The wire date ring is exactly the same size as the inside of the
time scale where the glass plates are glued and the hour and half hour are marked.
This makes the intersection of the wire and glass at 4 hours each side
of the bottom center, or 2 hours each side of the top center. Recall that with the
gnomon on the circumference, the entire 360 degree time scale is covered in only
12 hours instead of the 24 required for a gnomon in the center of the circular
time scale. With these sizes, the center of the date wire passes exactly through
the center point of the glass time scale.
The center wire of the analemma, or gnomon, should be exactly on the same radius
where the glass plates would come together at the top, if they where there.
The maximum tilt of the earth in the summer and winter is
23.4334 degrees. The tangent of this angle is, interestingly, 0.4334.
For a 24 plate circle, each plate is one half hour wide, or 15 degrees.
The chord of the 15 degree arc is 2R(sin(15/2)) = 0.2611xR.
(Note that 24 times this is 6.2653xR, a little less than 2piR=6.2832xR)
Starting with a unit width plate, the radius will be 1/0.261 = 3.8306487878 units.
The extremes of the analemma loop, in the summer and winter, must cast a shadow
directly on top of the date wire, then down to the time
scale. Around the noon hours, this will give a maximum excursion for the shadow of
0.4334 times the radius. The design fixes the analemma loop at twice this:
0.4334xDiamater or 0.8668xRadius. To keep the shadow of the date wire on the time
scale, the time scale, at the center, must be at least as wide as the analemma. The
model here chose to round the 3.320 up to 4 units wide for a 1x4 plate ratio. This can
be cut out of an 8x10 inch piece of glass with the last 2 pieces cut into 3 parts
each to use as spacers, assuming no breakage.
The metal dial follows along these same lines.
The time correction is about 16 minutes in November and about 14 minutes in February for
close to 30 minutes total. This is one unit plate width. This is the ratio that is
shown on the analemma plot. Only the scaling is left to be adjusted. The scale can
be set by the pdf scale factor or by changing the scale of a photocopy.
The adjustment of the analemma tilt is tricky. Around the
center hours, the projected shadow looks is basically uneffected by the tilt. At
the ends of the scale, however, the sunlight passes through the analemma like a
slot. It is only because the narrow shadow is projected on a sloping surface that
the shape again comes out correctly. It will be noticed that the wire size is
magnified. Some time was spent using a slot in a thin metal plate, but this still
has a paralax problem.: The center of the analemma is always correct. Near the ends
of the year, however, the the correct time has a non-perpendicular projection from
the center wire. A very slight downward bending of the loop, not the center wire,
corrects this to a reasonable accuracy. When checking this it can only be suggested
using a high intensity flashlight at a distance, or a candelabra bulb in the garage
to make the adjustments. This is another reason why the CDial is only recommended
for a 10 hour span. Interestingly, at the 14 and 16 minute error dates the paralax
is not particularly serious and there is no paralax when there is no error. It is
only near the ends of the year that a severe distortion sets in with a moderate
time error multiplied by a strong paralax effect. The Odial and VDial do not suffer a
paralax problem of this type because the time scale is effectively rotated rather
than using a gnomon shifted off center.