Re: plotting timelines for giant sundials
Hi John and other dialists Perhaps a precise solution would be to calculate the intersection of the hour line with the enclosing frame of your sundial. It must be done by a computer but its easy to give a very good precision. The result would be given as a length and a direction (north, east, south, west side of the sundial), the origin could be one of the two opposite corners. The only problem then is to precisely draw your frame, with parallel sides and a good perpendicularity. With one intersection point you can draw the line by joining it to the gnomon foot. I plan to include such kind of data in my Shadows program in a futur version. François Blateyron [EMAIL PROTECTED] Home page: http://web.fc-net.fr/frb/ Cadrans solaires / Sundials: http://web.fc-net.fr/frb/sundials/ -Message d'origine- De : John Carmichael [EMAIL PROTECTED] À : sundial@rrz.uni-koeln.de sundial@rrz.uni-koeln.de Date : lundi 24 mai 1999 03:21 Objet : plotting timelines for giant sundials Hello dialists: I have been giving more thought to the practical aspects of designing and constructing a very large sundial, particularly the problem of accurately laying out the time lines. THE PROBLEM: The plotting techniques which use tabulated angles or computation produce timeline plotting angles in degrees which the dialist must mark onto the dial plate using a protractor. These angles will be as precise as the number of decimal places used in the calculations. However, even though one takes great care to obtain precise timeline angles, this amount of precision is useless if one's protractor isn't equally precise. The graphical plotting method also requires an accurate protractor, of course. SOLUTION A: By definition, large protractors are more precise than small ones. So physically laying out the hour lines for a giant sundial would require a giant protractor. Even Robert Terwilliger's laser trigon wouldn't help because it's degree markings are too small. Computer drawn lines don't help either, because you can't easily enlarge a small paper drawing by a hundred fold. I'm thinking that during the construction phase of a very large sundial, I could make a temporary giant protractor located just outside the hourline radius. This would be a fairly simple thing to do using plane geometry. SOLUTION B: If the unit square method is used (Waugh, pg. 40-43), then no protractor is needed. One only needs a good long measuring tape for laying out the lines. ( The limits of precision would again depend on the number of decimal places used.) SOLUTION C: What if I built the gnomon first and use its shadow to tell me the position of the time lines With this method, no calculations, plotting, protractors or tape measures are needed. Using a shadow sharpener, the exact position of each timeline could be marked onto the dial face. Of course, using this method would require the proper EOT, DST, and longitude corrections. This method would also work well on an irregular surface. (I think) Marking the time lines would be easier and faster on those days when EOT=0, right? Do any of you have any thoughts on this problem and which would be the best solution? Thanks, John Carmichael
Re: plotting timelines for giant sundials
John, I currently have a similar problem of helping to delineate a large dial, this time a vertical decliner with a 17 foot gnomon which is to be carved directly into the wall of a tower. Needless to say, the wall is not absolutely flat. My current solution has been to build a laser trigon which will be mounted directly on the real gnomon. The protractor of the trigon is 300 mm in diameter. It has a ring of holes at 1.25 degree intervals, which corresponds to 5 minute intervals on the dial face. The laser assembly locates with a pin into this ring. The pin passes though a sliding vernier, which has 5 holes set at 0.25 degree intervals, thus allowing the individual minutes to be displayed on the dial. The precision required was achieved by drilling the holes in the protractor using an accurate rotary table clamped to the pillar drill. The alignment of the gnomon to be truely polar pointing is more difficult than drawing the hourlines - as the wall isn't guaranteed flat, there is no point of reference and its presence prevent you looking up the gnomon at the pole. My solution here is to mount a laser looking down (and parallel to) the gnomon. The laser beam hits a mirror stategically placed just below the gnomon. The mirror (first surface, optically flat) is aligned to be parallel to the equator by means of a theodolite. This theodolite is co-mounted with the laser and looks at the sun though a suitable filter. Its co-ordinates are set to values of the sun's instantaneous Declination and Local Hour Angle, obtained from a portable computer. When the gnomon is properly aligned, the laser beam reflects off the mirror and retraces its path to the laser, which is fitted with a surrounding screen to show the laser spot when it is slightly in misalignment. That's the theory - the proof will come next month! Any other suggestions welcomed. John Davis
Re: plotting timelines for giant sundials
Hi John, Here is a try: John Carmichael wrote: Snip THE PROBLEM: The plotting techniques which use tabulated angles or computation produce timeline plotting angles in degrees which the dialist must mark onto the dial plate using a protractor. These angles will be as precise as the number of decimal places used in the calculations. However, even though one takes great care to obtain precise timeline angles, this amount of precision is useless if one's protractor isn't equally precise. The graphical plotting method also requires an accurate protractor, of course. Snip I assume that you are at the Layout Stage here and want to precisely locate the hour and other marks on the actual surface of the Dial. For Celeste at: http://sciencenorth.on.ca/AboutSN/polaris/index.html the radius of the dial circle is 20/pi meters, about 6.366 m (just under 21 feet). When laying out the marks I found it easiest to measure the length along the arc of the circle from the reference at north to the various marks, using a flexible cloth surveyor's tape. The center of each brass 15 minute marker is positioned to within .5 mm of where it should be. There was some slop in the positioning when we placed the terrazzo matrix into the welded brass framework which holds the Roman numerals and the quarter-hour marks. I calculated the angles between each of the hour and quarter-hour marks and North. The length of the arc along the circumference of the dial for each angle is given by: arc length = (radius) x (angle in radians), the units being the ones to measure radius. or arc length=(radius)x(angle in degrees)x(pi/180) In the case of Celeste: The dial circle has a circumference, C, of 40 meters. (Another subject, but the reason for this is that both Celeste and Terra are at one millionth scale of Earth, and use the classical definition of the metre, namely, 1/10,000,000 of the distance between a pole and the equator.) Celeste's circumference of dial circle, C = 40 meters Radius, R, of dial circle = C / 2pi Celeste's Radius, R = 40 / 2pi meters = 20/pi meters L, length of Celeste's arc = (20/pi) x (pi/180) = 1/9 meters/degree ~ .1 meters/degree This is 111.1 mm or about 4.37 inches of arc length per degree of subtending angle. You can easily mark to the nearest millimeter, so you can easily mark to the nearest hundredth of a degree. In fact you can probably get down to a half a minute of angle in precision of marking. You can probably guess why I used a pipe for a 20 foot gnomon. (Yes, it is much easier for the eye to interpolate to the centre of two fuzzy shadow edges to make a reading then to debate where the actual shadow is on one side. The symmetry avoids all of the penumbral and diffraction difficulties.The error due to non-linearity of the dial scale is negligible. Besides I needed some rigidity.) Commentary on A, B and C: SOLUTION A: Snip I'm thinking that during the construction phase of a very large sundial, I could make a temporary giant protractor located just outside the hourline radius. This would be a fairly simple thing to do using plane geometry. It would be easier to turn your angles using a theodolite at the centre of the dial than to make a giant protractor. I used one to check the time marks before the terrazzo was poured and the hairline was on the brass in every case. Just remember to set the theodolite lower than usual, because you'll have to tilt the 'scope down to mark your angles. And you'll need a helper to hold the pencil point on the marks. SOLUTION B: If the unit square method is used (Waugh, pg. 40-43), then no protractor is needed. One only needs a good long measuring tape for laying out the lines. ( The limits of precision would again depend on the number of decimal places used.) I don't have Waugh's book. I assume he converts to rectangular coordinates to do the layout. Great solution if you have to transcribe curved or non-radial lines, but a lot of work at the layout stage. Your computer program can usually give you your x-y coordinates as a matter of course - just punch in points on the curves and note the coordinates off of the cursor coordinates. Sometimes it is easier to grid it as finely as you need and then interpolate to give you plot points. SOLUTION C: What if I built the gnomon first and use its shadow to tell me the position of the time lines Snip Guess who put up a temporary gnomon for a few sunny days before placing terrazzo! It worked superbly. I wouldn't build a big one without doing some field checking! Saves lot of potential embarrassment too. Big dials usually have a lot of volunteer (field supervisors) because they are usually very visible in a public place and these folk can usually be conscripted to hold cardboard and pinholes to sharpen the moving shadow and to call mark when the second hand sweeps through 12 on the electromechanical time manufacturer worn on the wrist. They can share the
Re: plotting timelines for giant sundials
John, SOLUTION C: What if I built the gnomon first and use its shadow to tell me the position of the time lines With this method, no calculations, plotting, protractors or tape measures are needed. Using a shadow sharpener, the exact position of each timeline could be marked onto the dial face. Of course, using this method would require the proper EOT, DST, and longitude corrections. This method would also work well on an irregular surface. (I think) Marking the time lines would be easier and faster on those days when EOT=0, right? I recently completed laying out a 6 metre high x 20 metre diameter horizontal dial which, to add to the problem, had a drainage 'cast' of 60:1 from the root of the style.The geometry of the latter is intriguing and I can send you a jpeg of my analysis. Other problems which arose however dictated a very large precision pivotting laser trigon, the machining of which took me two careful weeks. (jpeg available of the device in use) A chain is as strong as its weakest link however and the promised 'machined edge' of the cast iron gnomon turned out, on delivery to the site, to be left knobbly 'as cast' so all that careful machining of the trigon was to little avail. Even had it marked out the *theoretical* position of the shadow with the greatest precision the result would have been disappointing due to the umbra/penumbra. This is best illustrated by the twin Noon Lines from opposite edges of a 12 wide style which would have been set parallel in theory. Near midsummer at 55° north the shadow is 12 wide at the root of the style but only 10.5 wide at the numerals.(although individuals disagreed on what constituted the precise 'edge' ) The noon lines therefore taper towards the edge of the dial. Although I haven't checked this by direct observation I suggest that the taper will vary with the season because the much shorter shadow in summer will have a broader 'tip' that the 'off-the-dial' winter version. Perhaps the solstices are the best time for laying out such dials to obtain an average position?? Fortunately I was able to 'zero' the p.m.trigon on an observed local noon which solved some of the problems but the a.m. side had to ! be re-set. I would suggest that the ONLY way to set out a large dial with 100% reliability is by direct solar observation of at least alternate hourlines with perhaps a little interpolation in between. Or perhaps a ginormous pair of Dialling Scales :-) The second biggest problem for me was that such work has to be done by contractors working to budgets and deadlines. To them a sundial is just a public ornament to be completed as quickly as possible so that they can send in their account. And the biggest problem You've guessed it - NO SUN! 1998 must have had less sunshine in the northern UK summer than for many years. The locals grew used to the wild-eyed 'fool-on-the-hill' shouting imprecations at the sky as that bank of cloud obscured the only glimpse of sun that day after a frantic car journey to the site. And we do this for pleasure..??? Tony Moss
plotting timelines for giant sundials
Hello dialists: I have been giving more thought to the practical aspects of designing and constructing a very large sundial, particularly the problem of accurately laying out the time lines. THE PROBLEM: The plotting techniques which use tabulated angles or computation produce timeline plotting angles in degrees which the dialist must mark onto the dial plate using a protractor. These angles will be as precise as the number of decimal places used in the calculations. However, even though one takes great care to obtain precise timeline angles, this amount of precision is useless if one's protractor isn't equally precise. The graphical plotting method also requires an accurate protractor, of course. SOLUTION A: By definition, large protractors are more precise than small ones. So physically laying out the hour lines for a giant sundial would require a giant protractor. Even Robert Terwilliger's laser trigon wouldn't help because it's degree markings are too small. Computer drawn lines don't help either, because you can't easily enlarge a small paper drawing by a hundred fold. I'm thinking that during the construction phase of a very large sundial, I could make a temporary giant protractor located just outside the hourline radius. This would be a fairly simple thing to do using plane geometry. SOLUTION B: If the unit square method is used (Waugh, pg. 40-43), then no protractor is needed. One only needs a good long measuring tape for laying out the lines. ( The limits of precision would again depend on the number of decimal places used.) SOLUTION C: What if I built the gnomon first and use its shadow to tell me the position of the time lines With this method, no calculations, plotting, protractors or tape measures are needed. Using a shadow sharpener, the exact position of each timeline could be marked onto the dial face. Of course, using this method would require the proper EOT, DST, and longitude corrections. This method would also work well on an irregular surface. (I think) Marking the time lines would be easier and faster on those days when EOT=0, right? Do any of you have any thoughts on this problem and which would be the best solution? Thanks, John Carmichael
Re: plotting timelines for giant sundials
John, There is another solution, one well-known to machinists. Recalculate ALL your lines, positions etc. as x-y coordinates and then set out the dial in whatever size you want from some convenient origin. The only question is the resolution of points used to draw curved lines. If too sparse, the curves look like straight segments joined together. If too close, there is a lot of work! Thus you can plot it using units of mm, feet, or metres. This allows you to have a look at it beforehand. Another advantage is that you can also use just about any computer software to plot it for you. John Dr John Pickard Senior Lecturer, Environmental Planning Graduate School of the Environment Macquarie University, NSW 2109 Australia Phone + 61 2 9850 7981 (work) + 61 2 9482 8647 (home) Fax + 61 2 9850 7972 (work)
