SUNRISE ANGLE

The sun only rises vertically at the equator. At all other latitudes it rises diagonally, with a change in azimuth as it increases in elevation, with the amount of this azimuth change increasing as latitude.

Because of this factor, a determination of the solstice at sunrise requires a near instantaneous observation - before the change in azimuth creates an error in the observation.

However, this can be alleviated if instead of observing the sun rise on a flat horizon one observes it rise behind a "heel stone" as was done at Stonehenge. If the shape of the stone (mountain, or other distant object) has an angled curvature which matches the change in azimuth with change in elevation, then a longer period of observation can be used. If the leading edge of the sun is just barely visible at the time it is fully risen then it will appear to climb the edge of the heel stone until it climbs over the top.

Although this angle can be calculated by complicated geometry, the easiest method of determining the angle of rise is to obtain minute by minute data from the internet relative to both the increasing elevation and changing azimuth.

The data obtained for the winter solstice occuring on December 22, 2006 is as follows:

Time

Elapsed Time

Elevation

 

Azimuth

Increase from

Hr:Min:Sec

(Minutes)

(Degrees)

 

(Degrees)

start of sunrise

07:23:30

0

0.00

 

119.70

0.00

 

1

0.15

 

119.86

0.16

 

2

0.29

 

120.01

0.31

 

3

0.43

 

120.16

0.46

 

4

0.58

 

120.32

0.62

 

5

0.73

 

120.47

0.77

 

6

0.88

 

120.62

0.92

 

7

1.03

 

120.78

1.08

 

8

1.18

 

120.93

1.23

 

9

1.33

 

121.09

1.39

 07:33:30

10

1.48

 

121.24

1.54

 

11

1.64

 

121.40

1.70

The following is a plot of the degrees of elevation versus the increase in the azimuth for each of the 11 minutes following the sunrise at the winter solstice in San Francisco.

A heel stone should have one side sloped consistent with the slope of a smooth curve through these points if you wish to have a longer period of observation.