Hello all,
because
of the diameter of the Sun, the shadow of a “nodus” on a gnomon (or the spot
of light produced by a hole) has a not negligible dimension and moreover also
the lines drawn on the dial have
a certain thickness, to be seen
from a given distance.
For this
reason often the excessive precision in drawing a sundial does not produce any
improvement .
From the
theoretical point of view however I don't think that the analemma, calculated with the data
(declination and EOT) of a given year, is more correct than that obtained
using mean values on a space of time
multiple of 4 year.
The
values of Decl and EOT (in a given day of the year) change slightly and the
corresponding points of the analemma changes their place.
For
example in a vertical sundial calculated with Lat. = 46° and with an orthostyle length =1000 we
have that the points of the analemma
move as written below,
in a period 50 year long
.
- On
September 1 (EOT around =0) : 2.5
mm in horizontal and 25 mm in vertical (
I send a graph attached to a next message)
- on
February 11 (maximum EOT) : 2 mm in horizontal and 12 in vertical
- on
September 22 (Autumn Equinox) : 2 mm in horizontal and 16 in vertical
So the
shift in horizontal is negligible while the vertical one is not (around 3% of
the orthostyle)
The EOT
is normally used or to draw the curves of the analemma - on which almost
always we find the marks of days
in the years (for ex. the beginning of the months) - or to build graphs or
tables with which one can obtain the standard time of the clock from a sundial with Apparent Solar
Time.
In this
second case is opportune to use mean values, calculated (at 12h) on a
space of time multiple of 4
years.
The same
thing is worth for the declination: it is necessary to notice that on some
books we may find tables of the Sun’s Declination calculated at 0h, in the
period 1975 – 1985 : in this case the error on the true value of Decl can
reach, in the next 20-30 years, up to 30-35 primes
Brooke
writes:
Have you done a similar analysis where
there are 4 seperate approximations, one for each of the 4 years in a leap
year cycle?If this is done isn't the error reduced considerably?
Perhaps a
greater precision could be reached,
but I think that the thing would be little practice.
In fact
to read the time we would have to attach to every sundial 4 tables or 4 graphs
to find the value of the Eot of that year, etc. :-)
Fer
write:
Declination
marks on an EoT curve would be better then date marks for accuracy, however,
many times I would prefer date marks or datelines. A dial isn't a precision
instrument in most of the times.
I agree
completely, even if for the not experienced observers the daily
lines must be marked with some
dates.
The lines of the zodiacal signs are really
Declination lines: who looks at the sundial has to know (if he is
interested) to what days in the
year they correspond.
To replay
to Jim Tallman
The
declination lines (as those of the zodiacal signs) have very litle variations due only to the secular
change of the Ecliptic inclination. Their change due to this phenomenon is, in
the last 500 years, inferior to the precision with which the sundials were
drawn and to the 1500 knowledges.
In the
study of the Roman and Arab sundials the values of the ecliptic inclination of
the epoch are used, but
this is no very important !
For
example :
- year 0
23° 41 ' 42"
- year
1500 23° 30 '
15"
- year
2000 23° 26 '
22"
- year
2100 23° 25 '
33"
The
change, in 2000 years, is only of
15 '
A
regard
