Hi John, > This little distortion effect must be quite small...
You are right. > For practical purposes, you can call the shadow a circle... Right again. > ... even though it's a tiny bit elliptical. Yes again (though the tiny bit isn't quite an ellipse!). > If the disk is large, this effect becomes almost insignificant > doesn't it? Yes, again absolutely right. With a sufficiently large disc the distortion is indeed a trifle but... Some designers, hoping for a nice small shadow to pin-point the features on their dial furniture, like to have the disc as small as possible subject to it casting a shadow. This is when you have to be careful. There is nothing wrong with an elliptical shadow (that's what you get from a spherical nodus almost all the time) provided it doesn't fade away to nothingness! > I'm going to do the simple experiment tomorrow if I have time. > I also want to test how useful a horizontal disk is in the early > morning and late afternoon and I want to try a disk with a central > aperture hole. This can be a profitable experiment. You may not find any distortion at all unless you look out for it. The effect is best if the solar angle of incidence is about 70 degrees (that is the angle off the normal) so, on a horizontal surface, the altitude would be 20 degrees. If you hold a circular disc about 100mm in diameter about 1500mm from the surface you should see the effect. The anti-shadow from a hole about 15mm in diameter should distort nicely too and much more noticeably than the shadow of the outer rim of the disc. In my home town, many of the street lights have circular fittings at the top about 300mm in diameter and about 4500mm above the pavements. These distort nicely when the sun angle is low. You have to be careful. I found I got a lot of funny looks from passers-by when I was studying the shadows cast by street lights! It is important to note that for a wall dial you can easily get angles of incidence greatly in excess of 70 degrees. At noon on the summer solstice with a direct south-facing wall at latitude 52 degrees the angle of incidence is about 61 degrees and that is the *minimum* angle of incidence for the day. If the wall isn't direct south-facing, the angle of incidence is higher even at noon. I hope your experiments are rewarding. Frank King Cambridge, UK. -
