At 09:23 AM 5/2/99 -0700, you wrote: >Hello Nit Picking Old Timers: > >Roger states what we have all thought to be true, that as the >style recedes from the sundial face, the shadow's edge becomes fuzzy which >limits the degree of precision attainable. This effect is most noticible on >large sundials. However, it's not as bad as we think because the eye is >very good at estimating where the CENTER of the fuzz zone (the umbra) is.
This is just a gut level feeling, and I don't know enough math to prove or disprove it, but I don't think the correct point would be in the center of the fuzzy zone. (Am I correct in my belief that the fuzzy zone is the penumbra shadow?) Assuming you could safely look at the sun directly, stand so the entire disk of the sun is hidden behind the building in question. As you gradually step back, the percent of the sun's disk that is visible will grow at an increasing rate until half the disk is visible. After that the percent will continue to grow but at a decreasing rate until the entire disk is visible. I'm not sure this would put the correct point in the center of the penumbra shadow or not. As a test, you could make use of a device I read about called a "Shadow Sharpener", supposedly used by Chinese astronomers centuries ago. The shadow sharpener is simply a stiff sheet of opaque material with a clean edged round hole in the middle. I made one from the thin cardboard backing of a pad of paper, with a hole about half a barleycorn in diameter. To use, hold the sharpener a short distance (1 to 3 feet) away from the fuzzy zone, with one side facing the sun. An image of the sun will appear on the surface the shadow is on. Move the sharpener around until the image of the sun is bisected by the edge of the roof of the building, (or whatever comprises the gnomon). I believe then that the image of the gnomon will be in the exact place it would be if the sun was a point source. Try this and see if this point falls in the same place that your eye estimates it would. Charles
