## 4 Results and Discussion
### ASD System with One Branch Pipe with Twenty Holes  
The obscuration in the ASD system is shown in Figure 8. From case 1 to case 20, the location of the smokebox is from hole 1 to hole 20, respectively. When the smoke went through the pipe to ASD 1, the obscuration was different from hole 1 to hole 20. The pressure at ASD 1 for one branch pipe with twenty holes in the experiment was \(-69\pm 1.5\) Pa. In Figure 8a, the obscuration in the smokebox is shown to be 5%/m. Obscuration was measured at ASD. Firstly, when the smokebox was located at hole 1, the obscuration at ASD 1 was around 0.68%/m, and the obscuration at ASD 1 when the smokebox located at hole 20 was 0.045%. It means, the further away from the location it is, the lower the obscuration is. The obscuration data was shown in Figure 8b,c when the smoke chamber was set at 10%/m and 15%/m, respectively. The slope and obscuration ratio of ASD were also investigated. The value of these parameters was shown in Figure 9.  
Similarly, the slope and obscuration ratio were investigated to predict the fire source location. In Figure 9a, the relation between slope and normalized length was performed. When the smokebox is located at the hole near the ASD, the slope is largest. On the other hand, when the smokebox is located at the hole which is far away from the ASD, the slope is smallest. Moreover, the obscuration ratio in the ASD had the same trend as the slope in Figure 9b, the obscuration ratio is largest at which hole is located nearby the ASD. It had the same trend when the pipe had ten holes in Section 4.1. The fitting correlation between normalized length and slope in Figure 9a were derived as the following Equations (35)-(37) for the chamber obscuration 5%/m, 10%/m, and 15%/m, respectively. \[S=0.10045\mathrm{e}^{(-\overline{L}\ /\ 0.3217)}-0.00224 \tag{35}\]  
\[S=0.20022\mathrm{e}^{(-\overline{L}\ /\ 0.31965)}-0.0056 \tag{36}\]  
\[S=0.2692\mathrm{e}^{(-\overline{L}\ /\ 0.4029)}-0.01778 \tag{37}\]  
where \(S\) is the slope, \(\overline{L}\) is normalized length. Similarly, the fitting correlation between the normalized length and obscuration ratio in Figure 9b were derived as the following Equations (38)-(40) for chamber obscuration 5%/m, 10%/m, 15%/m. \[R=0.15971\mathrm{e}^{(-\overline{L}\ /\ 0.44202)}-0.00763 \tag{38}\]  
\[R=0.15146\mathrm{e}^{(-\overline{L}\ /\ 0.37618)}+0.000887 \tag{39}\]  
\[R=0.14815\mathrm{e}^{(-\overline{L}\ /\ 0.39748)}+0.00136 \tag{40}\]  
Figure 8: The obscuration at ASD (**a**) When chamber obscuration was 5%/m (**b**) When chamber obscuration was 10%/m (**c**) When chamber obscuration was 15%/m. Figure 9: (**a**) The slope and normalized length correlation; (**b**) the obscuration ratio and normalized length correlation; (**c**) the slope and obscuration ratio correlation. where \(R\) is obscuration ratio, \(\overline{L}\) is normalized length. From the Equations (35)-(37), the fire source location can be determined as the following equations with chamber obscurations of 5%, 10%, 15%/m, respectively. Figure 9.0  
Figure 9.1  
Figure 9.2  
When the fire occurs, the obscuration can be obtained at the ASD. From the obscuration data, the slope (S) of obscuration can be calculated. By applying Equations (41)-(43), the three predicted fire source location can be achieved. Using three predicted fire source locations to apply in Equations (38)-(40), the three-obscuration ratio can be obtained. Comparing these equation obscuration ratios with the experimental obscuration ratio, the exact obscuration ratio can be obtained and the exact fire source location can be derived. Based on Sections 4.1 and 4.2, the results show that the obscuration in the ASD system is not equal when the location of the smokebox is changed. When a fire occurs at the nearest hole, the obscuration is the largest. By changing the number of the hole in the pipe, the obscuration in aspirating smoke detection is changed. When increasing the number of holes on the pipe, the obscuration at the ASD decreases.