Computational analysis of the Daylight Factor is actually a bit more difficult than you might think. To be accepted by many regulatory authorities, the algorithm used must be based on an approved method. Thus, ECOTECT uses a geometric version of the Split Flux Method as outlined by the UK Building Research Establishment (BRE). This method has it limitations as it is essentially based on a manual method (as explained later) however it is an internationally recognised technique, is quick to calculate and is suitable for most types of conceptual design analysis. For more detailed analysis, ECOTECT allows you to export your model to RADIANCE for more complex and physically accurate daylight simulation.

ECOTECT's implementation of the Split Flux Method involves spraying a large number of imaginary light rays from each point of interest within the building. These points of interest can be spread out over an analysis grid or created individually as POINT objects within the model. Rays are generated pseudo-randomly but in an even distribution over the sky dome such that they each represent an approximately equal 3D solid angle. The green dots in Figure 1 below each represent a ray intersection point, in this case with a geodesic dome object centred on the analysis point to show the evenness of the distribution, and also within a simple enclosure.

Figure 1 - The pseudo-random test rays generated spherically during a daylight factor calculation, shown over a hemisphere and within a simple room.

Sky Component (SC)

If a traced ray passes through a transparent aperture and travels out towards the unobstructed sky, then that particular ray's solid angle contributes to the Sky Component and is modified by:

• the relative sky illuminance in that particular area of solid angle,
• the relative angle it makes with a horizontal (or vertical) surface, and
• the visible transmittance of each glazing material through which it travels.

Externally Reflected Component (ERC)

If the ray passes through an aperture and then strikes an external object, it contributes to the Externally Reflected Component and is modified by:

• the illuminance of the sky it would have hit,
• the external reflectance of the material assigned to the struck external object, and
• the relative surface angle and glazing transmittances.

Internally Reflected Component (IRC)

If a ray hits an opaque object before passing through an aperture, then it contributes to the Internally Reflected Component. In this case the internal surface reflectance of the object is stored and the altitude angle of the ray is then used to determine which parts of the IRC formula it contributes to.

Figure 2 - An example showing some exploratory rays passing through a window and hitting an external obstruction whilst others travel unobstructed towards the sky.

If you look at a Sun-Path Diagram, you can actually see by the overshadowing which bits of the sky dome are obstructed (shown below in GREEN, therefore becoming ERC), which are clear (shown in YELLOW, becoming SC), and which are internal surfaces (shown in DARK GRAY, becoming IRC). The sky colour values in Figure 2 are graded to indicate the sky illuminance distribution, in this case for a CIE Overcast Sky.

Figure 3 - SC, ERC and IRC shown projected onto a Sun-Path disgram from the point of interest.

As each ray represents an approximately equal solid angle of sky, summing up relative illuminance after modification and comparing it against the total unmodified illuminance gives a percentage value equivalent to the Daylight Factor. If this is done for a large number of points in a space, distributed over an analysis grid, then it is possible to plot Daylight Factor contours over an entire area of work surface. Figure 4 below shows such values for a range of different window configurations.

Figure 4 - Some example Daylight Factor contour plots, showing how it is possible to both visually and objectively compare different design configurations.

This method is quite flexible and can be used for appertures of any shape and in any orientation. Figure 5 below shows some examples of rooflight calculations.

Figure 5 - Comparing Daylight Factor distributions for different skylight configurations.

Limitations

The main limitation of the BRE Daylight Factor method is that it uses a relatively simple formula for the effect of internal reflections. To be fully compliant with this method, ECOTECT's ray-tracing cannot consider multiple reflections so the method will underestimate the performance of indirect daylight solutions that rely on the reflection of light off multiple surfaces to illuminate a space.

This is clearly illustrated in Figure 6 below. As soon as the grid is obstructed by the floor slabs in the lower floors, daylight factor values fall off very quickly, you can almost see them as defined lines. In real buildings the fall off is much more gradual than this, as shown in Figure 7, due to diffuse reflections and scattering by other internal surface materials.

Figure 6 - An example of BRE Daylight Factors falling off quite quickly when obstructed from direct sky or external reflections.

For more complex diffuse light simulations, use the RADIANCE software from Lawrence Berkeley Laboratories. This uses a hybrid reverse ray-trace technique to iteratively solve the radiant exchange of light between surfaces, resulting in a more realistic spatial distribution.

Figure 7 - A more realistic spatial distribution of light energy generated by RADANCE using a hybrid reverse ray-trace solution.

ECOTECT can export models directly to RADIANCE and can even invoke calculations and display results from within its own interface. In addition to simply generating rendered images, ECOTECT can use RADIANCE to analyse the Daylight Factors over an analysis grid and then import the raw radiances back into the grid, as shown in Figure 7. Obviously you will need to refer to the on-line help for detailed instructions on how to do this.

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