As you state:
1. a knot is only approximately equal to 1 min of latitude per hour (there are numerous cases where it's unusably wrong)
2. doesn't really help for longitudinal travel
3. maps are continuously projected to favor this mediocre form of navigation instead of something more accurate (see Mercator projection)
4. you could easily put kilometre lines on your charts instead of minutes of latitude and fix all the previous problems
Whilst it isn't precisely equal it's certainly precise enough for navigational purposes. What are the numerous cases of which you speak (i.e. give me a sea navigation scenario where the current definition of a nautical mile is unusuably wrong, may be easier to come up with an air one but again I think you'll struggle).
Certainly as a sailor (who routinely navigates yachts off-shore) 1 nm = 1 knot = 1 minute of latitude is very useful, especially when combined with a mercator projection. Lines of constant bearing are straight which is a very useful property. For longer ocean passages where you may want to sail a great circle route to save distance other projections are available.
Yes you could use kilometre lines but what's your positioning system going to be? It won't map well to lat/long so you'll need to come up with an entirely new coordinate system.
Given basically all charts available (and the surveying data behind them) are done in a lat/long system (though many different datums exist) it's a huge job to switch to the new coordinate system for little benefit.
The current system of units also works very nicely for celestial navigation. Measure angle (A) of body above the horizon. (90 - A) * 60 = distance in nm between you and the point on the earth that body is directly overhead.
Have you actually got any experience of navigating by sea or air or are you just assuming the system of units used is ill thought out and useless and everyone's crying out to use metric instead?
Will you really? Why not use UTM [0] + UPS [1] or MGRS [2]?
[0] https://en.wikipedia.org/wiki/Universal_Transverse_Mercator_... [1] https://en.wikipedia.org/wiki/Universal_polar_stereographic_... [2] https://en.wikipedia.org/wiki/Military_grid_reference_system
Plus as pointed out by another commentor the number of KMs around the earth is not a round number, so you need to do some fudging to get a metricised spherical coordinate system (and you want a spherical coordinate system because the 60th of a degree = 1nm equivilance is very useful for simplfying the mathematics required for navigation).
Modern, computerized charts don't need to lie flat or use only one projection visualization. Furthermore, you can add up-to-date ocean current, jet stream, wind, wave, and weather information to a computerized chart, along with a vehicle performance model, and automatically optimize a route for fastest travel time or lowest fuel consumption.
Nowadays, the unit of distance on the printouts and reports is only needed for human readability and loss-of-power emergencies. Once you have planned out your route, you can scale your backup hard copy with whatever unit your navigator feels most comfortable with, but inside the computer, the software most definitely has a "native" measurement unit, and those are usually in the base SI unit. All other units are converted from that native representation as necessary.
You can navigate your vessel in any coordinate system you like, as long as the conversion functions are coded correctly. And once they are, all charts are translated into all coordinate systems. If you like constant-bearing lines on Mercator projections, just print it out that way. If you like following currents and great circles, just make sure your navigation computer has a backup generator.
The fudging you mention is 99.9% handled just by using the WGS84 ellipsoid. If you're doing any fancy rocket science, you also need a somewhat detailed gravitational model mapped on top of it. Those sorts of calculations are most easily done in an ECR cartesian coordinate system, which easily translates to ECEF cartesian, which somewhat less easily translates to geodetic coordinates--it is actually easier to translate that in the other direction. Unfortunately for that math, no one knows where their house is on the Earth in XYZ coordinates. The amount of error creeping into your double-precision floats is almost insignificant at the scale you need with one or two extra conversions.
The math only needs one arbitrarily chosen unit. I have never seen nautical miles chosen as the unit for length.
Also, as defined by the French academy of science ~1800, the meter is 1/10,000,000th the distance from the north pole to the equator, on the meridian through Paris.
(The second is in turn precisely defined by particle physics.)
If that justifies knot then it also justifies kilometers, because it too was originally standardized on the earth's size.
Neither are exactly the size as originally defined.
A modern knot is 1852 meters. One minute of latitude is "about 1,855.325 m on the WGS 84 ellipsoid" says https://en.wikipedia.org/wiki/Nautical_mile. The difference is 0.16%.
A quarter of the Earth is:
1855.325m * 60 seconds/degree * 360 degrees/circle /4 = 10018755.0
= ~10018 km.
Straight lines on a Mercator projection aren't great circles, they're rhumb lines, and if anything they're a spiral on the sphere, not straight.
It's not the 1800's any more. We have computers and stuff, we don't have to rely on techniques developed for a time when your navigational tools consisted of a map, a compass and a sextant.
Note: The actual deviation from a great circle route is generally fairly minimal in practice.
PS: GPS is just another system that really can fail.
a Mercator projection will give you a bearing to steer to arrive at your destination, which can be followed by eye, autopilot, etc etc.
Calculating a great circle arc and plotting it, following a bearing which may only change by a degree or two but isn't constant, is an unnecessary complication on short routes.
Even commercial vessels will use those old techniques if they don't need to consider the longer range effects. Error correction in the human process is always a consideration.
(Not even talking about data entry errors in GPS systems, but that Malaysia - Melbourne story was Funny.)
This was supplanted by reference bar measurements in 1889 and 1927, by a count of emitted light wavelengths in 1960, and as the distance traversed by light in a vacuum in a specified time interval in 1983.
(So space is measured by time.)
The metric system has its own foibles, one of which is being based on the number of digits a phenotypical abundant primate on a minor planet of a backwater solar system happens to have. It has certain conveniences, but isn't the hallmark of unquestionable rationality some would like to think it is.
Using the SI units of metres and seconds applies a coordinate system on spacetime. One can take a coordinate interval using that, but careful observation shows that the coordinate system cannot be applied at all scales or agreed upon by all users.
In SI terms, the rate of the cycles of hyperfine structure transition frequency of Cs-133 atoms is strictly local to the atoms themselves, and non-local observers will see that rate only if their local Lorentz frame has the same velocity as the atom's, and they are on the same gravitational potential.
As we are not massless inhabitants of a Minkowski vacuum, errors accumulate with coordinate distance from the atom used as a source of frequency, and are observable with laboratory equipment at ranges of metres, and are already wholly non-negligible for practical applications (e.g. GNSS) at ranges comparable to the radius of the Earth and velocities comparable to the speed of sound at STP.
Sadly, SI predates modern conceptions of 3+1 spacetime and has not really adapted to what we know of our physical spacetime's properties.
I think that's more parochial than the base ten issue, personally. :-)
Arguendo, let's assume that you are right that the decimal numeral system arose because of the typical number of human fingers. Note, we do not have to agree for the sake of argument that the place-value system is intimately tied to decimal (and indeed in our history, the latter predates the former by several millennia).
That there are ten values per position is therefore parochial, but not as parochial as you think: almost every vertebrate has five digits per extremity (and essentially all of them embryologically[1]), and there are huge numbers of decapod arthropods extant and in the fossil record, and superorder Decapodiformes is an important group of cephalopods.
So if we use base ten because of the number of our fingers (this is far from proven, unfortunately; there are many examples of very different ways of counting and doing arithmetic on human fingers), it is reasonable to think that many plausible civilization-building non-primates would be liable to use similar representational systems. Unfortunately that conflicts with human history, in which there has been a wide variety of number representation...
[1] even in non-tetrapods: https://images.sciencedaily.com/2016/08/160817142550_1_540x3...
Some harder-core evodevo: http://www.scientificamerican.com/article/why-do-most-specie...
The base 12 system is way better. It has 2 3 4 6 as factors. It's so good we use it everywhere. 2x12 hours, 12 eggs, 12 doughnuts, 12 months, 60 minutes, 12 inches.
A base to be good needs many factors without being unwieldy. 10 is stupid as it skip the most useful ones 3 and 4. Nobody ever need to divide anything by 5.
The perfect measurement system would be SI with base 12.
"Nobody ever need to divide anything by 5"
So, what is left after you remove your "2 3 4 6 as factors" from your example up there of 60? If you work 35 or 40 hours in a week, how many hours should you expect to work on a work day?
Other possibly useful values might be 30 (235) or 210 (2357), which has factors of all the primes lower than 10.
The Babylonian system, based on 12, 30, 60, 120, 180, and 360 (223, 235, 2235, 2^3 * 3 * 5, and 2^3 * 3^2 * 5 respectively) have multiple useful subdivisions.
Base-ten decimal is fun, but produces non-finite values when fractional values are considered: 1/3 = 0.333..., 2/3 = 0.666..., etc. Systems in which those fractions are inherently supported, and for which by Benford's law you're likely to see the divisors 2 - 9 fairly frequently (https://en.m.wikipedia.org/wiki/Benford%27s_law), this can be convenient.
Particularly in an age of rulers, protractors, compases, and no digital electronic computors.
I've never understood why some Americans are so stubborn about the metric system. The rest of the world has essentially made the switch for various reasons but arguably the most advanced nation on earth can't?
Consider base-2 prefixes (now being known as kibi, mebi, gibi, etc)
1 kibibyte = 1024 bytes
1 mebibyte = 1048576 bytes
1 kibibyte = 10000000000
1 mebibyte = 100000000000000000000
1 gibibyte = 1000000000000000000000000000000
One kilometer would still equal 1000 meters. But that 1000 is now in base 12, not in base 10. So rather than 10^3 it's now 12^3. But that just seems strange because you grew up with base 10.
Eggs and doughnuts and many other things are measured in 12 because of its historical utility. It allows you to say things like "I'd like a quarter of dozen" and "a third of a dozen" which are not possible with 10.
Extending a bit further, if you want division by 2, 3, 4, and 5 you can go up to base 60. The Babylonians (among others) did this and nowadays we have 60 seconds in a minute, 60 minutes in an hour, 6 * 60 degrees in a circle, etc:
Specifically: use a units-aware calculator.
I've been doing a lot of calculations based on energy and related terms, and am finding GNU Units (and yes, distinctly specified as an alternative to, say, BSD Units, which has a small subset of features) a phenomenally useful tool.
It turns out that even SI units get confusing and non-base-ten-rational pretty quickly -- pretty much the moment you go from watts to watt-hours (and yes, there's an alternate unit of energy: Joules, but watt-hours turn out to be a really useful concept).
It turns out that units-based measurements are complicated, and keeping tabs manually is a PITA, and using a units-aware calculator is all kinds of awesome. I wrote a little paen to it a couple of years ago here: https://www.reddit.com/r/dredmorbius/comments/1x9u0f/gnu_uni...
What's powerful is that GNU Units doesn't just do straightforward converstions (e.g., what's 180 cm in inches), but can do calcuations of multiple quantities: energy per unit area times area to give energy for a given size of land, etc. Since you can specify the units of the result, there's also a built-in sanity check that your units correspond (a common source of error in physics calculations).
Where GNU Units really shines is in being extensible. You can define constants, values, or units that you want to have readily available. I've plugged in "hiroshima" (the equivalent energy content of the ~15 kt atomic bomb dropped over Hiroshima, Japan), as well as values for the land areas of earth, the various continents, and several nations and states, as well as other area and other metrics for planets and moons within the Solar System. This makes a few relative comparisons fairly straightforward.
I'm aware that metric is "more logical" by certain ways of thinking, but old-school units had their own logic:
Units of length were based off of body parts or could be rapidly assessed. An inch is roughly a thumb's width. A foot, obvious. A yard is roughly a man's pace. A cubit, the length from elbow to fingertips. A fathom, that width of a man's arms, outstretched, as you'd find them whilst measuring out a sounding line shipboard. An acre is the amount of land a man could plough in a day (the German for this recognises the origin explicitly: tagwerk, or "days work"). An acre-foot seems silly until you realise that knowing the area of a reservoir, you can calculate its capacity quickly by simply noting water depth in feet. A british thermal unit is handy if you're sourcing coal for a steam engine -- how much water are you going to heat and boil each day? A mile ("mille") was one thousand double paces, from a slightly shorter-than-typical-today Roman soldier. A furlong was, literally, "one furrow long".
Volume measures: "bushel" derives from "bosta", a handful. Cup is obvious, from a typical drinking vessel. "Gallon" originates from "galleta", latin for bucket or pail.
Measures of weight are ancient -- "pound" comes nearly directly from latin, "libra pondo", with the same meaning. Ton is derived from volume -- the weight of a tun cask. Grain is another obvious one.
What these have in common is that for a quick and dirty in-the-field (often literally) assessment, these measures offered an immediate and sensible-in-context quantification. Measuring land area in acres gave a sense of how much work was required for that land -- how much one man might farm in a year, or how many men and horses you'd need to work it. Egyptian stonemasons could measure out their work by arm, sailors water depths, soldiers distance, farmers grain, hydraulic engineers stored water, without any significant calculations. There's something to be said for that.
I'm not saying the units make more sense now. I am saying that failing to recognise the logic by which the units were derived misses some highly salient points.
I can recognise the logic in historical units of measurements, but I do think some of them are forced - "I want a third of a dozen" - wouldn't you just say you wanted four?.
You can put each finger in an up, down, or medial state, except the two thumbs which give only up or down. That gives base 28.
You can count binary on your fingers as a positional number system. That's base 2.
Base 10 is not the only base that's usable on our dexterous digits.
If you have all fingers on one hand, the thumb of the other hand, and the last joint of each of the remaining fingers removed, sure.
But 28 is the usual number of knuckles.
Also, I am not sure how that's relevant to NOAA?
Both constituencies use knots and nautical miles.
You make it sound like birds and fish check in with the NOAA before planning migrations.
Edit: and that they're really picky about units of measurement.
Historically, a meter was too. A line of longitude is a little over 20,000km.
... along the Equator
Going east means changing longitude, rising from -180 degrees to 180 and then resetting. Those degrees of longitude correspond to less and less distance at the poles (s=rcos(theta)*phi, if theta is angle north of the equator and phi is angle around the axis).
Wikipedia: "Worldwide, the knot is used in meteorology, and in maritime and air navigation—for example, a vessel travelling at 1 knot along a meridian travels approximately one minute of geographic latitude in one hour."