🚀 go-pugleaf

Sundials, especially modern ones, tell "secular" time, or what we have come to
know as equal hours.

The reason is simple...   the gnomen parallels the axis of rotation (on a 
good sundial, as opposed to a cheap KMart blue light special).   Since
the earth rotates 15 degrees per hour, we could theoretically make a 
dial by wrapping a cylendar around a gnomen, and marking it every 15 degrees.
The shawdow will move with a constant velocity of 15 degrees every hour, no 
matter what time of year.  If there was no axial tilt then this cylendar would
suffice.  But the tilt causes seasons. It will rise earlier some times of the
year (and much further to the north east), and much later at other times
(and further to the south east)  of the year.   This means that the cylendar
must be distorted to accomidate this.   The distorted figure is called the
cone of Dionysidorus.   This distorted cone has the property that the
rising sun shadow of the gnomen falls on a later hour in the winter than
in the summer.  But the projection of the movement is still 15 degrees
per hour.   The lines follow hyperconic sections, but are generally 
approximated by spericonic sections.

Now most people find the cone of Dionysdirous hard to build, so they project it
onto a flat surface.  This gives us the standard sundial.  Interestingly
enough, the transform of the hyperconic cone of Dionysidrous onto a flat
plate which is perpendicular to the zenith gives essentially straight
lines.   Other prjections onto the so called reclining declining dials (those
not at 90 degrees to the vertical or 90 degrees to the polar axis) give
complex hyperbolic sections, which are fun to compute, but hard to describe 
here without pictures.

Now, note that the sun moves with a constant angular velocity of 15 degrees
per hour on the ecliptic circle (although it's projection along the
horizon line is a function of the season).  This means that sundials
naturally give "equal" or "secular" hours.  "Unequal" or "liturgical"
hours (1'st hour at sunrise and 12'thhour ends at sunset) are not
"normal" for this projection.   This is solved by putting a "nodus"
on the gnomen, and using a horizon traversal projection on the plate.
This then makes each day 12 hours long.  the time is read from the position
of the shawdow of the nodus, and not from the edge shadow of the gnomen.
Interestingly enough, such a dial requires very complex scribing, or
it requires you to know the date to read it.

Such dials are out of fashion.

If anybody wants to know how to construct any of these goodies, I could make
up instructions.  I make sundials for the fun of it.  Seems very
appropriate in Arizona.   I've always wanted to use a helium blimp to
stretch a cable over the Great Meteor Crater in norhtern Arizona, and then
use white rocks to make a sundial on the floor of the hole.  But I'm sure
nobody would let me do it.  Still, it woud be the worlds biggest for a while.