What it shows
At the same moment the Sun makes the shadow of a tree and the shadow of a metre stick in the same proportion. If a 1 metre stick casts a 1.5 metre shadow and the tree casts a 9 metre shadow, the tree is 9 divided by 1.5, which is 6 metres tall.
The science
The Sun is so far away that its rays reach the stick and the tree at the same angle. Each object with its shadow forms a right triangle, and the two triangles have the same angles, so they are similar and their sides are in proportion. Height of tree divided by its shadow equals height of stick divided by its shadow. The method fails on uneven ground or when the shadow tip falls on a slope, so measure on level ground.
Materials
Cost: free. Many items come from home or from waste; spare parts such as LEDs, motors and wire are in the store.
- A metre stick or a straight pole of known length
- A measuring tape at least 10 metres long
- Chalk or pebbles to mark shadow tips
- A notebook and calculator
- A sunny morning or afternoon when shadows are long
Safety
For this project: Never look directly at the Sun. Measure shadows of trees from the ground only; do not climb.
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.
Choose a tree or a building on level ground whose whole shadow falls on the ground.
Stand the metre stick upright beside it and mark the tips of both shadows at the same time, since shadows move every minute.
Measure the stick's shadow from its base to the mark, for example 1.5 metres.
Measure the tree's shadow from the middle of its trunk to the mark, for example 9 metres.
Calculate the height: 1 divided by 1.5 equals tree height divided by 9, so the tree is 6 metres.
Repeat an hour later when the shadows are different lengths and show the answer comes out the same.
Measure something whose height you know, such as a classroom wall, to check the method.
Present a table of shadow lengths, ratios and heights with a diagram of the two similar triangles.
What you should see
Two measurements at different times give the same tree height within about 5 percent, and the known wall height checks out, showing the ratio method works.
Viva questions
A teacher or a judge will ask how it works. Try to answer each question before you open it, then compare.
1Why are the two triangles similar?
Both have a right angle at the ground and the same angle of the Sun, so all their angles match.
2Why must both shadows be measured at the same moment?
The Sun moves across the sky and the shadow lengths change, so the ratio only holds at one instant.
3A 2 metre pole casts a 3 metre shadow and a tower casts 30 metres. How tall is the tower?
20 metres.
4When is this method most accurate?
When shadows are long and sharp, in the morning or late afternoon, on level ground.
Take it further
Measure the Sun's angle from the stick and shadow using tan, and compare with the angle you get from a clinometer.
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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