 # Light distribution curves, illumination and isolux diagrams

Careful planning work is required to solve lighting tasks. The necessary information about the properties of luminaires is given in light distribution curves, illumination and isolux diagrams.

## Light distribution curves

Light distribution curves specify in what direction and with what intensity a luminaire emits light. The luminous intensity value in candela (cd) for a given luminaire is obtained through the multiplication of the value read off the diagram in cd/klm with the total luminous flux in kilolumen (klm) of the lamps used in the luminaire.

The luminous intensity values are given on the vertical axis, and the beam angles on the horizontal axis. In a polar representation, the diagram specifies what sections through the luminaire (C-levels) the curves refer to.

Half beam angles = (continuous line, C 180 – C 0 β = 28°) and (dotted line, C 270 – C 90 β = 92°). Light distribution curves are usually presented in a polar coordinate system. With floodlights, we specify the light distribution using Cartesian coordinates.

## Illumination diagrams

Illumination diagrams for floodlights (Picture left) specify the dimensions of the area limited by the two half beam angles (Picture right) and the average degree of illuminance of this area, depending on the distance. Using the parameters “floodlights – area – horizontal axis” it is possible to read off:

• the height (continuous line, C 0 – C 180 β = 27°) and the width (dotted line, C 270 – C 90 β = 76°) of the limited area on the vertical axis on the right
• the average degree of illuminance (parabola) in lux on the vertical axis on the left

Example: At a distance of 12 m, the half beam angles of the floodlight 84 503 limit an area of 5 m in height and 15 m wide. The average degree of illuminance on this area is 240 lx.Uniform illumination can be obtained if the distances between the floodlights correspond to the width of the area limited by the half beam angles. When a façade is illuminated from the ground, only about 1∕3 of the specified illuminance can be achieved.  ## Isolux diagrams

Isolux diagrams (Fig. 5) specify the distribution of the illuminance on a visible surface.Points with the same illuminance are connected to each other by means of curves (isolux lines). The luminaire is located vertically above the drawing layer at the mounting height (h) above the coordinate origin. Depending on the luminaire type, the mounting height (h) or the appropriate pole height (H) is specified. The light point interval is approximately twice the distance at which the isolux line which belongs to half of the value of the desired minimum illuminance runs.Example: In the isolux diagram shown here, the 0.5 lx line runs laterally at a distance of 15 m from the coordinate origin. If a path is to be illuminated – Emin ≥1 lx – then light point spacing of approx. 30 m must be selected. In the case of luminaires with rotationally symmetrical light distribution, the resulting isolux lines are concentric circles. ## Examples

#### Determination of the distance of a floodlight from the illuminated surface on the basis of a light distribution curve

The façade to be illuminated has a height of 8 m (blue line) and a width of 18 m (red line). The high-performance floodlight 84503 with flat beam light distribution has a half beam angle of 27° and 76°. At a distance of 16 m, the half beam angles cover the dimensions of the façade exactly.

The parabola specifies the average degree of illuminance in lux. These values can be read off on the light distribution curve y-axis on the left. The average degree of illuminance on this reference surface is therefore 150 lx. Changes in the distance of the floodlight influence not only the average degree of illuminance but also the size of the illuminated surface. It must be noted that the diffuse light illuminates more than the previously calculated surface. The façade would still be well illuminated with a size of 10 x 22 m.

#### Determination of the luminaire spacing a for pathway illumination of Emin = 1 lx on the basis of the isolux diagram

The bollards line the pathway and emit their light asymmetrically onto the ground. The 1 lx line and the 0.5 lx line are used as the basis for planning.
At 3.5 m, degrees of illuminance of 0.5 lx add up to 1 lx on the opposite side of the path. The luminaires should be positioned with a light point spacing of a maximum of 6.5 m. The specified maximum degree of illuminance can be taken as a planning reference for good uniformity.
The average degree of illuminance results from the arithmetic average of all degrees of illuminance on a surface, calculated from the number of measuring points on the x axis and on the y axis.

#### Determination of the luminaire spacing “a” for square illumination with BEGA light building element 88157 on the basis of the isolux diagram

For luminaires with rotationally symmetrical light distribution, the isolux diagram shows one quarter of the total luminous intensity. The average degree of illuminance for a square situation should be 10 lx. About 20 lx is reached directly at the luminaire. In order to obtain an average of 10 lx, the minimum illuminance between two luminaires should be about 2 to 3 lx. In the diagram, the red circles indicate these values. Consequently, luminaire spacing is 19 m.

#### Determination of the luminaire spacing “a” for square illumination with BEGA pole-top luminaires 99515 on the basis of the isolux diagram

The same principle applies for asymmetrical light distribution. In this case, the position of the luminaires varies. The luminaires are arranged singly along the edge of the square and in double versions on the surface of the square.