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Definitions

Nautical Mile

A nautical mile (NM) is defined as 1,852 metres.

The earth is an oblate spheroid (it is flattened at the poles) and 1 minute of latitude varies from 1,843m at the equator to 1,861 at the poles. The average distance is 1,852 – the nautical mile.

But for most surface navigation, the Earth can be assumed to be a sphere with radius ≈ 6,371 km.

How do you calculate the NM from this

For simplicity, marine navigation and charting are based on the spherical Earth assumption.

The Mercator Chart

A Mercator chart is a standard navigational chart used in marine navigation. It is based on the Mercator projection, which is a cylindrical projection of the globe onto a flat surface.

On a Mercator chart:

  • Meridians (lines of longitude) are vertical and equally spaced.
  • Parallels (lines of latitude) are horizontal but not equally spaced — they get farther apart as you move toward the poles.
  • This spacing distortion compensates for the curvature of the Earth to preserve angles and compass bearings, which is why rhumb lines (constant compass courses) appear as straight lines.
  • The result is a conformal map: angles and shapes are preserved locally, but area and scale are distorted, especially near the poles.

Meridional Parts

A Meridional Part is the length of a meridian (a line of constant longitude) from the equator to a given latitude, measured on a Mercator chart. It’s expressed in minutes of arc, like nautical miles, and it accounts for how the Mercator projection stretches the vertical (north–south) scale with increasing latitude.

Plain Sailing

Plane Sailing is a method of navigation that assumes the Earth is flat over short distances. It uses plane trigonometry to calculate the course and distance between two points based on the differences in latitude and departure (the east-west distance).

  • Used for: Short voyages (typically < 600 nautical miles)

  • Assumes: Earth is a flat plane

  • Calculations involve:

    • Difference in latitude (ΔLat)

    • Departure (East–West distance)

    • Course angle

    • Distance traveled

  • Formula:

    tan⁡(Course)=DepartureΔLatitudeand

  • Distance=Departuresin⁡(Course)tan(text{Course}) = frac{text{Departure}}{Deltatext{Latitude}} quad text{and} quad text{Distance} = frac{text{Departure}}{sin(text{Course})}

Mercator Sailing

Mercator Sailing is a method used for long-distance navigation that takes into account the Earth’s curvature. It uses a Mercator projection, in which meridians and parallels are straight lines, allowing navigators to plot a straight-line course (rhumb line).

  • Used for: Long-distance voyages

  • Assumes: Earth is a sphere, mapped onto a Mercator chart

  • Calculations involve:

    • Difference in longitude (ΔLong)

    • Meridional parts (logarithmic values accounting for convergence of meridians)

    • Rhumb line course and distance

  • Formula:

Rhumb Line

A rhumb line is an imaginary line on the earth’s surface cutting all meridians at the same angle, used as the standard method of plotting a ship’s course on a chart.