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mathematics

Land navigation

Land navigation 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 Land navigation rather than just read about it. In short: Land navigation is the discipline of following a route through unfamiliar terrain on foot or by vehicle, using maps with reference to terrain, a compass, and other navigational tools. It is distinguished from travel by traditional groups, such as the Tuareg across the Sahara and the Inuit across the Arctic, who use subtle cues to travel across familiar, yet minimally differentiated terrain.

Land navigation — main illustration
Land navigation — illustration

Key takeaways

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

Reference excerpt

Land navigation is the discipline of following a route through unfamiliar terrain on foot or by vehicle, using maps with reference to terrain, a compass, and other navigational tools. It is distinguished from travel by traditional groups, such as the Tuareg across the Sahara and the Inuit across the Arctic, who use subtle cues to travel across familiar, yet minimally differentiated terrain. Land navigation is a core military discipline, which uses courses or routes that are an essential part of military training. Often, these courses are several miles long in rough terrain and are performed under adverse conditions, such as at night or in the rain. In the late 19th century, land navigation developed into the sport of orienteering. The earliest use of the term 'orienteering' appears to be in 1886. Nordic military garrisons began orienteering competitions in 1895.

Mathematical basis Land navigation commonly represents position on a map using a local rectangular coordinate system, such as a grid printed on a topographic map. A movement from a known point can be described by a distance and an azimuth; this is equivalent to using polar coordinates. If an azimuth θ {\displaystyle \theta } is measured clockwise from north and the distance traveled is d {\displaystyle d} , the corresponding east and north components of displacement are

Δ E = d sin ⁡ θ , Δ N = d cos ⁡ θ {\displaystyle \Delta E=d\sin \theta ,\qquad \Delta N=d\cos \theta }

In field use, these are calculated graphically by plotting an azimuth line on the map with a protractor and measuring distance using the map scale. Distance traveled on foot may be estimated by pace count, while position may also be estimated or checked by plotting lines of position.

United States In the United States military, land navigation courses are required for the Marine Corps and the Army. Air Force escape and evasion training includes aspects of land navigation. Army Training Circular 3-25.26 is devoted to land navigation.

See also History of orienteering Navigation Piloting Wayfinding

References

Illustrations

Land navigation: One of 24 competitors at the night urban warfare orienteering course during the 2009 Department of the Army Best Warrior Competition at Fort Lee, Virginia
One of 24 competitors at the night urban warfare orienteering course during the 2009 Department of the Army Best Warrior Competition at Fort Lee, Virginia

Worked examples

Example 1 — a first encounter with Land navigation

Start with the simplest possible case. Write down what Land navigation 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 Land navigation 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 Land navigation 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 Land navigation

In research
Land navigation 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 Land navigation 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
Land navigation is common in secondary-school and first-year university syllabi. It links to neighbouring topics Military education and training, Military terminology, Navigation, so understanding it makes those chapters shorter.
In everyday life
Look for Land navigation 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 Land navigation in 20 minutes

  1. Read the reference excerpt below once, without taking notes.
  2. Close the page and write down what Land navigation 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 Land navigation out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Land navigation in simple terms?

Land navigation is the discipline of following a route through unfamiliar terrain on foot or by vehicle, using maps with reference to terrain, a compass, and other navigational tools. It is distinguished from travel by traditional groups, such as the Tuareg across the Sahara and the Inuit across th…

Why does Land navigation 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 Land navigation?

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 Land navigation.

Tags

  • Military education and training
  • Military terminology
  • Navigation
  • Navigational equipment
  • Orientation (geometry)
  • Orienteering competitions
  • United States Army doctrine

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