# Rhumb line in the Mercator projection

June 30, 2017 SorinMStamate

### Rhumb line in the Mercator projection

The Mercator projection is a plane conformal projection and is not perspective.

This projection is the most often use in navigation.

Both the meridians and parallels are expanded at the same ratio with increased latitude.

The expansion is equal to the secant of the latitude.

Since the secant of 90° is infinity, the projection canot include the poles.

Since the projection is conformal, expansion is the same in all directions and angles are correctly shown.

Rhumb lines appears as straight lines and the directions of which can be measured directly on the nautical map, using a protractor.

The distances can also be measured directly.

Great circles appear as curved lines concave to the Equator.

Small areas appear in their correct shape but of increased size.

As shown earlier in the article ‘Rhumb Line’:

The Rhumb Line: Is a conventional line on the Earth’s surface that intersects all geographic meridians at the same angle. It has the shape of a spiral that approaches the poles without going through them.

If the angle of intersection is 90° or 270°, the rhumb line is parallel to the equator.

And, if the angle of intersection is 0° or 180°, the rhumb line coincides with the meridian.

The rhumb line intersects all the meridians at the same angle, equal to the ship’s course, approaching from the Equator to the pole, without ever touching it.

The rhumb line is not the shortest distance between of two points on the globe.

The shortest distance between two points on the Earth is the large circle arc passing through those points, called the Great Circle.

However, on short and medium distances, navigation is done only on the rhumb line, due to the great advantage of keeping the same course and in solving the ordinary navigation problems.

Rhumb line in the Mercator projection _ v1.0