This project is a bit different - I used my Glowforge to make a precision scientific instrument to measure a shadow on the summer solstice, showing my latitude (38°) minus the tilt of the earth (24.5°). As you can see the shadow made an angle of 14.5° at solar noon today.
I cut a vertical piece 20 cm high out of draftboard and carefully mounted it at a 90° angle to a draftboard base, on which I inscribed a degree scale by using trigonometry (right triangle tangent tables giving opposite/adjacent angle ratios). Here I erred - this would have been clearer if I had also included a 20 cm ruler so it was more obvious how I converted the distance into the angle.
I aligned this flat board level and roughly facing north in a sunny spot and waited for the shadow to reach its shortest length - this would occur at 1:11 pm due to Daylight Saving and my location to the west of the center of my time zone. At noon the shadow pointed directly north and its length was 14.5°, exactly as predicted.
On the summer solstice, this angle equals my latitude minus the tilt of the earth. On the equinoxes, it simply equals my latitude, and on the winter solstice it will equal my latitude plus the tilt of the earth (though I’ll have to make a different scale because it would run off this board, and it’s usually raining here on the winter solstice.
I was pleased that this project turned out as well as it did and I was able to measure latitude and the earth’s tilt to within 0.5°. I’d like to refine this design a little bit so that it can be cut by anyone and used in any location.
How cool!
I have considered marking the location of the sunlight through the window on these events, and devising a paint scheme to fit it. A solstice/Equinox clock. trying to come up with something that doesn’t provoke the question of “What are all the weird lines on the wall about?”
I did this with the kids’ washable crayons on a glass shower door - it was really cool. Before I scraped it off (it was much tougher to clean up than advertised) I definitely started to use it as a clock.
I really like your project! Back in '07, I was an astronomer/developer of a citizen science project called Measure Your World that paired schools in the US and Chile to measure the Earth’s size using the Eratosthenes method. Your design would have been a nice addition, allowing the students to directly measure their latitude.
At our prior house in Longmont (before shopping centers and apartments blocked the view), I noted the position of sunrise on the solstices and equinox and mounted terracotta suns on the fence to mark each location. For a number of years, we enjoyed following the sunrise at “Wardhenge.”
Cool idea! I may have to do something like that.
Measure Your World is a great science lesson! I imagine the moment when Eratosthenes first realized the nature of the world he was standing on. Perhaps the first among all who had ever lived to look at the math - and understand what it proved.
A lesson like that would have been so much more enlightening than the “Columbus proved the world was round” that I was handed as a child.
