# Numerical Analysis of the Take-Off Performance of a Seaplane in Calm Water
## 1 Introduction
Recently, there have been some CFD studies focused on the hydrodynamic performance of seaplane hulls. [PERSON] et al. [11] investigated the hydrodynamic performance of a single seaplane hull numerically and experimentally. They adopted the model with fixed trim and heave to examine the effects of velocity, trim, and draft on hydrodynamic performance. [PERSON] and [PERSON] [12] investigated the hydrodynamics of a Wing-In-Gound (WIG) vehicle with towing tank experiment and CFD simulation. The fuselage together with floats were modeled resulting in the average error in trim angle and water resistance in comparison to experimental data, 4.3% and 8.4% respectively. [PERSON] et al. [13] verified the feasibility of URANS equations with VOF method on hydrodynamic analysis of a seaplane hull. They reported that the average error in trim angle and water resistance in comparison to experimental data are 3.26% and 3.12% respectively. However, the numerical investigations on the take-off performance of seaplanes combining the analysis of aerodynamics and hydrodynamics have been rarely published. [PERSON] and [PERSON] [14] simulated the take-off process of a fixed-trim amphibious aircraft with an efficient decoupling method that calculated aerodynamic and hydrodynamic performance separately in CFX and FLUENT. [PERSON] et al. [15] supplemented the decoupling method with an approximate equilibrium hypothesis which could efficiently estimate the acceleration in heave. It is evident that the decoupling method could save computing resources by simplifying the two-phase flow field around the seaplane, but a certain model error is expected owing to the interactions between the aerodynamics and hydrodynamics are ignored. Moreover, both studies adopted a fixed trim angle for the seaplane model, which is impractical for real operations. As the largest deviation in the resistance evaluations are related to the errors in the evaluation of trim angle, the rigid body dynamics should be introduced to determine the equilibrium trim angle of the seaplane at different speeds in response to aerodynamic forces, hydrodynamic forces, hydrostatic forces, and propeller thrust. This paper aims to investigate the take-off performance of a seaplane in calm water by numerically modeling the air-water two-phase flow around a seaplane that is free to trim and heave at different speeds ranging from standstill to leave the water based on commercial software STAR-CCM+ 12.02. The remainder of this paper is organized as follows: First, the numerical model is introduced, and the numerical setups are reported in detail. The computational domain size, boundary conditions, and grid refinements are described. Second, the numerical model is validated with benchmark data of F6 wing body and Fridsma hull respectively. Then, the seaplane planing on speeds ranging from the standstill to the takeoff are simulated to investigate the variations in heave, trim angle, and resistance characteristics against speed. In particular, a detailed analysis of the hydrodynamic resistance characteristics is presented. Additionally, a convergence study is performed to examine the influence of initial attitude and damping factors on the convergence time of 2 DOF motion.