Mike Cowham wrote:
Dear Friends,
I have a vertical east declining sundial that I believe was once
fixed to a church building. Its gnomon is missing.
What I wish to calculate is the latitude of the dial, and its
declination. I am sure that it is a very easy problem to solve, but so
far I have failed.
When I have this information, I hope to be able to locate its
original site, (I already have a rough idea of the area of England), and
maybe find some evidence of where it was fixed to the building.
The only real clue to its location is given by the angles made
by its hour lines - assuming them to be accurate.
Thanks in advance to anyone who may be able to help.
Regards,
Mike Cowham.
Cambridge, England.
Dear Mike,
Here I give just a number of formulae by which the latitude phi and the
declination d of a vertical sundial can be calculated, assuming the
pattern is well drawn.
Measure the angles of the following 2 hourlines :
- for east decliner : hour 6 and 9
- for west decliner : hour 18 and 15
Name these angles t45 and t90 and use positive signs for the angles.
Calculate :
P = cot(t45) - cot(t90)
Q = cot(t90)
X = P*P
Y = Q*Q
a = Y
b = X + Y - 1
c= -1
Z = (-b + sqrt(b.b - 4.a.c)) / (2.a)
or
Z = (-b - sqrt(b.b - 4.a.c)) / (2.a)
Take the positive answer for Z
Then
phi = atn(1/sqrt(Z))
d = asin(Q/tan(phi))
( sqrt is square root out of... )
Example :
t45 = 29 degrees
t90 = 68.78 degrees
X = 2.0044
Y = 0,1508
a = 0,1508
b = 1.1552
c = -1 ( of course )
Z = 0,7852
phi = 48.4552 degrees
d = 20.1244 degrees ( east or west )
I hope I didn't make any typing error.
Otherwise have a look in bulletin of De Zonnewijzerkring, 88.3, page 31.
Best wishes, Fer.
--
Fer J. de Vries
[EMAIL PROTECTED]
http://www.iaehv.nl/users/ferdv/
lat. 51:30 Nlong. 5:30 E