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Mapping the Louisiana Territory

adapted from "Pacing" and "Estimating Height"
by Dr. Gail Ludwig, University of Missouri-Columbia
Department of Geography

An important goal for Lewis and Clark was to begin to develop a map of the Louisiana Territory.  How were they able to accomplish this goal?  What were some things they had to know?


To create a map, Lewis, Clark, and members of the expedition had to determine the number of feet in their individual pace and use this information to estimate distance while walking. This skill allowed them to determine how far they walked in a day and how far groups of Native Americans and landmarks were from one another.  This human capital skill was an important component of developing a map. 

Would you like to learn this skill?  If so, here's what you do. 

  • Accurately mark off a 100-foot (30-meter) course. 
  • Walk normally over the course at least three times counting the number of paces you take during the three times you walk the course.  One pace is the amount of distance a person covers in two steps. 

The total distance walked divided by the number of paces taken is equal to the number of feet per pace (meters per pace).  For example, if you walked the course three times and took 150 paces, then 300 feet/150 paces = 2 feet per pace.

If you wanted to calculate your pace in meters and walking 90 meters required 150 paces, then 90/150 = 0.6 meters per pace.  Using this technique, you can estimate distances in the environment.  You can check your accuracy by measuring the length of a building, sidewalk, or hallway.  Then walk the distance, count your paces and estimate the distance.  If you consistently obtain a result that is inaccurate, recheck your pace on the 100-foot (30-meter) course. 

Using knowledge of their feet per pace, Lewis, Clark and expedition members could come very close to accurately calculating distance traveled, distance between landmarks and so on.  Knowing these distances was essential to developing a map.

Use the pacing method to determine the length and width of your classroom.

What problems might occur in calculating distances using the pacing method?

Estimating Height

Another important skill that Lewis, Clark, and other expedition members needed was the ability to estimate the height of objects.  Why was this an important skill?

If you can estimate distance and height, you are better able to create a map.  Estimating distance and height will also help you determine your location on a map.

There are different methods that can be used to estimate height:

  • the pencil method,
  • the shadow method, and
  • the head-to-ground method.

Estimating Height  The Pencil Method

To use the pencil method, you need a friend who knows his or her height and a pencil.  Then do the following.

  • Choose an object that you want to measure–maybe a tree in the backyard. 
  • Have a friend who knows his or her height stand close to the tree. 
  • Hold a pencil in your hand and extend your arm fully so that your elbow is locked.
  • Line up the top of the pencil with your friend's head.
  • Place your thumb on the pencil to line up with your friend's feet.
  • Now the pencil represents the scaled height of your friend standing against the object. 
  • See how many pencil lengths it takes to reach the top of the tree. 
  • If the person standing next to the tree is six-feet-tall (182 cm) and it takes six pencil lengths to reach the top of the tree, the tree is approximately 36 feet (1092 meters) high. 

Estimating Height The Shadow Method

To estimate height using this method, you will need two yardsticks or metersticks and a sunny day.  Then do the following.

  • Choose an object to measure such as a tree. 
  • Place a yardstick (meterstick) perpendicular to the ground and measure the length of the yardstick´s shadow. 
  • Measure the length of the tree's shadow.  Now you can use the formula below to estimate the height of the tree.

shadow of the tree  =  object height
shadow of the stick       stick height

Here's an example.

If a tree has a shadow that measures 12 feet and the yardstick has a shadow of 1 foot, then:

12 feet = tree height
1 foot         3 feet  

12 x 3 = tree height

The tree is 36 feet high.

Estimating Height Head to Ground Method

To use this method, you need to know your feet per pace.  Then do the following.

  • Choose the item you want to measure such as a tree. 
  • Stand with your back to the tree and several paces away from the tree.  Bend forward and touch your head to the ground (or get as close as you can). 
  • Look backward through your legs. 
  • If you can't JUST see the top of the tree, move further from the tree or closer to the tree and try again. 
  • When you can JUST see the top of the tree, its height will be about the same distance as the distance you are standing from the tree. 
  • Turn around and count the paces back to the object.  Then use the distance of your pace (feet per pace) to determine the height of the tree.

Try estimating the height of the same tree using each method.  Were the estimates pretty close?

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