Hi dialists: Hope you don't mind if I sum up what we've been discussing concerning optical resolution especially as it relates to the width of the gnomon. I think the best way of doing this would be with a practical design problem:
Let's say that you have a comission to build a very large horizontal sundial for a park downtown. It must be readable from the tops of the surrounding buildings, some of which are forty stories tall, about 400 ft. (121.92 m.). The gnomon will be a sphere 20 ft. high The minimum width of the gnomon is determined by 2 factors: 1) the maximum distance from style to shadow on dial face (east/west at dusk & dawn) the gnomon must be wide enough so that the shadow umbra does not disappear. 2) The shadow's width must be double the width indicated for optical resolution at a distance of let's say 500 feet. Of course the answer to factor #1 depends on the latitude of the sundial and the hour limits of the face. For this problem let's let this distance be 100 ft. Acording to Ross McCluney's fuzziness calculations, the gnomons width must be at least 1/100 the distance from style to shadow on dial face. this would give a minimum gnomon width of 100 ft./ 100= 1 ft. The answer to factor #2: The shadow must be 2 arcminutes wide at a distance of 500 ft. in order to be visible to the visually impared having lunch at the "Top of the world Restaurant". This is equal to 2 X .0035 inches X 500 ft = 1.75 inches. It's obvious that the fuzzy factor is far more important than optical resolution in determining gnomon width. In this case, the gnomon needs to be 12"/1.75"=6.9 times larger than necessary for visibility so that the shadow's umbra doesn't disappear. Bill Gottesman was right! However, I think that optical resolution is still important for determining the width of hour lines and other dial furniture. Have I got this all right now or am I missing something? thanks all, John Carmichael
