Chris Lusby Taylor <[EMAIL PROTECTED]> writes: > "Frans W. MAES" wrote: > > > I know one more case of > > an interesting bifilar dial. Using a pole style and a specially shaped > > curve in the equatorial plane, one may obtain a polar dial with > > straight, parallel E-W date lines, perpendicular to the hour lines. > > This principle was described in the Bulletin of the Dutch Sundial > > Society in 1979 by Th.J. de Vries. > > [...] > > http://www.biol.rug.nl/maes/zonwyzer/en/zwappi-e.htm > > > > This is an exciting sundial. Who would have guessed that you could achieve > straight, parallel, date lines? Brilliant. Is the formula for the curve > available, please? (Don't tell me - it's a catenary, right?)
The principle is relatively straightforward. As the description says, the pole style and base plate together constitute a polar dial. (Since the second shadow is not needed to tell the time, I would hesitate to classify this as a bifilar dial at all.) At any given time of day, the shadow plane will always cut the edge of the yellow glass at the same point. For different dates/declinations, the shadow of this point will move up and down by the distance L*tan(D), where D is the declination and L is the distance from the edge of the gnomon to the edge of the shadow. At noon, L must equal the height of the style, H. The trick is to make L = H for every time of day. If x is the distance from the base of the style, measured in units of H, and y is the distance above the base plate in the same units, then the equation for the necessary curve is this: x = (1-y)*sqrt(1-y^2)/y Have fun proving this! --Art Carlson
