Orienteering in Jamaica
|An Excerpt from a Workshop on Map-reading and
Orienteering in Jamaica|
The following are my prep notes for an Orienteering Workshop conducted at the Windsor Research Centre in Trelawny, Jamaica, from Nov 25 - 29, 2002. I served as one of the instructors. The participating organisations were the Forestry Dept, the JCDT and the Institute of Jamaica. A full report on the Workshop, by S. E. Koenig, can be found here. Further information on Jamaican datums is available via the Maps and GIS page.
R. S. Stewart
Good day everyone.
I’ve been asked to help with this course on map reading and orienteering. My purpose in being here is to share with you the techniques for using one of these, (hold up topo map), and one of these, (hold up compass), to do two things: To find your way around a forest, off-trail, without getting lost and to be able to locate a place when you’ve been given coordinates or a had a location marked on a map, figure out the best route there and back and do it all without getting lost. You’ll also be learning a lot of other things, but I hope I can at least leave you with those two skills.
I believe the intention is to have you put what you’ll learn to a real-world test later in the week… I suspect that once you’ve figured out how to do it, you’ll be surprised at how easy it actually is to do, and that you’ll also get some enjoyment out of knowing you can go anywhere out there, (wave at cockpit), without needing a trail to follow.
My background in this goes back first to hiking trips I’d take out through the bush in Canada… sometimes looking for good cliffs to climb, sometimes just looking around. Early on I got a compass, and maps for areas where I hiked, and figured out how to make what I saw, as I went along, match up with what was on the map. Back in ’87, when I first had a good look at the Cockpit, I could see how easy it would be to get lost out there… The first chance I had after I got back to Canada I hunted down copies of the Jamaican topo maps.
Since about ’95 I’ve been coming down a lot more often, mostly to find and explore caves. A lot of what you’ll be learning is stuff that I’ve had to use while I’ve been hunting for caves and a lot of that has been done in the Cockpit. At first it seems impossible because of all the hills… but it’s entirely doable without one of these, (hold up GPS), just with these, (hold up map and compass).
ELLIPSOIDS, GEOID, DATUMS
But before we get to the compass, we’re going to start with maps, that is, what they are, what they tell you, and how to read what they have to tell. I’m going to discuss the "what they are" then Michael Shwartz is going to take over for a while to discuss "what they can tell".
As most people know these days, the world is round, (hold up ball)… there’re a few holdouts but most of us are on side. What a lot of people don’t know is that it isn’t a perfectly round ball, it’s a squished ball, (flatten ball), and a bumpy one too. The reason it’s not round, but oval, is because it spins. If you’ve ever been on a ride that goes round in circles you’ll have felt what makes the earth oval; the official name for that effect is Centrifugal force. Because the Earth spins it makes the planet wider at the middle than it is from top to bottom. The line from top to bottom, right through the centre, that it spins around is called the Polar Axis. The line that runs around the outside halfway between the Poles is called the Equator. The distance from one side of the Earth to the other is more at the Equator than it is from pole to pole.
Another name for Oval is Ellipse. If it’s an ellipse in 3 dimensions, we call it an Ellipsoid, one of these, (hold up ball). This shape, the ellipsoid, is the basic model for our maps of the planet Earth. It’s true that if you’re just driving to Coxheath for a pack of Craven A’s it doesn’t matter if the Earth is a big sphere, a big ellipsoid or perfectly flat. When we want to make a map though, it becomes very important, the shape does, if we want the map to be right for a very large area like all of Jamaica.
Now, for a long time it was very tricky figuring out just how squished the ball is, what shape of Ellipsoid. Every person who tried to figure it out came up with a different shape, some wider, some not so wide. Eventually satellites came along and cleared up the situation quite a bit. The official Ellipsoid that all other older maps are compared to is called World Geodetic System 84, WGS84. That’s the one the GPS uses. WGS84 is the world standard. This model, the WGS84 Ellipsoid is part of what’s called a Datum, the Datum being the shape that a particular map is based on. The WGS84 Datum is just the ellipsoid, nothing else but a big squished ball. All other Datums are one ellipsoid or another with another set of definitions that tell where the centre is compared to WGS84. If the Datum has the same point in the Earth as its centre as WGS84, we call it Geocentric. If it doesn’t, we say that it is not Geocentric. We’ll get back to Datums in a little while.
You might remember me saying that the Earth is not only squished, but bumpy too. We’re going to get to the bumpy part now. It’s going to sound a bit confusing, but this is probably the hardest part of what you have to learn, so if you can follow this, you’re going to follow everything that comes after...
We’re going to discuss the GEOID.
Now, the thing that keeps us all on this rotating ball is, of course, gravity. Gravity sucks, as they say. The Earth has a lot of mass, weight if you like, and this attracts other masses, like us. The Earth though isn’t nice and smooth and steady in its weight, its mass, all through the planet. In places like mountains, there’s more mass, in oceans there’s less. That mass is what causes gravity, so the amount the Earth pulls you down changes from mountain to ocean. It also causes the sea to be pulled down differently from place to place. Now, sea level is what we use to measure height from. The sea level height is what we call the Geoid. Because of the differences in gravity from place to place, the Geoid is different than the WGS4 Ellipsoid, different from all the Ellipsoids, our models for all the maps. In Jamaica, it’s 15 m lower than WGS84. Where I live in Canada, it’s 20 m above. A good way to envision it is to imagine a circle, right around the Earth, that cuts canals through the continents and islands so that you have a giant ring of water, all at sea level. That ring isn’t our nice oval… in places it’s higher, in places it’s lower. Where it goes through Jamaica, the sea level is 15 m lower than the WGS84 Ellipsoid. WGS84 heights here would have the supposed sea level 50 feet higher than it is. This would make a map that listed elevations according to WGS84 out that much from true sea level, the Geoid. This obviously won’t be any good so what we need is a different Datum that has sea level at the right height. Ideally it would show the horizontal positions in the right spot and just compensate for elevation, just have a set of values to adjust for sea level height but be the same side to side and have north in the same direction as WGS84. Unfortunately, most Datums in use are based on old ellipsoids that have dodgy offsets and they often shift positions in all 3 directions compared to WGS84.
The Datum that the Jamaican government decided on is called JAD69. That’s what the 1:50,000 Jamaican Metric Grid maps use.
JAD69 is a modification of an older Datum based on an Ellipsoid called Clarke1866. It was determined by a man named Clarke in 1866 and is used for a lot of Datums around the world. It isn’t as accurate as WGS84, meaning it doesn’t show the true shape of the Earth as well as the much newer satellite one, WGS84, but if you take Clarke1866, and move it around a little it fits the surface of Jamaica pretty good. The centre of Clarke1866 and the centre of WGS84 don’t match up, that is, we say that the JAD69 Datum isn’t Geocentric, meaning that the centre of the ellipsoid isn’t at the centre of the Earth. This is the way a lot of Datums adjust for the Geoid difference and can work really well if the geocentric offset is well chosen. BUT, in a lot of cases old Datums are out anywhere from 100 m to 700 m because of ancient calculations. You always, always, have to remember about Datum shifts, especially if you use a GPS. We’ll return to datum shifts later when we discuss the GPS. The most important effect for us is that the latitude and longitude found on these maps don’t correspond to WGS84 lat and long. It doesn’t make any difference with Orienteering.
To sum up to this point:
The Earth is a flattened ball, or flattened sphere that is best modelled with an Ellipsoid.
An Ellipsoid is the shape used for a Datum.
Datums are designed to match the regional Geoid surface.
The Ellipsoid the GPS uses for its Datum is called WGS84.
All Datums are referenced to WGS84.
The Ellipsoid used in Jamaica for its JAD69 Datum is called Clarke1866.
The Geoid is the true sea level surface of the planet.
The Geoid is 15 m lower in Jamaica than the WGS84 Ellipsoid.
WGS84 positions are different than those in JAD69.
Take questions… ask a few… see if some of them followed it.
Possible test questions:
Q/ What is the shape of the Earth? A/ Ellipsoid
Q/ What is the Datum used by the Global Positioning System? A/ WGS84
Q/ What is the Datum used on the Jamaican Topo Maps? A/ JAD69
Q/ What is the Geoid? A/ Sea level
OK, we’ve covered the real, true shape of the Earth, now we have to have a look at how to take that mostly round surface and make it flat, for a map. The perfect map would be the exact same shape as the Earth but it would be rather impractical. If it were small enough to carry around you’d need a microscope to find Martha Brae. If it were large enough to find Martha Brae with a magnifying glass, you’d need a cane truck to transport it. We have to make it flat. That brings us to Map Projections.
(Get large round fruit that can be peeled)
The problem we run into trying to turn the surface of this ball into flat pieces can be seen by trying to peel this and lay it all out flat. If we cut it from top to bottom, say in 4 pieces, we have a hard time getting any of them to lay flat. The further from the centre of each peel, the worse it is. If we take thin slices from top to bottom, lots of them, it’s better but we still have to distort the peel when we lay it flat. Even if we do that, and put them side by side, we wind up with all the slices separated, except for at the equator, and if it were a map it would be a real pain when you get to an edge. There are a lot of different ways to peel the Earth, but they all involve a certain amount of distortion if you want to make it flat. The art of mapmaking is in the keeping of these distortions to a minimum. There have been a lot of clever solutions to this problem and we’re going to look at a few.
Most of the ways people have tried to make the Earth flat have involved what are called projections. These projections, and what they are will become more clear as we go along, fall into 3 main groups: Cylinders, Cones, and flat surfaces or Planes. We call these groups, Cylindrical projections, Conical projections, and Azimuthal projections, meaning using a plane.
If you have a look at the diagrams you have, (insert page #), you’ll see examples of these.
We’ll start with Cylindrical projections: (Draw circle on ball at equator). Now, we’re going to take this sheet of paper here, and make it into a big cylinder, or tube, that will fit around the planet, (the ball). We’ll line it up so it goes north – south, from pole to pole. I want you to imagine that this tube is clear and you can see right through to the surface of the planet. Imagine what you’ll see on the surface of the tube if you move that circle we drew onto the tube itself, that is if we project it onto the tube. That will make a map, of the circle, on the tube. We call this a cylindrical projection. Once we’ve moved that circle to the tube, (draw circle on sheet), we can unroll the tube and have a flat map. You’ll see that I put the circle on the equator of the ball and because we had the tube touching the ball at the equator, it comes out looking pretty good on our map… it looks like a circle.
We’re going to do it again but we’re going to draw another circle closer to the North Pole. Can any of you guess what might happen this time when we project it onto our tube? Let’s check it out. (Repeat demonstration with new circle). Looks pretty bizarre eh? No more round circle.
As you can see, the further you get from the equator, the more distorted the circle is.
We’ll get back to cylindrical projections and some maps based on them in a little while. Next though, we’re going to try putting some other shape made out of this sheet of paper around the planet here, and see how it fits. We’ll see how our circles project onto the paper.
We’re going to make a cone. (Make sheet of paper into cone). Let’s just pop it right on top of the North Pole. Ok. We’re going to look through this paper again and project our circles onto it. (Draw circles on paper). Now we’ll take the sheet, open it and check it out. You’ll see that this time, the upper, more northerly circle, looks a lot better. The one at the equator is pretty whacked looking though...
What we just did is called a Conical projection.
Let’s try it flat… Let’s just hold the sheet flat against the ball at the equator. (Repeat demo with circles). Not bad in the centre… totally wrong everywhere else. We call that an Azimuthal projection.
As you can see, the best projection depends a lot on where you live and how big a map you’re making, how large an area you want to cover.
Before we get back to cylindrical projections, I can tell you that the maps you’ll be using are in a conical projection. It’s the best solution for Jamaica. I want you to be a little familiar with cylindrical projections, though, so we’re going to look at an example of one of those that you’re all familiar with; the Mercator projection. That’s the one that your regular world map uses. We’ll get to the projection that Jamaican maps use shortly.
Gerardus Mercator lived in the 1500’s and was the first of the serious, modern mapmakers. It was his maps that popularized the names S and N America. It’s his projection that your common world map uses, the Mercator projection. We’re going to look at a special type, though, called the Universal Transverse Mercator projection. UTM.
Let’s make our cylinder again. You’ll remember that last time we lined it up from pole to pole. We don’t have to do that though, we can move it around. If we make it a transverse Mercator it means we’ve done this… (take cylinder and move to transverse position). Now you remember how the circle we drew at the equator looked not too bad? If we have the cylinder transverse, you’ll see that where the equator was before is now going from pole to pole. We call this new equator a tangent. We can move this cylinder around the whole planet with each spot we stop being another tangent. UTM does exactly that. It moves that cylinder around the planet, stopping 60 times as it goes. Each new spot defines a zone. Each one of these zones is fairly free of distortion. These UTM maps and positions are used a lot and you’ll run into them often. You can see that they work really well when the map you’re using is covering an area that stretches north – south. Jamaica, however stretches east – west. There is a different projection for Jamaica that works well and it’s a conical one.
The projection used for Jamaican topographical maps is called Lambert Conic Conformal. Lambert was a mapmaker. Conformal means that the shapes and distances are true on the map, and you know what Conic means. It’s that cone we sat on the Earth. Have a good look at the diagram on (insert page#). The one you see is almost like a party hat. We can use a different shaped cone, though, one that’s a lot higher and connects with the planet right along the middle of Jamaica. It’s really a perfect projection for an island shaped like Jamaica and that’s why it was used. It gives the least amount of distortion. On the maps you’ll be using the projection is Lambert Conic Conformal.
OK. We’ve covered the sea level shape of the earth, the Geoid, the squished ball we use as a standard model, the Ellipsoid, and how we try to make the whole works look right on a flat map, the Projection. Remember, the ellipsoid is the model, the geoid is the sea level surface and now we’re almost to the topo maps, the maps that describe the actual stuff that we walk on, the hills and valleys, the ups and downs, and we call that the topographical surface.
Before we move on to reading topo maps we’re going to discuss grids. A grid is a set of lines, two sets actually, that cross at right angles, like this, (draw grid on board). We start with a big cross, like this "+". We call the middle of the cross the, "origin". We can add lines above and below and on each side. The ones to the right and above the origin we call positive. The lines to the left and below the origin are said to be negative. What we use grids for is to show distances on maps in a fast and easy way. Most modern maps have all the main lines a km apart so we can see at a glance roughly how far it is from one spot to another. We can even take a ruler and measure distances to get it even more accurate. We’ll be looking at two types of grids today, the UTM grid and the Jamaican Metric Grid. We’ll start with the UTM grid.
You’ll remember that I said that there are 60 zones in UTM, that meaning we took the transverse cylinder and moved it around the planet stopping 60 times. What we wind up with are 60 really tall, skinny maps, like in (insert UTM fig. Page #), that all have a map origin here, on the equator and in the middle of the zone left to right. What we want now is to lay a grid on these maps that we can use for determining our position. The grid lines that go east-west, that is the ones showing how far north we are, are easy to define. We just say how far north of the equator they are in metres. The lines going north - south, the ones that we use to see where we are east - west on the map are a bit trickier. We could measure them from a line running right down the middle of the zone, from the map origin. If we do that you’ll see that the ones to the right will be +, and then we’d have to make the ones to the left, or west, -. It keeps things a lot easier if we have all the numbers + so what we use is something called a “False Easting”. False Eastings and False Northings are simply grid offsets to keep numbers positive. The centre of the map is the map origin. We move the origin of the grid a certain distance so that all the numbers are +, to the right of the grid origin, and to the north, or above the grid origin. The map origin of a UTM zone is the centre line of the zone where it crosses the equator. To keep all the numbers + we use a False Easting that is 500 km to the west of the map origin. That means that the map origin has an E – W position that is now said to have an Easting of 500 km. It’s a false number because it’s really the origin of the map and it’s to the East so we call it a False Easting. With UTM, north of the equator, all northings are +, because the map origin is at the equator, so we don’t need a False Northing. We will with Ja Metric Grid though. As you can see, we took our grid, and moved the whole thing 500 km to the west. The centre of the zone, the origin, has a False Easting of 500 km, and a Northing of 0.
Before we move ahead to the Jamaican Metric Grid let’s review what we just talked about:
Remember that the grid has been moved west of the map origin. The map origin now has a False Easting. In UTM we move the origin of the grid 500 km to the west and keep the origin at the equator if we’re on the north half of the planet. A False Easting on a UTM grid of 500 km is right in the middle of one of our 60 zones. A Northing on a UTM grid tells you how far north of the equator you are, if you’re on the northern half of the planet. If you’re south of the equator a False Northing of 10,000 Km is used… we haven’t covered that yet, we could if anyone is interested, but that situation doesn’t apply in Jamaica so it’s up to you… you can probably work it out by yourselves after you’ve learned about the Jamaican grid. Speaking of which, let’s move on to another type of grid, the Jamaican Metric Grid.
The Jamaican Map Projection has an origin at 18 N latitude, and 77 W longitude, in the JAD69 Datum. This position is not the same as what WGS84 calls 18 N, 77 W. When we talk about lat and long we use something called degrees. We’ll need to know about those for turning angles with a compass so let’s have a look at it now.
(draw circle and planet with lat/long)
A circle can be chopped up, like a pie, into little slices called degrees. There are 360 degrees in a circle, it’s a long story why there are 360, but just remember that there are 360 of these little slices of pie in a circle. We can think of the Earth as a circle and so we can use degrees to describe where we are. We need two sets, one for east – west, and another set for north – south. The ones that tell us where we are east – west, these ones that run from the north to the south, are called longitude and they start at 0 in England and count up by going to the east or west until they hit 180. 2 x 180 is 360. The ones that tell us where we are north – south, these ones that run east to west, are called latitude and start at the equator. We only need to go 90 degrees north or south to get to the pole so we call latitudes 0 to 90 north or south of the equator. 4 x 90 is 360, so we still have 360 slices going around the planet from top to bottom. The centre of the Jamaican topo map is at 18 N, 77 W, in the JAD69 Datum.
On the topo maps we want to have a grid to use to see where we are in a way that’s easier than lat and long, just like the grid that’s used for UTM. We also want all the grid numbers to be positive. The origin of the Jamaican maps is at 18 N, 17 W, in JAD69 and if you looked at a map you’d see that this is in the south-central part of the island. If we used that spot as the centre of the grid, where we are now in Windsor would have a minus number in it. What was done to make all the numbers be + was to move the grid origin 250 km to the west, and 150 km to the south of the map origin. This way every spot on the island is + something. What we have is a False Easting of 250 km and a False Northing of 150 km. The grid position of the map origin is 250,000 m E and 150,000 m N. That means 18 N and 77 W, the map origin, has an Easting of 250,000 and a Northing of 150,000. If you look at the topo maps you’ll see all the grid lines with the Eastings and Northings, in metres, marked at the margins.
Let’s compare the two grids we talked about:
UTM has 60 zones going around the planet. The origin for each zone is a spot on the equator that is also in the centre of the zone from east to west, or right to left. The UTM grid has a False Easting of 500 km, and if you’re in the northern hemisphere, no False Northing. The datum used for UTM is WGS84. The Jamaican Metric Grid is a grid that covers only one part of the planet, Jamaica. The origin of the Jamaican maps is near the centre of the island, at 18 N, 77 W, JAD69. The grid is moved to the west and south to keep all the numbers +. The grid has been moved 250 km west and 150 km south. That means there is a False Easting of 250,000 m and a False Northing of 150,000 m. The datum used for the Jamaican Metric Grid is JAD69.
(Ask a few questions, take a few, see if they followed any of it)
Possible test questions:
How many UTM zones are there?
What is the origin of the Jamaican maps?
What are the False Easting and False Northing of the Jamaican Metric Grid?
How many degrees are there in a circle?
A topographical map shows the hills and valleys. Mike is going to take over in a minute and show you how to read a topographical map, what they can tell you and what they represent. Later, I’ll be trying to show you how to find your way around the bush with a topographical map and one of these, (hold up compass). Let’s just make sure we’ve covered what we went through well enough.
Take questions… ask a few… see if some of them followed it.