I've just realized, thinking about it again, that the simplest realization of a 'helical' dial is a single sheet of metal given a half-twist of 180 degrees. So long as the edges are straight and the twist is distributed uniformly then the desired "line o'light" effect will be achieved.
And so we converge with the Sun Dagger thread. Like the rock slabs on Fajada Butte, your spiral converts a "horizontal" movement of the sun into a "vertical" movement of a shadow, a neat trick. What has me worried is the effect of a "vertical" movement of the sun, i.e., the seasonal change in declination. With a spiral having a finite period, won't the declination introduce an offset in the time?
I did spend some time on the maths and, if you get it right, then each surface is actually required to bend in only one direction at any point so bending should work. Good point about lumps, bumps and other irregularities though. This isn't a problem with 60 thin hexagonal sheets, of course, but them you have to align each one correctly, 8 degrees with respect to the one below - not a trivial taks I think.
I have my doubts. The edges of a spiral sheet are longer than the midline, so some streching, not just folding, will have to be done.
--Art Carlson
