# Numerical Study of Wave Effect on Aircraft Water-Landing Performance
## 4 Results and Discussions
### Calm Water vs. Wave Water
#### 4.1.2 Fuselage Impacting Stage  
In the fuselage impacting stage of the calm-water-landing case, as shown in Figure 11a, the rear-fuselage, step and part of front-fuselage are impacting on the calm water surface. During this stage, the increment vertical and axis-x accelerations are mainly generated by the increase in impacting area of front-fuselage from \(t=0.07\) s to the time moment when the maximum acceleration occurs. Moreover, the peak pressure on the fuselage at the time of maximum vertical acceleration (approximately \(t=0.1465\) s) is about \(250\) kPa, which comparable with that in the rigid wedge vertical impact by [PERSON] and [PERSON] [43]. Therefore, the overload and movement of the aircraft are governed by the hydrodynamic force as evidenced in Figure 8e,f. As depicted in Figure 8d (red shaded region), the aircraft pitch angle slightly decreases due to that the high pressure area is near the center of gravity of the aircraft, thus the overpressure zone around the rear-fuselage leads to a pitch-down motion. Additionally, we notice that there is a negative pressure area near the  
Figure 10: Comparison of aircraft landing in calm water and wave crest during the step impacting stage. step. This negative pressure is caused by the air-pocket phenomenon. Figure 11b presents the 3D view of free-surface evolution in which the zoom-in views clearly show that the air-pocket is formed by the water spray and step profile. As the air-pocket generated from \(t=0.07\) s to \(t=0.1\) s, the air-ventilation effect is weaken which results in a larger negative pressure region at the fuselage surface as shown in Figure 11a. After that, with the aircraft moving forward, the air suck-in tunnel is expanded and then leads to the reduction in negative pressure near the step region. This feature is exampled in the flowfield contours at \(t=0.156\) s. In the pitch-up stage of the calm-water-landing case, this air suck-in tunnel is further increased as demonstrated in Figure 11c, and the negative pressure near the rear-fuselage is formed which may be caused by the air-water mix effect. This negative pressure leads to a pitch-up motion as plotted in Figure 8d (red double-side arrow). In the rear-fuselage impacting stage of the wave-crest landing case, the rear-fuselage and step are impacting on the wave surface. Figure 12a presents the air-water phase contour at the symmetrical plane in this stage. It shows that there is a dramatic air-water mix region behind the step. This region leads to the oscillation of accelerations as shown in Figure 8a,c. Moreover, by comparing the vertical and axis-x acceleration curves in these two figures during the second stage for the calm water and wave crest cases, it is found that the acceleration value of the wave-landing case is smaller than that of the calm-water-landing case. This is due to the wave surface shape leads to a small impacting area. Similarly, the wave surface shape also results in the reduction in impacting area of the step as shown in the zoom-in figures of Figure 12a. Consequently, the axis-x acceleration is reduced as reported in Figure 8c. Figure 11: Time-snapshots of flowfield of aircraft landing in calm water: (**a**) air-water phase contour and pressure distribution during the impacting stage; (**b**) 3D view of free-surface evolution during the fuselage impacting stage; (**c**) air-water phase contour and pressure distribution during the pitch-up stage  
As the aircraft moving forward, the wave surface shape plays an even more important role in the front-fuselage on-flight stage. Figure 12b displays the air-water phase contour and zoom-in pressure distribution during this stage. It clearly demonstrates that the step and front-fuselage are on-flight because of the wave trough. Therefore, the overload of aircraft is mainly determined by the aerodynamics as illustrated in Figure 8e,f. We note that the aircraft experiences a pitch-down motion as plotted in Figure 8d. It may be caused by the pressure on the bottom surface of rear-fuselage.