Study of Underwater and Wave Gliders on the Basis of Simplified Mathematical Models

Both underwater and wave gliders are known as autonomous unmanned energy-saving vehicles which have recently found applications for monitoring the world ocean. The paper under consideration discusses simplified mathematical models of these platforms enabling the straightforward parametric investigation into relationships between their parameters and performance. In its first part the paper discusses equations describing the motion of an underwater glider (UG) in a vertical plane as a basis for derivations relating geometric, kinematic and hydrodynamic characteristics of UG and its lifting system with relative differential buoyancy and pitch angle. Obtained therewith are formulae for the estimation of the UG glide path speed, lift-to-drag ratio, range of navigation and endurance. The approach is exemplified for typical cases of the UG conceived as winged bodies of revolution and flying wings. The calculated results feature dependencies of the UG speed on its configuration and volume as well as on the angle of attack for different magnitudes of relative buoyancy. Also considered is an optimal mode of operation, based on the maximization of the lift-to-drag ratio. The second part of the paper is dedicated to the estimation of the thrust and speed of a wave glider (WG), comprising a surface module (float) and underwater module represented by a wing, with the use of a simplified mathematical modeling intended to clarify the influence of the parameters upon the performance of the WG. The derivations led to an equation of forced oscillations of the vehicle accounting for the interaction of the upper and lower modules, connected by a rigid umbilical. The exciting impact of progressive waves of a given length and amplitude is found through the calculation of the variation of a buoyancy force in accordance with the Froude–Krylov hypothesis. The derivatives of time-varying lift with respect to kinematic parameters, entering the equation of vertical motion of the WG, as well as coefficients of instantaneous and time-averaged thrust force, are found by resorting to the oscillating hydrofoil theory. The derivation of the available thrust and the approximate calculation of the drag of the vehicle with account of wave and viscous components enable the evaluation of the speed of the WG for the prescribed geometry of the craft and wave motion parameters.