A review of the analytical methods used for seaplanes’ performance prediction <s> Appendix A: <s> In order to study the dynamic behavior of ships navigating in severe environmental conditions it is imperative to develop their governing equations of motion taking into account the inherent nonlinearity of large-amplitude ship motion. The purpose of this paper is to present the coupled nonlinear equations of motion in heave, roll, and pitch based on physical grounds. The ingredients of the formulation are comprised of three main components. These are the inertia forces and moments, restoring forces and moments, and damping forces and moments with an emphasis to the roll damping moment. In the formulation of the restoring forces and moments, the influence of large-amplitude ship motions will be considered together with ocean wave loads. The special cases of coupled roll-pitch and purely roll equations of motion are obtained from the general formulation. The paper includes an assessment of roll stochastic stability and probabilistic approaches used to estimate the probability of capsizing and parameter identification. <s> BIB001 </s> A review of the analytical methods used for seaplanes’ performance prediction <s> Appendix A: <s> The towing tank experiments conducted at Yokohama National University from November 30 to December 9 in 2005 suggested a new way of suppressing a dangerous coupled motion between heave and pitch called porpoising. The research in this paper was developed on the observations made in the experiments and conducted numerical simulations to further investigate the parametric design space. Two linear-time-invariant models were developed: rigid-body planing craft (conventional float planes or flying boats), and flexibly supported planing craft. The latter could simulate the new method found in the experiments for suppressing porpoising. In this study, the stability of the oscillatory motions was analyzed to see the effect of design variables on the inception of porpoising. The parametric study of flexibly supported float planes in the context of porpoising was a new contribution in the conceptual design of seaplanes. <s> BIB002
The solution of the heave and pitch equations was obtained by using Visual Basic. The equations used for the added mass, damping and restoring forces and moments coefficients were obtained from reference BIB002 . The VB code developed is as follows: Figure 1 Seaplane operating phases. Figure 2 The three operating ranges of seaplanes  . Figure 3 Seaplane hull in displacement and planing modes  . Figure 2 Planing hull characteristics  . Figure 3 The six DOF of a planing hull BIB001 . 