Hi Peter,If we set a horizontal stereographic dial at 55deg N and move it to
35deg S, not changing its position in space, it becomes a vertical there.What
changes is the position of the observer on the globe - not the sundial.The
difference is that in a vertical position at 35deg S the upper halve of the
original dial is useless, as Sun rays are cut by the horizon in Adelaide.But
you can make the upper halve usefull in a simple way, by folding the sundial
along the horizon line !By doing it, you get a second (south-oriented) face for
your dial and preserve the all year functionality of the original 55deg
location !But you must remember to extend the gnomon rod to the south side !The
co-latitude similarity brought me an idea of establishing gnomonic twin cities,
for which one sundial would work !As a resident of the latitude of 51deg North
I'm looking for offers from lat. 39deg South !As the winter is coming in North
hemisphere, I will kindly accept offers for a courtsey visit to 39deg South
with a stereographic sundial at hand ready for experiments !Regards,Maciej
LoseOd: "Peter Mayer" <a1000...@adelaide.edu.au>Do: ml...@interia.pl;
peter.ma...@adelaide.edu.au; Wysłane: 2:12 Piątek 2022-11-04Temat: Re: Vertical
stereographic sundial
Hi Maciej,
Here's a puzzle for you
and others on the list. Does the usual 'co-latitude' rule for
other plane sundials hold for Oughtred/stereograph dials? I've
tried a quick empirical experiment using Orologi Solari
creating a vertical stereograph for my latitude (35S) and a
horizontal for the co-latitude (55N). The two seem identical
(except for the numbering of hours). It's not a 'geometric
proof' but it seems entirely reasonable.
I had meant to add in
my earlier post that a few years ago I, too, wrote a DeltaCad
macro for an Oughtred dial. Unlike the elegant trigonometry used
by Valentin, I tried to replicate the protractor, compass and
straightedge methods in a traditional construction. Once it
worked for my Southern Hemisphere location, I stopped working on
it, so it is really a beta version, but I'm happy to forward it
to anyone who is interested.
best wishes,
Peter
On 2/11/2022 5:25:29, ml...@interia.pl
wrote:
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Hi Peter,
Thank You for the links.
My plea concerned vertical stereographic sundials - not
the horizontal ones. I'm aware that there are a number of
programs to construct horizontal sterographic dials.
Helmut Sonderegger kindly proposed to include vertical
ones in Sonne, when he finds a time for it, and the info form
Valentin was that for the vertical plane he actually worked on a
spider dial, which is most interesting but of different type
than stereographic.
But I must admit that I was unaware of construction
possibilty of vertical stereographic dials (under the name
"vertical astrolabe") in Oroligi Solari.
Though, the program doesn't give any limits for the
gnomon - which in this type of instruments is no longer that 1/2
the dial's radius, as discussed in my paper, irrespective of
walls' declination, latitude and sundial's plane inclination. It
doesn't also give options for inclining dials. So there is some
space for it to be upgraded making this very nice typology more
approachable for sundial makers. Also, derivatives like the
four-sided, "gnomon-less" stereographic vertical sundial could
be included.
Drawing by hand (with CAD) is obviously time consuming,
but it allows for understanding of geometrical relations behind
and allows for inclusion of elements not available in the custom
software. So not being a skilful programmer, I will rather stay
with that ! But for the sundial makers it is obviously easier to
use a software.
Regards,
Maciej
Od: "Peter Mayer" <a1000...@adelaide.edu.au>
Do: sundial@uni-koeln.de; ml...@interia.pl;
Wysłane: 5:58 Poniedziałek 2022-10-31
Temat: Re: Vertical stereographic sundial
Hi Maciej,
Thanks for your recent post. Since no one seems to have
replied to your plea in the final paragraph for software to
draw a stereographic/Oughtred dial, here are some existing
open software options:
* Gian Casalegna's Orologi Solari will draw one:
azimuth: horizontal/vertical: astrolabe
*Helmut Sondereggers' Sonne will draw at least a horizontal
stereograph: Azimuthal: Sun Altitude
* Valentin Hristov has written some elegant code for
DeltaCad :www.math.bas.bg/complan/valhrist/az-ht.bas
[When I tried to re-run it a few minutes ago, it now seems
to be stuck in a loop which I haven't had time to debug.
I've attached an example which I created about 4 years ago].
So: no need to create a stereograph by hand!
best wishes,
Peter
On 27/10/2022 4:02:34, ml...@interia.pl
wrote:
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on links or open attachments from trusted senders.
Dear All,
As proven in a separate tread on "Sun elevation tool/
horizontoscope", stereographic projection is
a fascinating geometric construction with great potential in
gnomonics.
During last year I explored the idea of vertical
stereographic sundial and it resulted in
a paper describing several stereographic sundial types:
- vertical stereographic sundial, for walls of any
declination and for any latitude,
- four-sided stereographic vertical sundial, attractive for
its “gnomon-less” form,
- double – stereographic & polar – vertical sundial for
walls of any declination, a vertical reference to Oughtred’s
horizontal design,
- folded pocket, double stereographic & polar – vertical
sundial
- inclined, proclined and polyhedral stereographic sundials
The paper can be downloaded free of charge from Cursiva
publishers website:
http://cursiva.pl/e-ksiegarnia/vertical-stereographic-sundial-properties-construction-and-related-instruments/
or from Academia.edu website:
https://www.academia.edu/88820719/Vertical_stereographic_sundial_Properties_construction_and_related_instruments
Have fun with it !
Vertical stereographic sundials offer plenty of
possibilities for sundial makers
and I believe might be a very interesting addition to
existing sundial types.
As the geometric construction of vertical stereographic
sundials with CAD software is time-consuming,
it would be great to include it in existing sundial design
software.
I kindly ask sundial list members running such software,
please consider it !
Regards,
Maciej Lose
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The University of Adelaide, AUSTRALIA 5005
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