Dear Dialists,
This is my first message to the mailing list, so let me introduce myself:
I am a Bulgarian mathematician, but I am in Zimbabwe as a lecturer at the
Mathematics Department of the University of Zimbabwe in Harare.
In this message I want to comment first an observation which appeared a
few days ago (sorry that I do not keep the messages and cannot give the
name of the sender, by the way, where is an archive kept?). It was
mentioned that two sundials in Amsterdam situated close to each other have
their styles in different directions. This is possible and the reason
could be the following:
The face of a "classical" sundial is the projection of a SINGLE POINT,
which is at some distance from the surface (usially flat). Therefore THE
BASIC POINT OF THE STYLE IS IRRELEVANT !!! Sometimes the projection point
is like a small sphere or a hole at the end of the style, but very often
it is not marked at all.
The above mentioned fact is the basis of the rest of my message, where I
want to share my ideas for a possible general approach in constructing
sundials. This could be interesting aspecially to the people in the
mailing list, who have made or plan to make programs for drawing sundials.
The core is in transforming the "classical" sundial face into another face
(and both could coexist!).
The people now are interested primarily in knowing the "civil watch" time,
i.e. the "solar" time with two corrections - (1) the difference between
the longitude and the central meridian of the time zone, and (2) the
equation of time (EOT), i.e. the difference between the position of the
"real" and the "mean" sun.
Both corrections can be reflected on the "classical" face of a sundial,
where the so called "analemmas" appear (with the shape of the figure 8).
To be honest, it is almost always confusing which part - left or right -
of the analemma to use, because one and the same hyperbola represents two
different dates.
My suggestion is TO SPLIT THE ANALEMMAS by using additionaly any system of
straight lines, or circles, or combination of them, or what ever curves
you want, which are determined UNIQUELY for every date in the year (but it
is possible to show only 1st, 11th, and 21st of every month).
In this case it is INEVITABLE to use not a single point for projection,
but a suitable part of some (even curved) style.
As an example you can use the edge of a roof as a style and a system of
parallel vertical lines on the wall for the dates and the months (here the
style is parallel to the plane). Another example is to use the vertical
corner edge of the house and some system of lines on the horizontal plane
(if the lines are concentric circles centred at the corner, this is called
azimuthal dial, and the style intersects the plane).
In general, it is preferable to have a straight line as the style, a plane
as the face, and a system of straight lines or circles for the dates and
months (I will use only "lines" below).
I propose the following procedure:
Let the position of a point A be calculated using the corresponding time
and date - it appears on some analemma on a "classical" sundial face.
Let there be some system S of lines showing the dates and the months.
Then there are two cases:
(1) If the style INTERSECTS the plane at some point B, then continue the
line AB so that it intersects the line for the date in the system S at
some point C. Obviously, C is the projection of a different point of the
style in general.
(2) If the style IS PARALLEL to the plane (intersection point B from (1)
does not exist), simply make a line trough the point A in the plane, which
is parallel to the style, and find the intersection point C with the
corresponding date line in the system S.
The system S of date lines could be as a frame for the "classical" face
with natural shape rectangular or circular strips.
Let me stop the description here with the hope that it will start a
discussion.
For giant sundials like the one marked recently by John Carmichael and his
team (Congratulations!) this is not suitable (the SUN is more important
than the "civil" time), but even there a small model with both the
"classical" face and the described modification can be shown to the
tourists just to illustrate the two corrections for the longitude and EOT.
One more remark:
In principle, no calculations are needed if a person wants to make a
sundial and is patient enough to make marks during a one year period.
For example, I started recently the Task Scheduler on my computer to give
me visual and soung signal every 15 minutes. Then I make two marks on the
frame of the window:
(1) on a system of parallel horizontal lines for the months at the bottom
part, marking the shadow of one of the vertical edges of the window, which
is in fact a modified azimuthal dial, and
(2) on a system of parallel vertical lines on the side part, marking the
shadow of the upper horizontal edge, which is a modified dial measuring
the height of the sun.
I do not want everyone in the mailing list to be bothered by a discussion
if he/she is not interested in such topic. Perhaps it is better to send an
e-mail to my address
[EMAIL PROTECTED]
unless you think your suggestions and comments are useful to more people.
You can also visit my web page
www.uz.ac.zw/science/maths/personal/hristov/index.htm
where you will find my program for drawing QUADRANT SUNDIAL (my first
attempt to write in postscript language - I started it two months ago). In
this tipe of sundial a system of concentric circles for the dates is used
as a target (but no style exists - it is replaced by a two sided string
with something heavy at the gathered ends).
Hope that the topic in this message will be interesting for some people in
the mailing list and they will reply!
Sincerely yours,
Valentin Hristov
-17.76 (S), +31.05 (E)
/^\?
\__/___\__/
( @:@ )
---oOOOo--\_~_/--oOOOo----
| Valentin Z. Hristov |
| University of Zimbabwe |
| Mathematics Department |
| P.O.Box MP 167 |
| Mount Pleasant |
| Harare, Zimbabwe |
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