> A minute of arc on the planet Earth is 1 nautical mile.
Only if that minute of arc lies on a great circle route.
As an interesting addendum, when measuring distance made good on a nautical chart, you will use a divider to measure the straight line distance, then lay this onto the latitude scale to convert it to nautical miles.
If you were to use the longitude scale, you would be off by approximately the cosine of your latitude, because the lines of latitude() (apart from the equator) are not great circles.
() corrected longitude to latitude here - longitude is obviously great circles, latitude apart from the equator are not.
> > A minute of arc on the planet Earth is 1 nautical mile.
> Only if that minute of arc lies on a great circle route.
You missed out some context for that quote that already makes it clear that it's talking about a great circle:
> A nautical mile is based on the circumference of the planet Earth. If you were to cut the Earth in half at the equator, you could pick up one of the halves and look at the equator as a circle. ... A minute of arc on the planet Earth is 1 nautical mile.
I can believe that it's true that lines of longitude are not great circles, but I can't picture why in my head. Isn't a great circle formed by extending the shortest distance between two points on the surface of a sphere?
An arc along a line of longitude is a deviation in the latitude scale. Lines of longitude lie on great circles since they converge on the poles, but when you move a degree of longitude you are moving west or east along a line of latitude, and the only line of latitude which is a great circle is the equator.
The reason you use the latitude scale is that lines of latitude are equidistant between one another - it is the same distance between two lines of latitude no matter your longitude, but it is not equidistant between two lines of longitude at different latitudes. So even if your chart spans several hundreds of miles, the latitude scale remains constant across that distance regardless of the distortions of the projection used to render the globe onto the two dimensional chart surface.
> So even if your chart spans several hundreds of miles, the latitude scale remains constant across that distance regardless of the distortions of the projection.
I don't believe that is correct. The latitude scale of a Mercator projection chart will not be constant because the projection introduces some distortion. So 1NM at the top of the chart will not be the same distance as 1NM at the bottom of the chart. For this reason, you should always place your dividers roughly in the area you are going to be sailing in.
As I recall from my Yachtmaster course, the difference is not usually that great for day to day stuff, but for planning long passages on small scale charts it could be a significant error.
It's a really satisfying thing to work with paper charts, rolling rulers and dividers. These days for proper navigational planning it is all ECDIS (or WECDIS for really fun stuff) and electronic.
> These days for proper navigational planning it is all ECDIS (or WECDIS for really fun stuff) and electronic.
Its not strictly true that 'proper' navigational planning happens entirely on ECDIS, especially on smaller vessels. My preference while working on offshore tugs was to work out the rough voyage on paper first, before transferring them to ECDIS; the 2nd mates I worked with in training had a similar preference.
That said, paperless navigation is becoming more and more common (and saves a ton of time on chart corrections), and in that case you don't have a choice.
Nope. It's is derived from latitude, which is an angle measured at the centre of the Earth, and not the surface.
So you have the equator, and then 90 degrees north and south. Take one of those degrees, divide it by sixty (arc-minute), project it on the surface, and you have a nautical mile. That's regardless of where you are on the surface.
That's the original/historical definition; now it's 1852m.
No, but it's not oblate enough for the difference to cause any noticeable problems in navigation. The difference between an arc length of a minute at the equator vs a minute on the latitude scale is about 0.2% - less than the margin of error when reading a sextant.
Its interesting that the nautical mile is based on a more abstract number that would define when looking at maps and charts, rather then something more immediate and physical like the distance to the horizon when out on the ocean. Most imperial units seem to be based on simple laymen measurements.
Distance to the horizon is variable. Sea state, height of deck over water, visibility etc will all affect it. Whereas, with a sextant and a decent maritime chronometer it is very easy (*) to determine longitude and latitude.
Indeed, IIRC the intention was to define the meter so that the distance between the North Pole and the equator at the meridian through Paris would be exactly 10000 km, making the full circumference along that meridian and the one opposite it 40000 km.
EDIT: that information is already in the article, making my comment redundant and unnecessary.
From pole to equator it's 90 (deg) * 60 (minutes/deg) = 5400 nautical miles or 10000 kilometres.
Pretty much the only way I can remember the conversion factor. Well, that's not true, 1.852 also consists of the country code of the USA followed by the country code of Hong Kong, so that's easy.
Well, the article claims that that is the definition which is false. The definition of a meter is ‘the distance traveled by light in 1/299792458 of a second’ so a kilometer is a thousand times that.
The story in the article is the original, obsolete definition.
At what elevation are they measuring these arcs / circumference of the earth? At sea level? Feel like that needs to be explicit if we are trying to be technical. Because you can't "travel around the Earth at the equator" in "21,600 nautical miles, 24,857 miles or 40,003 kilometers" without going underneath a mountain or two.
They aren't. It was based on an early spherical model, but in the modern world a nautical mile is defined as exactly 1852 meters, period. The notion of the arc minute is historical context in the same way that a "mile" was originally a thousand (mille) paces.
I would never get used to how to remember the diameter of the earth. Now all I need to remember is how many km's are there in a nautical mile, get the length of the equator and divide it by pi. i.e. (360 x 60 x 1.85/3.14)
No, the nautical mile is hated by proponents of the metric system. As with all customary units, it favors a specific use-case at the cost of errors and conversions, has limited accuracy and doesn't handle orders of magnitude.
> As with all customary units, it favors a specific use-case at the cost of errors and conversions, has limited accuracy and doesn't handle orders of magnitude.
The nautical mile was not 'customary', but based on mathematical properties. Specifically, it was defined as one arc-minute (1/60 of degree) of latitude. Degrees of latitude are measure from the centre of the Earth and not the surface.
This is no more arbitrary than how the metre was defined:
> The metre was originally defined as 1⁄10,000,000 of the meridian arc from the North pole to the equator passing through Dunkirk.
What conversions do you typically do to/from NM? As far as I'm aware, it is only used for navigation, where all related info, such as speed, position etc. relate directly to it.
Only if that minute of arc lies on a great circle route.
As an interesting addendum, when measuring distance made good on a nautical chart, you will use a divider to measure the straight line distance, then lay this onto the latitude scale to convert it to nautical miles.
If you were to use the longitude scale, you would be off by approximately the cosine of your latitude, because the lines of latitude() (apart from the equator) are not great circles.
() corrected longitude to latitude here - longitude is obviously great circles, latitude apart from the equator are not.