Monday, March 8, 2010

How to measure sun angle with Gnomon

Materials needed
1. Gnomon with base
2. A plumb line (thread and nut)
3. Drawing Board of Half imperial Size or 40cmx 40cm square board (husk, ply) 12 mm thick
4. A Sheet of white paper, pencil, fine thread, a nut or other suitable weight for plumb line
5. Spirit level

Preparation
1. Paste/ tack white paper on drawing board/square board.
2. Make the board horizontal by using the spirit level.
3. Measure length of Gnomon several times. Record the Average length in millimetres. This is the height of the gnomon, H.
4. Place the three legged base centrally on the board Fix with three pins.
5. Mark with pencil the centre of the hole in the middle
6. Assemble the gnomon rod into the central hole
7. Make a plumb line by attaching a the weight to the end of a string
Your gnomon is now ready for use

Marking the shadow
1. Find a site that is flat and open sky where the sun is visible between 11a.m and 1 pm (A terrace for instance SouthEast to SouthWest segment)
2. Find a flat surface. Place the base board and check with the spirit level to ensure that the surface is perfectly horizontal.
3. Place Gnomon with base on the surface. Adjust the base board so that the gnomon is vertical. Check using a plumb line. This is very important
4. Between 11 am and 1 pm mark the tip the shadow formed by the gnomon every 5 minutes. Ensure that the stick is vertical throughout the observations.
5. Remove Gnomon from board.
6. Draw a smooth curve joining all the points through all the observations
7. Measure the shortest distance from the curve to the base of the pencil in millimeters several times. Record the average. This is the length L of the shadow

8. Construct a similar right angle triangle with sides proportional to the Gnomon height H and shadow length L, using a large scale factor. For example draw a horizontal line AM=2L; Draw a line 
AP perpendicular to it at one end, of length 2H. Join PM.

9. Measure the angle MAP. This is the angle between the vertical in your location and the direction of the noon day sun. This is the Sun angle and on the day of the equinox, this is the latitude of your location. The angle MPA is the altitude of the sun at the time of local noon.

See attached images for further clarification. For detailed information see demonstration video on the activity at youtube.


Setting up gnomon

Checking the board level with Spirit level

putting the gnomon on the board
Using plumb line to make gnomon vertical
Marking tip of the shadow by pencil
Marking the curve after the shadow markings

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