In this activity students will:
i) Learn about how a clinometer works;
ii) Use a 3D printed clinometer and the tangent trigonometric function 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:
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.
1) Pick a nearby object that you wish to measure the height and stand a certain distance from that object.
2) Look through the clinometer so that the top of the object that you wish to measure the height of is in the centre of the view piece.
3) Record the angle that the arm of the clinometer indicates (A in Image 5 of the Main Image Viewer). If you’re having problem reading the angle, hold the arm against the label once it stops moving.
4) Measure the distance between yourself and the object (d in Image 5).
5) Determine the height of the object above the level of the clinometer (h1 in Image 5), use the following equation:
Height (h1) = Distance between person and object (d) x tan(angle A)
Can your students explain why this equation works?
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).
Try this! The original function of the clinometer from which the 3D model was scanned from was to measure the cloud base height (the height of the bottom of a cloud). You can still try this out. The only addition piece of equipment that you need is a very powerful light (like a handheld spotlight) and a second person.
Wait until evening and then have the second person stand beneath some clouds and shine the light straight up in the air. You should see a bright spot where the light is hitting the bottom of the cloud. Now use the previous instructions to determine the height of the bright spot. Because of how high the clouds are you probably need to be standing 100 m or so away from the second person.
Trigonometry is the basis of how the clinometer works. When measuring the height of something (such as a tree) a right angle triangle is formed by the distance between the clinometer and the tree (d), the height of the tree above the clinometer (h1) and the diagonal line between the top of the tree and the clinometer (see Image 6 in the Main Image Viewer).
In a right-angled triangle, the tangent of one of the non-90˚ angles is equal to the ratio of the length of the side of the triangle opposite to the angle to the length of the side of the triangle adjacent to the angle:
tan(angle) = Opposite Length ÷ Adjacent Length
If we substitute the labels that we used in Image 6, we have:
tan(angle A) = h1 ÷ d
This can be rearranged to:
h1 = d x tan(angle A)
We can measure d. The clinometer measures angle A. With these two variables known, h1 can be calculated.
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 object. To get the actual height of the object, you’ll need to add h2, the distance between the group and the level of the clinometer.