Rankine's method

Key takeaways

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

Reference excerpt

Rankine's method or tangential angle method is an angular technique for laying out circular curves by a combination of chaining and angles at circumference, fully exploiting the theodolite and making a substantial improvement in accuracy and productivity over existing methods. This method requires access to only one road/path of communication to lay out a curve. Points on curve are calculated by their angular offset from the path of communication. Rankine's method is named for its discoverer William John Macquorn Rankine at an early stage of his career. He had been working on railways in Ireland, on the construction of the Dublin and Drogheda line.

Background This method makes sure that any line drawn from the known tangent to curve is a chord of the curve by constraining the deflection angle of line. Since end points of chords lie on the curve this can be used to approximate the shape of actual curve.

Procedure Let AB be a tangent line/path of communication or start of a curve, then successive points on the curve can be obtained by drawing an arbitrary line of length C i {\displaystyle C_{i}} from point A with an angle Δ i = ∑ j = 0 i δ j {\displaystyle \Delta _{i}=\sum _{j=0}^{i}\delta _{j}}

δ i = C i × 180 2 π R {\displaystyle \delta _{i}={\frac {C_{i}\times 180}{2\pi R}}}

where δ i {\displaystyle \delta _{i}} is deflection from nth chord in degrees. R is the radius of circular curve

C i {\displaystyle C_{i}} is arbitrary length of chord

Worked examples

Example 1 — a first encounter with Rankine's method

Start with the simplest possible case. Write down what Rankine's method claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In engineering, 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 Rankine's method 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 Rankine's method 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 Rankine's method

In research: Rankine's method appears in engineering 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 Rankine's method 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: Rankine's method is common in secondary-school and first-year university syllabi. It links to neighbouring topics Civil engineering stubs, Scottish inventions, Surveying, so understanding it makes those chapters shorter.
In everyday life: Look for Rankine's method 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.

How to study Rankine's method in 20 minutes

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

Frequently asked questions

What is Rankine's method in simple terms?

Rankine's method or tangential angle method is an angular technique for laying out circular curves by a combination of chaining and angles at circumference, fully exploiting the theodolite and making a substantial improvement in accuracy and productivity over existing methods. This method requires…

Why does Rankine's method matter?

Because it connects several engineering 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 Rankine's method?

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 Rankine's method.