## 2 Methods
### Mismatch Equation for Naval Multi-Function Console in a Submarine
[PERSON] and [PERSON] [33] and [PERSON] [16] suggested only the upper limit of the UEB, stating that the UEB does not limit the basic upper body movement as long as the UEB is lower than the height of the user's subscapula. However, as emphasized in NUREG-0700 [15], if the UEB is low enough to fail to support the lumbar regions, it cannot properly support the back and waist, leading to their excessive extension. Therefore, the lower limit of the UEB must be also considered. Figure 4: Deployment status of four submarine naval multi-function consoles. Equation (5) for the STC was devised based on the concept that the console operator's thigh should be able to fit under the worktable. \[\text{STT}+20+(2\times\text{WT})\leq\text{STC} \tag{5}\]  
The existing research recommended 20 mm for the sitting thigh thickness [28; 29; 36], but we added 10 mm considering the WT. TH is determined by SH, thickness of the worktable, and STC. Therefore, this can be expressed in Equation (6) as follows:  
\[\text{TH}=\text{SH}+\text{TT}+\text{STC} \tag{6}\]  
Combining Equations (1), (5), and (6), the lower and upper limits of TH can be determined as expressed in Equation (7). In Equation (7), STT, SEH, PH, and SSH were selected as the anthropometric variables, whereas TT, WT, and ST were selected as environmental variables. \[ \begin{split}\text{Max}&[\text{STT}+20+(2\times \text{WT})+\text{TT},\,\text{SEH}]+\left[(\text{PH}+\text{ST})\times\text{ Cos30}^{0}\right]\leq\text{TH}\\ &\leq(0.8517\times\text{SEH})+(0.1483\times\text{SSH})+\left[( \text{PH}+\text{ST})\times\text{Cos5}^{5}\right]\end{split}  \tag{7}\]  
In Equation (7), the lower limit of the TH was chosen to be the higher value in between STC and SEH. This means that, in the sitting state, the height from the floor to the console operator's thigh should be lower than the UTH, and the elbow should be able to reach the worktable comfortably. If TH is lower than SEH, it would be very difficult to rest the elbows on the worktable without bending down, and manipulation of the keyboard and track ball would force the operator to bend forward. Considering the context of a console operator who heavily uses keyboards and track balls, the tension in the shoulder and back muscles can only increase if the elbows are not comfortably sitting on the worktable. The upper limit of the TH was derived by multiplying SEH and SSH by specific coefficients and then adding the calculated numbers to the upper limit of SH. The coefficients multiplied by SEH and SSH are given by the research of [PERSON] [36] and [PERSON] [44], who mathematically calculated the range of motion of the shoulder's flexion and abduction when working on a worktable and resting the arms on the worktable. If the height of the worktable is greater than the upper limit suggested by Equation (7), the shoulders can be excessively elevated upwards, or the arms are opened too widely to the sides when the elbows are raised on the worktable. This can cause increased fatigue and lead to musculoskeletal disorders of the shoulder and arm after a period of repeated tasks with the given environment.