Once the amount of instantaneous radiation incident on a surface has been calculated, it is possible to determine how much of that radiation is either absorbed within or transmitted through any model surface. This depends on the material properties assigned to the surface. This is, of course, where things get complex because there is a wide range of 'interpretation' within the industry as to the exact meaning of different terms for material property that affect absorption and transmission - and some of these values even inter-relate.

Absorbed solar radiation (G_absorbed) is affected by the solar absorption value assigned to a material (F_abs), and its transparency value (F_trans). The transmitted component is affected by the transparency of the material (F_trans) as well as, for windows, their shading coefficient (SC) or solar heat gain coefficient (SHGC) and the effects of refraction (F_refract), such that:

For window/glazing materials the transmitted radiation is given as:

For opaque materials (those without a defined shading coefficient or refractive index):

The refraction based on a glass material’s refractive index is given by:

The basic properties that affect absorption and transmission in ECOTECT can be set in the Material Properties dialog for each material in the library, and are described as follows.

Solar Absorption and Colour

The amount of solar radiation that is absorbed by any surface is assumed to be all that isn't reflected or transmitted. For an opaque surface, its reflectivity is really a function of its surface colour. A highly gloss surface will reflect just as much solar radiation as a matte surface if their colours are exactly the same - its just that the matte surface will reflect diffusely in all different directions whilst the gloss will reflect the majority of light in a specular direction. The specularity value of a material is therefore not important unless considering the amount of radiation reflected from that surface onto other parts of the model.

In reality, colours are defined by a complex continuous spectrum in which some frequencies are absorbed more than others. However, colour specification in computer software is mostly done using only red, green and blue (RGB) components. Whilst these three values are sufficient for our eyes to perceive almost any colour, the relative energy value of solar radiation varies significantly with frequency.

It should also be noted that solar radiation comprises frequencies both above and below the frequency range we perceive as light. Therefore colour alone is not sufficient to fully define this property. As a result, ECOTECT allows you to assign opaque materials a solar absorption parameter with a value between zero and one. However, most people usually only know the colour of the material they are creating, so ECOTECT also monitors changes to each material's external colour and offers to calculate an updated solar radiation based on the new setting. Obviously this is not as accurate as entering the actual solar absorption value obtained from the manufacturer, however if you select a darker colour, this will affect the amount of solar absorption so you will be prompted to update.

To calculate the absorption value from the assigned colour, in which each RGB component is given as a value from 0 to 255, ECOTECT uses the following formula as described for daylight spectral response in the Radiance Technical Manual (Ward, 1994):

For opaque materials, ECOTECT simply uses the solar absorption value as a modifier for the incident radiation. For window/glazing materials, which do not have such a property, the absorption value is derived from the assigned external glass colour and is applied to that radiation which is not reflected or transmitted.

This gets a little trickier for transparent materials that are not WINDOW elements. As transparency is defined as the relative amount of light/radiation actually passing through an object, ECOTECT assumes that this is given by the manufacturer as relative to the amount of incident radiation (as this is the easiest and most obvious to measure). Thus, if a material is assigned a transparency of 0.5, then 50% of the incident radiation is assumed to pass through. This means that the assigned solar absorption value cannot be greater than (1 - transparency), otherwise a warning is displayed.

Transparency and Shading Coefficient

Another issue sometimes encountered in ECOTECT is the ability to define both a transparency and a solar heat gain coefficient value for a WINDOW material. Traditionally the solar heat gain coefficient is to solar radiation what the transparency value is to light. One difference is that the solar heat gain coefficient can also be used to account for the effects of external and internal shading, but not usually in a dynamic way.

However, to maintain consistency between WINDOW and other elements, both values affect the transmission of light through windows in ECOTECT’s calculation functions. In fact, both are completely inter-changeable and cumulative. Thus, if you specify both a transparency and shading coefficient of 0.5, the total transmission will actually be 25% (0.5 x 0.5 = 0.25).

There were a number of reasons for doing this:

• The first was that users were altering WINDOW transparency values and not seeing any change in the solar radiation - which caused much confusion to those new to the software.
• Second was the need to maintain consistency - if transparency affects solar absorption in a WALL or ROOF element, then it should also affect transmission in a WINDOW element.
• Thirdly, as they are cumulative, having the two values offers a way of applying dynamic shading to a window by using blanket coefficients derived from a more complex shading mask study. Alternatively, the transparency of the WINDOW material could be manipulated with a script to simulate dynamic shading without losing the solar heat gain coefficient data for that particular glazing configuration.

Refractive Index

Refraction is an effect that occurs at the interface between transparent materials of different densities, such as air and glass. The bending of light and solar radiation that results from refraction is due to the longer time it takes the waves to move through the denser of the two materials. It is dependent on two factors: the incident angle and the refractive index of each material. The main effect of refraction is to significantly increase the effective surface reflectivity at angles close to grazing incidence.

The refractive index property applies only to WINDOW materials and the transparent covers of SOLAR COLLECTORS. The higher its value, the greater the effect. ECOTECT ignores values less than 1.0 as this represents an air-to-air interface at which there is no refraction.

It is important to note that this effect is very different from the reflectivity of a shiny opaque surface. For opaque surfaces, shininess is a manifestation of the degree of specularity - which in turn means how much of the reflected light travels in a specular direction (exitAngle = -entryAngle when measured about the surface normal). Reflectivity actually depends only on the colour of the surface. Two surfaces with exactly the same colour, but one matte and the other gloss, will reflect exactly the same amount of light - its just that the matte surface reflects it diffusely in all different directions.

Specularity

The specularity value of a material is given in the range 0-1 and defines the concentration of reflected light/radiation in the specular direction. A mirror has a very high specularity, which means that the majority of the energy from a focused beam of light would be reflected at an angle equal to the incidence angle on its surface, but mirrored around its surface normal. If that same beam fell on a surface covered with talcum powder, the myriad of tiny individual grains would reflect parts of the beam in all different directions. Being very white the same amount of light would be reflected from the powder surface as from the mirror, but the reflection would be diffuse, spread out at all angles such that the patch of the beam incidence on the surface was visible from anywhere around it not just in the specular reflection angle.

Figure 5: The effect of different material specularity values.

Thus for short-wave radiation transfer, the reflectance of a material is multiplied by its surface specularity in order to calculate the effects of reflected radiation.

Emissivity

The emissivity value of a material is given in the range 0-1 and describes its ability to absorb and emit long-wave radiation. This occurs at much lower frequencies that light, usually referring to the infra-red radiation from objects at terrestrial temperatures (below 100°C). As a result, emissivity values are important in thermal calculations when considering long-wave radiant exchange between surfaces, but do not play a significant role in ECOTECT’s solar incidence calculations.

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