Objective. The purpose of this exercise is to provide some experience with using USGS 7.5 (or 15) minute quadrangles to determine locations in several coordinate systems, to determine elevations of points from contours, to derive the profile of a transect, determine inter-visibility along a transect, and to use a contour map to determine a route between points subject to slope constraints on trafficability.
Materials. Hard copy 7.5 (or 15) Minute USGS Topographic Quadrangle. Ruler (mm scale). Protractor. Tracing paper. Pencil (Keep the maps clean for the next user, please.) A long straight-edge, a table and drafting tape would be handy, but field expedients will do). Use this answer/work sheet .
Topo Quads. The USGS 7.5 (and 15) minute topographic quadrangle series of maps is (are) a remarkable achievement by any measure and these have been a standard map for many field uses for several generations of U.S. geographers. While the government printing office seems to be getting out of the map printing business, they do provide digital pdf copies of the maps for free and print on demand hard-copy. See the USGS Map Store web site, and follow the link to "Map Locator" or "US Topo", both of which seem to end up in the same place.
Topo sheets fall into the "general" or "reference map" category... they tell many stories including the topography or terrain (contours, bench marks), hydrography (streams, rivers, lakes, ponds, reservoirs, etc), cultural features (roads, trails, boundaries, transmision lines, railroads, buildings, mines, etc) and more. The symbols used to represent these and other features are documented here and in similar USGS publications.
Three coordinate systems are typically used on these maps. These are the latitude/longitude graticule, the Universal Transverse Mercator (UTM) grid, and the area's State Plane Coordinate grid. Where it is in use, the US Public Land Survey Township and Range system is also shown.
The latitude/longitude graticule is marked at the corners of the map. Remember that in the U.S. these are generally west longitudes and north latitudes. You will notice also that tics mark each third (2.5 minutes of the 7.5 minute, 5 minutes of the 15 minute) quadrangle, both on the map margins, where the tic labels drop the degrees, listing giving only the minutes and seconds, and internally, where four crossed tics divide the sheet into nine 2.5 (or 5) minute sub-quadrangles.
The UTM grid is shown with blue marginal tics that cross the neat-line, or with a grid overlay in black. Near the corners you will find complete Easting and Northings labeled, but generally, tics are labeled dropping the final three digits and with the thousands and the ten-thousands digits set in larger numerals; making it easier to read the thousand meter grids.
The SPCS grid, generally in feet, is shown in black tics which cross the neat line. Here, the tics mark a 10,000-foot grid.
The township and range system may also be present on your map. Usually it is printed in red. In the side margins you'll see some thing like "T. 43 N" and at top and bottom like "R. 1 E", indicating that Township 43 N and Range 1 East lies in the map at their intersection. Within that area you will find the (1 mile square) sections plotted and labelled.
With both the UTM and the SPCS grids you could lay a straight-edge across the map and pencil-in the grid from the tics. Further, you could interpolate locations to a finer precision, perhaps using an overlayed fine grid that shows the 100-meter, or even 10-meter divisions. (You can buy one or make your own.)
Take a moment to see what the map tells you about itself. Read the marginalia to determine the contour interval, the geodetic reference system (NAD27, NAD83, something else?), the UTM zone, the coordinate systems used, and the orientation to true north, magnetic north, and (UTM) grid north.
As you turn to the body of the map, ask yourself: where is this? and what is the place like? Get an overview of the terrain. Can you describe it's overall structure? What are the main topographic features? Where are the highest and lowest areas? How does the drainage run? How do the cultural features fit onto this backdrop?
Answer these questions:
Examine a topographic quadrangle to locate the several coordinate systems shown and the appearance of the sets of tics and labels.
Go back to the four internal lat/lon tics, and using a ruler divided to show millimeters, measure the distances between the tics (estimate to the nearest 1/10 millimeter), and calculate the ground distances in meters. At 1:24,000 scale, 1 mm => 2.4 meters. Right?
Just for closing the circle, go back to your highest and lowest points on the map.
You can generally interpolate elevations between contour lines. If you make a graph of elevation against distance along a transect line you will produce a profile of the terrain. (You'll probably want to scale the elevation and distance differently.) You can use the profile and a straight edge to determine whether points along the transect are intervisible or whether the terrain would block visibility.
Note the difference in elevation between your map's low and high points and the distance between them. Calculate the average slope between them (elevation difference)/(distance). Assume that you have a vehicle that can only climb grades of half that average slope. Your task here is to find a route between the points that does not exceed that grade.
For example, on the Sandy Ridge, Alabama quad, with its 10 foot contour interval, the tic at N 32d 2m 30s, W 86d 27m 30s is at about 315 feet elevation and the tic at N 32d 2m 30s, W86d 25m 0s is at about 382 feet elevation. The elevation difference is 67 feet. The distance between them is 163.3 mm on the map, or 3.9 km on the ground (= 163.3 mm x 24000 x .000001 km/mm). The slope is (67 ft / 3.9 km =) 17.17 ft/km. For ease, round it to 20 ft/km, and then take half of that 10 ft/km as the (arbitrary) steepest trafficable slope limit. Can you find a route from one tic to the other that does not exceed that slope?
Put in terms of contours crossed per km of ground space (or mm of map space), the route in this example should cross only one 10-foot contour per km traveled. In this exercise, even the best possible circumstance would have you traveling twice the straight-line distance between the points. In many cases, the tics have hills, ridges and valleys between them, meaning that you are going up and down more than just the elevation difference between the points. It could be a long trip.
It can generally be done, (anyone want to offer a proof of that?), but it is possible that the terrain you need is off the map sheet. If you get really hung up, for this exercise, try another pair of the graticule tic points.
Hints: Try to maintain grade, generally following contours. Spread your crossing of contours along your route so as to not exceed the allowable grade. Your route may curve around mountains and may end up much longer than the straight line between the points. Finding useful passes should reduce your need to gain or lose elevation.
Contours provide detailed terrain information --- you can read and use elevations from the map, determine slope and aspect, grok the terrain configuration --- but you may still find them occasionally confusing when you try to get a quick "lay of the land" impression of the terrain. Adding hill shading to portray terrain as if it's 3D shape were illuminated may help map readers see the terrain.
Imagine the Sun off to the northwest at an azimuth of about 315 degrees and an elevation of about 45 degrees. Which slopes would be most brightly illuminated? (The ones facing the sun.) Which ones least illuminated? (The ones facing away from it.) Which ones intermediate? If we "shade-in" areas appropriately, dark areas dark and lighter areas lighter, we'll create the impression of the illuminated terrain --- shaded relief. There are several automated ways to do this, and several manual techniques.
Tanaka's illuminated contours approach can be modified and done quite quickly with pencil and paper. Trace the contours, drawing them thinner and lighter where the terrain should be brightly illuminated and thicker and darker where the terrain should be in shadow. The impression created can be quite vivid.
Plastic relief. One could accomplish a similar effect with a pencil or charcoal, stump for 'smudging', and an artistic eye, by adding continuous feathered shading (based on interpreting the contours). The Swiss are famous for this though computer algorithms have replaced many skilled terrain artists.
List the answers to the numbered questions above on a sheet of paper. Attach the several plots to the sheet. Put your name on each page. Staple them together. Hand in the stack.