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Rail directions

Rail directions is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Rail directions rather than just read about it. In short: Rail directions are used to describe train directions on rail systems. The terms used may be derived from such sources as compass directions, altitude directions, or other directions.

Key takeaways

  • Rail directions belongs to mathematics; place it in that map before memorising details.
  • Learn the definition first, then one example that makes the definition concrete.
  • Connect Rail directions to a quantity you can measure, compute or draw — that is where exam questions come from.
  • Reproduce the core statement of Rail directions from memory before moving on to harder problems.

Reference excerpt

Rail directions are used to describe train directions on rail systems. The terms used may be derived from such sources as compass directions, altitude directions, or other directions. These directions are often specific to system, country, or region.

Radial directions Many rail systems use the concept of a centre or origin (usually a major city) to define rail directions. Often this location will also define the zero kilometre- or milepost of a line or network.

Up and down

United Kingdom In British practice, railway directions are usually described as "up" and "down", with "up" being towards a major location. This convention is applied not only to the trains and the tracks, but also to items of lineside equipment and to areas near a track. Since British trains run on the left, the "up" side of a line is usually on the left when proceeding in the "up" direction. On most of the network, "up" is the direction towards London as the busiest transport hub. In most of Scotland, with the exception of the West and East Coast Main Lines, and the Borders Railway, "up" is towards Edinburgh. The Valley Lines network around Cardiff has its own peculiar usage, relating to the literal meaning of travelling "up" and "down" the valley. On the former Midland Railway "up" was towards Derby. On the Northern Ireland Railways network, "up" generally means toward Belfast (the specific zero milepost varying from line to line); except for cross-border services to Dublin, where Belfast is "down". Mileposts normally increase in the "down" direction, but there are exceptions, such as the Trowbridge line between Bathampton Junction and Hawkeridge Junction, where mileage increases in the "up" direction. Individual tracks will have their own names, such as Up Main or Down Loop. Trains running towards London are normally referred to as "up" trains, and those away from London as "down". Hence the down Night Riviera runs to Penzance and the up Flying Scotsman to London King's Cross. This distinction is less meaningful for trains not travelling towards or away from London; for instance a CrossCountry train from Manchester to Bournemouth uses "up" lines as far as Reading and "down" lines thereafter.

Australia The railway systems of the Australian states have generally followed the practices of railways in the United Kingdom. Railway directions are usually described as "up" and "down", with "up" being towards the major location in most states, which is usually the capital city of the state. In New South Wales, trains running away from Sydney are "down" trains, while in Victoria, trains running away from Melbourne are "down" trains. An interstate train travelling from Sydney to Melbourne is a "down" train until it crosses the state border at Albury, where it changes its classification to an "up" train. Even in states that follow this practice, exceptions exist for individual lines. In the state of Queensland, "up" and "down" directions are individually defined for each line. Therefore, a train heading towards the main railway station in Brisbane (Roma Street station) would be classified as an "up" train on some lines but as a "down" train on other lines. In South Australia, there are two (2) up/down origins: Port Augusta and Adelaide.

China In China, railway directions with terminus in Beijing are described as "up" (Chinese: 上行, romanised: shàngxíng) and "down" (Chinese: 下行, romanised: xiàxíng), with "up" towards Beijing; while trains leaving Beijing are "down". Trains run through Beijing may have two or more numbers, for example, the train from Harbin to Shanghai K58/55 uses two different numbers: on the Harbin–Tianjin section, the train runs toward Beijing, the train is known as K58, but on the Tianjin–Shanghai section, the train is known as K55; the opposite train from Shanghai to Harbin is known as K56/57, while K56 is used from Shanghai to Tianjin and K57 is used from Tianjin to Harbin. Generally even numbers denote trains travelling in the up direction while odd numbers denote the down direction.

Hong Kong In Hong Kong, most lines have their "down" direction towards the terminal closer to Central, with the exception of Disneyland Resort line, where the down line is towards Disneyland to be consistent with Tung Chung line where it branches from. On Tuen Ma line, the "down" end is Wu Kai Sha. The up/down direction was switched in the former Ma On Shan line such that it could be connected with the former West Rail line. The direction is signposted along the track, with the mileage increasing in the up direction, and also on the platform ends.

Japan In Japan, railway directions are traditionally designated as "up" (上り, Nobori) and "down" (下り, Kudari). For JR Group services, trains heading towards Tokyo Station are considered "up" trains, while those heading away are "down" trains. Notable exceptions include the Yamanote Line and the Osaka Loop Line, which are circular routes. Another exception is the Keihin-Tōhoku Line and other through-running services that pass through Tokyo Station. Because this route is officially part of the Tōhoku Main Line north of Tokyo Station and the Tōkaidō Main Line south of it, trains are instead referred to as northbound or southbound. For private railway operators, the designation of "up" or "down" (if used at all) typically depends on the location of the company’s headquarters, with trains heading toward that location treated as "up" services.

Sweden In Sweden, "up" trains are generally trains heading north, while "down" trains are trains heading south. Trains in Sweden generally run on the left, (unlike roads which switched to running on the right in 1967), and so the up line (uppspår) refers to the left-hand track as viewed from an "up" train, while the down line (nedspår) is the left-hand track for "down" trains. Even numbers are always used for "up" trains while odd numbers are always used for "down" trains; however, bidirectional signalling is common, and thus trains do not necessarily use the track corresponding to their designation.

Taiwan In Taiwan, trains travelling north towards Keelung on the Western Trunk Line and towards Badu on the Yilan Line are considered "up" trains. However, on other parts of the network, the terminology "clockwise" and "counter-clockwise" is used instead.

… excerpt ends here. Continue reading the full article.

Worked examples

Example 1 — a first encounter with Rail directions

Start with the simplest possible case. Write down what Rail directions claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Rail directions before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Rail directions ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Rail directions

In research
Rail directions appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry
Engineering practice reuses Rail directions in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom
Rail directions is common in secondary-school and first-year university syllabi. It links to neighbouring topics Orientation (geometry), Rail transport operations, so understanding it makes those chapters shorter.
In everyday life
Look for Rail directions outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.
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How to study Rail directions in 20 minutes

  1. Read the reference excerpt below once, without taking notes.
  2. Close the page and write down what Rail directions means in your own words.
  3. Compare your version with the excerpt and mark what you missed.
  4. Work through the three examples above with pen and paper.
  5. Explain Rail directions out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Rail directions in simple terms?

Rail directions are used to describe train directions on rail systems. The terms used may be derived from such sources as compass directions, altitude directions, or other directions.

Why does Rail directions matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Rail directions?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Rail directions.

Tags

  • Orientation (geometry)
  • Rail transport operations

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