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