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Once the sky dome has been subdivided, with incidence and percentage shading calculated for each sky segment, it is possible to derive a range of useful values using only this information.

Sky Factors and Sky Components

The amount of sky actually visible from a particular point is an important indicator of its exposure to both daylight and solar radiation. A point at the centre of a cricket pitch is likely to 'see' around 90-95% of the sky as there are very few surrounding obstructions. However, a point on a street in a built up urban area will 'see' far less, maybe as little as 20-40%, whilst deep inside a room there may be no view of the sky at all.

If the luminous and radiant contribution of all parts of the sky were equal, then the visible percentage of sky could be used directly to calculate daylight levels and diffuse radiation values at any point. However, the sky is an anisotropic source, meaning that the contribution from different parts of it are not equal, sometimes varying quite significantly. There are two main reasons for this:

• The passage of the sun across the sky as well as reflection/obstruction by changing cloud formations mean that patterns of relative brightness and dullness are highly dynamic, changing almost minute by minute. As discussed earlier, statistical averages can be used to generate mathematical models of idealised sky types, all but one of which show significant variation near the current sun position and between the zenith and the horizon - this being of course the CIE Uniform Sky.
• Typically light is used and measured on flat surfaces. Both light and radiation from different parts of the sky arrive at different incidence angles on flat surfaces. Thus - as a result of the cosine law - the contribution of different areas will depend on the orientation of the receiving surface.

The terms sky factor and sky component refer to the actual contribution of the sky to daylight, after considering both luminous distribution and incidence angle effects. There appear to be no hard and fast rules as to the type of sky distribution to be used with either term, however they are typically calculated using either the CIE Uniform Sky or CIE Overcast Sky to remove the dynamic effects of any beam solar component.

Both values can be calculated directly from the shading mask. Only the shading and incidence angle layers are required, along with the diffuse radiation layer - but with no contribution from the beam radiation layer. As they are given as a percentage value, the diffuse layer is generated such that the sum of all sky segments totals exactly 100, using the user-selected CIE sky model to calculate the relative contribution of each individual segment. The resulting percentage is calculated by multiplying the layers in each segment together and then summing the product of all segments.

Vertical Sky Component

The Vertical Sky Component (VSC) is described by the UK Building Research Establishment (BRE) as "ratio of the direct sky illuminance falling on the vertical wall at a reference point, to the simultaneous horizontal illuminance under an unobstructed sky" [Littlefair, 1991]. It also states that the CIE Standard Overcast Sky model is to be used for the sky illuminance distribution. This means that the reference value for the VSC percentage is effectively the unobstructed horizontal sky component.

If we look at both the incidence angle effect and the distribution of diffuse radiation over the CIE Overcast Sky, as shown in Figure XXX below, we see a concentration of radiation at the zenith which arrives at the vertical surface at close to grazing incidence - hence having little effect. The result of this is that the maximum possible overcast sky radiation visible to a vertical surface is not 50% of that on the horizontal plane, but only 40%.

CIE Overcast Sky - Incidence effects for a vertical surface

Figure XXX: The two component shading mask layers for an unobstructed Vertical Sky Component.

The VSC is used in the UK as an indicator of daylight potential. Planning guidelines from the BRE give minimum VSC values for windows in a range of different situations and use it for comparative testing in more complex highly-overshadowed contexts.

The VSC is calculated from the shading mask in exactly the same way as for a sky factor using a CIE Overcast Sky. The diffuse layer is generated such that the sum of all segments totals exactly 100 and, once surface shading has been calculated from the geometry of the site, the VSC calculated by summing the product of the diffuse, shading and incidence angle effects layers in each segment.