I can think of three ways to incorporate the Equation of Time into a twisted band dial:
(1) A correction can be made in the hardware by simply turning the band around its axis. Since it is hung up on a polar support, this is easier to accomplish than with some other designs like horizontal plates. The drawback, of course, in addition to mechanical complexity, is that somebody has to constantly readjust the dial. (2) When the sun is at different declinations, the line of the shadow will be at an angle across the strip. Multiple lines can be put on the strip and you only have to read from the one with the angle matching the shadow. The drawback is the inherently bivalent nature of the analemma, i.e., for most dates there will be two lines that match and you still have to figure out which one to read. Furthermore, the accuracy is not great near the equinoxes because the EoT is changing but the declination is not. (3) The shadow is a line, but only a point is needed to tell the time. This opens up the possibility of adding date lines down the length of the strip and making the time lines the same wiggly shape as the Equation of Time graph (plus, ideally, an additional correction for the changing slope of the shadow mentioned above). To use the dial, you find the intersection of the shadow with the line for the current date and read the corrected time from the wiggly line passing through that point. I like this solution. It is easy to manufacture because all the time curves have the same shape and the same separation, and it is easy and accurate to use. Regards, Art Carlson
