# Effects of Vertical Glottal Duct Length on Intraglottal Pressures in the Convergent Glottis
## 3 Results
### Intraglottal Pressures
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Glottal Angle 1 Diameter**} & \multicolumn{4}{c}{**Vertical Glottal Duct Length**} \\ \cline{2-5}  & **0.108 cm** & **0.308 cm** & **0.608 cm** & **0.908 cm** \\ \hline \(0^{\circ}\,|\,0.01\) cm & 2a-i & - & - & - \\ \(0^{\circ}\,|\,0.04\) cm & 2a-ii & - & - & - \\ \(0^{\circ}\,|\,0.16\) cm & 2a-iii & - & - & - \\ \(-5^{\circ}\,|\,0.01\) cm & - & 2a-iv & 2b-i & 2b-iv \\ \(-5^{\circ}\,|\,0.04\) cm & - & 2a-v & 2b-ii & 2b-v \\ \(-5^{\circ}\,|\,0.16\) cm & - & 2a-vi & 2b-iii & 2b-vi \\ \(-10^{\circ}\,|\,0.01\) cm & - & 2c-i & 2c-iv & 2d-i \\ \(-10^{\circ}\,|\,0.04\) cm & - & 2c-ii & 2c-v & 2d-ii \\ \(-10^{\circ}\,|\,0.16\) cm & - & 2c-iii & 2c-vi & 2d-iii \\ \(-20^{\circ}\,|\,0.01\) cm & - & 2d-iv & 2e-i & 2e-iv \\ \(-20^{\circ}\,|\,0.04\) cm & - & 2d-v & 2e-ii & 2e-v \\ \(-20^{\circ}\,|\,0.16\) cm & - & 2d-vi & 2e-iii & 2e-vi \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Location of specific glottal configurations (glottal angle, minimal glottal diameter, and vertical glottal duct length) and the corresponding intraglottal pressure distributions in Figure 2.  
the beginning (opening phase) of the glottal cycle. This vertical glottal duct lengthening effect may therefore contribute to reducing the threshold pressure for phonation [6] (see below for a discussion that indicates inconsistencies in this regard). Also, the increased intraglottal outward pressure force may tend to push the vocal folds open wider, thus creating a larger glottal airflow waveform peak, as well as transfer more aerodynamic energy to the vocal folds. Thus, a longer vertical glottal duct length may aid in generating vocal fold oscillation. In Figure 2, the smaller the glottal minimal diameter, the more negative the minimum pressure dip. For example, the pressures drop to minimum pressures of \(-333.61\) Pa and \(-123.93\) Pa (an increase of \(62.8\%\)) for \(0.01\) cm and \(0.16\) cm minimal diameter cases, respectively, for the same \(1500\) Pa transglottal pressure and \(-20^{\circ}\) convergent glottal angle. With the greater pressure drop, the pressure rise (recovery) is also faster in this example. The convergent glottal angle also has effects on increasing the intraglottal pressure distributions. Figure 2 indicates that the intraglottal pressure increases when the convergent glottal angle increases, and the larger the glottal angle, the higher the intraglottal pressure and the lower the pressure dips near the glottal exit. For example, the pressures at the glottal entrance increased from \(1324.14\) Pa to \(1425.43\) Pa and then to \(1475.18\) Pa (an increase of \(11.41\%\)) when the convergent angle increased from \(-5^{\circ}\) to \(-10^{\circ}\) and then to \(-20^{\circ}\), for the case of \(0.01\) cm minimal diameter, \(0.308\) cm glottal duct length, and \(1500\) Pa transglottal pressure. The effect is less as the glottal duct length is increased. For example, the percent change decreases from \(11.41\%\) to \(1.18\%\) (\(1480.54\) Pa to \(1498.09\) Pa) when the glottal duct length increases from \(0.308\) cm to \(0.908\) cm for the above cases. These results suggest that the glottal angle has important potential effects on the intraglottal pressure distributions, especially for short glottal duct lengths. The lossless Bernoulli pressures are also shown in Figure 2. The difference between the lossless Bernoulli pressure distributions and the Fluent pressure distributions increased as the glottal diameter increased, transglottal pressure increased, or the glottal angle decreased. The pressure distributions for the lossless Bernoulli condition are always higher than for the Fluent distributions, indicating that the pressures are too high if one were to follow the Bernoulli approach to the end of the glottal duct, especially for smaller convergent angles.