Pete Swanstrom wrote:
>
> I do still have one big question that I wish to resolve, which pertains
> to my analemmic equatorial sundial. The question is, how long will it be
> before the changing analemma renders my current analemmic gnomon
> inaccurate? (Say until either the date positions on the gnomon have
> shifted by 1/4 day or more, or the EoT for some date has changed by over
> 15 seconds.)
I should have phrased the above question and example MUCH more
carefully. I should have stated "(Say until either the date positions on
the gnomon have permanently shifted by 1/4 day or more, or the EoT for
some date has permanently changed by over 15 seconds.)" Thanks to
everyone's responses, I believe I understand that there are really two
separate factors which affect the accuracy of this sundial.
The first factor is the 354.2424 day solar year, and the Gregorian
calendar leap year cycles. This causes various errors in reading the
date at different years, but these errors are always ultimately reset by
the addition of various leap days, as explained further below.
The second factor is the slowly changing shape of the analemma (due to
precession of the earth's axis, the shifting of the perihelion, changing
eccentricity and possibly a few other factors, which I will need Meeus
to explain to me) that do over a long period of time cause permanant
error in the shape of the analemmic gnomon and in the indication of time
and date. It is this permanent long-term error that I wish to
understand further.
Fer de Vries wrote:
>
> This already happens within each 4 year period.
> The begin of the seasons shift about 5h50m each year.
> In 3 years this is about 17.5 hours, more then half a day, and in 4
> years it should be nearly a day which is corrected by adding 1 day in
> our calendar. Than we start again.
>
> Fer de Vries, Netherlands.
I designed the analemmic gnomon with 365 date marks averaged about
(with 0 date error on) March 1, 1998. The dates indicated by the gnomon
would have been 1/2 day fast on 3/1/1996 and will be 1/2 day slow on
2/28/2000. This cycle resets itself with the addition of the the leap
day on 2/29/2000, and so the sundial is again 1/2 day fast on 3/1/2000
and the cycle repeats. The intent was to achieve the minimum average
date innacuracy during the total 4 year leap year cycle.
However, due to the solar year/calendrical differences that you
described, The date error on 3/1/2002 will not be not reset to exactly
0, but instead the date (not the time) indicated by sundial will be
0.0304 day (not 43.8 minutes) fast. With the Gregorian calendar system,
this date innacuracy changes by 0.2424 days per one year, but only
0.0304 days per 4 years, and only 0.2400 days per 100 years, and yet
only 0.0400 days per 400 years! This can be seen below.
HOW MANY DAYS THE DATE
DAYS IS FAST(+) OR SLOW(-) ON:
YEAR /YR FEB 28 MAR 01
---- --- ------ ------
1998 365 0.0000 0.0000
2000 366 -0.4848 0.5152
2002 365 0.0304 0.0304
2004 366 -0.4544 0.5456
....
2096 366 0.2448 1.2448
2100 365 0.2752 0.2752
2104 366 -0.6944 0.3056
....
2196 366 0.0048 1.0048
2200 365 0.0352 0.0352
2204 366 -0.9344 0.0656
....
2296 366 -0.2352 0.7648
2300 365 -0.2048 -0.2048
2304 366 -1.1744 -0.1744
....
2396 366 -0.4752 0.5248
2400 366 -0.4448 0.5552
2404 366 -0.4144 0.5856
Fer de Vries wrote:
>
> By this reason also the EoT changes more than 15 seconds at some days in
> a 4 years period, only due to the length of the year which isn't 365
> days exactly.
Luke Coletti wrote:
>
> Note that after twenty years, which falls on a four year boundary from
> the start, the delta is 1.3 secs.
I believe that the Analemmic gnomon compensates for this. Even though
the accuracy of the DATE indicated by the sundial changes from year to
year, I believe this DOES NOT typically affect indication of the correct
time, except during a solstice, when the date mark must be used to
accurately indicate the time. A one day date error during the solstice
would contribute a 30 second time error during the winter solstice, and
a 13 second error during the summer solstice. Other that that, even
though the dates shift back and forth around the analemma every year,
the analemmic gnomon shape still remains the same. Because time is noted
by the intersection of the edge of the analemmic shadow with the
equatorial dial time line, regardless of the position of the date marks
on the gnomon, the sundial should still indicate the correct time even
though there there is a change in EoT for the same day over different
years.
Luke Coletti wrote:
>
> Pete,
>
> One last thought on your dial, to correct the EoT variation
> mentioned earlier, you might consider including a four position
> adjustment mechanism to the Equatorial band.
>
> Luke
I have given this some thought, and I can not devise a simple four
position adjustment mechanism for the Equatorial band. Since the
analemmic gnomon is a figure-8 shape, not linear, I can adjust the
equatorial band linearly to be correct for several days, but not for the
whole year. If I am to improve the accuracy, then I guess that one
option would be to build 4 interchangeable gnomon plates, (same
analemmic shape, but with dates shifted 1/4 day,) one for each year of
the Leap year cycle.
Thanks! Pete Swanstrom.
http://netnow.micron.net/~petes/sundial
