Dear Keith, Ah, that's not quite what most replies assumed! Yes, you certainly can calculate straight hourlines radiating out from the foot of an arbitrary-length horizontal gnomon for a particular date. Here's how I would solve it:
As you may know or can probably visualise, a south-facing vertical sundial is exactly the same (as far as the sun is concerned) as a horizontal sundial at a latitude 90 degrees south of yours. Your horizontal gnomon sticking out at right angles to the dial becomes a vertical stick when transported 90 degrees to the south. (90 degrees south of Texas takes you to somewhere in the South Pacific, I guess.) So, your question is equivalent to asking about hourlines radiating from the foot of a vertical gnomon at a location 90 degrees south of you. Their angles are given by the sun's azimuth at that location on that date and time. That's a very well-known problem. For instance, the British Sundial Society Website (http://www.sundialsoc.org.uk/) has a formulas page (click on "Formulae and Glossary" in the left margin, then on "Equations". Scroll down to the azimuth equation.) Note that the azimuth equation needs you to know the sun's declination for that date. You could calculate it or look it up in tables. Also, be sure to put in the location's latitude as negative since it is in the southern hemisphere. If you are 30 degrees north, 90 degrees further south would be at -60. The top centre of your dial is equivalent to the due north point on the horizontal dial, so azimuths are relative to this. Good luck Chris Lusby Taylor 51.4N 1.3W ----- Original Message ----- From: "Keith E. Brandt, MD, MPH" <[EMAIL PROTECTED]> To: <[EMAIL PROTECTED]> Sent: Wednesday, September 10, 2008 5:39 PM Subject: Vertical South dial with horizontal gnomon > Sunny friends, > > Thank you for the numerous replies to my query. However, it is apparent > that I left out one key piece of info - I am only wanting the dial to be > valid for a single date. It is going to be used for people unfamiliar > with dials so it needs to be read as simply as a clock. Yes I know this > is an opportunity for education, but I feel this is the best way to > proceed. > > Therefore, the equation for the point of the gnomon would yield an angle > that I could use to calculate the hour lines. I would prefer the use of > an arbitrary length gnomon. > > So in summary, I'm looking for the formula for hour lines on a > south-facing vertical dial with a horizontal gnomon of random length, > drawn for a single date and single location. > > I'll look at the DeltaCad macro provided by Valentin, but if anyone has > the formula right off that would be helpful. > > > Keith > > > --------------------------------------------------- > https://lists.uni-koeln.de/mailman/listinfo/sundial > --------------------------------------------------- https://lists.uni-koeln.de/mailman/listinfo/sundial
