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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

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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, werner.riegler@cern.ch, http://riegler.home.cern.ch/riegler/sundials.htm