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where:
DF is the daylight factor (%);
Aw is the glazed area of the windows (m2);
A is the total area of all the surfaces in the room, including windows (m2);
is the angle of visible sky, measured in section from a point in
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the centre of the window (degrees);
T is the transmittance of the glazing to diffuse light and includes the maintenance factor (to account for dirt on the glass);
R is the area-weighted mean reflectance of the room surfaces.

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where Aw is the area of the glazing only, not including window frames, glazing bars or other obstructions.

7.8 Prediction of Sunlight
The prediction of sunlight penetration into a building can be an expensive and time-consuming process, requiring modelling and calculations.  It may be cost effective to work out sun paths and optimise external shading devices which are costly.17 It is usually left to professional daylighting consultants, who use a variety of tools to simulate daylight factors, glare problems and modelling.62

One of the simplest, and reliable methods of predicting the sunlight paths in a room is to produce a 3-D model of the room used under an artificial sky with an artificial sun (heliodon). Whilst this can be expensive, depending on the complexity of the model, the effects of light in the room can be seen directly.

The other available methods for predicting sunlight are computer programs and sun path diagrams.63  Computer simulation can sometimes be cheaper, depending on the level and cost of expertise available. Sun path diagrams can be used when no suitable computer program is available. All these forms of modelling are discussed in more detail in chapter 13.0.

7.9 Sources of Calculations for Window Design
Existing texts contain easily understood and practical examples of the various calculation methods necessary for window design. A review of these follows, allowing the reader to choose the appropriate source.

7.9.1 Designing Buildings for Daylight64 
Positioning the Window: pages 32 - 33.
Raises the issue of how the location of a window on a wall can affect the distribution of daylight within the room. Images and text describe the various locations, mainly in relation to an office situation. The principles can be transferred for use in considering window positioning in sports halls.

Model Box Exercise: pages 50 - 53.
Describes how to produce a simple shoebox model for experimenting with window locations, including rooflighting. Includes sections on preparing the box, alternative window arrangements, initial assessment, sketching what you see, comparing sketches and comparing with reality.

Window Design Exercise: pages 54 - 60.
A comprehensive guide to the design of windows, including preliminary design stages, detailed design, sun penetration and minimum daylight factor. Contains easily understood formulae for the detailed design stages and references to further studies in the CIBSE Window Manual65.

Accessories to Window Design: Appendix F, pages 83 - 95.
Contains all the necessary accessories used in the text for the design of windows and daylighting, including: haystack modelling template, masks for window sizing, window-wall templates, pepperpot diagrams and sunpath diagrams.

7.9.2 Lighting Design for Schools66
An Atrium: Appendix 8.3, pages 71 - 76.
Addresses the issues on atrium design, some of which are transferrable to sports halls. The clear images show the various ways of daylighting an atrium, including roof glazing, clerestories, ‘saw-tooth’ monitors, lay lights and an asymmetric roof profile. Sky glare, sunlight glare and solar gain are considered, along with electric lighting of such spaces.

7.9.3 The Design of Lighting67
Sunlight Availability: Example (b), pages 133 - 135.
Describes the method for calculating the sunlight availability using sunlight hours diagrams and overlays of the building outlines. Principal areas include method, a worked example (based on vertical sky component example on pages 130 - 133), and comment.

Average Daylight Factor: Example (c), pages 135 - 139.
This is used to predict the extent to which daylight will be a significant factor in the lighting of a room and is mainly used at the initial stage of a building design.

A worked example, based on the formula described in section 6.7, shows how the formula is used for calculating comparisons between daylighting between existing buildings and the effect that a new building would have on the daylighting situation.

Data: (i), pages 156 - 161.
Data sheets for sky diagrams, a daylight availability chart for London (see Appendix B for daylight availability in Scotland), typical reflectances of surfaces under diffuse daylight, transmittance values of windows, and artificial lighting tables.

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7.7 Prediction of Daylight  
Predicting daylight can be estimated by using the daylight factor equation. More accurate methods involve the use of computer programs, to plot daylight factor contours in a room, see further description in 12.2. Direct sunlight is excluded from the daylight factor calculations.

The daylight factor at any point on a sports hall floor can be calculated in terms of the light coming directly from the sky (Sky Component), the light reflected from outside surfaces (Externally Reflected Component), and the light reflected from internal surfaces (Internally Reflected Component).
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Fig 7.3 - The measurement of daylight factors is simpler, requiring only simultaneous metering of the internal illuminance and external horizontal illuminances under an overcast sky.

To calculate the average daylight factor the following formula is used:
The angle of visible sky for sports halls will be large, where rooflights are the standard method for admitting daylight. It is measured from the centre of the rooflight, in an arc sweeping from one side of the aperture to the other. If roof monitors or clerestories are used instead, the angle of visible sky is reduced, but still larger than for windows lower down.

The transmittance and dirt reduction values for the glazing can be found in Appendix A.

During the early periods of design it may be desirable to ascertain the area of glazing required to give a set daylight factor. In this case the daylight factor formula is inverted to give,