Points of Equal Sky Illuminance

Article 080

Jan. '04

It is possible to quickly estimate the Daylight Factor Sky Component at any position within a building by projecting points of equal illuminance density across the sky dome. If you generate a hidden line perspective view from that position, you can simply count up the number of points you can physically see through any windows. These points represent the portion of total direct Sky Illuminance visible from that position.
 
 

Figure 1 - Viewing Points of Equal Sky Illuminance
from a position inside a building.

Image created using ECOTECT v5.
 
 

In ECOTECT this is done using 200 points, each one worth 0.5% of the sky illuminance. At this particular viewing position 8 points are visible, resulting in an estimated Sky Component of 4%.

 
 

Obviously the exact distribution of these points depends on the sky type. The image below shows points distributed using the CIE Overcast Sky model, with a point density three times higher at the zenith than at the horizon. The points shown in red indicate those points visible from the viewing position illustrated above.
 
 
 
 

Figure 2 - 200 points distributed over the sky dome.

Image created using ECOTECT v5.
 
 

Sun-Path Projections
 

This same method can be used with points projected over a Sun-Path Diagram. This way, instead of having to set up a camera position and looking around to different windows, you can simply select a POINT object at the desired position and generate the diagram from there.
 
 

If you are using ECOTECT and have the Sun-Path dialog displayed, it will automatically generate overshadowing at the selected point, or even in a selected surface. You can then simply count up the number of points that you can 'see' through all the visible windows and skylights. In the example shown below, 16 points are visible (shown in red), resulting in an estimated Sky Component of 8%.
 
 
 
 

Figure 3 - Points of Equal Sky Illuminance distributed over a stereographic Sun-Path diagram, showing the overshadowing
pattern at the selected position.

Image created using ECOTECT v5.
 
 

You can obviously do this same calculation with all of the available Sun-Path projection methods. This includes spherical, waldram and the BRE projection. The image below shows the same point distribution on an orthographic (or cylindrical) projection.
 
 
 
 

Figure 4 - The same points as in Figure 3 projected over an orthographic or cylindrical Sun-Path diagram.

Image created using ECOTECT v5.
 
   
 
 

Different Sky Types
 

Different sky illuminance distributions will result in a different arrangement of points over the sky dome and the Sun-Path diagram. In ECOTECT, only the CIE Overcast and Uniform Sky models are currently supported. In addition, it is also possible to display points of equal Vertical Sky Component. In this mode, a vertical surface is assumed so the number of points at the zenith is reduced according to the Cosine Law of surface incidence.
 
 
 
 

Figure 5 - The different types of point distribution
corresponding to sky types and applications such as the
BRE Vertical Sky Component.

Image created using ECOTECT v5.
 
   
 
 

Related Links

Sky Illuminance
http://www.squ1.com/daylight/sky-illuminance.html
 
 

 

 

 

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