 6 in during the Japanese administration in 1942-1943, regauging occurred only on the relatively short Brumbung-Kedungjati-Gundih main line and the Kedungjati-Ambarawa branch line, as the rest of the line was already dual-gauge. In Los Angeles the 3 ft 6 in Los Angeles Railway, the Colorado and Southern Railway had both standard and narrow gauge trackage, and had dual-gauge track between Denver, Colorado and Golden, until 1941. Similarly, a section of the Denver and Rio Grande Western Railroads Alamosa-Durango Line from Alamosa, the East Broad Top Railroad and Coal Company formerly had considerable dual-gauge trackage in its Mount Union, Pennsylvania yard. Alaska and British Columbia are proposing dual gauge,1,435 mm standard gauge and 914 mm, track so that a narrow gauge tourist train and standard gauge ore trains can share the right of way
20.
Track gauge conversion
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In rail transport, gauge conversion is the process of converting a railway from one rail gauge to another, through the alteration of the railway tracks. An alternative to gauge conversion is dual gauge track, or gauge conversion of the vehicles themselves. Rails may be too light for the loads imposed by broader-gauge railcars, in some cases, gauge-convertible sleepers are installed before the conversion of the track itself. The sleepers must be enough to take the wider of the two gauges, and must be able to accommodate the fittings for both the existing and the new gauges. In cases where the difference between the two gauges is small, such as 1,000 mm and 1,067 mm track, or 1,435 mm and 1,524 mm track, in those cases, gauntlet track is required. Timber sleepers are always gauge convertible, provided that they are long enough, if the new gauge is wider than the old, a shorter sleeper than would normally be used can be tolerated, provided it still allows for secure fastening of the wider track. Concrete sleepers cannot be converted as an afterthought, but must have the future fittings cast in place when manufactured, steel sleepers should have the extra fitting incorporated when manufactured, though it is theoretically possible to drill or weld new fittings to the sleeper after installation. A special gauge-convertible sleeper, with a chair for the Pandrol clip. In June 2008, the South Australian government announced that by 2012 the Adelaide metropolitan network would be converted from 1,600 mm broad gauge to standard gauge, consequently, broad-gauge timber sleepers are progressively being replaced with gauge-convertible concrete sleepers on the metropolitan rail network. As of 2016, however, gauge conversion had not commenced, narrow-gauge railways often have a significantly smaller structure gauge, and therefore the rolling stock used has a smaller loading gauge in both height and width. Conversion to a track gauge will often require enlargement of the structure gauge on bridges, under road overpasses. Embankments and cuts could need widening as well, the minimum curve radius of narrow-gauge railways is often less than on tracks with a wider gauge, so route deviations might be required to allow the radius of curves to be increased. Track centres at stations with multiple tracks may also have to be increased, in this instance, the loading gauge of the broad gauge and standard gauge lines are essentially the same. Where vehicles cross a change of gauge, they must either be equipped for a change of bogie or have adjustable gauge axles. For example passenger trains crossing between the 1,435 mm system in France and the 1,668 mm in Spain pass through an installation which adjusts their variable gauge axles. This temporary alteration to allow through working is generally referred to as gauge change, in the event, few have been so converted, but one such is Victorian Railways R class R766. Because boilers and fireboxes are in the way locomotives can be converted only to a wider gauge, about 1860, the Bristol and Exeter Railway converted five 1,435 mm gauge locomotives to 7 ft gauge, and later converted them back again. In the 19th century, in the US, some broad 1,524 mm gauge locomotives were designed for conversion to 1,435 mm gauge
21.
Bogie exchange
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Bogie exchange is a system for operating railway wagons on two or more gauges to overcome difference in the track gauge. To perform a bogie exchange, a car is converted from one gauge to another by removing the bogies or trucks and it is generally limited to wagons and carriages, though diesel locomotives can be exchanged if enough time is available. Bogie wagons can have their gauge changed by lifting them off one set of bogies, the pin that centres the bogies and the hoses and fittings for the brakes must be compatible. A generous supply of bogies of each gauge is needed to accommodate the ebb, the bogies and wagons also need to have standardized hooks, etc. where they may be efficiently lifted. The two wheel sets on four-wheel wagons can be changed as if the wagon has been designed accordingly. Steam engines can be designed for more than one gauge, by having and this was done in the 1930s and beyond in Victoria for possible gauge conversion, though no engines were ever converted in this manner other than one heritage engine. Some 1,000 mm metre gauge Garratt locomotives of East Africa were designed for conversion to 3 ft 6 in gauge. The re-gauging was performed by simply reversing the wheel centres so that the spokes dished outwards, in the southern United States, some steam locomotives built by Baldwin were designed for easy conversion from 5 ft to 4 ft 8 1⁄2 in standard gauge. Diesel locomotives have bogies like wagons and carriages, only with more cables for the traction motors, in Australia, some classes of diesel locomotives are regularly gauge-converted to suit traffic requirements on the 1,435 mm,1,600 mm, and 1,067 mm networks. The simplest way to carry out bogie exchange is to lift the wagons off the bogies and this may require the wagons in a train to be uncoupled, and continuous brakes disconnected. As the bogies are swung out of the way, they sway, another way of carrying out bogie exchange is to lower the bogies onto a trolley in a pit, after which the trolleys are rolled out of the way and others return. This keeps the train couplings and continuous brakes connected, in addition, the bogies never need leave a solid surface, so they can be wheeled in and out more quickly. This method was used at Dry Creek railway station, Adelaide, between 1961 and 1995, Australia had five bogie exchange centres, which opened and closed as gauge conversion work proceeded. The gauges served were 1,435 mm and 1,600 mm, all the wagons involved had wagon codes ending in X, such as VLX. The centres were, Dynon, Melbourne, Victoria Wodonga near Albury on state border and this was done by one shift of 18 men, compared with the 100 men required if the same amount of freight were transferred wagon to wagon. Brest, Belarus – between 1,520 mm and 1,435 mm at the border to Poland Bogie exchange was used between 2 ft 6 in and 1,000 mm gauge on the Ferrocarril de Antofagasta a Bolivia Railway. Between 1,435 mm standard gauge and the 3 ft 6 in of the former Newfoundland Railway at Port aux Basques A bogie exchange station exists at the Chinese border to Mongolia, both the Moscow-Beijing passenger train and freight trains get their bogies exchanged. Mongolia has Russian gauge 1,520 mm, China has 1,435 mm. Also, a bogie exchange station exists in the Port of Turku with a short stretch of 1,435 mm gauge railway
22.
Variable gauge
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A variable gauge system allows railway vehicles in a train to travel across a break of gauge caused by two railway networks with differing track gauges. For through-operation, a train must be equipped with special trucks holding variable gauge wheelsets containing a variable gauge axle, the gauge is altered by driving the train through a gauge changer or gauge changing facility. As the train passes through the changer, the wheels are unlocked, moved closer together, or further apart. Installed variable gauge systems exist within the network of Spain. A system for changing gauge, without need for stopping is widespread for passenger traffic in Spain, used in services run on a mix of dedicated high-speed lines, similar systems for freight traffic are still rather incipient, as the higher axle weight increases the technological challenge. Variable gauge axles help solve the problem of a break-of-gauge without having to resort to dual gauge tracks or transshipment, systems allow the adjustment between two gauges. No designs supporting more than two gauges are used, there are several variable gauge axle systems, Talgo-RD. The Talgo system has been in service in Portbou and Irun, on the Spanish-French border. CAF-BRAVA The BRAVA system was designed in 1968 by the Vevey Company. The system was called the Vevey axle. The design was obtained and improved by Construcciones y Auxiliar de Ferrocarriles. Being developed in 2002 for use between Europe and Russia, Japan Railways RTRI to be used on motorised axles. PKP SUW2000 system produced by ZNTK Poznań for Polish State Railways, the Montreux-Oberland Bernois railway, Switzerland in preparation by Prose of Winterthur 1,435 mm /1,000 mm. The variable gauge systems are not themselves all compatible, only the SUW2000 and Rafil Type V systems are interoperable. In 2009, at Roda de Barà near Tarragona, a Unichanger capable of four different VGA systems was under development. VGA is particularly important with international railway traffic because gauge changes tend to more often at international borders. The maximum speed of the equipped with the different technologies vary. Only CAF and Talgo produce high-speed VGA, allowing speeds up to 250 km/h, a gauge changer is a device which forces the gauge adjustment in the wheels
23.
Track gauge in North America
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The vast majority of North American railroads are standard gauge. The first railroads in Canada in the 1830s were built to 1,435 mm, after a Royal Commission, in 1851 the broad gauge, called the Provincial Gauge or Indian gauge, was adopted by the Province of Canada government as the standard gauge. However, in the 1870s, most Canadian railroads were changed to standard gauge to facilitate interchange with U. S. railroads, the last broad gauge line closed in 1911. The Toronto subway uses an overgauge of 4 ft 10 7⁄8 in, the 3 ft railroad system of Guatemala no longer operates, see Rail transport in Guatemala. See Rail transport in Mexico The Panama Railroad was originally 5 ft as in much of the Southern United States and this gauge was converted to 1,435 mm when the line was rebuilt in 2000. Nowadays only the ship handling trains along the Panama Canal, called mules, in 1886, the southern railroads agreed to coordinate changing gauge on all their tracks. Over a period of 36 hours, tens of thousands of workers pulled the spikes from the west rail of all the broad lines in the South, moved them 3 in east. The new gauge was close enough that standard gauge equipment could run on it without problem, by June 1886, all major railroads in North America were using approximately the same gauge. The final conversion to standard gauge took place gradually as track was maintained. Now, the only rail systems in the United States are some city transit systems
24.
Track gauge in South America
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In South America, Argentina and Chile use 1,676 mm track gauge, as well as 1,000 mm or metre gauge. Brazil uses 1,600 mm and 1,000 mm, exceptions are the Estrada de Ferro do Amapá north of the Amazon River, which has 1,435 mm gauge, and the new Line 5 of São Paulo Metro, which also uses standard gauge. Argentina, Venezuela, Paraguay, Uruguay, and Peru use standard gauge, in the past a few lines in Northern Chile also had standard gauge, as the only international railway between Arica and Tacna, slightly more than 60 km, uses standard gauge. The El Cerrejón Coal Railway in Colombia is also 1,435 mm, there are and were also some lines using different narrow gauges, see the narrow gauge section in this list. Rail gauge in Europe Rail gauge in North America
25.
Rail gauge in Australia
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Rail gauges in Australia display significant variations, which has presented an extremely difficult problem for rail transport on the Australian continent for over 150 years. As of 2014, there is 11,801 kilometres of railways,17,381 kilometres of standard gauge railways and 3,221 kilometres of broad gauge railways. In the 19th century, each of the Colonies of Australia adopted their own gauges, however, with Federation in 1901 and the removal of trade barriers, the short sightedness of three gauges became apparent. It would be 94 years before all state capitals were joined by one standard gauge. The most common railway gauges in Australia are narrow, standard, the narrower 610 mm or 2 ft gauge is found on shorter lines, particularly sugarcane tramways in Queensland. Likewise the Richmond Valley and South Maitland Railway lines in the Hunter Valley also used standard gauge, the Whyalla Steelworks was built as a narrow line, being converted to standard gauge when the Commonwealth Railways Whyalla line opened. As a result, the Regulating the Gauge of Railways Act 1846 was passed which prescribed the use of 4 ft 8 1⁄2 in in England, Scotland, in 1846, Australian newspapers discussed the break of gauge problem in the United Kingdom, especially for defence. In 1847, South Australia adopted the 4 ft 8 1⁄2 in gauge as law, the recommendation was adopted by the then three colonies. Grey notes in his letter that South Australia has already adopted this gauge, at this stage Victoria and Queensland were still part of New South Wales. The overland telegraph communication with London was yet to be built, at that time the private Sydney Railway Company had begun planning its railway line to Parramatta. The chief engineer of the company was Irish-born Francis Webb Sheilds and this decision was endorsed by the NSW Governor, and Colonial Secretary Earl Grey in London agreed in 1851. However, Sheilds and his three subordinates resigned in December 1850 when the company cut their salaries for financial reasons, after the interim appointment of Henry Mais, in July 1852 the company selected a new Scottish engineer, James Wallace, who preferred the English standard gauge. The Government was persuaded to make the back to 4 ft 8 1⁄2 in and in January 1853 they advised the company that the Act requiring 5 ft 3 in would be repealed. In February 1853 the other colonies were sent a memorandum advising them of the pending change, in Victoria the memorandum was distributed to three railway companies and their responses were sought, with two replying and only one showing a distinct preference for 5 ft 3 in. In reply at the end of March, the companies were told the colonial Victorian government preferred 5 ft 3 in and the order was subsequently placed. In July 1853, the Government of Victoria advised New South Wales that it would use the broader gauge, concerns over the gauge difference began to be raised almost immediately. The 3 ft 6 in narrow gauge was introduced to Australia in 1865, the gauge was chosen on the supposition that it would be constructed more cheaply, faster and on tighter curves than the wider gauges. This was the first narrow gauge line in the world
26.
Geometry
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Geometry is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space. A mathematician who works in the field of geometry is called a geometer, Geometry arose independently in a number of early cultures as a practical way for dealing with lengths, areas, and volumes. Geometry began to see elements of mathematical science emerging in the West as early as the 6th century BC. By the 3rd century BC, geometry was put into a form by Euclid, whose treatment, Euclids Elements. Geometry arose independently in India, with texts providing rules for geometric constructions appearing as early as the 3rd century BC, islamic scientists preserved Greek ideas and expanded on them during the Middle Ages. By the early 17th century, geometry had been put on a solid footing by mathematicians such as René Descartes. Since then, and into modern times, geometry has expanded into non-Euclidean geometry and manifolds, while geometry has evolved significantly throughout the years, there are some general concepts that are more or less fundamental to geometry. These include the concepts of points, lines, planes, surfaces, angles, contemporary geometry has many subfields, Euclidean geometry is geometry in its classical sense. The mandatory educational curriculum of the majority of nations includes the study of points, lines, planes, angles, triangles, congruence, similarity, solid figures, circles, Euclidean geometry also has applications in computer science, crystallography, and various branches of modern mathematics. Differential geometry uses techniques of calculus and linear algebra to problems in geometry. It has applications in physics, including in general relativity, topology is the field concerned with the properties of geometric objects that are unchanged by continuous mappings. In practice, this often means dealing with large-scale properties of spaces, convex geometry investigates convex shapes in the Euclidean space and its more abstract analogues, often using techniques of real analysis. It has close connections to convex analysis, optimization and functional analysis, algebraic geometry studies geometry through the use of multivariate polynomials and other algebraic techniques. It has applications in areas, including cryptography and string theory. Discrete geometry is concerned mainly with questions of relative position of simple objects, such as points. It shares many methods and principles with combinatorics, Geometry has applications to many fields, including art, architecture, physics, as well as to other branches of mathematics. The earliest recorded beginnings of geometry can be traced to ancient Mesopotamia, the earliest known texts on geometry are the Egyptian Rhind Papyrus and Moscow Papyrus, the Babylonian clay tablets such as Plimpton 322. For example, the Moscow Papyrus gives a formula for calculating the volume of a truncated pyramid, later clay tablets demonstrate that Babylonian astronomers implemented trapezoid procedures for computing Jupiters position and motion within time-velocity space
27.
Rail transport
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Rail transport is a means of conveyance of passengers and goods on wheeled vehicles running on rails, also known as tracks. It is also referred to as train transport. In contrast to road transport, where vehicles run on a flat surface. Tracks usually consist of rails, installed on ties and ballast, on which the rolling stock, usually fitted with metal wheels. Other variations are possible, such as slab track, where the rails are fastened to a concrete foundation resting on a prepared subsurface. Rolling stock in a transport system generally encounters lower frictional resistance than road vehicles, so passenger. The operation is carried out by a company, providing transport between train stations or freight customer facilities. Power is provided by locomotives which either draw electric power from a railway system or produce their own power. Most tracks are accompanied by a signalling system, Railways are a safe land transport system when compared to other forms of transport. The oldest, man-hauled railways date back to the 6th century BC, with Periander, one of the Seven Sages of Greece, Rail transport blossomed after the British development of the steam locomotive as a viable source of power in the 19th centuries. With steam engines, one could construct mainline railways, which were a key component of the Industrial Revolution, also, railways reduced the costs of shipping, and allowed for fewer lost goods, compared with water transport, which faced occasional sinking of ships. The change from canals to railways allowed for markets in which prices varied very little from city to city. In the 1880s, electrified trains were introduced, and also the first tramways, starting during the 1940s, the non-electrified railways in most countries had their steam locomotives replaced by diesel-electric locomotives, with the process being almost complete by 2000. During the 1960s, electrified high-speed railway systems were introduced in Japan, other forms of guided ground transport outside the traditional railway definitions, such as monorail or maglev, have been tried but have seen limited use. The history of the growth, decline and restoration to use of transport can be divided up into several discrete periods defined by the principal means of motive power used. The earliest evidence of a railway was a 6-kilometre Diolkos wagonway, trucks pushed by slaves ran in grooves in limestone, which provided the track element. The Diolkos operated for over 600 years, Railways began reappearing in Europe after the Dark Ages. The earliest known record of a railway in Europe from this period is a window in the Minster of Freiburg im Breisgau in Germany
28.
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
29.
Curvature
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In mathematics, curvature is any of a number of loosely related concepts in different areas of geometry. This article deals primarily with extrinsic curvature and its canonical example is that of a circle, which has a curvature equal to the reciprocal of its radius everywhere. Smaller circles bend more sharply, and hence have higher curvature, the curvature of a smooth curve is defined as the curvature of its osculating circle at each point. Curvature is normally a scalar quantity, but one may define a curvature vector that takes into account the direction of the bend in addition to its magnitude. The curvature of more objects is described by more complex objects from linear algebra. This article sketches the mathematical framework which describes the curvature of a curve embedded in a plane, the curvature of C at a point is a measure of how sensitive its tangent line is to moving the point to other nearby points. There are a number of equivalent ways that this idea can be made precise and it is natural to define the curvature of a straight line to be constantly zero. The curvature of a circle of radius R should be large if R is small and small if R is large, thus the curvature of a circle is defined to be the reciprocal of the radius, κ =1 R. Given any curve C and a point P on it, there is a circle or line which most closely approximates the curve near P. The curvature of C at P is then defined to be the curvature of that circle or line, the radius of curvature is defined as the reciprocal of the curvature. Another way to understand the curvature is physical, suppose that a particle moves along the curve with unit speed. Taking the time s as the parameter for C, this provides a natural parametrization for the curve, the unit tangent vector T also depends on time. The curvature is then the magnitude of the rate of change of T. Symbolically and this is the magnitude of the acceleration of the particle and the vector dT/ds is the acceleration vector. Geometrically, the curvature κ measures how fast the unit tangent vector to the curve rotates. If a curve close to the same direction, the unit tangent vector changes very little and the curvature is small, where the curve undergoes a tight turn. These two approaches to the curvature are related geometrically by the following observation, in the first definition, the curvature of a circle is equal to the ratio of the angle of an arc to its length. e. For such a curve, there exists a reparametrization with respect to arc length s. This is a parametrization of C such that ∥ γ ′ ∥2 = x ′2 + y ′2 =1, the velocity vector T is the unit tangent vector
30.
Horizontal plane
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Alternatively, a spirit level, which exploits the buoyancy of a bubble, can be used to determine if the plane is horizontal. In radio science, horizontal plane is used to plot an antennas relative field strength in relation to the ground on a polar graph. Normally the maximum of 1.000 or 0 dB is at the top, other field strengths are expressed as a decimal less than 1.000, a percentage less than 100%, or decibels less than 0 dB. If the graph is of an actual or proposed installation, rotation is applied so that the top is 0o true north, see also the perpendicular vertical plane. In general, something that is horizontal can be drawn from left to right, although the word horizontal is commonly used in daily life and language, it is subject to many misconceptions. The concept of horizontality only makes sense in the context of a clearly measurable gravity field, i. e. in the neighborhood of a planet, star, when the gravity field becomes very weak, the notion of being horizontal loses its meaning. A plane is only at the chosen point. Horizontal planes at two points are not parallel, they intersect. Thus both horizontality and verticality are strictly speaking local concepts, and it is necessary to state to which location the direction or the plane refers to. In reality, the gravity field of a planet such as Earth is deformed due to the inhomogeneous spatial distribution of materials with different densities. Actual horizontal planes are not even parallel even if their reference points are along the same vertical line. At any given location, the gravitational force is not quite constant over time. For instance, on Earth the horizontal plane at a given point changes with the position of the Moon. On a rotating planet such as Earth, the gravitational pull of the planet is different from the apparent net force that can be measured in the laboratory or in the field. This difference is the force associated with the planets rotation. This is a force, it only arises when calculations or experiments are conducted in non-inertial frames of reference. Hence, the world appears to be flat locally, and horizontal planes in nearby locations appear to be parallel, such statements are nevertheless approximations, whether they are acceptable in any particular context or application depends on the applicable requirements, in particular in terms of accuracy. In this case, the direction is typically from the left side of the paper to the right side
31.
Horizontal and vertical
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The usage of the inter-related terms horizontal and vertical as well as their symmetries and asymmetries vary with context. In astronomy, geography, and related sciences and contexts, a passing by a given point is said to be vertical if it is locally aligned with the local gravity vector at that point. In general, something that is vertical can be drawn from up to down, girard Desargues defined the vertical to be perpendicular to the horizon in his Perspective of 1636. The word horizontal is derived from horizon, whereas vertical originates in the late Latin verticalis, in the context of a two-dimensional orthogonal Cartesian coordinate system on a Euclidean plane, to say that a line is horizontal or vertical, an initial designation has to be made. One can start off by designating the vertical direction, usually labelled the Y direction, the horizontal direction, usually labelled the X direction, is then automatically determined. Or, one can do it the way around, i. e. nominate the x-axis. There is no reason to choose the horizontal over the vertical as the initial designation. The following hold in the case, a) Through any point P in the plane, there is one and only one vertical line within the plane and one. This symmetry breaks down as one moves to the three-dimensional case, b) A vertical line is any line parallel to the vertical direction. A horizontal line is any line normal to a vertical line, c) Horizontal lines do not cross each other. D) Vertical lines do not cross each other, not all of these elementary geometric facts are true in the 3-D context. In the three-dimensional case, the situation is complicated as now one has horizontal and vertical planes in addition to horizontal and vertical lines. Consider a point P and designate a direction through P as vertical, a plane which contains P and is normal to the designated direction is the horizontal plane at P. Any plane going through P, normal to the plane is a vertical plane at P. Through any point P, there is one and only one horizontal plane and this is a new feature that emerges in three dimensions. The symmetry that exists in the case no longer holds. In physics, in engineering, and in construction, the designated as vertical is usually that along which a plumb-bob hangs. Alternatively, a level that exploits the buoyancy of an air bubble
32.
Multiview projection
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Along the y-axis, The top and bottom views, which are known as plans. Along the z-axis, The front and back views, which are known as elevations. Orthographic projections show the views of an object, each viewed in a direction parallel to one of the main coordinate axes. These primary views are called plans and elevations, sometimes they are shown as if the object has been cut across or sectioned to expose the interior, these views are called sections. Auxiliary views are taken from an angle that is not one of the primary views. A plan is a view of a 3-dimensional object seen from vertically above and it may be drawn in the position of a horizontal plane passing through, above, or below the object. The outline of a shape in this view is called its planform. The plan view from above a building is called its roof plan, a section seen in a horizontal plane through the walls and showing the floor beneath is called a floor plan. An elevation is a view of a 3-dimensional object from the position of a vertical plane beside an object, in other words, an elevation is a side-view as viewed from the front, back, left or right. An elevation is a method of depicting the external configuration. Building façades are shown as elevations in architectural drawings and technical drawings, elevations are the most common orthographic projection for conveying the appearance of a building from the exterior. Perspectives are also used for this purpose. A building elevation is typically labeled in relation to the direction it faces. E. g. the North Elevation of a building is the side that most closely faces true north on the compass, interior elevations are used to show detailing such as millwork and trim configurations. In the building elevations are a non-perspective view of the structure. These are drawn to scale so that measurements can be taken for any aspect necessary, Drawing sets include front, rear and both side elevations. A developed elevation is a variant of a regular elevation view in several adjacent non-parallel sides may be shown together. For example, the north and west views may be shown side-by-side, sharing an edge, a section, or cross-section, is a view of a 3-dimensional object from the position of a plane through the object
33.
Track transition curve
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A track transition curve, or spiral easement, is a mathematically calculated curve on a section of highway, or railroad track, where a straight section changes into a curve. It is designed to prevent sudden changes in lateral acceleration, in plan the start of the transition of the horizontal curve is at infinite radius and at the end of the transition it has the same radius as the curve itself, thus forming a very broad spiral. At the same time, in the plane, the outside of the curve is gradually raised until the correct degree of bank is reached. With a road vehicle the driver applies the steering alteration in a gradual manner. The actual equation given in Rankine is that of a cubic curve and this was also known as cubic parabola at that time. In the UK, only from 1845 when legislation and land began to constrain the laying out of rail routes and tighter curves were necessary. The true spiral, where the curvature is exactly linear in arclength, several late-19th century civil engineers seem to have derived the equation for this curve independently. Charles Crandall gives credit to one Ellis Holbrook, in the Railroad Gazette, Dec.3,1880, another early publication was The Railway Transition Spiral by Arthur N. Talbot, originally published in 1890. Some early 20th century authors call the curve Glovers spiral, attributing it to James Glovers 1900 publication, the equivalence of the railroad transition spiral and the clothoid seems to have been first published in 1922 by Arthur Lovat Higgins. Since then, clothoid is the most common given the curve. While railroad track geometry is intrinsically three-dimensional, for practical purposes the vertical and horizontal components of track geometry are usually treated separately, here grade refers to the tangent of the angle of rise of the track. The design pattern for horizontal geometry is typically a sequence of straight line, the degree of banking in railroad track is typically expressed as the difference in elevation of the two rails, commonly quantified and referred to as the superelevation. The simplest and most commonly used form of curve is that in which the superelevation. Cartesian coordinates of points along this spiral are given by the Fresnel integrals, the resulting shape matches a portion of an Euler spiral, which is also commonly referred to as a clothoid, and sometimes Cornu spiral. A transition curve can connect a track segment of constant non-zero curvature to another segment with constant curvature that is zero or non-zero of either sign, successive curves in the same direction are sometimes called progressive curves and successive curves in opposite directions are called reverse curves. The Euler spiral has two advantages, one is that it is easy for surveyors because the coordinates can be looked up in Fresnel integral tables. The other is that it provides the shortest transition subject to a limit on the rate of change of the track superelevation. However, as has been recognized for a time, it has undesirable dynamic characteristics due to the large roll acceleration
34.
Minute and second of arc
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A minute of arc, arcminute, arc minute, or minute arc is a unit of angular measurement equal to 1/60 of one degree. Since one degree is 1/360 of a turn, one minute of arc is 1/21600 of a turn, a second of arc, arcsecond, or arc second is 1/60 of an arcminute, 1/3600 of a degree, 1/1296000 of a turn, and π/648000 of a radian. To express even smaller angles, standard SI prefixes can be employed, the number of square arcminutes in a complete sphere is 4 π2 =466560000 π ≈148510660 square arcminutes. The standard symbol for marking the arcminute is the prime, though a single quote is used where only ASCII characters are permitted. One arcminute is thus written 1′ and it is also abbreviated as arcmin or amin or, less commonly, the prime with a circumflex over it. The standard symbol for the arcsecond is the prime, though a double quote is commonly used where only ASCII characters are permitted. One arcsecond is thus written 1″ and it is also abbreviated as arcsec or asec. In celestial navigation, seconds of arc are used in calculations. This notation has been carried over into marine GPS receivers, which normally display latitude and longitude in the format by default. An arcsecond is approximately the angle subtended by a U. S. dime coin at a distance of 4 kilometres, a milliarcsecond is about the size of a dime atop the Eiffel Tower as seen from New York City. A microarcsecond is about the size of a period at the end of a sentence in the Apollo mission manuals left on the Moon as seen from Earth, since antiquity the arcminute and arcsecond have been used in astronomy. The principal exception is Right ascension in equatorial coordinates, which is measured in units of hours, minutes. These small angles may also be written in milliarcseconds, or thousandths of an arcsecond, the unit of distance, the parsec, named from the parallax of one arcsecond, was developed for such parallax measurements. It is the distance at which the radius of the Earths orbit would subtend an angle of one arcsecond. The ESA astrometric space probe Gaia is hoped to measure star positions to 20 microarcseconds when it begins producing catalog positions sometime after 2016, there are about 1.3 trillion µas in a turn. Currently the best catalog positions of stars actually measured are in terms of milliarcseconds, apart from the Sun, the star with the largest angular diameter from Earth is R Doradus, a red supergiant with a diameter of 0.05 arcsecond. The dwarf planet Pluto has proven difficult to resolve because its angular diameter is about 0.1 arcsecond, space telescopes are not affected by the Earths atmosphere but are diffraction limited. For example, the Hubble space telescope can reach a size of stars down to about 0. 1″
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.
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
37.
Harmonic
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A harmonic is any member of the harmonic series, the divergent infinite series. Every term of the series after the first is the mean of the neighboring terms. The phrase harmonic mean likewise derives from music, the term is employed in various disciplines, including music, physics, acoustics, electronic power transmission, radio technology, and other fields. It is typically applied to repeating signals, such as sinusoidal waves, a harmonic of such a wave is a wave with a frequency that is a positive integer multiple of the frequency of the original wave, known as the fundamental frequency. The original wave is called the 1st harmonic, the following harmonics are known as higher harmonics. As all harmonics are periodic at the frequency, the sum of harmonics is also periodic at that frequency. On strings, harmonics that are bowed have a glassy, pure tone, harmonics may also be called overtones, partials or upper partials. In some music contexts, the harmonic, overtone and partial are used fairly interchangeably. Most acoustic instruments emit complex tones containing many individual partials, rather, a musical note is perceived as one sound, the quality or timbre of that sound being a result of the relative strengths of the individual partials. Oscillators that produce harmonic partials behave somewhat like one-dimensional resonators, and are long and thin. Wind instruments whose air column is open at one end, such as trumpets and clarinets. However they only produce partials matching the odd harmonics, at least in theory, the reality of acoustic instruments is such that none of them behaves as perfectly as the somewhat simplified theoretical models would predict. Partials whose frequencies are not integer multiples of the fundamental are referred to as inharmonic partials, antique singing bowls are known for producing multiple harmonic partials or multiphonics. An overtone is any partial higher than the lowest partial in a compound tone, the relative strengths and frequency relationships of the component partials determine the timbre of an instrument. This chart demonstrates how the three types of names are counted, In many musical instruments, it is possible to play the upper harmonics without the note being present. In a simple case this has the effect of making the note go up in pitch by an octave, in some cases it also changes the timbre of the note. This is part of the method of obtaining higher notes in wind instruments. The extended technique of playing multiphonics also produces harmonics, on string instruments it is possible to produce very pure sounding notes, called harmonics or flageolets by string players, which have an eerie quality, as well as being high in pitch
38.
Derailment
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A derailment is said to take place when a vehicle such as a train runs off its rails. This does not necessarily mean that it leaves its track, although many derailments are minor, all result in temporary disruption of the proper operation of the railway system, and they are potentially seriously hazardous to human health and safety. In emergency situations, deliberate derailment with derails or catch points is used to prevent a more serious accident. During the 19th century derailments were commonplace, but progressively improved safety measures have resulted in a lower level of such incidents. In the US, derailments have dropped dramatically since 1980 from over 3,000 annually to 1,000 or so in 1986, a traditional track structure consists of two rails, fixed at a designated distance apart, and supported on transverse sleepers. Some advanced track structures support the rails on a concrete or asphalt slab, the running surface of the rails is required to be practically continuous and of the proper geometrical layout. 170 broken rails were reported on Network Rail in the UK in 2008, in jointed track, rails are usually connected with bolted fishplates. The web of the rail experiences large shear forces and these are enhanced around the bolt hole, where track maintenance is poor, metallurgical fatigue can result in the propagation of star cracking from the bolthole. In extreme situations this can lead to a piece of rail at the joint becoming detached. Local embrittlement of the parent metal may take place due to wheel spin, the fishplates in jointed track may fail, allowing the rails to pull apart in extremely cold weather, this is usually associated with uncorrected rail creep. Derailment may take place due to excessive gauge widening, in which the sleepers or other fastenings fail to maintain the proper gauge, the crabbing effect referred to above is more marked in dry conditions, when the coefficient of friction at the wheel to rail interface is high. The running gear — wheelsets, bogies, and suspension — may fail, modern technologies have reduced the incidence of these failures considerably, both by design and intervention. The last condition applies if the suspension springing has a stiffness optimised for the condition, or for a compromise loading condition. The vehicle wheelsets become momentarily unloaded vertically so that the guidance required from the flanges or wheel tread contact is inadequate, a special case is heat related buckling, in hot weather the rail steel expands. This is managed by stressing continuously welded rails and by providing proper expansion gaps at joints, in addition, lateral restraint is provided by an adequate ballast shoulder. If any of these measures are inadequate, the track may buckle, a large lateral distortion takes place, junctions and other changes of routing on railways are generally made by means of points. In the early days of railways these were moved independently by local staff, accidents — usually collisions — took place when staff forgot which route the points were set for, or overlooked the approach of a train on a conflicting route. If the points were not correctly set for either route — set in mid-stroke — it is possible for a passing to derail
39.
Grade (slope)
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The grade of a physical feature, landform or constructed line refers to the tangent of the angle of that surface to the horizontal. It is a case of the slope, where zero indicates horizontality. A larger number indicates higher or steeper degree of tilt, often slope is calculated as a ratio of rise to run, or as a fraction in which run is the horizontal distance and rise is the vertical distance. The grades or slopes of existing physical features such as canyons and hillsides, stream and river banks, grades are typically specified for new linear constructions. The grade may refer to the slope or the perpendicular cross slope. There are several ways to express slope, as an angle of inclination to the horizontal, as a percentage, the formula for which is 100 rise run which could also be expressed as the tangent of the angle of inclination times 100. In the U. S. this percentage grade is the most commonly used unit for communicating slopes in transportation, surveying, construction, and civil engineering. As a per mille figure, the formula for which is 1000 rise run which could also be expressed as the tangent of the angle of inclination times 1000 and this is commonly used in Europe to denote the incline of a railway. As a ratio of one part rise to so many parts run, for example, a slope that has a rise of 5 feet for every 100 feet of run would have a slope ratio of 1 in 20. This is generally the method used to describe railway grades in Australia, any of these may be used. Grade is usually expressed as a percentage, but this is converted to the angle α from horizontal or the other expressions. Slope may still be expressed when the run is not known. This is not the way to specify slope, it follows the sine function rather than the tangent function. But in practice the way to calculate slope is to measure the distance along the slope and the vertical rise. When the angle of inclination is small, using the slope length rather than the horizontal displacement makes only an insignificant difference, Railway gradients are usually expressed in terms of the rise in relation to the distance along the track as a practical measure. In cases where the difference between sin and tan is significant, the tangent is used. In any case, the identity holds for all inclinations up to 90 degrees, tan α = sin α1 − sin 2 α In Europe. Grades are related using the equations with symbols from the figure at top
