A real navigation brain teaser!!

[matnoo]

The distance of a nautical mile was devised a very long time ago, before we had visited the equator or knew the exact diameter of the earth at the equator, or indeed, knew the earth was round!!

You cannot work out the size of the equator from england, as the curvature of the earth varies across latitude.

So as one nautical mile is defined as 1/60th of 1/360th of the equators circumference. At exactly 21600 nm, how the hell did they work out what a nautical mile was before they knew the circumference of the equator!!!

It cant be done!!!

Even if theyd have defined it before hand and then decided how many degrees and minutes to give the lat long system to suit, they couldnt have been that jammy to get it exact!?

I dont think for a second that its just chance!!!

This question has been given to me second hand and has apparently been asked to many RYA boffins and none can give an answer!

Mat

 

[MoodySabre]

I'm not very up on these things so I have never bothered my head with it. I always assumed that a NM was arrived at by calculating the curvature of the earth. If a mile was the straight line between A and B then a NM was that distance measure over the curve. I hope that's clear. E.g. the NM is the bow and the M is the string.

Obviously not the case unless it's the same answer as you get!

 

[matnoo]

yes, but that is only EXACTLY true at the equator as its only that part that the earth curves least.

Its pretty darn close everywhere else, but its not exact. The nm is defined by the equator.

Mat

 

[lw395]

One nautical mile is defined as 1852metres.
Its approximation is to the meridian, not the equator. The radius of the earth is fairly easily determined using a sextant or theodolite and any reasonable length of baseline, obviuosly the more accurately you can measure the angle, the more accurate your 'mile'. As you rightly say, the curvature is not exactly constant, so a mile has to be defined in metres, so that it will be constant. For those of us with paper charts, a minute of lat will do though!
Cheers,

 

[Cliveshep]

I always thought it was a unit of measurement used by the Royal Navy based on the length of the ships anchor cable, originally 100 fathoms, (6 feet=1 fathom), 10 cables making a nautical mile, later on becoming 608ft long making 6080ft for 10 cables and equal to the one minute of arc along a meridian, 6076 point something small rounded off. Our cousins across the pond have longer nautical miles which is why mileage on our boats always looks so much higher than theirs!

 

[jsl]

In fact the circumference is nearer 21638 nm, so presumably they estimated - rather accurately, from the look of things. I think the curvature calculations go back to...Eratosthenes, was it? Clever Greek chap?

 

[Twister_Ken]

Post round-earth theory I think. I seem to remember flat earthers like Parahandy measure distances in leagues - a league being the distance that a haggis can be hurled between breakfast and lunch.

 

[peterb]

The Greek, Ptolemy, estimated the circumference of the Earth. He got it wrong, but mainly due to relying on traveller's reports. He put the equator too far north and confused two different stadia, the Philetarian stadium at 500 to a degree of latitude and the Olympic stadium at 600 to a degree. He made the circumference 22,500 Roman miles. Correcting for his errors gives a circumference of 26,410 Roman miles, or 21,315 nautical miles. That's an error of less than 1.4%, and (unless you're using GPS) I bet that's more accurate than your navigation.

PS The fact that stadia were defined in terms of the degree shows the degree to which Greek geodesy had advanced.

PPS When I started writing this there was just the original post. When I looked at the thread, six other people had got in first. I must improve my typing speed!

 

[TigaWave]

Or 1 minute of latitude on any line of longitude, as all lines of longitude pass through the poles they are all lines of circumfrence.

But I had thought that the Nm was derived after it was known that the earth was round ish.

 

[Jonnysailboat]

Phew!... It's giving me headache just reading this lot! /forums/images/graemlins/confused.gif

Maybe they just "Googled" it!. That's what I did; 2 minutes of a job! 1852 metres, bish bosh!

 

[Guest]

[ QUOTE ]


The distance of a nautical mile was devised a very long time ago, before we had visited the equator or knew the exact diameter of the earth at the equator, or indeed, knew the earth was round!!

You cannot work out the size of the equator from england, as the curvature of the earth varies across latitude.

So as one nautical mile is defined as 1/60th of 1/360th of the equators circumference. At exactly 21600 nm, how the hell did they work out what a nautical mile was before they knew the circumference of the equator!!!

It cant be done!!!

Even if theyd have defined it before hand and then decided how many degrees and minutes to give the lat long system to suit, they couldnt have been that jammy to get it exact!?

I dont think for a second that its just chance!!!

This question has been given to me second hand and has apparently been asked to many RYA boffins and none can give an answer!

Mat

[/ QUOTE ]

Suggest you have it back to front ... NM was 1 minute of arc on earths surface ... and is not exactly on equator as I was taught at Nav school for the numerical measurement ... but slightly up ... The figure of 6080 feet was arrived at to be a mathematical data for computation only.
Navigation is really spherical trig in angles and arc ... think in those terms and leave aside 21600 nm and all that ... it starts to fall into clearer place ...

 

[bbg]

Even more specifically, Wikipedia says it is a minute of arc along a MERIDIAN - so specifically not along the equator.

If Wikipedia can further be believed, the modern definition of a nautical mile was not agreed upon until 1929. I am given to understand that several people believed, by that time, that the earth was round although it is perhaps less clear whether anyone had "visited it" by that time (I don't count Australians who had crossed it to get there because who ever counts Australians anyway?)

 

[fireball]

[ QUOTE ]
a league being the distance that a haggis can be hurled between breakfast and lunch.

[/ QUOTE ] does this distance decrease dramatically once the haggis has had his lunch?

 

[Guest]

[ QUOTE ]
Even more specifically, Wikipedia says it is a minute of arc along a MERIDIAN - so specifically not along the equator.

If Wikipedia can further be believed, the modern definition of a nautical mile was not agreed upon until 1929. I am given to understand that several people believed, by that time, that the earth was round although it is perhaps less clear whether anyone had "visited it" by that time (I don't count Australians who had crossed it to get there because who ever counts Australians anyway?)

[/ QUOTE ]

Wikipedia ... along a Meridien ?? No not as I was taught in Plymouth Nautical College for MN .... the arc is related to a circle of latitude a number of degrees displaced from the equator ... I just can't remember the darn latitude number !!!!

I will try and drag out some of my old cadet stuff I kept for Grandchildren !!

 

[bbg]

I don't profess any knowledge myself - so if Wikipedia is wrong you should let them know.

 

[Guest]

Re: A real navigation brain teaser!! wiki ...

Had this discussion before about Wiki ... it's reader / public updated ... anyone can amend / edit / submit article ... as I saw in another article - just cause it's on Wiki - doesn't mean its fact.
Look at the disclaimer at bottom of pages ...

I'm not saying I'm right - just repeating what I was taught at Nav School.

 

[johnalison]

No; for really practical navigation you should use the old measure of a Kenning, i.e. as far as on can ken, which is the distance to the next headland, about 20 miles or so. I'm surprised it fell out of use as it's so practical; "we sailed three kennings today"

 

[macd]

The size of the earth was known with a fair degree of accuracy by the ancient Greeks (Eratosthenes, as I think someone else suggests) so its diameter was certainly known whenever the Nautical Mile was defined. They didn't know it was a geoid (flatter at the poles), but even so their accuracy was probably greater than the precision of most other things in navigation. Incidentally, the notion that everyone thought the Earth was flat when Columbus crossed the Atlantic is poppycock (albeit poppycock I was was taught at school). The Greeks and Romans regarded it as a sphere, as did Bede and most other educated people, even in the 'dark ages'.
And I'm with the meridian lot on the definition of Nautical Mile (granted that doesn't necessarily speak to the way it may orginally have been defined, but such a coincidence almost beggars belief). Surely nothing else is compatible with Admiralty charts - no scale line, just lines of latitude. But correction/edification would be most welcome.
The metre, by the way, was also defined as a precise function of Earth geometry, although I forget exactly which.

 

[SnaxMuppet]

I believe 1NM to be the distance on the earth's surface along any line of longitude (or meridians, all meridians are lines of longitude but the one at 0 deg is the Prime meridian) subtended by an angle of 1 minute of arc at the centre of the earth.

In other words it is on a line of longitude and not the equator.

For the purposes of this discussion I am assuming that all lines of longitude are of equal length which is almost certainly not true but it is close enough for government work.

Now, the earth is not a sphere. It is slightly squashed as if it was squeezed at the poles and so the distance around the equator is slightly greater than the distance around a line of longitude and so the distance on the earth's surface on the equator subtended by an angle of 1 minute of arc at the centre of the earth will be longer than a NM.

So, if you want to represent a NM along a line of latitude (of which the equator is one) then it could not be on the equator but instead it would have to be a certain distance N or S of the equator. This may be where your definition of a NM came from.

 

[tome]

The nautical mile went through many iterations over the centuries as earth measurements became more accurate, culminating in the current definition in the late 1920's

The metre was standardised based on there being exactly 10 million between the equator and the poles, corresponding to 5400 (90 degs x 60 mins) arc-minutes each of a nautical mile. Thus a nautical mile is 1851.85m. This was rounded to 1852 and remains in use today

If you want an easy way to remember 1852, look at a calculator. The 852 figures form the central vertical column