Dear Edley, For a bifilar dial with 15 degree equal 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 plane at right angles to the dial surface, the substyle angle is 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 height is the angle in 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 being so 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 calculated style height is 30 degrees, the imaginary nodus chosen to be 10cm 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, so can 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
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