What it shows
The height of a tall object can be found from the angle of elevation and the distance to its base using tan of the angle. The clinometer measures that angle.
The science
In a right-angled triangle, the tangent of an angle is the opposite side divided by the adjacent side. If you stand a known distance d from a building and the angle of elevation of its top is theta, the height above your eye is d times tan theta. Add your eye height to get the full height. Surveyors use this idea in theodolites.
Materials
Cost: free. Many items come from home or from waste; spare parts such as LEDs, motors and wire are in the store.
- A cardboard protractor or a printed one
- A drinking straw
- Thread and a small weight (a nut)
- Tape
- A measuring tape
- Notebook and calculator
Safety
For this project: Do not look at the Sun through the straw. Measure on level ground and away from traffic.
Never use mains electricity: power models with cells, batteries or a low-voltage adapter. Sharp and hot tools, flames and lab chemicals need an adult or your teacher beside you. Keep magnets, button cells and small parts away from young children, and wash your hands after making.
All the safety rulesStep by step
8 steps. Do them in order, and test each part before you go on to the next. Write what you notice in a notebook as you go.
Tape the straw along the straight edge of the protractor.
Tie the thread at the centre point of the protractor and hang the nut as a plumb line.
Stand at a measured distance such as 20 m from the building.
Look through the straw at the top of the building and read where the thread crosses the scale.
Subtract the reading from 90 degrees if needed to get the angle of elevation.
Calculate the height above eye level as d times tan of the angle.
Add your eye height from the ground.
Repeat from 30 m and compare the two answers.
What you should see
The two heights agree within about a metre; a known object like a pole shows the method is correct.
Viva questions
A teacher or a judge will ask how it works. Try to answer each question before you open it, then compare.
1What is the angle of elevation?
The angle above the horizontal when looking up.
2Which ratio is used?
Tangent.
3Why add the eye height?
The angle is measured from your eye, not the ground.
4Why does the thread hang straight?
Gravity pulls the nut down.
Take it further
Measure the height of a tree and check it using shadow lengths.
Change one thing, measure what happens, and add a table or chart of your readings: that is what turns a model into your own investigation.
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