Error Analysis of a

Monumental Garden Variety

Sundial

Roger BaileyNASS 2009 Portland, OR

©Phil Palies

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?

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

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

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

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 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

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

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 offsetsare 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

-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

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

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

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

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

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

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

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

Artists

• David Govedere Sculptor

• Keith Powell Artist • Concept accepted

in 1994• Bronze sculpture

cast in 2003

©Phil Palies

©Phil Palies

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 athttp://www.flickr.com/photos/philthy_photography/sets/72157620424323215/