I want to design an experiment to show (in an educational context) how we can measure the radius of the Earth without using modern technology in order to demonstrate the engineering achievements of those who did it so long ago, and to show some practical uses for the maths involved.

The methods I know how to do this are:

  1. Place a stick vertically in the ground and another one many kilometers North of it and measure the shadow of both at exactly noon.
  2. Know the height of a mountain by a large lake or the sea and measure the distance you have to go until it disappears.
  3. Watch the sunset lying down and then stand up and watch it again, measuring the time difference between them and know your height.

The first two are impractical to do with the kids, but the third one shows potential. However, is there a way to do this during the day using shadows cast by buildings, or must the shadow come from the horizon? How could I design some simple equipment to allow me to do this experiment and calculate the radius of the Earth during the day?

Note: I am happy to use a digital stopwatch as the kids can easily see how people in the past might have used a mechanical clock to do the same thing (including measuring the length of a full day).

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    $\begingroup$ You could probably do 1) with a globe or other large ball as the earth matchsticks or similar as the sticks and a bright torch as the sun. $\endgroup$
    – nivag
    Jan 30 '15 at 9:24
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    $\begingroup$ Here is a nice method using only a photograph of the sun: orfe.princeton.edu/~rvdb/tex/sunset/ms.pdf $\endgroup$ Jan 30 '15 at 11:31
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    $\begingroup$ I like the idea of building a Sun/Earth model and doing the measurement on small scale. Can be done in addition to the large scale methods. $\endgroup$ Jan 30 '15 at 18:19

The experiment can be done during daylight but you need a very tall building overlooking the ocean & having an uninterrupted view of the horizon. This video show a group of US students doing the experiment You Tube - Measuring the Radius of the Earth

To get an accurate measurement you will need:

  • to be able to view the horizon unimpeded

  • have reasonably accurate way to measure vertical angle, a theodolite would be ideal, but not practical with younger kids

  • know the height of the viewing platform

The main reason why an unimpeded view of the horizon is required is for accuracy: the longer the target distance the more of the Earth's curvature is being considered. Also, the higher the building the further the viewable horizon.

The other thing is to decide which point on the horizon to measure to consistently.

One of the problems will be weather and air clarity, particularly heat shimmer, haze absence of fog etc.

The guys in the video had an error of 78% with their measurement due to air clarity, using a thick point marker and not having very accurate angle measuring equipment.

The third option you list could be done during a school camp by the sea, but I don't know that is practical or even possible in your situation.

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    $\begingroup$ Doesn't having a "very tall building" count as modern technology? They didn't have skyscrapers in Ancient Greece. $\endgroup$ Jan 30 '15 at 14:14
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    $\begingroup$ Well, apparently, the ancient Islamic scholar Al Biruni did it using a mountain. A tall building can be substituted for a mountain - both given you the advantage of height, they're just platforms. $\endgroup$
    – Fred
    Jan 30 '15 at 14:22

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