# Knot, Fathom, .... **URL:** \ **Category:** Cecil's Columns/Staff Reports\ **Created:** [September 22, 2000, 3:19pm UTC](https://boards.straightdope.com/t/knot-fathom/34143 "2000-09-22T15:19:29Z")\ **Posts on this page:** 20\ **Page:** 1
**Author:** ![Argos](https://avatars.discourse-cdn.com/v4/letter/a/c77e96/32.png) [@Argos](https://boards.straightdope.com/u/Argos)\ **Post date:** [September 22, 2000, 3:19pm UTC](https://boards.straightdope.com/t/knot-fathom/34143/1 "2000-09-22T15:19:29Z")
Whoops, Monty is in for a drubbing at the weekly staff meeting. A leauge = 3 statute miles or 483 meters?!? I’d check the numbers there. If a statute mile = 1.6093 kilometers that means a league is 4.8279 kilometers and a kilometer is 100 meters in length. I’d bet somebody dropped a zero. (Pesky editiors…) ---
**Author:** ![C\_K\_Dexter\_Haven](https://avatars.discourse-cdn.com/v4/letter/c/b2d939/32.png) [@C\_K\_Dexter\_Haven](https://boards.straightdope.com/u/C_K_Dexter_Haven)\ **Post date:** [September 22, 2000, 3:40pm UTC](https://boards.straightdope.com/t/knot-fathom/34143/2 "2000-09-22T15:40:34Z")
The Mailbag Answer being referred to is: [Knot, fathom,league, etc](http://www.straightdope.com/mailbag/mfathom.html) We’ll fix it. Thanks, Argos. This aint my week for math. [Edited by CKDextHavn on 09-22-2000 at 10:46 AM] ---
**Author:** ![Steve\_Ewing](https://avatars.discourse-cdn.com/v4/letter/s/a5b964/32.png) [@Steve\_Ewing](https://boards.straightdope.com/u/Steve_Ewing)\ **Post date:** [September 22, 2000, 6:00pm UTC](https://boards.straightdope.com/t/knot-fathom/34143/3 "2000-09-22T18:00:20Z")
…because you measure a line by passing it through your outstreched arms, length by length. A nautical mile==1 minute of latitude is used to simplify celestial navigation problems. In common use, it is equal to 2025 yards, and over practical distances we use 2000 yards==1 namutical mile. Steve (former submarine Quartermaster: [http://www.qmss.com](http://www.qmss.com)) ---
**Author:** ![TST](https://avatars.discourse-cdn.com/v4/letter/t/f6c823/32.png) [@TST](https://boards.straightdope.com/u/TST)\ **Post date:** [September 22, 2000, 6:56pm UTC](https://boards.straightdope.com/t/knot-fathom/34143/4 "2000-09-22T18:56:50Z")
While you’re fixing the Mailbag entry, you might note that since the earth is not a perfect sphere, the length of a minute of arc varies from place to place. In particular, the length of a minute of arc at the equator is known as a “geographical nautical mile” and is about 4 feet longer than the “international nautical mile”, which is the one that is 1.852 km. (And yes, I did notice that you said that these are “essentially” the same.) See [http://www.its.bldrdoc.gov/fs-1037/dir-024/\_3480.htm](http://www.its.bldrdoc.gov/fs-1037/dir-024/_3480.htm). The international nautical mile is the one used officially by the U.S. Navy. As Steve Ewing points out, a nautical mile is the same as a minute of latitude no matter where you are, so the latitude markings on on the left hand edge of most navigation charts also serve as a handy distance scale. Convenient, no? > [@](#): > > \*Originally posted by CKDextHavn \* > \*\*The Mailbag Answer being referred to is: [Knot, fathom,league, etc](http://www.straightdope.com/mailbag/mfathom.html) > > We’ll fix it. Thanks, Argos. This aint my week for math. > > [Edited by CKDextHavn on 09-22-2000 at 10:46 AM] \*\* ---
**Author:** ![tracer](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/tracer/32/20578_2.png) [@tracer](https://boards.straightdope.com/u/tracer)\ **Post date:** [September 22, 2000, 7:24pm UTC](https://boards.straightdope.com/t/knot-fathom/34143/5 "2000-09-22T19:24:30Z")
The penultimate paragraph opens with: > [@](#): > > The nautical mile is the length of one minute of arc of a great circle. A great circle is the intersection of the surface of a sphere with a (geometric) plane passing through the center of said sphere. Only problem is, nowhere in these 2 definitions can we deduce that a nautical mile is related to the size of the **Earth** , not just the size of any arbitrary sphere. I’ll bet you dollars to donut-holes that either (A) A nautical mile is defined as one minute of arc on a great circle _around the Earth_, or (B) a great circle is defined as the intersection of the surface of _the Earth_ with a geometric plane passing through the center of _the Earth_. ---
**Author:** ![Steve\_Ewing](https://avatars.discourse-cdn.com/v4/letter/s/a5b964/32.png) [@Steve\_Ewing](https://boards.straightdope.com/u/Steve_Ewing)\ **Post date:** [September 22, 2000, 10:35pm UTC](https://boards.straightdope.com/t/knot-fathom/34143/6 "2000-09-22T22:35:52Z")
I get to break out my trusty Bowditch, 1977 Ed. (the one I grew up with, not the stinky watered-down one-volume version --but I digress): “A _Great Circle_ is the line of intersection of a sphere and a plane through the center of the sphere. This is the largest circle that can be drawn on a sphere. The shortest line on the surface of a sphere between two points on that surface is part of a great circle. On the spheroidal earth the shortest line is called a _geodesic_. A great circle is a near enough approximation of a geodisic for most problems of navigation.” Inertial navigation systems and GPS might have to worry about it, but the margin of error on a chart is such that us everyday pencil-and-divider men (_real_ navigators) don’t sweat it. Steve (“Head west until you see the coast, and turn right.”) ---
**Author:** ![ignorance](https://avatars.discourse-cdn.com/v4/letter/i/8797f3/32.png) [@ignorance](https://boards.straightdope.com/u/ignorance)\ **Post date:** [September 23, 2000, 1:52pm UTC](https://boards.straightdope.com/t/knot-fathom/34143/7 "2000-09-23T13:52:43Z")
Argos\_ it would appear that those pesky-zero-dropping-editors may have had a go at your post as well, traditionally a kilometer is usually considered to be composed of 1000 meters in length (kilo --\> thousand). One day humanity may master mathematics and human communications to such a very high degree that it no longer becomes neccessary to crash a multimillion dollar spacecraft into the planet Mars as a demonstration of simplistic mathematical stupidities. Nahh, who am I trying to fool? Humanity is doomed by its very own nature. Bring on our cyborg replacements! ---
**Author:** ![bungie\_us](https://avatars.discourse-cdn.com/v4/letter/b/b38774/32.png) [@bungie\_us](https://boards.straightdope.com/u/bungie_us)\ **Post date:** [September 23, 2000, 6:14pm UTC](https://boards.straightdope.com/t/knot-fathom/34143/8 "2000-09-23T18:14:15Z")
. . . it seemed to me that you just sounded mean, Monty. ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [September 24, 2000, 5:07am UTC](https://boards.straightdope.com/t/knot-fathom/34143/9 "2000-09-24T05:07:16Z")
**ignorance** , I believe that that was **Argos\_** ’ point. He was saying that if one uses the value of the league cited in the article, then one gets that the kilometer is a hundred meters, thus converting the error into a more familiar form, so that the rest of us could recognize it. ---
**Author:** ![ignorance](https://avatars.discourse-cdn.com/v4/letter/i/8797f3/32.png) [@ignorance](https://boards.straightdope.com/u/ignorance)\ **Post date:** [September 25, 2000, 1:52pm UTC](https://boards.straightdope.com/t/knot-fathom/34143/10 "2000-09-25T13:52:38Z")
Thank you **Chronos** for clarifing my error for me, I’m apparantly self fulfilling my chosen nick in record time 😃 A difference for me in “intercultural perceptions”, if there had been a question mark placed after the word “length” in the OP, or if the number 1000 replaced the number 100 I would have understood Argos\_'s meanings precisely. Anyway, I do appreciate the intended meaning of Argos\_'s words _now_. However, something I’ve just never been able to begin to understand about the society of the USofA, why cling onto such an old fasioned and (seemingly to me) awkward system of measurement as the British imperial system? Afterall, didn’t the people of the USofA sensibly kick the English Crown out centuries ago? Having lived in a metric system using society all my life I find the metric system units of measurement so logically simple, self explanitary and easy to use that I’ve never comprehended why the USofA didn’t choose to make the change from the British imperial measurement system to the metric measurement system decades ago. Politics perhaps? (Politics, the ultimate expression in human evil and contempt for human rights?) If a “metric vs imperial debate” has been well covered in a thread or threads, would someone kindly point me in the direction of that (those) thread(s) so that I may more easily continue to further explore and expand my own **ignorance** in these matters? Thank you. ---
**Author:** ![tshirts](https://avatars.discourse-cdn.com/v4/letter/t/839c29/32.png) [@tshirts](https://boards.straightdope.com/u/tshirts)\ **Post date:** [September 26, 2000, 5:22pm UTC](https://boards.straightdope.com/t/knot-fathom/34143/11 "2000-09-26T17:22:07Z")
Don’t hold your breath on US metrication. People pretend it’s a new thing, but I had to learn it in elementary school (in 1954, I believe). When Sweden switched to the right hand side of the road, it seemed all the world was headed toward international standards in everything. When Jimmy Carter put kilometer signs out on a few interstate highways, I was heading a corporate panel on how we would make the transition when (not if) the military went metric, to increase it’s comonality with armaments partners. Now 30 years after that, we’re back to the random question like yours. I’d like to see it come (having used metric when I lived overseas), but I expect it’s still going to inch along, one industry at a time. 2-leter bottles, metric autos, wedding rings weighed in grams. And 40 years from now we’ll still have 8"x10" glossy photos. ---
**Author:** ![Chance\_the\_Gardener](https://avatars.discourse-cdn.com/v4/letter/c/eada6e/32.png) [@Chance\_the\_Gardener](https://boards.straightdope.com/u/Chance_the_Gardener)\ **Post date:** [September 27, 2000, 9:09pm UTC](https://boards.straightdope.com/t/knot-fathom/34143/12 "2000-09-27T21:09:44Z")
Ugh, the lack of conversion here is so depressing! I drove through Maine last month where the highway signs on I-95 actually do provide distance in miles and kilometers (though the speed limit is still in the old imperial system.) I heard that some highways on the Mexican border also have combined signs, but I’ve never been out there so I wouldn’t know for sure. I heard that certain interstates in Alabama had metric signs on them which were removed just this year. Get ready for the great leap backward… ---
**Author:** ![sailor](https://avatars.discourse-cdn.com/v4/letter/s/a587f6/32.png) [@sailor](https://boards.straightdope.com/u/sailor)\ **Post date:** [October 1, 2000, 6:31am UTC](https://boards.straightdope.com/t/knot-fathom/34143/13 "2000-10-01T06:31:55Z")
Well there are two threads discussing the same thing so I feel obligated to correct the same error in both. TST said: As Steve Ewing points out, a nautical mile is the same as a minute of latitude no matter where you are Not true. Only an approximation. Because of the shape of the earth, a minute of latitude is not the same length everywhere as it diminishes as you go from the equator to the poles. Length of a degree of latitude: ```auto latitude: meters: 90 1848.9 45 1852.3 0 1855.4 ``` The nautical mile was defined as 1852 m which is a good average value but NOT the value of a minute of latitude at the equator or any other specific place. ---
**Author:** ![RM\_Mentock](https://avatars.discourse-cdn.com/v4/letter/r/e274bd/32.png) [@RM\_Mentock](https://boards.straightdope.com/u/RM_Mentock)\ **Post date:** [October 1, 2000, 12:54pm UTC](https://boards.straightdope.com/t/knot-fathom/34143/14 "2000-10-01T12:54:11Z")
> [@](#): > > \*Originally posted by sailor \* > \*\*TST said: As Steve Ewing points out, a nautical mile is the same as a minute of latitude no matter where you are > > Not true. Only an approximation. Because of the shape of the earth, a minute of latitude is not the same length everywhere as it diminishes as you go from the equator to the poles. \*\* I think Steve Ewing and TST were making distinctions between geographical nautical miles, and international nautical miles. But, the length of a minute of latitude _increases_ as you go from the equator to the pole. ---
**Author:** ![sailor](https://avatars.discourse-cdn.com/v4/letter/s/a587f6/32.png) [@sailor](https://boards.straightdope.com/u/sailor)\ **Post date:** [October 1, 2000, 4:21pm UTC](https://boards.straightdope.com/t/knot-fathom/34143/15 "2000-10-01T16:21:35Z")
RM Mentock, not t try to pick an argument but I don’t see it so I would ask you to explain. The complete quote I was referring to: [quote] As Steve Ewing points out, a nautical mile is the same as a minute of latitude no matter where you are, so the latitude markings on on the left hand edge of most navigation charts also serve as a handy distance scale. Convenient, no? [quote] My reply is that a **nautical mile** is definitely NOT the same as a minute of latitude no matter where you are. I thing the quote is unequivocal in the meaning. The length of a minute of latitute **increases** as latitude increases? Wouldn’t this require the radius of the Earth to increase also? AFAIK the equatorial radiaus is larger. Can you explain both points to me? ---
**Author:** ![sailor](https://avatars.discourse-cdn.com/v4/letter/s/a587f6/32.png) [@sailor](https://boards.straightdope.com/u/sailor)\ **Post date:** [October 1, 2000, 4:24pm UTC](https://boards.straightdope.com/t/knot-fathom/34143/16 "2000-10-01T16:24:36Z")
Shoot. I should have used preview. My last post has several mistakes. Oh, well, I hope it’s unerstandable. ---
**Author:** ![sailor](https://avatars.discourse-cdn.com/v4/letter/s/a587f6/32.png) [@sailor](https://boards.straightdope.com/u/sailor)\ **Post date:** [October 1, 2000, 4:40pm UTC](https://boards.straightdope.com/t/knot-fathom/34143/17 "2000-10-01T16:40:22Z")
I should have also given this a minute’s thought before posting. I feel especially sheepish because of everybody _I_ should know this well. Those values I posted of a minute of latitude I calculated using the radius of the earth at that point. Now I realise that as the earth flattens you need to go a greater distance to have the meridian horizon depress by one minute. So, YES, the numbers I supplied are NOT valid (and I do not have any way right now of ascertaining the different lengths of a minute of latitude). Regarding the other part of the post. I still believe a nautical chart’s latitude is suppossed to represent latitude and not nautical miles. It is useful in that they are pretty much equivalent (especially at mid latitudes). ---
**Author:** ![sailor](https://avatars.discourse-cdn.com/v4/letter/s/a587f6/32.png) [@sailor](https://boards.straightdope.com/u/sailor)\ **Post date:** [October 1, 2000, 6:44pm UTC](https://boards.straightdope.com/t/knot-fathom/34143/18 "2000-10-01T18:44:21Z")
OK, after some research I foundthe extreme values of a minute of arc are 1842.9 m and 1861.7 m which means the extreme values deviate from the definition of NM by about 0.5% This, of course, would be insignificant when working on a paper chart, and in mid-latitudes the difference would be _much_ smaller. As a matter of precision and definition though, contrary to what was posted, the fact remains that a nautical mile is _NOT_ the same as a minute of latitude no matter where you are. ---
**Author:** ![sailor](https://avatars.discourse-cdn.com/v4/letter/s/a587f6/32.png) [@sailor](https://boards.straightdope.com/u/sailor)\ **Post date:** [October 2, 2000, 7:19am UTC](https://boards.straightdope.com/t/knot-fathom/34143/19 "2000-10-02T07:19:33Z")
Just to clarify further. The mail bag says > [@](#): > > The nautical mile is the length of one minute of arc of a great circle. A great circle is the intersection of the surface of a sphere with a (geometric) plane passing through the center of said sphere. The Equator is one great circle, so essentially a nautical mile is the the length of one minute of arc on the Equator. When the correct definition of the NM is 1852m (which equals approximately one minute of latitude at mid latitudes but definitely not at the equator) the definition given here [http://www.unc.edu/~rowlett/units/dictN.html](http://www.unc.edu/~rowlett/units/dictN.html) is correct but only sort of. Read it carefully and you will see the inconsistency. ---
**Author:** ![RM\_Mentock](https://avatars.discourse-cdn.com/v4/letter/r/e274bd/32.png) [@RM\_Mentock](https://boards.straightdope.com/u/RM_Mentock)\ **Post date:** [October 2, 2000, 7:33am UTC](https://boards.straightdope.com/t/knot-fathom/34143/20 "2000-10-02T07:33:53Z")
> [@](#): > > \*Originally posted by sailor \* > My reply is that a **nautical mile** is definitely NOT the same as a minute of latitude no matter where you are. I thing the quote is unequivocal in the meaning. > > The length of a minute of latitute **increases** as latitude increases? Wouldn’t this require the radius of the Earth to increase also? AFAIK the equatorial radiaus is larger. > > Can you explain both points to me? **First point** : “Nautical mile” has many definitions (my American Heritage Dictionary mentions two explicitly), so its use cannot be truly unequivocal. Context has to be considered. As you’ve since posted, the difference is small anyway as far as practical use is concerned. That’s why TST called it a “handy distance scale,” though it might be off by half a percent. We have to be careful not to use the longitude scale the same way. **Second point** : The definition of latitude is the crux. It is _not_ the angle made by the straight line to the center of the earth, as one might suppose. It is the angle made by the vertical to the earth’s ellipsoid. The second definition is used instead of the first because the second definition is what is measured by a sextant, approximately (dang, the more you know about it, the more weasel words you have to use). In short, a minute of latitude is longer at the poles because the earth is flatter at the poles–you have to go farther before the angle of the surface changes. I included [this link](http://www.uwgb.edu/dutchs/cosnotes/shapew2.htm) in that [other thread](http://boards.straightdope.com/sdmb/showthread.php?postid=777934#post777934). It has some discussion of latitude in the section labeled **Finding the Exact Shape of the Earth** , and diagrams (the green ones!) that illustrate what we’re talking about. [Another webpage](http://www.svanstein.se/maupertuis/data.htm) describes the debate, centuries ago, about the Newtonian gravitation theory and the Cartesian vortex theory, which was finally settled by determining whether the length of a minute increases or decreases as you go to the pole. [Next page](https://boards.straightdope.com/t/knot-fathom/34143.md?page=2)