Thứ Tư, 7 tháng 9, 2016

How do sundials work?

Part 1.  How Sundials Work.

From the earliest times people have regulated their lives by the apparent motions of the Sun and the shadows cast by its rays. We say ‘apparent’ because of course it is the rotation of the Earth on its axis which causes the moving shadows we observe every day. When the Earth rotates 15° it is just as though the Sun had moved 15° around its daily track. Diallists use both conventions but it is usually easier to regard the Sun as being in motion.

Perhaps the best place to begin an understanding of how sundials work would be to imagine a pictorial view of the Earth at the North Pole  In this diagram it is the Sun which seems to move at 15° every hour. The shadow-casting element of a sundial is usually called the ‘gnomon’ of which the edges are its ‘styles’.
Sun path
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Part 2.  Polar View.

Four views of the Earth as seen from the camera
pointing downward from above the north pole.
In these images the Earth is rotating with a stationary Sun.
Noon at Greenwich13:00 at Greenwich
14:00 at GreenwichAfter 24 hours at Greenwich
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Part 3.  The Equatorial Sundial.

It may be surprising that the sundial we visualized at the North Pole is actually referred to as an EQUATORIAL sundial.  This is because it is parallel with the Plane of the Equator.
Equatorial Dials
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Part 4.  The Polar Dial.

The Equatorial Dial is sometimes said to be the ‘Master Dial’ because it can be used to delineate many other kinds of sundial.  This is done by projecting its hour lines onto any suitable receiving surface.  The Polar Dial below is an obvious example.
Polar dials
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Part 5.  The axis of the Earth.
Mid-winter in the northern hemisphere is when the Earth’s axis is tilted away from the Sun. The Sun never rises at the North Pole between October and March while at the South Pole the Sun never sets.
Northern midwinterSouthern midwinter
Mid-summer in the northern hemisphere is when the Earth’s axis is tilted towards the Sun. The Sun never sets at the North Pole between April and September while at the South Pole, the Sun never rises.

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Part 6.  Dials at the poles and equator.

Dials at other latitudes
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Part 7.  Dials at other latitudes.

Dials at other latitudes
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Part 8.  Horizontal dials at other latitudes.

Horizontal dials at other latitudes
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Part 9.  Multiple Dial.

Multiple Dial
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Part 10.  Flat edged gnomons and the noon gap.  (Click to show larger versions)
Big dial westFlat edge (pm)Noon gap
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Part 11.  Horizontal dials at different latitudes.

Horizontal dials at different latitudes
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Part 12.  Solar Time, Correction for Longitude and Greenwich Mean Time (England).

The Sun takes four minutes to traverse one degree of longitude from East to West.
Sundials on the same line of longitude all tell the same time (shown on clocks for clarity).
Sundials on the 4° meridian are 16 minutes behind Greenwich time and those at 8° West are 32 minutes ‘slow’.

Example:  Plymouth is 4° 08’ West of Greenwich. Sundials in Plymouth are always 16 minutes 32 seconds slow.

In 1880, to avoid chaos when the first railways gave rapid east/west travel,
Parliament established Greenwich Mean Time (GMT) so all UK clocks told the same time as Big Ben.

Longitude correction
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Part 13.  Introduction to the analemma.

The first accurate mechanical clocks were made in 1656 by Dutch Scientist Christian Huygens. His later models were accurate to within one second per day.  If he set the clocks daily by the sundial he may have initially thought that the clock was varying in accuracy at different times of the year when in fact it was the clock which was accurate and the sundial which was varying. 
Christian Huygens pendulum drive
We now know that all clocks are continually ‘out of step’ with the sundial because day lengths, measured by the Sun, increase by a few seconds over a period of about three months then decrease by similar amounts over the next three months only to repeat the process for the next half year. We can see what is actually happening on the next page. 
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Part 14.  The analemma.
The analemma : setupIf you were to take a photograph on the same piece of film at ten day intervals at exactly 12 Noon on the clock you might expect to see something like the picture on the rightThe analemma : expected

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Part 15.  The equation of time.
The analemma : actualThe ‘figure eight’ is what would actually appear when the film was developed.

The figure eight is called The Analemma.

The difference between Solar Time and Clock Time is referred to as The Equation of time

For practical purposes we need either a daily table of corrections in minutes & seconds for the sundial or a graph from which daily adjustments can be deduced.
The equation of time
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Part 16. Equation of Time graph.

Equation of Time graph
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Part 17. Earth orbit diagram.

If the Earth stayed in one place and just rotated on an upright axis* then all days would have the same length. When we look at the Sun we are observing it from a moving platform. It is the varying speed around its elliptical orbit and the tilted axis which are responsible for the daily variations accounted for by the Equation of Time.

·         *Impossible of course as it is the orbital motion which prevents the Earth being dragged inwards by the Sun’s gravity.
Earth orbit diagram·          
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Part 18. Introduction to decliners.

A vertical sundial on a truly south-facing East/West wall has a central
vertical noon line and a symmetrical arrangement of hour lines.
The hours will begin at 6am and end at 6pm
South facing dial

Sundials on walls lying at an angle to truly East/West are said to ‘decline’.
In most cases the noon line will still be vertical but the gnomon
will be rotated to so that it continues to align with the Earth’s axis.
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Part 19. Walls declined from East / West.

Walls declined
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Part 20. Sundial Examples.  (click on each image to see larger version)
A  Horizontal Sundial with Equation of Time graph.B  Declined Vertical Dial   54° 20' N,  1° 26' W. Declination 14° East
Worsall stainless dialNorthallerton rotary dial
C  Universal Equatorial Dial.  Adjustable for any Latitude.
   (Northern Hemisphere Summertime and Wintertime Faces)
Universal Equatorial (Summer) Universal Equatorial (Winter) 
D.Polar Dial with cranked ‘wings’ to show hours from 6am to 6pm.
Flat polar dials cannot show early and late hours.
E   Bowstring Equinoctial Dial by sculptor Henry Moore.
Adler Planetarium, Chicago. (Clutter removed electronically)
Egham polar dialHenry Moore dial

F   Analemmatic Sundial.  If the user stands on the current date
on the central panel the shadow will show solar time.
Dateline Panel.
Brocks Hill analemmatic dialBrocks Hill calendar line

G   Polyhedral Sundial. Twenty equilateral triangular faces with
several declined and ‘reclined’ (not vertical) dials on each face.
H   Portable Horizontal Dial.
HolyroodBion portable dial

l   A  Heliochronometer converts Solar Time to Clock Time.J   The sloped & vertical gnomons of this replica Double Horizontal
dial tell Sun time, Moon time and displays the Sun altitude & azimuth.
Pilkington and Gibbs heliochronometerHenry Wynne double horizontal dial

K  The Capuchin Dial has a scale
resembling a monk’s cowl.
L   This ugly plastic ‘non-dial’ does nothing at all except display the ‘designer’s
 ignorance and persuade the general public that ‘real’ sundials don’t work.
Capuchin dial'None dial'

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