a novel sundial with double indicator and calendar
TRANSCRIPT
8/18/2008 W. Riegler 1
A Novel Sundial with Double
Indicator and Calendar
by
Werner Riegler
Annual meeting of the Austrian Sundial Society
24/25 September 2004, Oberperfuss, Austria
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Inauguration 30.9. 2003Solarcity Linz Pichling, Pegasusweg
48° 15.45 ' N
14° 21.53' O
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Die Equatorial Disc
Earth‟s Axis
Equator
Spring, Summer
Autumn, Winter
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The shadow moves uniformly by
15 deg/hour along the disc.
In spring and summer the dial is read on the top
side, in autumn and winter the dial is read on the
bottom side.
The dial is well know and exists in multiple
realizations.
Die Equatorial Disc
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Dial by W. Riegler, Grein, Austria (1995)
Placing a world map in polar projection on
the dial, the shadow indicates noon.
This dial is very elegant because of it‟s
simplicity and universality:
Moving the dial to another latitude one just
has to change it‟s inclination, moving it to
another longitude one just has to rotate it
around the axis.
At each place on earth the dial shows the time
from sunrise.
In order to keep the universality, the world
map and the dial have to be decoupled (time
zones).
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The edge of the disc casts a shadow on the
indicator one can therefore place a
calendar on the indicator.
Die Equatorial Disc
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Solarcity Linz/Pichling
Solarcity Linz/Pichling.
About 1300 flats.
All buildings are heavily relying on solar power.
The part of GWG Linz was built by the architects
Herzog und Stögmüller.
GWG Linz is financing projects
„Kunst am Bau‟ and the idea to place a sundial in
the GWG part of Solarcity was born.
Middle of 2002 the GWG asked me to conduct
this project.
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Johannes Kepler (1571-1630)
Lived in Linz from 1612-1626.
There he wrote one of his major works
“Harmonices Mundi (1619)”.
It was evident that a sundial in Linz should
relate to Kepler.
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The Equation of Time
The time shown by the equatorial sundial
(or any sundial which is a projection of the
equatorial dial) deviates by up to 16
minutes from the time on our watches
(UTC).
The correction, the equation of time, is
often displayed on the sundial as a table or
as a graph.
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Realization by W. Riegler, Grein, Austria (1993).
Sundial with calendar and table for the equation of time.
The Equation of Time
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The reason for the equation of time lies in the tilt of the earth‟s
axis and the non-uniform movement by the earth around the sun in
it‟s elliptic orbit.
Instead of seeing it as an „Error‟ or a „Correction‟ one can picture
the equation of time as an exact representation of the relationship
between the sun and the earth.
This gives the equation of time a much more positive and
fundamental character.
The Equation of Time
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Kepler‟s first and second law:
1) The planets move along elliptic orbits around the sun which is sitting in the
focus of the ellipses:
1) The connecting line between earth and sun covers equal areas in equal times:
Kepler’s Laws
Perihelion, January 4th
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Equation of Time and Solar Declination
The inverse function doesn‟t exist in analytic form and must be calculated numerically.
e … eccentricity of the earth‟s orbit: 0.0167
… tilt of the earth‟s axis towards the ecliptic: 23.44
t0… time between perhelion and equinox: 77.25 days
(Rad) x 4 x 360/(2 ) = equation of time in minutes
(Rad)
T … one year = 365.24 days
t … time in days since the equinox
Floor(x) = closest integer smaller than x
Declination:
Equation of time:
Kepler 1+2:
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Declination Equation of Time
Equation of Time and Solar Declination
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-20 -15 -10 -5 5 10 15 20
-30
-20
-10
10
20
30
The equation of time is a unique function of
• Kepler‟s first and second law with the
earth‟s orbit eccentricity as a
parameters
• The tilt of the earth‟s axis
• The distance of the perihelion to the
equinox
and it therefore symbolizes in a
unique way the relation between earth
and sun.
How can we „materialize‟ the equation of
time instead of presenting it as a table ?
Equation of time (min)
Dec
lin
ati
on
(d
eg)
Equation of Time and Solar Declination
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Every day, a different part of the shadow casts a shadow on the edge of
the clock. The indicator can therefore be shaped in a way to correct for
the equation of time. Idea by General Oliver (1866).
Correcting Indicator
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-500
-250
0
250
500
-500
0
500
-500
-250
0
250
500
-500
-250
0
250
500
-500
0
500
-500
-250
0
250
500
-500
0
500
-500
-250
0
250
500
-500
-250
0
250
500
-500
0
500
At 12:00 UTC + Equation of time + connection for longitude, the sun is exactly in southern direction at
the given declination of the day.
For each day this defines a ray starting from the edge of the disc at the position of the scale at 12:00 +
longitude correction + equation of time with angle of declination towards south.
The correcting indicator is then the tangential rotation body the the surface spanned by the above rays.
Correcting Indicator
Winter, Spring Summer, Autumn
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-50
0
50
x
-50
0
50
y
-200
-100
0
100
200
z
-50
0
50
y
-100
-500
50100
x
-100
-50
0
50
100y
-200
-100
0
100
200
z
-100
-50
0
50
100y
Two indicators
Correcting Indicator
Winter, Spring Summer, Autumn
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Well known realizations
Martin Bernhardt Connoisseur Sundials
Because the indicator must be changes twice a year the
realizations of this dial are usually small and simple.
Correcting Indicator
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Equatorial Disc with Correcting Indicators
Winter, Spring Summer, Autumn
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-100
-50
0
50
100
x
-100
-50
0
50
100
y
0
50
100
150
200
z
-100
-50
0
50
100
y-100
-50
0
50
100
x
-100
-50
0
50
100
y
-200
-100
0
z
-100
-50
0
50
100
y
If one wants to avoid changing the indicators twice a year, the „outer‟ part of it must
be semitransparent.
Spring, Summer Autumn, Winter
Equatorial Disc with Correcting Indicators
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Correcting Double Indicator
A „Grid‟ seemed to be the optimum
solution.
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Instead of changing the indicators we
find a „double shadow‟.
Spring, Summer
Autumn, Winter
Correcting Double Indicator
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A sketch on the scale explains which shadow has to be used at which date.
Correcting Double Indicator
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October 2003
Correcting Double Indicator
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Calendar
The edge of the disc casts
a shadow on the indicator.
This can be used for a
calendar.
In spring and summer the
time is read on the top
side of the dial and the
date is read on the bottom
side.
In autumn and winter the
time is read on the bottom
side of the dial and the
date is read on the top side
of the dial.
.
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October 2003
Calendar
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For reading the date, horizontal
(equatorial) lines were carved into the
indicators. One has to find the line that
touches the shadow. One then follows
this line until the „diagonal‟.
Along this diagonal, for each day of the
year a hole was drilled, the first of the
month is indicated by a larger hole.
Fro there the days can be counted up to
the shadow line.
The months are indicated by engraved
numbers next to the holes.
Calendar
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Realization
1:10 Model Models of semitransparent indicators
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1:1 ModelRealization
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Polar stereographic projection of the earth
Realization
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Baseplate for adjustment
Realization
Base
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Indicators made from solid pieces of brass
Realization
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Adjustment of the scale on the dial
Realization
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Installation on 19.9.2003
Realization
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… this novel dial solves the „sundial‟ problem,
i.e. it shows the time to the minute and the date to
the day over the whole year without intervention
…
…in addition the dial is universal i.e. it can be
placed at any point on earth where it will show
the time from sunrise to sunset ...
… Kepler‟s first and second law, the tilt of the
earth‟s axis against the eclipitic and the ditance
between perihelion and equinox are uniquely
defining the shape of the dial …
Conclusion
Werner Riegler, CERN PH, CH-1211 Geneve 23, [email protected], http://riegler.home.cern.ch/riegler/sundials.htm