Wow!
The analysis of the limitations of polar ceiling sundials made by Fer
de Vries is just splendid. Essentialy the problem is: if we move the mirror
inwards it could fall under the ceiling shadow and thus produce no dot of
light,
and if we move it outwards the ray of light goes back outside when the Sun
is high,
so, once again, we are in one of these equilibrium-of-forces problem. In my
opinion
the worst limitation is the one imposed by the size of the window, and I
guess there
are no general solutions and we are bound to a trial-and-error balance
analysis
for each case.
Maybe we could have several non-overlapping mirrors, each one for every
case, but
then our problem looses a lot of its simplicity.
Anselmo Pérez Serrada
> Dialists,
>
> In my mind I wanted to make a try for a polar ceiling dial at latitude 52
> degrees, mid
> Netherlands.
>
> In the attached picture you see the mirror M at a distance g from the
> ceiling.
> The polar pattern for this configuration is drawn below left and I want to
> have
> the hours 8 am - 4 pm on the dial, if possible. ( no longitude correction
in
> this story )
>
> The line BC then is about the limit of the space I need on the ceiling, or
> with
> other words, the mirror should be inward the room over a distance AB.
>
> Let's now have a look if the sun will shine on the mirror all year at
noon.
> It's obvious that I need to look for the limits at summer solstice.
>
> It is seen that during the summer solstice the sun can't shine on the
mirror
> at all.
>
> The first change I need to make is to cut of the ceiling at the line PCQ
in
> which C is the intersection point of the summer ray and the ceilng.
>
> In the hourline pattern the hours before 10 am and after 2 pm will be cut
of
> too and the first conclusion is that at summer solstice the dial is
useable
> from about 10 am to 2 pm.
>
> However, there are more things to concider.
>
> In this configuration the mirror will catch the sun at summer solstice
only
> at noon.
> Shortly before and after noon the mirror is in the shade.
>
> To see this we need to imagine a vertical south facing dial through AM
with
> a (pin)gnomon of length AC.
> That pattern is drawn below at the right side.
>
> At noon the edge of the ceiling gives a line of shadow KL and the mirror
> just catches the sun.
> Before noon and after noon this line of shadow moves down ( to the right
in
> the drawing ) and the mirror won't catch the sun.
> It sounds strange, after noon the altitude of the sun decreases and also
the
> shadow on a south facing dial decreases.
> Yes, this is true and can be seen with the shape of the dateline for the
> summer solstice. Before and after noon this date line in going down.
> So at the summer solstice my dial only gives a "flash" at noon and no
> more.......
>
> The third problem to concider is the width of the window.
> Because the mirror is inside the room the azimut of the lines from mirror
> through the edges of the window also will give limitations
> For this an analemmatic dial or Oughtred dial could be of use to see what
> the limitations are.
>
> Who will show us the first real polar-mirror-ceiling dial?
> Who has an inclined ceiling, higher at the south end?
> Won't that be better?
>
> Fer.
>
> Fer J. de Vries
> [EMAIL PROTECTED]
> http://www.iae.nl/users/ferdv/
> Eindhoven, Netherlands
> lat. 51:30 N long. 5:30 E
>
>
>
>
>
>
