Eratosthenes' method

Measurement instrument version 1.1. Because the shadow of the Front sight is to the right from the shadows of the Rear sight, arm is pointing to the left from the Sun. Shadow of the Front sight is also longer, which means, that the arm is pointing too high. 

 Eratosthenes' method is a nice way to make measurement of the Earth's circumference. It is also a very good way for schools to cooperate in different countries. Unfortunately using method needs some trigonometric skills, which are not familiar to the youngest students.

I made an optional tool for my granddaughters class (2. grade), so they can participate and make the measurement of the position of the Sun 26.3. in Vantaa Finland. 

First version of my tool. Proper also for artic research conditions.

Tool is based to the two armed spirit level, that I bought from local hard store.  Price less than 10 €.

1. Spirit level, so the angle is between horizontal  level  and position of the Sun.
2. The angle between arms.

3a and 3b. Two equal nuts fixed by super glue. They are on different sides of the arm operating like a sight of the gun.

3c and 3d. When there is no  gap between  shadows of the nuts, the arm is pointing directly to the Sun. When the length of the shadows of nuts are equal, the arms angle is the same as the Sun's position.

Later I made some product development to my measurement tool. The top picture is this version 1.1. I made two different sights. Front sight and rear sight. Similar ones as the ordinary guns have. 

 Rear sight. Two equal nuts fixed by super glue. Front sight is an equal nut in front of the tool just in the middle of the arm. Like in real guns.

When the shadow of the front sight is between the shadows of the rear sights, tool is pointing to the Sun. When the shadows are equal in lenghts, also the angle is right. As in this picture.

The angle of the Sun's postion in the sky ca be read as accuracy ca. 1 degree. It is good enough for the children of 2nd grade.

  From the spirit level is easy to check, that angle is between horizontal plane and Sun's position.

Some measuring using the old version.  

I like to  underline, that this method is optional. My grandaughter made measurements using the traditional method.  Grandfather only made the calculations.

 I used myself as a measuring rod.

Pupils of Mikkola Primary School in Vantaa, Finland measuring the posititon of the Sun. 

Here some astronomical facts concerning  26.3.2013 in Vantaa

   Length of Day: 12:47  

   Civil twilight begins: 05:19
   Sunrise: 06:02
   Sunset: 18:49
   Nautical twilight begins: 19:31
   Astronomical twilight begins: 20:24
   Sun Height 32 ° 03 noon at 12:25 pm
   Solar declination: 2 ° 23
   Sun Height 17 ° 14, azimuth 242 ° 49 (14:07 UTC)
   Solar radiation power of 596 W/m2 at midday
   lnc.: Tuesday 26.03.2013 (in 85 days)
   Location: Vantaa, latitude 60 ° 20 ', longitude 25 ° 05 '

 Result!

 The Greek team at work. We Finns have a phrase: "Happiness is only for somebody - summer is for everybody". As you can see, it is not true. At least now in Finland when I am writing this text 29.03.2013. 

My dog and my office 29.03.2013.