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30-727: The Nilgiri Mountain Railway (NMR), colloquially called the "Toy Train" by locals is a 1,000 mm ( 3 ft  3 + 3 ⁄ 8  in ) metre gauge railway in Nilgiris district , Tamil Nadu , India , built by the British in 1908. The railway is operated by the Southern Railway and is the only rack railway in India. The railway relies on its fleet of steam locomotives . NMR switched to diesel locomotives on

60-464: A gradient . The arrival of the new engines eliminated the disruptions in service that occurred frequently. The steam locomotives are marshalled at the downhill (Mettupalayam) end of the train. The average gradient in this rack section is 1 in 24.5 (4.08%), with a maximum of 1 in 12 (8.33%). Southern Railway carries out the majority of the locomotive repairs at the Coonoor shed but has rebuilt many of

90-409: A 71 percent grade instead of a 100 percent. But in practice the usual way to calculate slope is to measure the distance along the slope and the vertical rise, and calculate the horizontal run from that, in order to calculate the grade (100% × rise/run) or standard slope (rise/run). When the angle of inclination is small, using the slope length rather than the horizontal displacement (i.e., using

120-478: A little over 50 tonnes and cost Rs. 10 crore. They have pilot and primary burners. Separate tanks hold about 850 litres (190 imp gal; 220 US gal) of diesel and 2,250 litres (490 imp gal; 590 US gal) of furnace oil . The hauling capacity of this new engine is 97.6 tonnes (96.1 long tons; 107.6 short tons). It can run at a speed of 30 kilometres per hour (19 miles per hour) on plains and at 15 kilometres (9.3 miles) an hour climbing

150-415: A physical feature, landform or constructed line refers to the tangent of the angle of that surface to the horizontal . It is a special 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 ("rise over run") in which run is the horizontal distance (not the distance along

180-687: A vehicle can ascend while maintaining a particular speed is sometimes termed that vehicle's "gradeability" (or, less often, "grade ability"). The lateral slopes of a highway geometry are sometimes called fills or cuts where these techniques have been used to create them. In the United States, the maximum grade for federally funded highways is specified in a design table based on terrain and design speeds, with up to 6% generally allowed in mountainous areas and hilly urban areas with exceptions for up to 7% grades on mountainous roads with speed limits below 60 mph (95 km/h). The steepest roads in

210-739: Is 23.1% by the 67-Bernal Heights on Alabama Street between Ripley and Esmeralda Streets. Likewise, the Pittsburgh Department of Engineering and Construction recorded a grade of 37% (20°) for Canton Avenue. The street has formed part of a bicycle race since 1983. Grade, pitch, and slope are important components in landscape design , garden design , landscape architecture , and architecture ; for engineering and aesthetic design factors. Drainage, slope stability, circulation of people and vehicles, complying with building codes, and design integration are all aspects of slope considerations in environmental design . Ruling gradients limit

240-654: Is expressed as a percentage, the angle can be determined as: If the angle is expressed as a ratio (1 in n) then: For degrees, percentage (%) and per-mille (‰) notations, larger numbers are steeper slopes. For ratios, larger numbers n of 1 in n are shallower, easier slopes. The examples show round numbers in one or more of the notations and some documented and reasonably well known instances. In vehicular engineering , various land -based designs ( automobiles , sport utility vehicles , trucks , trains , etc.) are rated for their ability to ascend terrain . Trains typically rate much lower than automobiles. The highest grade

270-558: Is used in around 95,000 kilometres (59,000 mi) of tracks around the world. It was used by several European colonial powers including France, Britain and Germany in their colonies. In Europe, large metre-gauge networks remain in use in Switzerland, Spain and many European towns with urban trams , but most metre-gauge local railways in France , Germany and Belgium closed down in the mid-20th century, although some still remain. With

300-625: The NMR supplies networked computerized ticketing systems for onward journeys, it still issues Edmondson style manual tickets for the Udhagamandalam-Mettupalayam journey to preserve its 'World Heritage Site' status. Ticket booking is similar to conventional trains and can be done via the Indian Railway website. It is advisable to book tickets well in advance, especially during peak season. Metre gauge Metre gauge

330-424: The perpendicular cross slope . There are several ways to express slope: Any of these may be used. Grade is usually expressed as a percentage, but this is easily converted to the angle α by taking the inverse tangent of the standard mathematical slope, which is rise / run or the grade / 100. If one looks at red numbers on the chart specifying grade, one can see the quirkiness of using the grade to specify slope;

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360-466: The Great Western main line, nicknamed Brunel's Billiard Table, because the early locomotives (and their brakes) were feeble. Steep gradients were concentrated in short sections of lines where it was convenient to employ assistant engines or cable haulage , such as the 1.2 kilometres (0.75 miles) section from Euston to Camden Town . Extremely steep gradients require the use of cables (such as

390-639: The Guinness Book. Drawing on the U.S. National Elevation Dataset, 7x7 (magazine) identified ten blocks of public streets in San Francisco open to vehicular traffic in the city with grades over 30 percent. The steepest at 41 percent is the block of Bradford Street above Tompkins Avenue in the Bernal Heights neighborhood. The San Francisco Municipal Railway operates bus service among the city's hills . The steepest grade for bus operations

420-781: The Indian Railways are responsible for operating, maintaining and repairing the NMR. Between Mettupalayam and Coonoor , the line uses the Abt rack and pinion system to climb the steep gradient . The NMR is the only rack railway in India. NMR uses 'X' Class steam rack locomotives , most manufactured by the Swiss Locomotive and Machine Works of Winterthur in Switzerland , on the rack and pinion section of its tracks. The X Class locomotives are up to eight decades old, but

450-706: The Nilgiri Hills. However, it took the decision-makers 45 years to cut through the bureaucratic red tape and complete the construction. The line was completed and opened for traffic in June 1899. It was operated first by the Madras Railway under an agreement with the government. The Madras Railway Company continued to manage the railway line on behalf of the government for a long time until the South Indian Railway company purchased it. In 1907,

480-624: The Scenic Railway at Katoomba Scenic World , Australia, with a maximum grade of 122% (52°), claimed to be the world's steepest passenger-carrying funicular ) or some kind of rack railway (such as the Pilatus railway in Switzerland, with a maximum grade of 48% (26°), claimed to be the world's steepest rack railway ) to help the train ascend or descend. Gradients can be expressed as an angle, as feet per mile, feet per chain, 1 in n , x % or y per mille. Since designers like round figures,

510-463: The horizontal run by using the Pythagorean theorem, after which it is trivial to calculate the (standard math) slope or the grade (percentage). In Europe, road gradients are signed as a percentage. Grades are related using the following equations with symbols from the figure at top. The slope expressed as a percentage can similarly be determined from the tangent of the angle: If the tangent

540-546: The load that a locomotive can haul, including the weight of the locomotive itself. On a 1% gradient (1 in 100) a locomotive can pull half (or less) of the load that it can pull on level track. (A heavily loaded train rolling at 20 km/h on heavy rail may require ten times the pull on a 1% upgrade that it does on the level at that speed.) Early railways in the United Kingdom were laid out with very gentle gradients, such as 0.07575% (1 in 1320) and 0.1515% (1 in 660) on

570-753: The method of expression can affect the gradients selected. The steepest railway lines that do not use a rack system include: Gradients on sharp curves are effectively a bit steeper than the same gradient on straight track, so to compensate for this and make the ruling grade uniform throughout, the gradient on those sharp curves should be reduced slightly. In the era before they were provided with continuous brakes , whether air brakes or vacuum brakes , steep gradients made it extremely difficult for trains to stop safely. In those days, for example, an inspector insisted that Rudgwick railway station in West Sussex be regraded. He would not allow it to open until

600-540: The newest was completed August 2021 at the Golden Rock Railway Workshops in India. These locomotives give NMR a distinct charm, taking scores of passengers to Coonoor and Udhagamandalam, crossing 45.8 kilometres (28 mi), 108 curves, 16 tunnels and 250 bridges. The steam locomotives can be used on any part of the line, while the diesel locomotives can operate only on the section between Coonoor and Udagamandalam . Each diesel engine weighs

630-400: The numbers go from 0 for flat, to 100% at 45 degrees, to infinity as it approaches vertical. Slope may still be expressed when the horizontal run is not known: the rise can be divided by the hypotenuse (the slope length). This is not the usual way to specify slope; this nonstandard expression follows the sine function rather than the tangent function, so it calls a 45 degree slope

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660-547: The railway received four Double Fairlie locomotives to work the line. These were part of a batch built by the Avonside Engine Company in 1879 and 1880 for service in Afghanistan, but had been in store since 1887. The Fairlies continued in use until at least 1914. In September 1908, the line was extended to Fernhill. By 15 October 1908, it was extended to Udagmandalam . These extensions from Coonoor on

690-638: The revival of urban rail transport, metre-gauge light metros were built in some cities. The slightly-wider 1,009 mm ( 3 ft  3 + 23 ⁄ 32  in ) gauge is used in Sofia . Another similar gauge is 3 ft 6 in ( 1,067 mm ). Ferrocarril General Manuel Belgrano 23,489 km (14,595 mi) Mailani - Nanpara Railway (operating) 641 km (398 mi) Dakar–Niger Railway Grade (slope) The grade (US) or gradient (UK) (also called stepth , slope , incline , mainfall , pitch or rise ) of

720-529: The same gauge over a distance of 11 + 3 ⁄ 4 miles (18.91 km) were done at a cost of ₹ 2,440,000. The NMR and all of its assets, including the stations, the line, and the track vehicles, belong to the Government of India and are managed by the Ministry of Railways . The Southern Railway performs the day-to-day maintenance and management, but several programs, divisions and departments of

750-623: The section between Mettupalyam and Udhagamandalam . Local people and visitors led a campaign to return to steam locomotives in this section. In July 2005, UNESCO added the Nilgiri Mountain Railway as an extension to the World Heritage Site of Darjeeling Himalayan Railway . The site then became known as Mountain Railways of India . In 1854, plans were made to build a mountain railway from Mettupalayam to

780-736: The sine of the angle rather than the tangent) makes only an insignificant difference and can then be used as an approximation. Railway gradients are often 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 either case, the following identity holds for all inclinations up to 90 degrees: tan ⁡ α = sin ⁡ α 1 − sin 2 ⁡ α {\displaystyle \tan {\alpha }={\frac {\sin {\alpha }}{\sqrt {1-\sin ^{2}{\alpha }}}}} . Or more simply, one can calculate

810-413: The slope) and rise is the vertical distance. Slopes of existing physical features such as canyons and hillsides, stream and river banks , and beds are often described as grades, but typically the word "grade" is used for human-made surfaces such as roads, landscape grading, roof pitches , railroads , aqueducts , and pedestrian or bicycle routes. The grade may refer to the longitudinal slope or

840-755: The steam locomotives at the Golden Rock Railway Workshops. Many carriage repairs take place at Mettupalayam. Like the locomotives, major work on the carriages takes place at one of the larger railway workshops. The uphill journey takes around 290 minutes (4.8 hours), and the downhill journey takes 215 minutes (3.6 hours). It has the steepest track in Asia with a maximum gradient of 8.33%. During Meter Gauge era in 1990s, The Nilgiri Express used to run between Chennai(then Madras) & Udhagamandalam(then Ooty) directly. Timings were:- Madras 21.00; Ooty 10.20 & in return:- Ooty 16.30; Madras 05.50.But it

870-715: The world according to the Guinness Book of World Records are Baldwin Street in Dunedin, New Zealand, Ffordd Pen Llech in Harlech, Wales and Canton Avenue in Pittsburgh, Pennsylvania. The Guinness World Record once again lists Baldwin Street as the steepest street in the world, with a 34.8% grade (1 in 2.87) after a successful appeal against the ruling that handed the title, briefly, to Ffordd Pen Llech . A number of streets elsewhere have steeper grades than those listed in

900-711: Was stopped after NMR got UNESCO World Heritage Tag in 1994. As of 2007, a daily train crosses the rack section, which starts from Mettupalayam at 07:10 and reaches Udhagamandalam at noon. The return train starts from Udhagamandalam at 14:00, and reaches at 17:35. The train is scheduled to connect to the Nilgiri Express , which travels from Mettupalayam to Chennai via Coimbatore . A summer special service runs in April and May, starting from Mettupalayam at 09:30 am and from Udhagamandalam at 12:15 pm. Between Coonoor and Udagamandalam, four daily trains run each way. Even though

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