What it shows
On an equinox the Sun is directly over the equator at noon. The angle of the Sun above the horizon at your place is then 90 degrees minus your latitude, so a shadow measurement gives your latitude within a degree or two.
The science
Latitude is the angle between the equator and your place measured from the centre of Earth. At noon on an equinox the Sun’s rays make an angle with the vertical equal to your latitude. In a right triangle formed by the stick and its shadow, the tangent of that angle equals shadow length divided by stick height.
Materials
Cost: free. Many items come from home or from waste; spare parts such as LEDs, motors and wire are in the store.
- A straight stick or pipe about 1 m long
- A plumb line made of thread and a nut
- A spirit level or a transparent water-filled tube
- A tape measure
- Chalk
- A phone to check your latitude later
Safety
For this project: Do not look at the Sun. Work in sunlight with a hat and drinking water.
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.
Step 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.
Place the stick on level ground and check that it is vertical using the plumb line.
Start around 11:30 am (solar noon falls between about 11:30 am and 12:50 pm by the clock in India, depending on how far east or west you are) and mark the tip of the shadow with chalk every ten minutes until about 1:30 pm.
Write the time beside each mark and measure each shadow length.
Find the shortest shadow of the day; it marks local solar noon.
Calculate the ratio shadow length divided by stick height.
Use a calculator to find the angle whose tangent is that ratio; this is your latitude estimate.
Compare with the latitude shown by a map or a phone, and write the percentage error.
Repeat on a day away from the equinox and note that the angle differs by the Sun’s declination.
What you should see
A shortest-shadow ratio that gives a latitude close to the real value, for example about 28 degrees at Delhi. The shadow path chalk marks also show the noon direction as north to south.
Viva questions
A teacher or a judge will ask how it works. Try to answer each question before you open it, then compare.
01What is special about an equinox?
Day and night are nearly equal and the Sun is overhead at the equator.
02Why find the shortest shadow?
It marks the moment when the Sun is highest and due south or north.
03Why must the stick be vertical?
A tilted stick spoils the right triangle and the angle.
04What does latitude measure?
How far north or south of the equator you are, in degrees.
Take it further
Find your latitude on three different days and plot the Sun’s changing noon angle through the year.
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.
Free ebooks for this project
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