The most usable manual method for calculating Daylight Factors is the split flux method. This is based on the assumption that, ignoring direct sunlight, natural light reaches a point inside a building in three ways:

• Sky Component (SC)
  Directly from the sky, through an opening such as a window.
• Externally Reflected Component (ERC)
  Light reflected off the ground, trees or other buildings.
• Reflected Component (IRC)
  The inter-reflection of (SC) and (ERC) off other surfaces within the room.

Separate consideration of these components is justified by the fact that each is affected by different elements within the design. The resulting Daylight Factor is given as a percentage and is simply the sum of each of these three components:

Daylight Factor Protractors

The Split Flux Method uses Daylight Factor Protractors as a manual means of calculating the Sky and Externally Reflected Components. These protractors are available in many architectural science text books and can be photocopied onto acetate and overlayed directly on your drawings. The Useful Links section below contains a site where you can download reasonable quality images. Alternatively, you can download the DF Protractor Tool from Square One which you can use on a MS Windows computer to overlay on-screen your CAD drawings or scanned images, as shown in Figure 2 below.

Figure 2 - The DF Protractor Tool can be used to directly overlay CAD drawings and scanned images.

Click here to download this tool as a MS Windows application.

Sky Component (SC)

The Sky Component is determined using Daylight Factor Protractors, as describe above. The first protractor you use is for the vertical section of your design - it determines an unmodified Sky Component for an infinitely long window. To obtain the value, simply take the DF from the top of the window (head) and subtract off the value at the bottom (sill). Values below horizontal are considered to be zero as they will not contribute to light falling on top of a work surface. Don't forget to record the Average Altitude Angle of the sky as seen through the window. This is simply the bisector of the top and bottom angles (you can also think of it as going through the geometric centre of the window).

In the above example the top of the window is at an altitude angle of 34°, with a corresponding DF of 5.10%. However, the window sill is above the test point, so the point will not receive the full 5.10% of the light. The sill is at an altitude of 11°, with a corresponding DF of 0.17%. Thus, the amount of daylight received at the point from an infinitely long window with that cross section would be 4.93% (5.10 - 0.17). Note that, if the test point is above the window sill, the bottom aximuth line never goes below the horizontal (0°).

Window Width Correction Factors in Plan View

As most windows are not infinitely long, this value must to be corrected using the second protractor in plan view. To do this we first need the average altitude angle of the window. This is simply the bisector of the top and bottom altitude lines in section - in this case 22°. This angle will allow us to plot a concentric circle from which the window width correction factor can be generated.

Simply lay out the protractor in plan such that the centre point is exactly on the focal point and the main axis is parallel to the window. Determine the correction factor for both sides of the window by intersecting the lines from each side of the window with the altitude line of the centre of the window. In this case 22°, as illustrated in Figure 4 below.

If both the left and right sides of the window are in the same quadrant (ie: the same side of the 0 line), you must subtract the largest number from the smallest. If they are in separate quadrants of the protractor (on either side of the 0 line), you must add the two correction factors together.

Finally, multiply the total correction factor by the DF value determined in sectional view to get the overall SC from that window. If you have multiple windows, you have to go through this same process again for each one and sum up the final results.

Externally Reflected Component (ERC)

The Externally Reflected Component is determined in exactly the same way as the Sky Component, using daylight factor protractors. However, to simulate the lower light levels due to reflection off one or more surfaces, the final value is multiplied by 0.2. The 0.2 constant is simply an average reflectance which can be assumed for most normal building materials and natural surfaces.

Internally Reflected Component (IRC)

The Internally Reflected Component is derived using a simplified equation that considers the internal reflectance of different groups of surfaces inside the space and the total area of window. It is given by the following equation:

Where:

• W = Total window area (m²),
• A = Total internal surface area, including walls, floors, ceilings and windows (m²),
• p1 = Area weighted average reflectance of surfaces making up A, (use 0.1 as reflectance for glass).
• p2 = Average reflectance of surfaces below the height of the test point, usually a working plane of 600mm above the floor,
• p3 = Average reflectance of surfaces above the working plane, and
• C = Coefficient of external obstruction, as described below.

The coefficient of external obstruction refers to the average height of all external obstructions. If this includes buildings of different heights, then you have to work out an average height over the entire window width and use that. In the case of a single long fence, just use its top. Once you have that angle, use the following table to derive C.

Table 1 - Coefficients of external obstruction (C).

Useful Links

Methods of Daylight Factor (DF) Estimation
http://personal.cityu.edu.hk/~bsapplec/methods.htm
This page contains some high-resolution scans of daylight factor protractors. To download them, simply right-click and choose 'Copy' - the resolution is much larger than is displayed.

Corrections to Calculated Daylight Factor -- Algorithm 2.13
http://eande.lbl.gov/Task21/C2/algo2/Algo2_13.html

CBD-17. Daylight Design
http://irc.nrc-cnrc.gc.ca/cbd/cbd017e.html

Task 21 - Simple Design Tools Survey
http://aesl.hanyang.ac.kr/resource/daylighting/survey.pdf

Courtyards, Daylight, and Aspect Ratio
http://oikos.com/library/courtyards/daylight.html