Hello, I have many questions about sundial shadows. Hope this is interesting stuff. General issue is how to design the sundial so that it is most easy to read. This involves some engineering, and also some human perception issues. These are posed as open ended questions - I don't really expect answers - but many thanks in advance for your thoughts and comments.
1) How does one size a gnomen so that the shadow will be as sharp as possible? This obviuosly has to do with distance from dial surface, solar disk size, etc. But also may have to do with the eye's ability to see contrast. Given an optimum design, one could scale a dial and still have (relatively) the same sharpness, yet the eye would need to percieve the contrast at the edge of the shadow over a longer distance. Is there an optimal ratio for style tip size to distance from dial face? 2) The contrast of a shadow depends on the difference in lighting in the sunny part from the shadow part - how bright is the shadow? It is probably illuminated at the intensity of scattered light in the atmosphere - what is this? Does this vary significantly with sunrise - noon - sunset? 3) What "color" is a shadow? This is also probably a different spectrum of light from direct sun (different black body color temperature) - ie a different peak color. Since metals and plastics reflect color differently (one reflects its own color, the other tends to reflect the color of the incident light - I forgot which is which) - does the material on the face of the dial affect the percieved contrast? 4) Will the eye percive a point shadow (sharp point style) or a line shadow (like from a wall) better? For point shadows - how big a dark area (not counting the edge of the shadow were the solar disk size causes a gradient) is best? The eye tends to apply a "DOG" filter (if I remember correctly) = "Difference of Gaussian" (looks like a Mexican Top Hat) filter to images when sensing contrast. Thus the gradiaent at the edge of a shadow, as well as the width of the dark center of the shadow must matter at some size and scale. 5) Is it possible to have too bright a dial surface - making it difficult to look at the shadow? 6) Is a diffuse or specular surface best? 7) There are three aspects to reading the shadow - that is the shadow, the dial face, and the markings. What is the best marking color / material / etc? Should the markings be raised or engraved or flush? 8) The scattered light from the atmosphere tends to e polarized - would one be better able to see a shadow wearing polarized sun glasses? 9) Can you see the shadow move - can you sense its motion? How big a dial would you need (how long a shadow) to get a shadow speed that the eye could sense? Would a surface with colored inclusions (texture) help to perceive the motion? What size of texture would work best? How slow must something move before the human eye fails to percieve its motion? 10) All of these issues will be influenced by the angle of incidence of the shadow. Perhaps also by the extremes of the day. 11) Inverse problem - same issues but using a point of light rather than a shadow to mark the time. Thanks for your comments! - Ben Hoffmann, Minneapolis, MN USA
