Definition:Nautical Mile
Definition
The nautical mile is a unit of length which is used for air and sea navigation.
It was originally defined as the length measured along Earth's surface of one minute of latitude along a meridian.
It is now defined as exactly $1852$ metres.
\(\displaystyle \) | \(\) | \(\displaystyle 1\) | nautical mile | ||||||||||
\(\displaystyle \) | \(=\) | \(\displaystyle 1852\) | metres (by definition) | ||||||||||
\(\displaystyle \) | \(=\) | \(\displaystyle 10\) | cables | ||||||||||
\(\displaystyle \) | \(\approx\) | \(\displaystyle 6076\) | feet | ||||||||||
\(\displaystyle \) | \(\approx\) | \(\displaystyle 1 \cdotp 151\) | (international) mile | ||||||||||
\(\displaystyle \) | \(\approx\) | \(\displaystyle 0 \cdotp 999 \, 363\) | admiralty (UK nautical) mile |
Also defined as
Before $1929$, the nautical mile was defined as either:
- $6080$ feet (what is now known as the British admiralty mile)
- $6080 \cdotp 2$ feet (the American nautical mile)
Older textbooks may still refer to either of these now obsolete units as the nautical mile.
Also known as
Some sources refer to this unit as the international nautical mile.
Also see
Historical Note
The concept of defining base units of measurement based on the dimensions of Earth appears to have been introduced by Edmund Gunter.
In the early $1600$s he proposed the nautical mile as one minute of arc, or $\dfrac 1 {60}$ of a degree of latitude on Earth's surface.
However, as Earth is not perfectly spherical, but an oblate spheroid, one minute of latitude is not constant.
At the equator it is about $1843$ metres, but at the poles it is about $1861$ metres.
The French standard evolved such that a nautical mile is one minute of arc of a meridian at a latitude of $45 \degrees$, which was a measure of convenience, as it happened to match a more mundane measurement made a century earlier.
By the middle of the $19$th century, France had defined the nautical mile in terms of the metre that had been defined in $1791$.
This worked out at $1851 \cdotp 85 \mathrm m$, which was rounded to $1852 \mathrm m$.
This then became the French legal standard in $1906$, and was then sanctioned by many other countries using the metric system in $1929$, at the first International Hydrographic Conference in Monaco.
The USA and UK both used their own measurement, based on the average minute of arc of latitude defined on a sphere with the authalic radius of Earth.
This minute of arc of latitude measures $1853 \cdotp 2480$ metres or $6080 \cdotp 210$ feet.
The USA took the first $5$ significant figures, giving their nautical mile a measurement of $6080 \cdotp 2$ feet.
The UK took the first $4$ significant figures, giving their nautical mile a measurement of $6080$ feet, which is now referred to as the admiralty mile.
The USA finally adopted the international nautical mile of $1682 \, \mathrm m$, while the UK did not adopt it until $1970$.
Legacy measurements in admiralty miles are for convenience considered as being $1683 \, \mathrm m$.
Sources
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): Entry: nautical mile
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Entry: nautical mile
- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): Entry: nautical mile