A real navigation brain teaser!!

[macd]

Thanks, tome. Maybe you should write one.
'Course the classic 'flat earth' anecdote was when Slocomb had almost completed his round the world trip. When he called in South Africa he was feted by everyone -- including the premier who was an ardent flat-earthist. So did he tell Slocomb he must have taken a wrong turn?

 

[Guest]

[ QUOTE ]
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.

[/ QUOTE ]

Sorry but cannot agree with your explanation ...

It looks as though it should be Longitude by virtue that meridian distance is nearly constant by definition ... but it is not. Also that you measure the NM / distnace vertically on a chart border ...

It is in fact as far as I recall from my MN Nav college referenced to a latitude at xx degrees N / S of equator ...

Your "lecture" about the earths shape albeit nice to see is already part of my nav teachings from many moons ago ... and I may also correct it actually by mentioning that it is said the earth is an oblate spheroid - as that is the nearest definition anyone can use - but even that is not strictly true - the earth is depressed at each of the poles to a differing amount - so the earth is not actually symetrical about the equator. I can't remember which is actually the biggest hemisphere - I seem to recall the southern has it by a shade ...

It is a subject that can fascinate or drive you nuts ...


Oh and the metre - I thought it was based on the wavelength of some physical property ?

If you really want to get into measurement definitions - I used to have a text of Queen Elizabeth 1's definition of the Statute Mile - now I wish I could find it !!

If I find my old Nav books ........ I'll gladly quote ex ...

 

[tome]

Eeeh Nigel, where to start? I avoided contradicting you because I know you are sensitive on these matters but the nautical mile is defined along the meridian, not some imaginary parallel of latitude displaced from the equator

And the earth isn't an oblate spheroid. The most accurate definition is a geoid. The spheroid is merely used as an approximation to simplify the mathematics for numpties like me and you

As for the atomic definition of the metre, this was chosen for its close approximation to the real-world unit and for its stability and repeatability. They searched until they found a suitable atom which fitted the bill. In 1960 they adopted the definition of the metre as the wavelength in vacuum of the radiation corresponding to a transition between specified energy levels of the krypton 86 atom

Think you're getting your chickens and eggs confused

 

[Oldhand]

I am confused, I thought a nautical mile was a variable and is defined as the distance on the earth's surface of one degree of latitude at the latitude you are at. For this reason I was always taught to use the latitude scale of the chart in use to measure distances in nautical miles... have I done it wrong all this time?

 

[Guest]

[ QUOTE ]
I am confused, I thought a nautical mile was a variable and is defined as the distance on the earth's surface of one degree of latitude at the latitude you are at. For this reason I was always taught to use the latitude scale of the chart in use to measure distances in nautical miles... have I done it wrong all this time?

[/ QUOTE ]

It is one minute of latitude on the scale at side ... but yes.

The mathematical number of 6080 and later the metrication of it is to satisfy number freaks ...

And Tome ... I do not argue with Plymouth Nautical College - who know far more about it than you or me ... Maybe it has changed definition since the early 70's when I learnt this stuff ... maybe not ...
And where do you get "imaginary latitude" from ... just because I cannot lay hands on the text book I still have from those days and cannot state the actual latitude used as reference then - is no excuse for the comment.
I may be sensitive about it - not actually as much as you think - only because it was my "trade" before coming ashore.

I may have been taught wrong ... maybe my memory is playing tricks ... we all get older !!

I'll still stick with Dantons and Co ..... they did get me through my tickets - bless 'em !!

 

[BIG_PLANS]

Thought I understood all this before I read the above;

1' of longtitude on the equater = 1nm
1' of latitude = 1nm

The nautical mile does vary as to where you are but the true measurement is at the equater.

Is that overly simple?

Mike
/forums/images/graemlins/confused.gif

 

[SnaxMuppet]

I don't think you do have it wrong.

There is an assumption that is made and that is that 1 deg of latitude when measured as a distance on the earth (or a distance along a line of longitude/meridian on a chart) is the same regardless of the latitude at which it is measured.

As has been pointed out this is not actually true as every line of longitude along which you measure that distance is of a different length around the earth as the earth is not a perfect sphere.

However, the variation is not significant given that scale of the charts we use and the tolerances to which we measure.

That is how I understand it anyway.

Carry on measuring as you are except measure 1 minute and not a degree /forums/images/graemlins/smile.gif

 

[BIG_PLANS]

Is not alot of the differnece in length of the nm due to mercator projection charts?
I seem to remember that it stretches latitude the further north or south you go and that it is impossible to show the poles on a mercator projection.
Seem to remember lecture about charts with a light bulb at the center of the earth projecting shadows onto a tube!!!!

 

[SnaxMuppet]

[ QUOTE ]
Thought I understood all this before I read the above;

1' of longtitude on the equater = 1nm
1' of latitude = 1nm

The nautical mile does vary as to where you are but the true measurement is at the equater.

Is that overly simple?

Mike
/forums/images/graemlins/confused.gif

[/ QUOTE ]

This is a bit of an over simplification as the "squashed earth" means that the great circle that is the equator is significantly longer than the meridian great circles... if the earth was assumed to be a sphere then it might then be true /forums/images/graemlins/smile.gif

 

[SnaxMuppet]

[ QUOTE ]

Sorry but cannot agree with your explanation ...

It looks as though it should be Longitude by virtue that meridian distance is nearly constant by definition ... but it is not. Also that you measure the NM / distnace vertically on a chart border ...


[/ QUOTE ]

mmm... Didn't I put in the caveat about the meridians are not all of equal length? I thought I did anyway /forums/images/graemlins/smile.gif

I didn't say it "should" be constant, I simply regurgitated the definition I have always believed it to be and then explained where I thought the business of latitude N/S of the equator came from... that is all.

And you measure angles of latitude along the meridians don't you so I think it is you who misunderstood my explaination rather than the explaination being wrong I think... I will rea-read it to make sure <rereads>...

My explaination stands I believe - albiet I do admit that it is a simplified one given that I don't know any better /forums/images/graemlins/smirk.gif

Perhaps I should get out my commercial pilots training notes and see if I have forgotten all that stuff - perhaps I have - I am nearly 100 /forums/images/graemlins/smile.gif... I look good for 100 don't I /forums/images/graemlins/laugh.gif

 

[Guest]

[ QUOTE ]
I don't think you do have it wrong.

There is an assumption that is made and that is that 1 deg of latitude when measured as a distance on the earth (or a distance along a line of longitude/meridian on a chart) is the same regardless of the latitude at which it is measured.

As has been pointed out this is not actually true as every line of longitude along which you measure that distance is of a different length around the earth as the earth is not a perfect sphere.

However, the variation is not significant given that scale of the charts we use and the tolerances to which we measure.

That is how I understand it anyway.

Carry on measuring as you are except measure 1 minute and not a degree /forums/images/graemlins/smile.gif

[/ QUOTE ]

One of the biggest reasons that the latitude scale varies so much on a chart is that you are generally using Mercator Projection .... a spheroid shape distorted to be a flat square. This makes the polar regions approach infinity in latitude scale.
As you go higher in latitude you have to change chart projection system otherwise you find it harder and harder to work ...

The scales of latitude and longitude itself on a sphere or earths surface do not vary as much as you observe on a mercator chart as you are then working on the curved and not flat squared projection ... if you see what I mean !!

Example Greenland is distorted such that it is seriously increased in charted size compared to its real physical size ...

Now it gets even more interesting - as I mentioned earlier ...

Pick up a balle or apple - anything similar shape to earth ... Now imagine the parallels of Latitude, meridians of Longitude ... Observe what happens as you approach the poles ... the longitudes actually approach each other into a single infintesimal point - the pole ........ BUT the parallels of Latitude do not. In fact the Latitude is the near constant NOT Longitude. Look again and draw it on if you don't believe me .........
As said in Nav Class ... Poles are 90 deg Latitude ... but can be any Longitude you like ...........

Now tell me again ...

 

[matnoo]

Ok, well, ive been given 100 explainations about things that i wasnt asking about! Ok, definitions of atoms of meters and all that rah rah rah..

but the question remains:

We got a nm long before we reached the equator and long before we developed latitude and longitude or knew the earth was round, oblatoid, convex didjodesium, spherical-bumshapeoid, whatever!

Or was it just just mindnumbingly incredible luck that 1/60/360 of the earths circumference works out at 1nm, or bloody well as near as dammit.

Mat

 

[SnaxMuppet]

[ QUOTE ]
In fact the Latitude is the near constant NOT Longitude. Look again and draw it on if you don't believe me ........

[/ QUOTE ]

I believe you because you are right! The scale does not change when moving along a line of latitude on a chart where as it does change when moving along a line of longitude...

However, and this is the key to understanding what I was explaining, 1 deg of latitude will always be 60NM (or very close to it given the irregular shape of the earth) no matter where on the earth you are but that cannot be said about 1 deg of longitude because that distance then also depends on the latitude.

I think we are probably both right because in essence we are talking about different things and that our explainations, without diagrams and face to face discussion, are confusing both us and possibly everyone else. This is a subject best explained and discussed with pictures /forums/images/graemlins/smile.gif

Nuff said probably /forums/images/graemlins/smirk.gif

After all, there are thousands of pages on the net that will clarify this to people if they are interested and if anyone really has problems with it and would like help then I am always glad to discuss this via PM or email.

Very interesting topic though.

 

[tome]

Suggest you google Eratosthenes who first calculated the circumference of earth to reasonable accuracy around 230 BC, realising that the planet approximated to a sphere. The nautical mile evolved much later and you're chronology is a bit out of kilter

Now, about the UFO which just flew over...

 

[SnaxMuppet]

You are right... we have digressed /forums/images/graemlins/smile.gif

Take a look at this... very interesting article on units of measurement since before the Egyptians buiding of the great pyramid at Giza... it explains the nautical mile and this may be where it original came from... who knows!

http://www.genesisveracity.com/Articles/Article11.htm

I cannot agree nor disagree with this article... I am simply the messenger /forums/images/graemlins/smile.gif

 

[tome]

[ QUOTE ]
we all get older !!

[/ QUOTE ]

Isn't that the truth Nigel. What were we talking about?

 

[Andrew_Fanner]

ISTR my YM instructor remarking that the nm turned out to be a minute of arc at the latitude of Paris as a sop to the French after the prime meridian was defined as being in Greenwich.

He may have been wrong but its

a: a good dit for the bar

and

b: given the French quite plausible.

 

[bbg]

Since you are pressing this, I am going to call you on it -

[ QUOTE ]

Ok, well, ive been given 100 explainations about things that i wasnt asking about! Ok, definitions of atoms of meters and all that rah rah rah..

but the question remains:

We got a nm long before we reached the equator

when do you say "we" got a nautical mile? what year? how was it defined at that time? when do you say "we" reached the equator? please provide a source for all of the above

and long before we developed latitude and longitude or knew the earth was round, oblatoid, convex didjodesium, spherical-bumshapeoid, whatever! again, for each of these - who is "we", when is "when"? and provide a source.

Or was it just just mindnumbingly incredible luck that 1/60/360 of the earths circumference works out at 1nm, or bloody well as near as dammit.

Mat

[/ QUOTE ]

I think you have got your chickens and eggs mixed up. I understand lat and long came first, 1 nautical mile was defined as being 1 minute of arc of a meridian (being a great circle passing through the poles). Because the earth is nearly spherical, it is not surprising that 1 minute of arc of a meridian (1NM) is very nearly (near as dammit, as you put it) the same as 1 minute of arc of the equator (another great circle).

What is the problem other than that the assumptions underlying your question are incorrect?

 

[SnaxMuppet]

[ QUOTE ]
Since you are pressing this, I am going to call you on it -

I think you have got your chickens and eggs mixed up. I understand lat and long came first, 1 nautical mile was defined as being 1 minute of arc of a meridian (being a great circle passing through the poles). Because the earth is nearly spherical, it is not surprising that 1 minute of arc of a meridian (1NM) is very nearly (near as dammit, as you put it) the same as 1 minute of arc of the equator (another great circle).

What is the problem other than that the assumptions underlying your question are incorrect?

[/ QUOTE ]

matnoo doesn't seem to have a problem bbg. As I understand it his question is a perfectly valid one and one that I too am facinated with... I will rephrase the question here because I think it might be you who has got the right end of the wrong stick perhaps...

We have a NM. There are various definitions as discussed in previous posts but the generally accepted, albiet simplistic, one is that 1NM is the distance of 1 minute along any meridian.

However, the NM has been around for much longer than even meridians so how did it FIRST come into existance and how was it defined then if there were no meridians?

matnoo please correct me if it is I that has the wrong end of the stick /forums/images/graemlins/smile.gif

 

[tome]

The nautical mile wasn't conceived until AFTER the realisation that the earth was a sphere with meridians. I believe that this discovery was attributed to Pythagoras

So you and matnoo have events the wrong way round