Making and Using Inclinometers

Using an inclinometer, a person can calculate the height of something that he or she can’t easily measure with a ruler. This will come in handy when your group does the Bottle Blast-Off! activity. For your group, the incentive to make and practice using an inclinometer is that they will use it to measure the height of a rocket’s flight.

Making Inclinometers

Things to Talk About Before You Begin

Before you have your group start making inclinometers, we suggest you show them an inclinometer, if you've made one, and talk a little bit about it. Tell them that the inclinometer is a tool that lets them measure the height of something too tall to measure directly.

 An inclinometer has a protractor on it. What does a protractor measure? (A protractor measures angles.) If you are planning to build rockets, you might ask your group how a person could measure how high a rocket flies. You can compare its flight to nearby buildings that you know the height of. But what if there isn’t a building nearby? Or what if your rocket goes higher than a building? The inclinometer uses math to measure the rocket’s flight.

Making an Inclinometer

To make an inclinometer, follow the directions on Making Your Inclinometer. You can photocopy these instructions for your group or explain the steps one by one while members of your group follow your instructions.

If one person finishes before the others, we suggest you ask him or her to help people who are working more slowly.

Using an Inclinometer

You can print out Using Your Inclinometer and have members of your group follow the steps on that. Or you can demonstrate each step while your group follows along.

When you demonstrate how to use the inclinometer, be sure to look through the end of the tube that sticks out from the card. Otherwise, the weight will swing back and tap you in the face, amusing all the people in your group. You can either look through the tube or place the tube on your cheek and sight along the top of the tube.

Distance Matters

The angle a person reads on the inclinometer depends partly on how far the person is from the object he or she is measuring. To make sure people understand this, you might want to have two people sight on the same tall object—with one person standing several feet closer to it than the other. The person who’s closer will get a larger angle. Calculating the height of an object requires knowing both the angle and the distance to the object.

Try Both Ways to Read the Angle

We suggest that people work with partners. One person sights on the object being measured while the other person reads the angle.

We also describe how to read the angle without a partner. Pinch the string against the card to hold it in place. This takes a little practice. Be sure everyone tries this method. They'll need it if they use their inclinometers to measure the height of a rocket's flight.

What If People Get Different Answers?

Have the whole group stand the same distance from a tall object, sight on the top of the object, and read the angle using one of the two methods described above. Have everyone compare their angles.

If people are standing at different distances from the object, they will get different readings. If people are the same distance from the object, there will still be slight variations among the readings—but they should be within 5 or 10 degrees of each other. It’s normal to have some variation—that’s what a scientist would call experimental error. (In the Bottle Blast-Off! activity, we suggest that you have three people measure the height of each rocket's flight. By averaging the readings of three people, you'll get a more accurate result.)

Calculating an Object’s Height

You can print out copies of the Height Calculator Grid and have people work with those.

On the Height Calculator Grid, people will draw a triangle that's exactly the same shape as the same triangle out in the world.

Suppose one of the people in your group measured a flagpole and drew a diagram like this one. At the lower left corner of the triangle is the measurer's eye. At the top corner of the triangle is the top of the pole. At the third corner is part of the flagpole that’s at the measurer's eye level.

The triangle on the diagram is the same shape as the triangle in the world because the angles of these two triangles are exactly the same.
First, people measured an angle with their inclinometers. Then they drew the same angle on the grid paper.

The second angle that is the same in both triangles is the 90-degree angle formed by the intersection of the vertical and horizontal lines. In this case, that’s the vertical line of the flagpole and the horizontal line that marks the measurer’s eye level.

If two triangles have two angles that are the same, then these triangles are exactly the same shape. If a side on the little triangle is half as big as the same side on the big triangle, then the other sides of the little triangle must be half as big as the corresponding sides of the big triangle.

The triangle on the diagram is a scaled-down version of the triangle in the world. How much smaller is the triangle in the diagram? The side of each square on the grid paper represents 100 cm in the real world. The squares on the grid are about 1 cm tall, so the diagram is about 100 times smaller than the triangle in the world. By drawing a triangle that's exactly the same shape as the triangle in the real world, people can measure something indirectly that they can't easily measure with a ruler.

 Where's the Math? In math class, two triangles that are exactly the same shape are called similar triangles. Drawing similar triangles can help you figure out quantities that you can’t measure directly.

When people use their drawings to find the heights of objects, remind them to count the height of each square as 100 cm. You should also point out that the horizontal line on the bottom of the grid represents the eye level of the measurer. To find the real height of an object, people need to add the height of their eye level to the height above eye level they got from the grid drawing.