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Student Guide: Cartography: Projecting the Globe on a Rectangular Map

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Summary

Have you ever wondered how cartographers create a flat map of the spherical Earth? Use a balloon, a bottle cap, a permanent marker, scissors, a piece of cardboard, and some push pins to find out.

Useful Vocabulary

  • Map: Special kind of image that shows, as accurately as possible, spatial relationships between different features. In general, a map has the following characteristics:
    • Drawn to a scale,
    • Created with a specific purpose in mind, and
    • Only includes a small area — just enough to serve the map's purpose.
  • Cartography: The art and science of making maps.
  • Distortion: If something is not represented accurately, we say it is distorted. Common distortions in map projections are distortions in distances, shapes (direction), and area.
  • Equator: Imaginary circle around the center of Earth that is equidistant (the same distance) from the North Pole and the South Pole.
  • Line of latitude: Circles around Earth that are parallel to the equator. The equator is a special line of latitude.
  • Line of longitude: Imaginary lines running over the globe, connecting the North Pole with the South Pole. They are perpendicular (at a right angle) to the equator.
  • Map projections: Different ways or methods that cartographers use to create flat maps of the world. The Mercator projection, a common map projection, is shown here in Figure 1.
    Mercator projection of the world
    Figure 1. A Mercator projection of the world. In this projection, lines of longitude are vertical lines and lines of latitude are horizontal lines.

  • Equator and lines of latitude and longitude:
    Diagram showing the equator and two other lines of latitude (dashed lines) and two lines of longitude (yellow lines).
    Figure 2. Picture showing the equator and two other lines of latitude (dashed lines) and two lines of longitude (yellow lines).

Materials

To do this activity, you will need:

  • Surface covered with butcher paper (1)
  • Balloon, 12 inch (1)
  • Bottle cap, 2–3 cm diameter (1)
  • Permanent marker, medium-thick or thick (1)
  • Scissors (1)
  • Cardboard piece, 20 x 25 cm or larger (1); either thick cardboard or two layers of regular cardboard so the push pins do not stick through
  • Push pins (6)

Directions

  1. In this activity, you will use a balloon to represent the globe. You will project the globe on a flat surface. Inspired by methods used by scientists, you will draw equally sized circles all over the globe and then see how the circles are distorted in your final map.
  2. Blow up the balloon to about half full (a diameter of roughly 6 inches) and tie the balloon. The balloon represents the globe. The top of the balloon and the knot represent the North and South Pole, respectively.
  3. If you would like, use the permanent marker and label the top of the balloon with an "N" and the knot with an "S". This will remind you where the North and the South Poles are located.
  4. Draw the equator on the balloon with permanent marker. The equator is an imaginary line around the center of Earth, which is equidistant (the same distance) from the North Pole and the South Pole. Note: Once your marker lines are drawn, always set the balloon on the butcher paper or on the cardboard to avoid getting dirty prints on your work surface.
  5. Draw four equally spaced lines of longitude on the balloon with permanent marker. How is this balloon similar to the real globe, and how is it different from a real globe?
Balloon representing the globe with the equator and lines of longitude drawn on the balloon.
Figure 3. Picture of a balloon representing the globe. The equator and four equally spaced lines of longitude are drawn on the balloon. Note that only one line of longitude is visible from this angle, but there is one line of longitude on the left (barely visible), one on the right, and one on the other side of the balloon.
  1. Draw a total of 26 equally sized circles on the balloon. For each circle, place the bottle cap on the balloon and trace around it with permanent marker.
    1. Start with one circle centered on an intersection of the equator and a line of longitude. Repeat for the three other lines of longitude.
    2. Add four more circles on the equator that are equally spaced between the four circles already there.
    3. Add a circle on the North Pole (top of the balloon) and the South Pole (area with the knot).
    4. Add eight circles in the northern hemisphere, about midway between the equator and the pole, with two circles between each pair of lines of longitude. Note that these circles are located on the same line of latitude.
    5. Repeat step 6.d. for the southern hemisphere.
In the science activity, identical circles are drawn on the balloon by tracing a bottle cap with permanent marker.
Figure 4. Identical circles are drawn on the balloon by tracing around a bottle cap with a permanent marker, as shown in the top left picture. The final result is shown in the two bottom pictures (from different angles). The North Pole (N), South Pole (S), and the equator are labeled in all the pictures.
  1. Look at your balloon; how are the circles distributed?
    1. Are the circles on the equator equally spaced? How about the circles between the equator and each pole? Note that these circles are on the same line of latitude as well.
    2. Are all of the circles equally spaced?
    3. Look at a circle on an intersection of the equator and one of the lines of longitude. How would you describe the direction from this point to the circles that are closest to it in the northern and the southern hemispheres in terms of north, northeast, etc.?
  2. Use scissors to snip a tiny hole in the balloon, close to the knot. This will deflate (not pop!) the balloon.
A tiny hole in the balloon close to the knot allows the balloon to slowly deflate.
Figure 5. Scissors are used to snip a tiny hole in the balloon, close to the knot. This allows the balloon to slowly deflate.
  1. Once the balloon is deflated, cut it open along a line of longitude from the South Pole (the knot) to the North Pole, but stop a little before the very top of the balloon. Cutting over the very top increases the risk of the balloon ripping when it is stretched out in later steps.
In this science activity, you cut the balloon from one pole to the other, following a line of longitude
Figure 6. To cut the balloon open from one pole to the other, start at the knot, following a line of longitude, and cut all the way to the top, stopping a tiny bit before the very top, as shown in the picture on the bottom left.
  1. Put the cardboard in front of you on your work area. Place the push pins within reach.
  2. Work together and stretch out the balloon to be flat and as close to rectangular in shape as possible. One person can hold one side, while the other can hold the other side of the balloon. Try to get the equator straight and the lines of longitude as straight as possible. Note: Do not stretch the balloon too much, as this could rip the balloon.
    1. How do the circles change in form and size as you stretch the balloon?
    2. Why would you stretch the balloon into a rectangular shape?
    3. Why do you think you should keep the equator and the lines of longitude straight in a projection?
The balloon is stretched out to form a flat, rectangular shape.
Figure 7. The balloon is stretched out to form a flat, rectangular shape. Note that this picture only shows the globe with an equator and the four lines of longitude (remember, you cut along one of the four lines); your version will also have the circles so you can observe if there are any deformations.
  1. Work together to pin the stretched-out balloon onto the cardboard.
    1. Caution: Be sure to put the push pins in slanted slightly outward (away from the balloon), as shown in the figure below. Push pins that are pointing straight down or with the colored tips pointing inward might shoot out due to the tension in the balloon, causing a hazard.
The push pins need to be put in slanted slightly outward
Figure 8. The push pins need to be put in slanted slightly outward so the tension in the balloon does not propel them out.
  1. Occasionally, a balloon might rip in the process. If it does, hold the ripped edge with your fingers to make the observations. An extra push pin can sometimes help hold a ripped balloon.
  2. Look at your flat map, especially the size and distance of the circles.
    1. Are the circles all still the same size? If not, can you find regions on your map where they are? Remember, all circles were the same size on the globe.
    2. Are the circles still the same distance from each other? Remember, the circles on the equator were equidistant from each other; so were the circles between the equator and each pole. Also, the circles in the northern and southern hemispheres were drawn midway between the equator and each pole. Is this still the case on your map?
  3. Look at your flat map again, now concentrating on the shapes of the circles.
    1. Do all of the circles still look like circles?
    2. Do your observations indicate distortions in your map? Remember that you started with equal circles.
  4. Can you see if the relative direction with respect to each other is maintained in your projection? To check this, identify a circle on an intersection of the equator and a line of longitude. How would you describe the direction to the closest circles in the northern and southern hemispheres in terms of north, northeast, etc. on your map? Is this identical to how you described it on the globe in step 7.c.? If so, the direction has been maintained in that area of your map.
  5. The projection you created is similar to the Mercator projection frequently used to create world maps. Having done this activity and looking at the Mercator projection world map shown in Figure 1, would you conclude that North America is bigger than Africa, smaller than Africa, about equal in size, or do you not have enough information to compare their sizes.