Dividing Eq. (E.29c) by Eq. (E.29a) and leaving Eq. (E.29e) unchanged leads to the
final expressions for the module orientation in horizontal coordinates,
Finally, the cosine of the angle between the module orientation and the solar position
is given by
We will try to understand these results by discussing easy examples.
First, we look at a roof that faces eastward and has a tilt angle θ R . Then, a R = 90° − θ R
and A R = 90°. On this roof a solar module is installed at a tilting angle θ M with respect to
the roof. The modules are mounted parallel to the gradient of the roof. We thus have δ M =
90° − θ M and φ M = 270°. From Eqs. (E.30) we thus obtain
In the second example, the roof is facing southward and tilted at an angle θ R . We thus
have a R = 90° − θ R and A R = 180°. Now the module is tilted at an angle θ M with respect to
the roof and mounted perpendicular to the gradient of the roof. Hence, δ M = 90° − θ M and
φ M = 180°. Using Eqs. (E.30) we find