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Sunny
Day,
I
tried this out with a CAD drawing. I have attached a small file that shows
the results.
The
circle is 1.5" in diameter with a 0.25" diameter hole and the square is 1.5"
with a 0.25" square hole. Both plates are 1/16" thick.
These objects are parallel to a horizontal
surface.
I set
my location for a latitude of 50 degrees north and the date is June 20,
2006. I rendered the drawing at intervals of 1 hour from noon to 6 p.m.
local apparent time. I did not introduce fuzziness but the low
resolution of the image seems to have taken care of that. It's interesting
to note that the thickness of the plate did not come into play until 6
p.m.
Although this is not a vertical surface, it does illustrate the
concept.
Happy
Dialling!
Carl
Hi John,
It's not obvious perhaps, but I assure you the shadow on
a wall of any thin flat object parallel to the wall is exactly the same shape
and size as the flat object, regardless of the sun's direction, if you ignore
fuzziness.
At low angles of incidence of sunlight, the shadow will
be fuzzier but still basically the same size and shape. If the object isn't
thin, its thickness will also affect the shadow.
Try it with a CD: hold it parallel to a piece of card
and move them around. You should be able to verify that the CD's shadow on the
card is always circular. The hole in the middle looks a little bit squished at
very low angles, but it isn't bad.
I mentioned this at a BSS conference a few years ago
after a talk by Doug Bateman on his etched glass noon dial. Some didn't seem
to believe it at first.
Chris
----- Original Message -----
Sent: Tuesday, May 09, 2006 7:54
PM
Subject: Re: Conical Gnomon
Advantages
Hi Chris:
But I'm not so sure I agree with you about a
flat disk with a small hole. The aperture disk nodus you
described works fine when the sun is not at low angles relative to the
face. example: a direct south vertical wall dial around midday.
But if it's early morning or late afternoon, won't both the shadow of the
disk and the projected solar image elongate into long ellipses? In
fact, if the sun is hitting the disk nearly edge on, I bet the solar image
projection might disappear all together. If you could manually rotate
the disk so that it is perpendicular to the sun, then I would agree with
you. But sundial I'm designing is high above a doorway and can't be
touched.
Interested in anybody's comments on
this,
John
----- Original Message -----
Sent: Tuesday, May 09, 2006 11:00
AM
Subject: Re: Conical Gnomon
Advantages
Hi John et al,
If you want a circular shadow that doesn't elongate
when the sun is at a small angle to the dial face, you can use a circular
disc, held parallel to the plane of the dial. A large disc with a
small circular hole in the middle works very well, too.
The tip of a cone is an excellent idea, but I
imagine it would only be practical for dials that are above head height,
as the tip would seem dangerous otherwise.
Chris
51.4N, 1.3W
----- Original Message -----
Sent: Tuesday, May 09, 2006 5:12
PM
Subject: Conical Gnomon
Advantages
Hello All;
I have always been a big fan of spherical
nodi on a perpendicular gnomons. I just like the way they
look and when the shadow is only slightly elliptical, sundials with
them are pretty easy to read.
But in doing some shadow tests for a new
wall dial I am designing, I was greatly dismayed by how much the shadow
elongates when the sun is at a small angle to the dial face. The
shadow ellipse is so stretched along the major axis that the dial
would be very difficult to read.
So, it occurred to me that a nodus that is
the tip of a cone might be better. So instead of
guestimating the center of an ellipse, you look at
the shadow of the point of the cone. (To test this,
I attached a brass conical plumbob to a threaded brass rod).
I figured that a cone would work better than a flat arrow because it has
a uniform cross section around it and therefore would cast a uniform
shadow as the sun rotates around it during the day, unlike a flat
arrow.
The shadow tests on the conical gnomon
worked great even at low solar angles.
John
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