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Phases

Map of Phase III

Map of Phase III
The Human Sundial
Info Centre
Phase I & II
Phase III

Appendix

Calculating the X-Y Coordinates for the Time Positions

The x-y coordinates for the time positions are calculated using

  • the latitude l

  • the time t expressed in degrees. The time must be adjusted for your location within the time zone, so you will need to know both the longitude of your location and the longitude where your time zone begins. The correction is (24 hours x 60 minutes) divided by 360 degrees = 4 minutes/degree, for every degree of longitude west of the time zone longitude. For example, Calgary longitude is 114 degrees and the time zone longitude is 105 degrees. The correction from clock time to sundial time is 9 degrees x 4 minutes/degree= 36 minutes. We also adjusted our times by another hour to account for Daylight Savings Time.
x = sin t y = cos t sin l

    These two formulas will give a set of x-y coordinates for time positions on an ellipse with a major axis of 1 unit. To calculate coordinates for an ellipse with a different major axis, multiply all of the x-y coordinates by the desired major axis.

Example for Time Position Calculation for Calgary, Alberta
Latitude = 51 North
Longitude = 114 West

Clock Time Daylight savings

Sundial Time

t (degrees)

x = sin t

y = cos t sin l

x'

y'

6 am

4:24

-114

-.914

-.316

-2.056

-.711

7 am

5:24

-99

-.988

-.122

-2.222

-.274

8 am

6:24

-84

-.995

.081

-2.238

.183

9 am

7:24

-69

-.934

.279

-2.101

.627

10 am

8:24

-54

-.809

.457

-1.820

1.028

11 am

9:24

-39

-.629

.604

-1.416

1.359

12 pm

10:24

-24

-.407

.710

-.915

1.597

1 pm

11:24

-9

-.156

.768

-.352

1.727

1:36:21

12:00

0

0

.777

0

1.749

2 pm

12:24

6

.105

.773

.235

1.739

3 pm

1:24

21

.358

.726

.806

1.632

4 pm

2:24

36

.588

.629

1.323

1.415

5 pm

3:24

51

.777

.489

1.749

1.100

6 pm

4:24

66

.914

.316

2.056

.711

7 pm

5:24

81

.988

.122

2.222

.274

8 pm

6:24

96

.995

-.081

2.238

-.183

9 pm

7:24

111

.934

-.279

2.101

-.627

The x-y coordinates are for an ellipse with a major axis of 1 unit.
The x'-y' coordinates are for an ellipse with a major axis of 2.25 metres.
The highlighted row is solar noon, occuring at 1:36 p.m. Daylight Savings Time. The shadow direction of a vertical object at solar noon will be north.

Calculating the Gnomon Positions

The gnomon positions are calculated using:

  • the latitude l

  • the declination d. The declination for each month can be found from the SunAngle website.

  • Gnomon Position = cos l tan d. The gnomon is positioned along the y-axis.

Example for Gnomon Position Calculation for Calgary Alberta
Latitude = 51 North

Date

Declination

Gnomon Position

Gnomon Position for 2.25 m dial

Jan 1/00

-23.04

-.268

-.602

Feb 1/00

-17.22

-.195

-.439

Mar 1/00

-7.37

-.081

-.183

Apr 1/00

4.76

.052

.118

May 1/00

15.25

.172

.386

June 1/00

22.13

.256

.576

July 1/00

23.07

.268

.603

Aug 1/00

17.88

.203

.457

Sept 1/00

8.09

.090

.201

Oct 1/00

-3.39

-.037

-.084

Nov 1/00

-14.61

-.164

-.369

Dec 1/00

-21.89

-.253

-.569

Analemmatic Sundial for Calgary Alberta - Click here to view

Details of the Analemmatic Sundial

Installing an Analemmatic Sundial

Equation of Time

References

Appendix