Cartography: Flattening Earth

A distorted science project from Science Buddies

April 30, 2015 | |

Flat maps cannot accurately depict the surface of our round Earth. So how do map makers adjust? Try this hands-on activity and make your own mineature planet--then flatten it and see what happens!

Key conceptsMaps

Introduction

Background

Materials

• Surface covered with butcher paper or other protective material
• Medium-size balloon (for example, a 12-inch balloon)
• Bottle cap (such as one from a plastic water bottle)
• Permanent marker (medium-thick works best)
• Scissors
• Six pushpins
• Cardboard piece, 20-by-25 centimeters or larger (It should be either thick cardboard or two layers of regular cardboard so the pushpins do not stick through.)
• Two assistants (The activity can be done alone but is easier with assistants.)

Preparation

• You will use a balloon to represent Earth in this activity. Blow up the balloon to about half full and tie it. The top of the balloon and the knot represent the North and South poles, respectively.
• 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 each pole is located.
• Draw an equator on the balloon with permanent marker. Earth's equator is an imaginary line around its center, 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.)
• Draw four equally spaced lines of longitude on the balloon with permanent marker. Lines of longitude are imaginary lines running over the globe, connecting the North Pole with the South Pole. They are perpendicular (at a right angle) to the equator.
• Look: How is this balloon similar to a real globe? How is it different from a real globe?

Procedure

• Inspired by methods used by scientists (like Tissot's indicatrix method), you will draw same-size circles all over the globe (balloon), create a projection (flat map) and study its distortions.
• Start by drawing one circle centered on an intersection of the equator and a line of longitude. To do this, place the bottle cap on the balloon and trace around it with the permanent marker.
• Now draw similar circles centered on the intersections of the equator with the three other lines of longitude. You now have four circles on your globe.
• Add four more circles on the equator that are equally spaced between the four circles already drawn.
• Add a circle on the North Pole (balloon top) and the South Pole (area around the knot).
• Add eight circles in the Northern Hemisphere, about midway between the equator and the North Pole, with two circles between each pair of lines of longitude.
• Repeat the previous step for the Southern Hemisphere. You now have a total of 26 circles drawn on your globe.
• Examine your globe. Note that these circles are on the same line of latitude as well.
• Use scissors to snip a tiny hole in the balloon, close to the knot. Allow the balloon to deflate on its own rather than pop it!
• Carefully cut the deflated balloon 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.)
• Next you will create a projection of your Earth with drawn circles by stretching out the deflated balloon to form a rectangular, flat map.
• Put the cardboard in front of you on your work area. Place the pushpins within reach.
• Stretch the balloon to be flat and as close to rectangular in shape as possible. (It will be easier with an assistant.) One person can hold one side while the other holds 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 it.)
• Work together to pin the stretched-out balloon onto the cardboard. (Caution: Be sure to put the pushpins in slanted slightly outward, or away from the balloon.) Pushpins that are pointing straight down or with the colored tips pointing inward might shoot out due to tension in the balloon.
• Occasionally a balloon might rip in the process. If it does, hold the ripped edge with your fingers to make the observations. An extra pushpin can sometimes help hold a ripped balloon.
• Examine your flat map, especially the size of the circles. Remember, all the circles were identical in size on your globe when it was inflated.
• Study your flat map again, now concentrating on the distance between the circles. Remember, the circles on the equator were equidistant from one another; 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.
• Look at your flat map again, now concentrating on the shapes of the circles. Remember that you started with equally sized circles.
• Extra: Investigate if the relative direction of the circles, with respect to one another, is maintained in your projection. If so, the direction has been maintained in that area of your map.
• Extra: The projection you created is similar to the Mercator projection frequently used to create world maps. Find a Mercator projection world map and compare the size of North America and Africa.

Observations and resultsAs parts of the balloon are stretched more than others, the size of the circles is no longer identical on the map. This indicates that relative size and distance are distorted in this projection. Circles on the equator (or any other line of latitude) are still mostly equal in size, indicating that features located on the same line of latitude can be compared in size. Relative to the size at the equator, enlargement gets more prominent as you move away from the equator, and is most extreme at the poles. This explains why Mercator projections can provide misleading information when comparing size or distance. (Note that you cannot extrapolate all of your findings to Mercator projection. The balloon map you just created shows distortions on the edges that would not appear in Mercator projections.)

More to exploreWorld Geography, from Mr. NussbaumProjecting the Globe on a Rectangular Map, from Science BuddiesCylindrical Projection, from KidsGeo.comWhat Is Cartography?, from WiseGeek.com

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