Nautical Units and Angles

Nautical distance and depth
Points of the compass
Old Beaufort Scale of Sea Winds

I must confess that I know nothing of sailing, so I hope that I haven't made too many mistakes in the following!

Nautical distance and depth

6 feet = 1 fathom
15 fathom = 1 shackle
10 cables = 1 nautical mile
6080 feet = 1 nautical mile
Full fathom five thy father lies;
Of his bones are coral made:
Those are pearls that were his eyes:
Nothing of him that doth fade,
But does suffer a sea-change
Into something rich and strange.

Shakespeare - The Tempest

Fathoms measure depth. They have been in use since before 1600, and may be derived from "faethm", the Anglo Saxon word for "to embrace" (because it is roughly the distance from one hand to the other if your arms are out-stretched). Tim Chafer from Germany says "The English term is related to the German term 'Faden', which is also the general term for 'thread'. A 'Faden' or 'fathom' would thus originally have been the length of rope or thread you could stretch between the hands with the arms outstretched."
It's been pointed out to me by a correspondent "This comes from the manner of using what was originally an unmarked line to find the depth. Stretch the line across the chest as the former is pulled in. For most men this distance is in the order of six feet. A useful tip when a properly marked lead line is not available.".
I've had an interesting email from Edward Welbourne with a discussion on the origin of fathom. Since it is a little lengthy, I've put it on
another webpage.
Apparently, depth to coal seams is often measured in fathoms, so it's not just used in a nautical sense. I have also been informed that "fathoms were also used in Cornish Mines. Possibly it is a measure that crossed from sea to land as if you wanted some rope to haul things up a mine you had to buy it from Ropeyards who would be supplying it to their maritime customers in fathoms and cables. Dolcoath Mine in Camborne was one of the deepest with a level at 420 fathoms or 2520 feetvertical drop. There is a local saying about a person who keeps him or herself to themselves as being 'as deep as Dolcoath'".

Nautical miles measure distance. 1 nautical mile is the angular distance of 1 minute of arc on the earth's surface. As these differ slightly (6108' at pole and 6046' at equator) 6080 was adopted (this being it's approximate value in the English Channel). The International nautical mile is 1852 metres, so is very slightly different from the UK nautical mile.

1 UK nautical mile = 1.00064 international nautical miles
Now the International nautical mile is used throughout the UK, except in the Statutory Instrument 1995 No. 1804 which defines it as 1853 metres! If you want an irrelevant fact, one minute of arc on Mars is close to a kilometre (.987 km to be more accurate). Perhaps the French who defined the kilometre were really Martians!

A correspondent complains that the original definition of the nautical mile was pretty silly. "From the definitions provided, its length would vary not only with latitude, but with the direction one is facing. For instance, at the equator a longitudinal nautical mile would differ from a latitudinal one, because the radius of curvature is three dimensional and its center would change with orientation. (the earth has a relatively constant one along its equatorial plane)." He objects to NASA describing the International Space Station orbiting at an altitude of 211 nautical miles. Surely NASA should use a more sensible unit! (Although there is now a more sensible international nautical mile.)

A knot is a nautical measure of speed, one nautical mile per hour (or about 1.15 mph). The name comes from the knots tied in the log line used with the sand glass. The log line was thrown onto the sea and the knots in the line were counted as they ran out during the sand glass interval. The knot has been used since the 17c. It is sometimes called the sea mile. Again, the international knot is very slightly less than the UK knot.
I have been told by a correspondent "The knot : Two meanings. (Ignorance of this has led many "experts" into confusing others).
(a) Unit of speed= one nautical mile per hour. This is the normal definition today and comes, of course from the use of the Ship Log with its line marked (with a knot) every 47.3 ft or so and used with a sand glass.
(b) Unit of distance = one nautical mile.
Conrad, that great stickler for correct nautical speech, uses both definitions as convenient. Context makes everything clear."

The following information is given by Dick Grindley. "A cable was originally the length of (believe it or not) a hemp cable defined by the RN (although further complicated by whether it was a rope or a hawser laid cable), the shackle came later when anchor chains started being made of lengths of a number of un-dividable links joined up at a 'joining shackle'. So an anchor cable will always be an integral number of shackles long. In chart work the cable is still in use for the simple reason that charts are usually large & when you use them you tend to fold them to get at the bit you want. Having folded them the metric linear scale is never visible (must be someone's law ?) but at either side of the chart is the latitude scale in units of mins, sub-divided into 10 (a.k.a. the cable). So, when I did my chart work training at Dartmouth (a few years ago I must admit) we quite happily mixed metric depth & height with nm & cables for distance."

The shackle has given me some trouble. I've been given the values of 12 fathoms, 12.5 fathoms and 15 fathoms (which is the correct figure) to the shackle. I am indebted to Richard Sheppard for the following information.

  • Apparently, according to a quote from a 19th Century Seamanship Manual, ships were usually equipped with 12 shackles of *bower cable* where each shackle was a 12.5 fathom length. (Perhaps this is where the figure of 12 comes from?) These 12.5 fathom lengths were joined by shackles (hence the name) and by swivel links to overcome twisting. When paying out the anchor cable, counting the number of shackles passing gave a measure of the length used.
  • In 1949, the Royal Navy switched from 12.5 fathom shackles to 15 fathom shackles.
  • In 1970, the RN Hydrographic Charts Dept. switched their Nautical Mile from 6080 feet to 1852 metres (the International NM). At the same time, their Cable became a tenth of the International Nautical Mile.
  • Modern heavy mooring chain is usually sold in 15 fathom lengths or *shots*. The specification sheets quote the number of links per shot. Much of it seems to come from the Far East!
  • Light chain can be bought in arbitrary lengths.

  • I've also been sent "a (completely useless but effective) formula for calculating the amount of anchor chain to put out in your warship: Twice the square root of the depth of water in fathoms = the number of shackles of cable. (Charts now give depths in metres)."

    The Observer newspaper had a lot of trouble with the definition of a ship's tonnage. It appears in their readers' corrections column 3 weeks running. So for everyone else, here is their final definition:
    Tonnage is a measure of the internal volume of a ship, devised as a basis for charging habour dues. It is said to originate with 'tuns' of wine, one tun being equal to 252 gallons, roughly 42 cubic feet. The modern tonnage measurement, introduced by the Merchant Shipping Act 1854, is 100 cubic feet. Gross tonnage is the internal volume of the ship and Net (or Register) is the Gross tonnage less non-earning spaces, such as engine room and crew accommodation.
    However, I've received the following correction "Tonnage of ships is a difficult subject, and now the Gross Ton (GT) actually can't be converted. It is now a formula, adopted in 1969 and applicable to all ships since 1994:
    1 GT= (0.2+0.02*logV)*V
    where V is the volume measured in cubic metres of enclosed spaces on the ship. (The logarithm is base 10.)"

    I had an email from 'an ex-Marconi seadog' who told me some nautical slang - nothing to do with units of measure but I can't resist it!
    Tab Nabs = light treats (food)
    Doby = clothes for washing - verb dobying - doby dust = washing powder.
    To put someone ON THE SHAKE = to wake them up
    Deck head survey = sleeping
    From someone who "grew up in Calcutta, India":-
    The word dobyderives from the anglicized Hindi word "dhobi" whoch means the washerman. In India, most upper-middle class and rich including the old Raj used to send their clothes out wekly or bi-weekly to the Dhobi who would wash, starch & press the clothes & return them the next day. The places on the river where they would wash the clothes are called "ghats". My birthplace, Calcutta, is itself a corruption of the vernacular Kali Ghat which was a ghat next toa very large temple of Kali.

    Points of the Compass

    Compass Most people know the four main points of the compass, North, South, East and West (see left). These are known as the cardinal points of the compass. If you can't remember which way round "West" and "East", they read "we"!

    However, there are 32 points of the compass. The best way to see this is to build it up a bit at the time. Half way between North and East is North East. This gives 8 points. The North or South always comes first, and the East or West comes second. These eight points (N, NE, E, SE, S, SW, W, NW) are known as the principal points of the compass.
    Compass Now, imagine half way between East and North East. This is called East North East. (You could think of it as East North-East).

    The single point (North, South, East, West) comes first, and the double point (North East, North West, South East, South West) comes second.

    This makes sixteen points.

    Now imagine half way between each of these points. This makes up 32 points.
    To get the name of a point like this: take the nearest single or double name (such as North East). Then describe the movement to the new point by saying 'North East by North' to go anti-clockwise or 'North East by East' to go clockwise. So, starting from N and working clockwise, the points are: N, N by E, NNE, NE by N, NE, NE by E, ENE, E by N, E etc.
    I'm afraid I'm NOT going to illustrate this!

    As you can see, this is quite complicated. Now directions are given by degrees. North is zero, and the degrees go clockwise. So East is 90 degrees, and West is 270 degrees. This has the advantage that all bearings are equally simple, but it doesn't sound so romantic.

    A correspondent sent this to me:
    "It is interesting to note that to this day, whilst circles are divided into 360 degrees and compass courses are given in degrees (example; to steerEast the course is given to steer 090) the older system of compass points is still very much used as a quick system of reporting bearings of objects relative to the 'ships head'. thus if a lookout say, wanted to report a white light roughly 45 degrees on the Starboard bow he would call out "white light four points to starboard!" As there are 32 points in a full circle this gives 8 in a quarter (in this case the Starboard beam) so four points would be roughly halfway between the bow and the beam, looking forward on that side. Very quick, and rough but the system does work - it's been in use for many years - since the days of sail, so unlike the modern idea of change for changes sake it is left well alone! Why change a system that works?"

    I have been asked about ordinal points of the compass. I don't think this is a British phrase - rather an American one. But there seem to be several possible meanings:

    I would be interested to
    hear from anyone who could explain this. It all sounds very odd to British ears, since cardinal numbers are the 'normal' numbers - one, two, three, etc. - while ordinal numbers are the numbers in order - first, second, third, etc. So I don't see how you can divide up a compass rose in this way. It does make sense to call north, south, east and west the cardinal points, since those are the main points of the compass, and 'cardinal' means 'of fundamental importance'.

    Compass Compass

    If you look at the pictures above, you may notice that West and East seem to be reversed. This is not a mistake!
    If you were walking, and used a compass to get your bearings, you could use a simple compass with a fixed indicator dial. You turn the compass round until the needle aligns with North on the indicator dial. Now you know where North and the otherpoints of the compass are in the surrounding landscape, for example "That mountain is South West of me.". If you want to go in one direction, you find a landmark in the correct direction, put the compass away, and head for that landmark. Then you find another landmark in the correct direction in the same way.
    However, if you were in some vehicle, you wouldn't want to stop to fiddle round with a compass. Moreover, if you were in a ship, there might not be any landmarks! You need to fix the compass to a surface so you could look at it without using your hands, which you need to steer with. You also need to look at it continually to steer by. However, if you have a fixed indicator dial, once you have fixed the compass, the indicator dial would always point the same way, since that it fixed to the compass! So North on the dial is always the way the ship is pointing, regardless of where real North is! This doesn't matter if you are heading North, but what would you do if you wanted to go North East? If you steered the ship so the needle pointed to North East (in the dial was the conventional way round), then you would, in fact, be steering North West! However, if you make a new dial, with West and East swopped over, then you can steer the ship by having North fixed in the direction the ship is going, and steering the ship so the needle points the direction that you want to go.
    The compass above looks like a surveying compass. Here, you aren't fixing the compass to a vehicle, but you are sighting on an object using the sight-lines (which are fixed to the body of the compass, and so to the direction of North), and using the needle to read off the direction.
    This problem is resolved nowadays by having a floating indicator dial. In these, the whole dial, with North, South, East and West on it, is magnetised, and floats in a liquid. This means that the whole dial floats round and points to North, and so the points are in the correct place without any turning of the compass. So you can determine your direction without touching the compass, and without the dial being reversed. You can easily buy these as car compasses. However, this requires a compass with a sealed container with the liquid in. Perhaps this was harder to manufacture before plastics. It may also be difficult to sight using such a compass.

    For more information about compasses, see this Compass Tutorial.

    Compass Compass

    These compasses above are more conventional. The compass on the left has a fixed dial. You can see that I haven't bothered to turn it to aligh the needle on North on the dial. The right-hand compass has a pale blue floating dial. There is a bubble of air. You can see that the red arrow points North, and that West and East are automatically in the right place. It is surrounded by a black dial with degrees, if you want to use this method instead. But these are fixed, so you would need to rotate the compass to use them. I haven't bothered to do this, either.

    See below for a reference to a compass with 400 degrees rather than 360 degrees.

    While angles are, of course, not confined to the sea, they follow on from the previous subject. There are 360 degrees in a circle (or 'full turn'). This is a useful figure, since it can be divided in many ways, so if you want to divide a round cake into 3, it's 120 degrees, 4 pieces are 90 degrees, 5 pieces are 72 degrees, 6 pieces are 60 degrees, and so on. One degree is a very small amount, but if you want something smaller, then there are 60 minutes to a degree, and 60 seconds to a minute. So there are 1,296,000 seconds to a circle!

    My father, who was a gunner in World War II, said that to estimate small numbers of degrees of direction, you stretch out a straight arm, with clenched fist, knuckles upwards. The distance between the knuckles of the first and second finger was about three degrees, while between the knuckles of the second and third, or third and little finger was about two degrees. My husband who studied astronomy, thinks that a little finger nail is about one degree if you hold your arm out-stretched.

    People use different ways to describe a direction. The compass points will only work if you know where North is. For example, on the South coast of England, they mark on the road N,S,E,W because everyone knows where the sea is, and roads tend to run along the coast, or head towards or away from the sea. I notice that a correspondent about
    paper uses North to mean the top of a piece of paper - obviously because maps are supposed to have North at the top (although I've known some that don't - very disconcerting!) But you would never describe North as straight ahead. You can say straight ahead or left or right, or perhaps 'third on the left' if you're going round a roundabout, but this won't help you if you want to give a more precise direction. A good method is to use a clockface, such as 'two o'clock', or 'half past ten'. This imagines that twelve o'clock is straight ahead. So two o'clock is 60 degrees to the right. Once explained, anyone can use this system, while degrees tend to fluster people who think they are bad at Maths! But it's not quite as simple as that. The Oxford English dictionary said that in a plane, twelve o'clock could mean directly above you, so "Bandits at six o'clock" meant enemy aircraft below you. Planes work in three dimensions! My father (see above) gives yet another meaning, as used by an observation post to guide guns firing or describe where a shot had landed. Here, twelve o'clock is north, rather than the direction that you're facing. Obviously the observation post and the gunners might be facing in different directions, but north stays as north. You use the clock system rather than the points of the compass as everyone understands clocks.

    While I am talking about direction, it is notorious that the British (and a few other countries) drive on the left of the road while the rest drive on the right. The British have a reason for this. We drive on the left, because horses travelled on the left, and the reason for this is that you mount a horse on the left, and you don't want to mount a horse in the middle of the road! And you mount a horse from the left, because if you are wearing a sword, and if you are right-handed, the sword hangs from the left hip, and if you try to mount a horse from the right, it's liable to get between your legs, which is unpleasant when you sit on the saddle. Isn't that all logical? I wonder why the rest drive on the right!

    Jesse Deane-Freeman from Australia has told me this: "I wanted to mention (because we drive on the left also) another historical reason for driving on the left which was to keep the right hand free to either shake hands (or wave) with passers by - or to engage in sword or gunplay with a passing enemy. Apparently this was a defining factor in Napoleon's conversion of captured countries to right hand driving (because he was left-handed - I am as well so I understand his reasoning!). And this is apparently another historical reason for the English and therefore Australian retention of left hand driving - because we weren't converted by the French!"

    Now Napoleon being left-handed makes sense (it was all obviously the French's fault, as usual). It doesn't explain America, unless they were being deliberately anti-British but drew the line at metric measurements! I'm not so sure about fighting. When knights on horseback jousted, they didn't pass right side to right side as you might expect, even though that side was where their spears were. They passed left side to left side, as that was where their shields were, and the shields were supposed to protect them. However, pistols would make more sense. If you were passing an enemy on the right and were right-handed, you risked putting a bullet through your horses head. But cavalry never seemed to use guns.

    Getting back to angles: In Mathematics, we meet another way of measuring angles - radians. There are 2 pi radians to a circle, where pi is the ratio of the diameter of a circle to its circumference (round its edge). It should have its own symbol, but this might not work on all browsers, so I'm not using it. It looks like a minature Stonehenge. It is a very strange number, approximately 3.1416, but however many places of decimals you write, you never reach the accurate figure of pi, and the number sequences never start to repeat themselves continually. This is called an irrational number, and pi is, perhaps, the most famous example. I am tempted to call mathematicians pretty irrational to use a unit where you not only don't get a whole number of them to a complete circle, you don't even get a rational number (or fraction)! They would defend themselvese by stating that if you cut a slice of cake with angle of one radian, then its rounded edge is the same length as its straight sides (or the radius of the original circle). There are also formulae which are easier to deal with if you use radians rather than degrees.

    Another angle unit is the mil. This is a military unit for defining angles. The name derives from milliradian, and they are used because an angle of X mils is X metres wide at a distance of one kilometre. This means that if you drop a shell 200 metres to one side of the target (according to your map) and it's 4 km away, 200 divided by 4 is 50, so you swing your aim by 50 mils. Note that current OS maps have the magnetic and grid deviations shown in mils as well as degrees. There are 6283.1853 mils in a circle, but they seem to be rounded off to various values in use, such as 6283 and 6280. However, the US military made things 'simpler' by standardizing on 6400 mils in a circle. To make things even more interesting, the Russians, and perhaps others in Europe, use 6000 mils in a circle!
    I have had the following from Ian Hooker Lt(N) British Columbia: "Mils were first used for military purposes by the German Wehrmacht during World War II. After the war, other armies started using mils instead of degrees. NATO armies adopted the German standard of rounding 6283 up to 6400. Warsaw Pact armies also adopted the system but rounded 6283 down to 6000. The relationship between width at the target, range from observer to target, and angle is described by the mil relation: a target one mil wide in your binoculars and one metre in width is one kilometre away. This relation, which is good both for range estimation and for giving corrections to artillery, is also known as the W = RM rule. Nevertheless, the W = RM rule is not exact it is just a useful approximation when using angles up to about 400 mils."

    Gradian Protractor Anyone who seriously disapproves of metric systems may be pleased to hear that the French Revolutionary lot tried to define a 'metric' angle of measurement. This was gradians, and there were 400 to a circle (so 100 to a right angle). On the right is a gradians protractor. It is in the Museum of the History of Science in Oxford. It never caught on. They also tried to define time as 20 hours to a day, and 100 minutes to an hour, with an equal lack of success. (I'm surprised that they didn't try to define 400 days to a year!)
    One of my correspondents says "Grads are still in use, albeit in a restricted range of uses. They are still used a bit in parts of Europe and were common in photogrammetry not all that long ago (aerial photo measurement work)". In fact, in scientific calculators, you are often given the choice of degrees, radians or grads, much to the bewilderment of people who have never heard of grads! Another correspondent from Stockholm says "You note that the French tried for a compass of 400 degrees. A 400 degree compass is used by people that have a hobby of running through woods from point to point. In Sweden we call it Orienteering." In Britain we call it Orienteering as well, but I think we use a conventional compass with 360 degrees.

    Dave Brennan has sent me some photos of a compass with grads. He would be very interested in any more information about it. Email me if you have anything!

    Compass Compass


    I'd be interested to know of any more comments on compasses. Here are some links to more information about collecting compasses:

    Virtual Compass Museum By Oregon Trail Mercantile

    Kornelia's Pocket Compass Guide

    Another use of angles is measuring the gradient (or grade) of a road. (This has nothing to do with gradians, by the way). The grade of a road is measured as a percentage. For instance, if the road rises 25m for every horizontal distance of 100m, the road would be a 25% grade (you have travelled 25% vertically of the distance that you travelled horizontally). This 25% grade road would have an angle of ~14 degrees from the horizontal. A 100% grade road would have an angle of 45 degrees. "
    In Britain, we used to describe a road as, for example, one in ten. This was generally described as ten units along, horizontally, and one unit up, vertically. That would be a tangent measurement. However, it was usually done as ten units along the surface of the road (which was sloping, of course), and one unit up. That would be a sine measurement, and would be easier to do, since you could measure the 'along' distance actually on the road itself. For practical slopes, sine and tangent would be very similar, so it wouldn't matter which you used! Any comments on whether this is still is use, or whether both types were used, will be gratefully received.

    A Nautical Glossary partly based on Arthur Ransome's Swallows and Amazons

    Titanic Nautical Resource Center

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