Grid Systems The two most common grid systems in use in North America and are referenced on maps are the Latitude Longitude (Lat/Long) grid and the Universal Transverse Mercator (UTM) grid.

The Lat/Long grid has been in use for centuries and most people have heard of the basic terms of latitude or longitude.

The UTM grid is a metric grid system based on 60 grid zones around the globe and a set of values in meters from reference points of the grid. There are some aspects to this grid that make it very simple and easy to use even though the basic terminology is foreign to most people.

We will discuss the principles of how these two grids are set up and used to determine a set of coordinates for an exact location

Any grid consists of reference points, units of measurement, and some designation of direction to clearly identify a position.

A classic example is the basic X, Y graph as seen in Fig. 1 below. The horizontal line is the "X" axis and the vertical line is the "Y" axis. The two axis are the reference points. Direction is indicated by + and - on either side of the axis. Therefore, the Point "A" would be defined as +5,-4.

Figure 1

Figure 2 below shows these axis on the globe.

The significant issue than must be understood in using the Lat/Long grid is that the units of measurement are defined in Degrees.

Almost everyone knows that a circle is divided into 360 degrees. In working with the Lat/Long grid, we are dealing with a sphere where the reference axis are two circles. The one circle is around the center of the globe at the equator, and the other running vertical or North and South at the Prime Meridian.

Figure 2

The angular measurement is considered from the center of the earth for both of these reference circles.

Any given point of the globe can be defined by measuring degrees West or East of the Prime Meridian to get the value for Longitude, and degrees North or South of the Equator to get Latitude.

Figure 3 shows a simplified view of the angular measurement from the Equator and Prime Meridian with the center point of these reference circles being in the center of the earth.

Figure 3

Another important issue needs to be understood about angular measurement which is the fact that if we were only using degrees, we would not be very accurate because one degree of longitude or latitude at the axis is equal to approximately 69 statute miles. Therefore, the circle needs to be divided into smaller components to give us more accurate coordinates. Therefore, the Degree has been divided into 60 smaller units called Minutes and furthermore, these Minutes are divided into 60 Seconds (nothing to do with time).

The drawing in Figure 4 shows one degree of angular measurement and how that is divided into Minutes and Seconds.

Figure 4

This now gives us increments that are small enough so that at the surface of the earth, one second will be a distance of around 100 feet which gives us a much higher level of accuracy.

If you refer back to Figure 2, you will notice that the vertical lines or Meridians of Longitude converge at the North and South Poles. It is important to understand that those Meridians are still the same angular distance apart even though they will be closer together in linear distance the further North or South they are from the equator. This issue will become more apparent and have to be accounted for when you plot and read coordinates from maps. Linear distances for a given measurement of Degrees will be shorter for Longitude than the same angular distances for Latitude for positions significantly North of the Equator which includes all of North America.

The coordinates for a given location is the intersection of the Meridian of Longitude East or West of the Prime Meridian and the Parallel of Latitude North or South of the Equator as shown in Figure 2. A typical set of coordinates for a position in North America would be;

112E 27N 55O W - 112 Degrees, 27 Minutes, 55 Seconds West Longitude

34E 33N 15O N - 34 Degrees, 33 Minutes, 15 Seconds North Latitude.

The Lat/Long grid on Maps:

There are many maps available that provide information on Latitude and Longitude so that specific locations can be identified by their coordinates. Some of the most common of these are the USGS Topographical maps and U.S. Forest Service maps. These maps are made at different scales that provide varying levels of detail.

One of the most common of these maps is the USGS 1:24000 scale Topo Map. This is also called the 7 ½ Minute Topo or the 7 ½ Minute Quadrangle because it covers 7 ½ Minutes of Latitude and 7 ½ Minutes of Longitude. This map is popular with hikers, hunters, and others who need a significant amount of detail. One problem with having a map in such detail is that you need quite a few of them to see a larger area of the terrain. The average 7 ½ Minute Topo only covers about 49 square miles.

Figure 5

Regardless of the size of the map and its scale, the basic principles are the same for plotting or reading position coordinates. For our examples here, we will use a 7 ½ Minute Topo because its use is so common and readily available.

The first step in using a map to plot or read position coordinates is to locate the Longitude and Latitude reference points and 2 ½ Minute tick marks.

In our example, the bottom right corner of the map gives us the reference coordinates of 112° 15¢ West Longitude and 34° 07¢ 30² North Latitude. Notice since the Longitude is in even Minutes, the seconds are not given. North is always at the top of the map.

The very top of the map will show 34° 15¢ which is 7 ½ Minutes greater than the reference at the bottom of 34° 07¢ 30². The same progression of 2 ½ Minute intervals can be seen across the top and bottom of the map from 112°15¢ West Longitude to 112° 22¢ 30² which is also 7 ½ Minutes or 7 Minutes and 30 Seconds.

On most 7 ½ Minute Topos, the 2 ½ Minute Tick Marks are not connected from side to side or from top to bottom, but this is necessary for measuring coordinates in positions other than right by the borders of the map. Therefore, you will want to take a straight edge and connect the tick marks at the 2¢ 30² (two Minute, thirty Second) intervals so that your map will look like the one in Figure 4.

Now that you understand the layout of the typical map, you are ready to measure the coordinates of a given location on the map. Lets take an example where our location (indicated by "+") is somewhere in the middle section of the map as in Figure 5.

Figure 6

We can see by simple observation that the position is somewhere between 112° 17¢ 30² and 112° 20¢ West Longitude.

The position is also between 34° 10¢ and 34° 12¢ 30² North Latitude.

What we need to do is get exact coordinates, but you will notice that the map does not give any further breakdown than the 2 Min. 30 Sec. intervals. Therefore, an additional tool is needed in conjunction with the map to measure this position.

The Waypointer Ô is such a tool that is designed to measure the individual Minutes and Seconds for the 2 ½ Minute interval between the tick marks. A picture of one of the Waypointer Ô scales is pictured here in Figure 6.

The Waypointer scale is designed to fit exactly between the 2 Min. 30 Sec. Intervals on the 7 ½ Min. Topo. If the scale is placed vertically with the Zero mark at one of the 2 ½ Min. tick marks or reference lines that you drew, the 2 Min. 30 Sec. line will then exactly align with the next tick mark or reference line above it.

Figure 7

To measure Latitude with the Waypointer scale is then very simple. All you have to do is to place the zero end of the scale at the first reference line below your Position and measure up from the reference line to the desired position. Then add the amount measured to the value of the reference line.

For our example, the nearest reference line below our desired position is 34° 10¢ if we measure up from that line to the "+" at our desired location, we will get a value of 50" as seen in a magnified view Figure 7.

So our coordinate for Latitude will be 34° 10¢ 50². We arrive at this by adding the 50" our measurement up from the reference of 34° 10¢.

Unfortunately, the Longitude coordinate is not as easy to measure. The reason is the fact that we mentioned earlier that the Meridians of Longitude converge at the poles and therefore, come closer together in linear distance the farther north your position is above the equator. Their angular distance is the same, but when we are trying to measure with a tool such as a Waypointer scale, we are measuring linear distance.

Figure 8

It can be easily proven that the same number of degrees of Latitude is shorter in linear distance than that value of Longitude by simply taking a tape measure and measuring the vertical distance of a 7 ½ Minute Topo and then measureing the horizontal distance. The horizontal or Latitude measurement will be significantly less even they both represent 7' 30" of angular measurement.

So, it will be easily understood that our Waypointer scale will not fit within the 2' 30" increments between the vertical lines on our map. It will be significantly too long.

The simple solution to this problem is presented in Figure 8.

If we skew the scale at an angle such that the zero mark is on the vertical line to the right and the 2' 30" mark is on the other line we will be able to read any value in between.

We have to adjust the scale up and down until both ends are aligned properly and such that we have the desired position next to the scale so we can read its position from the right reference line.

In this example, we read on the scale 1' 15". If we add that to the reference line value to the right we get the following:

Page -12-

That is all there is to reading the coordinates of a position from the map. So the final set of coordinate in our example is:

Once you have determined a set of coordinates for a location or waypoint on the map, you can input them into your GPS receiver so that you can navigate to that location.

In using your GPS to navigate to a position obtained from a map, you need to be careful about several concerns.

The main concern is that you review the set-up of you GPS receiver and make sure that the Map Datum that is referenced on the map that you took the coordinates from is the same map datum selected in set-up on your receiver. Differences from one datum to another can create an error as much as a mile difference.

The other concern, is that you are careful in determining the coordinates from the map and equally careful with the data input process in creating the waypoint on your GPS unit. As you go out in the field, you can make some approximations of your distance from the waypoint as you reach certain readily recognizable landmarks. Use the map, scale, and compass or protractor to determine the distance bearing and see if your GPS unit confirms your calculations. If you see large differences in your calculations, check your figures. It pays to have more than one way to determine the accuracy of your data. If you find that your data agrees from known landmarks, then when you are out in the woods and not sure where you are, you know you can rely on the data you are getting from your GPS unit.

One other very useful function that you will want to be able to do is to take coordinates that you have saved from being out in the field and plot them on a map. Or possibly even plot them on the map while you are still in the field just to know where you are.

Although it would seem logical that plotting a position on the map from coordinates is the reverse of reading them from the map, there are a few little differences.

You first have to determine which map that the coordinates will be on. This is easy since your map gives coordinates of all four of its corners, you can determine if your coordinates fit within the range of latitude and longitude of that map.

Figure 9

The Longitude coordinates need to be greater than the longitude reference at the right of your map and less than the value at the left of the map. The longitude increases from right to left.

The Latitude of your position needs to be greater than the reference at the bottom of the map and smaller than the latitude reference at the top of the map. Latitude increases from bottom to top. This is of course for locations in West of the Prime Meridian and North of the equator like North America.

With a map that is prepared with the tick marks connected with reference lines as explained earlier, you can determine the section of the map that your position is within. Again for longitude, looking for values of the right line to be smaller and the left line to be larger. And for latitude the lower line having a smaller value and the upper line having a larger value.

Lets take an example from our typical 7 ½ Min. Topo. with a set of coordinates of the following waypoint:

Look at Figure 9 and determine which section of the map this set of coordinates will be in.

Those coordinates are located in the upper left section of the map so that is where we will begin working to plot the waypoint.

Our first step will be to plot a line across the section at the proper latitude. Our first step to do this is to find the difference between the value of latitude and the reference line below it so we know how much to measure above the reference line.

In our example, we have the latitude of 34° 14¢10², and our reference line below that is at 34° 12¢30². If we subtract:

--34° 14¢10²
- 34° 12¢30²
--------1'40"

Figure 10

Now that we know that we are going to have to measure up 1'40² (one Minute, forty Seconds) from our reference line of 34° 12¢30². We will make this measurement on the 112° 20¢ reference meridian and again on the 112° 22¢30" meridian. Now we will draw a light pencil line between these two measurements.

We now have a line in the upper left section of the map at 34° 14¢10² as in our example in Figure 10.

We know that the exact location of the waypoint is somewhere on this line. Once we plot the longitude we will have it pinpointed.

To start with we will again find the amount we need to measure from the closest reference line like we did with latitude. The closest reference line to the latitude coordinate is the 112° 20¢ reference meridian so we subtract this value from the value of the longitude coordinate to get the following:

This means that we need to measure 1Min. 15 Sec. West or to the left of the 112° 20¢ reference meridian.

To plot the longitude coordinate, we will again use the same technique as we did in reading longitude previously. Remember, we have that problem of the meridians converging at the poles, so they are closer together than they were at the equator and our 2'30" scale will be too long.

Figure 11

As illustrated in Figure 11, we skew the scale such that the zero end is aligned with the 112° 20¢ reference meridian line and the 2'30" mark on the 112° 22¢30" meridian line. Now we move the scale up and down so that we make our 1'15" mark on the scale cross the latitude pencil line we previously drew. Once we have placed the scale to measure this 1'15" mark on the 34° 14¢10² parallel we drew earlier, we have located the exact position on the map.