Neolithic Sunrise Calendars - Appendix A Calculations For Sunrises Angles

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Appendix A

Calculations and Internet Displays For Sunrises Angles

Contents -

Sunrise Point

Sunrises Horizon Compass Bearings

Google Earth Pro 2015 Ground View Sunrise Point Accuracy

The Equation for Midsummer Sun Rises (SR)

Midsummer Sunrises (SR) Equation Check

Conclusion

Required sites links -

Latitude and Longitude finder map

Magnetic north to true north conversion

Suncalc, progression of sun rise ref to date/location

Assume that -

Spring = 20 March

Midsummer sunrise = 23 June (21 – 25)

Autumn = 22 Sept

Midwinter sunrise = 22 Dec (20 – 23)

Sunrise Point

The first view of a clear sunrise is of a bright point of light. This is the top of the sun. The point is small and it's position can be accurately placed. As the sun continues to rise the glow around it tends to mask it and makes the position less easy to place. On a hazy morning it may be impossible to distinguish between the sun itself and the glow around it. Thus the point at which the bottom of the sun clears the ground cannot be seen. See photographs below.

Stonehenge from the Pine Post Holes at Midwinter Source - mobile photograph

The equation for midsummer sunrise, and Internet displays such as SunCalc, Google Earth ground view, and ESRL, all appear to show the first view of the sunrise.

Sunrises Horizon Compass Bearings

Any particular point on the earth’s horizon from a fixed observation point can be located by the standard trigonometric 360° clockwise circle with the North at 0°.

Thus the position of a sunrise can be noted as the number of degrees clockwise from grid North.

The equation for the position of the midsummer sunrise at any latitude gives the East-North angle ¶°. Hence to find the angle from North clockwise, ¶° must be subtracted from 90°, as shown in the diagram below. The angle for midwinter was found to be close to 90° plus ¶°.

So the progression of the sunrises seem to be symmetrical about East. This seems to be unlikely but was checked by personal observation and found to be reasonably correct.

See diagram below.

Google Earth Pro 2015 Ground View Sunrise Point Accuracy

The visable sunrise point is effected by the elevation of the ground above the horizon level relative to the observation position. The higher the elevation ( such as a steep hill for example ) the further South the sunrise appears.

In 'ground view' Google Earth Pro 2015 uses an average of horizontal samples to display the ground elevation, and this has the effect of flattening the elevations. Hence the difference between the 'street view', and the 'ground view' of the same hill. This flattening effect will move the sunrise point to the North.

The sampling characteristics have a greater effect on a high elevation with a steep incline. For lower elevations the effect is small.

Source of information for above section - Internet articles for the search terms 'Google Earth Pro Sunrise Accuracy'.

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The Equation for Midsummer Sun Rises (SR)

This is an approx guide to the midsummer sunrise angle (SR°) to true North at a particular location of latitude.

given sin ¶° ~ (sin i / cos L)

SR° ~ 90 - arcsine [ (sin i) / (cos L) ]

or SR° ~ 90 - arcsine (sin ¶°)

where i = the angle of the inclination of the earth’s axis (23.4°)

L = Latitude of the location ( Latitude and Longitude finder map )

¶° = the angle of the midsummer East-North sunrise at latitude L

SR° = the angle of the midsummer sunrise to true North at latitude L

It is assumed that the midsummer sunrise angle ¶° East-North is very approximately that of the midwinter sunrise angle East-South. Thus add 90° to ¶° to give the approx true North angle of midwinter sunrise.

Correction factor to give angles at approximately 2500 BC. - To be written -

- Midsummer Sunrises (SR) Equation Check -

St Catherine's Hill, Christchurch, Dorset - observation point south end, bottom of hill, small hillock, Lat 50.75 Long -1.79

Magnetic north to true north conversion (British Geological Survey)

Magnetic north is estimated to be 1° 59' west of true north at this location in July 2012, and 1° 47' in June 2013.

Magnetic compass readings;

Midsummer Sunrise 48° at 4.55 am compass reading, magnetic North, 24 June 2013 (low cloud)

or 50° true North, inc. 2° offset in June 2013

Midwinter Sunrise 126° compass reading, magnetic North, 17 Dec 2012 (cloudy horizon)

or 128° true North, inc. 2° offset in July 2012

In addition -

22 August 2012 75° at 6.10 am compass reading, magnetic North, 22 August 2012 (clear sky)

or 77° true North, inc. 2° offset in July 2012

SR equation calculations

Sin ¶° = Sin i / Cos L = Sin 23.4 / Cos 50.75

Hence ¶° = 38.88°

and SR° = 51.1° (midsummer = 90 - 38.88)

~ 128.9° (midwinter = 90 + 38.88)
assuming ¶° is approx. equal to East-South angle.

Hence

midsummer SR equation = 51.1°
Observed true N = 50°

midwinter SR equation = 128.9°
Observed true N = 128°

Stonehenge -

Sin ¶° = (Sin 23.4) / (Cos 51)
= 0.631

thus ¶° = 39°

and SR° = 51° (midsummer = 90 - 39)

~ 129° (midwinter = 90 + 39) assuming ¶° is approx. equal to East-South angle.

Hence midsummer SR equation = 51°
Observed true N = 51°

Hence midwinter SR equation = 129°
Observed true N = 131°

Conclusion,

The SR equation is reasonably accurate and appears to give the true north midsummer sunrise angles.

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