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Sky window and sunniness of a building

To get a better measure how long the sun (or any other planet's) light can be seen on a defined surface (like a back wall)  inside a building, a definition of sunniness is made:
sunniness = sum of days that the sun light is on a defined surface divided by the periodicy [days] of the sun.
(remark: 'sun' can be replaced by 'moon' [mooniness] or any other planet/star)
The smaller the sunniness is, the less days the sun shines on the defined surface and thus the chance that the building could have been deliberately designed to let the light in, is bigger. If the sunniness is zero, no light comes in and then there is a small probability for an alignment!
Remark: A small value of sunniness does not prove that there is an alignment, more indications (culture, reappearing sun, other buildings (statistical proof), geological circumstances, 'infrastructural' environment, etc.) are needed! A quiet standard room in a house facing appr. sunset/rise has a sunniness of >50%, so not that far from the sunniness of a passage (typical <25%)!

Some examples (measured and calculated):
 
Building Sunniness (meas.) Sunniness (cal.) Sunniness
standard room**
Maeshowe (winter solstice) 19%, 68 [days] 17%, 62 [days] 53%
Maeshowe (Megalithic Month) 1.1%, 4 [days] 1.9%, 7 [days] 53%
Newgrange 2.7%, 10 [days] 13.4%, 48 [days] 54%
Treasury of Atreus N.A. yet 24%, 88 [days] 
19%, 70 [days]*		 100%
Cairn T, Loughcrew N.A. yet 23%, 85 [days] 81%
Dutch passage mounds*** N.A. yet 30%, 110 [days] 23%
Knowth, western passage
N.A. yet
2.1%, 8 [days]
23%
Dowth, South
N.A. yet
25%, 91 [days]
Dowth North
N.A. yet
37%, 135 [days]
  

* Calculated with SkyMap.
**A standard room is 4 by 4 [m] and 2 [m] high, it has a window of 1 by 1 [m], a horizon of 0o, the same direction and latitude as the building and using the whole back wall as defined surface.
*** The Dutch passage mounds have a short passage (around 1.5 m), so that is why sunniness of standard room is smaller than of the passage!

Any comments are welcome to my ideas.

Comparable methods

The same method for determining the sky window is mentioned by Robert Lomas ([1999], page 280 and 413), but he calls it: Virtual aperture.
Another comparable method is defined by Cox ([2001], page 28) as: Standard view (it does not include the restriction of the horizon and it is restricted to the middle of the lower edge of 'defined surface').

Calculating the sky window and sunniness of a passage

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Determining geometry of passage (Default geometry is used from Maeshowe)

Coordinate system
You have to stand with your back to the defined surface (like a back wall) facing the outside. Going-right/going-up/going-out is positive and going-left/going-down/going-back is negative.

Location
Latitude: [o]

General information
Air pressure:[mbar] (at Eye height)
Temperature: [oC] (at Eye height)
Time of day: sun set/rise and night noon
Astronomical date:  (positive for CE and negative for BCE)

Two methods can be used here to determine the sunniness or declinations:

  1. The lay-out of the building can be provided. Go to here.
  2. Already known sky window (azimuths and apparent altitude measured with others means) can be provided. Go to here.
Lay-out of building
This option is only possible when this radio button  is active.

Horizon
Eye height:           [m]
Distance:             [km]
Distant object height:[m]

distant object               
vast plain horizon
given apparent altitude: [o]
apparent altitude[o]

Bird view of Maeshowe (for default values)

Cross view of Maeshowe (for default values)

Azimuth of reference axis of building:[o]

Defined surface (at z=0)

If you don't know where the boundaries of the light on the defined surface are, make lower edge -5 [m] and leave the others on the default values.
Upper edge:[m]
Left edge: [m]   Right edge:[m]
Lower edge:[m]

Middle boundary edges

Upper edge:[m]  Distance: [m]
Left edge: [m]
Distance: [m]		   Right edge:[m]
Distance: [m]
Lower edge:[m]  Distance: [m]

End boundary edges

Upper edge:[m]  Distance: [m]
Left edge: [m]
Distance: [m]		   Right edge:[m
Distance: [m]
Lower edge:[m]  Distance: [m]

azimuth and apparent altitude of sky window

(The boundary azimuths at Maeshowe were determined also in real live)
Maximum apparent altitude: [o]
Minimum azimuth:[o]   Maximum azimuth: [o]
Minimum apparent altitude: [o]
(this takes into consideration the apparent altitude of the horizon)

The sunniness can be found in this section.

Known sky window

This option is only possible when this radio button  is active.
(The boundary azimuths at Maeshowe are used as default)
Maximum apparent altitude: [o]
Minimum azimuth:[o]   Maximum azimuth: [o]
Minimum apparent altitude: [o]

The sunniness can be found in the below section.

sunniness, mooniness in major year or mooniness in minor year: [%]
Compare these azimuth values with sun/moon rises/sets. If they are comparable, the building could be aligned to the sun or moon. If you want to calculate the dates the sun gets through this window, please look at this link. Use the below values for average azimuth of sky window and width of sky window when running the link for the minimum apparent altitude and the maximum apparent altitude and then combine the found dates):
Average azimuth of sky window: [o], width of sky window: [o]
Minimum apparent altitude of sky window: [o], maximum apparent altitude of sky window: [o]
Declination area of this sky window: [o^2] (another possible measure of accuracy of the passage?)

Declinations (geocentric) seen through the sky window (with your back to the defined surface and facing the sky):

________
 
[o] [o] 
_
[o] [o] 
 
______
Compare these declination values with the table of important declinations values.

 rise and set azimuth of

SUN at  solstice equinox cross quarter (0.69*max. decl.) or
MOON at  major standstill limit  minor standstill limit

Azimuth of celestial object with its center at the horizon altitude:
summer/northern sun/moon rise [o]
summer/northern sun/moon set [o]
winter/southern sun/moon rise [o]
winter/southern sun/moon set [o]

If latitude is around the polar circle then, depending on the altitude of the horizon, the azimuth's can not be calculated and are thus not available [N.A.].

Compare these values with the sky window found above.

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Last major content related changes: Oct. 8th, 1999