# Numerical Study of Wave Effect on Aircraft Water-Landing Performance
## 4 Results and Discussions
### Wave Height Effect  
To study the wave height effect on the amphibious aircraft wave-crest-landing performance, five cases with the same wavelength of 40 m but different wave heights are compared. Figure 14 shows the numerical results in time. It can be seen that as the wave height increases from 0 (calm water) to 2 m with interval 0.5 m, the variations of accelerations, velocity and pitch angle of the aircraft have similar features in time. Before the aircraft impacts on the second wave, approximately \(t<0.5\) s, the aircraft landing performance is negatively correlated with the wave height. In contrast, the wave height positively influences the accelerations of the aircraft when \(t>0.5\) s. The general reason for these tendencies is the impact position between the free surface and the fuselage. The pressure distribution on the impact position is influenced by the wave height during the entire landing process. Consequently, it gradually changes the stages of the aircraft landing process from calm water-landing to wave-landing, i.e., fuselage impacting stage to rear-fuselage impacting and front-fuselage on-flight stages. Specifically, for the case of \(H=0.5\) m, the landing process is close to the calm water situation, except for a small increment of accelerations during \(t=0.5\)-0.6 s as illustrated in Figure 14a,c. For the case of \(H=1\) m, the feature of landing performance combines the characteristic of calm water and wave landing situations, including fuselage impacting stage, front-fuselage on-flight stage and second impacting stage. As the wave height increased to 1.5 m, the stage of the landing process is exactly the same with the case of \(H=2\) m. To further explore the mechanisms of these phenomenons, three moments are selected based on the variation of vertical acceleration as illustrated in Figure 14a (black dashed line) and the corresponding contours of five cases are compared. At \(t=0.16\) s, as plotted in Figure 14, the aircraft landing performance is negatively influenced by the wave height. Particularly, the acceleration of case \(H=0.5\) and \(1\) m is smaller than that of calm water case, and it drops to zero when the \(H\) increased to 1.5 and 2 m. These features are contributed by the wave surface slope and wave particle velocity. Figure 15 shows the comparison of flowfield of aircraft landing on wave surface with different wave heights at \(t=0.16\) s. Note that the air domain is blanked for better illustration. It can be seen that as the wave height increases, the wave surface becomes steeper and harder to be disturbed. Thus, when the step part of aircraft passed the crest position of first wave, the impacting/wetted area near the front-fuselage is reduced with the increment of the wave height. This is evidenced in the water phase contour in Figure 15. Another important factor is wave velocity. As shown in Figure 16, the vertical velocity of the wave field below the front-fuselage is negative and in the same direction as the vertical velocity of aircraft. It results in a reduction in the effective impacting velocity between the aircraft and free surface. In fact, the wave particle velocity is positively related to the  
Figure 13: Time-snapshots of flowfield of aircraft landing in wave field during the second impacting and pitch-up stage: the first and third lines are air-water phase contours; the second and fourth lines are corresponding pressure distributions at bottom surface of fuselage. As time forward, the effects of wave surface slope and wave particle velocity become more obvious. As shown in Figure 17, the impacting area near the front-fuselage and corresponding pressure decrease with the increment of the wave height. For the case of \(H=1,1.5\) and \(2\) m, the aircraft is almost on the front-fuselage on-flight stage at \(t=0.32\) s. In contrast, the aircraft landing performance in the case of \(H=0.5\) m is similar to the calm-water-landing case.