# Comfort Distance--A Single-Number Quantity Describing Spatial Attenuation in Open-Plan Offices
## 3 Results  
The comfort distances of the 26 offices of Ref. [17] for comfort criterion levels ranging from 30 to 50 dB are shown in Figure 4. The corresponding probabilities that the comfort distances exceeded the length of the office are shown in Figure 5.  
Figure 5 clearly shows that the probability \(P\) reaches zero when \(L_{\text{p,A,C}}>45\) dB. Therefore, this value was chosen as the comfort distance criterion. Further justification for this choice is given in Section 4.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Study** & **ID** & **N** & **Country** & **Comment** \\ \hline [PERSON] and [PERSON] (2013) [17] & I & 26 & Finland & a \\ [PERSON] et al. (2017) [3] & II & 21 & Finland & b \\ [PERSON] and [PERSON] (2018) [14] & III & 34 & Germany & c \\ [PERSON] (2019) [18] & IV & 4 & Laboratory & d \\ [PERSON] et al. (2018) [19] & V & 20 & Australia & e \\ [PERSON] et al. (2019) [20] & VI & 36 & Australia & f \\ [PERSON] and Desarnaulds (2020) [21] & VII & 22 & Switzerland & g \\ [PERSON] et al. (2020) [4] & VIII & 22 & Laboratory & h \\ \hline \hline \end{tabular} a. 26 separate offices, one path per office; b. 21 separate offices, one path per office; c. 13 offices with 2 to 4 paths; d. Conditions were built by researchers in a real office, why it is called as a laboratory setup; e. 20 separate offices, one path per office; f. 27 offices with one path, 5 offices with two paths, 2 offices with three paths; g. 22 separate offices; h. \(L_{\text{p,A,B}}\) and \(r_{\text{D}}\) were disregarded since background noise was adjustable. Mean of two paths. Six conditions with \(r_{\text{C}}>45\) m were ignored.  
\end{table}
Table 2: Eight studies I-VIII reporting measurement data according to ISO 3382-3. N is the number of reported paths.  
Figure 4: The range of comfort distance values, \(r_{\text{C}}\), as a function of the comfort criterion level, \(L_{\text{p,A,C}}\), for the 26 offices of Ref. [17] calculated by Equation (2). Mean, maximum, minimum, and 68% confidence interval (C.L) within the sample of 26 offices are shown.  
Figure 6 presents a statistical overview of the single-number values of ISO 3382-3 for the eight studies of Table 2 and the comfort distance calculated by Equation (2). The average of all 179 comfort distances was 9.3 m. The lower and upper bounds of the 68% and 95% confidence intervals were 4.7, 3.5, 13.8, and 25.3 m, respectively.  
Figure 7 presents an analysis of how the acoustic classes A-D of comfort distance could be set in a balanced way for the 26 offices of Table 1. We paid attention to three criteria: each class involves at least two offices, the classes are equally spaced, and some  
Figure 5: The probability \(P\) among the 26 offices of Ref. [17] that the comfort distance, defined by comfort criterion level \(L_{\text{P,A,C}}\), was larger than the room length.  
Figure 6: Distribution of measurement results according to ISO 3382-3 standard in the eight studies of Table 2. Bars are the means and whiskers are the 95% confidence intervals.  
offices (two worst ones) can remain unclassified. The limit values for classes A to D became 11, 9, 7, 5, 7, 9, and 11 m for \(r_{\rm C}\). The ranges for classes A-D are [0-5] m, [5-7] m, [7-9] m, and [9-11] m, respectively. Values of 11 m and higher are unclassified.  
Using the same criteria, the proposed limit values for classes A to D became 11, 9, 7, and 5 dB for \(D_{2,s}\), 47, 49, 51, and 53 dB for \(L_{\rm P,A,S,4m}\), and 6, 8, 10, and 12 m for \(r_{\rm D}\).