[EMAIL PROTECTED] (John Carmichael) writes: > I'm trying to understand your letter. Your design sounds very intrigueing. > In fact, I've often thought of carving a map of the state of Arizona onto > the dial face, with Tucson at the center of the dial. All the hour lines > would radiate out from Tucson. With my vertical pointer in the center and > the correctly oriented map on the face, you could point to any place within > the state, like a boyscout does with his map and compass. I could even put > latitude and longitude lines on the map. > > But I was going to use my cable coaxial gnomon, with a sphere on the cable > to serve as the nodus for date readings instead of a vertical style with > nodus sphere at tip. Your design would place Tucson north of center, and > the hour lines would radiate from a point south of Tucson (probably in > Mexico!). So with a vertical gnomon you would lose the ability to use the > poiner to take a compass bearing.
A neat idea to use the hours lines to show the azimuth, but that won't work with my idea. My hour lines wind up being wavy like the Equation of Time, and maybe bowed as well, so you can't use them to point anywhere. The main misunderstanding is that my design does not have a nodus. > >Methods which use the declination of the sun, either by using a > >specially shaped gnomon or by observing the shadow of a nodus, rather > >than an edge, are perhaps more esthetic, but they are inherently > >ambiguous at the solstices and double-valued the rest of the time. > > What do you mean by "inherently ambiguous at the solstices and double-valued > the rest of the time? The locus of the shadow cast by a nodus at, say, noon through the course of the year is the figure-eight-shaped analemma. When it is noon on any day, the shadow will fall on the analemma. But on most days, it will cross over the analemma twice, and you have to know which of these two crossings to use to tell time. You have to know whether the current date is in the first half or the second half of the year (which shouldn't be a big problem, even for absent-minded types like myself) and on that basis decide which branch is currently valid (which always is confusing, even for the mathematically and astronomically inclined). That's the double-valued part. The ambiguous part comes in because at the solstices, the shadow traverses the ends of the analemma loops tangentially, so it is hard to decide exactly when the crossing occurs. You don't have to choose between two distinct but well-defined candidates as during the rest of the year, but your one candidate becomes rather fuzzy, extending over several minutes. The only dates that are free of these problems are April 13 and August 31, the crossing point of the figure-eight. > >If we make the user do this work instead of the > >nodus, the figure-eight can be unfolded and made unambiguous. > Are you talking about a moveable nodus? No. No nodus. None. Like with an analemmic dial, the time is read by looking at the intersection of a shadow line and a time line. In the present case, there are a multiplicity of time lines, one for each day of the year (or as many as you have room for). In contrast, in a conventional dial, the shadow line coincides with the line marking the time. With a nodus, the position of the shadow point tells the time. > And from here on I'm completely lost! I can't imagine what the face might > look like, or the gnomon, let alone how you would calculate such a dial. > Wish I could see a picture! Here, here! Maybe someone can whip up a picture with Fer's program to give us something to point at while we're talking. (My PC is in the shop just now.) My idea is basically the azimuthal dial he mentions. My only contribution is pointing out that such a dial will still work even if the time lines are not circles and the gnomon is not vertical (or even necessarily straight). > If you design it, I'll build it (if it works!) It will look rather bizarre, but should be accurate and easy to read. I'm hoping you or Fer will be intrigued and do the calculations. (Unless you are willing to do a lot of dot-to-dot drawing, the first thing you will need is a mathematical representation of the shape of Arizona!) If not, I'll put it on my pile and get to it manana. Regards, Art
