error analysis of a monumental garden variety sundial roger bailey nass 2009 portland, or ©phil...
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Error Analysis of a
Monumental Garden Variety
Sundial
Roger BaileyNASS 2009 Portland, OR
©Phil Palies
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Questions for NASS Registrar
• How do I register this sundial?
• Now under construction at Soap Lake WA
• Is there a sundial expert we can consult?
Artist’s rendering from websitehttp://www.soaplakememorialstones.com
Is this a Sundial?
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Response from NASS “Expert”• 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?
Artist’s rendering from websitehttp://www.soaplakememorialstones.com
Data & pictures required On angles, size, location,etc
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Hour Lines for 47.4º Latitude
X
XIII
II
III
IV
V
VI
VIIV
VI
VII
VIII
IX
XI
Base
11°
23°
36°
52°
38°
20°
70°
90°
20°
54°
67°
79°
90°
110°
Soap Lake SundialLatitude N 47.4Hour Lines 5 AM-7PMWalking Shadow Designs
Angles from Noon N/S Line Same Angles from 6 am/pm E/W line
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Hour Lines for 47.4º Latitude
20.0°
38.1°
53.6°
67.0°
78.8°
90.0°
20.0°
11.2°
23.0°
36.4°
51.9°
70.0°
90.0°
20.0°
Soap Lake 47.4º
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Hour Lines for 37º Latitude
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Shadow Lengths through the Seasons
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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 Sun West Sun East16-May-2009 135 19.20 3.6 0.910 12:54:19 17:39:36 8:09:0117-May-2009 136 19.42 3.6 0.903 12:54:20 17:38:39 8:10:0218-May-2009 137 19.64 3.6 0.894 12:54:23 17:37:43 8:11:0219-May-2009 138 19.86 3.5 0.882 12:54:25 17:36:49 8:12:0220-May-2009 139 20.06 3.5 0.868 12:54:29 17:35:57 8:13:0021-May-2009 140 20.27 3.4 0.851 12:54:33 17:35:07 8:13:5822-May-2009 141 20.47 3.3 0.833 12:54:37 17:34:19 8:14:5623-May-2009 142 20.66 3.2 0.812 12:54:42 17:33:32 8:15:5224-May-2009 143 20.84 3.2 0.789 12:54:48 17:32:48 8:16:4825-May-2009 144 21.02 3.1 0.765 12:54:54 17:32:05 8:17:4226-May-2009 145 21.20 3.0 0.738 12:55:00 17:31:24 8:18:36
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Soap Lake, WAMineral Milligrams/LiterSodium 5760Bicarbonate 2480Sulfate 2540Carbonate 3840Chloride 2290Potassium 504Organic nitrogen 0.9Fluoride 7.2Ortho-phosphate 6.3Nitrate 0.7Calcium 2.5Magnesium 2.9
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Soap Lake Garden Club
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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
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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
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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
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Installation of basalt columns
Angles and offsetsare obvious
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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
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Error Analysis
-80
-60
-40
-20
0
20
40
60
80
0 3 6 9 12 15 18 21 24
Time of Day (Hours)
Err
or
(min
ute
s)
Dec=23.5
Dec=10
Dec=0
Dec=-10
Dec=-23.5
Latitude of Sundial: 47.4º, Gnomon Angle: 37º
June
May August
March Sept
Feb Nov
December
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Error Minimazation Considerations
• Users: – 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
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Sundial ConsiderationsC a n th e s u n d ia l w o rk ?
giving an impression of timeWhen most people will see it
D e s ig n fo r s u m m e r, s o la r n o o n + /- fo u r h o u rsD e s ig n b a s e d o n a p o in t g n o m o n , th e tip o f th e fe a th e rC a lc u la te d e s ig n fo r 4 7 ºH o ld th e g n o m o n tip fi x e dM o v e th e b a s e in te rs e c tio n to 3 7 º d e s ig nC a lc u la te s h a d o w p la n e s fo r 3 7 º a t v a rio u s tim e s o f d a y a n d d e c lin a tio n s o f th e y e a rC h o o s e th e b e s t c o m p ro m is e c o n s id e rin g u s eD e s ig n is fi t fo r p u rp o s e
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Shadow Plane AnalysisT h e 3 7 º g n o m o n h a s a s h a d o w p la n eS h a d o w p la n e in te rs e c ts th e b a s e a t a s p e c ifi c a n g leS h a d o w a n g le (S A ) v a rie s th ro u g h th e s e a s o n sT a n S A = S in G x S in A z / C o s G x T a n A lt + C o s G x C o s A z
giving an impression of timeWhen most people will see it
S p re a d s h e e t u s e d to c a lc u la te a ltitu d e , a z im ith a n d th e d e c lin a tio n , la titu d e a n d tim e a n g leS in A lt = S in D e c x S in L a t + C o s D e c x C o s L a t x C o s tS h a d o w a n g le c a lc u la te d fro m a ltitu d e , a z im u th a n d g n o m o n a n g leP lo tte d o n s u n d ia l d e s ig n b y Z o n 2 0 0 0 w ith D e lta C a d"E rro r A n a ly s is o f T h e H o riz o n ta l S u n d ia l-I" L a u o e s c h & E d in g e r, N A S S C o m p e n d iu m 2 -3 , S e p t 9 5
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6
637°
47°
37º Gnomon 21 June
47.4º GnomonAll Year
37º Gnomon21 Dec Solstice
37º GnomonEquinox
Gnomon
8.6°
17.9°
28.8°
42.4°
60.2°
82.6°
106.9°
Soap Lake SundialSeasonal Variation Gnomon 37º not 47.4ºWalking Shadow Designs
Equinox
Summer Solstice
Winter Solstice
33 3
3
11
1010
99
88
/7
5
5 4
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6
637°
47°
37º Gnomon 21 June
47.4º GnomonAll Year
37º Gnomon21 Dec Solstice
37º GnomonEquinox
Gnomon
8.6°
17.9°
28.8°
42.4°
60.2°
82.6°
106.9°
Soap Lake SundialSeasonal Variation Gnomon 37º not 47.4ºWalking Shadow Designs
Equinox
Summer Solstice
Winter Solstice
333
3
11
1010
99
88
/7
5
5 4
Shadow Plane Analysis
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Gnomon
Soap Lake Sundial37º Gnomon, 18º Declination 1 August CompromiseWalking Shadow Designs
8.8°
18.3°
29.4°
43.4°
61.7°
84.4°
108.6°
11.2°
23.0°
36.4°
51.9°
70.0°
110.0°
Equinox Shadow
Summer Solstice Shadow
Hour Angles 37ºGnomon
37°
47.4°
Hour Angles 47.4º Gnomon
1
2
3
4
5
6
7
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6
637°
47°
37º Gnomon 21 June
47.4º GnomonAll Year
37º Gnomon21 Dec Solstice
37º GnomonEquinox
Gnomon
8.6°
17.9°
28.8°
42.4°
60.2°
82.6°
106.9°
Soap Lake SundialSeasonal Variation Gnomon 37º not 47.4ºWalking Shadow Designs
Equinox
Summer Solstice
Winter Solstice
33 3
3
11
1010
99
88
/7
5
5 4
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Artists
• David Govedere Sculptor
• Keith Powell Artist • Concept accepted
in 1994• Bronze sculpture
cast in 2003
©Phil Palies
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©Phil Palies
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Finished Sculpture
• Curved offset feathered arm as gnomon
• Hour Lines and Posts
• Solar Noon +/- four hours
• 9AM to 5 PM
© Raymond Gravelle
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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
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Time Check III
• III solar II• Again the tip of
the feathered arm tells the time
• Hour lines diverging
• Time check OK
© Raymond Gravelle
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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
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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
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Acknowledgements • Raymond Gravelle: Challenge, data,
photographs, patience• Larry McDavid: Asking the right
questions• Phil Palios “Philthy Photography”
Photos of the dedication ceremony athttp://www.flickr.com/photos/philthy_photography/sets/72157620424323215/