What Is a 'Nautical Mile'? (2011) | Hacker News Reader

What Is a 'Nautical Mile'? (2011)

science.howstuffworks.com

79 pointsdevaroop49 comments

> 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.

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?

Lines of longitude are great circles. Grandparent must mean latitude: the equator is a line of latitude, and the only one that is a great circle.

Thanks, I've corrected my previous comment.

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.

Also at the equator - the earth is not a perfect sphere.

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.

What I mean is, at least in the US it is defined as an arc minute at the equator, not just any great circle.

True; I think that's the global definition anyway.

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.

I loved learning navigation. You peel away a layer and a new, more complicated set of skills presents itself.

It's good fun. Plotting tidal vectors to calculate course to steer is very satisfying, especially when you end up in roughly the right place!

> 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.

> Only if that minute of arc lies on a great circle route.

That's all arcs. A line of lattitude is not an arc.

> > 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.

>Only if that minute of arc lies on a great circle route.

I'm pretty sure to derive a nautical mile you have to use the equator, not just any great circle, because the earth isn't a sphere.

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.

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.

The length of people's feet vary and so does the amount of land a yoke of oxen could plough in one day.

I guess this mostly means that Nautical Mile is a unit that traces back to the introduction of the spherical coordinate system in cartography.

As a nice bonus this means your coordinate grid also gives a scale bar.

This makes measuring distance in nautical miles using a chart a lot more practical.

> Most imperial units seem to be based on simple laymen measurements.

I would not label the nautical mile as "imperial". It was based on mathematical properties of the planet:

> Historically, it was defined as one minute (1/60 of a degree) of latitude.

Just like the metre originally was:

> The metre was originally defined as 1⁄10,000,000 of the meridian arc from the North pole to the equator passing through Dunkirk.

* https://en.wikipedia.org/wiki/Nautical_mile

You can pick a NM right off the latitude scale on a marine chart with a pair of dividers. Its an eminently practical measurement for navigation.

edit: of course you could pick off distance with any kind of measurement; but my point is that it converts directly into minutes of latitude

The metre was originally supposed to be based on a division of the Earth's circumference as well.

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.

Mine also. ¯\_(ツ)_/¯

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.

Still bears highlighting, I think:

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.

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.

i would guess that would be mean-sea-level...

Possibly the geoid: https://en.wikipedia.org/wiki/Geoid?wprov=sfti1

It’s a surface describing constant (magnitude of) the acceleration of gravity.

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.

Hah! I was in the Navy and never knew that.

P.S.: Supply Corps, so never needed to know it.

> A kilometer is also defined using the planet Earth as a standard of distance.

Wrong. It used to be that way, but not anymore.

Which is why it says: ... you would have the traditional unit for the kilometer as defined in 1791 by the French Academy of Sciences.

Wouldn't you need the 1791 Earth, too?

The article doesn't mention that it's not the current definition.

The same can be said of the nautical mile. It is no longer defined as an minute of latitude and in instead exactly 1852 meters.

I teach this as part of the science of diving course and there is always an audible groan at the mention of the word "mile".

By the time I am done explaining the basis it is always funny how the classrooms attitude changes to "that makes a lot of sense".

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)

24901.5 mi is the number i memorized for circumference as a wee bairn, before i knew about oblate eccentricity.

The perimeter is 40,000 km. You just need to learn pi ;-)

It's the only mile that metric people approve of :-)

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.

Yes. This is the most annoying side-effect: industry-specific systems of measuring.

As I'm typing this, I'm looking at the power extension cord for my computer, which has a thickness 1.10 Micro Nautical Mile, ie. AWG 12, ie. 2.05mm…

> 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.

* https://en.wikipedia.org/wiki/Nautical_mile

It is now been translated in relation to the metric system as 1852m.

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.

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