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This I gotta try!
John
John L. Carmichael Jr.
Sundial Sculptures
925 E. Foothills
Dr.
Tucson Arizona 85718
USA
----- Original Message -----
Sent: Thursday, May 30, 2002 8:53
PM
Subject: Re: Shadow Sharpener Again
Hi Bill:
To determine offset of the
perceived shadow edge, I built a simple device consisting of a cardboard
test pattern, a white cardboard screen, and a stick to separate them
about 36". The test pattern was two parallel strips each exactly 1"
wide with a 1" gap between them. Over a three month period or so, at
different times of day, I would point this at the sun and measure the widths
of the shadows and the gap I observed on the white cardboard screen with
a dial caliper. The shadows of the 1" strips each averaged
about 0.72" wide and the shadow gap between the strips averaged about 1.28"
wide (at a distance of 36" away from the test pattern) giving an angular
displacement of arcsine(0.28"/2/36") = 0.222° for each edge. For
some real excitement, for my test pattern I could have used two parallel
strips 1.28" wide with a 0.78" gap between them, and it would have cast two
1.00" wide shadows 1.00" apart!
Have a great day. Pete S.
----- Original Message -----
Sent: Thursday, May 30, 2002 7:04 PM
Subject: Re: Shadow Sharpener Again
Pete,
Thanks for clearing this up.
Amazing how our fingers do not type what we think we have said! I
think your results are in good agreement with mine. Your difference in degrees
between the center of the Sun's image and the perceived edge of the
shadow of 0.222 deg corresponds to a difference in time between the passing of
the center of the Sun's image and the passing of the shadow of 53 sec.
(0.222
deg)(4 min of time/deg)(60 sec/min) = 53 sec
This is in good agreement
with my estimate of 40 sec.
I
can believe that there is a slight shift of the shadow toward the center of
the Sun's image when shadows are formed when the sky is hazy. However I
have not been able to measure this shift. I would be curious to know how
you made your measurements so I could try to repeat them here.
I made a theoretical study of this
phenomenon as follows. I plotted the illumination produced by a circular
object as it is progressively uncovered. This curve, of course, is
symmetrical about the center, and, to my surprise, is nearly a linear curve
except near the extreme ends. Because the eye's sensitivity is not
linear, but approximately logarithmic, I then plotted the data on a
logarithmic scale using EXCEL. On such a scale you cannot start with
zero when the disk of the Sun is covered, but must estimate the illumination
in the shadow by the light of the sky alone. Also the shadow will have
more illumination when the sky is hazy.
I took my old SLR camera, along with a
Kodak Neutral Test Card (Gray), outside and checked the exposure in the direct
sun and in the shadow of my garage.
On
a clear day I found the exposure had to be 5 f-stops greater in the shade than
in the Sunlight (a ratio of 1 to 128, or 0.0078). This amount was
added to all the calculated values, both sunlight and shade, the resulting
values converted to a percentage of the total illumination, and again plotted
on a logarithmic scale.
On a hazy day
I found the difference to be 4 f-stops or 1 to 32, or 0.031. In a
similar way I plotted a logarithmic curve for the change in illumination from
full sun and skylight to shade with skylight only.
These curves are asymmetrical, being
very steep just outside the shadow and very gradual near full sunlight. One
cannot, from these curves, tell where the eye would perceive the edge of the
shadow to be, but can be sure that it would be on the shadow side of the
center of the Sun's image, perhaps halfway between the log of the shadow''s
illumination and the log of the total illumination. This would put the
edge of the shadow 42 seconds from the middle of the Sun's image on a clear
day and 35 seconds on a slightly hazy day. If I interpret your results
correctly, these figures are in rough agreement.
Would like to hear more about your
analemmic/equitorial sundial.
Bill
Walton
Plymouth, MA, USA
42 N 71 W
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