Great circles, rhumb lines and convergency

Navigation · Chapter 3 · DGCA CPL and ATPL

Why the shortest route keeps changing direction, how much it changes, and how to turn one kind of bearing into the other.

Remember

Great circle: shortest, track changes. Rhumb line: constant track, straight on Mercator, spirals to the pole.
Convergency = ch long × sin(mean latitude) = GC at arrival − GC at departure.
I-D-D-I: NH east I, NH west D, SH east D, SH west I.
Conversion angle = convergency ÷ 2, the same at both ends.
Bearing back: draw the arrows; big angle at B = 180 + RL angle + CA.

What is the difference between a great circle and a rhumb line?

Great circle and rhumb line

The great circle: shortest, but turning • Pink: the great circle, the shortest way • Watch the aircraft's dial: its track keeps changing
The rhumb line: one steady track • Blue dashed: the rhumb line • Its dial never moves: here 090° all the way • Easy to fly, but longer
A rhumb line never stops • Keep 045° for ever: you cross every meridian at 45° • The line winds towards the pole: a spiral

What do the two lines look like on a chart?

On the chart

A Mercator chart • Pilots plot on a mercator chart • Every rhumb line is straight
The great circle curves • It is convex to the nearer pole • Trick: it makes a cave over the equator
In the southern hemisphere • Same rule: the curve bows towards the South Pole

Why do the meridians lean towards each other, and by how much?

Convergency

This lesson is part of the Navigation plan. See plans

How else can you find the convergency?

Two formulas for convergency

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Does the great-circle track get bigger or smaller?

Up or down: I-D-D-I

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Solve it: the great-circle track at the far end

Solve it: track at the end

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What is the angle between the great circle and the rhumb line?

Conversion angle

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Worked questions 9 and 10: both places on one parallel

Both on one parallel

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How do you draw a radio bearing on a chart?

Radio bearings on a chart

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Worked questions 1, 2 and 4: the bearing from B back to A

The bearing back

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Worked question 3: the difference between the GC tracks at A and B

Difference between the tracks

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Worked question 5: the great circle runs 270° at one point

Track 270° on a great circle

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Worked questions 6 and 7: which pair of latitudes gives the most convergency?

Greatest convergency

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Worked question 8: longitude of B on a Lambert chart

A Lambert chart question

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Test yourself on chapter 3

Test yourself

This lesson is part of the Navigation plan. See plans