Shading correction: basic principles and definitions

The shading correction can be used in conjunction with the automatic sun function or louvre adjustment. The function checks whether a window or a window group that is assigned to a room, for example, is temporarily placed in the shade by surrounding buildings or parts of its own building. Sun shading for windows that stand in the shadow of surrounding buildings or trees is not necessary and may even be disturbing under certain circumstances. On the basis of data entered regarding the facade and its surroundings, the shading correction determines which parts of the front are in the shade. Hence, it is then possible to decide whether the sun protection should be active for individual windows or window groups.
Apart from the current position of the sun, the shading of the individual windows depends on three things:

the orientation of the facade
the position of the windows
the positioning of the shading objects

The following illustrations are intended to describe these interrelationships and to present the parameters to be entered.

Orientation of the facade

Observation from above

Shading correction: basic principles and definitions 1:

For the pure observation of the shadow thrown on the facade, a two-dimensional coordinate system is ultimately required, therefore the x and y axis were placed on the facade. The zero point is thereby at the bottom left on the base, as if one were regarding the facade from the front. For the calculation of the shading objects the Z component is then also added. Its axis points from away the facade and has the same zero point as the X and Y axis.

The horizontal position of the sun (azimuth angle)in the northern hemisphere is by definition measured from the north. The facade orientation is likewise related to north, wherein the following applies to the line of sight from a window in the facade:

Line of sight	Facade orientation
North	β=0°
East	β=90°
South	β=180°
West	β=270°

The course of the sun in the southern hemisphere is different. The sun rises in the east as well. but at noon it is located in the north. Thus the definition of the facade-orientation is changed as well:

Line of sight	Facade orientation
South	β=0°
East	β=90°
North	β=180°
West	β=270°

Shading correction: basic principles and definitions 2:

All further explanations in this chapter are referring to the characteristics of the northern hemisphere. For the the subsequent parameterization of the shading-correction (FB_BARShadingCorrection / FB_BARShadingCorrectionSouth) only the facade-orientation is important, which can be taken from the above mentioned tables for either the northern or southern hemisphere.

The following two illustrations are intended to further clarify the position of the point of origin P₀ as well as the orientation of the coordinate system:

Observation from the side

Shading correction: basic principles and definitions 3:

The angle of elevation (height of the sun) can be represented using this illustration: by definition this is 0° at sunrise (horizontal incidence of light) and can reach maximally 90°, but this applies only to places within the Tropic of Cancer and the Tropic of Capricorn.

Observation from the front

Shading correction: basic principles and definitions 4:

Here, the position of the point of origin, P₀, at the bottom left base point of the facade is once more very clear. Beyond that the X-Y orientation is illustrated, which is important later for the entry of the window elements.

Position of the windows

The position of the windows is defined by the specification of their bottom left corner in relation to the facade coordinate system. Since a window lies flat on the facade, the entry is restricted to the X and Y coordinates.

Shading correction: basic principles and definitions 5:

The width and height must additionally be specified.

Shading correction: basic principles and definitions 6:

The position of each window corner on the facade is determined internally from the values entered. A window is considered to be in the shade if all corners lie in the shade.

Positioning of the shading objects

When describing the shading objects, distinction is made between angular objects (building, column) and objects that are approximately spherical (e.g. trees). Angular objects can be categorised according to the shadow they cast into square, shadow-casting facades, wherein one must consider which ones cast the main shadows over the course of the day:

Morning/midday

Shading correction: basic principles and definitions 7:

In the morning and at midday, the shadows are mainly cast by the sides S₁ and S₄; S₂ und S₃ need not be considered if they are not higher.

Afternoon / evening

Shading correction: basic principles and definitions 8:

In the afternoon and in the evening too, the total shade can be determined alone by the observation of S₁ and S₂. In this case, therefore, it is sufficient to specify S₁ and S₂ as shadow-casters. The entry is made on the basis of the four corners or their coordinates in relation to the zero point of the facade:

Shading correction: basic principles and definitions 9:

In this sketch only the upper points, P₂ and P₃, are illustrated due to the plan view. The lower point P₁ lies underneath P₂ and P₄ lies underneath P₃.

The input of shadow-casting ball elements is done by entering the centre of the ball and its radius:

Ball elements

Shading correction: basic principles and definitions 10:

A "classification" of the ball element as in the case of the angular building is of course unnecessary, since the shadow cast by a ball changes only its direction, but not its size.