Effective angle

Method

The sky light is treated as if it all arrived at one effective incidence angle, and the ground-reflected light at another. Both angles are polynomial functions of the tilt, fitted by Brandemuehl and Beckman (1). The curve is then evaluated at those two angles (2).

The math

1. Effective angles
2. Factors

$$\theta_{sky} = 59.7 - 0.1388\,\beta + 0.001497\,\beta^2,\qquad \theta_{gnd} = 90 - 0.5788\,\beta + 0.002693\,\beta^2 \tag{1}$$ $$F_{IAM,sky} = F(\theta_{sky}),\qquad F_{IAM,gnd} = F(\theta_{gnd}) \tag{2}$$

where

Symbol	Meaning	Unit
$\theta_{sky}$	the effective incidence angle of the sky light	degrees
$\theta_{gnd}$	the effective incidence angle of the ground-reflected light	degrees
$\beta$	the tilt of the plane	degrees
$F_{IAM,sky}$	the angular-response factor for the sky light	—
$F_{IAM,gnd}$	the angular-response factor for the ground-reflected light	—
$F(\theta)$	the angular-response curve of the incidence-angle modifier step; with the De Soto cover option, the plain-glass transmittance read at these angles (De Soto cover, equation 5)	—

References

1. Brandemuehl & Beckman 1980, Transmission of diffuse radiation through CPC and flat plate collector glazings, Solar Energy 24(5) 511–513

API

iam.diffuse_integration = effective_aoi

Symbols follow the symbol registry.