Wm. S. Maddux wrote: > > Dear Tom, > > So far on the list, various suggestions have addressed simulating the > angular size of the sun's apparent disk as a source, but if you are > interested in the geometry of the actual dial-style system as a whole, you > must deal with the problem of the optical distance of the sun. Comment: A luminous disk of any size which subtends an angular diameter equal to that of the sun and has approximately uniform luminance over its surface is equivalent to the sun for the purposes of illuminating a sundial to check the appearance of the gnomon's shadow.
> For example, in terms of dial geometry, we can customarily ignore parallax due > to horizontal displacements of a polar style of nearly 4000 miles near > sunrise or sunset, (the style being about that distance from earth's axis,) > because 4000/93,000,000 is a very small subtended angle ---- less than 9 > seconds of arc. For practical dialing accuracy purposes, even a minute or > two of arc would generally not matter. Nevertheless, for dial dimensions > of a few inches style height, and graduations on a dial plate perhaps a > foot or so across, parallax errors will be quite large for an uncollimated > source within the confines of a typical indoor work space. Comment: I thought this was a red herring until I made the attached drawing. Hope it helps understand this point. I'm sending it as a jpg file. Hope it comes through. > If you use a slide projector with a half-degree circular aperture stop.... How many millimeters diameter of a circular aperture stop will produce a beam spread of a half-degree? If the focal length of the projection lens is f in millimeters, then the radius in mm of the circular stop at the projection lens's focal plane will be r = f tan (0.5 degree) and the diameter will be twice this. This is using a slide projector lens as if it were a telescope in reverse, albeit a short focal length one. I agree with the rest of your points. Good contribution. Ross McCluney Attachment converted: MAC Hard Disk:parallax.jpg (JPEG/JVWR) (0000A4A8)
