Constant Forward Speed Research Articles

An Earth-fixed observer to ship waves

This work deals with the linear surface waves generated by a vessel advancing at a constant forward speed. These waves, known as ship waves, appear stationary to an observer on the vessel. Rather than exploring the well-studied stationary ship waves, this work delves into the physical properties of ship waves measured at Earth-fixed locations. While it might have been expected that analysing these waves in an Earth-fixed coordinate system would be a straightforward transformation from existing analytical theories in a moving coordinate system, the reality proves to be quite different. The properties of waves measured at fixed locations due to a passing ship turn out to be complex and non-trivial. They exhibit unique characteristics, being notably unsteady and short crested, despite appearing stationary to an observer on the generating vessel. The analytical expressions for the physical properties of these unsteady waves are made available in this work, including the amplitude, frequency, wavenumber, direction of propagation, phase velocity and group velocity. Based on these newly derived expressions and two-point measurements, an inverse method has been presented for determining the advancing speed and the course of motion of the moving ship responsible for the wave generation. The results from this study can be used in a wide range of applications, such as interpreting data from point measurements and assessing the roles of ship waves in transporting ocean particles.

Wave motions due to a point source pulsating and advancing at forward speed parallel to a semi-infinite ice sheet

The Green function, or the wave motion due to a point source pulsating and advancing at constant forward speed along a semi-infinite ice sheet in finite water depth is investigated, based on the linear velocity potential theory for fluid flow and thin elastic plate model for the ice sheet. The result is highly relevant to the ship motions near marginal seas. The ice edge is assumed to be free, or zero bending moment and shear-force conditions are used, while other edge conditions can be similarly considered. The Green function G is derived first through the Fourier transform along the direction of forward speed and then by the Wiener-Hopf technique along the transverse direction across both the free surface and ice sheet. The result shows that in the ice-covered domain, G can be decomposed into three parts. The first one is that upper ocean surface is fully covered by an ice sheet, and the second and third ones are due to the free surface and ice edge. Similarly, in the free-surface domain, G contains the component corresponding to that the upper water surface is fully free, while the second and third ones are due to the ice sheet and ice edge. In both domains, the latter two are due to the interactions of the free-surface wave and ice sheet deflection, which leads to the major complication. In-depth investigations are made for each part of G, and aim to shed some light on the nature of the wave motions induced by a ship advancing along a semi-infinite ice sheet at constant forward speed. Published by the American Physical Society 2024

Effects of piezoelectric energy harvesting from a morphing flapping tail on its performance

Monitoring fish migration, which can extend over distances of thousands of kilometers, via fish tags is important to maintain healthy fish stocks and preserve biodiversity. One constraint of current fish tags is the limited power of their batteries. Attaching a piezoelectric element to an oscillating part of the fish body has been proposed to develop self-powered tags. To determine the functionality and potential of this technology, we present an analysis showing variations of the generated voltage with specific aspects of the tail’s response. We also perform numerical simulations to validate the analysis and determine the effects of attaching a piezoelectric element on performance metrics including thrust generation, propulsive efficiency, and harvested electric power. The tail with the attached piezoelectric element is modeled as a unimorph beam moving at a constant forward speed and excited by sinusoidal pitching at its root. The hydrodynamic loads are calculated using three-dimensional unsteady vortex lattice method. These loads are coupled with the equation of motion, which is solved using the finite element method. The implicit finite different scheme is used to discretize the time-dependent generated voltage equation. The analysis shows that the harvested electric power depends on the slope of the trailing edge, a result that is validated with the numerical simulations. The numerical simulations show that, depending on the excitation frequency, attaching a piezoelectric element can increase or decrease the thrust force. The balance of required hydrodynamic power, generated propulsive power and harvested electrical power shows that, depending on the excitation frequency, relatively high levels of harvested power can be harvested without a high adverse impact on the hydrodynamic or propulsive power. For a specified frequency of oscillations, the approach and results can be used to identify design parameters where harvested electrical power by a piezoelectric element will have a minimal adverse impact on the hydrodynamic or propulsive power of a swimming fish.

Lumped hydrodynamics identification-based cascade control for vertical-plane tracking of a fin-driven autonomous underwater vehicle

This paper aims to achieve a simplified and effective vertical-plane tracking control for a kind of fin-driven under-actuated autonomous underwater vehicles (AUVs). To this end, a two-layer framework of offline identification and online control is constructed and implemented for depth-pitch coupled tracking control of an under-actuated AUV at a constant forward speed. A simplified three-order identification model for pitch dynamics is derived and then a dedicated recursive weighted least squares algorithm is used to complete the offline estimation of lumped hydrodynamics. Subsequently, relying on identification results, an online cascade controller with just two gains and without any adaptive estimation is proposed to track the pitch guidance angle and it is proven to be input-to-state stable. Finally, comparative simulation results illustrate the effectiveness and outperformance of this two-layer framework for vertical-plane tracking control of fin-driven under-actuated AUVs.

Adaptive Lane Change Trajectory Planning Scheme for Autonomous Vehicles Under Various Road Frictions and Vehicle Speeds

This paper proposes an adaptive lane change trajectory planning scheme to road friction and vehicle speed for autonomous driving, while considering both the maneuver safety and the comfort of occupants. In regard to achieve smooth trajectory, a 7th-order polynomial function is constructed to ensure continuity of the planned trajectory up to the derivative of the curvature (jerk). Unlike traditional planning methods that only consider very limited maneuvering conditions, the proposed scheme adapts to a wide range of road friction and vehicle speed, while ensuring enhanced occupants' ride comfort and acceptance. The proposed trajectory planning scheme creatively integrates all the dynamic constraints which are defined by road friction, safety, comfort and human-like driving style. It is shown that the proposed lane change planning algorithm reduces to the identification of exclusively the lane change duration given a constant forward speed. Illustrative simulation examples in MATLAB/Simulink have been conducted to demonstrate the validity of the proposed scheme. The acceptable traceability of the planned lane change trajectories is further demonstrated through path tracking analysis of a full-vehicle model in CarSim. Finally, experimental tests have been conducted based on Quanser's latest self-driving car (QCar) to verify the practical effectiveness of the proposed trajectory planning scheme.

Optimization of Gain Scheduled Controller for an Active Trailer Steering System Using an Evolutionary Algorithm

Car–trailer combinations can experience unstable motion modes such as trailer-sway, jackknifing and rollover that can lead to fatal accidents. These unstable motions can be mitigated with the use of an active trailer steering (ATS) system. Prior studies in ATS have leveraged the linear quadratic regulator (LQR) as an ATS controller but for many of these designs it was assumed that the vehicle and operating parameters were constant. In reality, vehicle and operating parameters may vary and have an impact on the stability of a car–trailer combination. In this paper, the weighting matrices of the LQR controller are determined using the GDE3 evolutionary optimization algorithm with the objective of addressing the design trade off between minimizing the car–trailer’s path-following performance for low vehicle speeds and minimizing the rearward amplification for high vehicle speeds. The effectiveness of the approach is demonstrated using a numerical simulation car–trailer model developed in the CarSim simulator. Our results show that the multi-objective tuned gain scheduling controller outperforms a non-tuned gain scheduling controller in terms of improving the lateral stability and the path following performance of car–trailer combinations in driver in the loop single lane-change maneuvers at a constant vehicle forward speed.

Ship motion-sloshing interaction with forward speed in oblique waves

Seakeeping properties of large LNG carriers with partially filled tanks are known to be influenced by sloshing inside their tanks, by wave conditions and wave heading, and by their forward speed. An efficient hybrid numerical method was developed to study wave-induced ship response coupled with sloshing-induced compressible fluid response inside the tanks of a 138,000 m3 LNG carrier at zero forward speed and at the constant forward speeds of 12 and 20 kn. Wave conditions considered were oblique regular waves at heading angles of 0, 30, 60, 90, 120, 150, and 180 deg. The numerical approach combined a nonlinear boundary element Rankine source code to solve the weakly nonlinear seakeeping problem with a Reynolds-averaged Navier-Stokes equations solver to compute the compressible sloshing flow inside the tanks. Coupling effects of the six degrees-of-freedom ship motions in beam waves were validated against comparable model test measurements of ship responses and against free surface elevations in tanks. Results demonstrated that sloshing affected the simulated seakeeping behavior of the subject LNG carrier advancing at forward speeds in oblique waves. As sloshing had the greatest influence on the ship's roll motions, a key aspect was the derivation of roll damping from model decay tests.

Inline forces and bow wave height on a vertical cylinder moving in waves — Experimental study and CFD validation

The aim of this paper is to investigate the inline force and bow wave height on a vertical cylinder moving at a constant forward speed in calm water and in regular waves. A series of physical model tests has been performed to investigate the effect the waves have on both the inline force and the bow wave height as well as to validate a Computational Fluid Dynamics (CFD) model that was developed using Caelus open source code. A stationary mesh was used in the CFD model and a new wave library was created based on the relaxation zone technique to incorporate the effect of adding a current with velocity equal to the speed of the moving cylinder while still generating the targeted wave field. The CFD results were compared to the physical measurements for the following cases: (1) generation of regular waves and current, (2) inline force and bow wave height on the cylinder moving in calm water and (3) inline force and bow wave height on the cylinder moving in regular waves. It was found from the model tests that both the inline force and bow wave height increased as cylinder speed increased. The maximum inline force and bow wave height measured on a stationary cylinder subjected to waves was amplified up to 9.6 and 2.7 times, respectively depending on the cylinder speed in case 3, which indicated a nonlinear relationship between the variation in maximum inline force and bow wave height due to wave–current interaction. The capability of the CFD model has been illustrated by the very good agreement (errors of about 3.0%) achieved with respect to the experiments for the different conditions of increasing complexity tested in this study.

Effect of forward speed on the level-crossing distribution of kinematic variables in multidirectional ocean waves

The influence of forward speed on stochastic free-surface crossing, in a Gaussian wave field, is investigated. The case of a material point moving with a constant forward speed is considered; the wave field is assumed stationary in time, and homogeneous in space. The focus is on up-crossing events, which are defined as the material point crossing the free surface, into the water domain. The effect of the Doppler shift (induced by the forward speed) on the up-crossing frequency, and the related conditional joint distribution of wave kinematic variables is analytically investigated. Some general trends are illustrated through different examples, where three kinds of wave direction distribution are considered: unidirectional, short-crested anisotropic, and isotropic. The way the developed approach may be used in the context of slamming on marine structures is briefly discussed.

Estimation of added resistance of an LNG carrier in oblique waves

Despite recent moderate oil prices, the reduction in fuel oil consumption of voyaging ships has been of great interest. Ships experience additional resistance from wind and waves in actual seas during their voyages, and those added resistance contributes the increase of fuel consumption. The accurate prediction of the added resistance is, therefore, crucial for developing highly energy efficient and low fuel-consuming ships.Ships routinely navigate along pre-determined routes between ports and thus relative heading angle is typically not controlled. Therefore, ships can encounter wind and waves coming from any direction. However, added resistance in oblique direction has less been studied by researchers than that in head seas. To predict the operating performance of ships accurately, more focus should also be given to added resistance in oblique direction.In the present study, the motions and added resistance of an LNG carrier are estimated by experimental investigations and numerical computations. The scaled model ship is towed at a constant forward speed in a square basin and the resistance increase is measured in regular oblique waves. Potential flow method and Reynolds-Averaged Navier-Stokes (RANS) based computational fluid dynamics method are employed to compare the magnitudes of motion and added resistance to those obtained from model test. The global trend of motion responses agrees reasonably at all heading angles between the results from experiments and numerical computations. In regard to the added resistance, however the level of accuracy is less favorable for both numerical methods. The discrepancy is further investigated by checking the relevant parameters in potential method, roll damping and relative phases. The detailed results are discussed and key finding is addressed.In the experimental and numerical investigations, the magnitude in the transfer function of added resistance due to waves is significant at bow quartering seas. In addition, the resistance increase appears to be not negligible even at the following and stern-quartering seas. Therefore, operating efficiency of a ship can be evaluated appropriately when contribution of all heading angles is properly taken into account to the evaluation of added resistance.

Parameter computation for a Lagrangian mechanical system model of a submerged vessel moving near a free surface

This paper describes the computation of parameters for a Lagrangian mechanical system model of a submerged vessel moving near an otherwise calm free surface using a medium-fidelity potential flow code. The software uses the boundary element method to solve for the flow potential on the body and the free surface. The model, a system of integro-differential equations involving functions of the velocity potential, is the “maneuvering” component of a Lagrangian nonlinear maneuvering and seakeeping model that was introduced in earlier work. Here, this nonlinear maneuvering model is reformulated and the potential flow software is modified to support parameter computations. Parameters are computed for a prolate spheroid moving parallel to a calm free surface at a constant forward speed. This motion induces a steady flow with respect to the body, which results in a steady surge force, heave force and pitch moment. These longitudinal forces and moment are computed using the reformulated Lagrangian nonlinear maneuvering model and the results are compared with basic panel code solutions for various depths and Froude numbers and for various computational parameter values.

Numerical Study on Unsteady Pressure Distribution on Bulk Carrier in Head Waves with Forward Speed

This study deals with wave-induced unsteady pressure on a ship moving with a constant forward speed in regular head waves. Two different numerical methods are applied to solve wave–ship interaction problems: a Rankine panel method which adopts velocity potential, and a Cartesian-grid method which solves the momentum and mass conservation equations under the assumption of inviscid and incompressible fluids. Before comparing l1ocal pressure distributions, the computational methods are validated for global quantities, such as ship motion responses and added resistance, by comparison with available experimental data. Then, the computational results and experimental data are compared for hydrodynamic pressure, particularly focusing on the magnitude of the first-harmonic component in different sections and vertical locations. Furthermore, the Cartesian-grid method is used to simulate the various wave-amplitude conditions, and the characteristics of the zeroth-, first-, and second-harmonic components of wave-induced pressure are investigated. The nonlinearity of pressure distribution is observed mostly from the pressure near the still-water-level of the ship bow and the normalized first-harmonic component of wave-induced pressure decreases as the wave steepness increases. Lastly, to understand the local characteristics of wave-induced unsteady pressure, the time-averaged added pressure and added local force are analyzed. It is found that the major contribution of the time-averaged added local force that occurs around the ship stem above the design waterline.

Hydrodynamic Analysis and Motions of Ship with Forward Speed via a Three-Dimensional Time-Domain Panel Method

A new three-dimensional (3D) time-domain panel method is developed to solve the ship hydrodynamic problem and motions. For an advancing ship with a constant forward speed in regular waves, the ship’s hull can be discretized and processed into a number of quadrilateral panels. Based on Green’s theorem, an analytical expression for Froude–Krylov (F–K) forces evaluation on the quadrilateral panels is derived without accuracy loss. Within the linear potential theory, the transient free surface Green function (TFSGF) is applied to solve the boundary value problem. To improve the efficiency and numerical stability of TFSGF evaluation, a precise integration method with variable parameters setting for extended identity matrix is developed to compute the TFSGF in the computation domain. Then, radiation and diffraction forces can be evaluated by means of the impulse response function method. The Wigley I hull form is taken as a study case, and the computed hydrodynamic coefficients, wave exciting forces, and motions by the present method are compared with previous literature experimental data and prior published results. It manifests that the three-dimensional time-domain panel method proposed in this paper has good accuracy.

Numerical simulations of a ship obliquely advancing in calm water and in regular waves

Numerical simulations of the S-175 containership obliquely advancing at constant forward speed in calm water and in regular waves were conducted using a potential flow method. A double-body potential and trailing vortex sheets, which modeled the flow field around the ship obliquely advancing in calm water, yielded transverse forces and yaw moment due to the lift effect. Perturbation potentials describing the free surface flow yielded first-order wave-induced motions and second-order wave loads. Evaluating and then averaging the associated second-order wave loads obtained the steady wave drift forces and moments. Generally, numerical predictions compared favorably to experimental measurements. A systematic analysis demonstrated that, in short beam waves, the transverse wave drift force attained considerable amplitudes, and these amplitudes increased rapidly at larger drift angles. The transverse force due to wave drift effects in beam waves and due to the lift effects in calm water were nearly of equal magnitude. Therefore, when predicting wave drift loads acting on a maneuvering ship, the effect of drift angle should be accounted for.

Development and control of a bicycle robot based on steering and pendulum balancing

This research focuses on the development of an electric bicycle robot which balances itself while moving at a constant forward speed. The bicycle robot is balanced by applying a pendulum mass moving together with heading steering to share the balancing load. The nonlinear dynamics model of a bicycle along with a pendulum is derived from the Euler-Lagrange equation of motion and nonholonomic constraints with respect to translation and rotation relative to the ground plane. This nonlinear model is then linearized around the upright position and combined with the DC motor model to obtain the completed linearized dynamics model. The robot's prototype is designed and built. The linear quadratic regulator (LQR) is implemented on the system to control its balance. The simulation results show that, by varying the control weighting matrix to increase the use of the pendulum's input, the system obtains better performance in both balancing and straight-line path tracking. In addition, the state weighting matrix can be varied to further improve the path tracking performance while still keeping the stability. Real experimental results are also in line with the simulation results.

Road vehicles travelling with time-dependent speed: theoretical study on the directional stability

In this paper, directional stability of road vehicles travelling at time-dependent forward velocity is investigated. The dynamical behaviour of the system is governed by a set of linear ordinary-differential equations with time-varying coefficients. A simple two degrees of freedom (DOF) model is considered, in order to better understand the effects of such a perturbation on the well-established bicycle model, which is frequently used in the literature as a first approach to get useful physical insights on vehicle dynamics. Numerical simulations show significative differences with respect to the prediction of the stability analysis in the case of constant forward speed. A moderately large variation on the forward velocity, indeed, can stabilise the vehicle which is statically unstable. Stability maps are obtained by means of the Floquet theory, with the aim to shed light on the modified vehicle dynamics. A final discussion is provided, which leads to outline the possible practical applications of the present investigation, together with future comprehensive studies.

A 3D direct coupling method for steady ship hydroelastic analysis

Asides from the influence of incoming waves, ships can experience steady motions, such as rigid-body sinkage and trim motions, and flexible-body vertical bending motions, due to a constant forward speed even under calm water conditions. In this paper, a novel approach to analyze steady-ship hydroelasticity, particularly for the steady-ship motions and surrounding steady-wave disturbances, is proposed using a three-dimensional (3D) direct coupling method, based on a higher-order boundary element method (HOBEM) and a higher-order shell finite element method (FEM). Within the linearized framework, a solution method is proposed based on a two-step procedure, using two types of Neumann–Kelvin (NK) linear flow models for the fluid part and a virtual work equilibrium equation for the structural part. The first step is to compute a mean position wave-resistance problem using the modified NK equation, the second step is to solve a perturbed position wave-resistance problem, by employing a classical NK model and a virtual work equation based on the first step’s solution. Detailed mathematical formulation and numerical procedures are described, and a few numerical results are illustrated. These include both rigid and flexible steady-ship motions, Von-Mises stress distributions, and wave-resistance coefficients for Froude numbers ranging from 0.15 to 0.5. Furthermore, the numerical results obtained using the present direct coupling method and a modal-based one are compared.

Effects of wave-field nonlinearity on motions of ship advancing in irregular waves using HOS method

The effects of incident-wave nonlinearity on motions of ships advancing in irregular waves are investigated here in statistical sense. The study is carried out by exploiting the combination of HOS method (High Order Spectral method) and time-domain Rankine source method incorporated with HOBEM (Higher-order Boundary Element Method). In the proposed model, HOS method is employed to simulate nonlinear irregular wave fields in cubic order and Rankine source method incorporated with HOBEM is applied to compute ship wave potential as well as disturbed potential, the equations of motions of ship advancing with constant forward speed in nonlinear waves are further established. Instead of employing simplified steady flow models such as uniform stream, steady ship wave potential is computed beforehand and applied to solve ship motions. Weakly nonlinear scheme considering nonlinear F–K (Froude-Krylov) and restoring forces is adopted.The proposed model is first validated in the case of linear regular and irregular waves via comparisons to experiment data and then applied to three different irregular sea states defined by spectrum with respective BFIs (Benjamin-Feir index). A series of long-time numerical simulations are carried out for both linear wave cases and nonlinear ones, and the statistical properties of nonlinear incident waves and the induced influence on ship motions are investigated and further analyzed. The analysis reveals that with large BFI, the skewness and kurtosis of wave surface elevation manifest departures from Gaussian values and the probability density function (p.d.f.) of the surface elevation performs departures from Gaussian behavior. In nonlinear cases, p.d.f. of instantaneous motions and motion amplitudes as well as exceedance probability of motion amplitudes are notably different from their linear counterparts. Higher possibilities for large motions occur in nonlinear cases.

EVALUACIÓN DE ÁREAS SUSCEPTIBLES A LA INUNDACIÓN POR MAREA DE TORMENTA GENERADA POR HURACANES EN EL ARCHIPIÉLAGO DE SAN ANDRÉS, PROVIDENCIA Y SANTA CATALINA, COLOMBIA

Debido a la posición geográfica del archipiélago de San Andrés, Providencia y Santa Catalina (SPSC),
 esta es la parte del territorio colombiano más expuesto a ser inundado por marea de tormenta generada por
 ciclones tropicales (CT). Entre los peligros asociados a los CT, las inundaciones suelen ocasionar los mayores
 daños. En este estudio se evalúa un escenario extremo de inundación por marea de tormenta asociada a CT
 para establecer las áreas susceptibles a la inundación en este archipiélago. Dada la escasez de CT históricos
 en este archipiélago, se generó una base de datos de CT hipotéticos, los cuales son un conjunto de eventos
 con una velocidad de viento constante (95.17 m/s), una velocidad de traslación constante de 5.87 m/s y un
 radio máximo de viento constante de 56.3 km, para trayectorias con cinco direcciones de aproximación al
 área de interés. Se evaluaron siete trayectorias paralelas para cada dirección, separadas por 6 km. La misma
 metodología fue utilizada para la isla de San Andrés, y separadamente para Providencia y Santa Catalina, se
 usaron diferentes eventos debido a la distancia entre ellas (90km). El modelo hidrodinámico se forzó con
 campos de viento y presión generados a partir de la base de datos de CT hipotéticos para determinar la marea de
 tormenta e inundación por CT en el archipiélago de SPSC. Los resultados obtenidos incluyen la envolvente de
 las envolventes individuales de la distribución espacial del espejo de agua (nivel del agua referido al nivel
 del terreno) de cada evento, reportando el escenario de inundación más conservador generado por marea
 de tormenta de CT en el archipiélago de SPSC. Las áreas propensas a inundación en la isla de San Andrés
 están ubicadas al Este de la misma, principalmente donde se encuentran los puertos de abrigo y en la parte
 Norte donde se encuentran los principales asentamientos humanos. Para la isla de Providencia estas áreas se
 encuentran al Este, en regiones circunvecinas al aeropuerto y al Norte, a lo largo del canal que la separa de la
 isla de Santa Catalina. Para esta última isla, las áreas propensas a inundación se encuentran al Sureste. Bajo
 este escenario de inundación el porcentaje de área afectada sería de 13.39%, 4.24%, y 4.43% para San Andrés,
 Providencia y Santa Catalina, respectivamente.

Numerical study on wave-induced motions and steady wave drift forces for ships in oblique waves

This paper considers numerical predictions of wave-induced motions and steady wave drift forces for ships in oblique waves. The velocity potential around the ship is computed via a time domain Rankine panel method. Based on the computed velocity potential, the six degree of freedom wave-induced motions were computed and then the second order wave loads were evaluated using a near field method. An artificial soft spring system was employed to control horizontal ship motions. The steady longitudinal and transverse wave drift forces and the steady yaw moment were computed for the KVLCC2 tanker at zero forward speed and for the S-175 containership at constant forward speed. Predicted results generally compared favorably to published experimental measurements. A systematic analysis of the effects of the soft spring system on wave-induced motions and steady wave drift forces demonstrated that, although the increased stiffness of the system changed the corresponding motion response of the ships, a spring's influence was negligibly small if its stiffness was weak enough.