Variable Map Scale Template   Edward Frank
  Jun 28, 2006 16:57 PDT 

Many of you have GPS units. The most common output format for these units is in Degrees and decimal minutes. Some models have other formats. You may also have 7.5 minute topographic quadrangles. As you know the height of one of these maps is 7.5 minutes, and the width is 7.5 minutes. If you were on the equator the maps would be equally high and wide. As you go northward the maps become progressively narrower than they are wide, until at the north pole (or south pole) they're wedge shaped. The problem is how to convert positions on the map to GPS coordinates and vice-a-versa. A set grid would not work if you were using maps from different latitudes as the longitude scale would change for each of these maps. It is awkward to use a calculator to determine the number of inches from the edge for each major division of latitude or longitude. However you can quickly determine the latitude/longitude position of a point on a map with a simple to make variable width grid.

Take a piece of wax paper about 36 inches long (you can use Mylar or other translucent or transparent plastic). Using a permanent marker make two lines parallel to each edge of the paper about an inch from the edge. (You can lay a yard stick along the edge and draw a line along its side). From a point near the middle of one of these lines make a mark. From this point draw a line perpendicular to the two lines and the edges of the paper across the middle of the sheet. This forms a giant H shape. From the point where this crossing line intersects the second line (one of the uprights of the H shape), mark points every two inches up and down the line, make 8 marks above the line and seven marks below the line for a total of 15. Then from the origin point where the line across the paper crosses the first line (the other upright of the H shape), draw a series of lines from this single origin point to each of the marked intervals on the opposite line. This forms a fan shape.

This fan has the property, that so long as a line crossing the fan is parallel to the edge of the paper the intervals between each of the rays of the fan are equal. Lay the marked paper on the topo map so that the edge of the topo map is parallel to the edge of the wax paper. Move the paper sideways until the length of the side of the map fits exactly between the outer rays of the fan. On a 7.5 minute map the points where each of the rays on the fan grid intersect the edge of the map are exactly 30 seconds or 1/2 minute apart. If you are using a 15 minute quadrangle then the intervals defined are 1 minute apart. You can mark these on the edge of the map. Do the same for both the sides (latitude) and the top and bottom (longitude) and you can draw a grid on the map that divides the region into 30 second (0.5 minute) rectangles.   A smaller scale can be made using a single sheet of clear plastic. Divide this into ten segments on the second upright of the H - one in the middle, five above, and five below. This can be placed on the map to further divide a particular rectangle into 0.05 minute (3 second) units.

If you work with topos from different areas this method will save you much effort in converting map point to and from GPS coordinates. And best of all, it basically costs you nothing as most people have these material lying around their home already.

Ed Frank