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Comment by codeduck | Hacker News Reader

> 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.

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> > 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.

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

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.

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.

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.

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.

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