QUADTOOL INSTRUCTIONS
Background maps from USGS. All other material Copyright © 2000 TCSAR

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OVERVIEW
Application
The QUADTOOL is for use with 1:24,000 scale topographic maps such as the 7.5 minute series from the USGS. The Lat/Long scale can also be used on 1:25,000 scale maps if the latitude method is modified slightly. These instructions assume use of maps in the North and West hemispheres. The tool can be used in other hemispheres, but the positive direction of latitude and/or longitude will be reversed.

The Tools
Starting with the individual tool (a.k.a. scale or ruler) directly above the name "QUADTOOL" and going in a clockwise direction, the tools are named MILE, SLOPE ANGLE, UTM (both sides of the upper right corner), LAT/LONG (along bottom), and FEET (left side). Detailed descriptions of each tool are found below.

Coordinate Systems
A typical USGS topographic map has up to four different coordinate systems delineated in the map or on the border of the map: UTM, LAT/LONG, STATE PLANE and PUBLIC LAND SURVEY. If you are using a GPS with your map, be sure the GPS datum matches your map datum! (Most USGS 7.5' series are still NAD27 CONUS) Set the coordinate display for either lat/long in dhhhºmm.mmm' format or in UTM. We recommend UTM.

Figure 1

1. UTM
   Universal Transverse Mercator. A metric coordinate system that is considered by many to be the best system to coordinate GPS and maps. Most USGS 7.5 minute maps have blue tick marks spaced at approx. 1.5 inches along the edges and are labeled with numbers where each label has two different sizes of characters. See Figure 1. These marks scale to 1000 meters apart and are used to draw the UTM grid. See "Gridding" below.
2. LAT/LONG
   Latitude and Longitude or Geographic coordinates. Each map spans exactly 7.5 minutes of both latitude and longitude. One third the way along each edge are black tick marks labeled with minutes and seconds (example: 32’30"). See Figure 1. These marks are 2.5 minutes apart and are used to draw the Lat/Long grid.
3. STATE PLANE
   State plane coordinates are used by surveyors. There are may be only two references to this system on the map (numbers in FEET, usually near the SW corner), so this system is of little use to navigators.
4. PUBLIC LAND SURVEY
   This is not really much of a coordinate system, but some agencies, such as the Forest Service apparently like to use it. This system was created to define the location of public land subject to homesteading. There were not very good surveys back then (but remarkable considering the equipment used). For land ownership, original marking on the ground takes precedence over description, so modern survey lines are skewed and offset to match original marks. Thus, this unpredictable system is only useful if the survey lines are drawn on the map. We’re talking about the red lines approx. 2.5 inches or one mile to scale apart, with numbers in the middle of each square. Do not rely on these lines to run true north or east, nor for the squares to be one mile square.

Gridding
To best use the QUADTOOL, the map needs to be gridded. We prefer to use the UTM system. Draw parallel lines 1000 meters apart that run exactly North-South and East-West and align with the blue UTM tick marks. It is useful to scale out another 1000 meters to the West and South and draw additional grid lines in the border. USGS provisional maps already have the UTM grid drawn for you!

If you need to use the lat/long grid as well, use a different color than used in the UTM grid. Draw lines aligned with the lat/long tick marks so that the map is divided into 9 big equal rectangles. If you measure very carefully, you will find the rectangles are actually trapezoidal, the northern edge is very slightly shorter than the southern edge. One will find, for maps of the same scale and projection, that longitude lines in Mexico are much farther apart than longitude lines in Canada. Longitude lines converge at the poles. Latitude lines do not converge. Because of this, one can only directly scale longitude along an East-West axis at only one latitude. Other latitudes require use of the proportion method.

UTM
Determining Coordinates of Map Feature
Place the upper right corner of the UTM tool on the map feature. Read the East distance at the Western grid line. See Figure 2. The East distance is 255 meters from Peak 10245 to the ⁰⁵09 grid line. Thus the full East coordinate is 0509255. Read the North distance at the Southern grid line. See Figure 2. The North distance is 500 meters from Peak 10245 to the ⁴⁸26 grid line. Thus the full North coordinate is 4826500. Get the Zone from the notes in the bottom left corner of the map. The example map is in zone 12. The full UTM coordinate is 12 0509255 4826500. The first number is the zone, the next is the number that increases to the right, then the number that increases in the up direction. The right direction is always written before the up direction.

Figure 2

Plotting Location of Coordinates
This is pretty much just reversing the above instructions. Given coordinates 12 0509255 4826500, find the intersection of the ⁰⁵09 grid line and the ⁴⁸26 grid line. Place the corner of the UTM tool at the intersection. Slide the tool right until it reads 255 at the ⁰⁵09 grid line. Now slide the tool up until it reads 500 at the ⁴⁸43 grid line. The corner of the tool is now at the specified coordinates on the map and looks like Figure 2.

LAT/LONG
Determining Coordinates of Map Feature
First determine the degree portion of the coordinates. Look in the South East corner of the map and note the whole degrees, ignore the minutes and seconds. The whole degrees apply to the entire map.

1. Latitude
   To determine the latitude, place the zero end (marked "S Lat à ") of the Lat/Long tool on the nearest lat/long grid line to the South and read the latitude minutes at the feature. See Figure 3. The summit of Peak 8225 is 1.22 minutes North of the grid line. Add this to the minutes latitude of the grid line and the whole degrees previously noted. Note that 30"(seconds) equals 0.5’(minutes). Be sure you do not confuse the two! In the example, 1.22’ + 30.0’ + 43° = 43° 31.22’.
2. 
   Figure 3
3. Longitude
   Remember that in the Western hemisphere, Longitude increases to the West. Thus the zero end (marked "E Long à ") of the lat/long tool should lie on the lat/long grid line to the East of the feature. Place the tool at an angle so the opposite end lies on the grid line to the West. See Figure 4. For more info on why this works, see "The Proportion Method" below. Maintaining the angle, slide the tool up or down until the edge intersects the feature and read the longitude minutes at the feature. The summit of Peak 8225 is 0.84 minutes West of the grid line. Add this to the minutes longitude of the grid line and the whole degrees previously noted. In the example, 0.84’ + 52.5’ + 110° = 110° 53.34’.

Figure 4

Plotting Location of Coordinates
This is pretty much just reversing the above instructions. Verify you have the right map by checking the lat/long noted at the corners of the sheet. Roughly estimate where the given coordinates will fall.

1. Longitude
   At your estimated location, place the tool at an angle with the ends over adjacent longitude grid lines, the zero end towards the East. Count from the East grid line up the scale to your given longitude and place a mark. The position will fall somewhere on a vertical line through this point.
2. Latitude
   Now orient the tool vertically so that the zero end lies on a latitude grid line to the South and the edge lies on the longitude mark you made above. Count from the South grid line up the scale to your given latitude and place a mark. This is the position for the given coordinates.

Slope ANGLE
This tool is used primarily for route evaluation in avalanche terrain. It is set up for maps with 40 foot contour intervals, as this is typical of maps depicting avalanche terrain. Other intervals can be accommodated by adjusting the number of index contours spanned.

Lay the tool along the fall line and find an angle zone that best aligns with a span of 2 index contours (400 feet vertical). See Figure 5. The example slope is about 35°.

Figure 5

MILE
Public Land Survey descriptions include references to ¼ sections and ¼ ¼ (1/16) sections. You can use the mile scale to divide sections (the red one mile squares) into quarters and 16ths to make sense of things such as SE ¼ of NE ¼ of Section 18 in T41N R116W. See Figure 6.

Figure 6

FEET
As long as the U.S. uses the English units of measure, it seems useful to be able to scale things on the map in feet.

THE PROPORTION METHOD
Some people have difficulty understanding why the measurement technique for longitude works. This is a simple exercise to illustrate the concept. Take a standard 12 inch ruler, a pencil and a some standard 8.5 x 11 letter paper. Mark at 1 inch increments along each long edge. Draw lines parallel to the short edge connecting the marks. You have divided the sheet into 11 equal rectangles, with the long side of the rectangle 8.5 inches long. OK, too simple.

Now turn the paper over and divide it into 11 equal rectangles that run the other direction, so that the long side of each rectangle is 11 inches long. One way is to use math. 8.5 inches divided by 11 is 0.773 inches. Measure the 0.773 distance 10 times and we have it, except if you’re not perfect, that last rectangle will not be quite the same as the rest. Now do the same for a 5 inch wide sheet. Now a 10.145 inch sheet. OK, never mind, you get the idea.

Now try this instead. Place the ruler at an angle on another sheet of paper so that the zero end is on one corner of the paper and the 11 inch mark is on the opposite long edge. Mark at 1 inch increments along the ruler. Slide the ruler until the 11 inch mark is at the opposite corner and the zero end of the ruler is on the other long edge. Make more marks at 1 inch increments. Now draw lines parallel to the long edge through all the marks. It doesn’t matter if the paper was 5, 8.5, or 10.145 inches long. If you tilt the ruler, you can evenly divide the paper into 11 spaces. You are proportioning the 11-1 inch increments down to fit the width available by tilting the ruler.

On the map, the longitude grid lines are 2.5 minutes apart. There are 25 major divisions of the lat/long tool. With this method, we can divide that 2.5 minutes into 25 equal increments, or 0.10 minutes, no matter how far apart the longitude grid lines are in Guadalajara or Yellowknife.

MORE INFORMATION

COORDINATE SYSTEMS, MAP PROJECTIONS, DATUMS, GPS SYSTEM
These instructions assume you know something about coordinate systems. If you need more information, take a look at http://www.colorado.edu/geography/gcraft/notes/coordsys/coordsys_f.html

GEOMAGNETIC FIELD SYNTHESIS
An even more important navigation tool than the QUADTOOL is a magnetic compass. Magnetic declination is constantly changing. Estimate what it is today where you are at http://www.ngdc.noaa.gov/seg/geomag/jsp/Declination.jsp

MAPS ONLINE
The map used for all the figures except the PLS Section is Rendezvous Peak, WY. You can download the whole map (2.8MB) at http://wgiac2.state.wy.us/scripts/sqltest/webform1.aspx?FileID=43 . Note that the maps are in GeoTIFF format, and not all software can handle the format or files that large. The USGS provides a free viewer(8.0MB). The PLS Section is on the Teton Village, WY quad at http://wgiac2.state.wy.us/scripts/sqltest/webform1.aspx?FileID=42 (2.4MB).

CREDITS AND CONTACTS
The QUADTOOL was developed by members of Teton County (WY) Search and Rescue as an aid to frequent navigation work. They first tried other tools that were available, but none really did the job quite right. Finally they designed their own, and field tested it at every opportunity. The current tool is the result of several years of refinement.

We liked the result so much, we decided to make it available to others. For more information on TCSAR, point your web browser to http://www.tetonwyo.org/sar/ .

Questions and comments can be e-mailed to tcsar at onewest dot net . Also see our FAQ's .

Tax deductible donations to TCSAR are always welcome. Send to Teton County Search and Rescue Volunteers, PO Box 1885, Jackson WY 83001.