# Numerical Analysis of the Take-Off Performance of a Seaplane in Calm Water
## 1 Introduction  
Seaplanes are powered fixed-wing aircraft capable of taking off and landing on water. They once played an important role in the early stage of modern aviation. But the rapid development of land-based aircraft and the growing investments in airports after WWII drastically reduced the demand for seaplanes, which resulted in the stagnation of seaplane technique for nearly half a century [1]. Recently, the development of the marine economy and the escalating tensions in maritime disputes has drawn people's attention back to water-based aircrafts for their wide applications in military and civil fields, such as maritime reconnaissance, anti-submarine, logistics service, sea rescue, etc. [2]. The design of a seaplane is an art of tradeoff between aerodynamics and hydrodynamics with the ultimate goal to achieve the desired hydrodynamic performance with the least loss in aerodynamic efficiency. The main challenge faced by designers for evaluating the take-off performance is the prediction on the resistance characteristics, since during take-off the seaplane is free to trim and heave in subject to the forces of hydrodynamics, hydrostatics, aerodynamics, and propulsion system. Evaluation of hydrodynamic performance isthe most challenging job because the seaplane disturbs the water surface into complicated wave flow that is difficult to predict. It is known that besides the fuselage geometry, the hydrodynamic resistance mainly depends on speed, water load, and trim angle which is defined as the angle between the keel of forebody and the water level. The water load and trim angle would be influenced by the aerodynamic lift and pitching moment respectively, which basically results in the coupling of hydrodynamic performance and aerodynamic performance that makes the prediction more complicated [3]. There are three available methods for investigating the resistance characteristics of seaplanes: experimental method, empirical method and numerical method. Towing tank tests are the common experimental implements to investigate the resistance characteristics of seaplanes in take-off. Since the towing tanks always have a limitation on the model scale and planing speed, a dilemma that researchers have to face in the scaling model tests is the inability to satisfy the similarity of theFroude number and Reynold number [4]. Moreover, the experimental method is too expensive and time-consuming for the preliminary design and optimization of a seaplane. Empirical methods are more efficient for the preliminary design. Several attempts [5; 6] have been made to estimate the resistance characteristics of seaplanes by adding aerodynamic models into Savitsky equations. Whereas, since the Savitsky methods were developed for the sample non-stepped planing hulls [7], the empirical methods lack accuracy for evaluating the hydrodynamics of unconventional hulls, especially for seaplane hulls characterized by a distinctive step at the bottom. The step introduces a sharp corner on the bottom which divides the fuselage into forebody and afterbody. The water flow is forced to separate at the step giving room to an air-filled cavity, which could reduce the wetted surface on the afterbody and prevent unfavorable suction that keeps the afterbody from leaving the water [8]. A recent study by [PERSON] expanded the empirical methods to estimate the hydrodynamics of stepped hulls through predicting the wake profile of forebody [9]. But the application of the methods is still limited to the range of parameters which are not applicable for seaplanes. Nowadays, numerical methods, especially Computational Fluid Dynamics (CFD) simulations, have become fundamental support for the analysis of aerodynamics and hydrodynamics. Reynolds-averaged Navier-Stokes (RANS) equations with turbulence models have been widely applied for the simulations of turbulence flow. Besides, the Volume of Fluid (VOF) method, which was proposed by [PERSON] and [PERSON] [10] in 1981, has been broadly used in solving the free surface problem.