Bill,
Thanks for this feedback. Although I had hopes that this puzzle would be solved, it looks more and more that to read civil time on a polar dial which doesn't move, or doesn't have moving parts, one has to put up with wavy lines.
We all appreciate your effort. Very best wishes, Mac
I had thought a civil gnomon was possible, and that it would be a complex 3-D structure. I tried to model it with 3-D software called Pro-Desktop, a free demo for a very expensive 3-D CAD software. After taking a few nights to learn the product, I found it unsuitable for this purpose, and today did a hands-on project in my workshop. I laid out half ( the afternoon) of a proper polar sundial, marked an east-west centerline from which to read the gnomon's shadow, and tried to reverse engineer the gnomon shape. By this, I mean that for each hour, I ran an inclined line backwards from the east-west centerline at an angle corrected for the equation of time and its corresponding declination. With this information, I cut material away from the gnomon to allow free passage of each shadowplane (or, more accurately in this case, each shadowline). The gnomon started out as a solid block, rather than a vertical plane, to give depth (width?) to the path of each shadow plane. I had expected that the result would be a complicated curving surface, with features of the analemma runing north/south, and of an astroid-like curve running east/west. I was wrong. The shadow planes for hours late in the day (5:00), cut into and erased all the features from planes earlier in the afternoon (1:00 and 2:00). In other words, if you make the gnomon work for 5:00, then it will no longer work for 2:00. I am very sorry to report this failure, but at least it lets me achieve closure, because I have spent way to much time obsessing about this topic. So, through a trial of reverse engineering, I enter the camp of a civil gnomon for a polar dial with straight hour lines as being impossible. Maybe this will help others to achieve closure too, or maybe become innovative enough to prove me wrong. Thanks to Mac and Fer for the polar wire gnomon information. It was really fun stuff to read and learn. Bill Gottesman -
-
