Finding Solar Noon from the shadow of a stake

I'm currently taking a course in Solar Power, and one of the assignments was to determine solar noon by taking multiple measurements of the length of the shadow of a stake from a location between the hours of 10:00 AM and 2:00 PM. While the weather this winter has been unseasonably warm in Northeastern Pennsylvania, it hasn't been consistently sunny, and being able to find a sunny day when I was available to do this exercise was a bit of a trick. But today was the day: the sun was shining and my schedule was clear!

The first trick was to find an appropriate stake. After a few tests with a five-foot tomato stake that left shadows that extended into places where I couldn't measure, I settled on a plastic utility stake with a metal spike and a flat foot. As this stake was 38.5" tall after being planted, it wasn't too hard to find a location where its shadow could be conveniently measured.

The next trick was measuring the shadow. Having managed to misplace all of my tape measures, I had to use two yard sticks laid end to end in the path of the stake's shadow. The white yardsticks made the shadow more visible on the dormant grass of my lawn. But the grass itself presented a problem with getting precise measurements. I would have been better off laying down a flat platform - a sheet of plywood, perhaps - and measuring the shadows there. Because of my measuring difficulties, I decided to measure to the nearest half-inch.

Then there were the clouds. The sky was only partly cloudy, but occasional wisps of cloud around the sun made the sunlight diffuse enough to cast fuzzy shadows. I started off taking measurements at roughly half-hour intervals, but realized I should take more frequent measurements as the sun was available. I had originally planned to take five measurements, one on each hour from 10:00 to 2:00, and then decided to take nine measurements, one every half-hour. In the end I took thirteen measurements - though forty-seven minutes passed between the next-to-last and last measurements, due to an extended period of cloud cover. (The break in the clouds I took advantage of for the last measurement lasted about five minutes.)

Here's the graph of my measurements. (Right-click to see full-sized.)

With the simple spreadsheet/graphing package I was using, I couldn't simply plot measurements against my irregular measurement times. I had to set this up as a "scatter plot", with the x-axis representing minutes elapsed from the start of the measurements.  The inelegance of the critical region - between 125 and 135 minutes from the start of observations at 10:07 AM - is probably the result of the crudeness of my measurements. In this region length was changing much more slightly over time, so more precise measurements would have been better. Still, this program calculated that solar noon for my location on this day was about 12:17 PM, which was 130 minutes from the start of observations - right in the range of 125-135!