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 point decl, t do 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 dial there as > well. > > > > The frosting was applied from a spray can, and the clear areas were simply > > masked off. For the lines, I used "Magic" tape - the type that doesn't > show > > up on photocopiers, cut into thin strips using a straight edge and craft > > knife. The numbers were made by removing the frosting using a stencil and > > Dremel drill fitted with a flexible drive shaft. > > > > In this dial, I frosted both the "inside" faces, so there is no glass > > between the nodus and the dial face. Hence, no refraction problems. But > in > > the "real thing" I would have to use the "outside" surfaces, and account > > would need to be taken of the refraction of two panes of glass. The > effect > > would change throughout each day, and through the seasons. The dial would > > also be smaller, the gap between the panes in my units is only 20mm. > > > > A quick test (sticking OHP film on the windows) shows that errors of about > > 15 minutes at the extremities - I guess the varying error is related to > the > > changing angle of incidence of the sunlight. > > My mathematics isn't up to the three dimensions involved - can anyone > help? > > > > Mike Shaw > > > > mailto:[EMAIL PROTECTED] > > > > http://homepage.ntlworld.com/jmikeshaw/ > > > > N 53º 21' 24" > > W 03º 01' 47" > > Wirral, UK. > > > > - > > > > > -
