Dynamic Sinkage Research Articles

Experimental study of a high-speed suspension hexamaran in calm water

This research proposed a high-speed hexamaran with a suspension system composed of springs and joints as a new type of multihull. To investigate its hydrodynamic characteristics in calm water, numerous model tests for two programs were carried out for the volumetric Froude number from 0.6 to 7.68. In one program, known for flexibility, there is a hexamaran equipped with a suspension system, while in the other program, known for rigidity, there is a hexamaran with no suspension system, but clamps instead of springs. Motion parameters like trim angle, dynamic sinkage, wetted surface, hydrodynamic lift, and resistance were determined, and the flow field was further analyzed. Based on the results of comparison experiments, it can be concluded that the suspension system of the hexamaran can change the ratio of each resistance component in the total resistance, improve the motion attitude and increase the wetted surface area at high speeds, which can avoid porpoising behavior and improve longitudinal stability. The high-speed hexamaran with a suspension system performs better than that with no suspension system when traveling at high speeds.

Prediction of the impact of biofouling roughness on a full-scale planing boat performance using CFD

This study investigates the crucial role of surface roughness caused by biofouling in contributing to increased drag in fast planing vessels. Through rigorous computational fluid dynamics (CFD) simulations using a full-scale reference hull, the impact of surface roughness on planing hull performance is examined. The results show that heavy slime roughness on the hull surface causes a significant increase in total resistance, ranging from 10% at low speeds to 80% at high speeds. Skin friction was identified as the most affected component of resistance, with additional changes in residual resistance. Although the change in residual resistance is relatively small, they give rise to dynamic phenomena such as variations in pressure distribution, wave elevation, and wave making formation. The study also explores the influence of surface roughness on dynamic lift forces, observing an increase in upward friction forces but ultimately concludes that overall hull performance was hampered due to the disproportionately higher increase in resistance caused by roughness (biofouling). Changes in dynamic trim, dynamic sinkage, and dynamic wetted surface area due to this roughness are also discussed.

Analysis of the double steps position effect on planing hull performances

Along with developing high-speed craft technology, the planing hull is growing with modifications for better performance. One such technology is stepped hull, both single and double. Planing hull with steps allows the boat to run at a relatively low drag-lift ratio with lower frictional resistance due to reduced wetted area. In this study, the hull was modified with variations in the position of the double steps, which aimed to determine the effect of the first and second step positions on the total resistance, dynamic trim, and dynamic sinkage generated by computational fluid dynamics (CFD). Based on the analysis results, variations in the position of the stepped can change the hull performance. Shortening the distance between the two steps and moving both rearwards toward the transom can lower the total resistance. The dynamic trim and dynamic sinkage decreased as the position of the two steps was shifted further forward. An equation created in a non-dimensional form relates the positions of two steps to the desired results of total resistance, dynamic trim, and dynamic sinkage, namely: {(x1-x2)/L + (x1x2)/(LB)} × Fr∇, where x1 is distance the first step from transom, x2 is the distance of the second step, L is the length of the boat, B is the beam of the boat, and Fr∇ is the volume Froude number.

Research on contact model of track-soft sediment and traction performance of four-tracked seabed mining vehicle

In response to the global demand for commercial mining of deep-sea manganese nodules, the four-tracked mining vehicle (FTMV) with excellent tractive and travelling performance is crucial for constructing the entire commercial system. In order to better evaluate the tractive and travelling performance of the FTMV, the dynamic sinkage phenomenon concerning soft seabed and front-rear track effect are proposed. Meanwhile, the pressure-sinkage and traction force-slip rate mathematical models are established based on terramechanics theory. The quantitative calculation was carried out based on the model and found that the grouser's parameters affect the sinkage depth of the FTMV. In the range of 10 ~ 20 cm, the height of the rectangular grouser increases by 1 cm, which will lead to a 0.15 cm of sinkage depth decreased. When the ratio of rectangular grouser thickness to track shoe length is between 0.1 and 0.3, every 1% increase in this ratio will decrease a 0.13 cm of sinkage depth. The maximum traction force obtained by the FTMV from the soft seabed sediment was 54.5 kN, which occurred when the slip rate of the track was 16%. Moreover, due to the front-rear track effect, the traction force of the front and rear tracks showed a significant difference, the front track contributed 32.4 kN, and the rear track contributed 22.1 kN when the traction force reached the peak. Furthermore, the optimization directions for track parameters were suggested according to the relationship surface of the track dimensional parameters-slip-traction. It was found that each track was 4.2 ~ 6 m long, with a length-width ratio of 3.2, which was conducive to the reduction of track slip and got relatively much traction force from soft seabed sediment. The simulation results confirm dynamic sinkage and front-rear track effect and verify the accuracy of the new traction force-slip rate model, providing a valuable reference for the development of commercial deep-sea mining vehicles.

Numerical Prediction of Hydrodynamic Performance of Planing Trimaran with a Wave-Piercing Bow

The central hull is the most important structure in the planing trimaran. In order to gain insight into the relationship between hydrodynamic performance and main hull shape, experimental tests and numerical simulations were carried out for volume Froude Number (FrΔ) ranging from 1.31 to 4.98. Dynamic sinkage and trim in the Dynamic Fluid Body Interaction (DFBI) six-degree-of-freedom model were considered. A validation study carried out by comparison of experimental test results with numerical results showed good consistency. To analyze the process of tunnel penetration and pressure change at the bottom of the boat, numerical simulation results for free surface, bottom streamline, and pressure distribution around the hull are given. A large triangular high-pressure area was observed in the front of the main hull for all volume Froude numbers. Consequently, the central drainage body, in reference to the profile of single planing craft with distinctive resistance performance, was redesigned into a wave-piercing shape. Total resistance, sinkage, and trim angle of the new model were then predicted by numerical method. The results show that the central drainage body has a significant impact on the hydrodynamic performance of the planing trimaran. Furthermore, the wave-piercing shaped main hull has a drag reduction effect.

A Numerical Method for Calculation of Ship–Ship Hydrodynamics Interaction in Shallow Water Accounting for Sinkage and Trim

AbstractSinkage and trim, which often occur to ships moving in shallow water, do not only have an effect on the ship–ship hydrodynamic interaction forces but also increase the risk of grounding. Potential flow-based online calculation of ship–ship hydrodynamic interaction forces without accounting for dynamic sinkage and trim is able to capture the hydrodynamic interaction effects with fair accuracy; however, there are still discrepancies in many cases, especially in the case of shallow water. An algorithm based on the potential theory has been devised for real-time simulation of the hydrodynamic interaction between two ships in shallow water accounting for sinkage and trim. The shallow water condition is modeled using the mirror image method. The sinkage and trim are solved iteratively based on the principle of hydrodynamic balance, where a mesh trimming procedure is carried out when the waterline is changed. Simulations are performed with and without accounting for the sinkage and trim, and comparison with experimental results shows a fair agreement.

Analysis of the flow conditions between the bottoms of the ship and of the waterway

A physical model test was performed, to which a scaled model (1:40) was designed and constructed to carry two Laser Doppler Velocimetry sensors and provide optical access at different locations along the hull to detect the stream close to bottom of the hull and resolving the boundary layer flow at the hull. The measurement campaign was conducted in a shallow water towing tank and included a range of water depths and ship speeds such that the influence of each became analysable. The purpose of the experiment is to provide validation data to further corroborate a numerical approach and to gain deeper insight in the flow conditions in the gap flow underneath the vessel in very shallow water. In addition the extension of the effect of propulsion on the dynamic sinkage and trim in very shallow water was checked. Even though for one particular ship design and restricted to model scale 1:40, the results are regarded a valuable basis for further investigations on this phenomenon.

Effect of gravity in wheel/terrain interaction models

AbstractPredicting the motion of wheeled robots in unstructured environments is an important and challenging problem. The study of planetary exploration rovers on soft terrain introduces the additional need to consider the effect of nonterrestrial gravitational fields on the forces and torques developed at the wheel/terrain interface. Simply reducing the wheel load under Earth's gravity overestimates the traveled distance and predicts better performance than is actually observed in reduced‐gravity measurements. In this paper, we study the effect of gravity on wheel/terrain interaction. Experiments were conducted to assess the effect of reduced gravity on the velocity profile of the soil under the wheel, as well as on the traction force and sinkage developed by the wheel. It was shown that in the velocity field of the soil, the decay of the tangential velocity component becomes gradual with reducing gravity, and the decay of the normal to rim velocity is slower in Lunar gravity. It was also found that wheel flexibility can have an important effect on the dynamics as the contact patch and effective radius vary periodically. These results were then used together with traditional semiempirical terramechanics models to determine and validate the simulated drawbar pull values. The developed simulation model includes the effect of wheel flexibility, dynamic sinkage, and gravity.

Do lunar rover wheels sink equally on Earth and Moon?

There has been a long discussion on how the low-gravity effects that LRUs (Lightweight Rover Units) on the Moon will experience, can affect mission planning and surface operations. In particular, the sinkage observed when regolith soil layers collapse under a normal wheel load has been an important source of contradiction in the field of Terramechanics in the last years. In this short report we review the different authors opinions on this topic, examining in detail their definition, methods, and results.The sinkage of static wheels under lunar gravity could be less than on Earth (fixing body dimensions and soil), given the decreased normal load experienced by loose regolith. This is known as static sinkage. On the other hand, if the wheels are in permanent rotation, the effect of poor soil’s bearing capacity in lower gravities can lead to a deeper intrusion of the wheels as compared to the case on Earth (dynamic sinkage). The dynamic and static sinkage are low in lunar gravity and have more or less similar values in case the wheel surface is plane (smooth). However, if the wheel under test incorporates grousers, the lugs motion and soil’s bearing capacity would make the separate effect of dynamic sinkage to be much larger than in plane wheels. Finally, we evaluated a method that (at difference from previous models), can express more accurately the effect of static and dynamic sinkage in different gravity environments. The novel semi-empirical approach to estimate wheel penetration into soils assumes a dependency from wheel parameters, slip and terrain mechanical properties, demonstrating an improved goodness-of-fit (R2) from 91 to 99%, distinctly in a gravity interval of 16 up to 2 times the gravity on Earth.

CFD-based numerical simulation of pure sway tests in shallow water towing tank

The pure sway tests in shallow water towing tank are numerically simulated for the DTC container ship model by using an unsteady RANS solver. The verification study in terms of mesh and time-step convergence for the assessment of numerical error and uncertainty is conducted. The hydrodynamic forces, the hydrodynamic derivatives and the reconstructed hydrodynamic forces from the resultant hydrodynamic derivatives are validated against experimental data in very shallow water, and a satisfactory agreement is obtained. Using the validated numerical method, systematic simulations are carried out considering the influences of water depth, ship speed and dynamic sinkage and trim on the hydrodynamic quantities during the pure sway tests. The effects of depth restrictions on the hydrodynamic forces are expressed by polynomial regression equations with the corresponding ratios of hydrodynamic derivatives in shallow water to those in deep water. Besides, the side wall effects of tank in very shallow water that affect significantly the results of model tests for ship speed close to the Schijf's limiting speed are analyzed. From the present study, the ability of CFD method in evaluating the shallow water effect and side wall effect on the pure sway test results in shallow water towing tank is demonstrated.

Experimental investigation of the wetted surfaces of stepped planing hulls

In the current study, experimental tests are conducted to evaluate the hydrodynamic characteristics and the bottom wetted surfaces of the planing hulls equipped by one transverse step. For this purpose, total resistance, dynamic trim angle, dynamic sinkage, reattachment lengths of the separated flow and forebody and aftbody wetted areas are quantitatively measured at different geometrical parameters of the step and hull velocities. Moreover, the bottom wetted surfaces are qualitatively investigated by analyzing the underwater photographs. Our experimental results are also compared by archival data with good accordance. Based on our experimental observations, dynamic trim angle and dynamic sinkage are enhanced by increasing in the height of the step and decreasing the longitudinal position of step from transom. However, lower total resistance is achieved for greater height of the step. In addition, total wetted area is enhanced by decreasing the step height and hull velocity. However, larger total wetted area is detected by an increase in the longitudinal distance of the step from transom. Finally, we formulated the wetted areas of one step planing hull according to the reattached flow patterns.

Numerical Prediction of Propeller-Hull Interaction Characteristics Using RANS Method

Abstract The paper presents the results of computational evaluation of the hull-propeller interaction coefficients, also referred to propulsive coefficients, based on the unsteady RANS flow model. To obtain the propulsive coefficients, the ship resistance, the open-water characteristics of the propeller, and the flow past the hull with working propeller were computed. For numerical evaluation of propeller open-water characteristics, the rotating reference frame approach was used, while for self-propulsion simulation, the rigid body motion method was applied. The rotating propeller was modelled with the sliding mesh technique. The dynamic sinkage and trim of the vessel were considered. The free surface effects were included by employing the volume of fluid method (VOF) for multi-phase flows. The self-propulsion point was obtained by performing two runs at constant speed with different revolutions. The well-known Japan Bulk Carrier (JBC) test cases were used to verify and validate the accuracy of the case studies. The solver used in the study was the commercial package Star-CCM+ from SIEMENS.

Computational fluid dynamics prediction of hydrodynamic forces on a manoeuvring ship including effects of dynamic sinkage and trim

Understanding the manoeuvring performance of a ship requires accurate predictions of the hydrodynamic forces and moments on the ship. In the present study, the hydrodynamic forces and moments on a manoeuvring container ship at various rudder and drift angles are numerically predicted by solving the unsteady Reynolds-averaged Navier–Stokes equations. The effects of dynamic sinkage and trim on the hydrodynamic forces are first investigated together with a grid dependency study to estimate the numerical error and uncertainty caused by grid discretization, and with a validation study combining the experimental data. The results show that the effect of dynamic sinkage and trim is non-negligible, since including it improves the hydrodynamic force predictions and reduces the numerical error and uncertainty, and the averaged error and uncertainty are smaller than the other computational fluid dynamics results where sinkage and trim were fixed with given values from model tests. Therefore, it is included in the subsequent systematic simulations regarding the influence of rudder and drift angles. The computed forces, moments and rudder coefficients at different rudder and drift angles on the container ship are compared with the benchmark model test data. From the computations, all the predicted quantities are in satisfactory agreement with the experimental data. The details of the flow filed and hydrodynamic forces, such as pressure distributions, transverse force distributions along the hull, velocity contours, streamlines and wave patterns are presented and discussed, and a deep insight into the physical mechanism in the hydrodynamic forces on a manoeuvring ship is obtained.

Automatic Adaptation of Tire Pressure According to Operating Conditions

The off-road vehicles have much higher rolling resistance due to tire sinkage. This paper presents a proposed system for automatic adaptation for tire inflation/deflation, according to operating conditions. The tire inflation pressure is manually changed by the driver to some prefixed pressure values. The proposed control system is based on calculating the instantaneous wheel slip ratio. As the slip ratio increases, the tire pressure decreases automatically to increase the contact area and to decrease the dynamic sinkage and vice versa. An algorithm for the control strategy is developed. The proposed system provides a continuous monitoring of tire pressures inside the tire and then to inflate/deflate according to terrain types. The results show that a low inflation pressure has a considerable effect on the net traction ratio where it improves the performance by 20% and the buffed tire has a better traction than lugged tire on sand.

Improved explicit-form equations for estimating dynamic wheel sinkage and compaction resistance on deformable terrain

The contact mechanics for a wheel and deformable terrain are complicated owing to the rigid–flexible coupling characteristics. This paper presents explicit-form analytical equations to estimate the wheel sinkage and compaction resistance of autonomous robots that require high-accuracy terramechanics models. The limitations of Bekker's equations were analyzed both theoretically and through experiments on slip/skid sinkages. The normal and shear stress distribution equations of the Wong–Reece model were improved through the use of a variable sinkage exponent to reflect the dynamic sinkage of robot wheels moving on deformable terrain. The improved integral-form equations were simplified to derive closed-form analytical equations for estimating the normal force, drawbar pull, and driving resistance moment; these were then used to derive explicit analytical equations to estimate the wheel sinkage and compaction resistance as functions of the vertical load, terrain parameters, wheel parameters, and sinkage exponent varying with the slip ratio. The experimental results for the contact mechanics of six different types of wheels and deformable terrain were used to verify the accuracy of the model.

부이 특성에 따른 궤도 차량 동적 거동

This paper focuses on the dynamic responses of a tracked vehicle crawling on extremely cohesive soft soil, each side of which is composed of two parallel tracks. The tracked vehicle consisted of 2 bodies. One body is the tracked vehicle body, which is assumed to be a rigid body with 6 DOFs. The other body is the buoy body. The two bodies are connected by a revolute joint. In order to evaluate the travelling performance of a 7 DOFs vehicle, a dynamic analysis program for the tracked vehicle was developed using Newmark's method and the incremental-iterative method. The effects of road wheels on the track and soil are not taken into account. A terra-mechanics model of extremely cohesive soft soil is implemented in form of relationships: normal pressure to sinkage, shear resistance to shear displacement, and dynamic sinkage to shear displacement. Pressure-sinkage relationship and shear displacement-stress relationship should represent the non-linear characteristics of extremely soft soil. Especially, since the shear resistance of soft soil is very sensitive to shear displacement, spatial distribution of shear displacement occurring at the contact area of the tracks should be calculated precisely. The proposed program is developed in FORTRAN.

New perspective on characterizing pressure–sinkage relationship of terrains for estimating interaction mechanics

Conventional pressure–sinkage models of characterizing bearing properties of terrains for vehicles are semi-empirical with poor adaptability and extrapolation ability; definitions of parameters are nonintuitive. The purpose of this paper is to provide more general and high-fidelity models for terrain characterization to satisfy the high requirements of autonomous wheeled vehicles, which should “understand” terramechanics in an accurate way on off-road terrains. Based on the analysis of conventional models and experimental results, new perspective and related equations on characterizing bearing performance are proposed. The stiffness modulus which is an intrinsic terrain parameter with determined unit of Pa/m has dominant role in governing the bearing performance. The sinkage exponent is variable as the function of various influential factors. Numerical analysis verifies that the new model with two meaningful parameters has high goodness of fit with Bekker’s model. Experimental results verifies that the new model using constant stiffness modulus and variable sinkage exponent reflects key factors such as dynamic sinkage, dimension effect, payload effect, and lug effect with high fidelity, which are not considered by the conventional models. This concept could be applied to various terrains and conventional vehicles.

Linear and Nonlinear Sectional Loads With Potential and Field Methods

A Rankine source method is applied to predict linear and weakly nonlinear sectional loads of a modern container ship. The method uses solution in the frequency domain, linearized with respect to wave amplitude about the nonlinear steady flow due to forward speed, which accounts for the nonlinear free-surface conditions, ship wave, and dynamic trim and sinkage. Weak nonlinearity of the sectional loads in waves (e.g., hogging-sagging asymmetry) is taken into account by pressure extrapolation and integration up to the estimated actual water line. The sectional forces obtained with this method are compared with the results of other methods, including (1) linear Rankine panel method, where flow due to waves is linearized about the double-body flow, (2) linear zero-speed Green function method with correction for forward speed, (3) fully nonlinear simulations based on field-based solution of Reynolds-averaged Navier–Stokes (RANS) equations, and (4) model tests. Comparison with RANS solution and model tests shows, that the proposed method can accurately predict sectional loads for small to moderate wave heights.

수치해석을 이용한 연약지반 4열 강체 무한궤도 차량의 최적 선회비 연구

This paper considers the steering characteristics of a four-row tracked vehicle crawling on extremely cohesive soft soil, where each side is composed of two parallel tracks. The four-row tracked vehicle (FRTV) is assumed to be a rigid body with 6-DOF. A dynamic analysis program for the tracked vehicle is developed using the Newmark-<TEX>${\beta}$</TEX> method based on an incremental-iterative scheme. A terra-mechanics model of an extremely cohesive soft soil is implemented in the form of the relationships of the normal pressure to the sinkage, the shear resistance to the shear displacement, and the dynamic sinkage to the shear displacement. In order to investigate the steering characteristics of the four-row tracked vehicle, a series of dynamic simulations is conducted with respect to the distance between the left and right tracks (pitch), steering ratios, driving velocity, reference track velocity, lengths of the tracks, and properties of the cohesive soft soil. Through these numerical simulations, the possibility of using a kinematic steering ratio is explored.

Development of an In-Door Tire Soil Bin Testing Facility Experimental Setup

The field testing may give the real conditions, but the uncontrolled environment may affect the results. In a soil bin, all driving conditions are controlled. Therefore a scaled soil bin was designed and established at MTC. The single wheel tester concludes the dynamic weight equal to that measured statically. Using an indoor soil bin, and measuring sensors the instantaneous wheel speed representing the theoretical speed and free wheel speed representing the actual speed were measured and recorded. Using the signals from two speed sensors, the instantaneous wheel slip is calculated. Also the dynamic sinkage due to wheel motion is measured using ultrasonic sensor. This paper presents a detailed experimental measuring of instantaneous wheel slip and dynamic sinkage on two surfaces; soft dry sand and hard surface. A theoretical control algorithm was developed and implemented. The control system using rotary valve and pressure sensor to control the tire pressure (inflation/deflation) based on the wheel slip ratio and dynamic sinkage.