A nautical mile?

[Dnathan]

I'm a bit confused about the definition of a nautical mile.

Some places I read it is 1 minute of a great circle, other places I read it is 1 minute latitude at equator (which is the only latitude also being a great circle right?) and on wikipedia - they claim a nautical mile by definition is 1852 meters exactly.

And a meter is 1/10.000 the distance from equator to the true north pole?

I know it is "beating the dead horse", but can anyone enlighten me here please?

[sgsslok]

this might help

http://www.onlineconversion.com/faq_07.htm

[Dnathan]

sgsslok though I did enjoy the history lesson :) - I kinda missed a conclusion?

[sgsslok]

from the first paragraph:

"Since the earth is 360 degrees of longitude around, and degrees are broken into 60 so-called "minutes"...... by definition, 1 minute of longitude at the equator is equal to 1 nautical mile. "

i guess there's really no definition to it...

1 nautical mile = 1.85200 kilometers = 1.1508 miles = 6,076 feet

-Lok

[High Wing Drifter]

1 nm = 6080 feet! Why say it is 6076?

[BEagle]

Ah-harr, Jim lad....

The length of the defining minute of arc varies from pole to equator. In Her Brittanic Majesty's English Channel, it is about 6080 ft. Which is what a UK nautical mile is defined as. Or, as those damn foreigners would have it, 185318.77 of their wretched centimetres.

Whereas the International Nautical Mile is 1852 metres. So a True Brit Nautical Mile is equal to 1.00064 of those upstart things dreamed up by Johnny Foreigner.

But the French did get one thing right. The length of the same minute of arc on Mars is more or less equal to one kilometre.

[Farmer 1]

And a meter is 1/10.000 the distance from equator to the true north pole?As far as I'm aware, it's not just along any meridian, but along the one that passes through Paris. Or has the brain faded beyond recall?

Also, I thought a nautical mile was defined as one minute of latitude at (something like) 48 degrees N?

[BEagle]

'Twas a French ploy to claim they invented the decimal system! But, as anyone knows, the UK did:

10 chains = 1 furlong

1 acre = 1 chain x 1 furlong

[forget]

Different Miles and How They Came to Be.

Under the Roman Empire, Rome became the center of the western world. All roads led to Rome and all distances were measured from Rome. The distances were based upon one thousand Roman paces of the Roman soldier. A Roman pace is equal to two of our steps and very near 64 inches. The Latin for thousand is mille from which we derived the word mile. Each Roman road had occasional small obelisk statues placed to indicate the distance from Rome much as Mexico today does from Mexico City. Hence, statute miles.

The first paths for ships were called Porotan Charts. These were lines drawn across the Mediterranean between the coastal ports. Where many of these lines crossed the mapmakers would draw wind roses. The wind rose initially varied but settled on the eight points. The predecessor to the compass rose and our eight-wind direction terms.

Thales of Miletus (640-546 BC) made a projection (use of shadows) of the region where he lived. Hipparchus in the 2nd century B.C had used sterographic (showing heights) and orthographic projections (perspective). Eratosthenes in 3rd century BC calculated the size of the earth circumference to be 24,000 miles. He developed a 16 point wind rose and use of `degree". He also wrote a description of the known world.

Ptolemy, a 2nd century Greek, made a world map and made a world size error when he calculated size of world's circumference to be only 18,000 miles. Eratosthenes' calculations had been lost to the western world with the destruction of the libraries of Egypt. Copies of scrolls from Eratosthenes were discovered in Constantinople by Polish researchers but it was over a hundred years before application was applied to nautical navigation. This corrected size of the world was drawn on navigational charts in 1669 by Jean Picard. No wonder that Columbus in 1492 had thought that he had reached India.

Ptolemy used the first conic projection plane map with the top as north. This made possible drawing of rhumb (one direction) lines from point to point on the globe. He devised the 60 minute and 60 second divisions of the 360 degrees in a circle. A mile at sea, on this world of Ptolemy, was essentially equal to a mile on the land. The length of a statute mile was 1000 (mille, from the Latin) Roman paces. A Roman pace is two of our steps.

A 1466 Chart of Nicolaus Germanus divided the degree into 60 equal spaces called miles. This was based upon an earth of 18,000 mile circumference and gave us a nautical mile the same length as a Roman statute mile. Other cartographers including Hipparchus and Mercator gave us a world with an overlying grid with numerical markings of longitude and latitude. Gerardus Mercator (Gerhard Kremer), Flemish, in 1569 drew world globe map with 180 degrees E/W longitude 0 to 90 N/S latitude. He made errors which were corrected by Edward Wright who published the computations required as "Meridional Parts" and made this knowledge universal. In combination, we now had a world which could be mapped in degrees of longitude and latitude. Each degree of longitude had divisions of 60 miles equal to a statute mile and each mile was again divided into 60 units called minutes and each minute was again divided into 60 units called seconds.

This was the kind of map and scale used by Columbus. The navigators of his time had not the timing device to make possible the exact determination of longitude. The best 15th Century data available to Columbus came from Ptolemy. The error by Ptolemy directly resulted in Columbus' declaring that he had reached and was exploring India. Columbus thought he had sailed through enough degrees of longitude to have reached India. He may well have, had the world been 18,000 statute miles in circumference.

When the world was computed to be 24,000 statute miles in circumference all the degrees and their divisions were longer and did not conform. More accurate computation of the world's circumference kept changing and finally came to 24,902 statute miles. The circumference of the earth has always been measured as 21,600 nautical miles (360 degrees X 60 nautical miles per degree). However, the individual nautical mile has ballooned by nearly a third through this recalculation of the earth's size. For many of the same reasons the U. S. has failed to convert to metric, later cartographers decided to use statute miles for land and the expanded nautical mile at sea.

Now we can see the background for the difference between nautical and statute miles and Columbus' reasoning. We have Columbus sailing around an earth at least 1/3 larger than he was led to believe. Based on available knowledge Columbus was quite justified to assume that he had actually reached and explored India.

For the navigator, it is very important that distance only be measured along the lines of longitude which has evenly spaced tick marks throughout. The elongated orange peel appearance of the region between lines of longitude means that various latitude lines will have tick marks at differing intervals although always 60 ticks per degree. Only at the Equator do the tick marks correspond to the size of those along the lines of longitude.

Johann Henrich Lambert from Alsace devised the lambert conformal conic projection in which the line you draw is the way you go. This is the charting used on aircraft. As with any flat map of a round surface it has areas of inaccuracy which increase in one direction or another. Errors exist along the top, bottom, and center parts of such a map.

A sphere cut by a plane always makes a circle. The sectional chart used in flying is drawn from such a plane. The globe for a specific chart area is given a cone for a hat. Then a plane is cut through the cone and the globe at right angles to the vertical axis of the cone. The lines of latitude and longitude are projected onto the plane as are the lines making the map. Sectionals are most inaccurate (stretched) in the six inches at the top and bottom. The center ten inches of the sectional for 5 inches up to five inches down from center is somewhat contracted in size.

What is the length of a nautical mile used on a sectional chart? According to the National Oceanic and Atmospheric Administration (NOAA), the standard length they use is 1,852 meters (6,076 feet). The NOAA is the government office that prints aviation and marine navigational charts.

[chuks]

Europe is using 6076 as the value for the nautical mile. That seems to be the agreed JAA value.

If you want to convert knots to feet per minute, multiply knots by 101.3 (or by 100 for a rough conversion). So 100 knots = 10 130 fpm, useful for things like determining gradients (ROC divided by GS). ( 1 knot equals 6079 feet per hour divided by 60 minutes per hour equals 101.3 feet per minute)

Flying around near the equator you can just use the grid squares as being 60 miles on a side; that value will be good enough for practical purposes.

You will notice this funny grid with curved lines on a Lmbert chart somewhere. That gives you the true values for a curved surface shown on a flat surface. There will be two standard paralells where the 'hat' cuts the surface of the sphere.

When you try making a wall decoration out of a couple of charts, check out how far off a point on the edge of one chart is from the same point on the edge of the next one. Hmm ....

[High Wing Drifter]

Europe is using 6076 as the value for the nautical mile. That seems to be the agreed JAA value.
How odd. I spent 9 months of my life being told by Bristol GS that it was 6080 in accordance with JAA learning objectives.

[Piltdown Man]

Forget - I really enjoyed that. For exams, the answer to a mile is the closest to 1,852 M, 6,076 ft or 5,280 ft for the statute mile. Using these values will get you the right answer. When flying, 6,000 ft and 1,850 M is close enough. And statues miles is what you drive when going to work - so who cares?

[Send Clowns]

Depends whether the question asks for the definition or asks you to actually use the nm.

The definition is the length of arc at the Earth's surface subtended by an angle of 1 minute at the centre of the Earth (or more accurately at the centre of curvature of that location).

To practically use the nautical mile use either 1852m or 6080 feet, either of which is a perfectly adequate average.

[forget]

Piltdown Man, If you enjoyed 'that' - you'll love this -

Although the Metric System was devised to simplify calculations it may well represent a major blunder by the Frenchmen responsible. It seems that a brilliantly simple system existed well over 10,000 years ago; one which related not only to the size of the Earth but also to mathematical constants such as ð, Pi.
In comparison to the arbitrary metre, ancient measures may have been perfectly 'natural', embodying the two most important aspects of any logical system of measurement: 'natural" time and distance. Within this system the fundamental sub- unit, and the one which linked mathematical constants with natural aspects appears to have been the Inch, now relegated to 2·54 centimetres.

The Inch: a Natural Unit of Measurement
Metrication of measurement was initially proposed as a means of simplifying calculations. The basic unit, the metre, at first sight seems to have many advantages. One metre is l00cm or l000mm. Very simple calculations of addition or subtraction are indeed made easier but the metre has a major weakness: it is an arbitrary length which doesn't relate to any natural measurement.
As a consequence there can be no logical relationship between two or more 'natural' functions, such as distance and time, and any relationship to mathematical constants could notpossibly exist.

The French, who originated the metre in 1792, decided that any basic unit of measure should, 'naturally' be based on the size of the Earth. Unfortunately the surveyors and mathematicians, rather than using the Equatorial circumference, chose the distance from the Equator to the North- Pole.
If the Earth were a perfect sphere then the metre would be a natural unit of measure. The Earth is not a sphere: the Equatorial circumference is some forty nautical miles greater than the Polar. The originalmetre wasdefined as one ten-millionth of the distance from Equator to Pole but, as no allowance was made for the flattening at the Poles, this was useless for navigation. As recently as 1960 the metre was re-defined (for the third time), and became 1,650,763·73 wavelengths of the reddish-orange light emitted by the isotope krypton-86 in vacuo.
In contrast to this arbitrary measure, the Inch has a natural harmony not only with time and the size of the Earth but also with geometrical constants such as ð.
The basis of this proposition is another unit of measurement, supposedly taken from the length of an average man's forearm, the Cubit. It is this unit which is accepted as having been used in the construction of the Pyramids.
Reference books on the subject agree on one point: the Cubit was 'about' 18·25 inches.
It is now suggested that the Cubit was 18·24 inches, precisely.

Evidence to support this is on view in Europe, ironically in Paris. The Obelisk of Luxor, now standing in the Place de Concorde, was presented to the French by the Viceroy of Egypt in 1831. Weighing over two hundred tons, the monument was carved from a single piece of red granite at about the time the Pyramids were constructed. It is reasonable to assume that the stonemasons involved would have used the standard measuring-unit of the time.

Today, we see this obelisk as being 76 feet tall, but how did the stonemasons see it? If the Cubit is indeed 18·24 inches, then the monument was designed to be 76 x 12/18·24, or 50 Cubits precisely. A reasonable figure to select, one might suppose, when the structure was still 'on the drawing-board'. Pyramids were also designed using the standard Cubit. Experts are undecided on the original dimensions of the Great Pyramid of Cheops. We know what they are today, after thousands of years of erosion, but what did the original plans show?

The base of the Pyramid measures 756 feet, or 9,072 inches or 497·3 Cubits. It would be reasonable to consider that the original base-length was 500 Cubits, and that erosion has removed only 2·7 Cubits (less than 17 inches per side). This supports the proposition that the dimensions of the Pyramid are accurately related to the size of the Earth: addition of base dimensions gives 2,000 Cubits or 36,480 inches, which is precisely one-half nautical mile, or 30 seconds of arc at sea level.
Consider the Cubit in relation to the size of the Earth: the (equatorial) circumference is 21,600 nautical miles, or 1,575,936,000 inches (an impractical figure); but what if the unit of measurement was the 18·24-inch Cubit?
Divide 1,575,936,000 inches by 18·24 and we have 86,400,000 Cubits, a number which will immediately be recognized by professional navigators as the number of thousandths of seconds in a 24-hour day. As the Cubit appears to have been defined by the predecessors of today's navigators, this should come as no surprise!

Fortunately for modern-day navigators the sexagesimal, or base-sixty system has survived within their field. 360 degrees, or 21,600 minutes, or 1,296,000 seconds still make up a full circle, as do 60 minutes an hour and 60 seconds a minute. As navigation is simply the relationship of distance, direction and time, this arrangement is perfectly logical; but how can the Cubit relate to both time and distance in easily-managed numbers?
If we accept that the circumference of the Earth is 86,400,000 Cubits, then 1 degree of arc = 240,000 Cubits and l minute = 4,000 Cubits - which is of course the one nautical mile used by navigators today; but as a sub-unit 4,000 Cubits perhaps makes more sense than 6,080 feet* or decimal fractions of the same**.
(* This is the UK Nautical mile, rejected by the metricators. ** 100 fathoms= 1 cable; 10 cables = 1 nautical mile.-Ed.)

In Solar time, 24 hours results in the passage of 86.4 million Cubits on the surface of the Earth below a vertically overhead sun. One hour would see the passage of 3,600,000 Cubits, one minute 60,000 Cubits - and one second, 1,000 Cubits.

Thus. the apparent passage of the sun over the Earth is precisely 1,000 Cubits per second
What of a mathematical relationship between 18·24 and accepted constants?

A radian is the central angle inscribed in a circle and subtended by an arc equal in length to the radius of the circle. This angle is 57o17'48·8". For most applications 57·3o is used. The related constant, ð, was supposedly discovered by the Greeks only 2,000 years ago. However, ð can be approximated by dividing one radian by the number of inches in a Cubit: 57·3 divided by 18·24 = 3·141... (and, of course, the number of inches in a Cubit can be found by dividing one radian by ð: 57·3/3·141 = 18·24.).

Could 18·24 be as much a numerical constant as ð? A definite relationship does exist between 18·24 and the 360o of a complete circle:
360 / (18·24 x 2) = 9·868, whose square root is 3·141, ð.
Another:
18·24 x 180 = 3,283, whose square root is 57·3, a radian.

So, was the Cubit an ancient, accurate navigational unit?

[chuks]

CAP 698, page 4, 'Conversions':

Feet (ft) to Metres (m) Feet x 0.3048

Nautical mile (NM) to metres (M) NM x 1852.0

So: 1852 divided by 0.3048 equals 6076 rounded off to the nearest whole number.

Here we are not talking about the real world, where, yes, a nautical mile has about 6080 feet but the wonderful world of measuring a gnat's wedding tackle using imprecise means and then trying to find the most nearly correct of four answers on a multiple-choice test.

[KrazyKraut]

Dear oh dear. What a conversation! Isn't PPruNe great?

Perhaps we should now start discussing the Metric Compass , as introduced by Flight Training News, April 2005, Issue 206?

Send an e-mail to [email protected] to receive your copy.

Yeah,

KK

[High Wing Drifter]

So: 1852 divided by 0.3048 equals 6076 rounded off to the nearest whole number.
I guess my dubious point is that it is just as easy to work with 6076 as it is with 6080..so why not indeed.

[Send Clowns]

You'll find, HWD, that if the question is in feet then it might well use the UK definition of 6080 feet rather than the ICAO definition of 1852m/6076 ft. Many are old CAA questions, and have not been changed.

[High Wing Drifter]

There SendClowns is the irony. I managed a mid nineties pass in Gen Nav and yet I didn't know that 1 nm = 6076 :\

[A.Einstein]

This is a great topic.
Since the Earth is an oblate Spheroid and not a perfect sphere, the notion of standardizing a distance between two points based on degrees of latitude is slightly flawed as it is assuming the world is a perfect sphere. This actually means that the length of a nautical mile as calculated between two points changes with latitude. Only a small amount however, and this is not enough to cause concern. If you want to get even closer to real distances and courses you need to revert to spherical trigonometry. At this point Mercator projections (charts) go out of the window, in this case you use Gnomic projections. This is how you need to navigate if you wish to take the shortest route using great circles.

The major problem with measurement is that many cultures have set their own standards over the years. Not everyone is even totally happy with the fact that 000 degrees longitude is set through Greenwich! The Japanese wanted to change that during the second world war.

Amazingly, in order to make sense of our own physical world, when using stellar Navigation on earth, we even assume that all stars are equidistant from the observer. How´s that for inaccuracy!

Just for some food for thought, here is another anomaly.
Distance is a scalar quantity and can be quantified by using speed and time, but to complicate matters, time is affected by speed, thus making it variable. It has been proved that when you fly from London to New York, even at sub sonic speeds there is a slight change in relative time. Therefore it follows, that if distance is scalar and cannot be changed and if the speed value used was a constant, something had to change to make the calculation work. Since the only variable in the equation was time, it means that time had to change. This is part of the theory of relativity

[chuks]

CAP 698 is a UK official document. So I would assume that 6076 feet IS the current UK and JAR value for a nautical mile. It is nothing personal, believe me! I will write whatever value they want me to use.

Another one is that one must use a Pooley's CRP-5 whizz-wheel. The last time I saw something like that was in an aviation museum. A Jeppesen CR-3 is much quicker, easier and more accurate but all the answers are predicated on using this antique CRP-5 artifact with its clumsy way of working compressibility into the equation. Sigh ...

The best one I have seen, so far, was a German test problem that had to be worked backwards to arrive at the Indicated Air Speed! Fiendishly difficult and totally pointless, since in the real world one glance at the airspeed indicator would give the answer to that.

[Dnathan]

Ok cool guys. I really enjoyed how you managed to explain pretty much everything else than what I asked about here :) - Are you all relatives of former pres. Clinton? How did you EVER get to talk about the theory of relativity??

I guess I will still be using 1852m for a nautical mile, and you can keep fighting over how many feet that is equivalent to.

God bless PPRuNe for accurate answers!

[Milt]

Does anyone know the numbers used by GPS algorithms for the nautical mile?

[KrazyKraut]

Since (1) GPS receivers work our nautical miles by measuring the distance between two coordinates (rather than an INS/IRS-style speed/time integration) - and (2) because the GPS model of the earth is quite an accurate oblate spheroid one, rather than a perfect sphere - one must assume that there is no fixed value that correlates x degrees to z feet (i.e. 1 degree = 60x6076ft or whatever).

It must rather be a variable calculation that takes into account where (i.e. latitude) those coordinates are located. In other words, the same distance travelled in degrees at the equator and at the poles would produce a (slightly) different "distance travelled" value in feet and NM.

Also, the altitude of the aircraft will have an effect, because flying the same angular distance between two coordinates will produce a greater actual distance as altitude increases. For GPS, altitude is a big deal, since the calculated geographic position on earth is merely the result of comparing the various psuedo-ranges from the satellites, which change as the aircraft altitude changes.

Mind you, not a lot of receivers will output feet as a distance unit once a certain threshold has been exceeded.

That's just my assumption. I'll check this with an authority on GPS and report back the definite answer.

This is quite an interesting point.

[chuks]

What a funny fellow you must be. You ask for the definition of a nautical mile, which is given to you on a platter as being, yes, derived from a certain value in metres, at least according to the CAA/JAA.

When you work it all out you get 6076 feet. That is the anwer to your original question.

What that has to do with the real world is another question because here we are in the realm of nerds, the sort of guys one would laugh at back in High School, with their thick spectacles held together at the bridge with tape and a selection of writing instruments in a plastic 'pocket protector' in the breast pocket of their wrinkled, white, short-sleeved shirt (one of five worn on successive days of the week until the weekend when they could get wild and crazy by donning a plaid flannel shirt on Saturday and a long-sleeved white one with a clip-on tie for Sunday church).

I have temporarily left the real world where I flew real airplanes for real money and never mind the niff-naff. (You have done all your take-off calculations when another passenger boards. What do you do? Correct answer: 'Recalculate everything because the performance values will have changed.' Yeah, right.) Now I am back in the domain of the nerds, and who is laughing now? Answer: they are! While I am fuming over the pointlessness (to me) of some of the questions they have already got the answer to three decimal places.

When handed lemons, make lemonade. Here one might as well learn to play nicely with the nerds. It's their ball and their rules.

[smith]

Yes, reduction in latitude means the nautical mile is measured at 45oN/S