Hello
David,
Thanks
for the good question. Although there are no hour lines possible for the
inverted polar dial of these dimensions at your latitude of 52 degrees, the
crack of sunrise and sunset may just show on the edge of the dial.
The
height of the gnomon (13) and width of the dial plate (37/2) works for a time
angle maximum* of +/- 55 degrees or +/- 3 hours 40 minutes from midnight.
At other times the shadows would either be too long or on the south side of the
plate. The dial would work well during the summer in polar latitudes when the
sun rise and set is less that 3:40 from midnight. This would limit your dial to
latitudes** to above 52.9 degrees even for the summer solstice. This is
based on the theoretical altitude of the center of the sun being zero.
For the observed first and last crack of sunset, you have to adjust for
semidiameter and refraction (dip).
Allowing for semidiameter (16") and refraction (32"), the*** crack
of sunrise/set on the summer solstice are at ~3:38:18. This time angle of
54.57 degrees would be just on your dial.
* Time
angle maximum: Tan t = 37/2/13 so t = 55 degrees.
**Sunrise/set time without dip and semidiameter corrections: Cos t = -
Tan L * Tan D. For t = 55 and D =23.44, L = 52.9.
**Sine
Altitude = Sin L x Sin D + Cos L x Cos D x Cos t. For Altitude =
-48" or 0.8 degrees, L = 52 and D =23.44, t solves to 54.573 degrees.
Roger
Bailey
Walking Shadow Designs
N 48.6
W 123.4
For
more fun like this, please refer to my presentation on Sunset Phenomenon on the
NASS Repository or I can provide copies on request.
-----Original Message-----
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Sent: January 25, 2004 11:40 AM
To: sundial@rrz.uni-koeln.de
Subject: Inferior polar dial
From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED]On Behalf Of [EMAIL PROTECTED]
Sent: January 25, 2004 11:40 AM
To: sundial@rrz.uni-koeln.de
Subject: Inferior polar dial
I think I know the answer to this one, and I'll say more in due course, but just to see what all you gurus say..........
What hour lines should be inscribed, and in what places, on an inferior polar dial for latitude 52N? The centrally-placed gnomon is 13 units high, the overall plate width (east-west) is 37 units and the north-south plate height is 26 units.
David Brown
Somerton, Somerset, UK
