Assessment of the IEQ Equations

Both of the IEQ equations derived by Wong and Ncube deliver maximum IEQ values when the lighting and temperature is optimum. However as the buildings in DSR state will operate in non-optimal conditions, the equations will need to deliver accurate IEQ results when the temperature and lighting are out of their expected values. As can be seen from the 3D plots, both of the equations deliver significantly different IEQ values when the temperatures approach 30° C (0.17 for Wong versus 0.7 for Ncube). Because of this noticeable difference, a numerical assessment is carried out to examine the differences between the two equations.

4.5.3.1. Assessment of IEQ Equations from Lighting Perspective

As discussed in the literature review, the relationship between productivity and lighting is highly task dependent. For short term effects, the visual portion of the task is most likely to be influenced by the change in lighting. However, this portion of the task also depends on two parameters, contrast and illuminance of the task environment. It is difficult to define exact conditions for office environments. However, if the following assumptions are made, it is possible to deduce which IEQ relationship is more relevant from productivity point of view:

 Office buildings are environments where cognitive work is more dominant.

 The main equipment used in offices is computers. Computer screens provide constant luminance regardless of the external environment. Hence the majority of the tasks (which are done by computers) that require visual feedback can be assumed to be little affected by external lighting.

165 When Rea's [48] RVP equation is run for a contrast level of 0.3, the resulting visual productivity graph that produces RVP versus lux level is found as in Figure 41(left). This shows that visual productivity drops to around 92 % when the light level is at its worst (200 lux) and around 98% when light level is at its best (800 lux). Because visual component of tasks carried out by a typical office worker is assumed to be low, this result from Rea is used as a reference to compare Ncube's and Wong's IEQ equations.

The graph on the left in Figure 41 shows Rea's RVP for minimum and maximum lighting conditions. On the right, Ncube's and Wong's IEQ results plotted over Rea's RVP graph.

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s can be seen in the comparison graph, the three graphs have a similar shape. Hence, it is possible to say that IEQ delivered by acceptance of workers is similar to the RVP index delivered by Rea when the contrast level is low. When lighting is decreased from optimum, both RVP and lighting acceptance drops slowly. As the decrease in lighting increases, the decrease in both RVP and IEQ accelerates.

Figure 41: Left: Rea's relative productivity index for a contrast level of 0.3. Right, comparison of Rea with Ncube's and Wong's IEQ equations for indoor temperature of 23° C.

166 The following can be deduced from this assessment:

 If the amount of lighting is higher than dictated by H&S executive, then productivity of a worker is expected to be above 90%.

 The productivity increases rapidly as the lighting is increased from this minimum value. The increase in RVP decelerates as light levels are increased.

 Both Ncube and Wong deliver similar results and they are comparable to Rea's relative productivity function for a contrast ratio of 0.3.

4.5.3.2. Assessment Criteria for Temperature

Thermal requirements are effective in all aspects of productivity in an office environment regardless of the task being carried out. Hence, comparison between IEQ and a productivity indicator is more relevant. Seppanen et al.'s [39] review on the performance of office workers in different room temperatures is a good indicator for such a comparison task because it is derived from various other studies.

Figure 42(Left) shows Seppanen et al's Temperature versus Productivity graph derived from their paper. The graph shows that relative performance drops to around 96% at 17° C and 27° C. The peak performance is achieved between 20° and 23.5° C. Figure 42(right) shows Wong's and Ncube's IEQ results when lighting is optimum superimposed on the Seppanen's.

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Figure 42:Left: Seppanen's relative productivity function for different indoor temperatures. Right, comparison of Rea with Ncube's and Wong's IEQ equations.

Unlike the situation in lighting, there is a significant difference between Wong's results and the others. At higher temperatures, IEQ index of Wong falls to around 0.65. This is much lower compared to Ncube (0.83) and Seppanen (0.91).

The following can be deduced from these numerical assessments:

 Ncube's IEQ equation delivers closer results to Seppanen's equation. Hence, under current assumptions, it is more suitable for being used as a productivity function.

The comparisons made above highlight the inconsistencies between different IEQ models. These inconsistencies prevent such models to be used as productivity indicators because more work needs to be carried out in this area. However, the studies of Ncube and Wong are the only ones available that present a numerical relationship between temperature, lighting and IEQ. Even though the applicability of their models as a productivity function requires lots more research, it is assumed in this study that they are the state of the art productivity functions that can be applied into a control system

168 for the purpose of DSR. Because of its resemblance to productivity functions developed by Rea and Seppanen, Ncube's IEQ function is selected as the main productivity function that will be used in the following sections.