Clinometers were used by early surveyors, explorers and scientists to quickly estimate the incline and height of any objects they encountered. While not as common these days, they are still a useful tool. In this activity your students will learn how to use a clinometer to determine how tall something is in their everyday life!
Overview and Background
In this activity students will:
i) Learn about how a clinometer works;
ii) Use a 3D printed clinometer and isoceles triangles to determine the height of an object.
Additional and Background Information
The clinometer, also called an inclinometer (or, in surveying, an Abney level) is an instrument that is used to measure angles on land. This information can then be used to determine such things as the incline of slopes and the height of mountains, trees and even clouds. Clinometers have been around for a long time. They initially began as a simple plummet tool (a string with a weight at the end of it), but by the end of the 18th century it became a sophisticated tool that included such things as bubble levels, sights and telescopes.
For additional information and more educational activities on clinometers, please visit:
Lesson Plan and Activity
Constructing the Clinometer
1) The following naming convention will be used in these instructions (see Image 1 in the Main Image Viewer).
2) Paste the clinometer label on to the body of clinometer with the glue stick. Place the label so that the edge of the “0” line is flat against the raised ridge and the round cut-out portion at the top of the label is flush against the hole (see Image 2 in the Main Image Viewer). This ensures that the measurements are accurate.
3) Insert the arm of the clinometer into the hole found on in the body of the clinometer (see Image 3 in the Main Image Viewer). Make sure that the shorter end goes in first. If the arm does not move freely you might have put it in backwards.
Note: If you do not wish to use the arm (or if the arm breaks), an alternate way to do step 3 is to tie a piece of thread around the rim of the hole on the body of the clinometer and, on the other end of the thread, attach a weight (such as a paper clip or washer). See Image 4 in the Main Image Viewer.
4) As you tilt the clinometer, the arm of the clinometer will point down. The number that it points to represents the angle that the clinometer is tilted above the horizon. Try it out! Make sure to hold the clinometer in a way so that the arm does not drag along the surface of the main body.
Note: This activity is best done with 2 people working together.
1) Pick a nearby object that you wish to measure the height and face it.
2) Look through the clinometer and slowly tilt it up until it reaches 45 degrees.
3) Walk toward the object while maintaining the clinometer at a 45 degree angle. This is where the second person can help out by making sure that the person with the clinometer does not trip over anything.
4) Stop walking once the top of the object is seen through the centre of the view piece of the clinometer.
5) Measure the distance between the person with the clinometer and the object (d in Image 5 of the Main Image Viewer). This is equal to the height of the object from the level of the clinometer (h1). Do your students know why is this?
6) This height that you determined is not the actual height of the object. To get the actual height you need to add the distance from the ground to whatever level the clinometer was at when the measurement was made (h2 in Image 5 of the Main Image Viewer).
Trigonometry is the basis of how the clinometer works. In this activity, the individual walks with the clinometer at a 45 degree angle until the top of the object is seen, for this explanation we’ll assume that it is a tree. At this point, it forms a triangle which has one angle at 90 degrees and the other two at 45 degrees. This is an isosceles triangle and the two sides of the triangle that touch the 90 degree angle are of equal length (see Image 6 in the Main Image Viewer). These two distances represent the distance between the clinometer and tree (d), and the height between the clinometer and top of the tree (h1), which is how you determine the h1 in this activity.
As indicated in the instructions, h1 is the not the actual height of the object, it is the distance between the level of the clinometer when it made its measurement and the top of the tree. To get the actual height of the tree, you’ll need to add h2, the distance between the ground and the level of the clinometer (see Image 6 in the Main Image Viewer).
1 – Glue stick
1 – Tape measure
1 – 3D printout of clinometer
1 – Printout of clinometer label