Mercator
Navigation · Chapter 11 · DGCA CPL and ATPL
Why the Mercator chart stretches towards the poles, what that does to its scale, and how great circles and rhumb lines look on it.
Remember
- Parallels spread by sec(lat) so shapes stay right: conformal, not equal area.
- Chart convergence 0: correct only at the equator. Poles not shown.
- D(lat) = D(equator) × cos(lat); the number is biggest at the equator.
- Latitude to latitude: D × cos(new) ÷ cos(old), after a sense check.
- Rhumb lines straight; great circles concave to the equator.
Why are the parallels further apart near the poles on a Mercator chart?
Why the parallels spread out
- On the globe, meridians meet • Meridians meet at the poles: 1 min of longitude is only cos(lat) NM (departure) • A cylinder round the equator makes them parallel • So east–west is stretched by sec(lat): × 2 at 60°
- The simple cylinder • The light puts each parallel at tan(lat) up the tube • Opened out, the round lake is stretched north–south • Shapes are wrong, so angles are wrong
- Mercator's repair (1569) • Move the parallels so their gaps grow by sec(lat), the same as east–west • The lake is round again: orthomorphic
- Straight lines keep one direction • Meridians are parallel, so a straight line cuts them all at the same angle • Every straight line is a rhumb line: why sailors loved it
What is true, and what is false, on a Mercator chart?
Mercator's properties
- Graticule • Meridians: straight, parallel, equally spaced • Parallels: straight, spreading towards the poles
- Conformal, but not equal area • Angles and small shapes are right • Areas are not: Greenland looks as big as Africa (Africa is about 14 times bigger)
- Convergence • chart convergence = 0 everywhere (meridians parallel) • Earth convergency = ch long × sin(lat) • So it is correct only at the equator
- Good for, bad for • Good: rhumb-line plotting, and charts near the equator • Useless near the poles • Radio bearings are great circles: convert them to rhumb lines before plotting
How does the scale of a Mercator chart change with latitude?
The scale changes with latitude
This lesson is part of the Navigation plan. See plans
Given the scale at one latitude, what is it at another?
Scale from one latitude to another
This lesson is part of the Navigation plan. See plans
Solve it: Mercator scale at another latitude
Solve it: Mercator scale
This lesson is part of the Navigation plan. See plans
How do great circles and rhumb lines look on a Mercator chart?
Great circles and rhumb lines
This lesson is part of the Navigation plan. See plans
Test yourself on chapter 11
Test yourself
This lesson is part of the Navigation plan. See plans