From oglesby@sover.net Fri Dec 31 14:00:03 2004 Date: Thu, 30 Dec 2004 21:42:09 -0500 From: Mac Oglesby To: Walter Sanford Subject: Re: "Sundial School" Hi Walter... > >> There are some excellent web sites which >> deal with sundial explanations. Bob Terwilliger's FAQ page on the >> NASS site is one. Another is >> http://www.mts.net/~sabanski/sundial/tsp/tsp.html ("The Sundial >> Primer"). There are a couple of small errors, but nothing serious, as >> far as I saw. > >I've seen the preceding website before; I'll look at it more carefully >(based upon your recommendation). I would appreciate it if you would point >out some of the errors you discovered (wonder if I'd notice 'em). It's very hard to include as much info as The Sundial Primer (TSP) does without having someone disagree with some of what's been said. Sometimes the errors are of omission. Some (much?) of the material has been taken directly from John Davis' Glossary, and although John has done a commendable job, there are items which perhaps should be rephrased when removed from the Glossary context. For instance, I'd suggest that the drawing TSP uses near the beginning (apparently adapted from Tony Moss' drawing for John's Glossary) should be identified as for the Northern Hemisphere. Here's a paragraph copied from TSP: "Centre (of a dial): the point where all the hour [lines], and a polar-pointing style, meet. This point does not always exist (e.g. on a polar dial or direct East or West dials, the lines meet at infinity). In simple horizontal and vertical dials, this point coincides with the root of a (thin) gnomon. In the case of a thick gnomon having two styles, there are two centres to the dial. The centre is often, but not always, the origin of the c0-0rdinate system used to describe the dial." I had to wince when I read about the parallel hour lines meeting at infinity. Further on, in the section about vertical declining dials, TSP states: "No vertical dial can have the sun shine on it for more than 12 hours." I have to admit that I was one of the large group who once believed this, but it's not true. Probably you recall the discussion on the Sundial Mail List about this earlier this year. If not, I'll look up the relevant messages for you. > > For example, although it's usually considered a >> difficult challenge to draw a dial face on a declining wall, one can >> delineate a dial on a wall, which may be declining and in fact need >> not be vertical, using only a few hand tools (no computers, >> calculators, or math tables) and without knowing ahead of time (or >> ever determining the measure of) the wall's latitude, declination, or >> how much it inclines or reclines. > >Care to specify the details of the process? I've been playing around with >the design of a ?declining? vertical sundial for a south-facing wall of >the school where I teach (not sure if the wall actually declines) -- so >far, it seems like there's no way to design/build the dial w/o using some >math! I'm VERY frustrated that I haven't had more time to experiment! OK, I'll outline the process, but please don't circulate it, for I believe Roger Bailey plans to give a talk on this type of thing at the Chicago NASS meeting. He may also be planning a workshop demonstrating how complicated dials may be draw with simple tools. I wouldn't want to spoil any of his presentation(s). The process detailed below is not the same as Roger's, but he did provide an initial nudge and some hints. I don't understand why material such as this hasn't been published. Perhaps it has and I just haven't seen it. Fer says he's known about this method for many years. It sort of depends on how you define "math," but here's a method to delineate a sundial on a wall (which may or may not be vertical, and may or may not decline) that uses very little math, and no trig at all! For this exercise, let's say one has a drawing compass, a protractor, simple hand tools, some string, and several pieces of wood, including a straight rod. Although we could determine the latitude of the place by observation, let's assume we know the latitude. Actually, we don't need a number -- a scrap of paper cut to illustrate the angle will do nicely. A) First, draw the meridian line using the equal altitude method (called the Indian Circle Method by Roger). For this step (only) we need sunshine. 1) Drive a nail into one of the flat boards, making the nail perpendicular to the board's surface. 2) Position the flat board so that it is horizontal and has one edge against the wall, just below where the dial is to be drawn. 3) Before noon, say at about 9:00, mark the location of the shadow of the nail's head. 4) Swing an arc on the board, using the distance from the foot of the nail to the marked point for the radius. 5) Mark the spot on the arc where the shadow of the nail head meets the arc in the afternoon. 6) A line connecting the two marks is an east-west line, so its perpendicular runs north-south. We have the meridian line. 7) Extend the meridian line to the wall. B) Draw a line on the wall (which may or may not be vertical) to show where the vertical plane passing through the meridian line intersects the wall. 1) Align a vertical flat board along the meridian line and slide it to touch the wall. Depending on whether or not the wall is vertical, you may have to cut the end of the board at a slant. 2) Mark the wall where the vertical board touches. Connect this mark to the point where the meridian line meets the wall. Remove the vertical board. C) Install the gnomon rod. 1) Sharpen both ends of a straight rod and position it so that one end touches the meridian line and the other touches the line on the wall. 2) Maintaining the contact between the rod's ends and the two lines, move the rod so that it meets the horizontal board at an angle equal to the latitude. 3) Attach supports for the gnomon rod and remove the horizontal board. Notice that we now have our gnomon installed, but we never needed to find the style height (angle between the gnomon and the wall) or the substyle position. Should we want the substyle line, drop a perpendicular from the gnomon rod to the wall. D) Draw the hour lines. 1) Create a winter (Northern Hemisphere) equatorial dial face and slide it onto the gnomon rod. Rotate the equatorial dial face until the 12:00 hour line aligns with a taut thread stretched between the gnomon's pointed tip and the meridian plane wall line. 2) Lock the equatorial dial so that it can't rotate and use the taut thread to locate each of the other hour lines (which, of course, will all radiate from where the upper pointed end of the gnomon meets the wall). Finis. Note: If declination lines for the solstices and equinoxes are required, use a simple string trigon to mark enough points to create smooth curves. Note2: It's also possible to delineate Italian and/or Babylonian hour lines on the dial without recourse to any math beyond what is used above. I'll explain at a later date, if you wish. >Ideally, I'd like to include a noon mark calendar (analemma) similar to >the ones featured on several of Robert Adzema's sundials. Problem is, I >have NO IDEA how to add this feature to a vertical sundial. Well, that's >not entirely true. I have some ideas re: how to "construct" the analemma >manually, but I can't imagine the result would be very accurate. Your >advice? When I drew a noon analemma for my southeasterly declining wall, I used Fer's Zonwvlak (DOS version). When Mike Shaw drew a noon analemma for his house, he used formulas supplied by Fred Sawyer. These formulas were published in the Compendium. Over a year's time you can draw an analemma on any surface by marking points every few days at noon. Bob Terwilliger has pictures of such on his web site. This might make a good school project. > > Probably the major reason to involve school children with sundials is >> so they can visualize how the elements of our solar system move. No >> math necessary. > >No math absolutely necessary, but knowing some math certainly helps to >deepen one's understanding. Agreed! And I'm all for including math. However, many children (and many teachers) are frightened by numbers or formulas or geometric constructions. > > A super project for a school (and maybe for an activity at a Chicago > > NASS workshop) would be to make a Maddux "spars" dial. See Compendium > > March 2002, or visit http://home.iae.nl/users/ferdv/spardial.htm >> >> I attach a photo of such a dial, constructed by members of a Scout >> Troop in a garden of Vijversburg House in Tietjerk, Netherlands. >> Check out Sundial of the Month for August 2004 in the Archives of De >> Zonnewijzerkring (NASS website has a link to De Zonnewijzerkring -- >> look under societies). > >Hmmm, I looked at the attached photo -- wouldn't be my first choice as the >type of sundial to use introduce teachers to sundialing! Fact is, I don't >get how (or why) it works! Although my knowledge of sundials is limited, I >bring more experience to bear upon the problem of "what makes the dial >tick?" than a typical teacher -- not sure it's reasonable to think novice >sundialists will find it easier than me to understand the dial. Tell me, >what am I missing? A great opportunity. Hunt up the article and read it. Then, if necessary, re-read it. If the concepts still aren't clear, I'll try to explain. Bill Maddux's designs are beautifully elegant. I'm sorry you didn't get to know him. It was my privilege to work with him (and Fer de Vries) on perhaps a dozen sundial articles. Warren Thom was also involved in some. Best wishes, Mac