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Hello Steve,
As I think to remember you asked for a procedure to
calculate a "monofilar" sundial.
I will try to give such a procedure for a dial with
a circular scale of datelines.
Solving the problem may be done in a number of ways
of course, however the best is the way one is used to.
Therefore I make use
of the mainprocedure as described on my site "A uniform method to compute flat
sundials"
This mainprocedure also is suitable for this
problem.
I don't rewrite that mainprocedure in this
mail.
Of course the procedure can be changed to suite
your needs.
Happy dialling,
Fer.
Fer J. de Vries
[EMAIL PROTECTED] http://www.iae.nl/users/ferdv/ Eindhoven, Netherlands lat. 51:30 N long. 5:30 E "Monofilar" sundial.
Procedure for normal year with 365 days as in 2002,
2006 and so on.
Inner circle is january 1
Outer circle is december 31
Define :
latitude phi
longitude LM
standard meridian SM
inclination of sundial's plane i
declination of sundial's plane d
radius of inner circel startR
radius of outer circle endR
Coordinates of style :
Define the style with 2 angles, related to the plane ( B ) and to the
x-axis ( C ).
( see attached figure ) We need 2
points to define the styleThe footpoint is in x4 = 0 y4 = 0 z4 =
0
The footpoint of the style also is the center of
the date circles.
The second point is x5, y5, z5
To calculate these coordinates some basic trig is
used ( see attached figure )
Think of the proper sign of x5 and y5
g = z5 ( must be > 0 ) Remark : g is dummy perpendicular gnomon at point
x5, y5, 0 with length z5
Calculate :
difference between inner and outer circle diffR =
endR - startR
longitude correction LC = SM - LM
The calculation of the wanted points :
loop for hourline : u = 0 to 23.9999 step "whatever
you want"
loop for month : m = 1 to 12
loop for day : day = 1 to
number-of-days-in-month
Calculate daynumber dn
Calculate the sun's declination decl for daynumber
( dn + 0.5 )
Calculate equation of time E for daynumber ( dn + 0.5 ) Calculate hourangle t = ( u - 12 ) * 15 + E + LC Call mainprocedure as in "Compute flat sundials" Output is : coordinates x, y of the shadowpoint of
gnomon g ( = z5 ) related to point x5, y5, 0
or point isn't real.
In the last case start with the calculation of the
next day
If point is real :
Related to the footpoint of the style the
coordinates of the shadowpoint are :
x6 = x5 + x
y6 = y5 + y
The line of shadow now is along the line
from 0, 0, 0 to x6, y6, 0
Calculate the angle A between this line of shadow
and the y axis of the coordinate system on the sundial's plane.
This y axis is the line of greatest slope, positive
in upward direction.
( or north for horizontal dial )
Calculate the radius of the proper
circle.
R = startR + ( dn - 1 ) * diffR / 364
( there are 365 circles and 364 spaces between the
circles)
coordinates of point of hourline on the sundial
:
x = R * sin(A)
y = R * cos(A)
Output this real point.
next day ( loop for day
) next m ( loop
for month )
next u (
loop for hourline )
Of course it isn't necessary to draw all the 365
circles.
Just draw the circles you want.
Also you may skip any number of days as you
want.
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