# View Factor Models

View factor models are used for radiative transfer calculations of the amount of radiation leaving one surface (A) that reaches a second surface (B). The view factor $$F_{A\rightarrow B}$$ is the fraction of the radiation from surface A that hits surface B. In the context of bifacial PV arrays, the surface B is the back side of the bifacial module or row of modules and surface A is a collection of surfaces near the array such as the unshaded ground, the shaded ground, the front of the PV modules behind the module of interest, etc.). View factor models rely on the fact that all radiation is conserved and thus the sum of all view factors from any surface A equals 1. View factors, also termed shape factors, configuration factors and angle factors, implicitly assume that all radiation is scattered isotropically from any reflecting surface. View factor models estimate the radiant flux (W) reaching the backside of a bifacial module as:

$$E_{B}=\sum F_{A\rightarrow B}\times E_{A}$$

where $$E_{B}$$ is the radiant flux (W) on the back-side of the bifacial module and $$E_{A}$$ is the radiant flux (W) reflected or scattered from each surface A.  Note that radiant flux (W) on surface B is equal to irradiance (W/m^2) on surface B multiplied by the area of B.

View factors can be computed by numerically integration. The view factor from a general surface A1 to another general surface A2 is given by:

$$F_{1\rightarrow 2}=\frac{1}{A_{1}}\int_{A_{1}}^{ }\int_{A_{2}}^{ }\frac{\cos \theta _{1}\cos \theta _{2} }{\pi s^{2}}dA_{2}dA_{1}$$

where $$\theta_{1}$$ and $$\theta _{2}$$ are the angles between the surface normals and a ray between the two differential areas.