High-speed planing craft operating in waves are subject to frequent water impact, or slamming, as a portion or whole of the craft exits the water and re-enters at high velocity. The global load induced by slamming can cause fatigue-related damages to structures. The local slamming can cause local damage to structures and its induced acceleration can cause damage to equipment and personnel aboard. Therefore the slamming loads in high-speed craft are critical design loads. Nowadays, due to the increasing use of composite materials in high-speed craft, the interaction between the hydrodynamic loading and structural response, or hydroelasticity, must be considered. In this work, a flexible V-shaped wedge, which vertically enters the calm water with an impact velocity, was examined experimentally and numerically to characterize the slamming of a representative cross-section of high-speed craft. Physical quantities of interest include rigid-body kinematic motions, spray root propagation, hydrodynamic loading, and structural response. In the experimental work, with varied impact velocity and flexural rigidity of the wedge bottom plate, a wide range of hydroelasticity factors were investigated. The intersection between the bottom plate and side plate is called chine. The phases before and after the spray root reached the chine are called chine-unwetted and chine-wetted phase, respectively. It was found that the maximum deflection and strain occur in the chine-unwetted phase while a structural vibration with rapidly decaying magnitude is observed in the chine-wetted phase. Furthermore, the kinematic effect of hydroelasticity changes the spray root propagation and hence the pressure, while the inertial effect elongates the natural period of the plate. Inspired by the experimental work, a computational framework was proposed to focus on the chine-unwetted phase. Several hydroelastic models can be obtained from this framework. The hydroelastic models were validated to show reasonable agreement with experiments. Various parameters were studied through the computational framework. The hydroelasticity factor was modified to account for the mass and boundary conditions. It was found that the nondimensional rigid-body kinematic motions and maximum deflection showed little dependence on the hydroelasticity factor. Hydroelastic effects increased the time it takes for the peak maximum deflection to be reached for small values of the hydroelasticity factor. Hydroelastic effects also have little influence on the magnitude of the maximum deflection. These discoveries further the understanding of hydroelastic slamming and show the potential to guide the structural optimization and design of high-speed craft. / Doctor of Philosophy / High-speed planing craft operating in waves are prone to frequent water impact, or slamming, as a portion or whole of the craft exits the water and re-enters at high velocity. The slamming loads in high-speed craft are critical design loads as the slamming can cause damage to the structures and equipment as well as injure personnel aboard. Nowadays, due to the increasing use of composite materials in high-speed craft, the interaction between the hydrodynamic loading and structural response, or hydroelasticity, must be considered. In this work, a flexible V-shaped wedge entering water is studied experimentally and computationally to characterize the slamming of a representative cross-section of high-speed craft. The contact point between the water surface and the wedge bottom is called the spray root. It was found that the hydrodynamic loading and structural response interact with each other through the spray root. The maximum deflection and strain occur when the wedge bottom is partially submerged while a structural vibration with rapidly decaying magnitude is observed when the wedge bottom is fully submerged. Using the hydroelasticity factor proposed by other researchers, the extent of fluid-structure interaction was quantified. Hydroelastic effects manifest themselves when the hydroelasticity factor is small These discoveries further the understanding of hydroelastic slamming and show the potential to guide the structural optimization and design of high-speed craft.

<p>Simulation of the planing hull in waves has been addressed during the last 25 years and basically been approached by strip methods. This work follows that tradition and describes a time-domain strip model for simulation of the planing hull in waves. The actual fluid mechanical problem is simplified through the strip approach. The load distribution acting on the hull is approximated by determining the section load at a number of hull sections, strips. The section-wise 2-dimensional calculations are expressed in terms of added mass coefficients and used in the formulations of both inertia and excitation forces in the equations of motions. The modeling approach starts from the hypothetic assumption that the transient conditions can be modeled based on those section-wise calculations. The equation of motion is solved in the time-domain. The equation is up-dated at each time step and every iteration step with respect to the momentary distribution of section draught and relative incident velocity between the hull and water and catches the characteristic non-linear behavior of the planing craft in waves.</p><p>The model follows the principles of the pioneering work of E. E. Zarnick differing on model structure and in details such as the modeling of the lift in the transom area. A major part of the work is concerned with experiments and evaluation of simulations with respect to performed model tests and to published experiment data. Simulations of model tests have been performed and comparisons have been made between measured and simulated time series. The link between simulation and experiment is a wave model which is based on a wave height measurement signal. It is developed and evaluated in the thesis.</p><p>The conclusions are in favor of the 2-dimensional approach to modeling the conditions for the planing hull in waves and among further studies is evaluation of simulated loads and motions to full-scale trial measurement data.</p>

Simulation of the planing hull in waves has been addressed during the last 25 years and basically been approached by strip methods. This work follows that tradition and describes a time-domain strip model for simulation of the planing hull in waves. The actual fluid mechanical problem is simplified through the strip approach. The load distribution acting on the hull is approximated by determining the section load at a number of hull sections, strips. The section-wise 2-dimensional calculations are expressed in terms of added mass coefficients and used in the formulations of both inertia and excitation forces in the equations of motions. The modeling approach starts from the hypothetic assumption that the transient conditions can be modeled based on those section-wise calculations. The equation of motion is solved in the time-domain. The equation is up-dated at each time step and every iteration step with respect to the momentary distribution of section draught and relative incident velocity between the hull and water and catches the characteristic non-linear behavior of the planing craft in waves. The model follows the principles of the pioneering work of E. E. Zarnick differing on model structure and in details such as the modeling of the lift in the transom area. A major part of the work is concerned with experiments and evaluation of simulations with respect to performed model tests and to published experiment data. Simulations of model tests have been performed and comparisons have been made between measured and simulated time series. The link between simulation and experiment is a wave model which is based on a wave height measurement signal. It is developed and evaluated in the thesis. The conclusions are in favor of the 2-dimensional approach to modeling the conditions for the planing hull in waves and among further studies is evaluation of simulated loads and motions to full-scale trial measurement data.

Experimental and numerical analysis of loads and responses for planing craft in waves is considered. Extensive experiments have been performed on a planing craft, in full-scale as well as in model scale. The test set-ups and significant results are reviewed. The required resolution in experiments on planing craft in waves, concerning sampling frequencies, filtering and pressure transducer areas, is investigated. The aspects of peak identification in transient signals, fitting of analytical cumulative distribution functions to sampled data, and statistical convergence are treated. A method for reconstruction of the momentary pressure distribution at hull-water impact, from measurements with a limited number of transducers, is presented. The method is evaluated to full-scale data, and is concluded to be applicable in detailed evaluation of the hydrodynamic load distribution in time-domain simulations. Another suggested area of application is in full-scale design evaluations, where it can improve the traceability, i.e. enable evaluation of the loads along with the responses with more confidence. The presented model experiment was designed to enable time-domain monitoring of the complete hydromechanic pressure distribution on planing craft in waves. The test set-up is evaluated by comparing vertical forces and pitching moments derived from acceleration measurements, with the corresponding forces derived with the pressure distribution reconstruction method. Clear correlation is found. An approach for direct calculations of loads, as well as motion and structure response, is presented. Hydrodynamic loads and motion responses are calculated with a non-linear time-domain strip method. Structure responses are calculated by applying momentary distributed pressure loads, formulated from hydrodynamic simulations, on a global finite element model with inertia relief. From the time series output, limiting conditions and extreme responses are determined by means of short term statistics. Promising results are demonstrated in applications, where extreme structure responses derived by the presented approach, are compared with responses to equivalent uniform rule based loads, and measured responses from the full-scale trials. It is concluded that the approach is a useful tool for further research, which could be developed into a rational design method.

<p>Experimental and numerical analysis of loads and responses for planing craft in waves is considered. Extensive experiments have been performed on a planing craft, in full-scale as well as in model scale. The test set-ups and significant results are reviewed. The required resolution in experiments on planing craft in waves, concerning sampling frequencies, filtering and pressure transducer areas, is investigated. The aspects of peak identification in transient signals, fitting of analytical cumulative distribution functions to sampled data, and statistical convergence are treated.</p><p>A method for reconstruction of the momentary pressure distribution at hull-water impact, from measurements with a limited number of transducers, is presented. The method is evaluated to full-scale data, and is concluded to be applicable in detailed evaluation of the hydrodynamic load distribution in time-domain simulations. Another suggested area of application is in full-scale design evaluations, where it can improve the traceability, i.e. enable evaluation of the loads along with the responses with more confidence.</p><p>The presented model experiment was designed to enable time-domain monitoring of the complete hydromechanic pressure distribution on planing craft in waves. The test set-up is evaluated by comparing vertical forces and pitching moments derived from acceleration measurements, with the corresponding forces derived with the pressure distribution reconstruction method. Clear correlation is found.</p><p>An approach for direct calculations of loads, as well as motion and structure response, is presented. Hydrodynamic loads and motion responses are calculated with a non-linear time-domain strip method. Structure responses are calculated by applying momentary distributed pressure loads, formulated from hydrodynamic simulations, on a global finite element model with inertia relief. From the time series output, limiting conditions and extreme responses are determined by means of short term statistics. Promising results are demonstrated in applications, where extreme structure responses derived by the presented approach, are compared with responses to equivalent uniform rule based loads, and measured responses from the full-scale trials. It is concluded that the approach is a useful tool for further research, which could be developed into a rational design method.</p>

Em geral, uma embarcação de planeio é projetada para atingir elevados níveis de velocidade. Esse atributo de desempenho está diretamente relacionado ao porte da embarcação e à potência instalada em sua planta propulsiva. Tradicionalmente, durante o projeto de uma embarcação, as análises de desempenho são realizadas através de resultados de embarcações já existentes, retirados de séries sistemáticas ou de embarcações já desenvolvidas pelo estaleiro e/ou projetista. Além disso, a determinação dos atributos de desempenho pode ser feita através de métodos empíricos e/ou estatísticos, onde a embarcação é representada através de seus parâmetros geométricos principais; ou a partir de testes em modelos em escala reduzida ou protótipos. No caso específico de embarcações de planeio, o custo dos testes em escala reduzida é muito elevado em relação ao custo de projeto. Isso faz com que a maioria dos projetistas não opte por ensaios experimentais das novas embarcações em desenvolvimento. Ao longo dos últimos anos, o método de Savitsky foi largamente utilizado para se realizar estimativas de potência instalada de uma embarcação de planeio. Esse método utiliza um conjunto de equações semi-empíricas para determinar os esforços atuantes na embarcação, a partir dos quais é possível determinar a posição de equilíbrio de operação e a força propulsora necessária para navegar em uma dada velocidade. O método de Savitsky é muito utilizado nas fases iniciais de projeto, onde a geometria do casco ainda não foi totalmente definida, pois utiliza apenas as características geométricas principais da embarcação para realização das estimativas de esforços. À medida que se avança nas etapas de projeto, aumenta o detalhamento necessário das estimativas de desempenho. Para a realização, por exemplo, do projeto estrutural é necessária uma estimativa do campo de pressão atuante no fundo do casco, o qual não pode ser determinado pelo método de Savitsky. O método computacional implementado nesta dissertação, tem o objetivo de determinar as características do escoamento e o campo de pressão atuante no casco de uma embarcação de planeio navegando em águas calmas. O escoamento é determinado através de um problema de valor de contorno, no qual a superfície molhada no casco é considerada um corpo esbelto. Devido ao uso da teoria de corpo esbelto o problema pode ser tratado, separadamente, em cada seção, onde as condições de contorno são forçadamente respeitadas através de uma distribuição de vórtices. / Generally, a planing craft is designed to achieve high speed levels. This performance attribute is directly related to the boat size and to the propeller plant power. Traditionally, during a boat design, performance analyses are carried out using results taken from systematic series or from others boat previously build by the shipyard and/or designer. Furthermore, performance attributes can be calculated by semi-empirical and/or statistic methods or by tests of reduced scale models. In the specific case of planing boats, the costs of reduced scale tests are too high compared to the design cost itself. Because of this, most designers do not perform experimental tests during the development of new boats. During the last years, the Savitsky method was extensively used to estimate planing craft effective power. The method uses a set of semi-empirical equations to calculate the forces acting on the boat, from which the equilibrium position and the required propeller thrust are determined. During the preliminary phases of planing craft design, the hull geometry hasn\'t been fully defined. Therefore, the Savitsky method is widely used during this phase, because it uses only the main geometrical characteristics to estimate the forces acting on the hull. Advancing toward the final phases of the design process, more detailed information is required. To execute the structural design, for example, the pressure field acting on the hull must be known, which can\'t be estimate using the Savitsky method. The main objective of the present study is to implement a computer method that can be used to estimate the fluid flow and pressure field acting on the hull of a boat moving with forward speed constant in calm water. The fluid flow around the hull is treated as a boundary value problem, in which the wetted hull surface is considered a slender body. The slender body theory enables to solve the problem separately, in each transverse section, where boundary conditions are respected by a sheet of vortices.

Em geral, uma embarcação de planeio é projetada para atingir elevados níveis de velocidade. Esse atributo de desempenho está diretamente relacionado ao porte da embarcação e à potência instalada em sua planta propulsiva. Tradicionalmente, durante o projeto de uma embarcação, as análises de desempenho são realizadas através de resultados de embarcações já existentes, retirados de séries sistemáticas ou de embarcações já desenvolvidas pelo estaleiro e/ou projetista. Além disso, a determinação dos atributos de desempenho pode ser feita através de métodos empíricos e/ou estatísticos, onde a embarcação é representada através de seus parâmetros geométricos principais; ou a partir de testes em modelos em escala reduzida ou protótipos. No caso específico de embarcações de planeio, o custo dos testes em escala reduzida é muito elevado em relação ao custo de projeto. Isso faz com que a maioria dos projetistas não opte por ensaios experimentais das novas embarcações em desenvolvimento. Ao longo dos últimos anos, o método de Savitsky foi largamente utilizado para se realizar estimativas de potência instalada de uma embarcação de planeio. Esse método utiliza um conjunto de equações semi-empíricas para determinar os esforços atuantes na embarcação, a partir dos quais é possível determinar a posição de equilíbrio de operação e a força propulsora necessária para navegar em uma dada velocidade. O método de Savitsky é muito utilizado nas fases iniciais de projeto, onde a geometria do casco ainda não foi totalmente definida, pois utiliza apenas as características geométricas principais da embarcação para realização das estimativas de esforços. À medida que se avança nas etapas de projeto, aumenta o detalhamento necessário das estimativas de desempenho. Para a realização, por exemplo, do projeto estrutural é necessária uma estimativa do campo de pressão atuante no fundo do casco, o qual não pode ser determinado pelo método de Savitsky. O método computacional implementado nesta dissertação, tem o objetivo de determinar as características do escoamento e o campo de pressão atuante no casco de uma embarcação de planeio navegando em águas calmas. O escoamento é determinado através de um problema de valor de contorno, no qual a superfície molhada no casco é considerada um corpo esbelto. Devido ao uso da teoria de corpo esbelto o problema pode ser tratado, separadamente, em cada seção, onde as condições de contorno são forçadamente respeitadas através de uma distribuição de vórtices. / Generally, a planing craft is designed to achieve high speed levels. This performance attribute is directly related to the boat size and to the propeller plant power. Traditionally, during a boat design, performance analyses are carried out using results taken from systematic series or from others boat previously build by the shipyard and/or designer. Furthermore, performance attributes can be calculated by semi-empirical and/or statistic methods or by tests of reduced scale models. In the specific case of planing boats, the costs of reduced scale tests are too high compared to the design cost itself. Because of this, most designers do not perform experimental tests during the development of new boats. During the last years, the Savitsky method was extensively used to estimate planing craft effective power. The method uses a set of semi-empirical equations to calculate the forces acting on the boat, from which the equilibrium position and the required propeller thrust are determined. During the preliminary phases of planing craft design, the hull geometry hasn\'t been fully defined. Therefore, the Savitsky method is widely used during this phase, because it uses only the main geometrical characteristics to estimate the forces acting on the hull. Advancing toward the final phases of the design process, more detailed information is required. To execute the structural design, for example, the pressure field acting on the hull must be known, which can\'t be estimate using the Savitsky method. The main objective of the present study is to implement a computer method that can be used to estimate the fluid flow and pressure field acting on the hull of a boat moving with forward speed constant in calm water. The fluid flow around the hull is treated as a boundary value problem, in which the wetted hull surface is considered a slender body. The slender body theory enables to solve the problem separately, in each transverse section, where boundary conditions are respected by a sheet of vortices.

A planing catamaran is a high-powered, twin-hull water craft that develops the lift which supports its weight, primarily through hydrodynamic water pressure. Presently, there is increasing demand to further develop the catamaran's planing and seakeeping characteristics so that it is more effectively applied in today's modern military and pleasure craft, and offshore industry supply vessels. Over the course of the past ten years, Vorus (1994,1996,1998,2000) has systematically conducted a series of research works on planing craft hydrodynamics. Based on Vorus' planing monohull theory, he has developed and implemented a first order nonlinear model for planing catamarans, embodied in the computer code CatSea. This model is currently applied in planing catamaran design. However, due to the greater complexity of the catamaran flow physics relative to the monohull, Vorus's (first order) catamaran model implemented some important approximations and simplifications which were not considered necessary in the monohull work. The research of this thesis is for relieving the initially implemented approximations in Vorus's first order planing catamaran theory, and further developing and extending the theory and application beyond that currently in use in CatSea. This has been achieved through a detailed theoretical analysis, algorithm development, and careful coding. The research result is a new, complete second order nonlinear hydrodynamic theory for planing catamarans. A detailed numerical comparison of the Vorus's first order nonlinear theory and the second order nonlinear theory developed here is carried out. The second order nonlinear theory and algorithms have been incorporated into a new catamaran design code (NewCat). A detailed mathematical formulation of the base first order CatSea theory, followed by the extended second order theory, is completely documented in this thesis.