I found the source of my confusion! While I have not yet traced out exactly where the calculation occurs,the apparent limiting of the Southward movement of the daily sun-path was due to the (default) height of the gnomon. Possibly, the spreadsheet extends the shadow length, when it falls shoort of some predetermined value, and that apparently happened right at (or very close to) the Equinoxes, for my latitude and the dimensions in the Data page.
I extended the gnomon height to 2.5 meters, leaving the E-W semi-major axis at 2.4 m. Now, I get a full set of hyperbolae! Dave 37.29N 121.97W On Mon, 15 Apr 2002, Willy Leenders wrote: > Dave, > > Only a p p a r e n t l y all dates from the Vernal Equinox through Summer > to the Autumnal Equinox, > passed through that same point, and only with latitudes of about 40 degrees. > When you generate a serial of dials for 65 degree you can see more difference. > > The distance from the centre of the ellips to the end of the shadow = a > tan(delta) cos(phi) + h tan(phi + delta) > with > a = the semi major axis > delta = declination of the sun > phi = latitude > > > Willy Leenders > 509 N 54 E > > Dave Bell wrote: > > > This is great! Thank you for sharing it, Helmut. > > > > After downloading it, I couldn't help playing with it for a while... > > I noticed something I hadn't before; maybe someone more knowledgable about > > analemmatic dials could explain it for me: > > > > I generated a series of dials, with the sun-path set for the major quarter > > points of the year, starting with the Summer Solstice. I noticed that > > three of the four paths all crossed the minor axis at the same point, but > > the Winter path was (more like I expected) 'way north of the ellipse. I > > ran more, filling in the missing months, and found that apparently all > > dates from the Vernal Equinox through Summer to the Autumnal Equinox, > > passed through that same point, while all dates in the remainder of the > > year were progressively farther North, with a maximum at Winter Solstice. > > > > Why don't the summer-ish paths fall to the South of the singular point? > > > > Dave > > 37.29N 121.97W > > > > On Mon, 15 Apr 2002, Sonderegger Helmut wrote: > > > > > Hi to Everybody, > > > > > > some time ago Roger Bailey designed an Excel-spreadsheet for analemmatic > > > sundials. I think, it was a presentation for the NASS-meeting at Hartford. > > > I made some changes and added some features. For those who are interested, > > > please download the extended version ANALEMM.zip from my homepage > > > http://webland.lion.cc/vorarlberg/280000/sonne.htm > > > (offered with permission by Roger). > > > > > > Hints at errors or any suggestions would be appreciated! > > > > > > Helmut Sonderegger > > > > > > - > > > > > > > - > -
