# Numerical Analysis of the Take-Off Performance of a Seaplane in Calm Water
## 6 Conclusions  
This paper aims to investigate the take-off performance of a seaplane by numerically modeling the air-water two-phase flow around a seaplane using RANS equations with VOF method. In order to determine the equilibrium trim angle and heave of the seaplane at different speeds, the free motion in trim and heave in response to aerodynamic forces, hydrodynamic forces, hydrostatic forces, and propeller thrust was realized by DFBI module and overset mesh technique. The numerical model was validated based on the benchmark model of the F6 wing body and the Fridsam hull.  
The seaplane planning at speeds ranging from the standstill to the takeoff were simulated. Based on the numerical results, we investigated the variations of heave and trim angle and their inherent relationship with the aerodynamic performance and hydrodynamic performance. The results prove that hydrodynamic performance plays a dominant role in governing the take-off performance, and the hydrodynamic performance was essentially determined by the pressure distribution and the location of the stagnation line. Besides, the results turned out that heave could be treated as a main parameter that reflects the contribution of buoyancy.  
The resistance characteristics are the main concern in this study. There are two humps of total resistance: the first hump occurred at the transition from displacement to planing, and the second hump happened at the high speed planing stage near the takeoff. The results show the hydrodynamic resistance contributed nearly all of the resistance at the first hump. And the increase of pressure resistance at forebody and friction resistance at afterbody were the major causes of the first hump of hydrodynamic resistance. We considered that the stagnation line located at convex surface at bow created a backward pressure component that considerably increased the pressure resistance at forebody. And the increase of friction resistance at afterbody is related to the afterbody sinking farther into the water as the trim increased. Furthermore, we found that the hydrodynamic resistance at high speed was significantly affected by the trim angle. The trim angel of a seaplane should be operated in an optimum trim range, typical between 4-6 deg, to minimize the hydrodynamic resistance. Otherwise, the hydrodynamic resistance would significantly increase as the trim angle deviates from the optimum trim range, resulting in a substantial second hump of resistance. Note that as the propeller thrust decreased with speed, more attention should be paid to the second hump of which the residual thrust might be less than the one at the first hump.  
The convergence study concludes that the utilization of damping terms is the most effective way to accelerate the convergence of the 2 DOF motion ending with a quasi-static state, while the offset between the initial trim angle and the final equilibrium trim angle only decides the amplitude of oscillation but barely affect the convergence time.  
This paper provides a numerical approach to predict the resistance and attitude of a seaplane taking off in calm water. The investigation on take-off performance gives a better understanding of the variation of aerodynamic performance, hydrodynamic performance, and hydrostatic performance during the takeoff, which would provide some guidance in the integrated design of aerodynamics and hydrodynamics of the seaplanes.  
Conceptualization, Y.G. and D.M.; methodology, Y.G. and D.M.; software, Y.G.; validation, Y.G. and X.L.; formal analysis, Y.G.; investigation, Y.G. and X.L.; resources, D.M.; data curation, Y.G.; writing--original draft preparation, Y.G.; writing--review and editing, M.Y. and X.L.; visualization, Y.G.; supervision, D.M. and M.Y.; project administration, D.M. and M.Y. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
Not applicable.  
The data presented in this study are available on request from the corresponding author.