On a
bright day with clear skies, the perceived edge of a shadow
appears near the outer edge of the penumbra. With
increasing haze or whenever the edge of a cloud passes by, the
perceived edge of a shadow moves inward toward the umbra. This
makes it impossible to design an accurate single-edged gnomon
(without using a shadow sharpener.) You eliminate this
problem with a double-edged gnomon such as a rod, cable,
pinhole, slit, etc.
[NOTE: see Pete's corrected message dated 5-30-02]
For an
analemmic/equatorial dial I made for a local park here in Boise, ID,
I used a single-edged gnomon with an analemmic shape. Prior to
building the gnomon I carefully measured shadow widths under
various haze conditions over a several month period. For our
local climate conditions, I found that I could best compensate for
the average perceived edge of a shadow by adding 0.222° radius to
the gnomon from solar centerline. Trying to explain this
another way, if you calculate a time mark's position
on a sundial with a straight line drawn from the center of
the sun across the top edge of the gnomon to the time mark,
then when you build the sundial you should increase the
height/width of the gnomon by 0.222° (measured from the time
mark back to the gnomon) to compensate for the perceived position of
the edge of the shadow.
Pete S.
----- Original Message -----
From: [EMAIL PROTECTED]
Sent: Thursday, May 23, 2002 7:20 AM
Subject: Shadow Sharpener Again
My request is that you will take the time to
"pull together" the results of your investigations, and publish, at
least via email and the Sundial List, a discussion of this
fascinating topic, including the implications for sundial designers.
I have tried some of your experiments myself, but confess that I'm
not sure how to interpret what I see.
Mac and Others,
Since the last description of an experiment on the difference in time between the passing of the center of the penumbra and the passing of the perceived edge of the shadow of a style, I too have been thinking about the implications for sundial designers. A 30 to 40 second difference will be of little consequence on most dials of moderate size. As Roger Bailey pointed out, EoT error and other errors may be of comparable size. However, the article in the June NASS Compendium "Subtleties Of Shadows: The Penumbra At Noon" set me to thinking about this phenomenon in more detail. In reading the time on a very large sundial, the "pinhole" shadow sharpener effect can reduce the random errors in reading a fuzzy shadow and thus lead to more precision (say down to +/- 10 sec). At the same time, knowledge of the penumbra effect can account for some of the systematic error (difference between the geometric shad! ow and the perceived shadow of about 30 sec) and thus lead to a more accurate reading of time.
As I said, I have been thinking about these things, as a different way of looking at the "Penumbra at Noon" effect and as to their implications on the design of large sundials and heliochronometers. I hope to do a few further experiments and some calculations, and to write these up in the form of a letter to the editor of the NASS Compendium.
Thanks for your encouragement, Mac.
Bill Walton
Plymouth, MA, USA
42 N 71 W
Please note my new e-mail address: [EMAIL PROTECTED]
