School of Surveying and Spatial Information Systems

The University of New South Wales


The Accuracy of Sundials

by V.P. O’Brien

Supervised by Assoc. Prof. A. H. W. Kearsley

Edited by J. M. Rüeger

October 2003


Aims

Although sundials themselves are not closely related to surveying, their operation and the methods used for their setout are associated with geodetic principles and aspects of planetary motion studied by and pertaining to those in the surveying industry. The aim of this thesis was to observe the accuracy of several sundials in the Sydney region, and detect errors and their possible sources.

After gaining information on the setout of these sundials, and conducting research in the variations of the Earth’s orbit around the Sun, mathematical error analyses were made. These determine the errors in indicated sundial time caused by imperfections in sundial construction and setout. Using all information gained from the research, sundial observations and formal error analyses, the practicality of each sundial was examined.

Fig. 1: Photo of the UNSW Millennium Sundial (taken on 2 May 2003)

Observations

Four sundials were chosen for observation purposes, these being the UNSW Millennium Sundial pictured in Fig. 1, the Sydney Royal Botanic Gardens Sundial, the Homebush Bicentennial Park Sundial and the Redfern Equatorial Sundial. The observation process consisted of the time indicated by the sundial being accurately measured while at the same instant recording Eastern Standard Time (EST). Observations were made to each of the four sundials on at least four various dates throughout the year (2003). On each day, numerous observations were made to each sundial to increase reliability of results.

Background Information

To be able to compare sundial times with the corresponding Eastern Standard Time, adjustments must be made to compensate for variations in the Earth’s rotation around its own axis, and around the Sun. These variations are expressed by the Equation of Time, a formula (more commonly expressed as a correction graph), that corrects for the obliquity of the ecliptic (tilt of Earth’s rotation axis) and the eccentricity of Earth’s orbit.

Fig. 2: Variations in Sundial Time (Local Solar Time) Caused by Complete Equation of Time (Powers, viewed 13 Apr 2003)

As sundials indicate local time, it is necessary that sundial times be adjusted to get standard time. Sundials indicate time relative to their position of longitude. To convert sundial times to standard times, the longitude at the sundial and at the standard meridian must be determined. Since the Earth rotates about its axis approximately once every 24 hours, the Earth rotates 15° every hour. In the Sydney region (approximate longitude 151°12’), the meridian used for standard time EST is longitude 150°. The difference of 1°12’ results in a time difference of approximately 4 minutes and 50 seconds. By subtracting the 4 minutes and 50 seconds from sundial time, and taking into account the time variation caused by the Equation of Time (indicated in Fig. 2), sundial time (also known as Local Solar Time) is converted to standard time.

Results

Table 1 summarises the primary information gained from observations made on the four selected sundials throughout the year. Most designs of sundials make use of a common component known as a gnomon. The gnomon can be identified on a simple horizontal garden sundial as the triangular shaped object used to cast a shadow onto a dial so that sundial time can be determined. Gnomons have two main specific dimensions: the style height and the substyle distance. The style height refers to the angle between the top edge of the gnomon and the plane of the dial face. The substyle distance is the angle between the line where the gnomon joins the dial face and the hour line indicating 1200 h. For horizontal dials, this 1200 h line is the line pointing to the South Pole. For vertical dials, this line is positioned vertically down from the dial centre (with exception to declining sundials where declination causes hour line positions to vary).

Sundial

Type

Longitude correction

Equation of Time correction

Estimated Reading Accuracy

Sundial Accuracy

UNSW

Vertical Decliner

N/A

Variable

± 2 min

≤ ± 2 min

Botanic Gardens

Armillary

- 4m 52s

Variable

± 30 sec

≤ ± 2 min

Homebush

Horizontal

- 4m 16s

Variable

± 1 min

≤ ± 3 min

Redfern

Equatorial

- 4m 49s

Variable

± 30 sec

≤ ± 2 min

Table 1: Summary Information for Observed Sundials

Style height and substyle distance values are calculated using formulae relating to the particular type of sundial. These formulae use elements relating to a sundial’s position and setout orientation. It is possible to use these formulae to investigate errors in time caused by imperfections in sundial construction, particularly style height and substyle distance. Error analyses were completed for vertical declining and horizontal sundials. Two examples of error analysis calculations are given in Table 2 for vertically declining sundials in the Sydney region at the time of 1500 h. In the first row, the error in sundial time produced by a +1° error in style height is calculated, while in the second row, the error in sundial time as a result of a +1° error in substyle distance is shown.

 

Time

Delta(t)

New Sundial Time

Error in Sundial Time

Error
+1°

24 h time

radians

degrees

Total

h

m

s

total

error sign

h

m

s

Style error

1500

0.834

47.773

15.034

15

2

3.4

0.0343

+

0

2

3.4

Substyle error

1500

0.802

45.961

14.994

14

59

38.4

0.0060

-

0

0

21.6

Table 2: Error Analysis Examples for Vertical Declining Sundials

Recommendations and Conclusions

Recommendations have been made so that problems detected in specific observed sundials may be avoided in future sundials. For example, the Homebush Bicentennial Park Sundial is a large sundial with heavy components. The part of the dial, that supports the gnomon, has sunk (due to the gnomon’s weight?), creating errors in sundial time as the style height has decreased. Care must be taken, so that the sundial foundations are strong enough to support the sundial’s total weight. The Redfern Equatorial Sundial is situated in a park that, at the time of observations (2003), was surrounded by large trees and apartment blocks. To warrant the effort and expense necessary for the construction of a sundial, it is recommended that careful planning be carried out in the initial stages to ensure that a suitable location (at that time as well as in the future) is selected so that the sundial can be used to its full potential.

By comparing some of the aspects observed for each sundial, including sundial accuracy, reading accuracy, aesthetic quality, location and practicality, it was established that the UNSW Millennium Sundial was the most suitable. Not only did observations prove to be of high accuracy, but the UNSW sundial was the only observed sundial that integrated the variation in sundial time caused by its position of longitude, so that this constant did not need to be considered.

Error analyses completed for vertical declining sundials and horizontal sundials did agree with expected results, after a number of check calculations were performed. For vertical declining sundials, the error analysis displayed larger errors in sundial time occurring when there was an error in gnomon style height rather than when the equivalent error occurred in substyle distance. The error analysis for horizontal sundials demonstrated that, for an incorrect style height, the greatest errors in sundial time occur around 0900 h and 1500 h.


Further Information:

For more information, please contact:

Assoc. Prof. A. H. W. Kearsley
Email: W.Kearsley@unsw.edu.au

Mail:
School of Surveying and Spatial Information Systems
University of New South Wales
SYDNEY NSW 2052
Australia

Phone: +61 (2) 9385 5308
Fax:     +61 (2) 9313 7493
WWW: http://www.gmat.unsw.edu.au

Mr V.P. O’Brien
Email: vinnieobrien@yahoo.com