Hi Peter, I think your calculations may be correct but the scale of the graph isn't. The x axis as in your attached picture has another scale then the y axis.
Best wishes, Fer. Fer J. de Vries De Zonnewijzerkring mailto:[EMAIL PROTECTED] http://www.de-zonnewijzerkring.nl Home mailto:[EMAIL PROTECTED] http://www.iae.nl/users/ferdv/index-fer.htm Eindhoven, Netherlands lat. 51:30 N long. 5:30 E ----- Original Message ----- From: "Peter Mayer" <[EMAIL PROTECTED]> To: "Sundial List" <[email protected]> Sent: Thursday, June 10, 2004 2:05 AM Subject: Locus ofintersections in bifilar dial > Hi, > > I've been quietly gnawing on two sundial puzzles for a while now. And > rather than suffer silently, a prisoner of my own inadequacies, I > decided to 'throw myself on the mercy of the court' so to speak. > > Puzzle the first. (I'll leave the second puzzle for another day when I > have the time to set it out with a bit of clarity...) > > > > I've been wondering, idly, for about a year, after having made a mock-up > bifilar dial, what the locus of the intersection of the N-S and E-W > threads is, during the day, and over the course of the year. > > More recently, partly inspired by the fantastic graphics on Fabio > Savian's webpage (www.nonvedolora.it/bifilare.htm) (I finally figured > out what a wonderful pun "non vedo lora" is; or I _think_ I have). So. > I got out my trigonometry books and tried to figure out what the > equations for x and y would be. I couldn't get Fabio's equations 2 and > 3 for x and y to work for me. > > So I went back to the diagram in Fred Sawyer's article "Bifilar > Gnomonics" _Journal of the British Astronomical Association_, Jun 1978, > 88(4):334-351. and _Bulletin of the British Sundial Society_, Feb 1993, > 93(1):36-44, also Feb 1995, 95(1):18-27. (Thanks, once again, Fred for > sending me a copy). After some stumbling around I derived equations for > x and y. And was both pleased, and mortified, to discover that Fred had > presented the same equations later on in his article: > > > > x = g1 sin t/(sin theta tan delta + cos theta cos t) > (10) > > > > y = g2(sin theta cos t - cos theta tan delta)/(sin theta tan delta > +cos theta cos t) (11) > > > > where: theta = latitude; t = solar hour angle; delta = solar > declination; g1 is height of the thread along the y-axis (= 1/cos theta > for a conventional bifilar dial); g2 is the height of the thread along > the x-axis (= tan theta in the usual case). > > > > I then put the equations in a spreadsheet and calculated the x and y > coordinates for a number of hour angles during the day. And repeated > the exercise for different solar declinations. I put the resulting > coordinates into a statistics software package and plotted the results. > (see the attached .gif which is c. 7 kb in size). (I hope the cryptic > legend is sufficiently clear for the purposes of my question) > > At first, I was quite pleased because the resulting family of curves was > roughly what I anticipated, from my conceptualisation of the bifilar > dial as a sort of dial cast by a vertical gnomon. But then arose my > puzzlement. Although the lines though the hour marks converge to a > point (as they should)...the angles _between_ hours are not equal. > Hence my puzzlement. Needless to add, I would be most grateful for an > indication of what am I doing wrong! > > warmest wishes, > > Peter > > -- > Peter Mayer > Politics Department > Adelaide University, AUSTRALIA 5005 > Ph : +61 8 8303 5606 > Fax : +61 8 8303 3446 > e-mail: [EMAIL PROTECTED] > > ----------------------------------------------------------- > This email message is intended only for the addressee(s) > and contains information which may be confidential and/or > copyright. If you are not the intended recipient please > do not read, save, forward, disclose, or copy the contents > of this email. If this email has been sent to you in error, > please notify the sender by reply email and delete this > email and any copies or links to this email completely and > immediately from your system. No representation is made > that this email is free of viruses. Virus scanning is > recommended and is the responsibility of the recipient. > > ---------------------------------------------------------------------------- ---- -
