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Latitude, longitude and chart datums

Peter Boyd 07 January, 2006 12:35:00

For thousands of years mariners used the position of the sun in the sky and the position of the stars at night to calculate how far north or south they were, but they had no means of calculating their position east or west. It was not until the 18th century that a ship's position east or west could be calculated at sea and this was through the lifetime's work of the humble English clock maker, John Harrison who triumphed over an arrogant and prejudiced scientific establishment to solve the problem of calculating longitude at sea. So in the five and a half thousand year history of maritime navigation, it is only in the last 250 years or so that mariners have been able to calculate in two dimensions where they are on the surface of the earth.

We have come a very long way since John Harrison's day. Through the technology of the Global Positioning System, (GPS), we can now determine our position on the earth's surface to within a meter or so of where we stand. However, even with such powerful technology at our disposal interpreting it and using it properly still requires a sound knowledge of the basics of latitude, longitude and chart datums, and that is what this article is all about.

LATITUDE

latitude.jpg
Latitude
Latitude gives your position north or south of the equator, and the equator is the line of zero degrees latitude. Positions above the equator are referred to as north or plus latitudes and positions below it are knows an south or minus latitudes. Lines of latitude are equally spaced from the north pole to the south pole and one degree of latitude is therefore the same distance on the ground at any point on the globe, and this distance is 60 nautical miles. This means that one degree of latitude in, say, Iceland and one degree of latitude at the equator both measure 60 nautical miles on the ground. Because lines of latitude are equally spaced from north to south poles, they are often referred to as parallels, and you may see or hear a latitude referred to by its number, such as the 39th parallel.

LONGITUDE

longitude.jpg
Longitude
Longitude gives your position east or west of a line drawn from the north pole to the south pole through Greenwich in The Untied Kingdom, and this is the line of zero degrees longitude, or The Prime Meridian. Positions to the east of it are known as east or plus longitudes and positions to the west of it are known as west or minus longitudes. Because lines of longitude get closer together the further north or south you go, one degree of longitude will translate to a different distance on the ground depending on how far north or south you are. For instance, one degree of longitude in Iceland is approximately 26 nautical miles, whereas one degree of longitude on the equator is approximately 72 nautical miles.

EXPRESSING YOUR POSITION IN LATITUDE AND LONGITUDE
One degree of latitude or longitude is divided into 60 minutes, and one minute of latitude or longitude is divided into 60 seconds. Usually, the context of any written or spoken discussion makes it clear that the minutes and seconds being discussed are angular minutes and seconds and not minutes and seconds of time. However, if there is any doubt, then the minutes and seconds in a mapping sense must be referred to as minutes or seconds of arc.

This means that the latitude and longitude of a position on the earth's surface can be expressed in 3 different ways, as follows:

1. Degrees and decimal degrees as in 50.0846 degrees North, 005.3175 degrees West
2. Degrees, minutes and decimal minutes, as in 50 degrees 05.096 minutes North, 005 degrees, 19.031minutes West.
3. Degrees, minutes and seconds as in 50 degrees 05 minutes 5.76 seconds North, 005 degrees 19 minutes 1.86 seconds West.

As explained earlier, the word north could be replaced with a + sign before the degrees, and the word west could be replaced with a - sign before the degrees. In either event, each of these three positions is exactly the same point on the surface of the earth just expressed in a different way. (In fact it happens to be the position of the author's boat on its mooring!). The convention for maritime navigation is to express your position in the second way above, namely, in degrees, minutes and decimal minutes, and if you are asked by the coast guard to give your boat's position over the radio, they will expect you to give it in that format. So if you were reading the position at 2. above over your radio to the coast guard you would say, "My position is five zero degrees zero five decimal zero nine six minutes north, zero zero five degrees one nine decimal zero three one minutes west".

LONGITUDE AND TIME
The earth rotates through 360 degrees every 24 hours and therefore through 1 degree every 4 minutes in a west to east direction, that is, counter-clockwise looking down on the north pole. This means that the sun 'rises' in the east, so people to the east of Greenwich see the sun rise before people at Greenwich and are therefore ahead of them in time. Thus every degree of longitude east of Greenwich, UK, is 4 minutes ahead of Greenwich time, and every degree of longitude west of Greenwich, UK, is 4 minutes behind Greenwich time. This is why positions west of Greenwich are known as minus longitudes and those east of Greenwich known as plus longitudes. Big countries like The United States of America and Russia must have time zones to cater for their time differences east to west. North America spans about 105 degrees of longitude and therefore has a time difference between the furthest point east and the furthest point west of around 7 hours. Russia spans nearly 150 degrees of longitude and therefore has a time difference east to west of around 10 hours. Because of this North America has 3 time zones going east to west and Russia has 11 time zones east to west. The UK spans only about 10 degrees of longitude, so we don't worry too much that the folks of Great Yarmouth see the sun rise 40 minutes before the folks of Enniskillen, whilst the folks of Enniskillen are quite happy, I'm sure, to have 40 minutes more of the sun before it sets than the folks of Great Yarmouth. So the UK does not bother to have time zones, and all clocks and watches in the UK read the same time.

CHART DATUMS
Having said all that, you would think wouldn't you that any fixed point on the earth's surface would have just one latitude and one longitude to describe where it is. Sadly this is not the case. It is hard to come up with an analogy which demonstrates the business of datums, but this is the best I can do. Get two sheets of A4 paper, line them up exactly and with the tip of your pencil punch a small hole through both sheets. Now give one of these sheets of paper to a helper and ask them to go into another room and divide the page into squares by ruling vertical and horizontal lines on it. You do the same with your sheet. Now call your helper back and ask them to tell you how many horizontal lines up from the bottom and how many vertical lines in from the left edge their punched hole is. I guarantee that your helper's punched hole will be a different number of lines up from the bottom and in from the edge than yours. Why? because you each drew your vertical and horizontal lines with different spacings. The hole is in exactly the same place on the sheet of paper, but you each describe it as being in a different place depending on how you have divided your page into squares. You both have different DATUMS, and this is the problem.

Replace the piece of paper in that analogy with the earth's surface and there are literally hundreds of different datums in use to record the position of a point on it. Sad, but true! Different countries have their own datums in which their country is mapped and if you have a GPS unit there are dozens of selectable datums pre-loaded into it so that the unit can be used anywhere in the world to match up with the maps and charts produced in that country to the county's own datum. If you are using your GPS unit in Australia, for instance, you will need to set it to the Australian ADG66 or ADG84 datum to match Australian-produced maps and charts, if you are in the USA you would probably be using maps and charts in the NAD83 or NAD27 datum to which your GPS unit must be set to match up with them. In the UK most maps and charts are in Ordnance Survey (OS) datum and in order to match your GPS unit to OS maps you would have to set it to OS datum.

There is a light at the end of this tunnel, however. In 1984 a world geodetic survey was published and it is now possible to produce maps and charts of the earth's surface to one common datum, which is abbreviated to WGS84. Many countries are in the process of converting their country's maps and charts to WGS84 datum, and the UK Admiralty have embarked on doing this for UK maritime charts which are currently in the OS datum. The trouble is that at the moment we are in an interim situation with some charts and maps being in local datums and some in the common WGS84 datum. It is therefore necessary to be VERY careful how you use paper maps and charts with your GPS unit because the difference between different datums can be as much as several hundreds of metres, which at sea could be disastrous in terms of navigation and collision avoidance, to say nothing of not being able to find all those fishing marks you have just spent half the day entering into your GPS unit.

So the golden rule is this: if you are transferring latitudes and longitudes to your GPS unit from another source make sure that your GPS unit is set to the same datum as the source from which the you are transferring the latitudes and longitudes. If the source is a paper map or chart, look for its datum and set your GPS to the same datum before you enter the latitude and longitude. If it is a friend being kind enough to give you his favourite fishing mark, you must push your luck and ask them what datum it is in. This also works the other way round, of course. If you transfer latitudes and longitudes from your GPS unit to a paper map or chart then the GPS unit must be set to the datum of the map or chart. Luckily technology takes over after this because once you have transferred a latitude and longitude into a GPS unit with the GPS set correctly to the datum of the map or chart from which the position came, then you can change the datum of the GPS unit as much as you like and the unit will automatically convert the latitude and longitude you entered to the new datum.

GPS ACCURACY
Those of us with GPS units on our boats will notice that when the unit is set to the degrees, minutes and decimal minutes format it gives a readout to 3 decimal places of minutes in both latitude and longitude, as in the position at 2. above. This means it is expressing latitude and longitude to one thousandth of a minute of arc in each case. It was explained earlier that one degree of latitude is 60 nautical miles, which means that one minute of latitude is one nautical mile and since one nautical mile is 1850 metres, your GPS unit is giving your latitude position to an accuracy of 1.85 metres. Longitude is a different matter because, as explained earlier, the distance of one minute of longitude on the ground depends on how far north or south you are. In the case above, where the latitude is 50 degrees north, one degree of longitude is approximately 39 nautical miles. So one minute of longitude at 50 degrees north is one 60th of 39 nautical miles, or about 1203 metres. Therefore, at latitude 50 degrees north your GPS unit is giving your longitude position to an accuracy of 1.2 metres

JOHN HARRISON
So there you have it, a brief look at latitude, longitude and chart datums, but I must end this article where I began it, with that truly remarkable man John Harrison. In 1714 the British Parliament had offered a generous reward to anyone who solved the problem of calculating longitude at sea, and Harrison devoted his life to that solution. His extraordinary story is told in the film Longitude which tells the story of the 40-year struggle of John Harrison, played by Michael Gambon, to solve the elusive problem of measuring longitude at sea all the time having to fight the arrogance and bigotry of The Royal Society. The film interweaves this story brilliantly with the struggle some 200 years later of the of shell-shocked British Navy veteran Rupert Gould, played by Jeremy Irons, to restore the glorious clocks that Harrison had built. Like Harrison, Gould is the most admirable of obsessives but also like Harrison, he risks his health and his marriage to accomplish his difficult task. If you have had enough interest in the subject to read this article I urge you to go to your video shop and hire or buy a copy of the film Longitude and watch it to appreciate just how much we who go to sea in boats owe to that extraordinary man John Harrison.