Warren Thom wrote:
>
> Can we draw a sundial from these equations? How are a and b related to
> latitude, declination of the sun, and hour angle?
The classic equations of the various conic sections are not directly
used in the process
of calculating the declination and hour lines of a sundial, this is done
through gnomic
projection.
However, the projected declination lines or date lines of a sundial are
graphs of the
various conic sections. Which conic section it is depends on the type of
sundial, the inclination
of the dial and the declination of the sun that it is evaluated at.
For a vertical dial, if the plates inclination is greater than the
sun's declination the
graph is a hyperbola, if the plates inclination is less the graph is an
ellipse. For a horizontal
dial the opposite will be true for the last two conditions. Lastly, if the
plates inclination is
the same as the sun's declination the graph will be a parabola, this is true
for both the
vertical and horizontal dial and can only occur if the plate is within the
tropics.
The plate can be thought to intersect a right circular cone with two
nappes which
represents the sun's position over the year. The classic conic sections are
then viewed. For
instance my lattitude is approx 36.5deg N, so for the horizontal dial which I
recently built, the
date lines are all elliptical since the plates inclination is always greater
than the sun's
maximum declination of approx 23.5deg.
regards,
luke
