The clock face of the bifilar sundial is the one at the lower bottom of the illustration. The semicircular azimuthal sundial is located above. The chain (thread 1) is attached above this clock face.
The inventor of the bifilar sundial (two-thread clock) is professor Hugo Michnik, a high school mathematics teacher in Beuthen, Upper Silesia, who issued a document regarding the 'Therorie einer Bifilar - Sonnenuhr' (Theory of a Bifilar Sundial) in 1922. He describes a sundial with a horizontal clock face. Two horizontal threads in different distances are situated above it. One thread is oriented in an East-West direction, the other in a North-South direction. The intersection of the shadow lines of the two threads is the shade producing point.
He proves that the intersection of the shadow lines on a normal horizontal clock designed for a style
parallel to the earth's axis shows the correct hours, if computed for a latitude
j and if the following formula is observed regarding a site latitude
sin j' = h' . sin j / h
h is the height of the East-West thread and h' the height of the North-South thread.
If the East-West thread (h) is lower than the North-South thread (h') by a factor of 1/sin j, the clock face is homogeneous, that is, all hour lines feature an angle of 15° to each other, ( h = h'.sin j).
Further development :
The idea of the bifilar sundial was further developed. Nowadays, clock faces of bifilar sundials may be constructed on surfaces in an arbitrary position, featuring homogeneous hour lines. Generally, it is possible to construct bifilar sundials with two threads in any position. Usually, the threads are rectangular to each other, however, this is not required. It is also not necessary that they are parallel to the clock face plane. There are infinite alternatives, including the umbrella sundials designed by Rafael Soler, Palma de Mallorca. Hyperbolic shaped gnomons are possible, as proven by the Dutch mathematician Th.J. de Vries.The bifilar sundial of Renzo Righi in Cogruzzo :
The bifilar sundial shown in the illustration was designed by Renzo Righi, Correggio(RE), and described
by Gianni Ferrari, Modena, in ' The Compendium' of the NASS, issue 7/4 (Dec 2000) in the article
"A Curious Property Of Bifilar Sundials".
It features a vertical 'thread' in the shape of a chain (thread 1). Its distance to the vertical clock face is d1 = 60cm. The second thread is also parallel to the clock face and tilted regarding thread 1 by the angle c. Its distance is d2 = 40 cm.
In order to achieve a horizontal equinoctial line with this bifilar sundial the angle c must meet the following requirement:
d1 = 60 cm
d2 = 40 cm
j = 44,82°
d = wall declination = -76,2°
This results in c = - 27°.
Last update : 27. December 2001