# Numerical Study of Wave Effect on Aircraft Water-Landing Performance
## 4 Results and Discussions  
### Calm Water vs. Wave Water  
The numerical results of aircraft movement of calm water and regular wave-landing events are depicted in Figure 8. Particularly, the separated accelerations by hydrodynamic and aerodynamic forces shown in Figure 8e,f are calculated by the integration of pressure distribution on the fuselage and wing-tail surface. The separated hydrodynamic acceleration is based on the fact that the interaction between fuselage and fluid is dominated by the hydrodynamic pressure on the fuselage [4]. Because the hydrodynamic force generated by the fuselage is far larger than the aerodynamic force of the fuselage since the density rate of water and air is 998/1.225, approximately 814.7. By comparing the red and black curves, it is found that the overall tendency of aircraft acceleration, velocity and pitch angle in calm water case and wave crest case is totally different. For the convenience of further exploring the mechanism of these two cases, the early process of water-landing is separately described as three distinctive stages according to the impacting position of the fuselage, variation of acceleration and pitching angle of the aircraft, i.e., step impacting stage, fuselage impacting stage and pitching-up stage. Figure 6: Results of time step dependency study: (**a**) vertical acceleration; (**b**) axis-x/horizontal acceleration. Figure 7: Computational global and zoom-in grid of the medium mesh, green curve represents the wave surface. Figure 9 shows three transient snapshots (\(t=0\), 0.5 and 1.0 s) of the whole computational domain movement, free surface evolution and mesh around the aircraft model during the calm water and wave crest landing process. Note that the snapshot in the 2D XOZ plane shows the whole computational domain movement. It can be seen that by using the rigidly moving mesh strategy in DFBI module, the computational domain is moving with the rotation motion of the aircraft and the free surface can be maintained with the same level in the ground-fixed coordinate XYZ, thus the reality of the simulation is guaranteed. In addition, the water spray around the fuselage is also shown. Thus, the rigidly moving mesh used in this study is able to deal with the movement of the aircraft in the calm water and wave surface landing simulations. Figure 8: Comparison of time–history results between calm water and wave crest aircraft landing simulation: (**a**) vertical acceleration; (**b**) vertical velocity; (**c**) axis-x acceleration; (**d**) axis-y rotation, pitch angle; (**e**) vertical acceleration by the hydrodynamics and aerodynamics; (**f**) axis-x acceleration by the hydrodynamics and aerodynamics. The first stage is named as step impacting stage due to the fact that the impacting position is located at the step area and the variation of aircraft movement for calm water case and wave crest case are similar during \(t\) = 0-0.0526 s. In contrast, the obvious differences in acceleration time-history curves are observed between these two cases when \(t>0.0526\) s. For the calm-water-landing case, the acceleration in the \(z\) (vertical) and \(x\) directions dramatically increase to maximum (\(a_{zmax}=2.795\) g and \(a_{xmax}=0.556\) g) in fuselage impacting stage, and then monotonically decrease in path-up stage from \(t=0.2024\) s to \(t=0.2024\) s.  
Figure 9: Comparison of transient snapshots (\(t=0,0.5\) and \(1.0\) s) of whole computational domain movement, free surface evolution and mesh around the aircraft model: (**a**) calm water-landing; (**b**) wave crest landing. The rectangular box is the computation domain; blue line and surface are the air-water interface; all snapshots are in the same ground-fixed coordinate XYZ with same views. \(t=1\) s. Notably, the pitch angle of aircraft increases in pitch-up stage as shown in Figure 8d.