Hi, Art! I've been forllowing this thread with great interest, and varying degrees of comprehension! I think your explanation this time has finally made it jell for me... I believe I see certain similarities to other dial designs (which in no way makes your concept less original or valuable!):
At an early stage in the dial's evolution, when you have created concentric rings of hour points, it looks like a flat, horizontal dial, with the hour lines drawn as dotted analemmae, rather than radials. Your way, reading the intersection of the paraxial gnomon's shadow with the correct ring allows easier interpolation between the hour curves than with "conventional" curved hour lines. When you introduce an arbitrary dial surface, I see the value of Bob Terwilliger's laser trigon. This device mounts to your (may be arbitrary) gnomon, and rotates to precisely project a ray parallel to that of the Sun at a particular time. The dialist then marks the point where the laser spot lies on the (arbitrary) dial surface. Now you can create Dali dials without so much calculation, or without knowing exactly the shape of the surface in three dimensions! Dave On 20 Jan 2000, Arthur Carlson wrote: > [EMAIL PROTECTED] (John Carmichael) writes: > > > Thanks for taking the time to explain the Dali dial to us gnomonistically > > challenged dialists. I think I'm beginning to understand it, but will have > > to think about it some more. What threw me off was that I was thinking that > > a Dali dial would be draped over the edge of a table! > > It could be, hence the thread title. > > Perhaps it's best to start by thinking about a "normal" sundial with a > horizontal plate and a paraxial gnomon. Design such a dial to read > clock time without any EoT correction. Then design another dial to > read clock time plus 5 minutes, another to read clock time plus 10 > minutes, and so on for +15 min, -5 min, -10 min, and -15 min (always > without any EoT correction). Now, to read the time from such a dial > you don't need the whole plate. Any ring will do. So cut a ring out > of each of the 7 dials you just made, but of different radii so that > the rings do not overlap. Properly position all the rings around a > single gnomon. Now if you want a +5 min correction, you just read the > time from the +5 min ring. For a -10 min correction, use the -10 min > ring. Label each ring with the dates that its correction is valid, > and you have a version of my sundial. At any given hour, the shadow > will always point in about the same direction, but will be shifted > right or left a bit due to the EoT. > > If you move away from a paraxial gnomon, the concept becomes a bit > trickier because a plate with radial hour lines will only be accurate > for a particular declination of the sun, that is, a particular date. > But, look! You are only using each ring for a particular date anyway, > so it doesn't matter. > > Someplace around here we realize that most of what we have learned > about sundials doesn't matter any more either. The gnomon could be > bent. The plate could be warped. You just have to make sure that the > shadow of the gnomon always crosses the date line at exactly one > point, and that this point is never in the shadow of something else > (like a fold in the plate). > > I used this extreme flexibility to propose a sundial with date lines > in the shape of Arizona, but only after I checked a map to see that > Tucson was conveniently located (somewhat south of the middle) and > that no line radiating from Tucson intersects the border more than > once. > > So. I think you have caught on to the concept by now. One thing I > like about some dial designs is their inevitability. The plate *must* > be horizontal if it is to always be illuminated when the sun is above > the horizon. The gnomon *must* be paraxial to minimize the difference > to clock time over the course of the seasons. This concept, in > contrast, has very few constraints, although it is in a sense more > accurate than the conventional form. How can this freedom best be > used? Can we require the dial to do something new, that other dials > can't? Is there an especially esthetic form? > > Have fun with it. > > Art >
