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

Place a Sphere on the End

[photo by Mario Arnaldi]

Midday

ix ninthvespers

iii thirdterce

Views of Pillar Dial with Sphere Gnomon

SideView

Gnomon

Midday

ix ninthvespers

iii thirdterce

SunsetSunrise

GnomonShadow

Gnomon with Sphere on Top

Delineated Shadow of Gnomon Sphere

Midday

ix ninthvespers

iii thirdterce

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

ix ninthvespers

iii thirdterce

SunsetSunrise

FlagShadow

GnomonShadow

Flag

GnomonSideView

FlagAdded

Gnomon

Notice that flaghas been setoffset from verticalparallel to shadow

Shadow of a Flag

Midday

ix ninthvespers

iii thirdterce

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

Detail of Typical Hour Number

W = .05 - .15 mm

10-30 cm

5-25 cm

Gap = .5 – 1.5 mm

Winter Shadows Movement

Winter1:00 PM

Winter Shadows Movement

Winter2:00 PM

Summer Shadows Movement

Summer1:00 PM

Summer Shadows

Summer2:00 PM