To All interested in glass sundials and the refraction problem.
Some one year ago I answered to Mike Shaw with a procedure to calculate a
double glass sundial.
This message I forward to the mailing list again.
Playing with the factors for the pin-gnomon and the thickness of the glass
panes
shows the effect of the refraction.
It depends strongly on the thickness of glass in the total thickness.
If you have Deltacad I can send a macro which calculates these double glass
dials and shows the pattern on screen.
Hourlines and datelines for a zodiacal calendar are shown as well as the
horizon line.
The pattern is drawn in two layers, a non-refracted sundial and a refracted
sundial.
Switch between the two layers to see them separate.
You need to change the values for the glass and the gnomon in the macro
yourself.
Send an e-mail if you want the macro to mailto:[EMAIL PROTECTED]
Best wishes, Fer.
Fer J. de Vries
De Zonnewijzerkring
mailto:[EMAIL PROTECTED]
http://www.de-zonnewijzerkring.nl
Home
mailto:[EMAIL PROTECTED]
http://www.iae.nl/users/ferdv/index-fer.htm
Eindhoven, Netherlands
lat. 51:30 N long. 5:30 E
- Original Message -
From: fer j. de vries [EMAIL PROTECTED]
To: sundial sundial@rrz.uni-koeln.de
Sent: Monday, July 29, 2002 5:01 PM
Subject: Re: Double glazing dial
Hello Mike,
Nice idea to make a double glazing sundial.
I dont know of any program to do the job for you but here you will find a
solution to calculates such a dial.
The window can have any declination or inclination as you want.
At my web site ( address below ) you may find a method to compute flat
sundials.
( See the link at the site )
We need the main procedure of that method with some extra routines to
solve
the problem.
For definitions and details look at my site.
I suggest to place the shadow casting point at some distance from the
outside pane to get a larger dial on your inside pane.
That distance I call g1
If you don't want to do this just take g1 = 0
The thickness of the outside pane is g2
The space between the two panes is g3
The thickness of the inside pane is g4
I assume:
- the refraction index of glass is ref and equal for both panes.
- the medium between the two panes acts like air with no extra
refraction.
- the panes are parallel.
Of course you have to declaire values for latitude phi and for the dial's
inclination and declination i and d.
Because (nearly) all the lines on the sundial will become curved, you need
to calculate a series of points ( decl, t ) for each line.
decl is the sun's declination
t is the hourangle of the wanted point.
For each pointdecl, tdo as is written below.
In decl, t
x0 = sin t . cos decl
y0 = cos t . cos decl
z0 = sin decl
R = 90 - phi
x1 = x0
y1 = y0 . cos R - z0 . sin R
z1 = y0 . sin R + z0 . cos R
if z1 0 point isn't real: sun is beneath the horizon.
R = d
x2 = x1 . cos R - y1 . sin R
y2 = x1 . sin R + y1 . cos R
z2 = z1
R = i
x3 = x2
y3 = y2 . cos R - z2 . sin R
z3 = y2 . sin R + z2 . cos R
if z3 = 0 point isn't real: sun isn't above the dial.
These are the coordiantes of the sun relative to the window.
Add new routine
x4 = x3 / ref
y4 = y3 / ref
z4 = sqrt( 1 - x*x - y*y ) ( square root out of (...) )
These are the coordinates of the sun corrected with the refraction index
ref.
Now we have to calculate the shadowpoints on 4 sundials
xa = x3 . g1 / z3
ya = y3 . g1 / z3
xb = x4 . g2 / z4
yb = y4 . g2 / z4
xc = x3 . g3 / z3
yc = y3 . g3 / z3
xd = x4 . g4 / z4
yd = y4 . g4 / z4
The final coordinates of the point are
x = -( xa + xb + xc + xd )
y = ya + yb + yc + yd
The x value gets a minus sign because you will draw the pattern from the
opposite side as the gomon is.
Use the two tests inside the procedure to exclude irrelevant points.
Also exclude points that are very far away of your sundial.
Show us what your final dial will be.
Best wishes, Fer.
Fer J. de Vries
mailto:[EMAIL PROTECTED]
http://www.iae.nl/users/ferdv/
Eindhoven, Netherlands
lat. 51:30 N long. 5:30 E
- Original Message -
From: The Shaws [EMAIL PROTECTED]
To: Sundial list sundial@rrz.uni-koeln.de
Sent: Sunday, July 28, 2002 8:53 PM
Subject: Double glazing dial
I have wondered for a while if it was possible to make use of the two
panes
of glass in double glazed units to make a window sundial.
To try out the concept, I made a prototype dial using two panes of
glass,
clamped 44mm apart (I just happened to have some wood that thickness).
The pane nearest to the sun carries a double arrow which acts as the
gnomon
nodus. The inner glass carries the dial face.
The dial was designed for a site which declines 76 degrees West of
South -
the back of my house.
I used Francois Blateyron's Shadow programme - Version 6.2.1
I have put a picture on my web page - follow the link to Double Glazing
Dial - there is a link to Jim Tallman's single glazing