An Experimental Investigation into the Eff ect of Bilge Keel Position on Landing Craft Utility Vessels Eksperimentalno istraživanje o učinku položaja ljuljne kobilice na desantnim pomoćnim brodovima

The issue of energy effi ciency in using fossil fuels and reducing the eff ects of greenhouse gas emissions is an urgent problem. So fuel-saving measures, including in the marine transportation sector, are needed, even if only by a small percentage. Landing Craft Utility (LCU) is a type of sea transport for defense matters that requires the addition of a rolling motion stabilizer for the safety and comfort of the ship, cargo, and passengers. The use of roll-damping devices can aff ect the increase in the resistance value of the ship and cause an increase in fuel consumption. The bilge keel is a roll-damping device that is suitable for LCU vessels. The experimental study roll decay tests and resistance tests were carried


INTRODUCTION / Uvod*
The ship will undergo the six degrees of freedom of ship motion in the sea.The rolling motion is the one that aff ects the comfort of the passengers.The roll motion damper system is part of the ship's free movement damper system.Fin stabilizers, interceptor trim tabs, gyroscopic, and bilge keels are some of the ship's rolldamping systems.External factors, such as the condition of the sea, and internal factors, such as the ship's ability to respond to the * Corresponding author movements of the ship itself, infl uent the ship's stability.Thus, the eff ectiveness of the roll motion devices is critical for the comfort of the crew and passengers, as well as the ship's safety.Roll motion is an important mode of motion related to vessel stability in which the ship can roll over if a few other coeffi cients are added [1].The freedom of movement must be restricted for reasons of safety and comfort.As a result, it requires a component of the roll movement damper system.The Bilge keel is one component that helps dampen roll motion.Due to the simple structure, low production cost, and signifi cant roll-damping eff ect, this component is widely used in ships and ship-shaped fl oating bodies.
Bilge keels are recommended as roll dampers because these devices can dampen roll resonance by up to 40% [2], can function eff ectively in overcoming roll motion over a wide range of sea conditions [3] and are optimal on stationary vessels or at low speeds [4].Bilge keel is simple to install and completely passive.When a ship encounters high waves, it positively aff ects anti-rolling performance, especially on ships with a shallow draft [5].The rotational distance between the tip of the bilge keel and the hull's center is important for its roll damping.The installation on the hull can increase total roll damping because it causes a lot of fl ow separation and dissipates the ship's kinetic energy.As a result, the popular placement of a 45-degree bilge keel on the hull or at the bottom and side hull transitions may not be the best confi guration [6].
Due to the bilge keel installation, the roll damping increases, causing the Response Amplitude Operator (RAO) value to decrease, and, as a result, the ship's motion decreases.When the width of the bilge keel is increased compared to the length, the damping coeffi cient increases.The wider the bilge keel, rather than the additional length, is more eff ective at reducing roll motion [7].Large damping is a vortex-induced phenomenon on ships with fl at hull surfaces [8].The large amplitude response area on fl at-hull ships results in greater damping, possibly because the large hull eddies are drawn down the fl at hull.Meanwhile, in the low-amplitude response region, the vortices are not pulled down but move 45° to the side [9].LCU is one type of ship with a dominant fl at hull shape, especially in the middle of the Parallel body.
The LCU Vessel serves nearly the same function as the Landing Craft Tank [10] and the Landing Ship Tank.The LCU is a ship designed to transport large-weight units such as tanks or armored vehicles, heavy vehicles and equipment.As a result, the ship will experience static and dynamic loads, which may aff ect the ship's dynamics.The LCU Vessel research objects have B/T > 3.5 by International Maritime Organization (IMO) provisions for stability.Ships with B/T are classifi ed as special ships for which very few studies are available.Installing of bilge keels on the ship's side aff ects the increase in the root mean square (RMS) value of rolling at low speeds and the decrease at high speeds.Bilge keels perform eff ectively at high speeds [11].The eff ect of hull shape on a planning hull type ship illustrates the diff erence in the total coeffi cient of resistance in various types of planning hulls [12].Maimun et al. [13] conducted experiments to evaluate the application of the bilge keel on the side of the hull based on variations in dimensions and positions, where the installation aff ects increasing the security and safety of the ship, despite providing an increase in resistance that is quite large on high-speed ships.
The installation of a bilge keel as a component of the damping system will inevitably increase total resistance.According to Molland et al. [14], the additional resistance caused by the installation typically ranges from 2% to 3% of the total resistance in the bare hull condition.Meanwhile, according to Liu et al. [15], installing a bilge keel reduces roll motion and can increase total resistance by 1.17%.Moreover, according to Maimun et al. [13], the installation resulted in a 14% increase in resistance at high speeds.A high resistance value will require a large ship thrust, which also requires much fuel and produces many carbon emissions.Lowering the resistance can reduce the Energy Effi ciency Design Index (EEDI), thus showing clear benefi ts for a lower EEDI [16].So, this is an interesting subject, and additional research studies are required to ensure that installing the bilge keel as a damper system does not signifi cantly increase resistance.Previous researchers conducted numerous studies on the bilge keel, but most were done numerically or with Computational Fluid Dynamics (CFD) software to solve the problem.Because of the high cost and completeness of the facilities available, there has been very limited use of experimental methods to determine the bilge keel eff ect.Generally, the analysis of the resistance test results is consistent with the numerical results [17].Ship model test experiments provide the most comprehensive data for predicting ship performance.This method still provides more accurate predictions of ship performance than existing to other methods can deliver [18].
A bilge keel is a passive object considered a resistance appendage [19].This study is an optimization eff ort to reduce roll motion by increasing the eff ectiveness of roll damping and searching for bilge keel positions with the least resistance by analyzing four placement variations and trying to increase roll damping while minimizing resistance.The recommended option is the criteria for the placement position with the greatest roll-damping eff ect and the eff ect of adding the smallest resistance value.
In this study, bilge keels were placed in several transverse positions with fi xed length and width dimensions to investigate the hydrodynamic eff ect on the resistance value and the hydrodynamic eff ect on the roll-damping capability of each bilge keel position.The eff ects were analyzed using the LCU ship model testing method at the Hydrodynamics Laboratory of The National Research and Innovation Agency, Indonesia.Experiments with ship models were carried out in calm water conditions.

The Geometry of Ship Model Test / Test geometrije modela broda
The study was conducted by testing experiments using a scale model of the LCU ship with variations in the placement position of the bilge keel to investigate the hydrodynamic eff ects on the ship's resistance and roll damping.A fl at plate depicting the bilge keel is installed in the selected position, and testing experiments are carried out alternately with several bilge keel position variations.Table 1 shows the dimensions of the ship model used for testing experiments.

Experiment Procedures / Procedure eksperimenta
The experiment was carried out in the test pond of the Hydrodynamics Laboratory -National Research and Innovation Agency Indonesia, which measures 234 meters in length, 11 meters in width, and 5.5 meters in depth.This facility has a carriage with a maximum speed of 9 m/s, a high degree of control and speed accuracy, and a towing force load cell dynamometer to determine the resistance value of ship models.Experiments were carried out based on variations in speed and the position of the bilge keel.The model ship (LCU) is drawn at a certain speed in calm water conditions, and the drag force caused by the model ship moving on the water's surface is measured.The model testing procedure was based on The International Towing Tank Conference (ITTC) guidelines for resistance testing, Recommended Procedures, and Guidelines 7.5-02-02-01 [20].
The results of each resistance test measurement on variations of the bilge keel position were compared to determine the eff ect of the placement on the resistance value [21].
Similarly, the roll decay test was performed in the same pond, with the model in a transverse position in the middle of the pond to avoid back waves caused by the rolling motion of the ship model.Previously, an inclining test procedure was used to determine the distribution of ballast loading based on the position of the center of gravity.The roll decay test is carried out in calm water by applying a few degrees of pressure to the ship model and then releasing it so the ship can roll freely.The test follows the ITTC procedures, Recommended Procedures, and Guidelines 7.5-02-07-04.5[22] for estimating roll damping.

Paint Smear Test / Test razmaza u boji
The placement of the bilge keel must follow the current fl ow pattern around the surface of the ship's hull to achieve good performance and has no signifi cant eff ect on the additional resistance on the ship caused by angular-induced drag on the speed of the ship's motion [23].A paint smear test was performed in calm water conditions at service speed to determine the current fl ow.Because the shape of the current fl ow changes as the speed increases, the paint smear test is carried out at a single operational speed [15], namely a model scale speed of 1,246 m/s. Figure 1 shows the paint smear test.The paint smear test results in forming lines in the paint that are superimposed on each frame station, as shown in Figure 1b.A consistent and inline fl ow pattern was selected from the fl ow lines of water currents around the surface of the ship's hull, which was used as the location for placing the bilge keel, as shown in Figure 2. Four locations were chosen to represent the position of the bilge keel as a research object.Each position is given the identities A, B, C, and D to distinguish it.Position A represents the bottom surface area at a distance of 0.43B from the centerline.Position B is at the bilge angle.Position C is located on the hull side of the model ship, 0.035 meters from the bottom, and position D is above position C approaching the water draft line.Figures 3 and 4 show the location of the bilge keel, which was chosen based on the pattern of water fl ow determined by the paint smear test results.In the longitudinal area, the mounting position is parallel to the midship body, around the midship position.
The dimensions of the bilge keel as a research object are based on existing literature, with a length dimension of 0.37L.Meanwhile, the width is 0.03B.Bhattacharyya [23] recommends a bilge keel length of 0.25 to 0.75 of the ship's length.Meanwhile, Sabuncu T. [24], as discussed again by Liu et al. [15], recommends the bilge keel's length of 0.25 to 0.50 of the ship's length and the bilge keel's width of 0.02 to 0.05 of the ship's width.The eff ect on drag will be minimal if the bilge keel thickness is very thin, such as the sharp tip of a bow ax.Generally, the bilge keel thickness of the ship's hull is very small.With its very thin dimensions, it aims to minimize the eff ect of adding ship resistance [25].

Roll Decay Test / Test ublažavanja valjanja
A series of roll decay tests were performed on a model with a fi xed scale at still water conditions to determine the roll damping coeffi cient [26], [22].The heel movement is performed by applying pressure to one side of the ship model until it reaches an initial angle (5°, 10°, 15°, 20°, and 25°), then quickly releasing the pressure so that the ship model experiences a roll motion.
Figure 5 shows the process of pressing the initial angle as well as the condition of the free model rolling after the initial corner pressure has been released.Other modes of motion are minimized during the test, and the propagation of the test wave edge causes no back wave disturbance.The experiment was repeated several times at each initial angle.Data recording begins before the model is released to ensure that there is no kick at the time of the release of the initial angle until the roll angle decreases or is less than 0.5.Additional testing was performed to obtain a suffi cient number of roll angle peaks.
Data is processed as a roll motion time trace to obtain the roll damping coeffi cient from the decay test, as shown in Figure 6.This roll decay testing procedure is intended to determine the roll damping coeffi cient curve and roll period as a function of roll amplitude.According to Lewandowski [27], the decrease in the amplitude of motion in the roll decay test is defi ned as a polynomial function of the average amplitude as follows: ( In Bertin's extinction coeffi cient , is defi ned as a function of the mean squared amplitude as follows: (2) So obtained: (3) The least squares method is used to calculate the values of a and b, which are shown in a plot of Bertin's extinction coeffi cient curve function ( , ), Where: and (4) The free decay equation of motion can be written as follows: ( Where; is the mass and added mass, B 1 and B 2 are linear and quadratic motion damping, and k is a restoring moment. The integral of equation ( 5) is the amount of energy lost in motion decay, Froude method, for each half period of the roll.So the equation: , where then equation ( 8) can be written as in equation (10): and (10) A curve of extinction is created from the values of and based on the results of the maxima-minima measurements on the roll decay test.The magnitudes of the linear and quadratic damping coeffi cients obtained using the least square method are indicated by the values of a and b in equation (1).The linear and quadratic damping values (B 1 and B 2 ) are obtained from equation ( 10), which will be used for the numerical prediction of the decay motion as in equation ( 5).

Resistance Tests / Testovi otpornosti
The resistance test in this experiment aims to determine how much the position of the bilge keel infl uences the increase in total resistance value.Previously, as described above, a paint smear test was performed to reduce the eff ect of installing a bilge keel on the total resistance value.As shown in Figure 7, the ship model is mounted on a towing carriage outfi tted with a resistance measurement system.The ship model is towed by a Towing Tank carriage, and the force that occurs when the model's speed is stable and the model is only pulled by a resistance dynamometer [28].The test was repeated several times with the condition of the ship model installed bilge keel according to its respective placement position.The model is towed at a speed close to the operational speed in calm water and full-load draft water conditions according to ITTC procedures.The towing process was carried out alternately for each bilge keel position.Resistance is measured using a Towing Force Dynamometer load cell in conjunction with a data acquisition and analysis recorder system.The testing is carried out by established procedures and is audited regularly by the National Standardization Agency.Moreover, test equipment has been calibrated regularly by both internal and external parties certifi ed and authorized to calibrate equipment.It is done to ensure that the test was performed by the procedure.
Several factors infl uence resistance value, including hull dimensions, water density, ship speed, water viscosity, gravity, and fl uid pressure.The total resistance value is stated in formula (11) with a Froude number to measure the resistance of objects moving in water (12).( 11) (12) Where is the total resistance value, is the total resistance coeffi cient of water density, S is the wetted surface area, and V is the velocity.The Froude scale distinguishes between full-size and model ships, while the Froude number is in the test.
Total resistance is the sum of several resistance components, namely viscous resistance (R V ), of which friction resistance (R F ) and pressure resistance, wave resistance (R W ), and air resistance are all components [29].Air resistance is frequently overlooked because its value is insignifi cant.Total resistance is a function of the Reynolds number and the Froude number [30], which is expressed as a formula: (13) The total resistance measured in the resistance test is expressed in the non-dimensional form: (14) The extrapolation procedure for the test results data is carried out by following the Froude hypothesis and the law of similarity to convert the data from the model test results into full scale: (15) With the provision of: The proportionality factor, also known as the form factor (1+k), is used to account for the eff ect of the three-dimensional hull shape.The extrapolation method raises the scale of the resistance results:    The bilge keel also aff ects friction and lift forces, decreasing rolling angular velocity [33].Figure 10 shows the roll decay test's time history for the bare hull model and the variations in the diff erent bilge keel positions.The roll period of variation B is greater than that of the other variations, as shown in the fi gure.Figures 12 and 13 show the extinction curve derived from the roll decay test results.Figure 12 is the result of using the Froude method to fi t the data obtained from the roll decay test results.The values of and in the curve of extinction fi gure are the coeffi cients of the linear and quadratic roll damping components, respectively.Figure 13 shows the value of Bertin's coeffi cient or the N coeffi cient obtained by solving Equation (3).

Coeffi cient of Roll Damping / Koefi cijent ublažavanja valjanja
Figure 12 represents a graph of the curve of the maxima and minima values from the roll decay test results at each variation in the position of the bilge keel placement as in equation ( 1).The curve line on the bare hull condition ship model is at the bottom and shows a decrease in motion amplitude on a small roll decay test.In variation B, however, the roll decay amplitude reduction curve is very dominant.It shows that the placement of the bilge keel has the highest damping coeffi cient in the variation of position B. Variation D can be the alternative option for the placement position because it has a lower extinction curve than variation B but higher than the other variations.The diff erence in total coeffi cient value between the bare hull condition and the placement in position B is estimated at 28.57%.Moreover, the diff erence in the total value of the coeffi cient with variations in the placement of the bilge keel in position D is estimated at 21.27%.
In this study, the damping calculations using the Froude energy method is validated by the relative decrement method referring to studies conducted by Kim et al. [34].As shown in Table 4, the damping value between the Froude energy and relative decrement methods is slightly discrepency.

Comparison of Resistance Value / Usporedba vrijednosti otpornosti
Figure 14 shows the resistance test results in the bare hull and bilge keel installation conditions in each variation of placement position.The resistance was measured at a model test speed of 0.89 -1.60 m/s, or 10 -18 knots on the full scale.The resistance test results on bare hull conditions show the lowest graphic trend.This result is understandable, given that the test model lacks the bilge keel appendages.The fi gure also shows that variations in the placement in position D have the lowest trend of resistance test results in the test conditions with the installation of bilge keel appendages.While in position B shows the greatest trend of the value of the resistance testing results Table 5 shows the data of each bilge keel placement variation's ship model resistance test results.From the results of the ship model resistance test, the calculation of the ship model resistance coefficient is then used in the extrapolation calculation to obtain ship resistance data.
Table 6 presents the results of full-scale ship resistance data for each bilge keel placement variation obtained by extrapolation calculation method using form factor.The Prohaska method is used to obtain the value of the hull form factor so that a form factor value of 1.372 is obtained.The diff erence in average resistance values between positions B and D is 4.76%, which can make position D an alternative option for bilge keel placement when the results of the damping roll test are also considered.Compared to bare hull conditions, adding the resistance value due to the placement in position D results in an average diff erence of 3.66%.While the addition of the resistance value due to the placement of the bilge keel in position B compared to the average bare hull condition is 8.84%.Table 7 presents the Eff ective Horse Power data for each bilge keel placement variation.Position B signifi cantly impacts the resistance value at all speeds (10 knots to 18 knots).As a result, the eff ective power required to move the ship is the greatest on average compared to variations in the position of other placements.While the minimum average eff ective power is in position C.This bilge keel is placed on the side hull close to the bilge area.At a speed of 16 knots, the eff ective power requirement in variation B is 2819 kW.At the same time, the eff ective power requirement without it is 2560 kW.The eff ective power requirements of position B increase by up to 10.12% compared to conditions without it.When in position C, the eff ective power requirement at an operational speed of 16 knots, compared to the condition without the bilge keel, increases by 36 kW or 1.41%.The eff ective power in each variation is shown in Figure 16.

Figure 1 Figure 2
Figure 2 Marking fl ow pattern lines from the paint smear test as the location for installing the chosen bilge keel.Slika 2. Markiranje linija uzoraka iz testa razmaza u boji kao lokacija za instaliranje odabrane ljuljne kobilice

Figure 3a Figure 4 a
Figure 3a Variations in the placement of the bilge keel based on the results of the paint smear test.Slika 3a.Varijacije smještaja ljuljne kobilice koje se temelje na rezultatima testa razmaza u boji

8 )Figure 5 Figure 6
Figure 5 The process of pressing and releasing pressure on the test model.Slika 5. Proces pritiska i oslobađanja pritiska na testnom modelu

Figure 7 17 )
Figure 7 Resistance testing installation scheme.Slika 7. Shema instalacije testa otpornosti of ship resistance, = Coeffi cient of model resistance, (1+k) = Form factor, = Coeffi cient of ship friction, m = Coeffi cient of model friction, and = The additional resistance coefficient for ship model correlation.Furthermore, the Prohaska method can be used to fi nd out the value of the hull form factor [31].This method is based on ship model testing, where a ship model is towed in a towing tank by the value of Froude Number (Fn) in the range 0.1 to 0.2 to obtain the resistance coeffi cient of the model and the friction coeffi cient of the m model.So that a plot can be made, as shown in Figure 8.The form factor value obtained is at the intersection of the / and F n 4 / axes.

Figure 9 Figure 9 Figure 10
Figure9represents the roll decay test results' roll period for ship models with and without bilge keels with diff erent placement positions.The fi gure shows that the roll period has no signifi cant diff erence in all bilge keel position variations.Whereas the period for the bare hull roll condition is 0.90102 seconds, the period at full scale is 5.2096 seconds, the shortest roll period of all variations.The test results show that almost the same roll period is possible because the center of gravity of the VCG (Vertical Centre of Gravity) and the radius of the gyration of the roll is the same.Diff erences can occur due to the length of the radius or distance of the bilge keel position from the center of gravity, both of which can aff ect the damping moment induced by the bilge keel[32].

Table 2
shows the results of the roll decay test for each roll damping component.The table shows that variations in the position of diff erent bilge keel placements indicate diff erent roll-damping coeffi cient values for the linear and quadratic components.Position B variation has linear and quadratic component values that are very dominant compared to other variations.While the D variation has a fairly large linear component value, it has a low quadratic component value.

Table 5
Resistance test results of ship model Tablica 5. Rezultati testa otpornosti na uzorku brodaTo obtain the damping values B 1 and B 2 from the relative damping method, the following equations can be used: and