Edley, Are you looking for a bifilar dial that is usable for any latitude? Such a dila is made. You may find an example at the website of "De Zonnewijzerkring". (address below) Follow the links Article of the month Archives 2009 Month 09-04.
It is a sundial by Sergio Garcia Doret, Brazil. Best wishes, Fer. Fer J. de Vries De Zonnewijzerkring http://www.de-zonnewijzerkring.nl Molens http://www.collsemolen.dse.nl Eindhoven, Netherlands lat. 51:30 N long. 5:30 E ----- Original Message ----- From: Edley McKnight To: Chris Lusby Taylor ; sundial Sent: Wednesday, January 06, 2010 9:31 PM Subject: Re: Quick Bifilar Dear Chris, Thank you for your rapid and full response. It does make the subject more understandable for me. (Several of the authors I mentioned do have methods that are not iterative, but seem slow and non-direct, Sorry for the mislabeling!) I'm thinking forward to the time we can toss one of these in our vehicle, pull it out when we stop and prop or fasten it against some convenient object, adjust the threads and have it fully usable in just a couple of minutes. Perhaps inputing the new values into a programmable calculator and solving directly for the thread positions and heights. Given GPS, an inclinometer, etc. Maybe this is too much to hope for? Yes, and Happy New Year also! Edley McKnight > Dear Edley, > For a bifilar dial with 15 degreeequal angle hourly separation on > any arbitrary surface anywhere in > the world, calculation of the positions and heights of the two > filaments is very easy. > > Start by imagining that you're planning a conventional dial with a > polar gnomon. Knowing the > latitude, dial surface inclination and declination, calculate the > substyle angle and style height. > > Some readers may like me to explain those terms: assuming the gnomon > to be a triangle in a > planeat right angles to the dial surface, the substyle angleis the > angle on the dial surface > between the foot of the gnomon and the vertical (or the steepest > line if the dial isn't vertical) and > the style heightis the anglein the triangle between the foot of the > gnomon and the style edge. All > the equations you need are on the Formulae page of the BSS Web site > (www.sundialsoc.org.uk). > Or, for a vertical dial you can use the incredible Samuel Foster > nomogram that Fred Sawyer > presented to the BSS Conference (and, I believe the NASS Conference) > a few years ago, since all > the equations you need are of the form sin(a)=tan(b)/tan(c). > > Now, to convert from the polar gnomon to a bifilar is remarkably > simple. Imagine that the > (imaginary) polar gnomon has a nodus point on it, at a height chosen > to give a balance between > beingso low that you lose accuracy and so high that its shadow moves > off the dial too quickly. > > Your two actual bifilar filaments need to be: > 1.Parallel to the dial, at right angles to the imaginary polar > gnomon, passing through the > imaginary nodus. > 2. Parallel to the dial,in the plane of the imaginary polar > gnomon,at a distance from the dial > exactly equal to the distance from the centre of the dial to the > imaginary nodus. (Suppose, for > instance, that the calculatedstyle height is 30 degrees, the > imaginary nodus chosen to be10cm > along the style edge from the centre of the dial,then filament 1 > will be 5cm from the dial ( > 10.sin(30) )and 8.66cm offset from the centre ( 10.cos(30) ). > Filament 2 will be 10cm from the > dial and pass directly over the centre. The two filaments are at > right angles to one another. > > That's it. The only tricky bit (as with any nodus)is choosing how > high to make the filaments to > balance accuracy against longevity, bearing in mind that the extra > height of filament 2 makes its > shadow move faster - twice as fast in my example - than that of the > imaginary nodus. > > To install the dial, note that you know the angle between the > imaginary gnomon and the vertical or > steepest line on the dial surface. Filament 2 and its supports are > in the plane of the imaginary > gnomon, socan be used to orientate the dial correctly. A horizontal > dial is installed with filament 2 > due north-south. > The time the dial should show directly under filament 2 is the same > as the time a polar gnomon > would show along the same line. That's easily calculated, even for a > declining, reclining dial. Note > that a vertical declining bifilar dial does not have 12 o'clock > vertical. > > As with a conventional dial in the same plane, the hour lines go > clockwise or anticlockwise > depending on whether the dial is visible from the north or south > celestial pole. For a polar dial (dial > plane at right angles to the equator) the style height is zero, so > filament 1 grazes the dial. You can > decide whether to use a clockwise dial with filament 1 north of the > centre, or an anticlockwise dial > with filament 1 to the south. > > Because the hour lines are evenly spaced, the dial can be made to > pivot about its centre (keeping > the filaments fixed) to allow daily adjustment to show mean time, > zone time, daylight saving > time,.... > > I hope this helps > > Happy New Year > Chris Lusby Taylor > > 51.4N 1.3W > > > > > ----- Original Message ----- > From: Edley McKnight > To: sundial > Sent: Tuesday, January 05, 2010 5:14 PM > Subject: Quick Bifilar > Dear Gnomonic Fans, > > At last, a working computer again. Sorry I've missed so many > fine threads. > > As far as I've been able to find, so far, the formulae and > software for Bifilar Sundials > involves an iterative process to discover the proper positioning > of the two lines in order to > insure the 15 degree equal angle hourly separation. It would > really be a help if given the > surface inclination, surface declination, latitude, longitude, > true north direction, eot, dial > circular diameter, etc. a direct solution of the line heights > and positioning with reference to > the dial surface were provided directly. I've Gianni's great > Bifilar program ( Which by the > way works with this new copy of Windows 7), Fred's "Bifilar > Gnomonics" Hristov's Deltacad > macros, Fer de Vries' two articles and other items from the NASS > repository number 44, but > so far I've not found a direct solution. Is there one out there > somewhere? I'm assuming the > threads are parallel to the dial surface. > > Yes, and a happy New Year to all of you! > > Best Wishes! > > Edley McKnight > > > --------------------------------------------------- > https://lists.uni-koeln.de/mailman/listinfo/sundial > > ------------------------------------------------------------------------------ --------------------------------------------------- https://lists.uni-koeln.de/mailman/listinfo/sundial
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