I had heard of the term ‘nautical mile’ and also of the term ‘knots’ but had no idea where they came from, only that they were terms used by aircraft pilots and seafarers. I knew that a nautical mile was a little longer than a standard mile (one nautical mile is now defined as exactly 1,852 meters or 1.151 miles) while a knot is just one nautical mile per hour. Why we still used two units of distance and speed that were so close to each other was unknown to me. I assumed that nautical miles and knots were retained for sentimental reasons.
But I have learned that those units have an interesting meaning and practical use in that one nautical mile originally was defined as one minute of latitude. If one takes the circumference of the Earth and divide it by 360 degrees (the number of degrees in a full circle) and then again by 60 (the number of minutes in a degree), the number that you get is one nautical mile. So by knowing the difference of two latitudes in degrees, one could immediately calculate the distance between them along a great circle (i.e., following a line of longitude) in nautical miles by multiplying it by 60.
One could do a similar calculation for the distance between two points on the Earth that are at the same latitude except that that works only at the equator since the lines of longitude converge to meet at the poles. That can be taken into account by multiplying the result by the cosine of the latitude angle.
Readers might be wondering why I seem to be so fascinated by such esoteric information. It is because occasionally I need to have an estimate for the circumference of the Earth and would need to look it up. But now I can calculate it in my head by taking 360 degrees and multiplying is by 60 to get the circumference in nautical miles. Since 360×60 is just 63x100, and since 63=216, that immediately gives me 21,600 nautical miles. The value in regular miles would be just 15% more.
The meter was originally defined also in terms of the Earth’s size in that in 1791 the French National Assembly gave it as “as one ten-millionth of the distance from the equator to the North Pole along a great circle, so the Earth’s polar circumference is approximately 40000 km”. But somehow that is not as easy to remember.
In this day and age where most factual information is just as far away as your phone and can be obtained in seconds, this ability to get an estimate for the Earth’s circumference in one’s head is utterly redundant. But I am old school and there is something appealing to me about information that can be obtained by reasoning rather than by looking it up.
Maybe the more interesting thing here is how individuals remember things like this. To me, 25,000 is sort of a “nice” round-ish number, and it is stuck in my head as the Earth’s circumference in (statute) miles. This is reinforced by the fact that there are 24 effective* time zones around the globe (for our 24 hour day). At the equator, each time zone is about 1000 miles wide on average (another nice round number). Further, where I live (NY state with a latitude of 43 degrees), that means that the average width of a time zone is about 700 miles (cosine 45 is 0.707, a number any electrical engineer has memorized). Thus, I can easily approximate the variations across a given time zone regarding sunrise, sunset, solar noon, etc. so long as a I know the east-west separation distance.
*In reality, there are more than this as not all time zones are “one hour wide”. Living where I do, the first thing that pops into mind is Newfoundland Time which is “out of phase” by 30 minutes (e.g., if it’s 7 AM here, it’s 8:30 AM Newfoundland).
There is also another connection between km and NM.
The metric system is built on powers of ten. Right angle was defined as 100 “new” degrees, each divided to 100 “new” arc minutes. km is one “new” arc minute. Therefore the distance from Equator to pole was 10000 km.
Since NM is one “old” arc minute, the length of the Equator is 21600 NM = 40000 km, or 54 NM = 100 km.
jimf @1:
And in the spirit of the OP, let’s not forget the nautical time zones the names of which are just the letters of the English alphabet except J.
Z (called “zulu” in radio-speak) is the 15° centered on the prime meridian, then A to I and K to M eastbound, and N to Y westbound. M and Y are the same 15° but separated by the international date line.
The zones bulge in and out near land to match national time zones. For example, Z bulges west quite a bit to include Iceland which observes UTC year-round.
Oops, the bulges I mentioned in my last paragraph aren’t shown on the drawing I linked to; but the zones are sometimes drawn with the extensions.
“At the equator, each time zone is about 1000 miles wide on average”
Or, put another way… The earth rotates at a thousand miles an hour (at the equator).
A French scientific expedition travelled to north Scandinavia in the 18 century to measure how much the Earth is flattened at the poles and thus define the length of the meter.
On the way back, they stopped at an estate in my town (Umeå) to calculate a first approximation of the result. It was the same house Linnaeus rested in on his journey to Lapland. Unfortunately, it perished when the Russian army burned down the town during the war of 1808.
sonofrojblake @ 5
Yes, the rotation is ca. 450 meters per second at the equator.
This is why the team of the
podcast “God Awful Movies” had great fun at an Islamic film titled “Day When Sun Rises In the West, Film That Shock (sic!) the World”.
For the sun to rise in the west, the rotation would first stop, killing everyone on the surface. Then -- without the centrifugal pseudoforce from the rotation -- the oceans would flow to the poles. Finally -- as the world started to rotate in the opposite direction -- everyone would get killed once again.
As they commented “it is hard to see how that would work in a physics context”.
Other inadvertently funny films include those claiming to prove the Earth is flat.
Or the ‘documentaries’ from “Goop”. And don’t make me start with the “Breatharians” (‘you really don’t need food to survive’).
For some reason, I can never remember that the distance from the equator to the North Pole is 10 million meters, but I find it easy to remember it is 10,000 kilometers.
I thought everyone knew that the Equator was 21 600 nautical miles around by definition, because each one was a minute of arc around the Equator, and the metre was originally defined as 1 / 10 000 000 of the distance from the North Pole to the Equator following the Great Circle through Paris? And if the Earth’s radius is about 6370 km (a multiple of 7, for reasons instantly comprehensible to us but perhaps less so to today’s youngsters), then its circumference is going to be somewhere about 40 000 km.
bluerizlagirl @9: Why would the radius in km being (approximately) a multiple of 7 be instantly comprehensible? It’s not to me. And I’m no youngster!
Oh, OK. 7π is very close to 22.
For me, the roundness of a number does not necessarily make it memorable. But knowing something specific, like that a nautical mile is one minute of arc, makes it easily retrievable.
The comments are wondrous!
So few people and so many ways of ‘intuitively’ ‘obviously’ ‘understanding’
how the surface of a 3-dimensional … works!
there are about πx10^7 seconds in a year. that is an easy number that i remember.
when i used that in a lab i was teaching, a student asked why it wasn’t exactly π.
i replied it’s because the earth’s orbit isn’t quite circular.
Robbo @14:
How do you think that works? The second is defined via the (synodic) rotation of the Earth. But since the Earth and Sun are not tidally locked, it has nothing to do with the length of a year, or the shape of Earth’s orbit.
Last year for some reason I felt compelled to work out that here, at ~30°N latitude, we spin around at about 900 miles per hour.
Trying to really grasp that velocity scared me enough that I couldn’t sleep that night.
@15, Rob Grigjanis
i was messing with my students. i let them know it was just a coincidence.
i also pulled this on them:
solving a physics problem for them on the board. got the final equation, plugged in the values and got 16/64.
i said, now you cancel the 6 in the numerator and the 6 denominator and you get 1/4 for the final answer.
a hush went through the class…then someone said “can you do that?”
i said nope. but it worked this time!
@14 Robbo
There are twelve seconds in a year: January 2nd, February 2nd,…
I’ll show myself out….
@18, randomboy
lol.
Robbo @17: Thing is, over the years I’ve read comments about physics on FtB that were much sillier than that, and obviously meant in earnest. How does one tell?
I think my favourite coincidental equivalence is that the kinetic energy of a ten-tonne truck at 60mph (that’s 96 km/h in civilised countries) is about a kilowatt-hour.
If the truck weighs 10 000 kg. and is travelling (60 * 1609.344) metres in 3600 seconds, that’s 26.8224 metres in one second. So the total kinetic energy is half the mass times the speed squared = 3 597 205.7088 Joules!
Which is almost scarily close to 3600 seconds in an hour, times 1000 for the kilo- prefix.