Hacker News new | ask | show | jobs
by gp 1031 days ago
1 nautical mile (~6076 ft) is exactly one minute of arc at the Earth's equator.

As a sailor, I wish that all miles were nautical miles because they have a real meaning. What good is 5280 feet?

9 comments

A mile is 5280 feet because it is 80 chains (survey chains) long. The chain's length is a byproduct of English land tax laws which were by the acre.

The roman mile was 1000 paces, or 5000 feet, which made a bit more sense.

https://en.wikipedia.org/wiki/Gunter%27s_chain

For those of you marvelling at Romans having a five foot (1.5 m) stride, a Roman pace was two steps, counted from the left foot down to left foot down again.
In my experience many people define pace the same way today. We were taught in Boy Scouts how to pace off a distance measuring 5 feet per pace, or every other footfall.
That's to account for possibly different (average) left/right steps.

Averages out better.

I have seen this argument before, but I'm not sure that I buy it. Even if you count every footfall, you are not magically going to somehow use, say, only your left foot. At the end of a km, you will have 600 double paces or 1199, 1200 or 1201 single paces. Well within the margin of error.

My hypothesis is this: Actually try to count every foot when you’re out. If you count only every second footfall, you can mentally go "a-one-a-two-a-three" and so on, but counting every foot, there are just too many of them. At least I get brain overload from it.

Same reason people count things out in twos. "How many shells did you collect on the beach?" "Let's see... two, four, six, eight.. I got nine shells"

They're both shortcuts to count things with half as much counting.

Maybe because you were kids and adult paces are a single stride?
Nope. Boy scouts, not cub scouts, so a lot of us were closer to adult stride than kid. If you measure a typical adult pace (same foot to same foot) it's probably just under 5 feet unless they're deliberately pacing to measure something. You get a feel for what it takes for your own pace to hit 5 feet so you can repeat it.
I used to teach orienteering and scout skills when I was a teenager. One of the first things we did was measure how long each kid's natural pace was so they could know how to pace out a distance. If the course said 600ft and the kid knows their pace was 3 feet then they would take 200 paces or 400 steps. Typically, unless you were a runt like me it almost always came out to 5 feet. Just kind of the way people work. 2.5 feet a step. Roughly 5 feet or 1.5 meters per pace.

It always got complicated with obstacles though. Especially since most of them didn't know how to do trigonometry yet. We usually just had them estimate which they got pretty good at after a few hours of counting paces.

You’ve ruined my mental image of the Romans all walking like John Cleese.
Like the marching hammers in Pink Floyd’s The Wall music video
I think more importantly would be how do pirates mark paces?
That's still how we pace in the military today, left foot to left foot and (while it differs for everyone) normally about 60 paces per 100m.
Don't worry, we've come full circle and defined the Data Mile to be exactly 6,000 ft.
Most other 'mile's are derivatives of the Roman mile which developed somewhat independently of the English units (foot, yard, inch, barleycorn, etc), ergo the weird conversion factors. The original Roman mile was 5000 Roman feet.

In fact, 1 nmi ≡ 1.852 km exactly.

Also from the original definition of the metre: 1/60 × 1/90 × 10^7 = 1851.85185185... m.

Inter-convertability was a defining trait of SI (or more precisely, its predecessors, MKS and CGS) from the very outset, which is why we have 1 m ≡ 1 s ≡ 1 kg ≡ 1 N ≡ 1 Pa ≡ 1 J ≡ 1 A ≡ 1 C ≡ 1 V ≡ 1 Ω ≡ 1 F ≡ 1 W ≡ 1 Wb ≡ 1 T ≡ 1 H ≡ 1 Hz (I use '≡' loosely here to suggest conversion factors, rather than its usual meaning of equivalence).

The only outliers in the SI are the kelvin, the mole, and the candela (and derived units from these). The former two are dealt with straightforwardly with the Boltzmann and Avogadro constants. I have issues with the presence of the candela in the SI.

> Most other 'mile's are derivatives of the Roman mile which developed somewhat independently of the English units (foot, yard, inch, barleycorn, etc), ergo the weird conversion factors. The original Roman mile was 5000 Roman feet.

Pre-metric Europe was full of units with weird conversion factors, based on a shared heritage (mixture of Roman and Germanic), but with lots of divergent evolution subsequently. England didn't really stand out; France, Spain, Italy, Germany, etc, were really no different.

Then the Continent did away with most of that complexity by adopting metric, and for whatever reason the English dragged their feet on doing that, and their American offshoots even more so. But the fact that people have forgotten that the French/Germans/etc used to have feet/inches/miles/pounds/etc too, [0] albeit with somewhat different definitions, makes people think English units were somehow unique. They never were. The uniqueness is in the slowness in replacing them with metric, not the units themselves.

[0] They still have some of these units for certain purposes. In France and Germany, the pound is still used, albeit redefined to be exactly 500 g. Nautical miles are used in maritime and aviation applications; American influence (and to a lesser degree British) led to the adoption of the Anglo-American foot as the unit of altitude in aviation – the foot French pilots use to measure altitudes is the English foot not the old French foot; etc

> American influence (and to a lesser degree British) led to the adoption of the Anglo-American foot as the unit of altitude in aviation

There are a few notes I have regarding this. The Airbus consortium initially set up the Airbus A300 cockpit entirely in SI units, but they realised this wouldn't sell well in the US, and they switched to feet and flight levels.

Airfield weather data, including pressure and temperature readings in everywhere but the US are given in hectopascals and degrees Celsius.

Many post-Warsaw Pact countries (Russia, China, Uzbekistan, Belarus, Ukraine until recently) used to have a completely metric unit setup for their air traffic controls. Both Boeing and Airbus cockpits have settings to output altimeter readings in metres.

> Then the Continent did away with most of that complexity by adopting metric, and for whatever reason the English dragged their feet on doing that, and their American offshoots even more so.

If there's one export of the US I despise more than anything else, it is making legacy non-SI units relevant again because of its outsize influence in traditional and social media.

I live in a country that metricated half a century ago, but I have Gen Z friends who measure their heights in feet and inches, and their gym weights in pounds. What the absolute hell.

The SI units are the pinnacle of standardisation and the culmination of a three-hundred-year long effort to make life easier for everyone. I have no idea why the richest country in the world can't metricate properly.

Get rid of legacy units, and we save billions in not printing the (XX fl. oz), (XX lbs), or (XX oz) on food packaging alone.

It is ironic that a country that did away with colonialism, a whole lot of tea, and embraced the French and their revolution, never embraced the French units, but stuck with the English units.

The early US came tragically close to adopting the metric system, and on more than one occasion.

I invite you to watch this amusing and relatively short video by History Maters on the subject: https://youtube.com/watch?v=BtKbq_zAr-A&pp=ygUWaGlzdG9yeSBtY...

As an American I will say this, almost nobody genuinely thinks that our measurement system is superior. I suspect the majority of us know it’s a janky system but it’s so difficult to change.

That being said, I switched over to Kilometers on my iPhone because of Pokémon Go. I’ve actually gotten to the point where I think of walking distance in metric more readily than in fractions of a mile, so metrification is making progress in unexpected and exciting ways!

It’s not ironic, it’s economic. People had other things to worry about during the Revolutionary War, and then afterwards there was an industrial revolution. (The tax on tea might have been the straw that broke the camel’s back, but the protectionist taxes on goods manufactured in the colonies was the real killer.) Once that was in full swing changing the units was impossible.

Every machine in every machine shop was geared towards manufacturing dimensions and tolerances specified in inches, tenths, and hundredths. Changing to metric would have required rebuilding or replacing all of them. England had the same problem. They had the most manufacturing capability in the world, and they weren’t about to spend all that money replacing all of that machinery.

Worse, the SI system isn’t really easier. The SI units were designed to make unit conversions easier, but in practice nobody actually converts units. In the US Customary system (as in the English Imperial system before it), every common activity has it’s own units.

Houses and furniture are measured in feet and inches, and you never ever convert those to miles. Why bother? Miles aren’t useful for measuring cupboards or rocking chairs.

Cooking uses teaspoons, tablespoons and cups, but you never need to convert between spoons and cups let alone cups and gallons or barrels or hogsheads. It is handy to remember that a tablespoon is three teaspoons though, because that can save you some time at the holidays when you have to scale your recipes up to feed all of your relatives.

The SI system is not really any different in practice.

> People had other things to worry about during the Revolutionary War

Well, the metric system was devised in France mostly during the Revolution, with the size of Earth surveyed while at war with most of Europe in order to get a good basis for the length of the meter.

> Cooking uses teaspoons, tablespoons and cups

Or millilitres and grams, which are basically equivalent for liquids, so you only need a kitchen scale to do most cooking as long as it's not an American recipe, and it's extremely easy to scale recipes.

> People had other things to worry about during the Revolutionary War

Actually there are plenty of examples of countries adopting metric after a revolution or gaining independence, so perhaps the US didn’t adopt metric in spite of the revolution rather than because of it.

Industrial revolution had nothing to do with it, given that the inch USA uses today is an inch created by a pissed off engineer (gauge block Inventor Carl Johansson) in European company making gauge blocks, who defined an inch to be 25.4 mm @ 20 degrees Celsius in 1912 - created by taking a reasonable metric approximation in between British and American inches.

The popularity of Johansson's blocks is Brits changed their definition of inch in 1930 and USA followed in 1933. Most countries that still used inches started to use "industrial inch" of 25.4mm in 1930s, the rest went metric.

> It’s not ironic, it’s economic.

> and then afterwards there was an industrial revolution.

> Every machine in every machine shop was geared towards manufacturing dimensions and tolerances specified in inches, tenths, and hundredths. Changing to metric would have required rebuilding or replacing all of them.

I don't think this argument makes anywhere near as much sense as you think it does: the part of the US which lags the most in metrication isn't industry, it is in everyday life, K-12 education, and consumer products/services; the US manufacturing industry is significantly ahead of US consumers in the adoption of metric. Entire industries in the US have adopted metric (most notably the US automotive design&manufacturing industry has switched to mostly metric). If the real issue were about industry, you'd expect industry to have the biggest lag, not to be ahead of consumers.

I think the real reason is actually cultural. Almost every country which successfully metricated, did so with some degree of government coercion – "you are going to start using metric now, and we aren't giving you a choice about it". The US cultural emphasis on individual freedom led it to refuse to go down that path, insisting that metrication be voluntary only – which is a large part of why, decades later, so little progress has been made. Similarly, the UK's insistence on retaining miles for road distances is due to cultural and political reasons, not any practical concern – Australia successfully converted all its road distance and speed limit signs to kilometres, despite having much longer roads than the UK does

Also, for all that US insistence on "freedom", it actually engages in anti-metric governmental coercion – consider the Fair Packaging and Labelling Act (FPLA), a federal law which makes metric-only packaging illegal for many categories of consumer goods.

> The SI units were designed to make unit conversions easier, but in practice nobody actually converts units

I can remember doing lots of unit conversions in science and maths classes in high school. If I'd gone on to study physical science or engineering at university, I'm sure I would have done plenty more. From an educational viewpoint, I think it is easier to teach students how to do science with SI units if they have already been taught basic metric units at the primary/elementary level, and are used to using them in everyday life. Whereas, students in the US start out with less familiarity with basic metric units, which makes learning to use SI units in science class more work for them

And every time I visit the US I find myself constantly trying to remember stuff like "what is an ounce, again?" "what's 60 degrees Fahrenheit in Celsius?". If the US finally finished adopting the metric system, it would eliminate the need for many unit conversions which are now required by international visitors, immigrants/emigrants to/from the US, journalists, businesses engaged in product localisation, etc

> Cooking uses teaspoons, tablespoons and cups, but you never need to convert between spoons and cups

Some countries (Australia I know is one, there are probably others) have defined metric cups, teaspoons and tablespoons. So this isn't really the argument against the metric system that you think it is

I just checked and one of my tablespoons is 4 of my teaspoons, but none of them is imperial :-)

On the other side, 1 liter of water is 1000 grams so if I need 100 cc I can put water in a glass and weight it.

Base ten is an unfortunate numeric choice and responsible for much of the hesitation to switch to metric. Maybe someday when we have millions of O'Neill Cylinder colonies, one of them will adopt base twelve instead, at which point the main reason against metric would go away.
> Base ten is an unfortunate numeric choice and responsible for much of the hesitation to switch to metric. Maybe someday when we have millions of O'Neill Cylinder colonies, one of them will adopt base twelve instead, at which point the main reason against metric would go away.

I've heard this argument many times before, but I don't think it makes much sense. The US customary / British imperial measurements are not consistently based on base 12. Yes, there are 12 inches to a foot; but there are 16 (not 12) ounces in a pound, and 128 (not 12 or 144) US fluid ounces in a US gallon (versus 160 UK fluid ounces in a UK gallon). Fahrenheit has 180 degrees between the freezing and boiling points of water, with water freezing at 32 degrees – none of which has much to do with base 12 either. There is no widely used unit corresponding to 12 feet or a twelfth of a mile. If you really want a system of units based on base 12, the US customary / British imperial system ain't what you are looking for.

Also, it ignores the fact that you can metricate while keeping a foot of 12 inches, if you define a new "metric foot" composed of 12 "metric inches". This has been done before – as I mentioned in an earlier comment, many European countries kept the pound when metricating, by defining a new "metric pound" of 500 g. Given the current standard US-UK inch is exactly 25.4 mm, one option would be to have a metric inch of 25 mm (= 2.5 cm), twelve of which would give a metric foot of 300 mm (= 30 cm, versus 30.48 cm exactly for the standard US-UK foot). Sure, having two different foots and inches (old and new) coexisting for a while might cause some confusion; but if the confusion isn't worth it, maybe base 12 isn't really worth it either. And to avoid the confusion, you could always give the new metric units different names ("moots and minches", maybe?)

A lot of traditional units are based on random reference points that were an issue from antiquity - consider how pretty much every market town kept their own measure references even if they used same terminology.

That said, Fahrenheit use of brine solution for 0 and his wife's armpit for 100 remains among most WTF for me.

When it comes to precision machining, even Americans seem to prefer to use "thous" (1/1,000") and "tenths" (1/10,000"). Isn't it strange that the preferred measurements aren't fractional: 1/1,728" and 1/20,736"? Why do you think that is?

What would a machine shop say if you called out a dimension as (5,081/20,736")?

I think they'd stare at it for a while, chuckle at your sense of humor, and then punch it into a calculator to work it out in decimals.

Or base 16 if the machine overlords have their way.
The biggest argument against base 10 is that one day our descendants will have to explain to aliens, "because the monkeys that built us had ten fingers".

Positively mortifying.

English dragged their feet on doing that

Pun intended? ;-)

It's also worth noting that English and American units also differ slightly --- one of the more common examples being that the US gallon is not the same as the Imperial gallon.

Footer to your footer. At least in the Netherlands, ounce is still used as well, it's defined to 100g.
That's over three times too big though.
in the end, who cares? It’s just a name on a unit. There is no law of nature that puts a limit on its value. There always have been many definitions for an ounce (one of the reason for going metric in the first place); this one is just a bit on the large side.
And everyone measures TVs in inches, somewhat bizarrely.
Are they actually designed and manufactured in inches, or only marketed in inches?

Almost everyone called 90 mm floppy disks "3.5 inch", despite the fact the formal standard which defined their dimensions was metric. I believe the same was true of the "5.25 inch" disks which preceded them. (I think the original 8-inch floppy disks were non-metric though???)

Strictly speaking, this is also a consumer-oriented thing, using the diagonal. The diagonal is also misleading, because it gives no information about the dimensions and aspect ratio of a given panel. Consider a 15.6" 16:9 display, versus a (now increasingly more common) 16" 16:10 display.

Panel manufacturers are all based in Asia, and measure only the edges in millimetres, as they should. Even xrandr outputs EDID data in millimetres.

CRTs were 4:3 and tiny, they could fit basically everywhere. The diagonal was more than enough for consumers. Computer monitors started to have different ratios but they were not as widespread as today, even in a world of laptops and mobile devices.

The last time I had to buy a TV set I was more interested in the width of the appliance (screen plus bezel) than in its diagonal because I had to fit it into a set space. I went to a shop with a tape ruler.

Gas and water pipes are often in inches too (Italy) probably because it's an old and critical infrastructure and nobody wants to risk mistakes by trying to fit a 1 inch pipe with a 25 mm one, or 1 1/4" with a 32 mm. Close but not close enough.

However I guess that even American engines are measured in liters or cc, cubic centimeters.

> Gas and water pipes are often in inches too (Italy)

English inches (now 25.4 mm) or Italian inches? (“once”/“oncia”-varied in definition between different parts of Italy, but was always at least a fraction more or less than the English one)

English inches.

I'm not sure I ever heard the Italian word oncia as a unit of length. I thought it was a translation of the imperial unit of weight, ounce. However all is possible in the world of the old semi forgotten traditional units.

We do measure TVs in Zoll here in German speaking countries, which has been redefined to exactly 1 in.
In the Netherlands we also colloquially use the 'ons' (ounce) which is defined though as 100g.
In Germany we've got 'Unze' (ounce) which is defined as ~30g which we only use when talking about precious metals.

What we do use is 'Pfund' (pounds lbs) which is defined as 500g.

I am amazed the nations of the world actually came to an agreement about what to use as base units and I can't even fathom what shit show it must've been before that.

I live a 30min drive away from the Netherlands and your ounce is already 230% more then my ounce.

But "hecto" (gram) is not used as a synonym?
No it's not, at least not in the Netherlands.
In Germany the short "hecto" stands for "hectoliter", when ordering larger amounts of beer.
This is commonly used in Italy modified in the form "etto"
China had their own mile. “The journey of a thousand miles begins with a single step” was actually only around 300 English miles long.
The modern Chinese li is defined as exactly 500 meters.
Laozi had some foresight to use meters in 500BCE.
And, similarly, the 斤 (jīn) is defined as 500g.
Kilogram is also an outlier, as it is the only base unit that comes with a magnitude prefix.
The base unit is gram, not sure what you mean
The base unit is indeed the kilogram, see https://www.bipm.org/en/measurement-units/si-base-units.
Interestingly, a mile was originally the less surprising 5000 feet. But in the 1500s the English changed the mile to be 8 furlongs, as that made for much easier math around the agricultural measurements of the time.

https://en.m.wikipedia.org/wiki/Furlong

I wish those medieval people had defined it as 5040 feet, then it would be divisible by 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 24, 28, 30, 35, 36, 40, 42, 45, 48, 56, 60, 63, 70, 72, 80, 84, 90, 105, 112, 120, 126, 140, 144, 168, 180, 210, 240, 252, 280, 315, 336, 360, 420, 504, 560, 630, 720, 840, 1008, 1260, 1680, and 2520.
For reference, 5280 = 2^5 × 3 × 5 × 11

(8 prime factors, 4 distinct)

So 5280 is better if you want to divide by 11, I guess! What a strange thing, how on earth did it end up with a factor of 11 in there...

Edit: it's complicated: https://math.ucr.edu/home/baez/inches.html

There are 11 fathoms in a chain, 10 chains in a furlong, and 8 furlongs to a mile.

Going the other way, 2 yards in a fathom and 3 feet in a yard. That accounts for all the factors above.

Is that why we have 90 degrees in a right angle, instead of 100?

90: 2, 3, 5, 6, 9, 10, 15, 18, 30, and 45

100: 2, 4, 5, 10, 20, 25, and 50

If we used grads, it would be a nice even 100,000 meters per grad, vs 111,111.111 per degree.

Connecting 1 mile to 5280 feet happened many centuries after the medieval period. Such precision wasn't really possible nor desired before the 18th century.

To be specific, 5280 feet = 1 mile didn't happen until 1959 and the United States needed higher precision and remove all the fuzziness out of the units. It might be inconvenient on some aspects, but it was also "close enough" to what miles were already established to be.

>To be specific, 5280 feet = 1 mile didn't happen until 1959 and the United States needed higher precision and remove all the fuzziness out of the units. It might be inconvenient on some aspects, but it was also "close enough" to what miles were already established to be.

uh what? are you sure you're not mixing that up with the international geophysical year or something? the mile has been 1760 yards since before the US even existed. it's called the imperial system because of the british empire. they couldn't have done the great trigonometrical survey of india without an accurate mile.

> I wish that all miles were nautical miles because they have a real meaning.

Could you define 'real' here please?

This feels like one of those 'customary is better because you can't divide 10 by 3 using only integers' claims.

You seem to be asserting that once you divide a circle into 360 arcs, then at a a certain distance from the focus, one of those arcs has a certain meaning.

I would say that because ~ 2 millennia ago the Greeks pinched the Babylonian's use of 360, and the Babylonians came to that number by perfecting a rough days-in-a-year measurement used for astronomy over the previous 2 millennia, a nautical mile now has a derived / coincidental meaning, more so than a 'real' one.

EDIT: And this is before contemplating the complications of living on an oblate spheroid - the NM's length depends on where you are.

Each of those arcs do have a meaning, they're called 'degrees' and any human being whose not being obtuse for the sake of argument would tell you that they're 'real'. The point of calling nautical miles 'real' is that you can do easy mental math with them to express a distance in terms of latitude and longitude.
I think you may have missed my point.

The actual length of a nautical mile only makes sense because we have this weird way of measuring earth (based on how we measure circles).

NM's were obviously defined using that weird numbering system - 360 degrees in a circle, 60 minutes in a degree, 60 seconds in a minute - so it shouldn't be a surprise that they 'feel real' within that system.

Given a quarter of the circumference of earth is ~ 10,000km, it seems ripe for using base-10 and metric units ... but for the fact, obviously, that these arc-based-at-6-thousand-km-from-the-centre measurements are highly variable and not hugely useful.

> The point of calling nautical miles 'real' is that you can do easy mental math with them to express a distance in terms of latitude and longitude.

And that's not true either.

At best it works for latitude -- even a small way from the equator you'll suffer the effects of longitudinal meridians converging.

But at that point, why not just do your mental math in minutes rather than (yet another) mile variant?

The math is not done in ones head but using a plotter on a chart. As long as latitude is defined as it is, nautical miles have meaning.
I didn't say 'in one's head', merely used the same phrasing as nmilo.

If you're using a plotter, then actual length is presumably irrelevant - any unit would do, yes?

I was not asserting that nautical miles don't have meaning - just that their meaning is even more arbitrary than most other units of measurement, except in this case they're extra useless because they align to what they ostensibly derive from only at or near the equator.

If you want to use something 'around that size', and you're very keen on avoiding metric at all costs, then why not just use the 'upstream' unit - a minute? Obviously it still suffers from converging meridians if you measure from a plane through the sphere, but I'm not sure what number of measurement problems you're happy to contend with.

You need some reference. The latitude grid is available anywhere on your chart, with multiple subdivisions, so even when your boat is shaking like crazy you'll be able to draw a course ad hoc (which requires estimating drifts due to wind and tide etc., which are conveniently given in knots (so nautical miles per hour)).

The coordinate grid may be arbitrary (though having a lot of factors is nice), but the derived nautical mile is not.

Right, but what’s the point of arguing about the real-ness of something you’re using without verifying it ever. The equator (or the 45th parallel, or any meridian) is not a circle; nobody ever said anything like “man, it’s so much more natural that the equator is 21638.778 nmi instead of that ugly 40,075.017 km”.
Well, latitude, or longitude at the equator.
What good is converting miles into feet anyway? I've never found a reason to perform that conversion, or reverse. A mile is just an arbitrary unit of distance that doesn't need to be related to any other. Even in sports, swimmers may casually call a 1650 yard swim 'a mile' but if you do the conversion it isn't. That doesn't matter to anybody though.

To be perfectly honest, I never remember how many feet are in a mile and the only times I've looked it up have been to calculate some meaningless trivia like how many tape measures it would take to stretch across the country, or some useless nonsense like that. Even then I usually just approximate 3 feet to a meter and 1.6 km to a mile, close enough.

The most simple example is adding or subtracting distances. You might say you don't need that, but I'd wager most people need to at some point.
Adding miles to miles or feet to feet make sense, but when do you add feet to miles?
Can you really imagine no scenario when this might happen? Like "A to B is one mile, B to C is 200 feet, how long is A to B to C"? You've never come across anything like this in your whole life?
Agreed. When I learnt about nautical miles and knots (nm/h) which is both used by aviation and sailors, I feel we should be using nautical miles for all travel distance.

Miles really don’t have much meaning.

If someone goes at 60 nautical miles per hour (111.112 km/h), for 360 hours (15 days), they cover the circumference of the planet around the equator. I.e go around the planet.

What good is a mile to begin with. Just use kms and then we have a nice round figure. Being from the US and as someone that does a lot of woodworking, I’m very used to inches but I can’t do anything beyond basic calculations in inches and always have to pull out a very specific carpenters calculator. It’s not trivial to add up 2’13/32” + 5’11/16”, there’s too much carrying over and doubling to equalize the denominators to do easily in your head. That’s just addition, dividing is a whole other beast.
Nautical miles are used in sailing because they correspond (nearly) directly to an arcminute of latitude which simplifies chart navigation.
IDK if 2.40625 + 5.6875 is any easier :)

Inches using base 2 for the fractions is useful.

> Inches using base 2 for the fractions is useful.

Why? You can't just say that without a reason.

(The numbers you cited above don't count, because you'd instead use 6.1 and 14.4 (or maybe 14.45) centimeters)

Certainly.

Let's say you are centering a 2 1/4" board on a 22" frame.

The edges need to be 8 3/8" apart.

It's a lot more common to divide lengths in halves (and quarters, etc) than tenths.

But say you have to divide a 8 3/8” board into 5 parts. That turns into an ugly 771/40. What do you even do with that using an imperial measuring tape?
I have never needed to divide a board into 5 parts.

But if I did that would indeed be difficult.

Are you visually or mentally impaired? I don't mean it in any condescending way. I can add those on the spot by just looking at the numbers and tell you result immediately, that's primary school level math in Europe.
Yes I'm mentally impaired.

That's why I like to do things that are easier.

2405.25 + 5687.5 is easily 8092.75. But in both cases not using a calculator and not doing an operation on it at least twice (if it has no log) is a recipe for wtf, imo. An expensive mistake requires only one miscalculation.
It isn't easier, but 6.112cm + 14.446cm is fairly easy. Especially if you drop thousandths, which you can only maybe get when measuring with a caliper...
Inches only use base-2 fractions down to 1/64", then they switch to thousandths of an inch (thou), with base-10.
Easier to type into any general purpose calculator. It’s also so much more accurate when trying to enter into any CAD/CAM software.

It’s also easier to add up 10 different decimal numbers than the same number of mixed numbers.

Yeah, I don’t think woodworking is the best example for arguing that metric is better than imperial. In fact, it’s one of the few disciplines where the imperial system as a decent argument for superiority.
Sorry, I dabble with woodworking and disagree heavily. I usually don't care for bigger precision than 1mm (so between 1/16" and 1/32"), and adding things up is a nightmare ("umm... 7 3/16" + 2 1/8" + 5 1/4" is... where's a goddamn pen & paper..."). Same with figuring out which line is which fraction of an inch on measuring tools. Things became tolerable once I got metric measuring tape.
Once you get past the dabbling stage it starts to get pretty natural. I don't think either system is better, the value is mostly tied up with what's on the shelves at the local home center and how your measuring tools are marked.
It's already natural when using metric, so I'll stick to it.
The stuff on the shelves is rarely sized precisely enough for the units to matter. I've bought 1/4" ply that measured much closer to 6.0 mm than to 1/4".
Sure, if tools are dirt cheap you can just sacrifice to Benford's Law and use base 10. If tools are not cheap, you'll learn to use base 2, one way or another.
I doubt I'll ever be able to quickly add fractions in base-2 (it doesn't happen often enough to train this), so pen+paper will always be a necessity if I wanted to stick to imperial. I could see getting the intuition for "which line is the eights vs sixteenths" over time though, but if the one-off calculations are going to be such a pain, I don't really see a point.
Metric woodworking just uses integer millimeters for everything.
My FIL is a fine art woodworker (makes stupidly nice furniture, canoes that are functional art, etc.), and he uses both. He’s done it so long that he can work with fractions instantly in his head, but he also fully admits that metric is way easier for a lot of it, and so uses both as needed.

About the only example of imperial being easier I can think of is that the thin-kerf saw blades he buys are American, and thus are measured in inches - 1/16” to be precise. It’d be tremendously annoying to deal with 1.588 mm. If he had a 1.5 mm blade, of course, it would be the other way around.

Woodworking measurement has two forms: lumber, which is notional, pre drying, shrinkage and rough handling, and cut, which is required to be beautiful. Sometimes, it isn't about feet and inches as much as "the same"
Plumbing is another example where imperial works and is even used in Europe. It doesn't matter that a pipe is 3", it may as well be called "type B", since all you care about is if it's big enough for the purpose (you look that up in building code) and if the parts match together. The moment you need to perform calculations is when imperial becomes a total PITA to use.
Minimum radius is much more important in plumbing I think than metric/Imperial. And screw-thread.
> It’s not trivial to add up 2’13/32” + 5’11/16”, there’s too much carrying over and doubling to equalize the denominators to do easily in your head.

Seems like straight forward arithmetic, but if using a calculator is a must, the HP 35s (RPN daily driver) handles fractional calculations elegantly without being a "very specific carpenters calculator":

  2.13.32 [Enter] 5.11.16 [+]

  8.09375
...and if you wanted that decimal as fractional display instead:

  [-->] [FDISP]

  8 3/32
Or you add 6.112cm to 14.446cm, which probably even children can do in their head reliably. But sure, you can do it using fantasy units, too :)
Now change that first number from 6.112 to 6.789 and watch that same child stumble.

I've always found it curious how Europeans pride themselves in speaking their native tongue + English...except its always a cultural flame war-inciting impediment when the communication barrier involves a mere arithmetic unit conversion. Doubly ironic when most of the world is consciously aware of what the prevailing USD exchange rate with their native currency is without complaint, whereas the average American simply doesn't have a clue how many Euros a US dollar gets them.

Similarly, if the Brits want to reference weight in stone, or Canadians want to sell me lumber in board-foot, I don't find that offensive in the least; I'm of the position that the impetus is on me to understand their measure, not for the one communicating to conform to my norms.

Why would there be any stumbling? Because it's two 6s? Because there's two carries?
The child would clearly have to mentally carry four times all the way down the chain:

    11 11
    14.446
  +  6.789
  --------
    21.235
Was that available on 48g perhaps?
Unsure with the 48g; trained myself since engineering undergrad days to not lean into graphing calculators. The feature existed since at least the 32sii, so it makes sense that successor 33s and 35s models also got it. Easily one of the most useful features that I've found for woodworking and converting arcmin/sec to decimal as the most common usecases.
I know of sexagesimal mode in 48g and used it, but haven't encountered anything for imperial units
I'm not a sea dog (or air dog), but even absent electronic calculation and navigation devices of the last half century or so, is there any real advantage to using nm vs any other unit? Other than for the presumably niche case of traveling exactly directly along the equator, that is.

nm are great because charts and speeds are in units of nm and kt of course, but what does "real meaning" give you exactly?

Am sea dog, I think it's just a little bit of smugness. Because it doesn't generally help (besides quickly estimating latitudinal distance or near-equatorial distance), unless you are actually doing dead reckoning with a chart or similar, which is rare today.

The equivalency with knots is great and all but it too is just a convention

To be precise, a nautical mile is always a minute of latitude, everywhere on earth. It is only a minute of longitude at the equator.
Ah, good point. In that case expand the niche cases to traveling due north or south.
In practice, when navigating by pen and paper, what you do is you measure a distance on the chart with a divider, then you put the divider (with the previously measured distance set) to the north-south scale on the side of the chart to read out the distance in nautical miles.

Now, of course, in principle charts could have a separate scale for distances in km, and we could use km for navigation just fine. But, well, I've never seen a nautical chart with such a scale.

And, at sea level. At altitude this no longer applies either because the circumference at altitude is greater.
Well, it still applies in aviation, as distance and ground speed used in navigation are measured at sea level irrespective of altitude.
...by around 0.1%. Which is why nobody is bothering with it, considering how susceptible to wind speed distances and velocities are up there.
I think the only advantage is when using old navigation devices. You measure altitude of sun at noon and that is your latitude, time of noon is your longitude. It also only works when going east-west, it falls apart any other angle.

These days, everybody has plotter or phone to measure position and speed and calculate distances.

It fits with the other unit: 1 knot is 1 minute of latitude per hour