Roger Bailey wrote: > > At 04:13 AM 9/6/99 -0400, Charles Gann wrote: > > > >Nice idea Mac! Perhaps Roger could design the dial to show time remaining > >until > > > >(1) sunset > >(2) civil twilight > >(3) nautical twilight, and > >(4) astronomical twilight > > Hello Charlles the diallist, > > The design of such a dial is not as easy as I originally thought in my > midnight lucubration. On the celestial sphere, these altitude lines are > parallel to the horizon. As Daniel Wenger pointed out, it is possible to > define these lines and tell twilight times on a spherical dial such as his. > Projected onto the plane of a vertical dial, the altitude lines are the > usual complex hyperbolic curves as typified by declination lines. It can be > done but I do not see a simple general solution. Each site would be a > unique design. > > By contrast, Italian hours have an elegant simplicity in showing the time > until sunset. No longitude or Equation of Time corrections are required as > the shadow tracks the actual path of the sun. The mathematical complexity > remains hidden. > > snip..... > Cheers, > > Roger Bailey > Walking Shadow Designs > N 51 W 115
Hello Roger, Charles, Mac and other interested diallists, In the message of Roger is written : The mathematical complexity ( of Italian lines ) remains hidden. You may find routines to compute these lines on my site.(address below) Use the link : Method to compute flat sundials and than Secondary procedures. In that methode also the wanted lines for hours to twighlight can be programmed. The basic procedure is simple. choose twilight = -12 degrees ( or other value ). choose the wanted hour h to twilight. loop for daynumber. calculate the sun's declination out of the daynumber. ( or loop for decl = -23.5 to 23.5 ). calculate the hourangle t for the sun's declination out of : cos t = (sin twilight - sin lat . sin decl) / (cos lat . cos decl) subtract h .15 degrees. We now have the hourangle and the sun's declination for one point. Calculate the shadowpoint of this combination. Repeat the procedure for as many declinations as you want. Do not check "if the sun is below the horizon", because it will be below the horizon. Do check "if the sun is at the wrong side of the dial's plane" For the Babylonion hours from twilight the same procedure may be used with using a minus sign for the calculated t out of cos t = .... and than add h * 15 degrees. Thus the math is not difficult, but you need some time for the programming. I never calculated these lines but I have seen some drawings in an Italian book with these lines. The book now is with a friend and I am not able to look for a picture. Happy dialling, Fer. -- Fer J. de Vries [EMAIL PROTECTED] http://www.iaehv.nl/users/ferdv/ lat. 51:30 N long. 5:30 E
