Hello Nit Picking Old Timers: Well, well, well; you are all truely amazing. I have given up on trying to write to each of you individually to thank you for your answers to my question about the definitions of "precise" and "accurate". The response was unbelieveable. I lost count at about 30!
I have already incorporated some of your ideas into the last draft of my "Sundial Owner's Manual" manuscript. I hope you don't mind. In fact, I 've printed out hard copies of the RELEVANT answers,(no lice, barlycorns, or barnyard atmospheres!), and am putting them into my heliochronometer folder for future reference. By the way, I have made similar folders that contain our previous discussions of EOT, DST, sunrises & sunsets, etc. etc. Might make a good book someday! I was going to let the present discussion die down, then go to heart of the matter: "What makes a sundial precise"? But Roger Bailey beat me to it. (see below). Roger states what we have all thought to be true, that as the style recedes from the sundial face, the shadow's edge becomes fuzzy which limits the degree of precision attainable. This effect is most noticible on large sundials. However, it's not as bad as we think because the eye is very good at estimating where the CENTER of the fuzz zone (the umbra) is. I was downtown the other day, sitting in the shade of a very tall building right next to the roof edge shadow fuzz zone which was about 18 inches wide. (Ross Mccluney could tell you how tall the building is). I was imagining that the edge of the building's roof was the style. At first I thought that that would make the sundial difficult to read. But then I realized that if you use the center of the umbra then your reading can be extremely precise. The diameter of the face of this huge sundial would be the size of a small park. What would be the smallest time divisions possible on such a large dial? one min., 30 sec., 5 sec.? Is a sundial with one second markings even possible? I think so, if and only if one reads it using the CENTER OF THE FUZZ ZONE. I'd love to hear your opinions on this one: What size would a sundial have to be to achieve one second precision (not accuracy) or better? And, for extra credit, what would be the velocity of the moving shadow on this giant sundial? A sincere thank you to all of you who have made the sundial discussion site such a valuable, educational, and entertaining experience. Please forgive me if I don'tt answer you all back personally. Back to the old grindstone, John Carmichael website: http:/www.azstarnet.com/~pappas (from Roger Bailey >Dear John Carmichael, > >Well done John, Your simple question again triggered an avalanche* of >responses from us nit picking old timers. > >By now the difference between accuracy and precision is well defined. I >would like to return the discussion to sundial design. The accuracy of a >dial depends on the skill of the designer, builder and installer. It should >take into account the latitude, longitude and orientation of the dial. > >The precision of a sundial is limited by the fact that the sun is not a >point source of light but is a disk about half a degree wide. The shadow >edge is fuzzy for half a degree as the sun is partially covered (penumbra >shadow) and then totally covered by the umbra shadow. Size does not matter. >A small dial seems to have a sharper shadow but it cannot be read as >precisely. A large dial allows division into smaller units of time but the >shadow is too fuzzy to read precisely. For a rod type of gnomon, the >problem is even worse. It may be too narrow to completely cover the sun >and produce the dark umbral shadow. > >There is a simple demonstration of this phenomenon that I observed one >morning. Stand by a window with the sun at your back and casting your >shadow on the floor. Move away from the window until the shadow of your >head is about 4 inches (10 cm) from the shadow of the top of the window. >Then slowly more to bring your shadow up to the window shadow. As the >penumbra shadows of your head and the window start to intersect, the dark >shadow will grow. The top of your head will seem to swell upward as the >shadows come together. Repeat to confirm the phenomenon. This is best done >in the privacy of your own home. > >In that twilight zone of partial shadow, a sundial cannot be precise. Half >a degree is two minutes of time. But there are techniques to minimize the >problem and read a dial to a precision of less than a minute. One is to use >a disk or ball on the gnomon to cast the shadow. A properly sized disk will >project a small dark umbral shadow at the center of the large fuzzy >penumbral shadow. The Romans used this technique by topping their obelisks >with spheres. > >Cheers from a swelled headed, nit picking, old timer, > >Roger Bailey >Walking Shadow Designs >N 51 W 115 >*where triggering an avalanche is not just a figure of speech! > > > >
