1. Navigation with Compass and Map
By Mark Thomsen

2. Your Location on Planet Earth
The intersection of two lines (longitude and latitude) specify a unique place on earth
(G) Coordinate systems; Spherical Geometry;(F)Functions

3. Your Location on Planet Earth
The are other ways and systems to determine your location on earth which we will not use; such as
GPS (Global Positioning System) coordinates have become popular as they give real-time coordinates and a location based on satellites orbiting earth
UTM (Universal Transverse Mercator) is a system that divides the earth into 60 zones that are 6 degrees wide and uses the metric system
(G)Coordinate systems

4. Longitude
“Definition: a measurement of distance, given in degrees east or west of the prime meridian. The prime meridian is a line that runs through the Greenwich Observatory in London, England. On a map or globe, lines of longitude are drawn from the North Pole to the South Pole” (NASA, 2015).
(MD) Measurement and Data

5. Latitude
“Definition: a measurement of distance, given in degrees north or south from the equator. Latitude lines are also called Parallels” (NASA, 2015).
(G) Parallel Planes
(MD) Measurement and Data

6. Planning a Trip Rationale and Context
I’ve frequently taken trips on foot, but have a limited sense of direction
I’d like to get a better sense of direction using a compass and see the accuracy of this method of navigation
The following trip I’ve made often and wished to analyze it using a map and compass
From: Downtown Burlington, Cherry Street
To: Saint Michael’s College
Traveling by foot and bicycle
Map: free from USGS (United States Geological Survey)

7. Understanding a Map
A topographic map represents a three dimensional view of a specific part of the earth
The USGS provides free topographic maps of most parts of the United States
Topographic maps are printed in color with green showing vegetation, white showing open terrain, and black used for man-made features such as trails, roads, and bridges
Contour lines or elevation lines (brown lines) show where hills, mountains, valleys, and canyons are located
(G) (MD) Topographical analysis (2D-3D geometry)

8. USGS Maps
The United States is divided into quadrants based on lines of latitude and longitude
Each quadrant is often named after significant geographical features or the city or town falling within the quadrant’s boundaries
(G)Coordinate systems

9. Dividing Degrees into Smaller Angle Measurements
Each degree can be divided into 60 minutes.
(1 degree = 60’)
Similarly, 1 minute can be divided into 60 seconds.
(1’ = 60’’)
(G) Angles; (RP) Ratios and Proportional Relationships; (NF) Number and Operations—Fractions

10. A Maps Area of Coverage USGS prints maps in what is known as series
7.5 Minute series (most common), and
15 Minute series
These maps also feature other ways of determining your position on the map or globe which we will not focus on such as the UTM system.
(G)Coordinate systems
(RP) Scales

11. What is the area of coverage of a 7.5 series map?
Convert 7.5 minutes (7.5’) into degrees?
𝟕.𝟓 ′ ∗ 𝟏 𝒅𝒆𝒈𝒓𝒆𝒆 𝟔𝟎 ′ =𝟎.𝟏𝟐𝟓 𝒅𝒆𝒈𝒓𝒆𝒆𝒔= 𝟏 𝟖 𝐝𝐞𝐠𝐫𝐞𝐞
So, a 7.5 minute series map shows an area of the earth’s surface that is 7.5 minutes of longitude wide by 7.5 minutes of latitude high
(RP) Scales; (MD) Measurement and Data; (NF) Number and Operations—Fractions

12. A Map’s Scale In a 7.5 minute map the scale will be 1:24,000.
So, one unit of measurement on the map will be equal to 24,000 units of the same measurement actual size.
In a 1:24,000 scale map one inch equals about four-tenths of a mile or about 2,000 ft.
The scale on a map is also given in kilometers and meters.
The scale also shows what contour intervals represent. For this map between contour intervals there is an increase or decrease of elevation of about 20 Feet.
(RP) Scales; Measurement and Data (MD)

13. Finding Longitude and Latitude on a Map
Degrees of longitude and latitude are indicated in the corners of the map.
Looking a the bottom left corner we see the following
So the bottom left corner tells us that longitude starts at 73 degrees 15 minutes, while the latitude starts at 44 degrees 22 minutes and 30 seconds.
(RP) Scales; Measurement and Data (MD)

14. Latitude Looking at our map we have the following:
Latitude starts at 44 degrees 22’ 30’’.
The next mark indicates 25’.
Since latitude increases as one goes north
The next tick mark is 2’30’’ from the initial mark (22’30’ + 2’30’’ = 25’ 0’’)
A similar analysis can be done for longitude
(RP) Scales; Measurement and Data (MD)

15. Finding the Map’s area of interest
(G) (MD) Topographical analysis (2D-3D geometry)

16. The Compass
A compass is a magnet. Since the earth has magnetic properties it acts like a large magnet.
A compass points toward the earth’s magnet north.
Maps are oriented to show geographic north.
(G) Angles

17. Declination
Since maps show geographic north, while a compass points to the earths magnetic north an adjustment needs to be made in the field.
Fortunately, maps indicate the angular difference between the two which varies depending on your location on earth.
Declination is either west or east depending on which side of geographic north the compass needle points.
Declination is west approximately 15 degrees for this trip (see above)
So the compass will have to be adjusted about 15 degrees WEST to compensate
(G) Angles

18. Compass Basics
(G) Angles

19. Compass Basics A compass usually features
A arrow indicating that direction of travel
A needle which acts as a magnet with clear north and south polarity within a sealed fluid
A rotating housing ring with 360 degrees, the cardinal directions N, S, E, and W.
A orienting arrow which allows the needle to be “boxed”
A built in declination adjustment that allows the orienting arrow to be adjusted to read true geographic north
Useful scales of measurement on the baseplate
(G) Angles

20. Planning the Trip
In designing this trip I used GeoGebra dynamic geometry software after uploading an image to determine the angles at each turn.
(G) Angles; Lines of Intersection; Parallel Lines

21. Planning the Trip in Stages
Total trip distance: approximately 2.8 miles
(G) Angles; Lines of Intersection
Measurement and Data (MD)

22. (G) Angles; (MD) Measurement and Data; (F)Functions: Distance
“Taxicab Geometry”

23. Using a Map and Compass
A map gives you the lay of the land in miniature
To use a map effectively you must orient the geographical map image to the land
To do this is fairly simple if you can identify landmarks and spin the map to match those landmarks
(G) Angles

24. Using a Map and Compass
First, the compass must be adjusted for declination
Next, line up your compass with the longitude of the map or a line parallel to it.
Then, with the compass on a line parallel to the north south longitude line on your map and in a location with a landmark you can sight north you rotate the map and compass together until the compass needle is “boxed” within the orienting arrow
Sight your next landmark, adjust the compass housing to the direction of travel, rotate the map and compass together until the compass needle is “boxed” within the orienting arrow
Follow the direction of travel with the compass until you reach your landmark and sight a new one that requires you to change direction or stay the course
Repeat this process as you sight each landmark on your trip
(G) Angles; Coordinate systems: translations of parallel lines

25. The Trip in Video
(G) (MD) Topographical analysis (2D-3D geometry)

26. Works Cited
Hodgson, M. (1997). Compass and Map Navigator: The complete guide to staying found. Riverton, WY: The Brunton Company.
How Stuff Works. (2006). How Compasses Work: Pole Magnetism [Photograph], Retrieved April 20, 2015, from:
International GeoGebra Institute. (2015). GeoGebra (Version 5.0) [Software]. Available from:
Knot Working (n.d.). Latitude-Longitude Grid [Photograph], Retrieved April 20, 2015, from:
NASA. (2014, October 9). Latitude. Retrieved from
NASA. (2014). Latitude [Photograph], Retrieved April 20, 2015, from:
NASA. (2014, October 9). Longitude. Retrieved from
NASA. (2014). Longitude [Photograph], Retrieved April 20, 2015, from:
NASA. (2014). Prime Meridian [Photograph], Retrieved April 20, 2015, from:
Pingstone, A. (2009). Walkers Compass [Photograph]. Retrieved April 20, 2015, from:
USGS Store: Map Locator and Downloader. (2012). VT_Burlington_ _TM_geo.pdf [Data file]. Retrieved from
Zobel, E. A. (2014). Angle Measurement: Degrees, Minutes, Seconds [Photograph]. Retrieved April 20, 2015, from: