Model Design for Further Spray Deflector investigation

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DEGREE PROJECT,

SECOND CYCLE, 30 CREDITS

STOCKHOLM, SWEDEN 2020

Model Design for Further

Spray Deflector investigation

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Abstract

Planing hull is one solution to break the speed barrier of conventional hull, but as the boat reaches a high speed, massive whisker spray will be developed and attached to the hull, which causes a notable resistance increase. A Swedish company Peterstep invented an innovative spray deflector that can deflect the spray backwards and harvest kinetic energy from the spray.

In the 2019 spray deflector project, many tests were done in Davison Laboratory Towing Tank, and there is a trim angle difference between plated and non-plated hulls. To investigate possible reasons, more tests are implemented in this project. According to the test results, the reason is determined as the different roughness of the hull and bottom due to differences in materials. Also, the tape for sealing the seam between hull and bottom plate affects the sharpness of the hard chine, thereby hindering the flow separation.

The model used in previous experiments is no longer suitable for the further investigation. The modular design caused the different running position of plated and non-plated hull. In addition, the hull is too slender for the wave test. Therefore, a new model is needed to satisfy the new objectives of experiments. In this paper, the detailed design is surrounded by design aims and restrictions, such as increase spray resistance and avoid porpoising.

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Abstrakt

Planande skrov är en lösning för att bryta hastighetsbarriären hos ett konventionellt skrov, men när båten når hög hastighet kommer omfattande whisker spray att utvecklas på skrovet, vilket orsakar en anmärkningsvärd ökning av motståndet. Ett svenskt företag Peterstep har utvecklat en innovativ sprutdeflektor som kan avleda sprayen bakåt och skörda kinetisk energi från sprayen.

Under sprutdeflektorprojektet 2019 gjordes många tester i Davison Laboratorys släpränna och det noterades en oönskad trimvinkelskillnad mellan modeller där skrovet byggts i en del eller med ett steg som fyllts igen med en bottenplatta. För att undersöka möjliga skäl till detta implementeras nya tester i detta projekt. Enligt testresultaten bestäms orsaken som skrovets och bottenplattans olika jämnhet på grund av materialskillnader. Även tejpen för tätning av sömmen mellan skrov och bottenplatta påverkar skärpan i slaget och hindrar därmed flödets avlösning.

Modellen som använts i tidigare experiment är inte lämplig för fortsatt utredningen. Den modulära designen orsakade olika gångläge beroende på hur skroven hade byggts upp. Dessutom är skrovet för smalt för vågproven. Det behövs därför en ny modell för att uppfylla målen med experimenten.

I det här arbetet har designen ytterligare designmål och begränsningar, som att mäta sprutmotståndet och att undvika porpoising.

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Acknowledgement

I would like to thank Bogdan Molchanov, Svante Lundmark, Fran Osmak, Luca Castaldi. Your great previous work on the spray deflector gives a great introduction of this technology and lets me keep up with the project more quickly.

I am deeply indebted to my supervisor, Mirjam Fürth, whose illuminating instruction and advice have guided me through every step of experiments and writing of this thesis. She gave me lots of expert suggestions as well as great helps.

I am profoundly grateful to Jack Bonoli, Mathew Green, Madeline Cohen. You give me massive help and support during the entire project. It is my pleasure to work with you.

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Abbreviations and Symbols

Acronyms

CFD Computational Fluid Dynamics CNC Computer Numerical Control

HSC High-Speed Craft

ITTC International Towing Tank Conference LCG Longitudinal Center of Gravity

PVC Polyvinyl Chloride SLR Speed to Length Ratio VCG Vertical Center of Gravity Greek symbols

𝛼 Angle between keel and stagnation line [𝑑𝑒𝑔] 𝛽 Deadrise angle of the hull [𝑑𝑒𝑔]

𝜀 Thrust inclination relative to the keel [𝑑𝑒𝑔] 𝜃 Angle between spray edge and keel [𝑑𝑒𝑔] 𝜆 Mean wetted length to beam ratio [−] Δ𝜆 Increase in 𝜆 due to spray [−]

Δ Hull displacement [𝑁]

∇ Displaced volume by the hull [𝑚3] 𝜌 Water density [𝑘𝑔/𝑚3_]

𝜏 The trim angle between the keel and still water surface [𝑑𝑒𝑔] Symbols

b Beam of the hull [𝑚]

𝐶d Aerodynamic drag coefficient [−] 𝐶𝐹 Skin friction coefficient [−]

𝐶𝐿𝛽 Lift coefficient of a hull with deadrise [−] 𝐶𝐿𝑜 Lift coefficient of a flat plate [−]

𝐶𝑝 Center of pressure on the hull bottom [𝑚] 𝐶𝑣 Beam Froude number [−]

D Diameter of the propeller [m]

e Lever arm between the pressure force and VCG [m] 𝑓 Lever arm between the thrust axis and VCG [𝑚] 𝑓a Lever arm between Ra and VCG [m]

𝑓f Lever arm between the friction force and VCG [m]

𝐹𝑛 Froude number [−]

𝐹𝑛∇ Volumetric Froude number [−] 𝑔 Acceleration due to gravity [𝑚/𝑠2] KT Thrust coefficient of the propeller [−] KQ Torque coefficient of the propeller [−] 𝐿𝑐 Chine wetted length [𝑚]

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viii 𝐿oa Length overall [𝑚]

𝐿wave Length of wave [𝑚] 𝐿𝑤𝑙 Waterline length [𝑚]

n Rotation speed of propeller [r/s]

𝑁 Normal force on the hull bottom due to pressure [𝑁] 𝑅air Aerodynamic resistance [𝑁]

𝑅𝑒 Reynolds number [−] 𝑅𝑓 Frictional resistance [𝑁]

𝑅PM Revolution speed of propeller [r/min] 𝑅𝑠 Spray resistance [𝑁]

𝑇 Thrust force [𝑁]

𝑉 The speed of the hull [m/s]

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1 Introduction

High-speed crafts (HSC) are widely employed in civilian use for recreation, racing and transport and in search and rescue. The high speed that conventional boats cannot achieve is a paramount feature. For example, rescue boat needs to reach the accident location as quickly as possible to avoid any personnel death, or a patrol with high speed is necessary for the coast guard to effectively prevent offshore illegal activities. The performance of HSC is outstanding in many areas and its demand grows notably in latest several years (De Marco, 2017).

Nevertheless, one of the drawbacks is the expensive fuel cost to achieve the high speed. The resistance of the boat rises exponentially with increasing speed at high speed range (Harvald, 1992). It means more fuel must be consumed for propelling the boat. In previous studies, many solutions and concepts were proposed for reducing resistance and validated by numerical method and experiments (i.e. stepped hull (Clement, 1964; De Marco, 2017; Savitsky and Morabito, 2010), trim tab (Sakaki et al., 2019), interceptor (Avci and Barlas, 2019; Sakaki et al., 2019) and spray rail (Clement, 1964; Seo et al., 2016)). The main principle of these technologies is to adjust running position or reduce the wetted or spray area, thereby reducing the frictional resistance. These technologies are commonly applied in HSC nowadays and lead to HSC’s performance improvement and operation cost cut-down. From the environmental point view, less contaminated gas and carbon dioxide are discharged into the atmosphere.

A novel concept, spray deflector, has been proposed by a Swedish company Petestep AB. It has different geometry and configuration from the conventional spray rail. It can not only deflect the whisker spray but also harvest kinetic energy from the spray (“Petestep AB,”). CFD simulations (Bjersten and Danielsson, 2014; Olin, 2017) and model tests (Molchanov et al., 2019; Osmak, 2019; Wielgosz, 2018a) have proved it has remarkable performance in resistance reduction. Moreover, experimental results indicate spray deflector can mitigate vibration and vertical acceleration of the hull, which could be a severe threat to crew’s comfort and safety (Bjersten and Danielsson, 2014).

1.1 Aim and Objective

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summer of 2020, a second free model was designed, this will be built over winter break 2020/2021 by students continuing on the project. This thesis therefore has three objectives, through which the effect of spray deflector technologies is investigated:

1. Plated and non-plated hull tests conducted in the Davidson Laboratory towing tank.

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2 Background

2.1 Wave resistance barrier

Water will be pushed away from the hull when a surface vessel moves in the water. The interaction between water and the hull generates waves, and the wave pattern will change with the speed of the boat. The longer the hull, the longer the wave generates, the higher wave propagation velocities Basically, the relationship between wave speed and wavelength can be expressed by the speed-length ratio (SLR, speed in knots divided by square root of length in feet) (Molland et al., 2011).

= wave 1.25 wave

V SLR

L = (1)

As the vessel exceeds a SLR of 1.25, wave crest is created at the bow and the trough is created at the stern. The hull starts to climb the bow wave while the wave tends to push the vessel back to the trough. As a result, wave-making resistance starts to grow dramatically (Rosén, 2004).

Higher installed engine power enables displacement hull to drive faster to achieve a speed-length ratio over 1.25. However, it is prohibitively expensive to do so. Therefore, the SLR of 1.25 is generally regarded as the theoretical speed limit for conventional displacement hulls (Savitsky, 2003).

One option to break the barrier of wave propagation speed is to use a planing hull. This hull form can generate a significant amount of hydrodynamic lift at high speeds and lift the forepart of the boat out of water. The frictional drag, thus, is decreased due to a smaller wetted surface area. The resistance curve of an HSC (Figure 1) shows that the optimal operational condition for planing hull is at the range over planing speed, and their hull form is disadvantageous below planing speeds. Once the hull crosses over the bow crest, the increase rate of wave resistance will begin to slow down critically (Squire, 1957).

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2.2 Planing mode

2.2.1 Flat plate

According to Archimedes’ principle, the weight of a boat at rest state is balanced by the hydrostatic lift. As the boat starts to move, it will push water out of the way, so a hydrodynamic force is acted on the hull by water. The pressure distribution of the hull changes as speed, and the hull will be lifted out of water when the boat reaches a certain speed. A hull predominately supported by hydrodynamic pressure is considered to be planing (Larsson and Eliasson, 1994).

The pressure distribution on a flat plate is shown in Figure 2. The small arrows indicate the direction of flow, and the point close to midship is stagnation point where the water flow hits the hull bottom perpendicularly. The flow then separates into two parts at the stagnation point. One goes backwards, and its direction gradually becomes parallel on its way to the bottom. Another one goes forwards, breaks into spray, and finally falls back to the water surface. The velocity of flow at the stagnation point is zero, which means all the kinematic energy of flow is transformed into pressure at this point. Thus, the hydrodynamic pressure is the highest at the stagnation point and drops to zero at bow and stern (Larsson and Eliasson, 1994). Pressure distribution on the bottom causes the bow is lifted and the stern sinks into the water, which allows a boat plan on the water surface.

Figure 2: Pressure distribution on a flat plate (Savitsky, 1964)

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Figure 3: Force on a flat planing plate (Larsson and Eliasson, 1994) 2.2.2 Planing hull

V shape is typical bottom geometry for planing hull. The angle between bottom and horizontal plane is called deadrise angle. V shape bottom can reduce the hydrodynamic force on the bottom, because the deadrise angle makes the hydrodynamic force separate into vertical and horizontal parts. The impact between V bottom and water happens more slowly than the flat bottom, reducing the vertical acceleration. On the other hand, less hydrodynamic lift is gained on the bottom due to deadrise angle. It means larger trim angle is needed to compensate the lift loss, thereby increasing the wetted area and frictional resistance (Larsson and Eliasson, 1994).

Another important characteristic of planing hull is hard chine. Unlike the rounded bilge, there is a sharp angle change at the intersection between the side and bottom. It helps flow separation at the stern and reduces the wetted surface of the transom (Larsson and Eliasson, 1994). The difference between hard chine and soft chine can be seen in Figure 4.

Figure 4:V bottoms with hard chine and soft chine(“Kayak materials & hull design,”). The angle between bottom and horizontal plane is deadrise angle, the larger

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2.3 Savitsky method and key definitions

Savitsky method (Savitsky, 1964) is a semi-empirical hydrodynamic method to predict performance and operating condition of planing prismatic hulls. This method was later amended include the whisker spray resistance and extended to apply to warped hulls. The theory in this section is based on the Savitsky papers (Savitsky, 1976, 1976, 1964, 1985; Savitsky and DeLorme, 2007).

Figure 5 is the underwater photo of a planing boat. The bottom consists of three areas: dry area, spray area and pressure area.

Figure 5: Underwater photo of boat at planing speed (Lundmark, 2018) 2.3.1 Pressure area

The wetted area of the bottom is the pressure area, which generates the lift force and most of the resistance. Savitsky method gives formulas for calculating the lift of a flat plat. A boat can be simplified as a lifting surface when it is planing. The nondimensional lift coefficient for planing boat can be written as:

2 2 0.5 L m g C V b 



 =    (2)

CLβ is the lift coefficient for a non-zero deadrise hull. The relation between hull with deadrise angle and flat plate is

0 0

0.6

0.0065

L L L

C

_

=

C

−

 



C

(3)

Froude number is a significant nondimensional parameter to represent resistance for displacement hull. Nevertheless, the wetted length of planing hull keeps changing while the wetted beam is almost constant value. Thus, a speed coefficient beam Froude number, denoted Cv, is employed for more precise numerical resistance estimation.

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Another important Froude number is volumetric Froude number denoted Fn▽, which is

commonly used in HSC model experiments since the Length at waterline, Lwl as the characteristic length in the regular Froude number, changes drastically for a planing hull (De Marco, 2017; Kim et al., 2013; Lotfi et al., 2015). For hull with advanced shape, it can be a better nondimensional reference parameter in ship performance experiments (Lundmark, 2018). 3 V Fn g =   (5)

As shown in Figure 5, distances measured from transom to spray root at keel and at chine are wetted keel length and wetted chine length. The mean wetted length is defined as the arithmetic average of Lk and Lc.

2 k c m

L L

L = + (6)

Mean wetted length to beam ratio is calculated in equation (7). It is for calculating the wetted surface area to obtain the skin friction coefficient.

/ m

L b

= (7)

There is no direct way to get Lk and Lc albeit the relation between lift coefficient and length to beam ratio are found by a series of systematic experiments. The lift coefficient is known, then the length to beam ratio can be calculated by iteration.

0 2.5 1.1 0.5 2 (0.012 0.055 ) L v C C    = + (8)

Equation (9) gives the position of center of pressure. Lcp is the distance from trailing edge to the center of pressure.

2 2 1 0.75 5.21 2.39 cp v w L C L  = −  ₊ (9) 2.3.2 Spray area

Stagnation line is a locus of stagnation point along the bottom, see Figure 5. It is located at the forward edge of the pressure area. Spray edge is formed by the spray reflected forward from the stagnation line. Spray area is the area bounded by the spray edge and stagnation line. The magnitude of angle α between keel line and stagnation line is calculated in equation (10). 2 tan atan tan

 





= (10)

According to geometric relation in the underwater sketch of hull, the length of stagnation line is:

/ 2

b C

sin

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2

 =  (12)

The whisker spray has direct contact with hull, which increases the wetted surface area. To include this effect, a factor △λ is used to estimate the increase of mean wetted length to beam ratio.

2 = 4 cos sin cos









 (13)

It is obvious to see that a small deadrise angle or a large trim angle will lead to a lower additional wetted surface area.

2.3.3 Resistance components

The resistance components for planing hull are pressure resistance, friction resistance, spray resistance, added wave resistance and air resistance. The pressure resistance comes from the hydrostatic and hydrodynamic lift forces acting normal to the bottom. The projection of lift force in horizontal direction represents the magnitude of pressure resistance. 0 0 ( ) p cos R mgsin cos     + = (14)

The friction is directly related to the wetted surface area. For a planing boat, the wetted surface induced by whisker spray also needs to be included. The ∆λ term is the increase in wetted surface area due to spray. CF in equation (15) is the skin frictional coefficient calculated according to ITTC (ITTC, 2014a).

2 2 0.5 ( ) f F b R C V cos     =     +   (15)

The effect of wave generated due to regional sea state on the resistance is called added wave resistance. Savitsky (Savitsky, 1976) gives formulas for estimating added wave resistance at SLR (Speed to Length Ratio) ration of 2, 4 and 6. The value for other SLRs can be interpolated from the given SLR of 2,4 and 6. Added wave resistance increases fast at low SLR and achieve the peak at middle SLR, then drops significantly at SLR around 6. However, the equations for added wave resistance are empirical and based on limited data, so they must be used in the specific range of applicability (Savitsky, 1976). Air resistance is the aerodynamic drag from air. It is negligible at low speeds and it becomes about 6% to 13% of total resistance at high speeds.

2

0.5

air air d

R =  V AC (16)

A is the frontal area of hull, Cd is the aerodynamic drag coefficient based on the dry area and approximately equals to 0.7 (Savitsky and DeLorme, 2007).

2.3.4 Equilibrium equations

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Savitsky method (Savitsky, 1964) gives formulas to calculate the lever arms for all the forces. The bow-down moments are written in equation (17), (18), (19). These equations are used to compute the running position of boat and magnitudes of unknown forces.

Figure 6: Force equilibrium on a planing boat (Larsson and Eliasson, 1994)

( ) [ ] h e cos sin M g m f cos cos       + =   −  (17) [ ] f f f f M R f e tan cos   =  −  − (18) [ ] a a a f M R f e tan cos   =  −  − (19) 0 h f a M =M +M +M = ₍₂₀₎

The trim angle at a certain speed can be solved by iteration until the moment equilibrium in equation 20 can be satisfied (Savitsky, 1964). The trim angle will not only affect the hydrodynamic performance but also seakeeping stability such as porpoising.

2.4 Spray deflection technology

Spray rail and spray deflector are two efficient solutions to deflect whisker spray and reduce the wetted surface area. Another benefit is additional lift can be obtained from redirecting spray downward (“Petestep AB,”).

2.4.1 Spray rail

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Figure 7:Geometry of spray rail (Larsson and Eliasson, 1994)

Spray rails are fitted longitudinally and the spacing in transversal direction is usually 25% half width. Its bottom surface should be inclined downwards for better reflection. Spray rails will redirect the spray downwards when spray flows sideward and have impact with the spray rail. A proportion of spray energy is transformed to lift force during the impact (Molchanov et al., 2019).

Clement (Clement, 1964) carried out towing tank experiments for validating the effect of spray rails. These experiments compared the difference between longitudinal spray strips which extend about 70 percent of the hull length from bow to stern and spray strips located only forward of stagnation line. The result indicated although the long spray strip reduces the resistance at high running speeds, it also increases the resistance at low speeds. However, with the spray strips located only forward of the stagnation line, a maximum reduction in high-speed resistance of 6% is obtained, with no increase in low-speed resistance. The flow direction behind the stagnation line is almost parallel to spray strips, and spray strips could be submerged in this region, which would increase the friction due to the addition of wetted area. Afterwards, Clement (Clement, 1964) performed more experiments using another shorter and wider model. In this study, the resistance reduction was up to 15% at Fn▽= 6.0 with long spray rails. Both the long and

short spray rails designed for Fn▽= 6.0 achieve a 7% resistance reduction. This verifies

the assumption made in previous experiments that short spray rails can achieve the full effect when they have optimal fitted position and a suitable angle with the keel line. (Seo et al., 2016) implemented a series of model tests to investigate resistance and seakeeping performance for HSC with spray rails. Results revealed that in head seas, heave and pitch motions of the hull are reduced by the spray rails. Moreover, the fore perpendicular vertical acceleration diminished by 11.3%. The full-scale effective power was obtained from the extrapolation of model test results, which shows that spray rails have no adverse effect on the hull resistance. On the other hand, the hull with spray rails can improve the seakeeping ability.

2.4.2 Spray deflector

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company Petestep AB. The V-shaped strips are placed slightly forward to stagnation line, and a closer distance to the stagnation line enables strips to have higher deflection efficiency. As seen in Figure 8, the red arrows represent the direction of spray. The spray is redirected downwards and backwards and offers additional thrust and lift to the hull. As a result, lower hydrodynamic resistance and less fuel consumption can be achieved (“Petestep AB,”).

Figure 8: Spray redirection by spray rails and deflectors (“Petestep AB,”) The boat equipped with deflector will also ride softer in waves. Petestep’s research result showed the peak vertical acceleration will drop by 30% at waves by using deflectors. Spray deflectors help the boat to have less pounding and noise when sailing at rough seas. (“Petestep AB,”)

One more study was about the effect of the deflector and its optimization. Olin et al (Olin, 2017) performed CFD simulations to investigate the resistance reduction effect of spray deflector. They modelled the hull as a wedge shape. The spray formation of the hull with and without deflector can be seen in Figure 9 where more spray flows around the bare hull while the hull equipped with deflectors redirect most of spray backwards. The highest total drag reduction can reach 32% compared with the bare hull, and 4% of total drag reduction is from additional thrust by redirecting spray backwards.

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The first attempt to validate Olin’s results was done by (Wielgosz, 2018a). However, there were some obstacles during these model tests. First, the size of model could not produce large enough spray resistance to ignore the effect of calibration error. Second, the flow state for full scale boat is transitional flow while state for model is laminar flow. The spray resistance contribution is different for these two conditions. Moreover, the vibration was severe due to size of model and dry chine (Wielgosz, 2018b). Unfortunately, the validation did not success since it was too hard to satisfy the requirements of numerical study physically. In the further study, a new model was manufactured to evaluate the performance of spray deflector in calm water and irregular waves. Two hull configurations, a bare hull and a hull with deflectors, were used and results were compared in same running trim angle. The series of tests indicated if deflectors are not submerged, deflectors can lower the total drag up to 12.1% in calm water. On the other hand, submerged deflectors will cause additional resistance up to 3.2% compared with the bare hull. Deflectors also have a influence on seakeeping ability. At low or medium speed range, the bow acceleration can be decreased by 10.8% in waves(Wielgosz, 2018a).

To further validate the effect of spray deflector, (Molchanov et al., 2019) and (Lundmark, 2018) did towing tests for three bottom configurations (bare hull, spray rails and spray deflectors) in calm water and irregular waves. A stepped hull was used in the test and the modular design allows the configurations to be changed easily. The three different configurations are shown in Figure 10. It was noticed that the trim angle obtained by experiments was smaller than the empirically determined trim and the resistance is underpredicted compared to the Savitsky method. The result also showed spray rail can achieve up to 10% drag reduction while spray deflector can reduce resistance ranging from 10% to 25% (Molchanov et al., 2019). The spray rail configuration did not change the running trim angle compared with the bare hull. However, the spray deflector increased the trim angle about 1 degree at all speeds (Lundmark, 2018). Thus, the reduction was a combined result of trim angle change and spray redirection. Consequently, the individual deflection efficiency is difficult to analyze in this study.

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A further experimental study was done by (Osmak, 2019) and (Castaldi, 2019). A new tapered deflector was designed for better spray deflection. The thickness is small at the keel and gradually increases to the chine. The reason to have this design is the deflector at the keel does not deflect much spray and will increase the risk of submersion. Results of this study showed that the Savitsky method overpredicts the trim with up to 6.5% and underpredicts the drag with up to 9%. The bare hull and deflectors configurations were tested at the same running condition so that the influence of spray deflection can be evaluated solely [4]. Four deflection phenomena appeared in the tests. Figure 11 shows the strips are parallel to the stagnation line, which generates 2% drag reduction.

Figure 11: Strips parallel to stagnation line (Castaldi, 2019)

Figure 12 shows the stagnation line is divergent to the strips, so the deflection efficiency decreases instead of increasing.

Figure 12: Strips divergent to stagnation line (Castaldi, 2019)

Figure 13 shows the stagnation line has a larger angle than the strips. The end of deflector touches the water, which causes up to 0.5% resistance increment.

Figure 13: Strips touching stagnation line (Castaldi, 2019)

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reduction. The stagnation line intersects the strips at the middle and air cavities occurs there, which is beneficial to decrease the wetted area. (Castaldi, 2019)

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3 Methodology

In this chapter, the experimental model and setup are introduced, and the test method, procedure and result processing are explained.

3.1 Towing tank

The experiment is implemented at the Davison lab high-speed towing tank, which is 95.4m long, 5m wide and 2.29m deep. The carriage is supported by monorail and driven by the cable. Its highest towing speed is 18.3m/s, but it is usually operated at speed below 11m/s for model safety. The wave maker can generate regular and irregular waves with wave height up to 0.6m. It can make different wave types like ITTC, Pierson-Moskowitz and JONSWAP.

3.2 Existing model and spray deflectors

The spray deflector has been studied for three years at Stevens Institute of Technology, and this project is the follow-up of previous researches. The model employed at last two years (shown in Figure 15) served excellently in experiments. In this project, it will still be used to investigate the optimal placed distance of deflectors for direct comparison.

Figure 15: Experimental model

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The modular design was the special characteristic of the model. In the series of experiments, three bottom configurations (bare hull, spray rail and spray deflector) were tested. The detachable bottom design made the configuration switch much easier, and it saved test time and manufacture cost at the same time (Molchanov et al., 2019). This model was designed through parametrical method in Orca 3D. The modular design is shown in Figure 16. The purple part is the main waterproofing hull, and the grey part is the plate insert.

Figure 16: Bare hull with inserted plates (Molchanov et al., 2019)

The model from (Wielgosz, 2018a) was chosen as the parent model because it is the only model that has experimental data for spray deflector. The final model dimension was scaled from parent model with considering all the design restricts. The detailed description about model design can be seen in (Molchanov et al., 2019). Some important parameters of model are listed in Table 1. CNC machine was used to mill the model from a foam block. Afterwards, sanding and polishing were repeated many times to make the surface as smooth as possible. The inserted plate, spray rail and deflector were made of expanded PVC foam. Before each test run, clay was filled in seams and holes to reduce the roughness of hull surface.

Table 1: Model dimensions

Parameter Imperial unit SI unit

Length overall Loa 71′′ 1.80m Waterline length Lwl 66′′ 1.68m Beam b 14.2′′ 0.36m Displacement ∆ 46.06 lbs 20.89 kg Deadrise angle β 20° 20° LCG 21.6′′ 0.55m VCG 5.25′′ 0.13m

3.2.1 ExistingSpray deflector configurations

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hydrodynamic force (Osmak, 2019). For maximizing the effect of spray detaching, the running speed should be as high as possible. On the other hand, the model is tested at a series of volumetric Froude numbers, and the position of stagnation line keeps changing with different speeds. Therefore, it is impossible to design one deflector to fit all speeds. Three deflectors were designed for low, medium, high speed ranges, enabling them function better. Each deflector was designed to be parallel to stagnation line at one specific Fn▽, but they were tested in a speed range. Figure 17 shows the speed range

for deflectors in Fn▽, and the Fn▽ in bold are their design speeds.

Figure 17: Fn▽ range for low, medium and high speed deflectors

The crucial part of the design is the deflector placement and geometry, which will affect the spray detachment efficiency directly. The principle of the design is to place the deflectors parallel to the stagnation line and leave an suitable offset distance between them. Thus, deflectors will not be submerged by water and can deflect as much spray as possible. Figure 18 demonstrates the geometry relation between deflectors and the stagnation line.

Figure 18: Deflectors placement at 4.46 Fn▽

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Figure 19: 3D model design of deflector strips at 4.46 Fn▽ (Osmak, 2019)

3.3 Experimental equipment

According to ITTC guidelines (ITTC, 2014c), parameters such as speed, resistance, trim, heave, accelerations should be measured in the tests. Sensors and apparatus shown in Figure 20 are employed for data recording. Model’s heave and pitch motion are set free while motions in other four degrees of freedom are limited by carriage.

Figure 20: Model and equipment setup [12]

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3.4 Experimental setup

Both calm water and wave conditions will be studied. Bottom configuration, model weight balancing, measurement equipment calibration and computer recoding system should be settled down before running the tests.

3.4.1 Calm water test

There are four bottom configurations (non-plated bare hull, plated bare hull, hull with spray rails and hull with spray deflectors) in the calm water test. Assembling bottom configurations is the first step. Screws and tape are used to attach bottom plates, spray rails and deflectors. Then clay and tape are used to fill the holes, seams and smooth the edges to reduce the hull roughness. The hull and all sensors installed in the model are weighted and balanced in the air for having same weight and LCG, so the drag difference is solely affected by the spray deflection.

After assembling and weight balancing, the model is put into water. All the sensors are connected the computer for calibration. Drag balance and heave post are zeroed, and inclinometer and pitch pivot box are calibrated. The measured trim and pitch readings in static floating condition are recorded.

Before each run, towing speed, towing time and braking time should be set, so the model can be accelerated to required speed and run enough time to record the result. An appropriate time interval between each run should be taken to let the water recover to calm state (ITTC, 2002). Tests for each speed are repeated three times to guarantee data validity and minimize the influence of measurement errors. The actual running speed, drag, trim and heave are recorded in the dap5 system. Also, three cameras are set before tests to take overwater front and back view videos and underwater photos. These photos are the useful for measuring the stagnation line position and analyzing experimental results by observing the running position and the flow state.

3.4.2 Irregular wave test

The wave test aims to investigate the effect of deflectors on vertical acceleration under normal operational condition, so the irregular wave will generate with ITTC standard

spectrum. Many previous experiments performed at significant wave height to hull

beam H1/3/BC = 0.222, 0.444 and 0.666 referring to (Fridsma et al., 1971). Nevertheless, these sea states could be too severe for small HSC (Rosén et al., 2017). In recent HSC model experiments, H1/3/BC from 0.15 to 0.25 is commonly used (Begovic et al., 2016; De Luca and Pensa, 2019; Ikeda and Katayama, 2000). H1/3/BC = 0.2 is chosen, leading to the wave height H1/3 = 0.108m. Observed wave heights basically follow the Rayleigh

distribution, and the relation between peak period Tp and H1/3 can be calculated based

on this distribution (Dinh et al., 2013). The peak period Tp = 1.34s when H1/3 = 0.108m.

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4 Result and discussion

4.1 Trim of plated and non-plated hull

Three different bottom configurations in last year tests (2019) can be seen in Figure 10. For spray rails and deflectors configurations, they were directly installed on the non-plated hull. Thus, the running position of non-plated and non-non-plated hull must be same so that the individual effect of spray rails and deflectors can be identified. The only geometry difference is non-plated hull has a step at the bottom. Despite the step, the running position should be same because the forepart of hull is entirely lifted out of water (seen in Figure 21). However, the plated and non-plated hull had different drags and trim angles in the 2019 testing.

To investigate the reason why this happened, these tests are repeated. Additional weights are added to non-plated hull for compensating bottom plate weights, and both configurations are balanced in the air to have same LCG. The removal of the bottom plates could affect the attachment point with carriage and change the running position. The tow point is therefore raised for the non-plated condition with the plate thickness so that the distance from the keel to the tow point is the same in both conditions. The hull has rough edges due to the uneven matching between bottom and plates. Clay and tapes are used to make the edge as smooth as possible (in the plated condition).

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Table 2: Test results for non-plated and plated bare hull Run Name Run Number Speed Aim Speed

Actual Drag Trim Heave Zero Speed Dummy

with plates dr1 0 0 0.002 3.3943 0.0002

Slow speed start with

plates 2 10 10.01168029 8.5247 6.621 0.1521

Slow with plates 3 19.55 19.519 9.6675 5.2245 1.8239 medium with plates 4 20.63 20.59 9.8406 4.9276 1.881 fast with plates 5 21.71 21.665 10.0362 4.6139 1.9464 Zero Speed Dummy

without plates dr6 0 0 -0.0017 3.792 0.0001

slow speed start without

plates 7 10 10.03 8.9482 7.0229 0.1226

slow without plates 8 19.55 19.704 9.5797 5.8825 1.9397 medium without plates 9 20.63 20.604 9.9958 5.705 2.0196 fast without plates 10 21.71 21.798 9.8203 5.3089 2.0881 There are some possible reasons resulting in the difference. The hull and bottom plates are made of foam and PVC respectively. The roughness of material varies, causing different skin frictions. Besides, the rough edge could increase the wetted surface, and escalate the frictional coefficient by disturbing the flow state and reaching a lower Reynolds number. The use of tape for remaining continuity at the edge could also be a reason. Its elasticity makes the hard chine not shape enough for the flow separation. Figure 22 displays the underwater photos, clear flow separation can be observed at hard chine of non-plated hull but cannot be observed in the plated hull.

Figure 22: Underwater photos, non-plated hull in the left and plated hull in the right. Flow separation at the hard chine can be seen inside the red circles of the left photo

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Last, the position putting weights are much higher than the bottom plates, so VCG of two configurations vary a lot. However, the VCG only affect the lever arm ff, which almost has no effect on trim angle and drag.

4.2 New model for towing tank testing

After using the present model for two years it was apparent that it is not suitable for the further testing. The model was designed as modular hull; 2018’s deflector design required PVC plates to be screwed on to the hull. As a result, the unsmooth edge caused the running position difference between plated and non-plated bare hull. Besides, from the seakeeping point view, its L/B ratio is too large for wave test, because a slender hull is subject to higher vertical acceleration at waves (Larsson and Eliasson, 1994).

4.2.1 Design objective

The major objective of the new model is to be eligible to generate higher spray resistance to total resistance ratio, thereby enhancing the spray detachment function of deflectors. Spray resistance is affected by four parameters: speed, beam, deadrise angle, model mass. The present model’s dimension is used to analyze the influence of parameters (displayed in Figure 23, Figure 24, Figure 25 and Figure 26) at different trim angles. From these figures it is clear that the spray resistance contribution increases with speed, beam, deadrise angle, and a lighter hull has a higher spray resistance ratio.

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Figure 24: Spray resistance contribution as a function of beam for different running trim angles

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Figure 26: Spray resistance contribution as a function of mass for different running trim angles

Parameters are scaled up or down by 20% to show the impact of different parameters on the spray resistance contribution. As seen in Table 3, changing beam is the most efficient way to increase the spray resistance.

Table 3: Effect of hull dimension on spray resistance contribution

Parameter Trim 4° Increment Trim 5° Increment Trim 6° Increment Original Spray Resistance (of total resistance) 9.75% 8.53% 7.29% Beam b (20% increase) 14.38% 47.5% 13.01% 52.5% 11.29% 54.9% Deadrise β (20% increase) 11.97% 22.8% 10.71% 25.6% 9.47% 29.9% Mass m (20% decrease) 12.20% 25.1% 10.98% 28.7% 9.52% 30.6% 4.2.2 Design limitations

Besides the goal to maximize spray resistance, there are some constraints in the design. The towing tank dimensions give a maximum length limit as 2.4m from (ITTC, 2014b). Referring to Equation (5), the upper speed limit is 40ft/s that limits the weight of model to be lighter than 52lbs for achieving the highest testing Fn▽ of 5.93 (Lundmark, 2018).

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water periodically as the consequence of dynamic instability (Ikeda and Katayama, 2000). It should be avoided in the test otherwise larger amounts of data cannot be recorded and the effectiveness of tests is ruined. In order to predict porpoising, the empirical formulas given by Savitsky equation (21) (Savitsky, 1964) and Celano equation 21 (Celano, 1998) can be used.

2 1.87 0.54 80.87 0.193 0.0017 0.312 2 2 2 L L L crit C C C  = − + + + −  −  (21) 0.7651 0.2629 0.1197 (15.7132) 2 L crit C exp  ₌  _− ₍₂₂₎

CL is the lift coefficient and be calculated by the formula 22.

2 2 2 L C V b



 = (23)

The range of application of these two empirical formulas are different. With a low load factor C∆ (see equation (24)) of 0.34 (Day and Haag, 1952), the empirical formula in equation (21) is more suitable and thus applied to our model design.

3 C gb



  = (24)

Three parameters beam, longitudinal center of gravity and hull weight are related to porpoising limit according to equation (21). To study the effect of each variable on porpoising, one parameter is changed solely, and other parameters are fixed at each time. The results are shown in Figure 27, Figure 28 and Figure 29. The dashed line is the porpoising limit, and the solid line is the running trim angle predicted by Savitsky method (Savitsky, 1964). The area below the dashed line is the stable planing regime, and the area above the line indicates a high probability of porpoising.

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Figure 27: Effect of beam on porpoising limit and running position.

As seen in Figure 28, the running trim angle will be smaller when the position of LCG is more forward. Only one limit curve is shown in this figure, which means three limit curves are overlapped, so change the position of LCG does not affect the porpoising limit.

Figure 28: Effect of LCG on Porpoising limit and running position

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Figure 29: Effect of hull weight on Porpoising limit and running position Overall, narrowing the hull is the most efficient way in the design stage to avert porpoising. The adjustment of LCG can be a backup solution if the porpoising still happens in later experiments. In addition, although changing the weight of hull cannot affect the porpoising limit, it can be used to obtain the optimal running position for the model.

4.2.3 Parameter analysis

Dimensional parameters interact with each other, so the design process needs to make the compromise between them for the most desired property. The priority is to maximize the spray resistance contribution to overall resistance. Beam has the largest influence on it. Thus, the hull should be as wide as possible if the requirement of porpoising is satisfied. A hull with lower L/B ratio than the conventional hull has higher spray resistance contribution, but L/B ratio cannot be very low considering porpoising. An appropriate range for L/B ratio is 3.5-4. When L/B ratio is fixed, the hull is expected to be as long as possible to achieve a larger beam. The deadrise for HSC is normally ranging from 10 to 30 degrees. Models with high deadrise angle can be subject to lower acceleration which is beneficial for wave tests. At the same time, high deadrise angle can increase the spray resistance proportion. On the other hand, (Clement, 1964) points the spray rail can only function well for deadrise below 20 degrees.

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convectional bow. Hence it can be manufacture-friendly and eligible for both calm water and wave tests.

4.2.4 Design iteration

Some dimensions are defined by design limitations and parameter analysis; However some parameters have an interdependence thus an iterative approach was used. It can be seen in Figure 30.

Figure 30：Iteration flow for determining model parameters

The range of L/B ratio is defined as 3.5-4, and an initial value of 3.5 is used together with the maximum length of 2.4m to allow for a larger beam. Then parameters are input into Orca 3D design assistant, and a model can be drawn in Rhino. The displacement can be calculated in Rhino for checking if desired Fn▽ (2.97-5.93) can be achieved.

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Figure 31: Porpoising check for the new model and the model designed by (Molchanov et al., 2019). Dashed lines are the critical trim angle to porpoising for

models. The solid lines are running trim angles estimated by Savitsky method (Savitsky, 1964).The green circles are actual running trim angle measured in tests of

(Molchanov et al., 2019) where no porpoising was experienced and at the red star marker porpising was experienced.

The final model dimensions are listed in Table 4.

Table 4: New model dimensions

Parameter Imperial unit SI unit

Length overall Loa 85′′ 2.16m Waterline length Lwl 80′′ 2.02m Beam b 21.2′′ 0.54m Displacement ∆ 47.2 lbs 21.4kg Deadrise angle β 20° 20° LCG 25.6′′ 0.65m VCG 6.3′′ 0.16m

The model is a prismatic hull and is designed in Orca 3D by using parametric definition. After that, shape modifications are implemented for the hull continuity and bow shape. The 3D model in Rhino is shown in Figure 32.

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4.3 Design of free running model

Few studies are involved with free running model test for HSC in situ, but it can provide valuable information and result since the test environment is more similar to reality. Differ from towing tank tests, the free running model has no restriction at six degrees of freedom, and the impact of wind and wave will also be included.

The free running model has been designed in collaboration with Jack Bonoli and Madeline Cohen current undergraduates at Stevens Institute of Technology. It includes four parts: hull, propulsion and power system, steering system and sensors. The hull design is the same as the towing tank model test for the direct result comparison, however it would be retrofitted to install the propulsion system and the weight would need to be reduced (Xinguo et al., 2020).

4.3.1 Propulsion and power system

The propulsion system will be powered by a set of lithium polymer batteries and provide thrust for the free-running model and keep it running at a constant speed. The system includes a brushless DC motor, an ESC (electronic speed control), a drive shaft and a thruster.

The SLRs of most recreational and utility vessels that have been manufactured and employed are between 5 and 10, see Figure 33. To represent the majority of HSC, the SLR of 10 was chosen as the maximum SLR in later tests and the matching speed is 25 knots.

Figure 33:Maximum SLR for 31 utility vessels (yellow bars) and 31recreational vessels (red bars).

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for the maximum speed is 267N and the required power is 3.4KW.

Figure 34: Thrust and power estimated by Savitsky method

The speed and torque of the DC motor need to be determined according to the dimension of the propeller. (ITTC, 2008) pointed out that the diameter of the propeller should be greater than 10cm to measure the torque more accurately. However, for a podded propeller, it will work as an azimuth thruster and must be modified instantaneously to obtain a constant torque (ITTC, 2008). Most propellers with a diameter of 10cm found on the market have a pitch diameter ratio (P/D) of 1.0. A thrust coefficient KT of 0.22, and a torque coefficient KQ of 0.036 are given for this P/D ratio by the propeller chart of (Molland et al., 2011) for the Gawn series. The selected thruster is listed in Table 5.

The advancing speed of the hull depends on the RPM of motor and the dimension of the propeller. To reach the highest running speed, the RPM must be greater than 7700 r/min according to Equation (25) (Molland et al., 2011). Equation (26) (Molland et al., 2011) is used to check whether the propeller can provide sufficient thrust. At the RPM of 7700 r/min, the thrust is 371N which exceeds the required thrust. Equation (27) (Molland et al., 2011) gives a torque requirement of 2.2 Nm for the motor.

/ max RPM V Pitch (25) 2 4 T T =n D K (26) 2 5 Q Q=n D K (27)

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model will run at different speeds, and system identification will be implemented in Simulink to obtain transfer functions for the entire speed range.

Figure 35: Speed control flow chart

An infrared sensor is required to measure the RPM of the DC motor. Unlike the towing tank tests, the resistance of free running model is hard to complete. However, when the model is running at a constant speed, the resistance can be calculated by subtracting thrust deduction from thrust of the propeller. Thus, a dynamometer will be used to measure the shaft thrust to evaluate the dynamic performance. The sensor required by the speed controller is listed in Table 5.

Table 5:Costs and specifications of components for propulsion and powering

Thruster Cost (USD) Thrust (N) Weight (kg) Location

Lewmar Gen2 Bow Thruster

1,826.44 637.432 20 Hodgesmarine.co

m

DC Motor Cost (USD) Power (kW) Max RPM Location

Turnigy AquaStar 112.91 5.28 21900 hobbyking.com

Rotation speed Sensor

Cost (USD) Name Weight (kg) Location

Infrared Sensor 11 OSOYOO

LYSBO1157HIJO

0.045 Amazon.com

Battery Cost (USD) Capacity (mAh) Volts (V) Location

URUAV 5S 88.48 6200 18.5 alexnld.com

4.3.2 Steering system

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34 ( ) p ( ) i ( ) d ( ) d u t K e t K e t d K e t dt  = +

_

+ (28)

Where e(t) defines the error signal, Kp defines the proportional gain, Ki defines the integral gain, and Kd defines the derivative gain (Larrazabal and Peñas, 2016). The steering system consists of a thruster, a controller, a global positioning system (GPS) and an inertial measurement unit (IMU), some other electronics and sensors. A thruster will be used to steer instead of a rudder since the heading adjustment of rudder has a time delay, which is inefficient for HSC. The control process is shown in Figure 36.

Figure 36: Control system flow diagram

The PID controller receives the error from the input and output of the system and makes corrections to the thruster to reach the desired heading(Demetriou et al., 2016). The input of the system is the current heading and position of the model collected from IMU and GPS. The Simulink model of the guidance system is shown in Figure 37.

Figure 37: Simulink model of the guidance system

The transfer function of the feedback system between the current heading angle and the outputted thruster angle is given in Equation (29).

2 0.847 ( ) 1.55 0.918 h s s s = + + (29)

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to be Kp = 78.5 and Kd = 17, but they may be changed after all the components are assembled and the testing.

To test the PD controller, an Adafruit BNO055 orientation sensor, a HC-SR04 ultrasonic sensor, and a TOYEN remote control boat were wired to an Arduino Uno board. The remote control boat is only used to test the control system, consisting of the guidance system and PD controller. The wiring set-up is shown in Figure 38, and the testing performed in a swimming pool can be seen in Figure 39.

Figure 38: Remote control boat wiring set-up

Figure 39: Remote control boat pool testing

The full integration of the Simulink model for the test is still under development. The controller will be adjusted based on the results of the test run. Further testing is needed to improve the performance of the PD controller and the connection route between components.

4.3.3 Sensors and equipment

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Table 6: Sensor components and costs

Item Component Cost (USD) Weight (kg) Location

GPS Spot Trace GPS 100 0.088 Rei.com

IMU XSENS MTI-7-T 406 0.016 Mouser.com

Digital Compass PNI RM3100 Magnetometer 36 0.017 Amazon.com

RC Reciever FrSky 8XR 36 0.017 Amazon.com

RC Transmitter FrSky Taranis X9D 218 0.67 Amazon.com

LIDAR Sensor LIDAR-Lite 3 Laser

Rangefinder

130 0.016 Robotshop.com

WIFI Router ASUS RTN66U 5GHZ Router 304 0.816 Amazon.com

Two wave buoys will be deployed to record the test environment parameters to take changes in sea state into consideration. They should have appropriate size for easy transportation and deployment. An additional requirement is that the wave buoys can monitor as many wave parameters as possible to allows fewer supporting instruments to be required. Ultrasonic sensors are taken as the supplement to monitor wave characteristics and are installed in the forepart of the model. Several wave buoys, ultrasonic sensors and their specifications are listed in

Table 7 for comparison.

Table 7: Potential wave buoys and ultrasonic sensors

Name Cost (USD) Diameter (cm) Weight (kg) Location

Wave Buoys

Spotter V2 4900 42 5.4 sofarocean.com

Wavesense NA Placed on Buoy NA fugro.com

Micro Wave Buoy NA 50 33.5 hiseamarine.com

TRIAXYS Mini Wave Buoy

32000 60 60 axystechnologies.com

Mini Wave Buoy NA 60 <50 hiseamarine.com

Ultrasonic Sensors

ToughSonic 3 NA 33.4 0.4 senix.com

BUS0039 277.09 30 NA balluff.com

UK1F-E4-0A 158 18 NA automationdirect.com

Banner Engineering 252.73 18 NA alliedelec.com

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5 Summary and Conclusion

This thesis focuses on investigating the trim angle difference of plated and non-plated hull, and the design of experimental models for the study of spray deflection technologies for HSC.

To figure out the reason of trim angle difference, specific treatments are implemented to expel the disturbance before the test. Additional weight is added to compensate for the weight of the bottom plate for the non-plated hull. Both configurations are balanced to obtain the same LCG. Clay and tape are used to make the edges as smooth as possible. The hulls are towed three times for each test speed to minimize the effect of the error. To satisfy new objectives of the further research on spray deflection, a new model for towing tank test is designed. The design revolves around the design goals and constraints such as maxing the spray resistance and avoiding porpoising. Considering the complexity of the interaction among parameters, detailed analysis and design iteration are done to obtain the optimal hull for the towing tank test. The 3D model is drawn in Rhino software.

A free running model is also designed to study the performance of spray deflectors in the real sea condition. The free running model composes of a planing hull, propulsion system, steering system, and sensors. To directly compare the results, the hull dimensions are the same as the model for towing tank test model, but the bottom at the stern will be modified to install thrusters. To allow the model run in a straight line at a constant speed, a speed controller and steering system are needed and modeled in Simulink. Most items required for propulsion and steering are selected. The preliminary test of the steering system is carried out on a remote control boat. Although the system is still under development, the testing process gives suggestions for improving the steering system.

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6 Future work

Previous work on spray deflectors showed they can reduce resistance for the HSC. However, there are still many improvements can be done to achieve the full potential of this technology. Here are some suggestions for the future development.

6.1 Placing position of deflectors

Each deflector is designed to be parallel to the stagnation line of its design speed. However, it is hard to figure out the optimal parallel placing distance. Previous experiments gave the benefit graph for some speeds, however, to find the regularity how the spray deflection efficiency change, more Fn▽ and placing distances should be

tested.

6.2 Ventilation phenomenon

The previous testing result shows the spray deflector can achieve the highest resistance reduction when the stagnation line crossing the mid of deflectors. The reason behind this should be analyzed further. Is it the cause of spray area reduction, the air cavity, or the joint effect, and how much they contribute to the resistance reduction? Additionally, there may be other explanations for that.

6.3 Wave test

The hydrodynamic force will increase dramatically when the HSC starts planing. The impact between wave and hull could cause personnel’s injury and structure damage. It is necessary to carry out wave tests to investigate the effect of spray deflector on the vertical acceleration and resistance in waves.

6.4 Free running model test

More tests should be done to check the effectiveness of the propulsion and steering system and ensure these sub systems can function well individually. Many problems could happen during the integration of free running model due to compatibility between each subsystem. Therefore, the controller must be re-tuned regarding the further free running tests until it can allow the boat to reach the desired running condition as quickly as possible.

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Model Design for Further Spray Deflector investigation

Model Design for Further

Spray Deflector investigation

Abstract

Abstrakt

Acknowledgement

Table of Contents

Abbreviations and Symbols

1 Introduction

1.1

Aim and Objective

2 Background

2.1

Wave resistance barrier

2.2

Planing mode

2.3

Savitsky method and key definitions



0.0065

C

=

C

−

 



C

 













2.4

Spray deflection technology

3 Methodology

3.1

Towing tank

3.2

Existing model and spray deflectors

3.3

Experimental equipment

3.4

Experimental setup

4 Result and discussion

4.1

Trim of plated and non-plated hull

4.2

New model for towing tank testing





4.3

Design of free running model



5 Summary and Conclusion

6 Future work

6.1

Placing position of deflectors

6.2

Ventilation phenomenon

6.3

Wave test

6.4

Free running model test

7 Reference

_