The SUNDIAL programme and the construction of sundials The offered programme has been developed as a practical tool for purposes I had needed. Here is the history of it, with some suggestions regarding sundials and (as an appendix) solar collectors and windows. At the last decade of the millenium, after the overthrow of the communist regime in Czechoslovakia, my observatory has been asked to help in making new sundials on the historic buildings. As a practical astronomer employed at the Brno observatory and a handy craftsman I began my work at this field. My first sundial can be seen at the northern tower of the church at Louka, southern suburb of Znojmo. The church belongs to the giant monastery, abandoned already by Joseph II. As the facade seemed to be directed exactly at west, the construction had been a simple geometric task. A local craftsman had then painted the hour numbers at marked places along an equinox line. The second sundial is at the inner facade of the gate of the Rajhrad monastery. This was the first one made together with Milivoj Husak, a well known Czech painter living in Lelekovice, just north from Brno. In this case the task was more difficult: the wall has been oriented somewhere to south-south-east and not exactly vertical. At first, I have attempted to find the exact orientation of the wall by simple tools without much computation, just knowing the declination of the Sun and the local latitude. Then I have checked and refined it by waiting for the Sun coming just in the azimuth of the wall (I had a programme saying the Sun's position already), but, no wonder, it was a bit hampered by clouds. Then I have positioned the stylos (the shadow-casting shaft, parallel with the Earth axis), and checked its positioning by waiting for the local noon. Then the shadow meets the vertical hung down from the shaft root, of course. Finally, I marked the hour lines by means of a large protractor attached perpendicularly to the shaft. However, I was not quite satisfied with its accuracy. Similarly, marking the solstice hyperboles, equinox line and the hyperboles between them with help of a simple tool attached to the shaft was quite straightforward, but the accuracy was less then one centimeter for more distant marks. It would do no problem in reality, but considering that my work should be there exposed for centuries, and wanting to stick to the ``astronomical accuracy'', I tried to refine the picture. The solution has been to write a programme, that would say me the cartesian coordinates of all the relevant marks in a suitable reference system on the wall. So, I began to develop my programme Sundial. I have applied its output to the wall in Rajhrad, and was quite content at last. The only slight problem was, that the wall has been rather a complicated surface instead of a smooth plane, but the departures from a mean plane were tolerable. Milivoj Husak had then used just some marks, namely the hour lines. Then I got an idea, that the programme can help me to find an accurate azimuth of the wall as well. Almost any moment of the sunshine should be enough for that. The key was in measuring the length of the shadow, cast on the wall by an object of a known distance from the wall. A matchbox suffices when the sunshine was almost tangent, otherwise a ruler can be used (in reality a pair of rectangles is better, to ensure perpendicularity to the wall and to get a well-defined shadow reference point). Next sundial, again with Milivoj, has been made at Hrotovice, at the east-south-east facade of a castle (now a town hall and a marvelous meeting place). In this case the stylos had to be a mere point (i.e., a ball ideally) located at the end of a thin shaft simply perpendicular to the wall. When I came there in the morning with a laptop to compute the sundial accurately, I has been disappointed by chaotic results and runtime errors. No wonder: getting the wall orientation from the length of shadows cast on it was hardly possible at the moment, as the Sun was almost in the same azimuth as a line perpendicular to the wall. I had to wait almost till the noon to get accurate results. Then I had corrected my programme to warn (dull astronomers as me, e.g.) that the azimuth of the plane can not be determined well by the shadow-length method at such a time interval. The Hrotovice sundial contains all possible features, including an analema (the ``eight'' showing the differences of the solar and mean times). Next sundials at Straznice (facade of a synagogue) and Cejkovice (inside the upper court at the Templar fortress) were both approximately south oriented and painted by local painters (Tomas Hajek in case of Straznice). The programme worked well in both cases. Then I have entered the world of solar water heating systems and wanted to compute the amount of incident energy in a most unfavourable case of a roof oriented almost exactly to the west. Such an orientation was really the case for a system I have helped to assemble. It occurred to me, that a slight extension to my Sundial programme could do the job. It was really the case, and I have then added also the possibility of using no glass, or one or two layers of it. It appeared, that in the important part of the year when the Sun can really supply the people with enough warm water, even the azimuth at right angle to south is tolerable, and not at all so bad as I had expected. (At the same time I have corrected a slight blunder due to premature rounding inside the algorithm.) The same output applies to the windows as well, of course (they are just often vertical, not slanted as roof solar panels). Actually, the relative amounts of energy incident on absorbers and interiors for different azimuths is still closer to unity, because of the strayed radiation. My programme considers only direct sunshine (it is not a simple science to get accurate results by including strayed light, varying in time and place a lot). My last sundials, up to now, are twins at the Kapucin court in Brno (below the Petrov hill). These are rather marvelous paintings by Milivoj Husak, working as sundials in the same time. One of them is almost south, the other is west-to-south. The shafts are rather subtle, as the sundials will be mostly read from proximity. That's all, for the moment. Technical details (how to attach the stylos accurately and durably to the wall, e.g.) are another issue. For the astronomical part, just run SunDial with an H option to produce the sundial.hlp file, describing all the parameters controlling its work. And make a lot of precise sundials afterward. Jan Hollan, Nicholas Copernicus Observatory and Planetarium in Brno, March 1998 Appendix, for those who cannot run the programme at the moment: a copy of SunDial.hlp ----------------------- SunDial h A# h# F# DL# X# XS# Y# YS# TA# R# {S/B} W[output file name] L# Ddd[.mm[.yy] Thh[.mm[.ss]] UT# AL# P# {Left/Right} M# E[[:]] AB# N# Q { PT[LaTeX picture file name] / PP[Encapsulated PostScript file name] } plots a sundial on the screen. Parameters (on the first line) are: H writes this information into SunDial.hlp A Azimuth of the direction perpendicular to the sundial plane (default 180=S) h# angular height of that direction /1 degree (default 0, i.e. vertical wall) F# latitude (in degrees, too; default 49.2 = latitude of Brno) DL# How many minutes is the local time ahead of that which you want to plot X# horizontal shift of the plot in percent of the screen width XS# side along X coordinate (default 100 per cent of the screen) Y# vertical shift of the plot in percent of the screen height YS# side along Y coordinate (def. 94 % for VGA to match A4 landscape) TA# is the "hour" along which the analema (the "8") is to be plotted R# is the "Radius of projection" = magnification (default 1) S asks for a Short description instead of a long one. B asks for a short description on the Bottom of the screen BR- plots no border (BC would plot a circular border) W asks for making an output file (default SunDial.txt) The parameters on the second line concern the case, that the Azimuth of the plane is not known, but its angle towards the Sun in some instant is. The time is to be given in that case at least; the other parameters have some default values. L# is the Longitude of the place / 1 degree, western as negative, default 16.6 D# the Date (missing values are taken from the system date) T# the Time of observation UT# is the t-UTC difference / 1 h (default 1 from Nov. to March, else 2) AL# distance between the shadow tip and the foot of its source (ALong the plane, default 1) P# how much is the shadow tip nearer to the plane then its source (default 0, i.e. Sun lies just within the plane) Left/Right - whether the Sun was to the left or right (default Left) When the sun shines onto the plane almost tangentially, you can measure AL and P in such a way: press two matchboxes to the plane some one meter apart and so, that the first bow casts shadow on the second one. In another cases, when the shadows are not that long, but still changing their length with time sufficiently, press a pair of rectangles to the plane so that they stay perpendicular to the plane. One rectangle should have a circular hole near its end, and should face the Sun. Mark by the pencil the foot of the shadow-casting rectangle and the centre of spot of light cast through the hole. Then note the time, and measure the distance (AL) of the spot from the projection of the hole (it lies inside the outline of foot of rectangle). The quantity P is the distance of the centre of hole from the plane (given by the rectangle dimensions). M# 9 (default) or 24 needle printer for hardcopy; Ctrl+PrintScreen or P makes hardcopy to "prn", any # to file named Sundial.e9 (or *.e24) in the TEMP directory (M1 asks for a CS212-25 printer) PT output file with a LaTeX version of the screen (default screen.tex) PP - " - an Encapsulated PostScript - " - screen.eps) In the resulting plot, the pole is shown as a circle, the cross gives the projection of the "gnomon", the shadow-casting point, of the sundial, the line on the right side is its distance from the sundial. The "hour lines" are given for each degree of the declination of the Sun, the "hyperboles" are given for solar ecliptical longitude = n * 30 degrees and for each 10 minutes. The "8" shows the difference of the true and mean solar time - the arrow connects Oct. 11 and 21 (dots are shown for 1.,11. and 21. of each month) E[[:] shows an exposition table afterwards, is a name of file to which the information should be appended, is a name of file of the same structure, which should serve as a comparison (default comparison is for 45 degrees over south at latitude 49.2 degrees). This is for evaluation of solar collectors and windows. Further parameters for this purpose are: AB# absorption of radiation in glass at normal incidence (default 0.10) N# refractive index of glass (default 1.5, as an average for solar spectrum) Z#[mag|%] is extinction of solar radiation for Sun in zenith (default 0.3 mag, i.e. 24%; default unit is 1 magnitude for #<10) Q batch mode: do not wait for a pressed key at the end No parameters are obligatory, ? gives this help (A program from Jan Hollan, N.Copernicus Observatory and Planetarium in Brno.)