Appelbaum geometric closed form

Method

The shaded fraction of the collector is the closed-form geometry of Appelbaum and Bany for parallel rows, applied to the bare collector width without inactive bands. The formula gives zero once the rows clear each other, so a tracker has no special backtracking case. With the Electrical shading effect step set to According to strings, every strip the shadow touches is lost entirely, with no ramp over the cell width. With that step set to Linear, the shadow removes only its own share of the direct light.

The math

$$F_{sh} = \max\!\left(0,\ 1 - \frac{P\,\sin\psi}{W\,\sin(\beta + \psi)}\right) \tag{1}$$

where

Symbol	Meaning	Unit
$F_{sh}$	the shaded fraction of the collector	—
$P$	the row pitch, the distance between the rows	m
$\psi$	the profile angle: the height of the sun seen in the plane perpendicular to the rows	degrees
$W$	the collector width	m
$\beta$	the tilt of the module plane from the horizontal	degrees

References

1. Appelbaum & Bany 1979, Shadow effect of adjacent solar collectors in large scale systems, Solar Energy 23(6) 497–507

API

array.shading_model = geometric

Symbols follow the symbol registry.