Hi Charles, In the quick test I did today, I did not take measurements that would provide an experimental answer. My conclusion from observing the progress of the shadow is that the Shadow Sharpener would determine accurately the edges of the penumbra. The movement of the vertical eclipse is symmetrical across the disk so the center point of interest would be half way between the start and end of the eclipse, when the image is a perfect hemisphere. The light curve would be "S" shaped, starting slowly, having the most rapid change as it passed the center and then flattening out as it approached the full shadow of the umbra.
Observationally I expect things are different. We are dealing with shades of grey. The start of the penumbra seems to be harder to detect than the end at the umbra so the mid grey point I would expect the observational mid point to be closer to the umbra than the true mid point determined by the Shadow Sharpener. As Edgar Allen Poe once wrote: "The shadow that divides life from death is at best shadowy and vague. Who is to say where one ends and the other begins". We now have a motto for the GIANT PRECISION SUNDIAL. Roger Bailey Walking Shadow Designs N 51 W 115 10:25 PM 5/3/99 -0400, [EMAIL PROTECTED] wrote: >Greetings wonderful dialers all ! > >Regarding Phil Pappas suggestion that the true shadow point is in the >center of the prenumbra, I still have doubts. > >I haven't had time to make a shadow sharpener to see if the point is in the >perceived center or not, but in the meantime, I was wondering if anyone >could show, mathematically/graphically, the increasing intensity of light >as one moves from the darker edge of the penumbra shadow to the lighter >edge, and to show at what point on this curve of increasing light the sun >would be bisected by the gnomon? I suspect it is closer to the darker edge >rather than the center. > >As a point of interest, I read that the Shadow Sharpener was used to >precisely locate the noon shadow of the tip of a tall vertical gnomon >several days before and after the solstices. With these points accurately >plotted, it was then possible to interpolate the exact time that the >solstice occured, even if it happened at night at the observer's location. > >Charles > > >
