True incidence angle

Method

Each direction of the ground in front of the plane is read on the angular-response curve at its own incidence angle and weighted by the cosine of that angle times its solid angle (1). On a plane tilted 35° with the Fresnel curve for anti-reflective glass the ground factor is 0.830. A plane that is not tilted sees no ground, and its factor is 1.

The math

1. Ground-reflected light

$$F_{IAM,gnd} = \frac{\int_{gnd} F(\theta)\,\cos\theta\,d\Omega}{\int_{gnd} \cos\theta\,d\Omega} \tag{1}$$

where

Symbol	Meaning	Unit
$F_{IAM,gnd}$	the angular-response factor for the ground-reflected light	—
$F(\theta)$	the angular-response curve	—
$\theta$	the incidence angle of the ground direction	degrees
$d\Omega$	an element of solid angle below the horizon, taken where $\cos\theta > 0$	sr

References

1. Duffie & Beckman, Solar Engineering of Thermal Processes, 4th ed., Wiley 2013

API

iam.ground_iam_angle = true_angle

Symbols follow the symbol registry.