Earth Dial Fundamentalswith a Look at a New Digital Dial
Robert L.Kellogg, PhD.
December 2009
Horizontal Earth Dial
EARTH 2004
TWO WORLDS - ONE SUNLatitude: 38 Degrees
7
89 10 11 12 1 2 3
4
5
Irish Stone Pillar Dial with Reconstructed Gnomon
[photo by Mario Arnaldi]
Midday
ix ninthvespers
iii thirdterce
Views of Pillar Dial with Sphere Gnomon
SideView
Gnomon
Midday
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SunsetSunrise
GnomonShadow
Gnomon with Sphere on Top
Delineated Shadow of Gnomon Sphere
Midday
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1 PM2 PM
3 PM
4 PM
5 PM
SphereShadow
WinterSolstice
SummerSolstice
Equinox
North Point
HorizontalEarthDialMade on Same Principle
Gnomon Shape(To Scale)
Horizontal Earth Dial
E A R T H 2 0 0 4
TW
O W O R L D S - O N E
SU
NLatitude: 38 Degrees
7
8
910 11 12 1 2
3
4
5Gnomon
Now look at shadow of a Flag instead of a Sphere
Midday
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iii thirdterce
SunsetSunrise
FlagShadow
GnomonShadow
Flag
GnomonSideView
FlagAdded
Gnomon
Notice that flaghas been setoffset from verticalparallel to shadow
Shadow of a Flag
Midday
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1 PM2 PM
3 PM
4 PM
5 PM
FlagShadow
WinterSolstice
SummerSolstice
Equinox
Flag
North Point
Shadow Plane
two parallel plates replacethe ancient gnomon and flag. A slit is etched in the front plate. Light shines through to the second plate
Summer
Slit twist angle is same for laying out hour angles:
tan() = cos(lat) tan(HA)
for lat = 54°HA = 3 hours
gives slit twist = 30°.4
Equinox
NP
WinterSlit
slitillumination at different
seasons
Alignment of Three Vertical Planes
Opaque Plane with Slit
TranslucentScreen
Hour Line Mask for 3 pm at 30.4°
and extends from winter to summer
solstice
Generating Slit for 3 pm at 30.4°
Sunbeam illumination
through both slits onto
translucentscreenGnomon
Height
Opaque Plane with Slit
Shadow Duration – Rectangular and Wedge Slits
Gnomon Wedge
Summer
NP
Winter
w = wo + ’ = width of slit
W=R ’ that is a bit smaller than duration
R ’+w+p
shadow motion
w = wo
Summer
NP
Winter
w = width of slit
shadow motion
W+w+p
W = width of mask opening
R
Gnomon Slit
R
pwoR
R
pwW
)cos()(cos
)(cos720(min)
2
2
H
R
pwoRt
)cos()(cos
)(cos720(min)
2
2
H
R
pwWt
Time Error – Rectangular vs. Wedge Slits
0 50 100 150 200 250 300 350-2
0
2
4
6
8
10
12
Day of the Year
Min
ute
s
Digital Wall - Duration and Arrival Time
9AM and 3PM
Duration
Late Arrival
wedgerectangle
0 50 100 150 200 250 300 350-2
0
2
4
6
8
10
12
Day of the Year
Min
ute
s
Digital Wall - Duration and Arrival Time
10AM and 2PM
Duration
Late Arrival
wedgerectangle
0 50 100 150 200 250 300 350-2
0
2
4
6
8
10
12
Day of the Year
Min
ute
s
Digital Wall - Duration and Arrival Time
11AM and 1PM
Duration
Late Arrival
wedgerectangle
0 50 100 150 200 250 300 350-2
0
2
4
6
8
10
12
Day of the Year
Min
ute
sDigital Wall - Duration and Arrival Time
Noon
Duration
Late Arrival
wedgerectangle
Look at Both Planes Simultaneously
S
W
Observer Looking South at Local Noon Side View
Slits
NumberMask
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