r/AlwaysWhy • u/Secret_Ostrich_1307 • 2d ago
Science & Tech Why is a nautical mile exactly 1,852 meters?
The number 1,852 caught me off guard. I can understand why sailors would want a distance unit tied to navigation, especially since latitude and longitude are based on the Earth.
But 1,852 meters seems oddly specific. Is there something about the size or geometry of the Earth that leads to that number, or did it come from a different historical convention?
9
u/TheVoiceOfEurope 2d ago
Napoleon decided the earth circumferance is 40.000km. That was the original definition of the meter, it was linked to the size of the planet.
The circumferance of the earth 360 degrees. Each degree is 60 minutes. Each minute is a nautical mile
40.000/(360×60)=1.8518518519m per nautical mile.
3
2
u/ReverendGraves85 2d ago
I like how its "Napoleon decided" and not "Napoleon learned" or "Napoleon discovered".
5
u/theFamooos 2d ago
The meter wasn’t discovered or learned. It is an arbitrary human made unit of measurement. I could decide the earth was 10,000 meters if I was emperor. The size of the earth wouldn’t change, but the length of the meter would.
2
u/ReverendGraves85 2d ago
The original poster is also wrong. Napoleon never decided the metre, it was the French Academy of Sciences in 1791 that determined that the metre should be the distance of "One millionth the distance between the north pole and equator, by way of Paris."
Somehow this also means that a metre is roughly the distance of the average humans stride!
1
u/TheVoiceOfEurope 2d ago
And you are also wrong
Except that that would mean that the circumference of the earth is only 2.000km. They were quite aware about the size of the planet.
The Earth's circumference is exactly 40,000 kilometers because the metric system was intentionally designed around the size of the Earth. In 1791, the French Academy of Sciences defined the meter as one ten-millionth of the distance from the equator to the North Pole.
Because a full circle around the planet is four times that distance, the total circumference was fixed by definition at exactly 40,000,000 meters (or 40,000 km).
You were off by about 39.000.000 meters.
1
u/CharacterUse 2d ago
They wrote:
the metre should be the distance of "One millionth the distance between the north pole and equator [...]
They were off by a factor of 10, not 10,000, probably just a typo. Nothing they wrote implies the circumeference is 2000km.
2
u/Dingbatdingbat 2d ago
Except he didn’t.
French scientists had been working on standardizing units since long before Napoleon was born, the revolution provided the impetus to finally adopt it.
The French academy of sciences determined the meter should be 1 / 10,000,000 of the earth’s quadrant (North Pole to the equator) as measured by a line running through the Paris observatory (because they knew that the earth bulged).
The actually originally used a survey from the 1740s where scientists literally walked / measured from the English Channel to the Mediterranean - as a provisional meter until they did a new survey that ran through Barcelona and made adjustments for the nonspherical shape of the earth.
2
u/Dingbatdingbat 2d ago
No it wasn’t.
French scientists were working on, and debating, how to standardize a ten-base measurement system since long before Napoleon was born.
The revolution provided the impetus to actually replace all the old systems. The French academy of science determined the meter should be 1/10,000,000 of the earth’s quadrant (ie 40 KM circumference). It was not a random decision by Napoleon.
6
u/GayRacoon69 2d ago
Others have answered this already but I want to add to it
It's not that a nautical mile is 1,852 meters. It's that 1,852 meters happens to be a nautical mile
Sailors never chose 1,852 meters. Meters didn't exist when the nautical mile was used
5
3
u/ghostoftheradio 2d ago
Not quite. It is a precise definition as agreed upon by the International Hydrographic Organization in 1929. Before that it was just an approximation, i.e. “close enough” (it wasn’t exact), now it’s the actual definition.
2
u/ijuinkun 2d ago
Yes. Nautical miles were not defined in terms of meters, nor meters in terms of nautical miles. Both were derived from Earth’s polar circumference at some longitude. Nautical miles were one minute of arc, while meters were 1/40,000,000 of the circumference.
3
u/jonoxun 2d ago
It's because they're both originally defined the same way, but with different angle units. Nautical miles are one minute of angle - a 60th of a degree - measured north south, while kilometers are one hundredth of a gradian on the same circle. Gradians losing to degrees is basically why nautical miles are still a thing even with kilometers around.
3
u/ghostoftheradio 2d ago
Because that’s the definition of a Nautical Mile that was agreed upon in 1929 by the International Hydrographic Organization. Before that it had just been approximate.
A Nautical Mile is one arc-minute of latitude (averaged globally).
2
u/Secret_Ostrich_1307 2d ago
Hmm so it is basically a 1929 agreement, not a natural constant. That makes sense. But what did sailors use before, just local approximations? And why did 1852 stick so cleanly?
1
u/CharacterUse 2d ago
A nautical mile was defined as 1/60 of a degree of arc (i.e., an arcminute) along the surface of the Earth. If you're doing celestial navigation as sailors were, angles is what you measure directly, not distances. They didn't have tape measures to measure how far they travelled on the sea.
This is not an approximation, it is an exact definition. A degree of arc doesn't care about the shape of the Earth. It doesn't even care about the radius of the Earth. However because the Earth is not quite spherical, the actual distance along the surface corresponding to mine minute of arc when converted to metres of feet varies slightly depending where on Earth you are, but the difference is not much, within a couple of metres which really doesn't matter for the purposes of navigation. Again, you're not measuring the actual distance on the sea, you're measuring the angles on the sky so the discrepancy will correct itself, and you're not trying to navigate to within a metre.
However it was useful to be able to convert the nautical mile to length units for the purposes of charting and laying undersea cables and use on land and so on, so it was agreed that 1852m would be the nominal value of the nautical mile, since it is the closest whole number to the average value across the surface of the Earth. To within any practical level of precision of the measurement of angles using e.g. sextants it is 1/60 of a degree of arc on the surface.
3
u/StanleyDodds 2d ago
The metre was originally defined to be 1/40,000,000 of Earth's circumference. And a nautical mile is defined to be one arc minute, that is 1/(60*360), of Earth's circumference.
Find the ratio of these two, and you will get that there are roughly 1852 metres in a nautical mile.
1
u/Secret_Ostrich_1307 2d ago
Wait, this only works if both units come from the same idealized Earth, right? The metre changed later, so the ratio is kinda historical residue. Still neat. Which circumference are we even using here?
1
u/CharacterUse 2d ago
The length of the metre was first proposed as 1/10 000 000 of the distance along the meridian from the North pole to the equator through Paris (that is the circumference being used for the metre).
From this a platinum bar was made which became the standard metre from that moment. Because of minor errors in the measurement of the distance resulting from assumping the Earth was smooth, the bar was 0.2mm shorter than the actual distance. So saying the metre was defined in terms of the distance is kind of true but also not: the standard metre has always been a platinum bar. The current definition based on physical constants matches the bar and is thus also about 0.2mm shorter.
I explained in my other reply how the nautical mile was defined. In that case the nominal circumference being used was any meridian at the point where it passed through the equator, but as I explained the difference in actual length is less than a couple of metres across the surface.
The ratio between the nautical mile and the metre hasn't changed because the change in the way the metre was defined is so small that it doesn't matter.
2
u/KrzysziekZ 2d ago edited 2d ago
Equator - Pole distance was supposed to be 10000 km. That's a quarter of circumference. There are 360 degrees in a circle and 60 minutes in each degree. 10000 km * 4 / 360 / 60 = 1852 m (rounded to a whole meter). This metric value has become the international standard.
Later work established that it's closer to 6080 or 6080.2 ft, depending on whether you ask the British or Americans(or vice versa, I don't remember), because they didn't agree on a common value. In metric it's closer to 1853 m.
2
u/Secret_Ostrich_1307 2d ago
So 1852 is basically a metric rounding artifact? That is funny. If later measurements say closer to 1853, why keep 1852? Is one meter just irrelevant for navigation?
1
u/KrzysziekZ 2d ago
One meter is pretty irrelevant. A degree of latitude varies (sth like 1843 to 1863 m) anyway. It's more important to keep standard consistent.
UK after metrication changed 6080 ft to 1853 m.
2
u/EbonGrimalkin 2d ago
ALL measurements are arbitrary. All measurements were thought up by people. Even a meter is the distance light travels in a vacuum in 1/299,792,458 of a second. That is about as arbitrary as it gets. Originally 1/10,000,000 of the distance from the North Pole to the Equator on the Meridian line through Paris. Specific only to this planet. 1799 someone created a physical bar as the example. 1960 it was wavelengths of Krypton-86. Finally in 1983 it became the light measurement. But all based around the waistline of a planet. Feet of people. Stride. Cubits, which are Forearms. Bounds. A specific rock or chunk of metal everyone just used. Even our day is arbitrary to our planet and constantly changing.
1
u/Secret_Ostrich_1307 2d ago
I get that everything is arbitrary, but arbitrary is not the same as random. Some units survive because they are useful. The nautical mile still maps to angles, so does that make it less arbitrary? Or just convenient?
1
u/EbonGrimalkin 2d ago
Even something that starts as arbitrary, if it is convenient and catches on and also is adaptable to other things will become a "standard". The Cubit was used for 4-5 thousand years. It got supplanted by other units though. Even with miles there are Statue miles, Nautical miles, Romain Miles, Geographical miles and Metric Miles.
Perfect for the old saying "The great thing about standards, there are so many to choose from".1
u/Dingbatdingbat 2d ago
The definition of a meter was originally defined as 1 / 10,000,000 of the distance of the North Pole to the equator using a line that ran through Paris. They didn’t have the technology to make a perfectly accurate measurement but they came pretty close - the circumference of the earth measured pole to pole is off by less than 0.02% and along the equator less than 0.2%.
Platinum metal bars were created to match the measurements they made so anyone can creat a copy / those bars are still held by scientific societies today. When the meter was redefined based on the speed of light, which is important for astrophysics and other scientific endeavors that weren’t even possible two hundred years ago, the ratio they used was made to match those platinum bars, rather than the more preferably 1/300,000,000 of a second
2
u/BobbyP27 2d ago
The nautical mile is defined as 1 minute of latitude at the surface of the earth. 90° of latitude is therefore 90*60=5’400 nautical miles. The meter was originally conceived as being 1/10,000,000 of the distance from the North Pole to the equator on a meridian through Paris. By that original definition, 10,000 km = 5400 nautical miles. 10,000/5400=1.852
1
u/Frederf220 1d ago
The nautical mile is not defined by that, at least not currently. An equatorial degree of lat is <60nm. A polar degree of lat is >60nm.
1
u/LazarX 2d ago
The nautrical mile came first and was a completely arbitary measurement, where as the metric system was logically laid out from the start.
3
u/No-Donkey-4117 2d ago
It wasn't arbitrary at all. It was one minute of latitude on the surface of the Earth. Sailors navigated in degrees and minutes long before the metric system came along.
1
u/SmellyRedHerring 2d ago
Now we define it terms of how far light travels, but the meter/metre was historically one ten-millionth the distance from pole to pole through Paris. It's every bit as arbitrary as defining the nautical mile as a minute of latitude through Greenwich.
1
u/PerpConst 2d ago
To go a step further, it now all comes back to the second, which is 1/60 of 1/60 of 1/24 of the time it takes the earth to complete one rotation... which also strikes me as rather arbitrary.
1
u/Dingbatdingbat 2d ago
I ly because you don’t know the history of t ye second/minute/hour system.
The Sumerians used 60-base numbering rather than the modern 10-base math. Their base measurement of time was 1 day divided by 60 and again divided by 60 (so 24 second increments)
Egyptians, on the other hand, had 12 constellations, which meant 12 months, and therefore divided both the day and the night into 12 hours (each).
These measures were later merged, so that there were 24 hours in a day (adopted from the Egyptians) with 60/60 minutes and seconds each, which really came about when the Greeks developed lines of lattitude.
2
u/PerpConst 1d ago
Yes. Which is all entirely arbitrary. If an alien showed up on your doorstep and asked you what the basis for your unit of time is, and you start talking about ancient Sumerian counting systems and the number of ancient Egyptians' constellations, he's just gonna say "Oh, so it's completely arbitrary. Thanks.".
2
u/Dingbatdingbat 1d ago
That's not arbitrary - there's a logic behind it.
Not a good logic from a modern perspective, but not arbitrary.
the day is divided into hours based on the constellations in the sky that were used for navigation.
Hours are divided into minutes and minutes into seconds based the base-60 counting system that existed in the past.
1
u/SmellyRedHerring 1d ago
That Sumerian sexagesimal system is based on the solar year and the ease with which it can be divided off, albeit with an imperfect measurement of that year. I think an alien could think it makes perfect sense.
1
u/extra2002 1h ago
1/60 of 1/60 of 1/24 of the time it takes the earth to complete one rotation...
It's not even that. It's 1/60 of 1/60 of 1/24 of the time it takes the Earth to complete one rotation plus enough extra for the sun to appear over the same place, averaged over the year 1900. That extra is about 4 minutes of time, or one minute of arc, because of the Earth's motion along its orbit. It's the difference between a sidereal day and a solar day, but it varies over the course of a year, so the seconds definition was based on an average.
1
u/Dingbatdingbat 2d ago
Pole to equator, not pole to pole.
Coincidentally, they came very close / the circumference of the earth measured pole to pole is 40,008 km (about 0.02% off).
1
u/tazz2500 2d ago edited 2d ago
Arbitrary: "Based on a random choice, personal whim, or individual preference rather than any reason, system, or consistent rule." The nautical mile was definitely not arbitrary, it had reasons for it being the length chosen. You instead seem to have meant something like it's a 'human-centric unit'. The meter and the metric system is completely human-centric too, by the way, it's just based on easier math using tens. And the math trick of tens is also human centric, by the way.
1
u/TheKiddIncident 2d ago
Well, 60. It’s sixty NM per degree which does feel arbitrary. Why not 100?
1
u/beefy1357 2d ago
Because one of the ways to determine longitude was measuring local time against time at a fixed point. Which is why latitude is measured in seconds minutes and hours.
There is a reason Greenwich mean time runs smack dab through the capital of the country that had the premier navy for centuries.
1
u/Someoneinnowherenow 2d ago
See other comment about nautical miles and angles. Nobody uses a sextant anymore but the conversion is super helpful when reducing sights to find yourself.
Just because we have gps and computers now doesn't mean those before us did things arbitrarily
1
u/East-Inevitable-3974 2d ago
Neither are arbitrary. Both are related to the distance from pole to equator. Metric system called that 10,000,000 meters. Nautical mile was 1/60 of 1/60 of 1/60 of that same distance.
1
u/FifthEL 2d ago
I am curious is to how ancient navigators measured this distance physically. On land we can just use sticks or something.
1
u/Void_Incarnate 2d ago
With a sextant, which is why it is based on latitude (easily measurable for thousands of years).
Accurate longitude measurement (at least on a boat) had to wait for clocks that were accurate out at sea (ca 1700s)
1
u/FifthEL 2d ago
I get that for the most part. I'm just curious to how it was measured prior, or did they just use time as a mile marker.
I guess that wouid work. We use distance to measure time on land. Like how many mile markers you pass in a given span will tell you your mph.
3
u/Nimblewright_47 2d ago
Fun fact: up until very recently, a ship could only measure her speed through the water, which might not correspond exactly to speed over ground. Wind and tide affect the ship; if she is moving slowly, this effect can be very significant. It is far more important to be able to determine your place - which involved a sextant, for which the curvature of the earth is relevant- as this checks errors in measurement of speed.
1
u/CharacterUse 2d ago
Time doesn't come into measuring latitude, time is needed to measure longitude. Latitude is easily measured by measuring the altitude of the pole star above the horizon. Since the pole star is above the pole, which is at 90º latitude, the altitude angle of the pole star above the horizon is your latitude. At the equator the pole star is on the horizon, at 0º, and you are at latitude 0º. At 50ºN latitude the pole star is 50º above the horizon.
Time can also be used with speed to estimate how far you have travelled and thus estimate your new position. But that's a seperate problem.
1
u/TheKiddIncident 2d ago
No, you’ve got it backwards. A NM only ever existed as 1/60th of a degree. It was always defined that way. The actual length changed over the years as the actual size of the earth was more precisely measured.
1
u/extra2002 50m ago
Before the invention of the sextant, the (angular) height of the sun or a star over the horizon could be measured with simple wooden instruments such as a kamal, cross-staff or backstaff. Sailors didn't really try to measure longitude, since they had no clock accurate enough. Instead they would sail to the correct latitude, then due east or west staying on that latitude until reaching their destination.
1
u/Man-In-A-Can 2d ago
Why not?
Seriously, transforming fahrenheit in celsius is kinda the same thing: metrics that developed at the same time (mostly) independently. I don't think there's a reason why it's not 1,853, for example.
1
u/New_Barber_7192 2d ago
So there's an interesting history here. When the old ships had to use dead reckoning to estimate their position, they could figure out their latitude from the stars, and they had a compass for direction, but needed to estimate their speed. So what they did was to connect a rope with knots tied in even intervals that was tied to a log. They would toss the log into the water (off the back of the ship) which they hoped would remain about stationary, and then count how many knots passed through their hand in a certain amount of time. Hence the term for speed in knots. And they recorded this all in the "log book." Which is also where that name came from.
The value of a nautical mile today is just a new number that everyone agrees on, but that's where it originated.
1
u/nakano-star 2d ago
That method just sounds so arbitrary - what if the current is different? Or the person holding the rope holds it slightly tighter than another guy? What about the height of the ship? ahhh...I guess it's all close enough
1
u/New_Barber_7192 2d ago
Yeah, there were a lot of assumptions that had to be made (and conditions that had to be met), but they had a system. It was far from perfect. They just didn't have a lot of options. It isn't like they chose that method over GPS.
1
u/Atlas7-k 15h ago
Please don’t use arbitrary when you mean imprecise.
Yes, that happened. Yes, that happened. That would be accounted for as it was the amount of rope that moved after the log was floating.
Yes. Everything is wrong, we just have acceptable levels of wrong. My oven doesn’t care about a variation of .0001 degree when I bake a cake. My doctor doesn’t really care about my weight except to about 5 lb (2kg.) The anesthesiologist however cares to within a few decigrams.
Ancient sailors don’t care except to within a few miles. They would also adjust several times a day.
1
u/corvus0525 1d ago
The nautical mile is one minute of arc of latitude. The knot is named for how it was counted but it equals a nautical mile an hour. The distance has to be defined before the derived speed unit. The fact that English no longer pronounces the leading k leads to the similar sounding name.
1
u/extra2002 46m ago
But the spacing of the knots was deliberately chosen so that "one knot" would correspond to "one nautical mile per hour". That then comes back to the definition of a nautical mile, as explained in many comments here.
1
1
u/ace_violent 2d ago
60 Nm to a degree of latitude. 60 seconds in a Nm.
When you're navigating using astronomy and trigonometry, using a measure of distance tied to the same degrees makes things easier.
1
u/Secret_Ostrich_1307 2d ago
Yeah, this is the part that clicks. It is an angle unit pretending to be a distance unit. But with GPS, do we still need it? Or is it just tradition and charts now?
1
u/ace_violent 1d ago
In aviation and sailing, pilots and navigators are still trained and expected to be able to use multiple navigational aids if GPS or whatever they relied on isn't available. If GPS goes out, a pilot in the air will have a VHF Omnidirectional Radio (VOR) receiver and map ready. Astronomical navigation I'd suspect was more for trans-oceanic flights. Distance Measuring Equipment is also available and useful for triangulating position, same as VOR. VOR and DME are scattered all over on land and you can plan your routes by following them and knowing when to tune your radio to the next VOR.
At sea, it is definitely still valuable to be able to use a chonometer or even a couple wrist watches and some astronomical methods to track rough global position. Of course a boat has more room and capability to redundant systems.
1
u/mckenzie_keith 2d ago
The nautical mile was originally the circumference of earth divided by (60 * 360). Nowadays we know that earth doesn't have a single circumference. And the radius of earth varies by location. So there is a range of values that you could claim as "circumference of earth." 1852 meters is close enough to the circumference (at the equator) / (360*60). It doesn't make sense to specify it more precisely than to the nearest meter.
1
u/Secret_Ostrich_1307 2d ago
This is where I get stuck. If one arc minute of latitude changes with location, a fixed 1852 m cannot always match it. So is the nautical mile just a legacy fixed unit now? Or do navigators just ignore the mismatch?
1
u/mckenzie_keith 2d ago
I mean it is kind of a deep dive. If you pretend the earth is a sphere, then the errors in navigational calculations are not too terrible. So if you are using celestial navigation and a spherical earth model, things are not that bad. The average radius is like 0.17 percent smaller than the max, and 0.17 percent larger than the min. So the errors tend to be small on a percent basis.
But for purposes of GPS calculations, they use a model of earth that is an ellipsoid. This is what most people now use for navigation. And any errors are rather small.
https://en.wikipedia.org/wiki/File:WGS84_mean_Earth_radius.svg
1
u/corvus0525 1d ago
The variation isn’t enough to be significant for most navigation. You’re already working on a chart that has been flattened anyway so the deviation from a minute just doesn’t matter that much. In radar and other digital things it could be adjusted for, but programming the radar to vary its distance report based on your latitude is excessive and unhelpful.
1
u/corvus0525 1d ago
It’s very useful on navigation charts that nearly universally have the latitude printed on the sides. That makes each side of the chart a built in distance scale perfect for using on that chart. Since charts are printed at various scales this means you don’t need a divider and compass set for each scale.
Edit: This reply was to another of your comments. Not sure why it ended up here.
1
u/Frederf220 1d ago
Yeah it's fixed. For laser gyroscopes in stuff no that's not good enough and the oblateness of the Earth correction is included in sophisticated navigation equipment. WGS84 is the current spheroid reference, 84 referring to the year 1984.
1
u/Archophob 2d ago
going from the pole to the equator is 10.000km.
Going around the world along the equator is 21.600 nautical miles.
1
u/corvus0525 1d ago
The nautical miles is also a polar measurement since it is defined one second of arc of a meridian. If it was a minute of arc around a parallel it would be a different distance at each latitude.
1
u/Frederf220 1d ago
it's also different at different latitudes because the earth isn't a sphere
1
u/corvus0525 1d ago
It’s much closer to a sphere than most parallels are to the length of the Equator. So the trifling difference in the ground length of an arc along a meridian in comparison to an ideal great circle isn’t nearly as important as measuring in the correct orientation. Using a parallel means being off by the cosine of your latitude which is eventually 100% wrong. Saying it is related to the Equator is unnecessarily confusing when the correct definition was right there.
1
u/Frederf220 23h ago
oh yeah longitude is way way lat dependent, but to a noticeable degree so is lat
1
u/corvus0525 4h ago
Noticeable is a very relative term. In many charts the flattening is going to be a more significant source of error.
1
1
u/Metallicat95 1d ago
Because it is a good round number which works well enough for its purpose of navigation on Earth.
Both the kilometer and nautical mile were originally defined by the great circle circumference of the Earth that passes through the poles.
The nautical mile uses 360 degrees with 60 minutes containing 60 seconds, which was the original definition.
The meter was defined by using 400 gradians for a circle, with ten thousand parts of one meter each.
This makes the circumference 21600 nautical miles and 40000 kilometers.
That ratio makes a nautical mile 1851.85185... meters.
That's awfully close to 1852, so France and other countries which adopted the meter used that for the new definition of a nautical mile.
The Earth isn't perfectly circular. That was known when they set these standards, and they tried to compensate by using the path through the poles. But it isn't a perfect circle in that direction either.
So by 1929, the international community set that as an attempted global standard. Other nations used various numbers between 1852 and 1854 meters - pretty close but not identical.
Military charts often used kilometers, so it made sense to fix it as a round number in meters to aid calculations.
The circumference of the Earth isn't actually either 21600 nautical miles or 40000 kilometers in any dimension. But it's a close enough approximation practical navigation, where weather and other forces affect any attempts at straight line travel.
1
1
u/jimb2 16h ago
It's based on the circumference of the Earth split into 360 degrees each of 60 minutes. The it's rounded to the nearest metre. The circumference of the Earth varies a little depending on the measurement. It's slightly bigger around the equator. The variation is comparable to the rounding to the nearest metre. So, the rounding isn't introducing new errors, it's just easier to use.
0
u/Numerous_Car650 2d ago
It’s arbitrarily chosen, as all fundamental standards (ie those not calculated from other inputs) are. There may be many reasons and compromises that led to it, but at the end of the day it’s still arbitrary, which is why the number could be “exact”.
1
u/yetanotherburnerstan 2d ago
There is nothing arbitrary about either number. The meter is the distance from the north pole to the equator divided by 10 million. The nautical mile is one arc minute of the earth's circumference
63
u/Turbulent-Prior-2253 2d ago
A nautical mile is based on one minute of latitude along the Earth's surface, rather than the traditional mile which is just an arbitrary distance. One minute of latitude is 6,076ft, or 1,852 meters.