Extending the Three-Phase Method to the F-Matrix Method

Overview: As discussed previously in Chapter 1, when considered within the context of the Three-Phase Method, the F-Matrix involves intercepting the flux-transfer between the glazing aperture(s) and the sky with an additional matrix that accounts for flux-transfer within the façade. The equation for the Three-Phase Method, as described in Section 3.2 is:

…………………………… [4]

The above equation can then be reinterpreted for F-Matrix Method as:

…………………………… [5]

The schematic diagram for the F-Matrix Method is shown in Figure 61.

Figure 61. Schematic diagram for the F-Matrix Method. The F-Matrix Method employs the same set of Radiance programs as the Three-Phase Method. The Façade matrix is created with rfluxmtx by assigning glazing apertures as ‘sending surfaces’ and F-apertures as ‘receiving surfaces’.

Comparing equations [4] and [5], also Figure 34 and Figure 61, it is clear that the Three-Phase Method and the F-Matrix Method only differ in how the Façade (F) and Daylight (D) matrices are calculated. The workflow for the F-Matrix Method described in this chapter builds on the workflow for the Three-Phase Method. The model used for the simulation is shown in (b) of Figure 17. With the exception of the external shading device, this model is exactly similar to the one used for the Three-Phase calculations. So, the commands for creating the View Matrix and Transmission matrix will be the same as those used in the Three Phase Method (documented in Section 6.3.1.1 (View Matrix) and Section 6.3.1.2 (T Matrix) of Chapter 6 respectively). Since the Three-Phase Method calculation in Chapter 6 did not include the external grates, a new octree containing the grates needs to be created for the F-Matrix simulations:

oconv -f materials.rad room.rad overhang/aluminiumGrate.rad > roomFmtx.oct

The next three sections describe the steps for creating different types of F-matrices.