Whoops. no sooner had I pressed Send than I realised another problem. Very sorry. I shouldn't have extrapolated from the polar gnomon case to the vertical gnomon. The formula Carl gives for the distance from a vertical cylinder at which the umbra vanishes is:
ud = r / tan (16/60) = 214.9 x r where "r" is the radius (D/2) of the cylinder. This is wrong for a vertical gnomon, as it doesn't take into account the angle between the rays and the axis of the cylinder. When the sun's altitude is Alt, the formula should be ud = r cos(Alt) / tan (16/60) = 214.9 x r x cos(Alt) This is affected by latitude, as the sun's altitude varies with latitude. For a polar gnomon the formula is also wrong, but the effect is much less. When the sun's declination is Dec, the formula should be ud = r cos(Dec) / tan (16/60) = 214.9 x r x cos(Dec) However, declination is never greater than 23.5 degrees, so the worst case is ud=194 x r, or ud=97 D, which isn't far off the figure of 105 I had before. The rule of thumb of making the diameter of a rod gnomon about 1/100th the distance to the dial is correct. Very sorry for the confusion. Brain not in gear. Chris Lusby Taylor --------------------------------------------------- https://lists.uni-koeln.de/mailman/listinfo/sundial
