Error Analysis of
a Monumental
Garden Variety
Sundial
Roger Bailey
NASS 2009
Portland, OR
©Phil Palies
Questions for NASS Registrar
Artist’s rendering from website
http://www.soaplakememorialstones.com
Is this a Sundial?
• How do I
register this
sundial?
• Now under
construction at
Soap Lake WA
• Is there a
sundial expert
we can consult?
Response from NASS “Expert”
Artist’s rendering from website
http://www.soaplakememorialstones.com
• A sundial is an
instrument designed
to tell time
• The gnomon must be
straight and at the
correct angle
• The hour lines
depend on the
location and are
different for each
hour.
• What is now cast in
bronze & cement?
Data & pictures required
On angles, size, location,etc
Hour Lines for 47.4º Latitude
Angles from Noon N/S Line
XII
XI
I
Same Angles from 6 am/pm E/W line
11°
X
II
23°
36°
IX
III
90°
52°
VIII
79°
IV
67°
54°
70°
V
VII
Base
90°
38°
20°
VI
VI
110°
V
Soap Lake Sundial
Latitude N 47.4
Hour Lines 5 AM-7PM
Walking Shadow Designs
20°
VII
Hour Lines for 47.4º Latitude
11.2°
90.0°
23.0°
78.8°
36.4°
67.0°
51.9°
53.6°
70.0°
38.1°
90.0°
20.0°
20.0°
20.0°
Soap Lake 47.4º
Hour Lines for 37º Latitude
Shadow Lengths through the Seasons
Orientation
• Use the sun’s shadow to determine the orientation
• Table of times when the sun is south, east or west
• Spreadsheet corrected for EQT and Longitude
Date
DOY Declination EQT EQT º Noon South
16-May-2009 135
19.20
3.6 0.910
12:54:19
17-May-2009 136
19.42
3.6 0.903
12:54:20
18-May-2009 137
19.64
3.6 0.894
12:54:23
19-May-2009 138
19.86
3.5 0.882
12:54:25
20-May-2009 139
20.06
3.5 0.868
12:54:29
21-May-2009 140
20.27
3.4 0.851
12:54:33
22-May-2009 141
20.47
3.3 0.833
12:54:37
23-May-2009 142
20.66
3.2 0.812
12:54:42
24-May-2009 143
20.84
3.2 0.789
12:54:48
25-May-2009 144
21.02
3.1 0.765
12:54:54
26-May-2009 145
21.20
3.0 0.738
12:55:00
Sun West
17:39:36
17:38:39
17:37:43
17:36:49
17:35:57
17:35:07
17:34:19
17:33:32
17:32:48
17:32:05
17:31:24
Sun East
8:09:01
8:10:02
8:11:02
8:12:02
8:13:00
8:13:58
8:14:56
8:15:52
8:16:48
8:17:42
8:18:36
Soap Lake, WA
Mineral
Milligrams/Liter
Sodium
5760
Bicarbonate
2480
Sulfate
2540
Carbonate
3840
Chloride
2290
Potassium
504
Organic nitrogen
0.9
Fluoride
7.2
Ortho-phosphate
6.3
Nitrate
0.7
Calcium
2.5
Magnesium
2.9
Soap Lake Garden Club
Healing Waters
• Spa treatment
like the thermal
mineral baths in
Europe
• Bathing in the
alkali waters,
soaking in the
mud, cures people
afflicted with
Buerger's
disease and other
ailments
[
www.geocaching.com GC1DJWD
Modern Spa Treatment
• Spa treatment is now
an sensual indulgent
luxury
• ‘You deserve it”
• Hot rocks
• Hot oil massage
• Aromatherapy
• Soap Lake missed the
market
• “Calling the healing
Waters” a new focus
Concept
• Centre of Interest for
Soap Lake
• Build it and they will come
• Theme: Calling the healing
waters
• Reflects ethnic and
historical themes
• Mighty winger warrior
protecting and comforting
maiden with catch basin
for healing waters
Installation of basalt columns
Angles and offsets
are obvious
Error Analysis
• Sculpture is a poor
sundial
• A worst case scenario
• Feathered arm at
~37º but curved and
offset from center
• Base at ~30º is offset
vertically
• Various parts of the
structure cast
shadows on the hour
lines on the base
Error Analysis
80
Latitude of Sundial: 47.4º,
Gnomon Angle: 37º
June
60
40
May August
Error (minutes)
20
March Sept
0
0
3
6
9
12
-20
Feb Nov
-40
Dec=23.5
Dec=10
Dec=0
-60
Dec=-10
December
Dec=-23.5
-80
Time of Day (Hours)
15
18
21
24
• Users:
Error Minimazation
Considerations
– People going to the park to enjoy the beach and water.
– Good time not regimented time
• Season:
– Summer not winter
– Spring and fall if the weather is good
• Time
– 9 AM to 5 PM Summer
– Peak mid-afternoon
• Impression:
– Form follows fashion, not function
– Looking good is most important
Sundial Considerations
• Can the sundial work?
– giving an impression of time
– When most people will see it
• Design for summer, solar noon +/- four hours
• Design based on a point gnomon, the tip of the
feather
• Calculate design for 47º
– Hold the gnomon tip fixed
– Move the base intersection to 37º design
• Calculate shadow planes for 37º at various times of
day and declinations of the year
• Choose the best compromise considering use
• Design is fit for purpose
Shadow Plane Analysis
• The 37º gnomon has a shadow plane
• Shadow plane intersects the base at a specific angle
• Shadow angle (SA) varies through the seasons
• Tan SA= Sin G x Sin Az/ Cos G x Tan Alt +Cos G x Cos Az
– giving an impression of time
– When most people will see it
• Spreadsheet used to calculate altitude, azimith and
the declination, latitude and time angle
• Sin Alt = Sin Dec x Sin Lat + Cos Dec x Cos Lat x Cos t
• Shadow angle calculated from altitude, azimuth and
gnomon angle
• Plotted on sundial design by Zon 2000 with DeltaCad
• "Error Analysis of The Horizontal Sundial-I"
11
47.4º Gnomon
All Year
1010
37º Gnomon
Equinox
8.6°
17.9°
37º Gnomon
21 June
9
3
9
28.8°
37º Gnomon
21 Dec Solstice
33
3
8
8
Gnomon
42.4°
47°
60.2°
/
7
6
82.6°
37°
6
5
106.9°
54
Soap Lake Sundial
Seasonal Variation
Gnomon 37º not 47.4º
Walking Shadow Designs
11
47.4º Gnomon
All Year
1010
37º Gnomon
Equinox
8.6°
17.9°
37º Gnomon
21 June
9
3
9
28.8°
37º Gnomon
21 Dec Solstice
33
3
8
8
Gnomon
42.4°
47°
60.2°
/
7
6
82.6°
37°
6
5
106.9°
54
Shadow Plane Analysis
Equinox Shadow
1
8.8°
2
Hour Angles 37ºGnomon
11.2°
Hour Angles 47.4º Gnomon
18.3°
23.0°
3
36.4°
29.4°
Gnomon
43.4°
4
51.9°
Summer Solstice Shadow
47.4°
61.7°
70.0°
5
110.0°
84.4°
37°
6
108.6°
7
Soap Lake Sundial
37º Gnomon, 18º Declination
1 August Compromise
Walking Shadow Designs
Winter Solstice
Equinox
11
47.4º Gnomon
All Year
1010
37º Gnomon
Equinox
8.6°
17.9°
37º Gnomon
21 June
9
3
9
28.8°
37º Gnomon
21 Dec Solstice
33
3
8
8
Gnomon
42.4°
47°
60.2°
/
7
6
82.6°
37°
6
Summer Solstice
5
106.9°
54
Soap Lake Sundial
Seasonal Variation
Gnomon 37º not 47.4º
Walking Shadow Designs
Artists
• David Govedere
Sculptor
• Keith Powell Artist
• Concept accepted
in 1994
• Bronze sculpture
cast in 2003
©Phil Palies
ies
Finished
Sculpture
• Curved offset
feathered arm
as gnomon
• Hour Lines
and Posts
• Solar Noon +/four hours
• 9AM to 5 PM
© Raymond Gravelle
Time Check XII
• XII is XI solar
• Hour Line band =
post widths
• Tip of shadow in
the middle of
hour band
• Curve and offset
of feathered arm
is obvious
• Time check OK
© Raymond Gravelle
Time Check III
• III solar II
• Again the tip of
the feathered
arm tells the
time
• Hour lines
diverging
• Time check OK
© Raymond Gravelle
Summary
• Objectives met
• Sculpture looks
good, an excellent
focal point on the
Soap Lake beach
• Sundial is fit for
purpose
• Time indications
OK in the summer
9AM to 5 PM
© Raymond Gravelle
Toolbox
• NASS Compendium & Presentations
• “Error Analysis of The Horizontal Sundial"
Lauoesch & Edinger
• “Error Analysis of Garden Variety Sundials”
• Software: Zon 2000, DeltaCad, Excel
• Spreadsheets:
• Error Analysis Garden Variety Sundials
• Shadow Angles
• Meridians and Prime Vertical
Acknowledgements
• Raymond Gravelle: Challenge, data,
photographs, patience
• Larry McDavid: Asking the right
questions
• Phil Palios “Philthy Photography”
Photos of the dedication ceremony at
http://www.flickr.com/photos/philthy_photography/sets/72157620424323215/