Numerical calculation of manoeuvring coefficients for modelling the effect of submarine motion near the surface

Given the significant amount of time modern submarines conduct operations near the surface of the ocean, there is significant value in the capacity to predict the behaviour of a submarine operating in the near surface region. During most near surface operations, the primary forces involved are due to transient ocean waves and are statistical in nature. Yet there is also a contribution from the motion of the submarine near the surface, which has received less attention from researchers. The aim of this thesis is to determine the nature of the changes that occur in the manoeuvring forces acting on a submarine due to its own motion when operating near the ocean surface. Currently, coefficient-based manoeuvring models are utilised to predict deeply submerged submarine motion. However, research has shown that these coefficients change when near the surface due to the proximity and form of that surface. Utilising numerical computation with validation against experimental results, the sources of coefficient variation from their deeply submerged values in the near surface region are identified. The parameters that this variation depends upon are assessed, and the coefficients of motion that vary as a result are identified. Two novel methodologies based upon the use of numerical planar motion are proposed by which the variation found in the near surface region can be measured across the operating envelope and the changes found for a standard submarine form are thus determined. The results of these tests show that, of the coefficients assessed, those that have the most significant impact upon submarine motions in the near surface region are: • Coefficient of normal force as a function of square of the axial velocity; • Coefficient of normal force as a function of velocity in the z-axis; • Coefficient of normal force as a function of acceleration in the z-axis; and • Coefficient of pitch moment as a function of velocity in the z-axis. Note: the z-axis is vertical in the submarine’s frame of reference. It was also found that the amplitude of a numerical planar motion can be reduced to a minor fraction of a submarine’s diameter without loss of accuracy. More significantly, motions of such scale were found to render the coefficients approximately constant over the period of oscillation. This allows the utilisation of this method for the numerical estimate of linear acceleration and velocity coefficients in the near surface region, which are not obtainable via conventional methods. The ability to estimate these coefficients — along with those obtainable through extending these methods to simulating pure pitch — will enable substantially improved modelling of submarine motions in the near surface region, enabling better design choices and operational control