An Investigation into Dynamic Stability of Waterborne Aircraft on Take-off and Landing

Masri, Jafar (2020) An Investigation into Dynamic Stability of Waterborne Aircraft on Take-off and Landing. Doctoral thesis, Northumbria University.

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Abstract

This research contributes to the knowledge of dynamic stability of waterborne aircraft and ground effect phenomenon. Hereto an analytical and computational study has been performed during which the motion of waterborne aircraft in take-off and landing is predicted. An analytical tool that can be used to predict the nonlinear heaving and pitching motions of seaplanes is presented. First, the heaving and pitching equations of motion are presented in their general Lagrangian form. Then, the equations are simplified to a form of nonlinear equations known as the forced Duffing equations with cubic nonlinearity. The system of motion is assumed to be driven by a sinusoidal head sea wave. The equations are then solved using the Poincare-Lindstedt perturbation method. The analytical solution is verified with CFD simulations performed on Ansys Fluent and AQWA. The solution is used to extend Savitsky’s method to predict porpoising which is a form of dynamic instability found in high-speed boats and seaplanes.

The results of the analytical tool are in very good agreement with the results obtained from Fluent and AQWA. However, as the motion is assumed to be 2D in Fluent, heaving amplitude is slightly over predicted. Moreover, the frequency of oscillations of the 2D simulations is found to be unsteady. The unsteadiness in frequency increases with the increase of the length of the hull. Nevertheless, the amplitude of the pitch motion is slightly less than the amplitude predicted analytically. The discrepancy in the results is due to the characteristics of the 2D simulations that assumes that sea water will only pass underneath the hull which will make the buoyancy force greater as less damping is experienced. This is also a consequence of the fact that parameters within the analytical model of heave and pitch are calculated using a strip theory which considers only hydrodynamic effects, while Fluent also incorporate aerodynamic contributions. Similarly, AQWA is a 3D platform that only takes in consideration hydrodynamic effects. Hence, the results of AQWA are slightly less in amplitude than that predicted analytically. In addition, it was found that the frequency of oscillations obtained using AQWA increases with time while in the analytical approach, the frequency of oscillations can only be assumed to be constant for the whole period of motion. The increment in the oscillations indicates that porpoising is taking place. Nevertheless, it was found that heaving terms control the amplitude of motion and pitching terms control frequency of oscillations. The pitching nonlinear term has an effect on the amplitude of motion but not significant. Finally, the analytical method of Savitsky that is used to predict the porpoising stability limit is extended to find the porpoising limit for a wider range of pitch angles. In addition, the porpoising limit is predicted for a planing hull that is moving under the effect of head sea waves. When the seaplane is moving through head sea waves at a fixed pitch angle, porpoising takes place at a lower speed than what Savitsky has predicted.

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