Messing with a Topo Sheet

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.)

Part 1 - Get the Overview

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:

  1. What is the name of the quadrangle?
  2. What scale is it?
  3. What contour interval is used?
  4. What is the highest elevation on the map?
  5. What is the lowest elevation?
  6. Briefly describe the terrain.

Part 2 - Coordinates in Several Systems

Examine a topographic quadrangle to locate the several coordinate systems shown and the appearance of the sets of tics and labels.

  1. Find the latitude, longitude and elevation of each of the four internal graticule tics. List them.
  2. For each of the four internal tics, find the UTM Easting and Northing by interpolation on the map sheet.
  3. For each of the four internal tics, find the SPC Easting and Northing by interpolation on the map sheet.
  4. For each of the four internal tics, find the Township Range and 1/4 1/4 section.
  5. You can check your UTM and SPC position estimates using an online coordinate converter, like these:
    Montana's UTM to Lat Lon converter and
    NGS / NOAAN's SPC to Lat Lon converter
    Australian Gov't Geodetic Calculation Methods web page.
  6. How well do your interpolations agree with the calculated coordinates?
  7. . Now, lets use that skill...
  8. What are the UTM easting and northing of the lowest point on the map?
  9. What are the UTM easting and northing of the highest point on the map?

Part 3 - Scaling Distances

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?

  1. What is the distance (in meters) between the two southern tics?
  2. What is the distance (in meters) between the two western tics?
  3. What are the distances (meters) between the diagonal tics?
  4. Think about how these compare to the coordinate differences from Part 2, what you know about the lengths of degrees of latitude and longitude, and what you know about dimensional stability of paper.

Part 4 - Direction.

Just for closing the circle, go back to your highest and lowest points on the map.

  1. What is the direction between the lowest point and the highest point on this quadrangle?
    Azimuth from low point to the high point relative to True North:
    Azimuth from high point to low point relative to Magnetic North?

Part 5 - Elevation Profiles and Intervisibility

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.

  1. Pick two of the internal tics and draw the profile of the terrain between them. Lable the horizontal axis in meters and the vertical axis in feet or meters depending on which the map uses.
  2. Are any places along the transect invisible from either end? Indicate them on the profile diagram.
  3. Attach the profile to your report.

Part 6 - Slope and Trafficability Routing

Re-written with the help of the Spring 2013 class...

The task here is to design a route between the lowest and highest points on your map such that the route's slope never exceeds the slope of the steepest road already on your map sheet.

You already have identified the highest and lowest points on your map.

So, now find the steepest 100 meters of road on the map. How many contours are crossed by that 100 meters of road? How many feet of 'rise' per 100 meters of 'run' is that? Let's consider that the limit of 'trafficability' for your map.

Now, design a route between the map's higest and lowest points such that it is never steeper than that limit and trace it on the tracing paper supplied (tape sheets together if you need to).

Cast in terms of contours crossed per distance of ground space (or of map space), your route should never cross more contours in 100 m than did the steepest road.

In some terrain, this may be fairly easy to do. In some it may be devilish. Crossing contours obliquely gets you more run per rise and you could 'surpentine' back and forth across a steep slope to reduce the effective grade. Notice too that your route may tend to follow along between contours running 'back into' draws and even circling around a peak. In many cases, the points will 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 (dis-)proof of that?), but it may be that the terrain you need is off the map sheet.

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 could reduce your need to gain or lose elevation.

  1. Once you have your route planned out, plot or trace it onto the tracing paper and attach it to your report.

Part 7 - Hill Shading.

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.

  1. Try one of these techniques on a "section" or 1/9 of the quadrangle (use the internal graticule tics to delineate the ninths) depending on the terrain that you have and your artistic inclinations. Attach the artwork to your report.

The Report

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.