2 May 1997 rev 5 whit
Purpose
We often wish to determine the latitude and longitude of a site where a GPS receiver is unable to make an accurate measurement. This might be the case at our GLOBE biology study site because the satellite signals are blocked by overhead canopy. The technique introduced in this activity allows students to determine the location of their desired site by making a GPS measurement at a nearby offset site.
Overview
After identifying locations where we wish to know a latitude and longitude but are unable to make a direct GPS measurement, students will move north or south of the desired location until they can perform a successful GPS measurement at an "offset" site. They will record the offset site's latitude and longitude measurement and the distance between the sites. Then they will arithmetically infer the location of the desired site.
Time
Two class periods
Frequency
Once per site
Skill Level
Advanced
Prerequisite
Understanding of GPS Protocol
Geometry
Concepts and Skills
Concepts
The latitude and longitude of a location can be inferred from its relationship to a nearby known location.
Magnetic Variation
Skills
Determining your local magnetic variation
Using a compass to determine true north and south
Using a measuring tape to measure length
Determining location as an offset from another location
Adding and subtracting of angles measured in degrees and minutes
Materials and Tools
GPS Receiver
Magnetic compass
Tape measure
Pencil or pen
Offset GPS Work Sheet for recording measurements and computing results
Preparation
Identify sites where you would like to make a GPS location measurement but cannot because the signal is blocked. Then find the nearest open area to the north or south of these sites.
Determine your local magnetic variation (see below).
What if you cannot make a GPS latitude and longitude measurement at your study site because the GPS satellite signals are obscured by thick foliage? See Figure 1.
You can move to a nearby location offset from your desired site where the GPS receiver can receive the satellite signals. You then can determine the location of your desired site by measuring the compass direction and distance between the offset and desired sites. In general, we need to use trigonometric skills to determine the desired location. However, if we restrict ourselves to moving directly north or south from the desired site, we can determine the desired site's latitude and longitude using only arithmetic and some knowledge about our planet.
Figure 1 (6-23) Clear and Blocked Views to a GPS Satellite
Our planet is almost a sphere. All circles of circumference that intersect the equator and each pole are the same size and are called meridians. By dividing Earth's circumference of 40,074 kilometers by 360 degrees, we learn that there are 111.32 kilometers in a degree of circumference. By again dividing this by 60, we learn how many kilometers or meters are in one arc minute of circumference (1.855 km/minute or 1855 meters/minute). GPS receivers typically present locations to the nearest 0.01 arc minutes, which is 18.55 meters of latitude on Earth. (Why do GPS receivers present results to the nearest 0.01 arc minutes? See GPS Activity "Working with Angles".)
Knowing the distance north or south between our desired and offset sites allows us to determine their difference in latitude. For typical walking distances, this will be fractions of an arc minute.
Figure 2 (6-24) Meridians, Dimensions, Lines of Constant Latitude
On Earth, the magnetic north and south poles do not line up exactly with the true north and south poles (along our planet's spin axis). Presently, Earth's magnetic north pole is slowly moving and presently located in Canada's North West Territories about 11 degrees away from our north pole. Additionally, magnetic properties of Earth's composition vary slightly between locations contributing a unique distortion to Earth's magnetic field at any given site.
Consequently, a typically small variation of a few degrees must be added or subtracted from magnetic compass measurements to determine the actual direction to our north pole. This magnetic variation depends on your location. For example, near the Atlantic coast of North Carolina, USA, a compass needle points about 8.5 degrees west of true north. During one recent year, this difference changed about one tenth of one degree in Wisconsin, USA demonstrating that substantial changes can occur during your lifetime and quickly antiquate contemporary charts and maps which indicate magnetic variation.
How important is correcting for this potential source of error? If you were to use a compass to travel north by 100 meters in coastal North Carolina without compensating for the 8.5 degree local magnetic variation, you would be about 15 meters west of a line to true north. If you were trying to identify a particular 30 by 30 meter Landsat pixel, this might put you up to half way into the adjacent pixel.
You can learn the value and direction of your local magnetic variation by asking a local surveyor, asking someone who uses topographical, nautical, or aeronautical charts, or looking on similar navigation charts yourself.
Determine your local magnetic variation.
Go to your desired site. Mark it. Attempt to perform the GPS protocol to confirm that a good GPS measurement is difficult.
Using the compass to determine directions and removing your error due your local magnetic variation, move either true north or south to reach the nearest open area in which you can successfully perform the GPS protocol. (This website can help you perform the latitude, longitude, and elevation averaging operations required by the GPS protocol.)
Record your latitude and longitude. Mark this as the offset site.
Record whether you should go north or south to get from your offset site back to the desired site.
Measure and record the distance between your offset and desired sites. You may confirm a tape measure measurement with the pacing techniques discussed in the Land Cover/Biology Activity "Determining Pace".
Follow the directions on the work sheet to determine the latitude of the desired site:
Determine latitude difference in minutes from the distance value,
Add or subtract this with the measured latitude value (See GPS Activity "Working with Angles"),
You now have the latitude of the desired site; the longitude is the same as that of the offset site.
What if the result of your addition or subtraction to the measured minutes of longitude is greater than sixty or less than zero? This means that you had moved into the next whole degree and would need to add or subtract one to the number of degrees then adjust the minutes to be between zero and sixty. Avoid this problem by converting both the difference angle and the latitude to decimal degrees before doing any arithmetic then converting the result back to degrees and minutes afterwards. See the GPS Activity "Working with Angles" for details on angle arithmetic.
Where on Earth could this procedure work correctly if you were to move east or west? Anywhere on the Equator. Why? Because the circle of latitude (0 degrees) at the equator has about the same circumference as any meridian.
In general, why can we not do this for any direction other than north or south? Unlike lines of constant longitude, lines of constant latitude have different circumferences. For example, the circumference of 0 degrees latitude (the Equator) is about 40,074 kilometers. However, at 45 degrees north or south latitude, the circumference is only 28,337 kilometers. At the poles, the circumference goes to zero. This is why some say that you can walk all the way around the world with just a few steps at the poles! (See Figure 2)