Subtask C2--New Daylight Algorithms

ETSU contract E/5A/1350/2665
Daylighting algorithm collation

The algorithms

P R Tregenza
S Sharples

School of Architectural Studies
University of Sheffield
PO Box 595 The Arts Tower
Sheffield S10 2UJ
May 1993. Revised December 1995.


This work is a compilation of algorithms for computing daylighting. It covers calculation of every stage from extra-terrestrial solar illumination to inter-reflection of light in a room. Most of the procedures listed are based on published sources but some new algorithms have been written where there was a clear gap in the computational sequence.

In many cases algorithms have been chosen from several alternatives. Where published comparisons (of accuracy or computational efficiency) are available these have guided the choice, but few such studies exist in the literature. In general the selection has been made on the bases of   a. common application and   b. consistency in the use of a systematic geometrical framework or parameters common to successive equations. As far as possible, the form of the equations given is that of the source publication but names or symbols have been changed when they differed from the recommendations of the CIE Vocabulary , and a listing of units, symbols and suggested names for computer variables is given in an appendix. Only algorithms related to light are included; computation of radiation for thermal analysis is well-covered in existing texts and in particular by the SERC meteorological data base.

The work was carried out under a contract with the Energy Technology Support Unit, and the authors thank Dr I McCubbin and Mr P Dolley of ETSU for their help and direction. They are grateful also to Dr P J Littlefair of the Building Research Establishment and to other colleagues for advice and technical information. In particular the authors thank Mr J A Lynes of the Hull School of Architecture for his invaluable guidance and constructive criticism at every stage of the project.

Commission Internationale de l'Eclairage, International lighting vocabulary, 4th edition. Commission Internationale de l'Eclairage, Vienna (1987).

Page J K and Sharples S, The SERC meteorological data base Volume II: algorithm manual, 2nd edition. Department of Building Science, University of Sheffield (1988).

Available light

1.1 Solar geometry
1.11 Solar declination
1.12 Equation of time
1.13 True solar time and hour angle
1.14 Solar altitude and azimuth
1.15 Astronomical daylength
1.16 Shadow length
1.17 Ground shadow area of a rectangular building

1.2 Sunlight
1.21 Illuminance turbidity factor
1.22 Relative optical air mass
1.23 Extraterrestrial solar illuminance
1.24 Illuminance from direct sunlight

1.3 Skylight
1.31 Daylight availability: global & diffuse
1.32 Clear sky luminance and illuminance
1.33 Overcast sky luminance and illuminance
1.34 BRE average sky luminance and illuminance
1.35 Daylight coefficients and subdivision of the sky

1.4 External surfaces
1.41 Light reflected from the ground
1.42 Luminance of external obstructions
1.43 Specular reflection in external surfaces
1.44 Obstruction of the sky by trees

Daylight factor methods

2.1 Total
2.11 Daylight factor definition
2.12 Average daylight factor
2.13 Corrections to calculated daylight factor

2.2 Externally reflected component
2.21 Externally reflected component of the daylight factor

2.3 Sky component
2.31 Sky factor for unglazed vertical rectangular opening
2.32 Sky component for unglazed vertical rectangular opening
2.33 Sky component for unglazed horizontal rectangular opening
2.34 Directional transmittance of clear glass
2.35 Directional transmittance of non-clear glass
2.36 Diffuse transmittance of non-clear glass
2.37 Diffuse reflectance of non-clear glass

2.4 Internally reflected component
2.41 Average internally reflected component for vertical windows
2.42 Minimum internally reflected component for vertical windows
2.43 Average internally reflected component for rooflights

Finite area methods

3.1 Form factors
3.11 Configuration factor and form factor definitions
3.12 Form factor for identical parallel, opposite rectangles
3.13 Form factor for two perpendicular rectangles
3.14 Configuration factor for element parallel to rectangle
3.15 Configuration factor for element perpendicular to rectangle
3.16 Configuration factor and form factor with triangular subdivision

3.2 Radiosity method
3.21 General radiosity method using triangular patches (Currently Missing)
3.22 Test for hidden points with triangular subdivision
3.23 Daylight coefficient: direct component
3.24 Solution of inter-reflection equations

Ray tracing methods

4.1 Monte Carlo method
4.11 General procedure for Monte Carlo method
4.12 Random emission from point source and diffusing surface
4.13 Monte Carlo reflection at a surface


5.1 Geometrical framework
5.11 Axes and coordinates
5.12 Direction cosines of the normal to a plane
5.13 Angle between two vectors
5.14 Distance and direction between two points
5.15 Interception of a ray and a plane
5.16 Test whether a point lies on a plane
5.17 Sides, internal angles and area of a spherical triangle
5.18 Subdivision of a spherical triangle

5.2 Symbols and names of variables

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