## 3 Application to Virtual Fit Analysis Method to Pilot Oxygen Mask Design
### Design of Pilot Oxygen Mask by Virtual Fit Analysis  
Ergonomic boundary shapes were derived for the oxygen masks of the four size categories (small narrow, medium narrow, medium wide, and large wide) by an iterative process of the five-step design approach by virtual fit analysis in Figure 4. In the first step (S1), initial mask boundaries were prepared by projecting the design landmarks of the existing oxygen masks onto the corresponding RFMs in Figure 5b and then each mask boundary was placed on the 3D face images (small narrow: 34, medium narrow: 121, medium wide: 76, and large wide: 105) which belong to corresponding size group by considering the mask-wearing positions in Table 1. In the second step (S2), the horizontal distances between the mask boundaries and the 3D face surfaces were calculated. In the third step (S3), the appropriateness of each mask boundary was assessed for each face section in terms of accommodation percentage (Equation (1)), which indicates the proportion of horizontal distances within the lower and upper limits for each vertical location (indicated by two red lines in Figure 9). Note that the lower and upper limits of the horizontal distance between mask boundary and face surface by face section for each mask size category were identified by analyzing, out of the 82 pilots, the profile photos of those satisfied with their oxygen masks at a usability evaluation survey of MBU-20/P oxygen \begin{table}
\begin{tabular}{l l c c c c} \hline \hline
**Mask-Wearing Positions** & **Size of Mask** & \(\mathbf{n}\) & **Average** & **SD** & **Min** & **Max** \\ \hline \multirow{4}{*}{Sellion to D1 * vertical distance} & small narrow & 21 & 17.8 & 6.6 & 5.3 & 31.4 \\  & medium narrow & 23 & 16.4 & 6.3 & 5.2 & 29.7 \\  & medium wide & 19 & 17.8 & 5.1 & 4.1 & 25.3 \\  & large wide & 22 & 11.5 & 6.2 & 4.3 & 13.2 \\ \hline \multirow{4}{*}{Sellion to D1 horizontal distance} & small narrow & 21 & 5.3 & 3.2 & 0.6 & 12.9 \\  & medium narrow & 23 & 5.8 & 2.3 & 1.9 & 10.6 \\  & medium wide & 19 & 4.0 & 2.2 & 0.5 & 7.9 \\  & large wide & 22 & 6.6 & 2.4 & 3.0 & 11.7 \\ \hline \multirow{4}{*}{Supramentale to D8 * vertical distance} & small narrow & 21 & 7.3 & 3.3 & 2.0 & 14.5 \\  & medium narrow & 23 & 9.9 & 5.1 & 0.5 & 19.5 \\ \cline{1-1}  & medium wide & 19 & 9.9 & 4.6 & 2.7 & 16.8 \\ \cline{1-1}  & large wide & 22 & 13.6 & 7.1 & 3.2 & 26.2 \\ \hline \multirow{4}{*}{Supramentale to D8 horizontal distance} & small narrow & 21 & \(-\)0.5 & 2.5 & \(-\)4.1 & 3.5 \\ \cline{1-1}  & medium narrow & 23 & \(-\)0.3 & 2.0 & \(-\)2.9 & 2.9 \\ \cline{1-1}  & medium wide & 19 & \(-\)1.1 & 2.4 & \(-\)4.5 & 3.5 \\ \cline{1-1}  & large wide & 22 & \(-\)2.3 & 2.9 & \(-\)9.9 & 3.1 \\ \hline \hline \end{tabular}
* D1: nasal root point; D8: bottom lip point.  
\end{table} 
Table 1: Mask-wearing positions (unit: mm) for four mask size categories. Figure 8: A photo-based placement of the 3D face and mask images for the identification of mask-wearing positions (illustrated). (**a**) A profile photo of a pilot while wearing the MBU-20/P oxygen mask; (**b**) a transparent film with a printed photo placed on the monitor; (**c**) an alignment of the 3D face and mask images to their corresponding images of the printed photo on the film. mask conducted by [PERSON] [35]. In the fourth step (S4), each mask boundary was modified by adjusting the locations of the design landmarks. The steps S2 to S4 were iterated until an appropriate boundary was found for each mask size category. Lastly, in the fifth step (S5), the oxygen mask design was completed for each mask size category by combining the appropriate mask boundary and the outer parts (Figure 1a). \[ \begin{array}{l}\text{accommodation percentage at vertical location $i$}\\ =\frac{\text{Number of $HD_{ij}$ satisfying $LL_{i}\leq HD_{ij}\leq UL_{i}$}}{\text{Number of faces}}\times 100\end{array}