# Investigation and Design of the Transonic Laminar Flow Characteristics in a Laminar Aircraft
## 3 Results and Discussion of Sensitivity Analysis
### Sensitivity Analysis of \(\alpha\)  
The calculated states of this section are listed in Table 6. From the results in Figures 19-21, it is found that all the effects of increasing \(\alpha\) on the characteristics of the \(C_{p}\) curves and the transition position have a strong regularity. The positive direction of \(\alpha\) is shown in the coordinate system in Figure 20. As \(\alpha\) increases, the favorable pressure gradient on the upper surface becomes small, gradually shown in Figure 19, and the transition position is gradually advanced, reflected in Figures 20 and 21. When the \(\alpha\) increases from 0 degto 4 deg, the transition position is advanced from approximately 57% to 30% of the chord of the central experimental wing. The change in \(\alpha\) affects the laminar flow characteristics by affecting the shape of the favorable pressure gradient at the front of the \(C_{p}\) curves (the segment from 0% to 30% of the chord). From Figure 19a,b, it can be observed that the two adverse pressure gradient zones form as the \(\alpha\) increases to 4 deg, while the transition occurs near the start point of the first adverse pressure gradient. This indicates that the laminar flow zone is very sensitive to the adverse pressure gradient. A small local adverse pressure gradient is possible to cause TS instability. In short, decreasing \(\alpha\) has a beneficial effect on expanding the length of the laminar flow zone but decreases the lift of aircraft. The trade-off between lift and laminar flow needs to be decided by the aircraft designer. Expanding the length of the laminar flow zone on the wing surface to reduce drag as much as possible while lift requirements are still met. Finally, the process and interrelationship of each sensitivity factor are shown in Figure 22. The direction of the arrow represents the affected object, and the width of the arrow line represents the influence weight. The transonic transition is affected by a variety of interacting factors that include pressure gradient, _FSTI_, _Re_, _Ma_, \(\alpha\), etc. _FSTI_ affects global flow stability, and its effect is not easily overridden by other factors. The transition position advances with increasing _FSTI_. The pressure gradient affects local flow stability. Especially the favorable pressure gradient is a landmark factor of local transition but not necessarily a decisive factor in maintaining the local laminar flow zone under transonic conditions. In most cases, a larger favorable pressure gradient zone implies a larger laminar flow zone. However, once the values of _FSTI_ and _Re_ are too extreme, the relationship between the length of the favorable pressure gradient and the laminar zone length is not clear. _Re_ affects the flow stability indirectly by changing the characteristics of the boundary layer. Its increase leads to an earlier transition, but its effect is easily covered by the strongly favorable pressure gradient. The effect of _Ma_ on the transition is highly nonlinear and affects the transition mainly by changing the pressure gradient. Its effect on the transition is divided into two phases. The first phase has no shock wave. In this process, as the _Ma_ increases, the favorable pressure gradient zone gradually extends with the delaying of the transition and the appearance of the tendency to form a shock wave. In the second phase, the shock wave has been formed. The pressure gradient is more stable than the first phase. Therefore, it is difficult for the _Ma_ increase to affect the transition position. \(\alpha\) affects the transition location by changing the pressure gradient. Increasing \(\alpha\) causes the transition to advance. In short, the essence of the transition is the disruption of flow stability caused by the increase in flow entropy. _FSTI_ affects global flow stability, while pressure gradient affects local flow stability. _Re_, _Ma_ and \(\alpha\) indirectly affect the flow stability, and among them, _Re_ is easily determined by the pressure gradient.