IN DEGREE PROJECT VEHICLE ENGINEERING,SECOND CYCLE, 30 CREDITS

, STOCKHOLM SWEDEN 2018

Experimental Evaluation of Spray Reduction Technologies

SVANTE LUNDMARK

KTH ROYAL INSTITUTE OF TECHNOLOGYSCHOOL OF ENGINEERING SCIENCES

Acknowledgements

I would like to thank Bogdan Molchanov for colaborating with me on this project and his help, patience,focus and friendship during the ups and downs of this project as well as making this project the adventureit was.

I would like to thank Dr. Mirjam Fürth and Mathew Green for all their help and support during thisproject. You made me feel welcome and provided me with a productive and fun work environment whichwill be sorely missed. Together with all the people at Stevens Institute of Technology and The David-son laboratory I would like to give a special thank you to Dr. Raju Datla, Professor Michael DeLorme,Uihoon Chung, Douglas Meding and Lori D’Nicoula for all the help, support and patience during my stay.

I would also like to thank Chiara Wielgosz for starting this project and helping me through it andtogether with Julien Fraize and Jane Igubadumbe among others for making me feel at home in a newcountry.

A special thank you to my Professor Karl Garme of the swedish Royal institute of Technology foryour feedback and support during this project and for pushing me to make this project as great as itcould be, and Professor Anders Rosén of the swedish Royal Institute of Technology for bringing me thisproject and all the helpful discussions.

Thank you to the Clarence Dybeck and Gibson-Cronstedt foundations for believing in the projectand making it possible for me to be a part of it.

Finally I would like to give a special thank you to my parents for always believing in me and sup-porting me through my life and my family and friends who have supported me through the years.

Svante Lundmark

Hoboken, New Jersey, September 2018

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Abstract

This report concerns the efficiency of a novel spray deflector design. The novel design is analyzed andcompared to a bare hull and a bare hull fitted with spray rails by experimental testing in a towing tank.The bespoke hull has a modular design where different inserts can be installed to make the parent hullinto a bare hull, spray rail, low speed or high speed deflector. The hulls are analyzed in two environments,calm water and irregular waves, where the hulls are compared in drag resistance, running trim and heavefor calm water and in bow and center of gravity accelerations for waves.

The calm water results show that the deflectors lower the total resistance with up to 25% comparedto the bare hull and by over 15% compared to the spray rail configuration, while also affecting the run-ning trim of the hull, raising it by about 1°compared to both spray rail and bare hull. The heave is alsoaffected but not to the same degree, the low speed deflector and the spray rail hull show a similar increasein heave compared to the bare hull as long as the deflector is at its design speed or lower. Because ofthis change in running position no conclusion about the specific removal of spray resistance on the partof the deflector compared to spray rails can be stated. The deflector design used in these tests changethe running trim which has significant influence on the resistance.

The irregular wave tests indicate that the current deflectors have a small influence on the verticalaccelerations compared to the bare hull. The difference is similar to the spray rail setup where theaccelerations at center of gravity for both designs show an increase while the spray deflector exhibitedlower accelerations in the bow area.

Several improvements have been stated that would improve the current design for the next series ofexperiments.

List of Figures

2.1 Waves created along a moving displacing hull, Rosen [15] . . . . . . . . . . . . . . . . . . 32.2 Effect of speed on resistance for different hull shapes . . . . . . . . . . . . . . . . . . . . . 42.3 Bodyplan for the 90E boat for the swedish military, Rosen [15] . . . . . . . . . . . . . . . 42.4 Spray rail design by Clement, [2] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.5 Achieved lift in percent of hydrodynamic and hydrostatic pressure, with planing speeds . 62.6 Flow and pressure on planing flat plate, Eliasson et al [4] . . . . . . . . . . . . . . . . . . 72.7 Forces on planing flat plate, Eliasson et al [4] . . . . . . . . . . . . . . . . . . . . . . . . . 72.8 Deadrise angle shown on Storebro 90E hull . . . . . . . . . . . . . . . . . . . . . . . . . . 82.9 Schematic view of resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92.10 Spray area on model hull by Clement [2] . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92.11 Hull at speed showing the wetted area and its components . . . . . . . . . . . . . . . . . . 102.12 Spray on model hull by Clement, [2] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102.14 Spray rails mounted to experimental hull . . . . . . . . . . . . . . . . . . . . . . . . . . . 112.15 Hull beneath with PeteStep deflectors, picture from PeteStep patent [13] . . . . . . . . . . 112.16 Petestep hull drawing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122.17 Flow and cross section comparison: spray rails vs. Petestep design . . . . . . . . . . . . . 122.18 Flow on deflector, Olin [11] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132.19 Hull flow comparison, Olin [11] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132.20 Model hull by Wielgosz [23] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142.21 Model hull from beneath, Wielgosz [23] . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

3.1 Position of sensors and weights in model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

4.1 Spray resistance influence on total resistance because of L/B ratio. . . . . . . . . . . . . . 234.2 Model design with detachable plates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244.3 Model design with detachable plates, bare hull left, spray rails center, pray deflector right 244.4 Theoretical resistance for chosen model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 254.5 Predicted stagnation lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264.6 Deflector designs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

5.1 Empty test matrix for bare hull test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 275.2 Speed range for test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285.3 Filled test matrix for bare hull . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285.4 Camera set up for experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 295.5 Comparison between Savitsky prediction and the experimental values in trim for bare hull 305.6 Comparison stagnation line, Savitsky model (yellow) and experimental results (red) . . . 305.7 Comparison between Savitsky prediction, experimental and Savitsky post processing in

resistance for bare hull . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 315.8 Force breakdown and comparison to experimental results . . . . . . . . . . . . . . . . . . 325.9 Comparison between spray rails and bare hull in trim . . . . . . . . . . . . . . . . . . . . 335.10 Comparison between spray rail and bare hull in drag . . . . . . . . . . . . . . . . . . . . . 335.11 Comparison between spray rail and bare hull in heave . . . . . . . . . . . . . . . . . . . . 345.12 Theoretical spray resistance removal vs. actual experimental difference . . . . . . . . . . . 355.13 Comparison between bare hull, spray rail and deflectors in trim . . . . . . . . . . . . . . . 365.14 Comparison between bare hull (top), spray rail(mid) and deflectors (bottom) in trim at

Fn∇=5.87 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 365.15 Comparison between bare hull, spray rail and deflectors in drag . . . . . . . . . . . . . . . 375.16 Visualisation of deflector position and stagnation lines at Fn∇=5.09 . . . . . . . . . . . . 385.17 Comparison between bare hull, spray rail and deflectors in heave . . . . . . . . . . . . . . 395.18 Accelerations at Fn∇=1.47 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

ii

5.19 Accelerations at Fn∇=4.3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

C.1 Wave data from low speed runs for bare hull . . . . . . . . . . . . . . . . . . . . . . . . . . 52C.2 Wave data from high speed runs for bare hull . . . . . . . . . . . . . . . . . . . . . . . . . 53C.3 Wave data from low speed runs for spray rails . . . . . . . . . . . . . . . . . . . . . . . . . 53C.4 Wave data from high speed runs for spray rails . . . . . . . . . . . . . . . . . . . . . . . . 54C.5 Wave data from low speed runs for Deflector 1 . . . . . . . . . . . . . . . . . . . . . . . . 54C.6 Wave data from high speed runs for Deflector 1 . . . . . . . . . . . . . . . . . . . . . . . . 55

iii

List of Tables

2.1 Main particulars for Olin model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122.2 Main particulars of Wielgozs model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

3.1 Sensor weights and locations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173.2 Froude scaling laws . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

4.1 Design constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234.2 Model parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 254.3 Design speeds for deflectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

5.1 Main test speeds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285.2 Test speeds theory comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285.3 Wave spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 405.4 Acceleration comparison with DNV prediction . . . . . . . . . . . . . . . . . . . . . . . . . 405.5 Acceleration comparison, Fn∇=1.47 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 415.6 Acceleration difference, Fn∇=4.3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

A.1 Measured values for Bare hull at Fn∇=5.0866 . . . . . . . . . . . . . . . . . . . . . . . . . 49A.2 Measured values for Bare hull at Fn∇=5.0866 . . . . . . . . . . . . . . . . . . . . . . . . . 49A.3 Significant uncertainties for bare hull at Fn∇=5.0866 . . . . . . . . . . . . . . . . . . . . 49A.4 Combined uncertainty for each hull and speed . . . . . . . . . . . . . . . . . . . . . . . . . 50A.5 Expanded uncertainty for each hull and speed . . . . . . . . . . . . . . . . . . . . . . . . . 50

B.1 Test matrix, average values and standard deviations, bare hull . . . . . . . . . . . . . . . . 51B.2 Test matrix, average values and standard deviations, spray rails . . . . . . . . . . . . . . . 51B.3 Test matrix, average values and standard deviations, Deflector 1 . . . . . . . . . . . . . . 51B.4 Test matrix, average values and standard deviations, Deflector 2 . . . . . . . . . . . . . . 51

C.1 Test matrix, speed and number of encounters . . . . . . . . . . . . . . . . . . . . . . . . . 52C.2 Average running values for entire encounter period . . . . . . . . . . . . . . . . . . . . . . 55

iv

Contents

List of Figures ii

List of Tables iv

Nomenclature vii

1 Introduction 1

2 Background 32.1 Planing craft . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32.2 Froude number . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62.3 Planing of flat surface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62.4 Planing of a V shaped hull . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82.5 Resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82.6 Spray . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92.7 PeteStep deflector design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2.7.1 Previous experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

3 Towing tank test 153.1 The towing tank . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153.2 The ITTC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

3.2.1 Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153.3 Uncertainty analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

3.3.1 Froude scaling laws . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203.3.2 Non dimensional units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

3.4 DNV GL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

4 Model Design 224.1 Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224.2 Design constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224.3 Model specifics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

4.3.1 Design speeds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 254.3.2 Deflector design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

5 Experiments 275.1 Calm water setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 275.2 Calm water test, Savitsky prediction vs experimental comparison . . . . . . . . . . . . . . 29

5.2.1 Results and discussion, comparison: Savitsky model, bare hull . . . . . . . . . . . . 295.2.2 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

5.3 Calm water setup, Same LCG . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 325.3.1 Result comparison: Bare hull and spray rail hull . . . . . . . . . . . . . . . . . . . 325.3.2 Result comparison: Bare hull, Spray rail and deflectors . . . . . . . . . . . . . . . . 355.3.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

5.4 Calm water setup, trim . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 395.4.1 Results and discussion, equal trim . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

5.5 Waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 405.5.1 Results and discussion, waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

6 Conclusions 43

7 Future works and improvements 44

v

References 46

Appendices 48

A Uncertainty calculations 49

B Complete Results calm water setup one 51

C Complete results wave tests 52

vi

Nomenclature

Acronyms

CFD Computational Fluid Dynamics

CG Center of Gravity [%]

HSC High Speed Craft

ITTC International Towing Tank Conference

LCG Longitudinal Center of Gravity [%]

MLV Motor Lifeboat Vessel

RANS Reynolds Average Navier-Stokes

SLR Speed to Length Ratio [ Vs2√LwL

]

V CG Vertical Center of Gravity [%]

Greek symbols

α Stagnation line angle [deg]

β Deadrise angle [deg]

∆ Ship displacement [N]

∇ Displaced volume [m3]

π/2 Pile up multiplier

ρ Water density [g/m3]

ρD Water density, design craft specific [g/m3]

ρM Water density for model craft [g/m3]

τ Trim angle [deg]

θ Spray boundary angle [deg]

Symbols

R̂T Resistance for each run [N]

RT Mean value of resistance [N]

aD Gravitational acc. for design craft [g]

aM Gravitational acc. for model craft [g]

a1/10 Highest 10th of the accelerations

a1/3 Highest 3rd of the accelerations

Bw Ship wetted width [m]

C Stagnation line length [m]

CD Drag force [N]

CL Lift force [N]

CS Whisker spray friction coefficient

CT Total resistance coefficient

CL0 Zero deadrise lift coefficient

CLβ Non-zero deadrise lift coefficient

d Ship draft [m]

Fn Froude number

Fn∇ Volumetric Froude number

FnB Beam Froude number

g Gravitational constant [m/s2]

h Heave measured at CG [m]

Hs Significant wave height [m]

LC Whetted chine length [m]

LK Whetted keel length [m]

Lw Wave length [m]

Lcp Dist. center of pres. to trailing edge [m]

Loa Ship length overall [m]

Lwl Ship wetted length [m]

m Mass [kg]

N Number of repeats

Ra Air resistance [N]

RP Pressure resistance [N]

RS Spray resistance [N]

RV Viscous resistance [N]

RHD Hydrodynamic resistance [N]

Rtot Total resistance [N]

Tp Significant wave period [s]

u Standard deviation/uncertainty in unit ofmeasure

u′ Standard uncertainty of repeat test [%]

V Flow speed [m/s]

Vs Ship speed [m/s]

Vw Wave speed [m/s]

vii

Chapter 1

IntroductionThis report focuses on the spray develpoed by a high speed craft and its design. A high speed craft isany water craft which can achieve a certain speed compared to its length.

More specifically it is a craft able to reduce the negative resistance from the hydrodynamic forces.This can be done in several ways, either by using twin hulls, hydrofoils, air cushions or a planing monohull. In this report the focus is on a high speed craft planing mono hull and how it can be improvedfrom the point of spray resistance.

When a high speed craft is planing there are several forces affecting its hull, such as the hydrodynamicresistance, air resistance, spray resistance and friction forces. These forces increase the resistance of thehull and thus lowers the fuel efficiency and speed of the hull. Air resistance, friction and viscous forcesare well known and ship designers try to minimize them. Typically by minimizing the wetted area of thehull by separating the wetted area into multiple smaller areas by using a stepped hull or using twin ortriple hulls as in catamarans and trimarans.

Spray resistance comes from the area on the outside of the hull wetted by the water spray generatedwhen the hull is running on the surface of the water. The spray adds frictional resistance to the totalship resistance and is something that can be removed. Historically the spray is removed by fitting socalled spray rails to the hull that redirect the spray out to the sides, however they are not 100% effectiveand can even add resistance if badly designed.

In this report a novel design for lowering the negative influence of spray called a spray deflectorinvented by the Swedish company Petestep AB [13] is discussed and tested to see if it can remove alarger portion of the spray resistance by redirecting the spray backwards and in doing so utilize thekinetic energy from the spray itself for propulsion and stability. The deflector design is also anticipatedto increase the damping of the vertical accelerations experienced by the hull and raise the comfort andstability of the crew (Bjersten Danielsson 2014,[1]).

The design will be tested in both calm water and irregular waves to see its effect on resistance, trim,heave and vertical acceleration. The results will be compared against a standard bare hull and the sprayrail design commonly used on HSC which also aims to reduce the spray by deflecting it sideways (Clement1964, [2]).

In previous years, spray deflection has become more interesting to ship designers leading to moreresearch in this area. Previous studies has been performed which includes a CFD analysis and scaledmodel tests of a real ship using this design (Olin et. al 2016 [11]; Wielgosz et. al 2018[23]). These testshave so far been inconclusive as to the validity of the new design, the CFD showed great promise butthe results where not repeatable in towing tank experiments. This prompted the first model test witha more realistic hullshape which showed positive results but improvements where suggested for a secondset of experiments.

For this experiment a larger model with a four piece modular design is used. Where two separate setsof deflectors, one for low speed and one for higher speed, can be attached and tested as well as a barehull and spray rail configuration. The aim is to use the same parent model for all test by easily changingthe hull bottom in such a way that the different designs can be evenly compared, where all variables notrelated to the hull bottom stays as similar as possible. It also enables the same hull to be used, savingmaterial and time in manufacture and makes any additional tests possible.

The larger model will increase the resistance effects as well as make the flow different, increasing theefficiency of the deflectors and giving reliable data for analysis.

The hulls will then be tested in a towing tank for a wide speed range following a bespoke experimentalsetup, to assess the efficiency of the design as the speed, trim and center of gravity changes.

1

Previous researchSpray deflection has been the subject of discussion for some time although not a high priority for researchuntil recently. In 1964 Clement [2] proposed a design called spray rails which is still used through outthe industry, however its effects on the vertical accelerations of a hull is still estimated by rule of thumbwhile a method to predict the spray resistance for calm water was developed only recently (Eliasson andLarsson,2000 [4]; Savitsky, 2007 [19]).

The spray deflector design by Petestep has potential and thus has been the interest of some previousacademic research. Olin et. al (2016) [11] did a numerical study which showed a reduction of up to 28%and a thrust increase of 4% in comparison to a bare hull. The numerical study was tested experimentallyby Wielgosz et. al (2018) [22] which showed the experimental setup to be impossible to reproduce.

Wielgosz followed this study with another where a scaled version of a Marine Rescue Vessel (MRV)was used as a template for the hull and fitted with deflectors, Wielgosz 2018 [23]. The model was tocompare the effects on a bare hull and a Petestep deflector hull investigating resistance and verticalaccelerations. The study showed a reduction of up to 12.1% in resistance and a reduction of verticalaccelerations of up to 10.8%.

CollaborationThese experiments are a collaboration between Bogdan Molchanov and Svante Lundmark for their masterthesis work at the Royal Institute of technology, KTH, Stockholm Sweden; Aalto university, Finland;Stevens University Hoboken NJ USA. The work was done jointly by both Bogdan and Svante withBogdan focusing more on the model and Svante more on the experimental setup. This report is writtenby Svante Lundmark and thus focuses more on the experiments and their setup, while another reportwritten by Bogdan Molchanov focuses on the design and manufacture of the model, Molchanov (2018)[10].

2

Chapter 2

Background

2.1 Planing craft

A moving object immersed or partially immersed in a fluid will experience primarily two types of forces,hydrostatic and hydrodynamic. The hydrostatic forces is a results of the objects weight, where a floatingobject experiences a force from the fluid equal to its weight spread on all sides immersed in the fluid.The hydrodynamic forces comes from the hydrodynamic pressure exerted on the hull when its movingin the fluid, pushing each water particle aside, creating waves as shown in figure 2.1.

By increasing the speed, the hydrodynamic force will increase and thus have an increasing impacton the hulls total resistance (Savitsky 1964, [16]; Savitsky 2007, [19]; Larsson-Eliasson 2000, [4]; Rosen,2004 [15]).

The bow wave will create a high pressure and thus a peak or crest of the wave. In reaction to thishigh pressure area, an equal low pressure area will develop behind it called a trough. Sets of peaks andtroughs will form along the hull in reaction to the pressure differences giving the recognizable sinusoidalwave form along a displacing hull as seen in figure 2.1.

Figure 2.1: Waves created along a moving displacing hull, Rosen [15]

The wave crests and troughs create lift and suction effects on the hull. When subjected to lowerspeeds the craft spans several wavelengths and the vertical effects of these pressure forces cancel out butcreates drag resistance on the hull. By studying the peaks and troughs it has been proven that thereexists a relationship between the waves speed and length as a fixed relation. This relationship is true forall water waves and is called the speed to length ratio, SLR. The ratio is shown in equation 2.1, wherethe Vw is the Wave Speed and Lw is the wave length (Savitsky 1964, [16]; Rosen 2004,[15]).

SLR =Vw√Lw

= 1.25 (2.1)

Equation 2.1 shows that the propagation speed of a wave of a certain length is always the same.

At lower speeds, a crafts weight is entirely supported by buoyancy forces, the pressure variations fromtrough and crest will even out when looking at the hull as a hole, making the crafts draught and trimthe same as for its zero speed and the hydrodynamic drag dominated by friction.

Thus the hydrodynamic drag exerted on the ship can be predict by looking at its speed and length.When the SLR reaches 0.9, representing roughly two waves along the ship, the drag experienced becauseof wave making is starting to have a large impact on the ship (Savitsky 1964 [16]).

When the hull reaches SLR=1.25 it reaches what is called the wave barrier. At this speed the wavemaking resistance starts to become a dominant force. For SLR just over 1.25 the craft is in essence trying

3

to climb over its own bow wave. The stern will be in the trough section of the wave, here the regularrounded stern common for displacing hulls is going to increase the draft as it results in a negative pressurewhich increases with the speed of the hull making the wave resistance a virtual limit to increasing thespeed of a displacing ship (Savitsky 1985, [17]). The suction can be counteracted or at least lessened byusing a flatter buttock and a transom stern. A flat transom stern improves the flow separation from thestern of the ship thus removing the negative pressure on the stern. By increasing the speed at this pointthe trim and drag will decrease and the hull is lifted out of the water, this is when it is considered to beplaning (Rosen, 2004 [15]).

Since wave generation and its associated drag depends on the wetted length of the ship, planing has alarge impact on the drag experienced by the hull (Savtisky 1985, [17]; Rosen, 2004 [15]). At the momentthe hull starts planing, it will experience a dip in drag when the hull climbs over its bow wave andsubsequently travels on top of the water. This effect is illustrated in figure 2.2 where the hydrodynamicdrag of a ship is calculated for a displacing hull and a planing hull, showing the characteristic "hump"mentioned above as the wave barrier. The planing hull experiences a dip in drag right after the pointof planing, the drag at this speed is reduced since the wave making resistance now has a negligebleinfluence on the total drag and the spray resistance instead becomes the main contributer, comparedto a displacing hull where the drag rises almost exponentially with the speed as a function of the waveresistance( Payne, 1982 [12]).

Figure 2.2: Effect of speed on resistance for different hull shapes

Giving the HSC (High speed craft) its transom stern helps with flow separation in the stern but asimilar effect is experienced along the sides by the water flowing out. for example the water coming outon the right corner of the hull will at that point create suction which will drag that side of the hull downtowards the water surface. The flow separation achieved by a transom stern can be utilized at the sidesby using hard chines.

Hard chines are flat surfaces at the very edge of the hull which redirects water flow out from thehull as well as giving a hard edge to the sides (Clement, 1964 [2]; Savitsky, 2007 [17]). In figure 2.3 asimplified body plan of the Storebro 90E is shown where the chines can be seen at each side as short flatsurfaces.

Figure 2.3: Bodyplan for the 90E boat for the swedish military, Rosen [15]

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Another way of removing this suction effect is to remove the water flow along the sides using sprayrails, as in figure 2.4, which will redirect the water spray before the chines which is a big help in higherspeeds. This design will be covered more in depth in section 2.6.

(a) Hull with spray rails, beneath (b) Hull with spray rails,bow

Figure 2.4: Spray rail design by Clement, [2]

Equation 2.1 shows that the speed at which the wave barrier is encountered depends on the speedand length of the hull, and thus can be changed or manipulated by changing the design speed or bychanging the length of the hull. In essence, both the design speed and the length of the hull change thelength of the ships waterline, the wetted length Lwl. Changing the length of the ship could thus allow aship which did not plane at a certain speed to now plane at the same speed. By changing the speed itis possible to let the hull lift out of the water thus shortening the Lwl. The hull could also be designedto act more like a lifting surface, lifting the hull higher from the water shortening the LwL. The hullcan also be modified by adding so called interceptors and trim planes to the hull. These are small platesmounted at the rear of the ship which, much like the flaps on airplane wings, redirects the flow in theaft and making it possible to control the lift on the hull continuously.

The length and the width also affects this drag speed relation. For a long and slender hull thetransition occurs more gradually. The transition shown in figure 2.2 is for a short and wide hull forwhich the barrier is more significant. This phenomenon comes from the fact that a wider hull will havea much more significant wetted area than a slender hull which affects the frictional resistance.

It is very hard to determine an exact speed for which all craft starts to plane, this is because thereare a lot of things that effects this, such as the hull design and geometry mentioned above, the centerof gravity, if it is fitted with interceptors etc. For this reason tests where made by Savitsky et al, [17]in 1985. From the extensive testing he suggested three separate limits in SLR, shown in equation 2.2 to2.4, that can be used to connect the hull type to its characteristics at an early design stage.

DisplacingVw√Lw

< 1.25 (2.2)

Semi-planing

1.25 <Vw√Lw

< 2.8 (2.3)

Planing

2.8 <Vw√Lw

(2.4)

They are separated in this way because, for SLR<1.25 the ship is completely displacing, for 1.25<SLR<2.8the hull experiences both hydrodynamic and hydrostatic forces, and at SLR>2.8 the ship is predomi-nately carried by the hydrodynamic forces (Savitsky and Brown 1976, [18]). This is illustrated in figure2.5 where separation of the lifting forces follows the curve with the straight lines representing the separatestates of planing, figure 2.5.

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Figure 2.5: Achieved lift in percent of hydrodynamic and hydrostatic pressure, with planing speeds

2.2 Froude number

The Froude number, Fn is a non dimensional unit of speed based on several experiments preformed byWilliam Froude in mid 19th century, shown in equation 2.5, which is widely used in engineering circuits.Here the speed Vs and Lwl of a ship is used together with the gravitational acceleration g.

Fn =Vs√

g ∗ Lwl(2.5)

The length is not the important geometric size for a planing craft however, since when the ship isplaning the wetted length of the ship changes. The characteristic length can be changed for the maximumwetted beam since it does not change as much for a normal hull design, giving a Froude speed-beamratio, equation 2.6.

FnB =Vw√g ∗Bw

(2.6)

For hulls with very advanced hull shapes the displacement volume in m3 of the hull can be used toget a non dimensional speed, as in equation 2.7.

Fn∇ =Vw√g ∗ 3√∇

(2.7)

In this report all values are shown in non dimensional values such as the volumetric Froude numberin equation 2.7. This equation is however dependent on the displacement of the hull. Thus it is not veryuseful at an early design stage if the weight and displacement is unknown. Instead it is easier to use thespeed length ratio SLR from equation 2.1 or the beam Froude number from equation 2.6 as they dependon the length or the width of the ship respectively, which are dimensions that are often set early in thedesign process.

This is true for this report where the hull was initially designed using SLR and then converted toFn∇ when the displacement was final. Thus all graphs and tables in this report is presented in Fn∇,even the ones which appear before the displacement was known. These have been recalculated to Fn∇using the correct displacement for continuity.

2.3 Planing of flat surface

As mentioned, a hull at zero speed is influenced by a hydrostatic force in the form of buoyancy. Whenthe hull is moving in relation to the water, an added hydrodynamic force starts to affect the hull whichrepresents the hydrodynamic pressure exerted on the hull by the water particles which it is now tryingto move out of its way. It is also responsible for the wave making resistance. A flat plate exposed tothese forces was used by Savitsky [16] to explain and find calculations for planing craft in 1964, figure2.6.

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Figure 2.6: Flow and pressure on planing flat plate, Eliasson et al [4]

Here the flow beneath a flat plate is shown as the plate is skimming atop the water surface, with itsvelocity vectors shown. Following the water flow, i.e the small arrows on the bottom, it is observed thatthey arrive at a stagnation point where a maximum pressure, and therefore lift, is concentrated. Fromthis point the flow is separated in to two directions, one going forward and one going aftward. Towardsthe rear, the pressure diminishes quite evenly until the plate ends. Towards the front however, the waterflow follows the surface and gradually separates from it falling away as spray.

The resulting force from the hydrodynamic pressure becomes tilted backwards normal to the plate.The pressure force creates two components, one lift force that works vertically and one that is orientedbackwards and thus becomes a resistance force, figure 2.7.

Figure 2.7: Forces on planing flat plate, Eliasson et al [4]

Parallel to the plate there will be a friction force from the water to plate movement. As you cansee in figure 2.7 the friction will result in a rearwards drag component as well as a small reduction inlift, since the friction follows the plate at its trim angle τ and thus will have a negative vertical forcecomponent.

As have been mentioned before, Savitsky did extensive test on this and published in 1964 a compre-hensive study detailing how to calculate the lift for a planing plate, CL0, [16], shown here in equation2.8.

CL0 =m ∗ g

0.5 ∗ ρ ∗ V 2 ∗ b2(2.8)

Where V is the speed in m/s. With equation 2.8 Savitsky found that you then can calculate significantvariables for the planing shape as, equation 2.9

CL0 = τ1.1 ∗ (0.012 ∗ λ0.5 + 0.0055 ∗ λ2.5

Fn2b

) (2.9)

Where τ is the trim and λ is the wetted length-beam ratio, 2.10,

λ =LwBw

(2.10)

and Lm is the arithmetic average of the wetted keel length LK and the wetted chine length LC . Oftencalled mean wetted length,

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Lm =Lk + Lc

2(2.11)

Savitsky also determined a formula for finding the center of pressure, which is the distance fromcenter of pressure to the trailing edge, Lcp, shown in equation 2.12.

LcpLw

= 0.75− 15.21∗C2

v

λ2 + 2.39(2.12)

These are the main formulas used for calculations pertaining to planing flat plates with the keyformulas 2.9 and 2.12 credited to Savitsky, the most used formulas for predictions within planing crafts.

The way the formulas are used is by iteration. Starting by assigning a reasonable nominal value tothe trim angle τ and then iterating equations 2.9 to find λ since the LK and LC usually aren’t knownduring the initial design.

2.4 Planing of a V shaped hull

The flat plate theory is very useful, but very few HSC hulls are flat. A HSC usually has a very charac-teristic deep V shaped hull, giving the HSC hull the ability to cut through the waves and the surface ofthe water. The angle of this V shape is very significant for many reason. The angle of the V is calleddeadrise and often denoted β. It is defined as the angle between the outer part of the hull and thehorizontal plane at the keel according to figure 2.8

Figure 2.8: Deadrise angle shown on Storebro 90E hull

A hull with deadrise will direct the water out towards the sides, thus lowering the lift since thehydrodynamic lifting force is separated into a vertical component and a horizontal. Equation 2.8 thenhas to be corrected to get 2.13 for the lift generated by a hull with a deadrise (Savitsky’s [16]; LarssonEliasson, 2000 [4]).

CLβ = CL0 − 0.0065 ∗ β ∗ C0.6L0 (2.13)

Comparing this with equation 2.8 we can see that the adding of a dead rise to a planing body willlower the lift.

To get optimum lift it is better to have a small deadrise, commonly used in the 1930’s. However, thedeadrise also affects the vertical acceleration.

A flat plat hitting the water surface will cause a violent deceleration, the plates surface will encounteran opposite force and come to a dead stop. This means that the ride gets very bumpy and harsh withhigh vertical accelerations. A deadrise angle will pierce the surface and gradually lower its speed. Thismeans that energy is diverted from the lifting force to act as a shock absorber. For HSC and especiallycraft that are going to be used in the ocean or large lakes, a deadrise angle is crucial for both passengerand driver safety as well as the integrity of the hull (Bjernsten et. al, 2014 [1].

2.5 Resistance

Resistance can be defined as a force working against the desired outcome of a system. The total resistanceof a craft, Rtot, can theoretically be divided into several components. Two main components, theHydrodynamic resistance RHD and the air resistance, Ra. The air resistance is the resistance stemming

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from the area of the ship above water catching the wind. The Hydrodynamic resistance however canbe divided further into three mayor parts: the pressure resistance RP , the viscous resistance RV andthe spray resistance RS . A schematic picture of the different components of the resistance for a HSC isshown in figure 2.9.

Figure 2.9: Schematic view of resistance

The sources of RV and RP have already been explained in previous sections as well as the airresistance.

2.6 Spray

Spray, or whisker spray as it is also called, is the water which is forced to change its direction and travelforward and to the sides of a HSC hull as it moves through the water. The spray originates in theseparation of water flow at the stagnation point of the hull, shown in figure 2.6. There it is shown thatfor the flat plate, part of the water is pushed forward along the surface for a short distance and thenseparates and falls down towards the water. For a hull with a deadrise this means that the spray willmove forward and out towards the sides forming a triangular wetted area on the hull, see figure 2.10.

Figure 2.10: Spray area on model hull by Clement [2]

This area is called the whisker spray area or spray area. The area is constrained by the two lines,stagnation line and spray boundary line. The position of the stagnation line and spray edge can be foundusing a trigonometric formula in equation 2.14, Savitsky 1964 [16].

α = atanπtanτ

2tanβ(2.14)

Where π/2 is the so called pile up factor relating to the increase in wetted keel length, LK , by the buildup of water at the bow. The length of the stagnation line, C, can now be calculated as equation 2.15.

C =b/2

Sinα(2.15)

and the angle of the spray boundary line, θ, as in equation 2.16.

θ = 2α (2.16)

Where α, LK and LC can be seen in figure 2.11.

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Figure 2.11: Hull at speed showing the wetted area and its components

It is the size of this area that dictates the amount of spray resistance that the hull experiences. Whenthe spray hits the hull it adds a spray resistance to the total resistance because of the friction betweenthe spray and the hull.

The sprays contribution to the total resistance can be predicted using an addition to the Savitskyformulas in section 2.3, Savitsky et al (2007) [19].

The spray will cause an increase of the mean wetted length λ, called ∆λ, Which is dependent on therunning position and hull geometry, see equation 2.17

∆λ =CosΘ

4SinΘCos2β(2.17)

Giving the viscous resistance RS as in equation 2.18

RS =1

2ρV 2∆λb2Cs (2.18)

Where CS is the frictional coefficient in the whisker spray.In 1974 E.P Clement did towing tank tests to see if the resistance of a HSC could be lowered by

deflecting this spray from the hull. In figure 2.12 a picture, from E.P Clement’s paper [2] is shown, inwhich the spray from a HSC hull can be seen.

Figure 2.12: Spray on model hull by Clement, [2]

Since the spray adds to the total resistance, it is of interest to remove as much of it as possible. tothis end spray rails where applied to the hull to try and redirect the flow.

Spray rails are longitudinal rails attached to the hull which re direct the spray away from the hull.The rails should be mounted so they cover the spray area as in figure 2.10. The spray rail should havea smooth crossover to the hull so as to redirect the spray without creating unwanted turbulence, as infigure 2.13b, with a triangular cross section and a sharp outer edge as to induce flow separation, LarssonEliasson 2000, [4].

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(a) Spray rail flow (b) Spray rail cross section, Wielgosz [23]

Clement’s extensive tests with spray rails conclude that, at a Fn∆=5, spray rails could lower theresistance of a HSC hull with about 8-10%, introducing the benefits to reducing the spray and thus thewetted area on the hull. The spray rails can be seen mounted on the test hull in figure 2.14.

Figure 2.14: Spray rails mounted to experimental hull

Here the spray rails are mounted on the experiment hull in the predicted spray area. The yellow andred material is a clay which is used to smooth out hard edges and fill small holes.

2.7 PeteStep deflector design

The company PeteStep [13] has invented a new design for spray deflectors. The idea is to not only deflectthe whisker spray but redirect it. This means that using the Petestep design the spray can be directeddownwards thus helping stabilizing the craft and create lift as well as lowering the resistance. There isalso an added advantage of directing the spray flow so that a small increase in thrust could be achievedby harnessing a part of the kinetic energy in the spray.

By predicting the stagnation line in figure 2.10 or the stagnation point in fig 2.6, you can predictwhere the spray will form. If a wall or edge can be mounted just before this point, the subsequent spraycan be redirected from the hull thus reducing the wetted area of the hull.

Figure 2.15: Hull beneath with PeteStep deflectors, picture from PeteStep patent [13]

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The direction of the redirected flow will depend on the shape of the cross section of the deflector. Infigure 2.16a a cross section of the hull with its deflectors are shown. In figure 2.16b an enhanced imageof figure 2.16a is shown where we can see that the deflectors are angled in such a way as to redirect theflow down and somewhat inward towards the already submerged hull.

(a) Hull behind with PeteStep deflectors, picture fromPeteStep patent [13]

(b) Hull enlarged, behind with PeteStep deflectors,picture from PeteStep patent. [13]

Figure 2.16: Petestep hull drawing

If the correct angle between the outer edge and the deadrise is used, the spray and its energy couldtheoretically be directed down and aftwards resulting in a rise in lift force, a damping effect on verticalacceleration, reduced wetted area and resistance giving a small increase in thrust compared to sprayrails, as seen in figure 2.17.

Figure 2.17: Flow and cross section comparison: spray rails vs. Petestep design

The increase in thrust can be viewed as a reduction in resistance since it dose not create more thrustbut essentially recuperates some of the energy lost to the spray.

This design is what this thesis aims to evaluate. A model with a simplified version of this is made andexperimented on with its design explained in section 4 according to the experimental setup in section 5.

2.7.1 Previous experimentsThis novel design for deflecting the whisker spray and its potential gains has been tried in full scaleand is showing promising results [13]. Previous studies have been made on the design, but more data isneeded.

Olin 2016

In 2016 Olin et al did a numerical analysis of the PeteStep deflectors,[11]. Using the RANS-equationbased volume of fluid method, VOF method, CFD analysis. Which showed promising results using aprismatic hull with the particulars in table 2.1.

Table 2.1: Main particulars for Olin model

Lwl Bw β d Vs τ ∆ Lwl

bw

7 3.2 18.6 0.2 40 3.8 1350 2.19

This comparatively wide ship is well suited for deflectors since width has a large impact on the wettedarea. A wide ship gets a significantly higher wetted area thus the deflectors redirecting the flow makes

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has a large impact. Olin et al’s flow analysis show how the flow is redirected by the deflectors, figure2.18.

Figure 2.18: Flow on deflector, Olin [11]

In figure 2.18 the redirection of the flow by the deflector is shown. The spray is not only redirectedto reduce the wetted area, by redirecting the flow aftwards extra thrust can be gained. In figure 2.19two prismatic hulls are shown at 4 m/s, where the flow behind the hull can be seen.

(a) Bare hull (b) Deflector hull

Figure 2.19: Hull flow comparison, Olin [11]

The hull in figure 2.19a is without deflectors and shows how the water flow is going out to the sidesof the transom. The hull in figure 2.19b is equipped with deflectors and shows how the flow is moreconcentrated to the middle of the hull, reducing the wetted area and thus lovering the resistance..

By making a CFDmodel and predicting the flow change the deflectors would infer, Olin et al concludedthat the PeteStep design could reduce the wetted area more than existing spray rails resulting in areduction in the total drag with up to 32% and generate a 4% increase in thrust.

Wielgosz 2017

In an effort to validate Olin et al’s results, model tests was performed in 2017 at Stevens Institute ofTechnology by Wielgosz. The first test are done with a model which is a close match to the model usedby Olin, Wielgosz 2018, [23]. Unfortunately the lack of repeatability in the results show that the sizeof the model and the set up applied in the numerical simulations is not viable for experimental evaluations.

The next tests described in Wielgosz, 2018 [22], a series of experimental tests where performed ona motor lifeboat vessel, MLV, hull design modified to have deflectors. The test were conducted in bothwaves and calm water and strive to get data on the reduction in drag and vertical acceleration as wellas the potential thrust gain that would confirm the numerical results by Olin et al.

Weilgosz used one of the hull design used by Soletic et al,[20]. The model was made out of a lightfoam which then was coated with paint and epoxy, figure 2.20a and 2.20b

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(a) Hull at rest (b) Hull at speed

Figure 2.20: Model hull by Wielgosz [23]

The hull is a scale model of a MLV vessel with a higher length to beam ratio with its particulars asdescribed in table 2.2, (Soletic 2010, [20]: Wielgosz 2018 [22]).

Table 2.2: Main particulars of Wielgozs model

Lwl Bw β d Vs τ ∆ Lwl

bw

1.12 0.24 20 - 4-6SLR - 6.67 5.08

Wielgozs experiments showed a decrease in total resistance of 12% for calm water when both deflectorpairs where above the water surface, [23]. If one deflector pair was submerged, the results showed thatthe reduction in resistance diminished to about 3.2%. A decrease of 10.8% in bow accelerations for lowand medium speeds was shown independent on the number of deflectors fully submerged.

The model used was quite small and Wielgozs found that for this size of ship, in the particular speedstested, the water flow and the spray was laminar. This could have a significant effect on the level ofimprovement since full scale ships experiences turbulent or transitional flow of water. This is due to thatfact that the RN depends on the real speed, in knots or m/s and not the non dimensional SLR or Fnused for models.

Figure 2.21: Model hull from beneath, Wielgosz [23]

Wielgosz suggest that a wider model or a larger deadrise should be used so that a transitional flowcan be achieved to see if the change in flow changes the removed resistance significantly. The differencesin length to beam ratio could also affect the results since a slender hull benefits less from the deflectors.

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Chapter 3

Towing tank test

3.1 The towing tank

The test will be performed at the Davidson laboratory towing tank at Stevens Institute of Technologyin Hoboken New Jersey USA. The tank it self is 95 m long and 5 m wide with a depth of 2 m which canbe varied by adding false bottoms to simulate shallower water. At one end there is also a 12 m long surfbeach which can be raised and used to test the effects of erosion. The tank is equipped with computercontrolled over and under water cameras, as well as a wave maker and a "skimmer" used to level outand remove waves between runs.

The wave maker is capable of both irregular, regular and pseudo random waves as well as pulses,complex periodic waves and dual and triple wave trains. The advanced control software can create wavesof several different wave spectra’s such as Pierson-Moskowits, JONSWAP, ITTS and ISSC etc. with amaximum wave height of 0.46m.

The model is attached to a light weight high speed unmanned carriage where all recording equipmentis housed, such as the sensor signal conditioner and recorder including a close up camera. The carriagetravels along a monorail in the ceiling allowing the carriage to achieve a top speed of up to 30.48 m/swith a speed control of 0.03 m/s. For experiments a constant speed of 18 m/s can be achieved but forsafety reasons a maximum constant speed of 11 m/s is advised.

3.2 The ITTC

When doing any type of testing it is of great importance that the results are repeatable and reliable.To facilitate this there are guidelines which if followed make it easier for other people to belive in

the results and to replicate them if needed and do calculations for uncertainty of the measured values.For towing tank experiments good guidelines are provided by the International Towing Tank conference,ITTC [9]. The ITTC is a conference which takes place every three years where experts from all overthe world meet and discuss how towing tank test should be preformed and validated. The guidelinesare separated depending on what type of ship or marine structure you are testing, as well as whatinformation you want from the test. Be it resistance, stability, propeller efficiency etc. The experimentalsetup for these tests will primarily be guided by the high speed craft specific ITTC High Speed marinevehicle section 7.5-02-05 [8]. The analysis of the results will be guided by ITTC Guide for uncertainty7.5-02-02-02 [5].

3.2.1 MeasurementsFor calm water the interesting measurements are resistance, pitch and heave. For wave runs the focus ison acceleration at CG, accelerations at the bow, number of wave encounters and number of wave peaksand troughs.

Drag and Pitch

To measure the drag, an LVDT equipped drag balance is used, rated for 222.4 N (50 lbf) meaning that itcan measure forces up to 222 N. An LVDT measures the drag from the elastic deformation of the metalin the drag balancer, measuring the elastic movement in the metal and converting it to a drag value.The drag balance is calibrated statically by measuring five known weights and fitting a curve to the realvalues. Giving an absolute error of ±0.06 N. The drag balance is then mounted on a pitch pivot box.The pitch pivot box measures the pitch angle through a rotational potentiometer mounted inside the box

15

measuring the movement between two gears. This measurement is used in the wave runs to accuratelymeasure the number of waves the hull encounters. The pitch is also calibrated statically and for fivepositive and negative angels, calibrated to within ±0.0161 deg.

The signals from both the LVDT and the pitch pivot box are recorded in the same way. The signalis converted and then recorded by a 16 bit to analog converter and recorder. The signal is then averagedby a Microsoft DOS based analysis program called DAP51c. Both the averaged measurements and thereal time sensor readings can be obtained from the DAP51c program and given over for analysis.

The pitch pivot box with the drag balancer is mounted to the heave post and to the hull and thusbecomes the place where the thrust from the monorail carriage is transferred the hull.

Heave

The heave is measured from a potentiometer mounted by the heave post. The potentiometer has a wheelmounted to it where a string is running. The string is mounted at the top and bottom of the heave post,when the post moves the wheel is spun by the string and the potentiometer registers the movement. Thisis then converted to a distance in height. This is calibrated to with in ± 0.2 mm.

Accelerometers

For the vertical accelerations in waves a set of accelerometers are used to measure the acceleration atcertain points along the hull. The sensors are 30g Schaevitz closed loop torque-balance transducers whichcan be mounted any where on the hull. In this application, one is put as close to the LCG position aspossible and another is mounted closer to the bow. The accelerometers are calibrated statically to within ±0.03g.

Inclinometer

To measure the static and running trim a gravity referenced Inclinometer is used. Made by Schaevitz, itis their LSO series which is a fully self-contained, fluid damped, flexure suspension, servo inclinometer. Itis a precision industrial grade sensing instrument designed to meet the needs of a variety of commercial,industrial, and aerospace applications. This device is delivered fully calibrated to within ± 0.0005 deg.

Wave encounters

For wave runs, the actual amount of waves that impact the hull will have to be measured. If the wavesare irregular or otherwise non consistent, the number of wave peaks and troughs must be analyzed. Thisis done by analyzing the difference between the movements in pitch and heave of a data point. If thedifference is bigger than a set value, called a buffer value, the program logs it as a peak or a trough. Ifthe current value was a value significantly higher (bigger than the buffer value) than the previous valueis registered as a peak and the program then starts to look for a trough value. This is done automaticallyby the Dap51c program used and then displayed after the run, showing both the number of measuredheave encounters and the number of measured pitch encounters

Sensor positions

The sensors and their position is shown in figure 3.1 and table 3.1

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Figure 3.1: Position of sensors and weights in model

# Unit Name LCG[mm]

VCG[mm]

Mass[kg]

1 Foam Hull 787.4 114.3 9.592 Inclinometer 317.5 152.4 0.353 Pitch Pivot Box 548.6 158.8 1.194 Drag Balance 548.6 222.3 2.695 Attachment Bar 548.6 304.8 0.716 Heave Post 548.6 685.8 2.697 CG Accelerometer 444.5 151.1 0.138 Bow Accelerometer 1318.3 151.1 0.139 Aft Ballast 76.2 177.8 Varies10a CG Ballast 548.6 431.8 Varies10b CG Unload Spring 548.6 - Varies11a Bare Hull Plate 650.2 63.5 3.2711b Spray Rails 825.5 63.5 0.0911c Low speed deflector 1104.9 71.1 1.2211d High speed deflector 977.9 73.7 1.35

Table 3.1: Sensor weights and locations.

Summation and averages

The actual measurements from the pitch, the drag balancer and the heave is taken as the average of thesensor values during the run. The tank is set up to start the measurement at a set distance from thestart. Depending on the desired speed of the carriage the acceleration is changed so that the hull hasreached a stable state before the measurements, this distance is set to 51 m giving the carriage ampletime to accelerate and slow down.

The speed of the carriage is measured by the same program which controls speed and acceleration, aswith the pitch and drag the values for every second is averaged over the run and a real value of speed isgiven to be compared to the value that was aimed for. The temperature of the water is measured downto ±0.05 degrees by a digital thermometer in the water.

3.3 Uncertainty analysis

When measurements are taken there is always a chance that they are accurate enough. A measurementof temperature can be influenced by a strong breeze or even somebody standing to close. For this reason,best praxis is to take an average of several (at least two) measurements at the same set up. When

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an average value is used it is also good to show the uncertainty of the measurements, meaning theprojected error margin of the value. The ITTC has very good guidelines for calculating the uncertaintyof measured data points. For these experiments "The General Guidelines for Uncertainty Analysis inresistance Tests" is used [5]. It is vital to analyze the gathered data and calculate the averages, thestandard deviations and general uncertainty of the measurements. The ITTC guideline breaks down theaverage and uncertainty calculation different depending on what is measured and how it is measured.

Resistance, trim, heave and speed

When repeat test are performed the ITTC recommend that a mean value of the repeats are adopted asthe best estimate of the measured value. A simple mean value calculation is used for this, the equationfor the resistance is shown in equation 3.1 where RT is the mean value of resistance for the runs, N thenumber of runs and R̂T the specific value of resistance for run j.

RT =1

N

N∑j=1

R̂T j (3.1)

With the mean calculated, the standard deviation of the measurements can be calculated as inequation 3.2.

s =

√√√√ 1

N − 1

N∑j=1

(RT − R̂T j)2 = u(R̂T j) (3.2)

Now with both the standard deviation and the mean, the uncertainty of the measurement can beshown according to equation 3.3 in the measured unit, Newton in the case of drag resistance, and inpercent according to equation 3.4.

u(RT ) =s√N

(3.3)

u′(RT ) =

sRT√N

(3.4)

The equations above are shown, as stated previously, for the drag resistance but can be changed totrim, heave or speed by changing RT to the appropriate variable.

The value u′(RT ) is then used to calculate the total combined uncertainty.As previously stated, this can be used to calculate the repeatability of the towing speed as well.

However the speed is also used later for the combined uncertainty as u′4 which is just the standard u′(V ),equation 3.4 but for the speed V, multiplied by 2:

u′4 = 2u′(V ) (3.5)

Water temperature

The water temperature is measured constantly during the tests to ensure that the density of the waterin the tank is at the same level. For the water temperature the ITTC has a small note for makingthe measurement easy to handle. Since the water temperature usually is measured with an accuracy of±°0.1C the uncertainty can be taken as 0.002% which is negligible, but still should be added when doingthe combined uncertainty.

Model geometry and form

Generally when you are making models and doing comparisons it is with respect to a real ship. Whencomparing to a real hull much care and time has to be made so that the model is as good a match aspossible, both in geometry and how the water is affected or affecting the hull. In these experimentshowever there is no real hull to compare to since this hull is designed for this specific experiments.Because of this a large part of the uncertainty analysis regarding the model becomes superfluous.

However, because of manufacturing tolerances and design tolerances there will of course be thingsthat differ. When a new hull is inserted, the whole hull is gone over to find high spots and low spotslike screw holes and edges which are then covered in clay or sanded down by hand to make them smooth

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and lower their influence on the tests. For more information on the model, design and manufacture readMolchanov 2018, [10]. The effects of this change in plates is considered negligible on the model geometryresults since the hull is at all times compared to it self.

Combined uncertainty

Following the ITTC [5], it is advised to calculate the combined uncertainty. The combined uncertainty isthe uncertainty of the measurement with respect to every measurement gathered during the test such asair and water temperature, sensor calibration etc. The uncertainty for resistance designated uc, dependson four main uncertainty values calculated, General Guidelines for Uncertainty test, ITTC 7.5-02-02-02(2014) [5].

The water temperature uncertainty

u′3 = u′(ν) = 0.0002 (3.6)

which is the change in viscosity of the water, shown in previous section.Towing speed as above:

u′4 = 2u′(V ) (3.7)

The dynamo-meter calibration uncertainty u′(RT ) , Which is simply the sensor calibration errordivided with the average measured value, as:

u′2 =error

value=

0.06

RT(3.8)

Where 0.06 is the calibration error from section 3.2.1 for drag sensor.And the uncertainty from hull balancing u′1, which is the scaled uncertainty of the displacement as:

u′1 =2u′(∆)

3(3.9)

This is shown to be equal to the uncertainty in the water density which, if the water temperature changeis around ± 0.5°C, gives a uncertainty of about ± 0.01%.

These can now be combined to a total uncertainty:

u′c =√u′(∆)2 + u′(RT )2 + u′(ν)2 + u′(V )2 (3.10)

Which gives the total uncertainty for the combined mean of the resistance from the runs made atthat speed.

And the expanded mean Up as:

Up = 2 ∗ u′c (3.11)

Where 2 is used for a confidence level of 95%.

An example of the uncertainty calculations as well as the combined and expanded uncertainties forall speeds are shown in appendix A and said uncertainties are shown with the calculated resistance inappendix B.

Wave encounters

Wave encounters are measured through two different reactions of the hull, by pitch change or by heavechange. By using these values it is possible to determine which part of the wave caused the accelerationexperienced by the hull. Since a wave has both a peak and a trough it is essential that both instances (orparts) of the wave are analyzed to be able to arrive at a conclusion for the hulls seakeeping characteristics.Both parts also has to be encountered in enough instances to be able to conclusively use the data. Toensure this, the ITTC sets a minimum average of 75 encounters for a RMS analysis of accelerationsand motions and an average of 100 encounters if the extreme slam pressure needs to be determined, [6].Since the lab standard is 100 averages this is what will be chosen for these test and it will also give theopportunity to analyze the extreme values.

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3.3.1 Froude scaling lawsWhen doing experiments and towing tank test it is good practice to scale the values from real shipsdown to smaller numbers, or when comparing between two models, where not all parameter are thesame, scale them to match. Since many of the parameters guiding the physics concerning ships and hullsare geometrydriven this has to be done very carefully.

For the main dimensions (length, width, draft), a factor µ is often used, where µ is the scaling factor.This factor can be had simply from the dimensions as in equation 3.12

µ =LDesignLModel

(3.12)

With µ most of the values concerning a ship can be scaled according to table 3.2 (Steen 2017,[21]).

Table 3.2: Froude scaling laws

Physical parameter Unit Multiplication factorLength [m] µ

Structural mass [kg] µ3 ∗ ρDρMForce [N] µ3 ∗ ρDρM

Moment [Nm] µ4 ∗ ρDρMaeleration [m/s2 aD = aM

Time [s] õ

Pressure Pa=N/m2 µ ∗ ρDρMSpeed [m/s] VM = VD√

µ

By using these scaling laws the error in calculations is minimized and it opens up more data forcomparison and design purposes.

3.3.2 Non dimensional unitsWhen doing experiments on hulls and ships it is useful to use non dimensioned units. This makes it easierto compare bespoke model hull designs to real ships even when when they have different geometries anddimensions. This is especially true for planing craft where the geometry of the hulls wetted area canresult in significant changes for different speeds. The ITTC recommends to use non dimensional unitsfor both speed, resistance and heave. Where the speeds has been covered in section 2.1 equation 2.7.The resistance is normalized by the displacement:

Rt∆

(3.13)

and the heave normalised by the cube root of the displaced volume as:

h3√∇

(3.14)

3.4 DNV GL

The DNV is a company which works to make ships more safe and energy efficient. During the yearsthey have been in business they have gathered a large set up rules and regulations that if followed willminimize the risk of accidents and deaths at sea. Many countries now require ships to conform to theserules before they can enter a port or be sold in the country.

For this report these rules will be used to estimate the accelerations that the hull will be subjected toduring the wave tests. This is done by using the high speed craft specific manual: Rules for classification,High speed and light craft, part 3 chapter 1, [3] formulas 2.2.2 for SLR>3, 2.2.3 for SLR<3 and 2.2.4 forbow accelerations.

The formulas presented for high speed craft accelerations in the DNV manual are specific to the typeof hull and ship used as well as where on the hull the accelerations is measured and where the hull issupposed to be used. These formulas are not shown in this report but can be found in DNV rules forhigh speed craft [3].

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Note, the formulas require the length, speed and weight to be scaled to achieve an accurate acceler-ation. This can be done using the scaling laws described in section 3.3.1 and the approximate scalingfactor of 12.8 shown in section 4

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Chapter 4

Model DesignIn this section the steps taken to design the model craft will be explained.

4.1 Design

A bespoke hull was designed for this project to encompass the novel spray deflector design. A single hullwhere the bottom part could be changed depending on the design was to be used since the project alsocalled for a bare hull and spray rail design as a baseline for the tests.

Several possible hull shapes where considered for the hull but the final choice for a parent modelfell on the model used by Wielgosz [23]. The hull geometry was simplified to a prismatic hull shape inorder to make the model conform easier to Savitsky’s empirical model [19], as the Savitsky method wasdeveloped with prismatic hull shapes and is the model used for the location and geometry of both thespray rails and the spray deflectors. Simplifying the design and making the theoretical calculations moreexact as well as removing uncertainties associated with non prismatic hulls. The prismatic design alsoaids with the modular design, since it makes the hull bottom symmetric.

Thus the hull was made prismatic from the transom stern to the intersection between the keel andthe fore most stagnation line so that during the calm water tests the immersed part of the hull would beprismatic.

The bow shape was formed as a simple rounded shape with reasonable hydrodynamic properties atdisplacing speeds and wave tests since the model will be tested for speeds where the bow will not beinteracting with the water.

Since the object is to see the changes in resistance due to spray area, it is crucial that the magnitudeof spray resistance is large enough that the difference with or without spray can be quantified. Meaningthat the magnitude of the spray resistance RS becomes an important design parameter. However it alsoneeds to have a large impact on the total resistance so that its removal is noticeable, meaning that thespray resistance needs to attribute a certain minimum percentage to the total resistance. To achieve thisthe trim needs to be low, thus minimizing the induced drag, and flow in the spray area needs to have ahigh Reynolds number, ensuring that the flow is in a transitional or turbulent state.

4.2 Design constraints

Initial constraints discussed for the model design consisted of constraints which could not be changed,such as logistical and safety measures. Which were then joined by optional constraints.

Towing tank

The towing tank it self sets a few of the base constraints. As mentioned above the tank is generally notrun at speeds above 11 m/s which will dictate the flow state.To minimize the influence and uncertainties from wave and wash, the ITTC recommend that the modelhas a maximum length two times smaller than the width of the tank and at least 0.8 times smaller thanthe tank depth. Giving a maximum model length of 2.45 [m] for this tank. The length also limits themaximum speed since longer models will have a lower maximum Fn. Talking to people with experiencein the towing tank, it was strongly suggested to limit the maximum weight of the model to 22.7 [kg] forthe wave tests to ensure the safety of the hull and the equipment.

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Manufacturing constraints

New models made in house are usually milled from a block of closed cell marine grade foam. The foamis delivered in 1.22x2.44 [m] block with a user-specified depth and density choice of 160-250 kg/m2. Themilling machine it self takes off 0.0254 [m] extra when it cuts, lowering the maximum length to 2.37 [m].

Spray area

It was decided to place a minimum limit on the theoretical spray magnitude of 1 N and that this wouldbe at least 5% of total resistance, this was done so that the resulting resistances would be large enoughthat they would not be as effected by measurement error.

These three initial constraints, summarized in table 4.1, make the basis to the design since they arethings that cannot realistically be changed.

Table 4.1: Design constraints

Towing tank limitationsMaximum speed Vmax=11 m/s Limits FnMax

Towing tank dimensions Tank width: Lm <2.5[m] Wave backlashTank depth: Lm< 2.475 [m]

ManufacturingBlock size and tool path Lm < 2.37[m] allowance for tool path

Foam density ∆< 22.7 [kg] Model cost and weightSpray area

Transitional flow state Re>1.5*106 Transitional flow limitSpray resistance magnitude Rs>1 N Minimize errorSpray resistance contribution RS

Rtot>5% Validate technology

Length to beam ratio

To determine the L/B ratio matlab was used to predict different spray resistance magnitudes from L/Bratio. For a short and wide hull the potential gain from removing the spray resistance is good but thepercentage of total resistance that is due to spray is relatively small. Conversely, for a long and slenderhull the spray resistance percentage is higher but the magnitude of the spray resistance is smaller, [2].Meaning that there is a tradeoff between the two, shown in figure 4.1.

Figure 4.1: Spray resistance influence on total resistance because of L/B ratio.

Using initial dimensions that guaranty the transitional state of the flow, the length and beam wasvaried separately to see the effects of resistance while the LCG was scaled according to Froude scalinglaws to ensure identical running conditions. Given previous constraints as well as the fact that a modelwith an L/B ratio above 6 has a unsatisfactory load carrying capacity as well as adding complicationswith manufacturing, an L/B ratio of 4-5 would be the optimum choice.

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Modular design

To save cost a modular design of the hull was chosen, which could be adapted to both bare hull andspray rail design as well as to deflectors. Two deflectors where to be tested, designed for different speeds.One for higher speed and one for a lower speed. This meant that one hull had to be able to be modifiedin four different ways. To change the bare hull to spray rail is a simple act of attaching the spray railsusing tape or glue on the bare hull itself, [2]. The deflectors however had to be able to be removed andreattached.The parent hull design is shown in figure 4.2 with the bare hull plates mounted.

Figure 4.2: Model design with detachable plates

The darker part is the foam hull section with the bare hull plats made out of PVC shown in lightercolor. This PVC part could then be changed to the desired design, shown in figure 4.3.

Figure 4.3: Model design with detachable plates, bare hull left, spray rails center, pray deflector right

Figure 4.3 also shows the design of one of the spray deflectors that will be used whose design will beexplanied in the next section.

4.3 Model specifics

The only thing left to specify was now the length and displacement that satisfies the constraints in table4.1. Using the maximum allowed displacement of 22.68 [kg] it was scaled against the reference modelused in Wielgosz [23] using froude scaling laws. The scaling factor was aquired using equation 4.1.

µ =3

√22.68

6.67≈ 1.5 (4.1)

Looking at the model from Wielgosz [23]. It had an actual Loa/B ratio of 4.67. Which meant thatif the same ratio was adopted for this model, the data would be comparable. It was also suggested byexperienced towing tank personnel that the models length did not exceed 1.82 [m].

This gives the particulars as in table 4.2.

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Table 4.2: Model parameters

Parameter Parent hull Model dimensions SI Model dimensions ImperialDeadrise β 20 deg 20 deg 20 degBeam B 0.24 [m] 0.36 [m] 14.2 [in]

Length overall Loa 1.22 [m] 1.80 [m] 71.0 [in]Length of waterline Lwl 1.12 [m] 1.68 [m] 66.0 [in]

Displacement ∆ 6.67 [kg] <22.68 [kg] <50.0 [lb]Lwl/B 4.67 4.67 4.67LCG varied 0.55 [m] 21.6 [in]

4.3.1 Design speedsTo confirm that the model satisfied all the constraints its particulars was run through the Savitsky model[19] & [16] for Fr∇ 1-7, plotted in figure 4.4

Figure 4.4: Theoretical resistance for chosen model

The red dashed line shows when the magnitude of the force exceeds 1 Newton and the black dot-dashed line shows when it exceeds 5%. This indicates that the 1 Newton threshold is achived at aboutFr∇ 3.5 and that the 5% threshold is achieved at about Fr∇ 4.9. Which proves that theoretically themodel satisfies the constraints for Fr∇ 4 .9and upwards.

4.3.2 Deflector designThe two deflectors are modeled after the design patented by Petestep and explained in section 2.7. Eachdeflector is designed for one particular speed. To meet the spray resistance magnitude requirement a highspeed deflector, deflector 2, was designed for Fr∇ 5.87, giving it good theoretical resistance values. Thisis a quite high speed but it will be very telling of the efficiency of the deflectors. A low speeds deflectorwas also designed, called deflector 1. This time for Fr∇ 4.3. This does not fulfill all the resistancerequirements but it is a more realistic speed. It is also a speed which allows running in waves withoutrisk to the equipment. The deflectors environment and predicted values are shown in table 4.3

Table 4.3: Design speeds for deflectors

Design speed Fr∇ Flow state Designed Spray force [N] Rtot ContributionDeflector 2 5.87 Transitional Calm water 7.26 11.67%Deflector 1 4.30 Laminar Waves 1.55 3.72%

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Using the Savitsky formulas [19] & [16], the LK and LC can be predicted for the hull at differentspeeds. Which in turn can be used to show the stagnation line on the hull as figure 4.5a and the chosendesign stagnation lines in figure 4.5b.

(a) Predicted stagnationlines for speed range (b) Stagnation lines for deflectors 1 and 2

Figure 4.5: Predicted stagnation lines

Because of the modular design of the hull the deflectors had to be simplified for manufacturingpurposes. Instead of tapering of into the keel as can be seen in figure 2.15 and 2.16, they have a constantthickness from chine to keel. The Cross section of the deflector is triangular so the angle for the edgetowards the hull is 90deg shown in figure 4.6b.

(a) Deflectors top (b) Deflector 2 cross section

Figure 4.6: Deflector designs

For a more indepth description of the manufacturing and design of the deflector see Molchanov, 2018[10].

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Chapter 5

ExperimentsIn this chapter each experiment will be shown together with the results and discussion of said results.

Primarily, the deflectors will be compared to spray rails in how efficiently they remove the spray andreduce the wetted area of the hull in calm water. To get a baseline, a bare hull will be tested as well andthen the spray rail and deflector hulls compared to it for resistance, trim and heave. Two sets of testswhere made in calm water, one where the hulls all had the same LCG and one where they had the sameaverage running trim.

Secondly, the vertical accelerations will be measured during irregular wave runs. Once again thespray deflectors will be compared to the spray rails and the bare hull to see how they affect the verticalaccelerations at the bow and center of gravity.

The model with accompanying sensors was attached to the towing carriage by a heave post at theLCG.

5.1 Calm water setup

The model was tested with four different hull configurations at 5 different speeds each and comparingthe measured values from each speed between the hull configurations. The model was run at each speedat least twice, so that an average of the gathered values could be established and thus a more valid resultshown. For each test the real speed, drag resistance, heave, trim, water temp, Lk and Lc was writtendown on paper and in a test matrix together with the speed aimed for and the calculated Lk and Lc forsaid speed, figure 5.1.

Figure 5.1: Empty test matrix for bare hull test

As mentioned in section 4, two deflectors where designed and manufactured for the hull. This wasdone in an effort to cover a sufficient speed interval. The first deflector was designed for a lower speed ofFn∇=4.3, the second for Fn∇=5.87 and the same LCG as the bare hull, 0.32%L. In accordance with theITTC HSC resistance test [7], one lower and one higher speed than the design speed was chosen for eachdeflector which the bare hull and spray rail also would be subjected to, as well as an intermediary speedbetween the design speed and the added speed to help define humps or hollows in the characteristics ofthe deflectors. Resulting in two higher speeds and two lower speeds in increments of 0.78 Fn∇.

This means that each deflector would be tested for five different speeds with small increments, givinga comprehensive picture of the effects of each deflector. Due to time shortage the bare hull and spray railhull could not be tested for all these nine speeds. Instead they would be tested for five speeds includingthe design speed of each deflector one lower, one higher and one middle speed in increments of 1.58 Fn∇.The speeds for each hull configuration is shown in table 5.1.

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Table 5.1: Main test speeds

Bare hull 3.52 4.30 5.09 5.87 6.65 Fn∇Spray rail hull 3.52 4.30 5.09 5.87 6.65 Fn∇Deflector 1 3.52 3.91 4.30 4.70 5.09 Fn∇Deflector 2 5.09 5.48 5.87 6.26 6.65 Fn∇

To get a good baseline and to be able to confirm the design of the model compared to the designconstraints, three extra low speeds where added to the hull and the spray rail tests shown in figure 5.2.

Table 5.2: Test speeds theory comparison

Bare hull 1.47 2.20 2.94 Fn∇Spray rail hull 1.47 2.20 2.94 Fn∇

The assumption is that the Savitsky model [19] & [16] used to design the hull is most accurate forthe speeds just after planing and then show a successively larger error compared to the experimentalresults. Therefore these lower speeds would be tested and compared to the theory as a proof of concept.

The total speed range will therefore be as in figure 5.2.

Figure 5.2: Speed range for test

The hulls were run according to their speed ranges, first in ascending order and then in descendingorder, using a skimmer and waiting for the waves and ripples to die down, noting the results in separatetest matrices, figure 5.3.

Figure 5.3: Filled test matrix for bare hull

During the run both video and still pictures where taken over water and still pictures under the wateras well. The hull was marked on the side, the bottom and at the keel in one inch increments so that thelengths of water line and thus the wetted area could be calculated from the under water pictures as seenin figure 5.4

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(a) Under water picture of bare hull run at Fn∇=2.94

(b) Over water picture of bare hull run at Fn∇=2.94

Figure 5.4: Camera set up for experiments

5.2 Calm water test, Savitsky prediction vs experimental com-parison

The model was designed using resistance, stagnation line and LCG gathered using the Savitsky model[19] & [16]. This section aims to compare these empirical results to the experimental values gatheredfrom the bare hull runs.

The Savitsky method [19] & [16] is only applicable for 0.6<FnB>13 and gets less accurate as thespeeds increases. Since the speed range used in this test correspond to 1.3<FnB>6 it is expected thatthe lower of the tested speeds will be more accurate than the higher speeds.However since the data is athand a comparison is interesting to see how much they differ. This is technically not a separate test buta proof of concept and an initial way of confirming the validity of the experiments and their results.

Since the formulas are based on forces and lever arms it could also be interesting to see what happensif you combine them with experimental results. Using the experimental wetted area as it is shown inunderwater pictures, the Savitsky model [19] & [16] where used on the observed wetted area to increasethe accuracy of the method and then compared to both the experimental values and the purely empiricalSavitsky method. If this proves to be a reliable method it might be possible to break down each totalresistance from the experimental runs into separate forces according to section 2.5. By doing this it wouldbe possible to trace any differences in resistance from different hulls to a specific type of resistance.

5.2.1 Results and discussion, comparison: Savitsky model, bare hullIn figure 5.5 the average measured trim during the experiments and the calculated trim from the Savitskymethod [19] & [16] is plotted against the speed Fn∇.

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Figure 5.5: Comparison between Savitsky prediction and the experimental values in trim for bare hull

Figure 5.5 shows the measured values and the lower figure shows how much the Savitsky method[19] & [16] differs from the experiments. This shows that for this hull the Savitsky [19] & [16] methodpredicts on average a 0.62 degree higher trim than what is actually achieved by the hull. Showing theinert error of the Savitsky method [19] & [16] and its usefulness in initial design but not as an exactprediction.

This trim difference can be visualized using the under water pictures in figure 5.6.

Figure 5.6: Comparison stagnation line, Savitsky model (yellow) and experimental results (red)

Since the location of the stagnation line is directly dependent of the running trim it follows that thetheoretical stagnation line is going to be off from the experimental, and as can be seen in the picture thetheoretical stagnation line, shown in yellow, is different from the experimental results.

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This in turn means that the pressure area and the wetted area will differ, meaning that the predictedresistance also will be off.

In figure 5.7 the non dimensional resistance compared to the Fn∇ speed for the savitsky modelprediction [19] & [16], the experimental results for the bare hull and the calculated drag using theexperimentally determined wetted area and equations 2.9 - 2.11 from LK and LC are shown and in thebottom graph the difference in resistance for the two empirical models are compared to the experimentalresults.

Figure 5.7: Comparison between Savitsky prediction, experimental and Savitsky post processing inresistance for bare hull

The yellow bars show how much of a discrepancy there is between the results from the post processedwetted area calculation and the experimental results while the black bars show the discrepancy for thepure Savitsky method [19] & [16] compared to the experimental results.

As expected the Savitsky prediction, [19] & [16], is reasonably close for speeds between 1.5< Fn∇ <3.5where the code has an error of about 3-5% which can be considered reasonable. That it is under predictingfor the lower speeds is not that strange either since the hull essentially becomes displacing. Then forthe higher speeds the difference rises rapidly to about 15% from FN∇=4.3, which seems to follow thediscrepancy seen previously for the trim.

The post processed values from the experiment with the Savitsky model [19] & [16] shows a greatimprovement from the prediction. The error becomes much smaller, going from 18% to about 4% forthe highest speed. It is however not consistent in its accuracy. This inaccuracy will be affected by theLK and LC values, which the resistance calculation is based upon, as they are measured by eye frompictures of the hull, giving an accuracy of at best ± 25 mm.

In figure 5.8 the forces for the bare hull at the two design speeds is shown compared to the experimentalresult.

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(a) Force breakdown at Fn∇=4.3 (b) Force breakdown at Fn∇=5.87

Figure 5.8: Force breakdown and comparison to experimental results

The total measured resistance from the experiments is here divided into the separate forces thataffect the hull, as shown previously in figure 2.9. The forces are here calculated using the wetted areagiven by the underwater pictures and the formulas from the Savitsky method, [19]. The yellow piece isthe difference between the experimental results and the post processed results. Showing that 12% of themeasured resistance at Fn∇=4.3 is missing from the theoretically calculated resistance. This discrepancycannot be attributed to any one force but is most likely a summation of several small errors in most of,if not all, of the separate resistance forces.

For the lower speed comparison in 5.8a the discrepancy is as high as 12% which is three times as highas the calculated spray resistance for the same speed. Meaning that the discrepancy in the calculation isactually higher than the interesting value. The notion that the wetted area can be used to break downthe forces is very good but for these results it will not be possible to use. The comparison in figure 5.8bfor the higher speed, the discrepancy has diminished to about 6% and the spray drag increased to 15%,which is better but still a very large margin for error.

5.2.2 ConclusionsThe Savitsky method is a great method in the early stages of hull design as you can predict the shipsreactions with only the most basic geometries and weights. When you get to a more complete stage andstart to design the hull shape the methods falters and a more exact method is required.

By using the underwater pictures of the hull and calculating the different parts of the total resistanceusing the savitsky method a more accurate picture can be had of the forces. It is however again notaccurate enough, breaking down the forces shows a large discrepancy between the real resistance and thepredicted one.

5.3 Calm water setup, Same LCG

The previous section shows that the experiments give good consistent values which show good compa-rability. In this section we start analyzing the interesting values and compare the bare hull to the otherhull designs. For the experiment, the different hulls were loaded to the same LCG for each run withan accuracy of ± 0.2%. All hulls where then run according to section 5.1. The results are separatedin 2 sections where the first focuses on the comparison with spray rails and then the second with thedeflectors.

5.3.1 Result comparison: Bare hull and spray rail hullThe focus is now moving to the experimental results and their comparisons, starting with the spray railsand comparing that to the bare hull with figure 5.9 where the trim is plotted.

32

Figure 5.9: Comparison between spray rails and bare hull in trim

Looking at the top graph in figure 5.9 the two hulls running trim looks extremely similar whichalso seems the case when looking at the specific differences in the lower graph. It shows that the trimdifferences is negligible between the bare hull and the spray rails. The highest difference in measuredrunning trim is about 0.1 degrees, small enough to be considered a measurement error.

The resistance is shown in figure 5.10.

Figure 5.10: Comparison between spray rail and bare hull in drag

Looking at the resistance graph in figure 5.10 it shows that for lower speeds the spray rails actually

33

increase the resistance compared to the bare hull by up to 9%. This probably comes from the sprayrails being submerged for speeds up to Fn∇=3.5. Even though the rails to our best efforts where madestreamlined they will increase the turbulence and drag when submerged. As the speed increases theresistance decreases as the spray rails rise out of the water and into the spray area.

It looks like the spray rails are just removing the spray with no other adverse effects on the hull whatso ever.

In figure 5.11 the heave is compared to the speed as a non dimensional unit.

Figure 5.11: Comparison between spray rail and bare hull in heave

Here once again the values for the lower speeds where there is no spray and the rails are completelysubmerged the difference is negligible. Then around Fn∇=3 the heave for the spray rails starts toincrease and then stays a little bit above the bare hull for the remainder of the speed range.

By using the same post process as in figure 5.7 the theoretical spray resistance can be plotted againstthe decrease in drag because of the spray rails as figure 5.12.

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Figure 5.12: Theoretical spray resistance removal vs. actual experimental difference

The graph shows that the spray rail actually removes more than just the spray resistance at Fn∇=4.3 and 5.09. This extra decrease in resistance could be from the hull rising higher out of the wateras the spray rails start to work in the spray area. which actually seems to be supported by the heavechange shown for the speeds Fn∇>3.5.

This indicates that the spray rails actually give a small increase in lift and is then an indicationthat by deflecting the spray from the hull there is definitely the possibility of harnessing the sprayskinetic force for other purposes. As the speeds rise above Fn∇<5.09 the spray rails are starting to leavethe spray are and become a part of the dry area of the hull which can be seen in the decrease in sprayresistance reduction. At the highest speed of Fn∇ 6.65 the spray rails has gone from the 100% reductionat Fn∇=5.09 down to 30% decrease.

Conclusion

The addition of spray rails has a small effect on the resistance of the hull and on the heave making thehull ride a little higher in the water, reducing and redirecting a small part of the energy in the spray.Interestingly the changes that can be seen in figures 5.11 and 5.10 dose not seem to affect the trim asin figure 5.9. This could be an effect of positioning of the spray rails and thus in essence where thestagnation lines are. By only changing the heave and not the trim, spray rails are increasing the liftbeneath the CG position lifting the hull straight up.

5.3.2 Result comparison: Bare hull, Spray rail and deflectorsThe experimental results for the deflectors are now added to the previous bare hull and spray railscomparisons. Looking at figure 5.13 we see the average running trim for all hulls.

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Figure 5.13: Comparison between bare hull, spray rail and deflectors in trim

Here a large difference can be seen. It seems the deflectors have a large effect on the running positionof the hull. The deflector hulls are experiencing about 1deg higher running trim for every speed. Thedifference in running trim can even be seen in the over water pictures of the hulls shown in figure 5.14.

Figure 5.14: Comparison between bare hull (top), spray rail(mid) and deflectors (bottom) in trim atFn∇=5.87

Note that the running trim at Fn∇=5.09 in figure 5.13, the speed where both deflectors where tested,have virtually the same running trim even though designed for significantly different speeds and thushave quite different geometries, figure 4.6.

In figure 5.15 the drag differences are shown for all hulls.

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Figure 5.15: Comparison between bare hull, spray rail and deflectors in drag

The deflectors, marked in green and purple, create lower resistance at every speed compared to bothspray rails and bare hull, with a minimum decrease of about 10%. At their design speeds they are bothmore than twice as efficient as the spray rails in lowering the drag.

The results shows that the resistance is consistently lower for the deflectors. This would of course beaffected by the running trim, where the higher trim would give the deflectors a lower resistance.

The reason for the large speed range was to see how the efficiency of the deflectors changed whenthe running speed moved further from the design speed. The expected outcome was that above andbelow the design speed, the drag reduction would diminish. As is evident from the graph however thedrag reduction more follows the actual resistance breakdown from figure 4.4. Since it is the reduction inpercent that is increasing it could mean that the change the deflectors cause is getting more and moresignificant with the higher speeds. This does not mean that the deflectors remove more of the spray butshows that the higher the speed the more you can gain from having deflectors.

From figure 4.4 we see that the influence of spray resistance on the total resistance becomes larger andlarger as the speed increases. Which means that the efficiency of the deflector most likely is decreasingwhen the speed goes further from its design speed, but as the influence of spray resistance on the totalresistance increase with higher speeds the amount of removed total resistance would be comparablyhigher for the higher speed compared to the lower.

Looking at Fn∇=5.09 it is interesting to notice the reductions at this speed in particular since thedeflectors where both run for this speed. It seems the deflector designed for the higher speed, deflector 2,has a bigger reduction potential at this speed than deflector 1. Going back to figure 5.13 the trim for thetwo deflectors are basically the same with only a difference of 0.04°which can be considered negligible.The difference in amount of removed resistance is 2% which is large enough to show that there is adifference which is not affected by the trim of the hull. Looking at figure 5.16 the underwater picturesfor both deflectors at this speed can be seen,

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(a) Left: deflector 1, Right: deflector 2 (b) Design stagn.line in blue, Exp. stagn. line red

Figure 5.16: Visualisation of deflector position and stagnation lines at Fn∇=5.09

In figure 5.16a it looks like the area of the hull which is touching the surface is larger for deflector 1than for deflector 2 which could be a part of the higher resistance for deflector 1. In figure 5.16b the edgesof the deflectors (design stagnation line) are marked in blue while the real stagnation line (experimentalstagnation line) is marked in red. It shows that the shorter deflector 1 allows the forward part of the hullbottom to touch the water creating spray before the deflector and making the area touching the waterbigger. The longer deflector 2 has a larger area in front of the point where the stagnation lines meet andcan thus catch the spray going forward.

Looking at the heave comparison in figure 5.17 there seems to be a similar amount of added lift aswith the spray rails.

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Figure 5.17: Comparison between bare hull, spray rail and deflectors in heave

The graphs in figure 5.17 shows the heave comparison for deflector 1. Initially the deflector cause asimilar heave change to the spray rails, but as the speed increases the heave for the deflector becomesmore like the bare hull as it is going out of its designed speed range. So contrary to the spray rail wherethere is a small lowering of the resistance, no change in trim and a constant increase in heave comparedto the bare hull. The deflector seems to change the trim and initially the heave, as the speed increasesand the front part of the deflector starts to hit the water and become submerged the change in heavediminishes even as the trim change dose not.

5.3.3 ConclusionThe deflectors have an obvious positive effect on the hull, lowering the resistance at all tested speeds.Why they do this is not as clear. The design is supposed to remove the spray by deflecting it and then usethe deflection to harness the kinetic energy for propulsion, but since the deflectors increase the runningtrim of the hull which on its own cause a lower total resistance, the decrease in resistance could be morea product of the change of trim than the deflection of spray.

The change in trim can be due to a few different causes. Since the deflector was designed using thetheoretical stagnation line given by the Savitsky method,[19] & [16], it is not perfect for the hull sincein section 5.2.1 it was shown that this method over predicts with about 0.6°which we know from figure5.6 will put the deflector to far back and thus changing the trim. It is also conceivable that as the sprayis deflected it creates a resulting vertical force as well as a small horizontal force, increasing the lift andthus the trim as well as giving a small thrust increase.

5.4 Calm water setup, trim

A second calm water tests was done to see if the change in trim could be removed and thus the changesin resistance be traced to another variable. Instead of using the design LCG for all hulls, the runningtrim of the bare hull and spray rail hull was to be set to the same trim as which the deflectors whereexperiencing. This was accomplished by changing the balance of the hull, shifting the LCG further backand increasing the running trim.

Since the running trim of the deflectors where already known from previous tests, only the bare hulland the spray rail hull was run again. Except for the previous mentioned changes everything was keptthe same.

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5.4.1 Results and discussion, equal trimUnfortunately there are no results for these runs. When the trim was increased the hull very quicklystarted porpoising and thus the experiments had to be aborted. The only thing that really can beconcluded from this tests is that the deflectors makes it possible for the hull to run at a level of trimwhich it normally can’t achieve with out porpoising.

5.5 Waves

The wave tests were performed on bare hull, spray rail and deflector 1 hull. This is because the speedfor which deflector 2 is designed is too high, the integrity of the model can not be sustained and it wasdecided that the design speed for a tested deflector should be part of the test, and since this speed is avery high speed for deflector two, Fn∇=5.87, it is likely that the hull will be skipping on the peaks ofthe waves rather than experiencing slamming.

The high speed deflector could of course be tested exclusively for the lower speeds but because oftime shortage it was decided that the focus would be on deflector 1.

They will be tested at two different speeds, one low and one high, to see how they behave and if thereis some correlation between the supposed damping effects and the placement of the deflectors.

The speeds are 1.47 Fn∇ which corresponds to SLR 2 for this hull. SLR 2 is a very common speedfor wave analysis and is something that can be used for comparisons with [23] and [20]. The higherspeed is the design speed of the deflector at Fn∇=4.3. The measured accelerations will be compared toeach other and to the calculated vertical accelerations using the DNV GL rules for high speed craft, [3],discussed in section 3.4.

The big difference for this test is the waves. The hulls performance in waves was evaluated with ascaled version of sea state two in the Pierson-Moskowits spectrum for irregular waves. The same spectrumas used by Wielgosz [23]. Using the Froude scaling laws and the scale constant µ from equation 4.1, [21],the wave height Hs = 0.096 [m] and wave period Tp = 1.65 can be obtained as in table 5.3

Table 5.3: Wave spectrum

Wave spectrum Sea state Wave height [m] Wave period [s]Pierson Moscowits 2 0.096 1.557

As mentioned in the uncertainty calculations in section 3.3 the number of runs will be controlled bythe number of wave encounters according to the ITTC standard for seakeeping tests during irregularwaves, [6]. The target is the higher average of 100 peaks and troughs where an average of the number ofregistered wave peaks and wave troughs encountered shall be close to 100. When this average is achieveda statistical highest third and highest tenth of the accelerations measured are compared between thehulls. The extreme values are also compared though they are harder to interpret due to the nature ofwaves and really require a lot more wave encounters if conclusions are to be made.

5.5.1 Results and discussion, wavesAs for calm water, the initial comparison will be between the experimental results for the bare hull andthe DNV GL rules discussed in section 3.4. In table 5.4 the accelerations are shown for the comparison.

Table 5.4: Acceleration comparison with DNV prediction

Cg comparison Bow comparisonFn∇=1.47

Measurement Bare hull DNV GL Bare hull DNV GLa1/3 [g] 0.37 0.53 1.48 0.85a1/10 [g] 0.56 2.55

Fn∇=5.87Measurement Bare hull DNV GL Bare hull DNV GL

a1/3 [g] 1.01 2.28 2.04 3.65a1/10 [g] 1.60 3.64

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The CG a1/10 acceleration at low speed and bow accelerations at the higher speed Fn∇=5.87 is verysimilar for the bare hull and the DNV GL estimation. The bow values at 1.47 however are far off, theDNV GL is actually about half of the experimental value.

The DNV GL rules are used as a safety margin when designing new ships and should therefore bethe highest accelerations a ship is subjected to. It is therefore strange that the accelerations for the lowspeed bow comparison is so far off. However, the DNV rules for calculating the bow accelerations issimply multiplication of the CG estimation with a longitudinal distribution factor chosen between 0-2depending on position.

This could explain why the a1/10 values conform better to the DNV since they increase the toleranceof the hull to accelerations. It is strange however that the bow accelerations at 1.47 is so much higherthan the DNV. Of course at those low speeds the bow shape should have an impact on the accelerationsand the model has a very full (wide and short) bow which if hit by waves would cause a harder slamthan a more slender design.

Furthermore, DNV GL rules are like many classification rules based on Savitsky and Brown’s (1976)assumption that the acceleration peak values are exponentially distributed, however Razola et al (2016)[14], showed that the Weibull shape parameter has a much larger range (1 corresponds to exponentialdistribution and they determine values from 0.7 to 3)

Its hard to draw any conclusions from this more than the fact that the highest a1/3 measured is lowerthan the design acceleration.

Comparing to the bare hull, the following graphs and tables show the difference in acceleration forthe three hull configurations.

Figure 5.18a and 5.18b show the accelerations for the hulls at the lower speed of Fn∇ = 1.47.

(a) CG acceleration (b) Bow acceleration

Figure 5.18: Accelerations at Fn∇=1.47

The accelerations at CG seem to indicate that the deflectors actually increase the accelerations. Thisis not the case for the bow accelerations, the highest third is a little lower while the highest tenth andthe extremes are basically the same. The same can be seen if we look at the exact numbers, displayedin table 5.5

Table 5.5: Acceleration comparison, Fn∇=1.47

Cg comparison Bow comparisonMeasurement Bare hull Spray rails Deflector 1 Bare hull Spray rails Deflector 1

Highest 1/3rd [g] 0.37 +0.08 +0.15 1.48 +0.01 -0.18Highest 1/10th [g] 0.56 +0.15 +0.34 2.55 +0.03 +0.09

Extreme [g] 1.09 +0.4 +1.49 4.92 +0.1 +0.11

Both the deflector and the spray rail hull has a small increase in the accelerations except for thehighest third in the bow. What is interesting is that the differences at the bow are very low, with a

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minimum of +0.09 g for the deflector, which is small enough to be a measurement error or a disturbancein the water at the time. Even though 100 encounters was achieved the differences is so small it is hardto put any value on it. At CG there is a clearer picture that both the spray rails and the deflector seemto increase the accelerations compared to the bare hull.

In figure 5.19a and 5.19b the same data is plotted but for the higher speed of Fn∇=4.3.

(a) CG aelerations (b) Bow aelerations

Figure 5.19: Accelerations at Fn∇=4.3

Here there is a more apparent difference in the accelerations but the same trends as where seen inthe previous figures can be seen here. The acceleration at CG is a little higher for the spray rails anddeflectors while the accelerations at the bow are lower.

In table 5.6 the measured values are tabulated to get a more exact feel for the numbers.

Table 5.6: Acceleration difference, Fn∇=4.3

Cg comparison Bow comparisonMeasurement Bare hull Spray rails Deflector 1 Bare hull Spray rails Deflector 1

Highest 1/3rd [g] 1.01 +0.08 +0.09 2.04 +0.01 -0.28Highest 1/10th [g] 1.6 +0.2 +0.33 3.64 -0.03 -0.36

Extreme [g] 3.3 +0.79 +2.98 6.88 +0.87 +0.95

Looking at the numbers in table 5.6, the differences are now bigger and as was mentioned, followingthe same trend as before. Lowering the accelerations at the bow while slightly increasing the accelerationsat CG. This is probably because of the simplified design of the deflector. The constant edge runningtowards the keel is trapping the water and air instead of letting it dissipate along the sides.

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Chapter 6

ConclusionsA bespoke modular hull was developed, able to be configured into 4 different hulls, used for the testingof present and future technologies in spray deflection as well as standard hull designs. The modular hullsatisfied the design goals and worked well.

The empirical model based on the Savitsky method used for the design and prediction of results wascompared to the experimental results for the bare hull. This proved the assumption that the Savitskymethod on its own overpredicts running trim and underpredicts drag. For this reason the method cantbe used to theoretically estimate the separate resistance components from the total resistance accuratelyas we hoped. The method is very good in the initial step to get under way but it cannot predict the trimand placement of the stagnation lines accurately enough to use in final design of the deflectors.

Tests conducted with same LCG for calm water shows the importance of spray deflector technologies.The spray rail design acquire a reduction of up to 10% in drag without changing the hulls runningposition.

The deflectors decrease the drag by even more with a minimum decrease of 10% and maximum of upto 25% verified in the test, however they also change the running trim at all speeds of about 1°. Thischange in running trim and pressure area for the hull, will on its own result in considerable changes tothe resistance. This shows the positive effects a deflector can have on the hull and its resistance butdue to the change in running position individual effects and resistances can not be determined unless asimilar trim angle is achieved.

The change in heave experienced by the deflector follows the heave change shown by the spray railsetup where a similar increase in heave can be seen, this is until the speed goes above the design speedfor the deflector where heave increase compared to the bare hull diminishes as the speed increases.

The test aiming at matching the trim shows that the bare hull starts to porpoise when nearing therunning trim of the deflectors, which was not considered during the design stages. It does show that thedeflectors allow a hull to run at a higher trim with otherwise would make it porpoise.

The many questions which have arisen in this project speaks to a void in the knowledge in the areasurrounding spray deflection and spray resistance. The significance for spray resistance which will onlybecome more and more important as speed requirements, new technologies and efficiency gets a largerrole in ship design and with the predictions that engines will soon reach a point where their improvementswill not be enough the spray will become the next problem to solve.

The test performed in irregular waves tell that deflector design has no more influence on the verticalaccelerations than the existing spray rail configuration. For a more fare comparison in irregular wavesadditional experiments with updated placement and geometry are required. The spray rails, which hasvirtually the same running and starting trim as the bare hull, show the same trend in lowering theaccelerations at center of gravity that the deflectors do.

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Chapter 7

Future works and improvementsIn this section the things that, with hindsight, can be improved are written. They are separated insections based on the different sections in the report.

Model design

The deflectors in this work were designed using theoretical prediction of the stagnation line. From theresults we can see that this method was not reliable enough for this type of precise design, especially forthe higher speeds. Instead it would be preferable to design the deflector from the experimental stagnationline thus getting a more accurate and more efficient deflector. This could possibly be achieved by usinga more accurate method, perhaps CFD based, and thus improve the positioning of the deflector.

This would also aid prediction of the spray forces and the flow state of the spray and relating theviscous characteristics of the spray and their resistance to model size.

The deflector geometry should be updated. The deflectors as they are now have a consistent thickness,or height, from the hull at all positions. This has a tendency to make them behave more like a steppedhull instead of a pure deflector. To separate the effects of the deflection of spray, it would be preferableto taper the deflector towards the keel. Making the deflectors look more similar to the Petestep design[13] and thus removing the error that could be coming from the design simplification.

The spray rails could be made better by making a smoother taper at the start and end of the rail,removing some of the turbulence and thus resistance that was experienced in this experiment, both forslow speed resistance and high speed turbulence created by the separation at the end of the rail. It couldalso be beneficial to make them longer so they cover a larger speed range, this especially if the samespeed range is used again.

Experimental design

With more time a lot of the errors and questions regarding the results could be removed. More testsin general but specifically running the deflectors for more speeds. Comparing deflector 1 to deflector 2at several speeds both higher and lower would show more conclusively how they compare at workingoutside their designed speed.

Lowering the increments between test speeds would increase the prediction and the analysis of theresults a lot. This would again increase the number of tests and the time that is required in the towingtank but it would also be easier to trace changes in the trim and heave to changes in flow and runningconditions for the hull.

It could even be a good idea to shorten the speeds range drastically and do really small incrementsof speed changes to really go into detail of what actually happens with the spray and try to focus onwhat actually is instigating the changes in resistance.

Experiment

Time is a reemerging factor here, as it is the most important variable for experimental planing and setup.With more time the test could either be done in smaller steps so that each data point and each resultcould be analyzed to see what can be improved or changed for the next experiment.

On the other hand separating the experiments adds more uncertainties in the form of setup and cal-ibration errors, therefore doing the experiments in one go or at least running them continuously would

44

minimize the errors in setup and increase the comparability in the results. But this requires a highly spe-cific experimental setup and very precise knowledge of what is really supposed to be tested and evaluated.

Controlling the trim of the hull would be very useful in this application since the deflectors have sucha big impact on it. Controlling the trim with out locking the hull and forcing it to act in a specific wayis hard especially if the same LCG is also a must. It would however be very beneficial.

Results and analysis

One of the biggest error creators in this project is the constant mixing of units. Starting the project byanalyzing the type of units considered the best for the field is crucial to minimize the error during analysis.

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References[1] Peter Bjersten and Jonas Danielsson. A watercraft vessel with a planing hull. 2014.

[2] Eugene P. Clement. Reduction of Planing Boat Resistance by Deflection of the Whisker Spray.Technical Report DTMB-1929, David Taylor Model Basin, November 1964.

[3] DNV-GL. Rules for Classification - High Speed and Light Craft, Part 3 Chapter 1. Det NorskeVeritas, 2015.

[4] Rolf Eliasson and Lars Larsson. Principles of yacht design. A&C Black, London, 2 edition, 2000.

[5] ITTC. 28th International Towing Tank Conference, General Guide for Uncertainty Analysis inResistance Tests. In Recommended Procedures and Guidelines, volume 75-02-02-02, page 11, 2014.

[6] ITTC. 28th International Towing Tank Conference, Seakeeping Tests. In Recommended Proceduresand Guidelines, volume 75-02-05-04, page 14, September 2014.

[7] ITTC. 28th International Towing Tank Conference, High speed craft, Resistance. In RecommendedProcedures and Guidelines, page 19, September 2017.

[8] ITTC. 28th International Towing Tank Conference, High Speed Marine Vehicles. In RecommendedProcedures and Guidelines, volume 75-02-05, page 19, September 2017.

[9] ITTC. 28th International Towing Tank Conference, Register. In Recommended Procedures andGuidelines, volume 0-0, page 10, September 2017.

[10] Bogdan Molchanov. Benchmark Testing of Spray defelector technologies for high speed craft. PhDthesis, KTH Royal Institute of Technology, September 2018.

[11] Linus Olin, Mireia Altimira, Jonas Danielsson, and Anders Rosén. Numerical modelling of spraysheet deflection on planing hulls. Proceedings of the Institution of Mechanical Engineers, Part M:Journal of Engineering for the Maritime Environment, 231(4):811–817, December 2016.

[12] Peter R. Payne. The spray volume shed by an uncambered planing hull in steady planing. OceanEngineering, 9(4):373–384, January 1982.

[13] PeteStep Ab. Petestep.se. May 2018.

[14] Mikael Razola, Katrin Olausson, Karl Garme, and Anders Rosén. On high-speed craft accelerationstatistics. Ocean Engineering, 114:115–133, March 2016.

[15] Anders Rosén. Loads and Responses for Planing Craft in Waves. PhD Thesis, KTH, Stockholm,2004.

[16] Daniel Savitsky. Hydrodynamic design of planing hulls. Marine technology, 1(1):71–95, 1964.

[17] Daniel Savitsky. Planing Craft. 97:113–141, 1985.

[18] Daniel Savitsky and P. Ward Brown. Procedures for hydrodynamic evaluation of planing hulls insmooth and rough water. Marine Technology, 13(4):381–400, 1976.

[19] Daniel Savitsky, Michael F. DeLorme, and Raju Datla. Inclusion of whisker spray drag in perfor-mance prediction method for high-speed planing hulls. Marine Technology, 44(1):35–56, 2007.

[20] Luke Soletic. Seakeeping of a Systematic Series of Planing Hulls. page 19, March 2010.

[21] Sverre Steen. Lecture 2: General Modelling and Scaling Laws. NTNU, Experimental methods inMarine Hydrodynamics, page 21, August 2017.

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[22] Chiara Wielgosz. Experimental Evaluation of Novel Spray Deflector for Planing hulls. PhD Thesis,KTH Royal Institute of Technology, March 2018.

[23] Chiara Wielgosz. Experimental validation of numerical drag prediction of novel spray deflectordesign. April 2018.

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Appendices

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Appendix A

Uncertainty calculationsThe uncertainties are calculated as described in section 3.3, which follows the described uncertainty cal-culations from reference [5]. In the following section the calculations for the uncertainty of the measuredresistance will be shown for the bare hull at the speed of Fn∇ to show how it is calculated. In tableA.1 The measured speed and the measured total drag that the hull was experiencing during the run isshown.

Table A.1: Measured values for Bare hull at Fn∇=5.0866

Measured First run Second runSpeed Fn|nabla 5.1219 5.0909Total Resistance 60.3104 60.4795

Using the equations previously shown in section 3.3 we get the uncertainties u and u’ for the resistance.

RT =60.3104 + 60.4795

2= 60.395 (A.1)

s =

√1

2− 1[(60.395− 60.3104)2 = 0.1195N (A.2)

u(RT ) =0.1195√

2= 0.0845N (A.3)

u′(RT ) =0.119560.395√

2= 0.0014 = u′4 (A.4)

Using the same calculation method for the measured speed gives us table A.2

Table A.2: Measured values for Bare hull at Fn∇=5.0866

Measured First run Second run Average u’Speed Fn∇ 5.1219 5.0909 5.1064 0.0030

Total Resistance 60.3104 60.4795 60.395 0.0014

The uncertainty as of the calibration of equipment can be taken as the sensor calibration deviationwhich then is divided with the average measured value, as:

u′2 =0.06

60.395= 0.001 (A.5)

To get the combined uncertainty we use equation 3.10 , with the significant uncertainty values as intable A.3

Table A.3: Significant uncertainties for bare hull at Fn∇=5.0866

Name value symbol Described in sectionHull ballasting u′1 0.0001 3.3

Sensor calibration u′2 0.001 3.2.1 and appendix AWater temperature u′3 0.0002 3.3

Towing speed u′4 0.006 3.3 and appendix A

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u′c =√

0.00012 + 0.0012 + 0.0022 + 0.0062 = 0.0065 = 0.65% (A.6)

These same calculations can be done for every resistance measurement at every speed for each hull.This is not shown here but the results, the total combined uncertainty for each speed and hull is shownin appendix B and together with the measured values in table A.4.

Table A.4: Combined uncertainty for each hull and speed

Fn∇ 3.52 3.91 4.30 4.70 5.09 5.48 5.87 6.26 6.65u′c %

Bare hull 0.17 1.42 0.62 0.82 0.33Spray rails 0.16 0.13 1.43 1.87 0.07Deflector 1 0.18 0.18 0.15 0.39 0.69Deflector 2 0.77 0.42 0.48 0.53 0.96

The expanded mean, UP , is simply u′c multiplied by 2, as shown in section 3.3. This gives theuncertainty with a 95% statistical confidence level, shown in table A.5.

Table A.5: Expanded uncertainty for each hull and speed

Fn∇ 3.52 3.91 4.30 4.70 5.09 5.48 5.87 6.26 6.65u′c %

Bare hull 0.34 2.84 1.23 1.64 0.65Spray rails 0.31 0.27 2.86 3.74 0.15Deflector 1 0.36 0.37 0.30 0.77 1.39Deflector 2 1.53 0.84 0.96 1.06 1.93

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Appendix B

Complete Results calm water setup one

Table B.1: Test matrix, average values and standard deviations, bare hull

Speed [Fn∇] Heave [mm] u [mm] Trim [deg] u [deg] Drag [N] u [N] u′c%3.5215 34.1380 0.1016 4.2745 0.0105 38.9040 0.0689 0.264.3041 39.2050 0.1145 3.365 0.0110 48.2050 0.1579 1.435.0866 42.1770 0.1143 2.6455 0.0335 60.395 0.0845 0.655.8692 44.0820 0.0127 2.0160 0.0250 75.2130 0.0645 0.856.6517 45.5430 0.0127 1.534 0.0080 94.976 0.0111 0.38

Table B.2: Test matrix, average values and standard deviations, spray rails

Speed [Fn∇] Heave [mm] u [mm] Trim [deg] u [deg] Drag [N] u [N] u′c%3.5215 36.7030 0 4.2960 0 39.0580 0 0.254.3041 41.8340 0 3.3180 0 45.1780 0 0.245.0866 45.0600 0.0762 2.5525 0.0025 54.9710 0.0467 1.445.8692 46.8760 0.0635 2.0040 0.0150 68.3080 0.0133 1.886.6517 48.1840 0.0762 1.5205 0.0035 86.9740 0.1134 0.21

Table B.3: Test matrix, average values and standard deviations, Deflector 1

Speed [Fn∇] Heave [mm] u [mm] Trim [deg] u [deg] Drag [N] u [N] u′c %3.5215 36.2210 0.1524 5.1415 0.0125 34.9610 0.2091 0.273.9128 39.1420 0.0762 4.6660 0.0110 37.2340 0.1023 0.274.3041 41.0980 0.2032 4.2210 0.0160 41.2730 0.0534 0.254.6954 42.4820 0.0635 3.8990 0.0060 45.5590 0.0334 0.435.0866 42.7490 0.0762 3.6485 0.0015 50.2050 0.0045 0.72

Table B.4: Test matrix, average values and standard deviations, Deflector 2

Speed [Fn∇] Heave [mm] u [mm] Trim [deg] u [deg] Drag [N] u [N] u′c %5.0866 39.6500 0.8766 5.1415 0.0125 34.9610 0.2091 0.795.4779 40.1070 0.8076 4.6660 0.0110 37.2340 0.1023 0.465.8692 40.5730 0.6426 4.2210 0.0160 41.2730 0.0534 0.526.2608 39.7010 0.9059 3.8990 0.0060 45.5590 0.0334 0.566.6517 41.0470 0.4320 3.6485 0.0015 50.2050 0.0045 0.99

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Appendix C

Complete results wave tests

Table C.1: Test matrix, speed and number of encounters

Hull Speed [Fn∇] Total pitch enc. Total heave enc. Av. wave enc. Av. trim [deg]Bare hull 1.47 133 96 114.5 5.714Bare hull 4.3 154 96 125 3.372Spray rails 1.47 127 99 113 5.705Spray rails 4.3 152 98 125 3.345Deflector 1 1.47 131 100 115.5 6.456Deflector 1 4.3 148 97 122.5 4.493

Figure C.1: Wave data from low speed runs for bare hull

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Figure C.2: Wave data from high speed runs for bare hull

Figure C.3: Wave data from low speed runs for spray rails

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Figure C.4: Wave data from high speed runs for spray rails

Figure C.5: Wave data from low speed runs for Deflector 1

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Figure C.6: Wave data from high speed runs for Deflector 1

Table C.2: Average running values for entire encounter period

Fn∇=1.47 Fn∇=5.89Hull Avr. heave [mm] Avr. Trim [deg] Avr. heave [mm] Avr. Trim [deg]

Bare hull -3.843 5.714 47.166 3.372Spray rails -3.585 5.705 47.200 3.446Deflector 1 -2.330 6.456 51.604 4.493

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