RE-EVALUATION OF RESISTANCE PREDICTION FOR HIGH-SPEED

RE-EVALUATION OF

RESISTANCE PREDICTION FOR

HIGH-SPEED

ROUND BILGE HULL FORMS

by

Jae Won

Bachelor of Science Hong-Ik University

2008

A Thesis submitted to the College of Engineering at

Florida Institute of Technology in partial fulfillment of the requirements

for the degree of

Master of Science

in Ocean Engineering

Melbourne, Florida

July 2012

© Copyright 2012 Jae Won All Rights Reserved

The author grants permission to make single copies

We the undersigned committee hereby approve the attached thesis RE-EVALUATION OF RESISTANCE PREDICTION FORHIGH-SPEED

ROUND BILGE HULL FORMS By

Jae Won

Prasanta Sahoo, Ph.D. Associate Professor Ocean Engineering Committee Chair Swain Geoffrey, Ph.D. Professor Oceanography and Ocean engineering

Kirk Daniel R. , Ph.D. Associate Professor Mechanical and Aerospace Engineering Department George Maul, Ph.D. Department Head Professor Marine and Environmental Systems

Abstract RE-EVALUATION OF RESISTANCE PREDICTION FOR HIGH-SPEED

ROUND BILGE HULL FORMS

by

iv

Jae Won

Principal Advisor: DrPrasanta Sahoo

Predicting the resistance of a high-speed monohull has been of interest to Naval Architects for several decades. Even though considerable amount of research has been carried out in this area, there remains a degree of uncertainty in the accurate resistance prediction in the early design stage.

This research thesis attempts to investigate a method for enhancing the accuracy of resistance prediction methods for high-speed round-bilge monohull form vessels for a wide range of volumetric Froude numbers

(Fn). While a number of systematic series are in existence, their data are either not readily available or scattered in various internal reports and publications which makes it difficult for practicing naval architects to exploit the knowledge base. In this thesis the following high-speed round bilge systematic series hull forms have been considered for regression analysis, namely:

NPL (1969)

S-NPL (1994)

SKLAD (1972-1980) and

AMERC (1984-2000)

Earlier objective of this thesis was to obtain a common regression equation for a wide parameter space which would be encompassing all the above systematic series. As this was not feasible due to lack of data in areas that were considered crucial, hence separate regression analysis has been carried out for each series. The new regression equations have been proposed for a broad range of geometrical parameters so that a designer has an instant tool to make a decision regarding powering prediction in the design stage.

v

Table of Contents Abstract .................................................................................................. iii

List of Keywords..................................................................................... vi

List of Figures ....................................................................................... vii

List of Tables .......................................................................................... x

List of Abbreviations .............................................................................. xii

List of Symbols...................................................................................... xiii

1. Introduction ...................................................................................... 1

3. SOUTHAMPTON EXTENDED NPL SERIES .................................. 5

4. SKLAD SERIES ............................................................................... 8

6. REGRESSION ANALYSIS ............................................................ 14

7. REGRESSION ANALYSIS TECHNIQUE ...................................... 20

8. FORWARD STEPWISE REGRESSION PROCEDURE ................ 24

9. FINAL REGRESSION MODEL AND RESULTS ............................ 25

10. WETTED SURFACE AREA COEFFICIENTS (BOJOVIC (1998)) .. 37

11. CONCLUSIONS .......................................................................... 40

References ........................................................................................... 42

APPENDIX 1 : AMECRC SERIES REGRESSION RESULTS .............. 43

APPENDIX 2 : SKLAD SERIES REGRESSION RESULTS .................. 50

APPENDIX 3 : S-NPL SERIES REGRESSION RESULTS ................... 64

Appendix 4A: NPL Series (Radojcic, 1997) .......................................... 69

Appendix 4B: Wetted Surface Area Coefficients (Bojovic, 1998) .......... 70

Appendix 5 : AMECRC Series Experiment Results .............................. 72

Appendix 6 : SKLAD Series Experiment Results .................................. 79

Appendix 7: S-NPL Series Experiment Results .................................... 85

vi

List of Keywords Mono-Hull Forms Resistance of Systematic Regression Analysis High-Speed Round Bilge Hull Forms

vii

List of Figures Figure1: NPL Series Parent Hull Body Plan[Bailey(1976)].........................................4

F i gu r e2 : R a ng e o f Pa ram et e rs C o ver e d i n N PL a n d S - N PL Ser i es

[Bojovic (1998)].................................................................. ..............................4

Figure3:Southampton Extended NPL Series [Molland et al (1994)]……………………..6

Figure4: SKLAD Series Parameter Space [Radojc ic et al (1999) ] . . . . . .9

Figure5: SKLAD Series Parent Hull Plan [Radojc ic et al. (1999)] . .. . . . .9

F i g u r e 6 : A M E C R C P a r e n t H u l l B o d y P l a n [ S a h o o a n d D o c t o r s

( 1 9 9 9 ) … … … … … … … … … … … … … … … … … … … … … … … … … … … … 1 2

Figure.7: Change in Hull Shape of AMECRC Series [Sahoo and Doctors

(1999) ] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

Figure.8: AMECRC Systematic Series Parameter Space [Sahoo and Doctors

(1999) ] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

Figure 9: AMECRC Series Observed and Predicted(Model 1).............. .43

Figure 10: AMECRC Series Observed and Predicted(Model 2)...............43








Figure 18: AMECRC Series Observed and Predicted(Model 10)...........47





Figure 23: SKLAD Series Observed and Predicted(Model 1)……............50


viii








Figure 32: SKLAD Series Observed and Predicted(Model 10)… ..........54

Figure 33: SKLAD Series Observed and Predicted(Model 11)… ..........55

Figure 34: SKLAD Series Observed and Predicted(Model 12)……........55
















Figure 50: S-NPL Series Observed and Predicted(Model 1)..……...........64






ix




Figure 59: S-NPL Ser ies Observed and Predicted(Model 10).… ... ... ...68

x

List of Tables Table 1: Round Bilge Hull Systematic Series [Bojovic(1998)] . ........ . .....7 Ta b l e 2 : S K L A D S e r i e s P a r a m e t e r s a n d R a n g e [ R a d o j c i c e t a l . (1999)]................................................................................................... 8 Ta b l e 3 : P a r a m e t e r s f o r H SD H F a n d A M EC R C S ys t e m a t i c S e r i e s [Sahoo and Doctors(1999)]................. ........................... ........................12 Table 4: AMECRC Systematic Series Parameter Range [Sahoo and Doctors (1999) ] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 Table 5: S-NPLSystematic Ser ies Parameter Range.. . . . . . . . . . . . . . . . . . . . . . . .16 Table 6: SKLADSystematic Series Parameter Range...........................17 Table 7: AMECRC Series Regression Coefficients................... ............28 Table 8: AMECRC Series Regression Coefficients ............................... 29 Table 9: S-NPL Series Regression Coefficients ............................ ........30 Table 10: S-NPL Series Regression Coefficients ....................................31 Table 11: S-NPL Series Regression Coefficients ....................................32 Table 12: NPL Series Regression Coefficients (Radojcic 1997) .............33 Table 13: SKLAD Series Regression Coefficients .......... ....... ...............34 Table 14: SKLAD Series Regression Coefficients ................................35 Table 15: SKLAD Series Regression Coefficients ................................36 T a b l e 1 6 : A M E C R C S e r i e s – C S R e g r e s s i o n P a r a m e t e r andCoefficients............... ................................................................. ............38 T a b l e 1 7 : S K L A D S e r i e s – C S R e g r e s s i o n P a r a m e t e r and Coefficients............................................. .................................... ....39 Ta b l e 1 8 : N P L & S - N P L S e r i e s – C S R e g r e s s i o n P a r a m e t e r s and Coefficients.......................................................... ...........................39 Table 19: NPL Series Regression Coeff icients .................... ...... ......... .69 T a b l e 2 0 : A M E C R C S e r i e s C S R e g r e s s i o n P a r a m e t e r s and Coefficients..................................................................................... 70 T a b l e 2 1 : S K L A D S e r i e s C S R e g r e s s i o n P a r a m e t e r s and Coefficients............................................. ........................................70 Ta b l e 2 2 : N P L & S - N P L S e r i e s – C S R e g r e s s i o n P a r a m e t e r s and Coeff ic ients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .71 Table23: AMECRC Series Experiment Results for Model 1 ..... .... . . . . . . . .72 Table 24: AMECRC Series Experiment Results for Model 2 ................72 Table 25: AMECRC Series Experiment Results for Model 3 ................73 Table 26: AMECRC Series Experiment Results for Model 4 ......... .......73 Table 27: AMECRC Series Experiment Results for Model 5 ............. . . .74 Table 28: AMECRC Series Experiment Results for Model 6 ............ ....74 Table 29: AMECRC Series Experiment Results for Model 7 .............. . .75 Table 30: AMECRC Series Experiment Results for Model 8 ........ ........75 Table 31: AMECRC Series Experiment Results for Model 9 ....... .........76 Table 32: AMECRC Series Exper iment Results for Model 11 .. . .. . .. .. . 76 Table 33: AMECRC Series Exper iment Results for Model 10 . . .. .. .. .. .77 Table 34: AMECRC Series Exper iment Results for Model 12 . . .. .. .. .. .77 Table 35: AMECRC Series Exper iment Results for Model 13 ... . . .. . . . . .78

xi

Table 36: AMECRC Series Exper iment Results for Model 14 ... . . . .. . . . .78 Table 37: SKLAD Series hull parameters....................................... ......79

Table 38: SKLAD Series Experiment Results for Fn=1.00........ .... . ... .80

Table 39: SKLAD Series Experiment Results for Fn=1.25........ .... . ....80

Table 40: SKLAD Series Experiment Results for Fn=1.50........... . . . . . .81


Table 42: SKLAD Series Experiment Results for Fn=2.00.......... .. . ....82


Table 44: SKLAD Series Experiment Results for Fn=2.50........... . . ....83

Table 45: SKLAD Series Experiment Results for Fn=2.75........... . . ....83

Table 46: SKLAD Series Exper iment Results for Fn=3.00 . . . .. . . .. . .. . .84 Table 47: S-NPL Series Hull Parameters................................. ............85 Table 48: S-NPL Series Experiment Results for Model 3b ........... . . . . . . .85 Table 49: S-NPL Series Experiment Results for Model 4a .......... . . . . . . . .86 Table 50: S-NPL Series Experiment Results for Model 4b .......... . . . . . . . .86 Table 51: S-NPL Series Experiment Results for Model 4c ........ ....... ...86 Table 52: S-NPL Series Experiment Results for Model 5a ........... . . . . . . .87 Table 53: S-NPL Series Experiment Results for Model 5b ......... .. . . . . . . .87 Table 54: S-NPL Series Experiment Results for Model 5c ....... ... . . . . . . . .87 Table 55:S-NPL Series Experiment Results for Model 6a ......... .. .... ....88 Table 56: S-NPL Ser ies Exper iment Results for Model 6b .. . . . . . .. . . . . . . .88 Table 57: S-NPL Ser ies Exper iment Results for Model 6c.. ... .. .. . .. .. ...88

xii

List of Abbreviations AMECRC Australian Maritime Engineering Cooperative Research Center NPL National Physical Laboratory S-NPL Southampton Extended NPL SKLAD Series Developed in former Yugoslavia

xiii

List of Symbols B Beam (waterline) CB Block coefficient CF ITTC '57 ship model correlation line CR Residuary resistance coefficient

Cs Wetted surface coefficient (S/2/3) CT

CW

Total resistance coefficient Wave Resistance Coefficient

Fn Froude number

Fn Volumetric Froude number g Acceleration due to Gravity B/T Beam-Draft ratio L Length (waterline) L/B Length-Beam ratio L/∇1/3 Slenderness ratio LCB Longitudinal center of buoyancy from amidships LDWL length on DWL (V=0) Rn Reynolds number RR Residuary resistance RT Total resistance of bare hull S Wetted surface area T Draught at DWL V speed Δ Displacement

Displacement volume

Mass density of salt water (1.026 t/m3) at 15°C

Running trim angle

Kinematic viscosity

1

1. Introduction Inspired by industry interest, a systematic research leading to the better performance prediction of high-speed round-bilge, transom-stern monohull forms have been conducted. This thesis presents the results of a comparative study on resistance of systematic series of high-speed displacement mono-hull forms developed and tested at Australian Maritime Engineering Cooperative Research Center, SKLAD systematic series of round bilge hull forms developed in former Yugoslavia, NPL and S-NPL series of hull forms developed and tested at University of Southampton, UK. The speed independent regression analysis was performed and independent sets of regression equations were derived from the same set of experimental data. The regression analysis was developed using a ‘classical’, multiple linear regression analysis, as well as a novel technique – non-linear estimation. The latter presents a generalization of the former and enables any form of regression model and loss function to be explored. The non-linear estimation approach proved to be superior. Computational fluid dynamics (CFD) techniques are becoming increasingly popular in analyzing fluidflow problems in almost all branches of engineering, especially in resistance prediction of ships where complex fluid flow exists, although absolute accuracy is still limited. Application of CFD techniques in resistance prediction of ships is relatively new and is gaining ground as time passes by. The towing-tank tests provide better absolute accuracy; modification to hull forms is very limited from both practical and financial point of view. This hampers testing of different hull forms unless serious financial commitments can be made. In this respect, CFD techniques and theoretical formulations have an added advantage in the sense that rapid modifications to hull forms can be carried out and results obtained so that a comparative study could be made within a few hours. In this way, a naval architect is in a better position to select a good design from the resistance point of view.

2

A good high-speed design should have favorable resistance qualities so that operational capabilities are not degraded. Innumerable investigations have already been carried out on systematic series hull forms in order to predict resistance of such high-speed hull forms. In this thesis, focus is primarily on development of regression equations for accurate resistance prediction in the initial design stage from the experimental results obtained from the above mentioned systematic series hull forms. The need for better hull forms and the increased interest in resistance performance call for better data and algorithms to be available at the design stage in order to obtain the right balance between resistance and other conflicting requirements. This paper provides an exhaustive study of the following:

Results of calm-water resistance tests of a systematic series of 14 high-speed round-bilge displacement hull forms of the AMECRC systematic series.

Results of calm water resistance tests of 27 high-speed round bilge hull forms of the SKLAD series.

Results of calm water resistance tests of 10 high-speed round bilge hull forms of NPL and S-NPL series.

Subsequent development of regression equations for the above series for rapid estimation of resistance and powering of round bilge high-speed hull forms within the geometrical design space.

3

2. High-Speed Hull Forms

Resistance data for high-speed round bilge form obtained at NPL were originally presented in 1969. The work was extended to examine the effect of the hull parameters on calm water resistance, Bailey (1976). Experimental investigations involved testing of 22 models where the bare hull models were bereft of any keel or appendages. The water line length LWL and the block coefficient CB of the models were set at 2.54 m and 0.397 respectively, where the B, T and the displacement of the vessel were varied. The model was also designed to have the LCB at 6.40% of LWL aft of amidships. These vessels were divided in to 7

groups according to their slenderness ratio, L/1/3.

Figure1represent the parent hull form of NPL series. Figure 1 show that a line perpendicular to the sheer profile base line and the half breadth centerline. Most lines drawings are arranged with the sheer profile and half breadth one above the other so just rule the line at right angles to the sheer profile base line and the half breadth centerline. Include the base line, the centerline, the buttock lines, and the waterlines, these lines are. This body plan is made in two parts. The right-hand part is a view looking directly aft at the forward port side of surface, while the. The left-hand part is a view looking directly forward at the after half of the port side. This arrangement prevents the frame lines at the after end from obliterating or fouling the frame lines at the forward end.

Figure 2 describes the distribution of geometrical parameters of

NPL and S-NPL series. The range of L/B and B/Tfor variable L/1/3has also been shown.

4

Figure 1:NPL Series Parent Hull Body Plan [Bailey(1976)]

Figure 2:Range of Parameters Covered in NPL and S-NPL Series

[Bojovic (1998)]

5

3. SOUTHAMPTON EXTENDED NPL SERIES

Resistance data for high speed round bilge forms obtained at NPL were originally presented in 1969. The purpose at the time was to add to the limited information that was then available for one type of vessel. S-NPL series various kinds of forms as ten slender round bilge models were derived from the NPL series. The calm water resistance testing of the S-NPL has been described by Molland et al. (1994). The models were tested as monohulls and in catamarans configurations with different hull spacing.

The body plan of the hull forms are shown in Figure 3.S-NPL and NPL series has so many different models as change in Hull Shape of series.This figure is show that shape of the ship as test models and for a given displacement there is a change wetted surface area with change in B/T or L/B. S-NPL series has a wide range of hull separations was tested and overall the experiments covered over a lot of model configurations and each over a speed range up to a Froude number.

Table1 presents a historical progression of high speed

displacement of the series. The performance ofround bilge hulls is most

strongly dependent upon according to their slenderness ratio, L/1/3. That table is come in various range and Froude number.They may be different series, but they have similar parameter range.Also, the

volumetric Froude number Fnrange from 0.15 to 3.0 but most papers

focus onFnrange of 1.0 to 2.0.

6

Figure 3: Southampton Extended NPL Series [Molland et al (1994)]

7

Table 1: Round Bilge Hull Systematic Series [Bojovic(1998)]

Series

(No. of Models) L/

1/3 L/B B/T CB LCB Fn

Nordstrom

(12*) 5.65-7.72 4.83-6.94 3.16-3.57 0.373-0.41

0.9-2.0

De Groot

(31*) 5.23-7.75

0.8-2.7

Marwood-Silverleaf

(30*) 5.2-8.2

.45-1.12

Series 63 (5) 4.5-6.4 2.5-5.75

0.9-2.2

Series 64 (27) 8.04-12.4 8.45-18.26 3.0-4.0 0.35-0.55

0.1-1.5

SSPA (9) 6.0-8.0 4.62-8.20 3.0-4.0 0.4

1.0-2.0

NPL (22) 4.47-8.30 3.33-7.50 1.5-2.5 0.397 6.4% L aft 0.3-1.2

S-NPL extended

(10) 6.3-9.5 7.0-15.1 1.5-2.5 0.397 6.4%L aft 0.1-1.05

YP (3) 5.57-5.72 3.97-5.17 3.06-5.05

0.1-0.6

SKLAD (27) 4.5-8.5 4.0-8.0 3.0-5.0 0.35-0.55

1.0-3.0

NRC (24) 6.62-7.93

3.0-5.0 0.35-0.55

0.2-1.0

D-Series (13) 6.3-6.93 5.68-7.05 3.0-3.75 0.48-.52

0.15-0.80

VTT (4) 6.586 5.41-6.25 4.39-6.90 0.45-0.60

0.6-3.8

MARIN HSDHF

(40) 4.3-13.1 4.0-12.0 2.5-5.5 0.35-0.55

0.1-1.2

AMECRC HSDHF

(14) 4.3-8.7 4.0-8.0 2.5-4.0 0.40-0.50

0.1-1.0

8

4. SKLAD SERIES

SKLAD series of models were carried out at the Brodarski institute, in the former Yugoslavia in from 1972 to 1980. SKLAD series has twenty seven high speed round-bilge and semi-displacement hulls were developed and used for the research. Models derivied from the parent cover volume was kept constant at 0.230 m3, the length of the models varied from 2.7 to 6m. There are three kinds of group as block coefficients CB, L/B ratio and B/T ratio.

The ranges of varied parameters are outlined in Table 2 and the series’ parameter space is illustrated in Figure 4. SKLAD series has same L/B range with AMECRC but rest of parts more wide value. It will be show that various result in range, can bring out the best results. The parent hull form of SKLAD series has been shown in Figure 5.The variation in LCB tested in the twenty seven models selected from 8.8%, 9.3% and 9.2% of the LWLaft of amidships for CB=0.35, 0.45 and 0.55 respectively. In Figure 5, the after body bottom with a flat bottom have nearly vertical sides. This design provides far more stability than single chine hull. But, forward part is simplest type of chine as be the single chine V shape. This type of hull is among the simplest to build, but this style is lack of stability. V shape isgood seakeeping and reduce the resistance.

Table 2:SKLAD Series Parameters and Range

[Radojcic et al. (1999)]

Parameters Range

L/B 4.0 – 8.0

B/T 3.0 – 5.0

CB 0.35 – 0.55

L/1/3 4.5 – 8.5

LCB %LWL aft of midship 8.8, 9.3 and 9.2 for each

CB

9

Figure 4: SKLAD Series Parameter Space [Radojcic et al (1999)]

Figure 5: SKLAD Series Parent Hull Plan [Radojcic et al. (1999)]

10

The Prismatic Coefficient (Cp) is a measure of the fullness of the boat, the higher the number the fatter the ends and the more efficient at high speeds. A diamond shape would cut through the water best, but that's not actually the case. A high Cp also has the advantage of reducing pitching. The modelhave a constant prismaticcoefficient CP, of 0.715. The series models were tested over the volumetric Froude

number range Fn from 1.0 to 3.0.

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5. AMECRC SERIES

The HSDHF series a 10-year project started in 1979 at MARIN, Maritime Research Institute Netherlands, to improve the performance of high-speed displacement vessels, especially with regard to their seakeeping qualities.The AMECRC series is based on the HSDHF. This research project is on combatant vessel design. This project was support by the Royal Netherlands Navy, the United States Navy, the Royal Australian Navy and MARIN.The research goal is a significant improvement in the performance of transom stern, round bilge monohulls could be obtained.

The 13 models were developed by systematic variation of L/B, B/T and CB, Sahoo and Doctors (1999).Table3 compare the geometrical parameters range of each series as HSDHF and AMECRC. Figure 6 show the AMECRC Parent Hull Body Plan. AMECRC body plan has more a sharp angle than SKLAD series on after body bottom. The flat hull also makes the boat more stable in calm water.

The cube is change in Hull Shape of AMECRC Series as can see at a single glance in Figure 7. All the 14 models have the same waterline length of 1.6 m.

Figure 8, AMECRC series is the block coefficient CBof the models were set at 0.396to 0.5. Models deriving from the cover length-beam ratios, L/B of 4 – 8 and beam draft ratios of 2.5 – 4.0. The AMECRC series more narrow experiments range than the HSDHF.

The models were tested in the Ship Hydrodynamics Centre at the Australian Maritime College. All models were constructed with a water line length of 1.6 m. Calm water tests were conducted at speeds from 0.4 to 4 m/s, corresponding to Froude Number (Fn) from 0.1 to 1.0. During testing, the models were free to sink and trim, and resistance, trim and rise of center of gravity were recorded.

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Table 3: Parameters for HSDHF and AMECRC Systematic Series [Sahoo and Doctors (1999)]

HSDHF

AMECRC

L/B

4 – 12

4 -8

B/T

2.5 – 5.5

2.5 – 4.0

CB

0.35 – 0.55

0.396 – 0.50

Figure 6: AMECRC Parent Hull Body Plan [Sahoo and Doctors (1999)]

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Figure 7: Change in Hull Shape of AMECRC Series [Sahoo and Doctors (1999)]

Figure 8: AMECRC Systematic Series Parameter Space [Sahoo and Doctors (1999)]

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6. REGRESSION ANALYSIS

The regression analysis includes many techniques for modeling and analyzing several variables, when the focus is on the relationship between a dependent variables and one or more independent variables. More specifically, regression analysis helps one understand how the typical value of the dependent variable changes when any one of the independent variables is varied, while the other independent variables are held fixed.

This thesis deals with data that have linear and nonlinear

relationship between adependent variables which isresiduary resistance and independent variables which volumetric Froude number, beam-draft ratio, block coefficient, etc.From the equation of that line the same parameter can be predicted within the valid range.

Elementary Statistical Terminology

Correlationcoefficient is a vital aspect used to calculate and range from -1.00 to 1.00.

P-level is the probability of obtaining a test statistic at least as extreme as the one that was actually observed. A significance level of 0.05 would deem as extraordinary any result that is within the most extreme 5% of all possible results under the null hypothesis. In this case a p-value less than 0.05 would result in the rejection of the null hypothesis at the 5% (significance) level.

the degree to which two or more predictors (independent or X variables) are related to the dependent (Y) variable is expressed in the correlation coefficient R, which is the square root of R-square.

Residual is the difference between the observed value of the dependent variable and the predicted value.

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Hull form parameters

The analysis Hull form parameters should be in non-dimensional form.

The analysis hull form parameters should give a uniform coverage of the space defined..

All the parameters that may have a significant effect on the dependent variable should be included in the analysis, and any parameters that are not included should either be constant or should have an insignificant influence on the dependent variable.

The extreme values of all varied parameters should be carefully defined.

Table 4 table 5 and 6 show that each system series parameter ranges.

Assumptions Regarding Regression Analysis Application

The principal parameters of the hull whose performance is being predicted must fall within the range of parameters values covered by the data.

All parameters that are constant in the analysis data set, must have that same constant value in the proposed design (comment: if a certain parameter is constant, it does not reduce the prediction accuracy, only prevents the investigation of the effect of that parameter).

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Table 4: AMECRC Systematic Series Parameter Range

[Sahoo and Doctors (1999)]

Model L/B B/T CB Model

Disp.(kg) L/1/3

1 8 4 0.396 6.321 8.653

2 6.512 3.51 0.395 11.455 7.098

3 8 2.5 0.447 11.454 7.098

4 8 4 0.447 7.158 8.302

5 4 4 0.395 25.344 5.447

6 8 2.5 0.395 10.123 7.396

7 4 2.5 0.396 40.523 4.658

8 4 2.5 0.5 51.197 4.308

9 8 2.5 0.5 12.804 6.839

10 8 4 0.5 8.002 7.998

11 4 4 0.5 32.006 5.039

12 8 3.25 0.497 9.846 7.464

13 6 3.25 0.45 15.784 6.379

14 6 4 0.5 14.204 6.606

Table 5: S-NPL Systematic Series Parameter Range

Model L/B B/T CB L/1/3

1 7.00 2.00 0.397 6.27

2 10.40 1.50 0.397 7.40

3 9.00 2.00 0.397 7.41

4 8.00 2.50 0.397 7.39

5 12.80 1.50 0.397 8.51

6 11.00 2.00 0.397 8.50

7 9.90 2.50 0.397 8.49

8 15.10 1.50 0.397 9.50

9 13.10 2.00 0.397 9.50

10 11.70 2.50 0.397 9.50

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Table 6: SKLAD Systematic Series Parameter Range

Model L/B B/T CB L/1/3

1 6.00 4.00 0.350 7.43

2 4.00 4.00 0.350 5.67

3 8.00 4.00 0.350 9.01

4 6.00 3.00 0.350 6.75

5 6.00 5.00 0.350 8.01

6 4.00 3.00 0.350 5.15

7 4.00 5.00 0.350 6.11

8 8.00 3.00 0.350 8.19

9 8.00 5.00 0.350 9.71

10 6.00 4.00 0.450 6.84

11 4.00 4.00 0.450 5.22

12 8.00 4.00 0.450 8.29

13 6.00 3.00 0.450 6.21

14 6.00 5.00 0.450 7.37

15 4.00 3.00 0.450 4.74

16 4.00 5.00 0.450 5.62

17 8.00 3.00 0.450 7.53

18 8.00 5.00 0.450 8.93

19 6.00 4.00 0.550 6.40

20 4.00 4.00 0.550 4.88

21 8.00 4.00 0.550 7.75

22 6.00 3.00 0.550 5.81

23 6.00 5.00 0.550 6.89

24 4.00 3.00 0.550 4.44

25 4.00 5.00 0.550 5.26

26 8.00 3.00 0.550 7.04

27 8.00 5.00 0.550 8.35

18

Selection of Independent Variables

Independent variables are generated as functions of varied hull parameters and/or speed.

Independent variables should be in non-dimensional form. When there is theoretical evidence as to the form that the independent variables should take, an attempt should be made to utilitiesthat form.

When a regression equation has two highly correlated variables as useful independent variables, it is wrong to further include their product as an independent variable because it will lead to some instability in the equation. And it is unnecessary as it will not add significantly to the accuracy of the equation.

It is possible to have two highly correlated independent variables which if one is included in the regression equation without the other is not effective, but if both are included then the equation is more accurate.

It also possible to have two highly correlated independent variables in a regression equation which both have significantly non-zero coefficients, but which predominantly explain the variance of each other rather than the variance of the dependent variable. Each of these could become insignificant, if the other is removed from the equation.

Production of Good Regression Analysis

Each independent variable used in the regression equation should have a high significance level, generally not lower than 95%.

It should not be possible to improve the accuracy of the equation by introducing extra independent variables.

It should not be possible to exclude an independent variable from the equation without significantly reducing the accuracy.

19

The regression equation should not contain more than ten independent variables, Fairlie-Clark (1975). Fung (1991) concluded that residual error starts to stagnate after inclusion of 1 to 17 terms. More terms in a regression equation may contribute to a better fit to the data, yet give a poorer interpolation result, Savitsky et al. (1976).

20

7. REGRESSION ANALYSIS

TECHNIQUE

Regression analysis is widely used for prediction and forecasting.

Apply regression analysis to some experiments data and show how to interpret the results of this analysis. Techniques have been tried to

predict RR/ with L/B, B/T, L/1/3 and CB.Hull form and loading parameter were transformed in to another set of variables with a range from -1 to 1.

S-NPL and AMECRC has a different equation. But AMECRC and SKLAD series has similar equations, AMECRC and SKLAD series hull

forms where the parameter space has varying L/B, B/T, L/1/3 and CB, S-NPL series has a same equation until equation number (3) and number (7) but S-NPL series did not choose the equation number (8) because they have a fixed the block coefficient. The equation developed for S-NPL is similar to the equation developed by Radojcic (1997) for NPL hull forms which have 27 terms, and the equation developed for AMECRC and SKLAD series have 48 terms.

When you use a regression equation, do not use for the independent variable that are outside the range of values used to create the equation. That is called extrapolation, and it can produce unreasonable estimates. Using values outside that range is problematic.

21

S-NPL hull series:

2

)/()/(

2

)/()/(

minmax

maxmin

1BLBL

BLBL

B

L

x

(1)

2

)/()/(

2

)/()/(

minmax

maxmin

2TBTB

TBTB

T

B

x

(2)

2

)/()/(

2

)/()/(

min

3/1

max

3/1

max

3/1

min

3/1

3/1

3

LL

LLL

x

(3)

2

3

2

227

2

3

2

126

2

2

2

125

2

3

3241

3

3233

3

2221

3

2213

3

1202

3

119

3

318

3

217

3

1162

2

3151

2

3143

2

213

1

2

2123

2

1112

2

110329318217

2

36

2

25

2

143322110

xxaxxaxxa

xxaxxaxxaxxaxxaxxa

xaxaxaxxaxxaxxa

xxaxxaxxaxxaxxaxxa

xaxaxaxaxaxaaRR

(4)

22

AMECRC & SKLAD hull series:

2

)/()/(

2

)/()/(

minmax

maxmin

1BLBL

BLBL

B

L

x

(5)

2

)/()/(

2

)/()/(

minmax

maxmin

2TBTB

TBTB

T

B

x

(6)

2

)/()/(

2

)/()/(

min3/1

max3/1

max3/1

min3/1

3/1

3LL

LLL

x

(7)

2

)()(

2

)()(

minmax

maxmin

4BB

BBB

CC

CCC

x

(8)

23

2

4

2

348

2

4

2

247

2

3

2

246

2

4

2

145

2

3

2

144

2

2

2

1433

3

4422

3

4411

3

4404

3

339

2

3

3381

3

3374

3

2363

3

2351

3

2344

3

133

3

3

1322

3

131

3

430

3

329

3

228

3

1273

2

426

2

2

4251

2

4244

2

3232

2

3221

2

3214

2

220

3

2

2191

2

2184

2

1173

2

1162

2

1154314

4213321241113110219

2

48

2

37

2

26

2

15443322110

xxaxxaxxaxxa

xxaxxaxxaxxaxxaxxa

xxaxxaxxaxxaxxaxxa

xxaxxaxaxaxaxaxxa

xxaxxaxxaxxaxxaxxa

xxaxxaxxaxxaxxaxxa

xxaxxaxxaxxaxxaxa

xaxaxaxaxaxaxaaRR

(9)

24

8. FORWARD STEPWISE REGRESSION PROCEDURE

Stepwise regression includes regression models in which the choice of predictive variables in carried out by procedure. This takes the form of a sequence of tests. Theindependent variables are introduced based on significance testing using the t-test.Forward selection which involves starting with no variables in the model. Figure out the values and including them if they are statistically significant. Backward elimination, with all candidate variables and testing them one by one for statistical significance and will be deleting the data with not significant. These two ways are processing after that variables to be include or excluded.

This model has been used for all of the analyses described in this paper. F-values, mentioned above, where selected so that the final regression model contains no variables with a statistical significance (p-level) greater than 0.05 (5%).The acceptance and rejection of each independent variable is purely based on the F-test.Specifically, p-level represents the probability of error. A wayto test for error in models created by step wise regression.

When conducting regression analysis results could become unstable if highly correlated independent variables are included in the regression model. Control over this matter was achieved by setting the tolerance level from 0 – 0.001 (0% - 0.1%). That means that variables whose tolerance was under this level were considered redundant with the contribution of other independent variables already in the equation.

25

9. FINAL REGRESSION MODEL AND RESULTS

The regression equations, initially RR/ has been derived from the experimental data. AMECRC and S-NPL systematic series had their own published experimental data, also SKLAD systematic series had a regression equation developed by Radojcic et al. (1999) based on CR.

An equation which graph is a straight line is called a linear function and not straight lines are called nonlinear functions. These experimentsthrough analysis have been performed to arrange the results for the specific Froude numbers. The final results have a certainty values and uncertainty value. The certain values use for solution in predicting the resistance for a range of round bilge high speed vessel. But the uncertainty is throw it away, that number is very small as small enough to be ignored.

Regression equations have been derived out for a wide range of

Fn.Each series have different ranges of Fn are for AMECRC systematic series 1 to 2, S-NPL systematic series 1 to 2.5 and SKLAD

systematic series 1 to 3. All three series have increments of 0.1 for Fn.

These way through can get the regression equation find out for all

range of Fn. The accuracy with R2 = 0.9999 or higher. The predicted

values are close to the actual experiment values in RR/. Regression equation obtained by Bojovic (1998) for calculating the wetted surface area coefficient (CS) has been reproduced.

It is to be noted that regression coefficients which do not play a significant role in the regression equation have been ignored in the equations as shown. Table 4 depicts the regression coefficients for the AMECRC Series which needs to be read in conjunction with final equation (10). Table 6 represents the regression coefficients for the SKLAD series as per the equation (11).Table 5 represents the regression coefficients for the S-NPL series as final the equation (12).

26

Final Equation for AMECRC Series:

2

4

2

348

2

3

2

144

2

2

2

143

2

3

4411

3

4404

3

3391

3

3374

3

236

3

3

2354

3

1333

3

132

3

1272

2

425

4

2

3232

2

3224

2

2203

2

2191

2

218

4

2

1173

2

1162

2

115431442133110

2

48

2

37

2

2644330

xxaxxaxxa

xxaxxaxxaxxaxxa

xxaxxaxxaxaxxa

xxaxxaxxaxxaxxa

xxaxxaxxaxxaxxaxxa

xaxaxaxaxaaR

R

(10)

Final Equation for SKLAD Series:

3

2

4262

2

425

1

2

4244

2

3232

2

3221

2

321

4

2

2203

2

2191

2

2184

2

117

3

2

1162

2

115431442133212

41113110219

2

48

2

37

2

26

2

15443322110

xxaxxa

xxaxxaxxaxxa

xxaxxaxxaxxa

xxaxxaxxaxxaxxa

xxaxxaxxaxaxaxa

xaxaxaxaxaaR

R

(11)

Final Equation for S-NPL Series:

3

318

3

217

3

1162

2

315

1

2

3143

2

2131

2

2123

2

111

2

2

110329318217

2

36

2

25

2

143322110

xaxaxaxxa

xxaxxaxxaxxa

xxaxxaxxaxxaxa

xaxaxaxaxaaR

R

(12)

27

FinalEquation for NPL Series, Radojcic (1997):

2

3

2

227

2

3

2

1261

3

3233

3

2223

3

120

2

3

119

3

1163

2

2131

2

212

2

253322110

xxaxxaxxaxxaxxa

xxaxaxxaxxa

xaxaxaxaaR

R

(13)

28

Table 7: AMECRC Series Regression Coefficients

Fn∇

ai 1.0 1.1 1.2 1.3 1.4

a0 0.023279 0.034820 0.043599 0.052891 0.058922

a3 -0.008744 -0.057167 0.045517 0.038712 0.011354

a4 0.000000 -0.001121 -0.004731 -0.007199 0.000000

a6 0.000000 0.000000 0.000000 0.000000 0.000000

a7 -0.070453 -0.033467 0.000000 0.000000 0.000000

a8 0.000000 0.000000 -0.000432 0.000000 0.000000

a10 0.000000 0.007160 0.019157 0.019932 0.000000

a13 0.000139 0.000000 0.000000 0.000000 -0.181207

a14 0.000000 0.000000 0.000000 0.000000 0.000000

a15 0.000000 0.000000 -0.001237 -0.001734 -0.004292

a16 0.032385 0.000000 0.000000 0.000000 0.023031

a17 0.000000 0.067810 0.010202 0.009221 0.007989

a18 0.000000 0.000000 0.000000 0.000000 0.000000

a19 0.000192 0.000000 0.000000 0.000000 0.000000

a20 0.000000 0.000000 0.000330 0.000000 0.000000

a22 0.000519 0.000281 0.000000 0.000000 0.000000

a23 0.000000 0.000000 -0.017570 -0.021384 -0.018890

a25 0.000203 0.000240 0.000278 0.000777 0.001442

a27 0.001214 0.005210 0.000000 0.000000 0.000000

a32 0.000000 0.000000 0.000000 0.000000 -0.003142

a33 0.000000 0.000000 0.000000 0.000000 0.000000

a35 0.000000 0.000000 0.000000 0.000000 -0.000020

a36 0.000000 0.000000 -0.000234 -0.000264 0.000751

a37 -0.001588 0.003025 0.000000 0.000000 0.000000

a39 -0.001583 -0.001543 -0.001528 -0.000669 0.004185

a40 0.000000 0.000000 0.000000 0.000000 0.000000

a41 0.000000 0.000000 0.000000 0.000000 0.179873

a43 0.000000 0.000000 0.000000 0.000000 0.000484

a44 0.076139 0.054637 0.000000 0.000000 0.000000

a48 0.000000 0.000000 -0.005561 -0.001832 0.000000

29

Table 8: AMECRC Series Regression Coefficients

Fn∇

ai 1.5 1.6 1.7 1.8 1.9 2.0

a0 0.058922 0.060310 0.061116 0.062020 0.063321 0.064799

a3 0.011354 0.029665 0.042866 0.043796 0.044749 0.046324

a4 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000

a6 0.000000 0.000085 0.000235 0.000000 -0.000135 -0.000224

a7 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000

a8 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000

a10 0.000000 0.008773 0.063675 0.059540 0.039398 0.027767

a13 -0.181207 -0.161623 -0.099871 -0.092767 0.000000 0.000000

a14 0.000000 0.000000 0.000000 0.000000 0.000000 0.011370

a15 -0.004292 -0.002888 -0.002333 -0.001814 0.000673 0.002024

a16 0.023031 0.019266 0.000000 0.000000 0.000000 0.000000

a17 0.007989 0.007992 0.008120 0.008199 0.000000 0.008268

a18 0.000000 -0.000002 -0.000045 -0.000007 0.000000 0.000000

a19 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000

a20 0.000000 0.000000 0.000000 0.000034 0.000357 0.000887

a22 0.000000 0.000000 0.000000 -0.000115 -0.001280 -0.001846

a23 -0.018890 -0.018580 -0.018543 -0.019067 -0.019147 -0.019658

a25 0.001442 0.001074 0.000742 0.000640 0.000000 0.000000

a27 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000

a32 -0.003142 -0.003920 -0.061195 -0.053412 0.000000 0.000000

a33 0.000000 0.000000 0.000000 0.000000 0.000000 -0.002056

a35 -0.000020 0.000000 0.000000 0.000000 0.000000 0.000000

a36 0.000751 0.000448 0.000000 0.000000 0.000000 0.000000

a37 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000

a39 0.004185 0.002173 0.000000 0.000000 -0.014279 -0.026312

a40 0.000000 0.000000 -0.002961 -0.001232 -0.000659 0.003173

a41 0.179873 0.139400 0.099838 0.084237 0.000000 0.000000

a43 0.000484 0.000222 0.000000 0.000000 0.000000 0.000000

a44 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000

a48 0.000000 0.000000 -0.003133 -0.000912 0.000000 0.000000

30

Table 9: S-NPL Series Regression Coefficients

Fn∇

ai 1.0 1.1 1.2 1.3 1.4 1.5 1.6

a0 0.132000 0.182900 0.246610 0.270100 0.306850 0.321000 0.340200

a1 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000

a2 0.000000 -0.005800 -0.001790 0.002322 0.006722 0.010900 0.006900

a3 -0.164469 -0.070217 0.152991 0.154071 0.154341 0.157987 0.173786

a4 0.000000 0.000000 0.000000 0.000000 0.0000000 0.000000 -0.092700

a5 0.000000 0.014750 0.021110 0.022010 0.0236000 0.024387 0.025110

a6 -0.832000 -0.128182 -0.002626 -0.021242 0.054373 0.080082 0.019911

a7 0.069900 0.042910 0.000000 0.000000 0.000000 0.000000 0.000000

a8 0.772112 0.063600 0.000000 0.000000 0.000000 0.000000 0.000000

a9 0.191745 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000

a10 -0.091300 -0.041930 0.000000 0.000000 0.001320 0.007209 0.007209

a11 0.000000 0.000000 0.000000 0.000000 0.043305 0.055346 0.055346

a12 0.000000 0.000000 -0.024990 -0.010090 -0.024990 0.000000 0.000000

a13 -0.070730 -0.016582 0.336234 0.163834 0.000000 0.000000 0.000000

a14 0.000000 0.000000 0.000000 0.000000 0.000000 0.011360 0.018288

a15 0.000000 0.000000 0.195793 0.182336 0.231202 0.026548 -0.025454

a16 0.041000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000

a17 -0.020000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000

a18 0.000000 -0.241509 -0.413858 -0.241509 -0.241534 0.000000 0.050092

31


Fn∇

ai 1.7 1.8 1.9 2.0 2.1 2.2 2.3

a0 0.383000 0.396300 0.232400 0.265840 0.395900 0.462320 0.518220

a1 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000

a2 0.000000 0.000000 0.127260 0.157760 0.087760 0.000000 0.000000

a3 0.218347 0.229730 -0.185538 -0.375285 -0.001246 0.243706 0.248740

a4 -0.121500 -0.129900 0.190030 1.657930 0.365230 -0.173220 -0.114220

a5 0.038207 0.041107 0.070020 0.070020 0.050902 0.036020 0.035040

a6 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000

a7 -0.010200 0.009020 0.460100 0.616710 0.009671 0.000000 0.000000

a8 0.204036 0.216173 -0.114575 -1.491900 -0.006549 0.439785 0.398790

a9 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000

a10 0.000000 0.000000 -0.131290 -0.251379 -0.240032 -0.249980 -0.326698

a11 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000

a12 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000

a13 0.000000 0.000000 0.000000 0.000000 -0.013829 -0.032637 -0.40483

a14 -0.034224 -0.019619 0.000000 0.000000 0.000000 0.414395 0.359695

a15 -0.035009 -0.025946 0.000000 0.000000 0.000000 0.000000 0.000000

a16 -0.003200 0.000000 0.000000 0.000000 0.000000 -0.357990 -0.500299

a17 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000

a18 0.076498 0.123328 0.211792 0.211792 0.059834 0.000000 0.000000

32


Fn∇

ai 2.4 2.5

a0 0.520010 0.535910

a1 0.000000 0.000000

a2 0.000000 0.000000

a3 0.251983 0.256493

a4 -0.044280 -0.004773

a5 0.034880 0.036920

a6 0.000000 0.000000

a7 0.000000 0.000000

a8 0.337688 0.298664

a9 0.000000 0.000000

a10 -0.354420 -0.442020

a11 0.748347 1.059690

a12 -0.020014 -0.047540

a13 0.000000 0.000000

a14 0.000000 0.000000

a15 0.000000 0.000000

a16 -0.812280 -1.010080

a17 0.000000 0.000000

a18 0.000000 0.000000

33

Table 12: NPL Series Regression Coefficients (Radojcic 1997)

Fn∇

ai 0.8 1.0 1.2 1.4 1.6 1.8

a0 0.012677 0.031092 0.057789 0.070863 0.080384 0.092592

a1 -0.008102 0.000000 0.008445 0.004134 0.000962 0.005733

a2 0.000061 -0.041840 -0.042841 -0.044967 -0.041259 -0.043200

a3 -0.002725 0.007983 0.015331 0.013614 0.014880 0.022856

a5 -0.001185 0.002904 0.010337 0.043687 .009803 0.008203

a12 0.004254 -0.003601 0.000000 0.005111 0.012468 0.012205

a13 -0.025702 0.000000 -0.000655 -0.013831 -0.0138512 -0.043373

a16 0.001395 0.000062 0.000000 0.002578 0.004118 0.005143

a19 0.004913 0.005626 0.004361 0.004098 0.004899 0.004763

a20 -0.006901 0.002059 0.010917 0.001183 0.000667 0.002649

a22 0.0015476 0.000000 -0.003984 0.011616 0.030670 0.033934

a23 -0.008887 0.002059 0.006095 0.001874 -0.004834 -0.006093

a26 -0.008427 0.005375 0.016808 0.006989 0.001094 -0.001804

a27 -0.033521 0.010811 0.008090 -.023857 -0.057101 -0.064610

ai 2.0 2.2 2.4 2.6 2.8 3.0

a0 0.105658 0.113350 0.118892 0.123105 0.120589 0.115058

a1 0.010769 0.007299 -0.001703 -0.014977 -0.041899 -0.077104

a2 -0.046379 -0.042913 -0.039950 -0.034003 -0.017179 0.005255

a3 0.031878 0.031266 0.023441 0.008990 -0.022888 -0.067378

a5 0.007646 0.013292 0.026694 0.043975 0.057718 0.071086

a12 0.010455 0.000922 -0.018860 -0.043354 -0.046133 -0.048405

a13 -0.050962 -0.050318 -0.036356 0.000000 0.051148 0.057769

a16 0.006964 0.008068 0.009177 0.009824 0.009804 0.008532

a19 0.010023 0.012955 0.012276 0.006514 -.008769 -0.0034102

a20 0.002493 -0.003659 -0.018867 -0.033644 -0.057179 -0.101116

a22 0.044572 0.047574 0.025806 -0.015288 -0.047272 -0.062657

a23 -0.009345 -0.010929 -0.015162 -0.020789 -0.019478 -0.051664

a26 -0.010127 -0.017531 -0.033868 -0.050023 -0.060285 -0.118198

a27 -0.081529 -0.080688 -0.063470 -0.014102 0.040157 0.073258

34

Table 13: SKLAD Series Regression Coefficients

Fn∇

ai 1.1 1.2 1.3 1.4 1.5 1.6

a0 0.514490 0.514500 0.033000 0.151930 0.184010 0.291100

a1 3.307790 3.307100 0.000000 -0.181832 -0.258900 -0.458840

a2 -1.245830 -1.240130 0.000000 0.000000 -0.101200 -0.410120

a3 -2.018538 -2.020252 0.022618 0.004887 -0.392518 -0.904121

a4 -1.124810 -1.125010 0.000000 -0.190500 -0.322280 -0.682280

a5 0.107000 0.110200 0.000000 -3.000290 -4.300000 -6.291000

a6 0.104930 0.105130 0.003140 -0.268900 -0.295000 -0.355000

a7 -0.051416 -0.051552 -0.024654 -0.129486 -0.259737 -0.501016

a8 -0.125596 -0.126960 0.004951 0.099210 0.205800 0.295790

a9 0.332970 0.333000 0.000332 1.204560 2.458000 3.443880

a10 0.144829 0.144538 0.045032 2.382015 3.300639 4.709449

a11 0.171950 0.172400 0.000000 0.075602 0.091000 1.102000

a12 -0.041558 -0.041140 -0.017393 -0.046948 -0.631805 -0.974578

a13 -0.059260 -0.058450 0.001120 -0.000920 -0.003100 -0.003100

a14 0.045711 0.045319 -0.013831 0.033548 0.022952 0.424163

a15 -0.011950 -0.012000 0.000000 0.000000 -0.109310 -0.163100

a16 -0.015240 -0.015454 0.000000 0.000000 0.466265 0.684129

a17 -0.002091 -0.001200 0.000000 0.000000 0.000000 0.000000

a18 0.000000 0.000000 0.004440 0.002301 -0.075920 -0.169100

a19 -0.013544 -0.013435 0.000000 0.022484 0.040595 0.080602

a20 -0.000100 -0.000100 0.000000 0.000000 0.000000 -0.004820

a21 -0.010419 -0.010320 0.000000 0.000000 -0.040433 -0.074708

a22 -0.000070 -0.000074 0.000935 0.002385 0.022823 0.022823

a23 -0.005809 -0.005892 0.001216 -0.007646 -0.053793 -0.078843

a24 0.031920 0.032690 0.000000 0.000000 0.196600 0.196600

a25 -0.009720 -0.009960 -0.001470 -0.076840 -0.011900 -0.011900

a26 -0.006905 -0.007298 0.001209 -0.010200 -0.079738 -0.097846

35


Fn∇

ai 1.7 1.8 1.9 2.0 2.1 2.2

a0 0.290520 -0.946900 -0.529200 0.144270 0.154970 0.441000

a1 -0.459100 -10.680000 -9.600000 0.000000 0.007320 2.523600

a2 -0.409020 3.010000 2.890000 -0.270200 -0.274290 -0.826700

a3 -0.905007 4.326742 3.273624 -0.491029 -0.490221 -1.716405

a4 -0.679920 2.020000 2.020000 -0.265620 -0.278620 -0.920000

a5 -6.300570 -12.502400 -9.502400 -2.360790 -2.360171 -0.642000

a6 -0.355096 -1.193600 -1.004936 -0.006920 -0.009807 -0.236300

a7 -0.503653 -0.942108 -0.672746 0.133167 0.133549 0.326781

a8 0.297000 0.982000 0.982000 0.051650 0.053650 -0.032000

a9 3.444920 6.179900 5.102900 0.986230 0.995770 1.336090

a10 4.722063 8.903337 6.177496 1.263691 1.277852 0.000000

a11 1.110730 1.534900 1.530000 0.615970 0.617900 0.242020

a12 -0.974905 -2.150571 -2.143091 0.016562 0.016380 -0.334933

a13 -0.002800 0.039900 0.036200 0.031924 0.031620 -0.264600

a14 0.424889 0.687107 0.661725 0.233695 0.233866 0.369425

a15 -0.163000 -0.286100 -0.286100 -0.176921 -0.175510 -0.156020

a16 0.686616 1.325339 1.343567 0.192446 0.188852 0.029412

a17 0.000000 0.000000 0.000000 0.032470 0.030070 0.081400

a18 -0.168610 -0.326000 -0.299000 -0.027500 -0.027300 0.049200

a19 0.080537 0.226760 0.221313 -0.002720 -0.002901 0.005773

a20 -0.004436 -0.003400 -0.002800 0.004660 0.004810 0.014500

a21 -0.074748 -0.116025 -0.106664 -0.023703 -0.023703 -0.054954

a22 0.022902 0.049719 0.049719 0.013791 0.013725 0.003296

a23 -0.080174 -0.142526 -0.125676 -0.066766 -0.067235 -0.102433

a24 0.200200 0.272000 0.232000 0.077920 0.066720 0.005100

a25 -0.011500 -0.013100 -0.009000 0.005990 0.000180 -0.025600

a26 -0.103293 -0.184095 -0.164560 -0.028295 -0.029063 -0.025417

36


Fn∇

ai 2.3 2.4 2.5 2.7 3.0

a0 0.430900 -0.800500 -0.849000 -1.027000 -0.071000

a1 2.533410 -6.822500 -6.845000 -8.282000 0.152050

a2 -0.828200 2.013600 2.114000 2.557500 0.000000

a3 -1.712414 3.641935 3.665198 4.434621 0.365467

a4 -0.919760 2.041200 2.042000 2.470001 0.358200

a5 -0.640400 -3.148100 -3.250100 -3.929500 2.070100

a6 -0.239005 0.017600 0.014000 0.016350 0.451090

a7 0.326988 0.120784 0.122116 0.147800 0.439181

a8 -0.029980 0.180090 0.179000 0.217000 -0.300050

a9 1.346920 0.000000 0.000000 0.000000 -1.963500

a10 0.000000 1.576129 1.582055 1.914298 -1.962954

a11 0.239152 0.901400 0.913900 1.106900 0.394500

a12 -0.334926 0.377340 0.378648 0.456788 0.991281

a13 -0.269900 0.192300 0.182000 0.219600 0.007400

a14 0.370006 -0.177378 -0.173057 -0.209512 -0.424762

a15 -0.155620 -0.274000 -0.261000 -0.317000 -0.178400

a16 0.029034 0.185366 0.192810 0.232316 -0.395423

a17 0.081920 0.035400 0.035000 0.043000 0.057000

a18 0.049170 -0.018700 -0.011000 -0.013006 0.161000

a19 0.005843 -0.011510 -0.015250 -0.018296 -0.108932

a20 0.010200 0.010300 0.008299 0.010089 0.012600

a21 -0.053627 0.013672 0.011075 0.013355 0.039884

a22 0.005157 0.027503 0.029006 0.034939 0.016097

a23 -0.098371 -0.069272 -0.056022 -0.067901 -0.019495

a24 0.005390 0.090400 0.093900 0.115000 -0.000339

a25 -0.027200 0.024000 0.030960 0.038000 0.015809

a26 -0.028359 -0.029702 -0.031805 -0.038449 0.024912

37

10. WETTED SURFACE AREA COEFFICIENTS (BOJOVIC

(1998))

Since the wetted surface area determination has already been carried out by Bojovic (1998), these are also being reproduced in Tables 16 to 18. The regression model for the wetted surface area coefficient would have the following form as shown in the following equations. Various questions are about WSA and the effect on speed, which has more WSA as a catamaran or a monohulls.

WSA has two major applications for vessels as speed and power calculations of displacement hulls. Also, anodes, determine how many of a certain size based on area. There is hardly any difference except that hull area must be calculated up to the load waterline and light waterline but this calculation is for light waterline.

The wetted surface area coefficient is given by:

3/2

SCS

(14)

For AMECRC Series, the coefficients ci are shown in Table 16:

3/1

3/1

5

1

3/4

4

1

3/2

3

3/2

2

3/2

3/2

10

BB

BBBS

CT

BcC

B

Lc

CT

B

B

LcC

T

BcC

B

LccC

(15)

38

For SKLAD Series, the coefficients ci shown in Table 17:

3

3

13/4

2

3/2

3/23/2

10

B

Lc

CT

B

B

LcC

T

B

B

LccC

BBS

(16) For NPL and S-NPL Series, the coefficients ci are shown in Table 18:

3/23/2

7

2

6

3/2

5

3/22

4

1

3

2

2

3/2

10

T

B

B

Lc

T

B

B

Lc

T

Bc

T

B

B

Lc

T

Bc

T

B

B

Lc

T

B

B

LccC

S

(17)

Table 16: AMECRC Series – CS Regression Parameters and

Coefficients

C0 3.328344

(L/B)2/3CB-2/3 C1 0.744941

(B/T)CB-2/3 C2 0.352265

(L/B)2/3(B/T)CB-1 C3 0.046307

(L/B)4/3CB-1 C4 -0.037945

(B/T)1/3CB-1/3 C5 -1.367162

R2 C6 0.999543

St. error C7 0.02013

39

Table 17: SKLAD Series – CS Regression Parameters and Coefficients

C0 2.456288

(L/B)-2/3(B/T)2/3CB2/3 C1 0.434391

(L/B)-4/3(B/T)-1CB C2 -0.013612

(L/B)-3 C3 0.000188

R2 C4 0.99862


Table 18: NPL & S-NPL Series – CS Regression Parameters and Coefficients

C0 4.445787

(L/B)2/3(B/T) C1 0.252716

(L/B)-2(B/T)-1 C2 -186841481

(B/T)-1 C3 -14.463151

(L/B)-2(B/T)-2/3 C4 131.22276

(B/T)2/3 C5 23.016071

(L/B)2(B/T) C6 -0.008127

(L/B)2/3(B/T)2/3 C7 0.528452

R2 C8 0.99892


40

11. CONCLUSIONS

The purpose of this study is to provide a set of regression models for various round bilge high-speed hull forms. The regression equations would be provided viable first estimates of the resistance characteristics of hull-form in early design stages.

This thesis has a three main systematic series as AMECRC and S-NPL, SKLAD. These series had their own published experimental data. AMECRC and S-NPL, SKLAD appear to be similar, but these series are different as parameter space for each of the systematic series different considerably.

In the linear regression model, the dependent variable is assumed to be a linear function of one or more independent variables plus an error introduced to account for all other factors. In the above

regression equation, RR/ is the dependent variable and any other

factors are the independent as Fn, L/B, B/T etc. The goal of regression analysis is to obtain estimates of the resistance of the series at each range as the goal is prediction, or forecasting. The experiment and predicted the final values are small differences and it has been ignored in this result.

Comparison states that the Froude number is to be used to determine the resistance of a partially submerged object moving through water. In this paper the Froude number is replaced by Froude volume

numberFn. The ranges of Fn are for AMECRCsystematic series 1 to 2, S-NPL systematic series 1 to 2.5 and SKLAD systematic series 1 to 3. The Froude number is incremented for each step.

Regression equation obtained for all Fnhave a higher degree of accuracy with R2values between within obtaining the coefficients of the equations. The experiment and predicted values are quite close.

41

CR as a function of Froude number for the monohulls and also is obtained by subtracting CFgiven by the ITTC 1957 model ship correlation line from the total resistance coefficient CT.AMECRC and SKLAD series are similar parameter has been checked. But the results are different. Because the body plans of two series is very different. For

this reason, will be different the RR/ in different CR. It is primarily considered the body plan has to be compared when check the resistance prediction of the series.

A study on the variation RR/in parameters with L/B, B/T and has

been carry out FN/. The results of this calculation are in appendix. If the displacement of the ship when built exceeds the design figure then the ship resistance will be greater than that anticipated at the design stage.

The experiments results are presented for systematic results for calm water resistance, trim, and sinkage of monohulls. For example, NPL series CB has been kept at 0.397 throughout the series. Further tests on models will be change to another number within a range. It is a more significant change of the CBthrough to predict the result accurately.

Also, air and propeller are deserves serious consideration. Many experiments with no wind present. The airflow can influence trim and sinkage, which again affect the resistance. If a model is made with complete structure below the main part of towing tank carriage in a model, the towing carriage will affect the airflow. Also, wind tunnel tests and CFD are commonly used to estimated the air resistance. This experiment will make the results more accurate. And propeller will affect the flow around the ship. This means the resistance on the hull is not the same with and without the propeller. We can determine the ship speed when we know the hull interaction coefficients, the resistance, and the propellers.

Baird(1998) defines a high speed vessel as a craft with maximum operating speed higher than 30 knots and a fast vessel supported by submerged hull such as a monohulls and catamarans. And, the design and safety of high-speed craft is regulated by the High Speed Craft Codes.For this reason, it involves consideration from various angles. The regression models are to be used with due care with regard to type of hull form used in monohull configuration.

42

References [1] Bailey, D., The NPL High-speed Round Bilge Displacement Hull

Series, RINA, Maritime Technology Monograph No. 4, 1976.

[2] Bojovic, P., Resistance Prediction of High-speed Round Bilge Hull Forms, Australian Maritime College, 1998, n.p.

[3] Jin, P., Su, B., Tan, Z., A Parametric study on High-Speed Round Bilge Displacement Hulls, High-Speed Surface Craft, September, 1980.

[4] Mercier, J.A., Savitsky, D., Resistance of Transom-Stern Craft in the Pre-planing Regime, Davidson Laboratory Report 1667, Stevens Institute of Technology, June, 1973.

[5] Molland, A.F., Wellicome, J.F., Couser, P.R., Resistance Experiments on a Systematic Series of High-speed Displacement Catamaran Forms: Variation of Length – displacement Ratio and Breadth-Draught Ratio, Ship Science Report 71, University of Southampton, 1994.

[6] Radojcic, D., Princevac, M., Rodic, T., Resistance and Trim Prediction for the SKLAD Semi Displacement Hull Series, Oceanic Engineering International, Vol 3, No.1, 1999, pp. 34 - 50.

[7] Radojcic, D., Rodic, T., Kostic, N., Resistance and Trim Predictions for the NPL High-speed Round Bilge Displacement Hull Series, RINA Symposium – Power, Performance and Operability of Small Craft, Southampton, UK, Sept 15-16. 1997.

[8] Sahoo, P.K., Doctors, L.J., Hydrodynamics of AMECRC Systematic Series – High – Speed Displacement Monohull Forms, Australian Maritime College, 1999.

[9] Odd M. Faltinsen,. Hydrodynamics of High-Speed Marine Vehicles,

Norwegian University of Science and Technology, 2005

43

APPENDIX 1: AMECRC SERIES REGRESSION RESULTS

Figure 9: AMECRC Series Observed and Predicted (Model 1)


0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.5 1 1.5 2 2.5

RR/ Δ

Fn

Expt 1

Prediction 1

0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.5 1 1.5 2 2.5

RR/ Δ

Fn

Expt 2

Prediction 2

44



0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.5 1 1.5 2 2.5

RR/ Δ

Fn

Expt 3

Prediction 3

0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.10

0.5 1 1.5 2 2.5

RR/ Δ

Fn

Expt 4

Prediction 4

45



0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.5 1 1.5 2 2.5

RR/ Δ

Fn

Expt 5

Prediction 5

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.5 1 1.5 2 2.5

RR/ Δ

Fn

Expt 6

Prediction 6

46



0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0.5 1 1.5 2 2.5

RR/ Δ

Fn

Expt 7

Prediction 7

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.5 1 1.5 2 2.5

RR/ Δ

Fn

Expt 8

Prediction 8

47



0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.5 1 1.5 2 2.5

RR/ Δ

Fn

Expt 9

Prediction 9

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.5 1 1.5 2 2.5

RR/ Δ

Fn

Expt 10

Prediction 10

48



0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.5 1 1.5 2 2.5

RR/ Δ

Fn

Expt 11

Prediction 11

0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.5 1 1.5 2 2.5

RR/ Δ

Fn

Expt 12

Prediction 12

49



0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.5 1 1.5 2 2.5

RR/ Δ

Fn

Expt 13

Prediction 13

0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.5 1 1.5 2 2.5

RR/ Δ

Fn

Expt 14

Prediction 14

50

APPENDIX 2: SKLADSERIES REGRESSION RESULTS

Figure 23: SKLAD Series Observed and Predicted (Model 1)


0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.5 1 1.5 2 2.5 3 3.5

RR/ Δ

Fn

Expt 1

Prediction 1

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0.18

0.5 1 1.5 2 2.5 3 3.5

RR/ Δ

Fn

Expt 2

Prediction 2

51



0.00

0.01

0.01

0.02

0.02

0.03

0.03

0.04

0.5 1 1.5 2 2.5 3 3.5

RR/ Δ

Fn

Expt 3

Prediction 3

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.5 1 1.5 2 2.5 3 3.5

RR/ Δ

Fn

Expt 4

Prediction 4

52



0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.5 1 1.5 2 2.5 3 3.5

RR/ Δ

Fn

Expt 5

Prediction 5

0.00

0.05

0.10

0.15

0.20

0.25

0.5 1 1.5 2 2.5 3 3.5

RR/ Δ

Fn

Expt 6

Prediction 6

53



0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0.5 1 1.5 2 2.5 3 3.5

RR/ Δ

Fn

Expt 7

Prediction 7

0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.5 1 1.5 2 2.5 3 3.5

RR/ Δ

Fn

Expt 8

Prediction 8

54



0.00

0.01

0.01

0.02

0.02

0.03

0.03

0.04

0.5 1 1.5 2 2.5 3 3.5

RR/ Δ

Fn

Expt 9

Prediction 9

0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.5 1.5 2.5 3.5

RR/ Δ

Fn

Expt 10

Prediction 10

55



0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.5 1.5 2.5 3.5

RR/ Δ

Fn

Expt 11

Prediction 11

0.00

0.01

0.01

0.02

0.02

0.03

0.03

0.04

0.04

0.05

0.05

0.5 1.5 2.5 3.5

RR/ Δ

Fn

Expt 12

Prediction 12

56



0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.5 1.5 2.5 3.5

RR/ Δ

Fn

Expt 13

Prediction 13

0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.5 1.5 2.5 3.5

RR/ Δ

Fn

Expt 14

Prediction 14

57



0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.5 1.5 2.5 3.5

RR/ Δ

Fn

Expt 15

Prediction 15

0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.5 1.5 2.5 3.5

RR/ Δ

Fn

Expt 16

Prediction 16

58



0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.5 1.5 2.5 3.5

RR/ Δ

Fn

Expt 17

Prediction 17

0.00

0.01

0.01

0.02

0.02

0.03

0.03

0.04

0.04

0.05

0.5 1.5 2.5 3.5

RR/ Δ

Fn

Expt 18

Prediction 18

59



0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.5 1.5 2.5 3.5

RR/ Δ

Fn

Expt 19

Prediction 19

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.5 1.5 2.5 3.5

RR/ Δ

Fn

Expt 20

Prediction 20

60



0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.5 1.5 2.5 3.5

RR/ Δ

Fn

Expt 21

Prediction 21

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.5 1.5 2.5 3.5

RR/ Δ

Fn

Expt 22

Prediction 22

61



0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.5 1.5 2.5 3.5

RR/ Δ

Fn

Expt 23

Prediction 23

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0.18

0.5 1.5 2.5 3.5

RR/ Δ

Fn

Expt 24

Prediction 24

62



0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.5 1.5 2.5 3.5

RR/ Δ

Fn

Expt 25

Prediction 25

0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.5 1.5 2.5 3.5

RR/ Δ

Fn

Expt 26

Prediction 26

63


0.00

0.01

0.01

0.02

0.02

0.03

0.03

0.04

0.5 1.5 2.5 3.5

RR/ Δ

Fn

Expt 27

Prediction 27

64

APPENDIX 3: S-NPL SERIES

REGRESSION RESULTS

Figure 35: S-NPL Series Observed and Predicted (Model 1)


0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.5 1 1.5 2 2.5 3

RR/ Δ

Fn

Expt 1

Prediction 1

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.5 1 1.5 2 2.5 3

RR/ Δ

Fn

Expt 2

Prediction 2

65



0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.5 1 1.5 2 2.5 3

RR/ Δ

Fn

Expt 3

Prediction 3

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.5 1 1.5 2 2.5 3

RR/ Δ

Fn

Expt 4

Prediction 4

66



0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.5 1 1.5 2 2.5 3

RR/ Δ

Fn

Expt 5

Prediction 5

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

0.50

0.5 1 1.5 2 2.5 3

RR/ Δ

Fn

Expt 6

Prediction 6

67



0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

0.50

0.5 1 1.5 2 2.5 3

RR/ Δ

Fn

Expt 7

Prediction 7

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

0.50

0.5 1 1.5 2 2.5 3

RR/ Δ

Fn

Expt 8

Prediction 8

68



0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.5 1 1.5 2 2.5 3

RR/ Δ

Fn

Expt 9

Prediction 9

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

0.5 1 1.5 2 2.5 3

RR/ Δ

Fn

Expt 10

Prediction 10

69

Appendix 4A: NPL Series

(Radojcic, 1997)

2

3

2

227

2

3

2

1261

3

3233

3

2223

3

120

2

3

119

3

1163

2

2131

2

212

2

253322110

xxaxxaxxaxxaxxa

xxaxaxxaxxaxaxaxaxaaRR

Table 19: NPL Series Regression Coefficients

Fn∇

ai 0.8 1.0 1.2 1.4 1.6 1.8

a0 0.012677 0.031092 0.057789 0.070863 0.080384 0.092592

a1 -0.008102 0.000000 0.008445 0.004134 0.000962 0.005733

a2 0.000061 -0.041840 -0.042841 -0.044967 -0.041259 -0.043200

a3 -0.002725 0.007983 0.015331 0.013614 0.014880 0.022856

a5 -0.001185 0.002904 0.010337 0.043687 .009803 0.008203

a12 0.004254 -0.003601 0.000000 0.005111 0.012468 0.012205

a13 -0.025702 0.000000 -0.000655 -0.013831 -0.0138512 -0.043373

a16 0.001395 0.000062 0.000000 0.002578 0.004118 0.005143

a19 0.004913 0.005626 0.004361 0.004098 0.004899 0.004763

a20 -0.006901 0.002059 0.010917 0.001183 0.000667 0.002649

a22 0.0015476 0.000000 -0.003984 0.011616 0.030670 0.033934

a23 -0.008887 0.002059 0.006095 0.001874 -0.004834 -0.006093

a26 -0.008427 0.005375 0.016808 0.006989 0.001094 -0.001804

a27 -0.033521 0.010811 0.008090 -.023857 -0.057101 -0.064610

ai 2.0 2.2 2.4 2.6 2.8 3.0

a0 0.105658 0.113350 0.118892 0.123105 0.120589 0.115058

a1 0.010769 0.007299 -0.001703 -0.014977 -0.041899 -0.077104

a2 -0.046379 -0.042913 -0.039950 -0.034003 -0.017179 0.005255

a3 0.031878 0.031266 0.023441 0.008990 -0.022888 -0.067378

a5 0.007646 0.013292 0.026694 0.043975 0.057718 0.071086

a12 0.010455 0.000922 -0.018860 -0.043354 -0.046133 -0.048405

a13 -0.050962 -0.050318 -0.036356 0.000000 0.051148 0.057769

a16 0.006964 0.008068 0.009177 0.009824 0.009804 0.008532

a19 0.010023 0.012955 0.012276 0.006514 -.008769 -0.0034102

a20 0.002493 -0.003659 -0.018867 -0.033644 -0.057179 -0.101116

a22 0.044572 0.047574 0.025806 -0.015288 -0.047272 -0.062657

a23 -0.009345 -0.010929 -0.015162 -0.020789 -0.019478 -0.051664

a26 -0.010127 -0.017531 -0.033868 -0.050023 -0.060285 -0.118198

a27 -0.081529 -0.080688 -0.063470 -0.014102 0.040157 0.073258

70

Appendix 4B: Wetted Surface Area Coefficients (Bojovic, 1998)

Table 20: AMECRC Series – CS Regression Parameters and Coefficients

L/B 2/3CB-2/3 B/T CB

-2/3 L/B 2/3B/TCB-1

Cs 3.328344 0.744941 0.352265 0.046307

L/B 4/3 CB-1 B/T 1/3 CB

-1/3 R2 St. error

-0.037945 -1.367162 0.999543 0.02013

Table 21: SKLAD Series – CS Regression Parameters and Coefficients

L/B -2/3B/T -2/3CB2/3 L/B -4/3 B/T -1 CB

Cs 2.456288 0.434391 -0.013612

L/B -3 R2 St. error

0.000188 0.999543 0.02013

71

Table 22: NPL & S-NPL Series – CS Regression Parameters and Coefficients

L/B -2/3 B/T L/B -2 B/T 1 B/T 1 L/B -2 B/T 2/3

Cs -4.445787 .252716 -186.841481 -14.463151 131.222762

B/T 2/3 L/B 2 B/T L/B 2/3 B/T2/3 R2 St. error

23.016071 -0.008127 0.528452 0.998923 0.03395

72

Appendix 5: AMECRC Series Experiment Results

Table 23: AMECRC Series Experiment Results for Model 1


Number Fn Speed Drag Rn 103 CT 10

3 CF 10

3 CR RT RR RR/ RT/

(Run) (m/s) (grams) N N

1 0.30 1.189 121.22 1.83E+06 5.355 4.128 1.227 1.189 0.2725 0.00439 0.01918

2 0.35 1.387 168.58 2.14E+06 5.471 4.001 1.470 1.654 0.4443 0.00717 0.02667

3 0.40 1.585 230.56 2.44E+06 5.729 3.896 1.833 2.262 0.7236 0.01167 0.03648

4 0.45 1.783 298.88 2.75E+06 5.868 3.807 2.061 2.932 1.0298 0.01661 0.04728

5 0.50 1.981 368.39 3.05E+06 5.858 3.730 2.129 3.614 1.3132 0.02118 0.05828

6 0.55 2.179 436.58 3.36E+06 5.738 3.662 2.076 4.283 1.5496 0.02499 0.06907

7 0.60 2.377 502.93 3.66E+06 5.554 3.601 1.953 4.934 1.7347 0.02797 0.07956

8 0.65 2.575 568.41 3.97E+06 5.349 3.547 1.802 5.576 1.8782 0.03029 0.08992

9 0.70 2.773 634.90 4.27E+06 5.151 3.498 1.653 6.228 1.9991 0.03224 0.10044

10 0.75 2.971 704.61 4.58E+06 4.980 3.453 1.527 6.912 2.1194 0.03418 0.11147

11 0.80 3.169 779.51 4.88E+06 4.842 3.412 1.430 7.647 2.2588 0.03643 0.12332

12 0.85 3.368 860.78 5.19E+06 4.737 3.374 1.363 8.444 2.4293 0.03918 0.13618

13 0.90 3.566 948.27 5.49E+06 4.654 3.339 1.316 9.303 2.6296 0.04241 0.15002

14 0.95 3.764 1039.88 5.80E+06 4.581 3.306 1.275 10.201 2.8393 0.04579 0.16451

15 1.00 3.962 1131.02 6.10E+06 4.496 3.275 1.221 11.095 3.0139 0.04860 0.17893


3 CF 10

3 CR RT RR RR/ RT/


1 0.30 1.189 192.39 1.85E+06 6.954 4.117 2.836 1.887 0.7698 0.00685 0.01680

2 0.35 1.387 295.16 2.16E+06 7.838 3.991 3.847 2.896 1.4211 0.01265 0.02577

3 0.40 1.585 426.49 2.47E+06 8.671 3.887 4.784 4.184 2.3085 0.02054 0.03723

4 0.45 1.783 567.83 2.78E+06 9.121 3.798 5.324 5.570 3.2513 0.02893 0.04957

5 0.50 1.981 706.98 3.09E+06 9.199 3.721 5.478 6.935 4.1304 0.03676 0.06172

6 0.55 2.179 837.10 3.40E+06 9.002 3.653 5.349 8.212 4.8795 0.04342 0.07308

7 0.60 2.377 955.77 3.71E+06 8.636 3.593 5.043 9.376 5.4755 0.04873 0.08344

8 0.65 2.575 1063.98 4.02E+06 8.192 3.539 4.653 10.438 5.9288 0.05276 0.09288

9 0.70 2.773 1165.20 4.32E+06 7.735 3.490 4.246 11.431 6.2738 0.05583 0.10172

10 0.75 2.971 1264.38 4.63E+06 7.312 3.445 3.867 12.404 6.5595 0.05837 0.11038

11 0.80 3.169 1367.00 4.94E+06 6.948 3.404 3.544 13.410 6.8402 0.06087 0.11934

12 0.85 3.368 1478.06 5.25E+06 6.655 3.366 3.288 14.500 7.1653 0.06376 0.12903

13 0.90 3.566 1601.18 5.56E+06 6.430 3.331 3.099 15.708 7.5706 0.06737 0.13978

14 0.95 3.764 1737.53 5.87E+06 6.263 3.298 2.964 17.045 8.0681 0.07180 0.15168

15 1.00 3.962 1884.98 6.18E+06 6.132 3.268 2.864 18.492 8.6370 0.07686 0.16455

73




3 CF 10

3 CR RT RR RR/ RT/


1 0.30 1.189 159.32 1.83E+06 6.112 4.128 1.984 1.563 0.5074 0.00452 0.01391

2 0.35 1.387 261.88 2.14E+06 7.381 4.001 3.380 2.569 1.1764 0.01047 0.02286

3 0.40 1.585 391.85 2.44E+06 8.456 3.896 4.559 3.844 2.0728 0.01845 0.03421

4 0.45 1.783 529.98 2.75E+06 9.036 3.807 5.229 5.199 3.0088 0.02678 0.04627

5 0.50 1.981 663.80 3.05E+06 9.167 3.730 5.438 6.512 3.8627 0.03438 0.05795

6 0.55 2.179 786.53 3.36E+06 8.977 3.662 5.315 7.716 4.5687 0.04066 0.06867

7 0.60 2.377 896.10 3.66E+06 8.594 3.601 4.993 8.791 5.1071 0.04545 0.07823

8 0.65 2.575 994.09 3.97E+06 8.124 3.547 4.577 9.752 5.4940 0.04889 0.08679

9 0.70 2.773 1084.74 4.27E+06 7.643 3.498 4.145 10.641 5.7714 0.05136 0.09470

10 0.75 2.971 1173.91 4.58E+06 7.205 3.453 3.752 11.516 5.9972 0.05337 0.10249

11 0.80 3.169 1268.03 4.88E+06 6.841 3.412 3.429 12.439 6.2351 0.05549 0.11071

12 0.85 3.368 1373.12 5.19E+06 6.562 3.374 3.188 13.470 6.5443 0.05824 0.11988

13 0.90 3.566 1493.75 5.49E+06 6.367 3.339 3.028 14.654 6.9699 0.06203 0.13041

14 0.95 3.764 1631.98 5.80E+06 6.243 3.306 2.938 16.010 7.5327 0.06704 0.14248

15 1.00 3.962 1786.38 6.10E+06 6.168 3.275 2.893 17.524 8.2189 0.07315 0.15596


3 CF 10

3 CR RT RR RR/ RT/


1 0.30 1.189 124.33 1.83E+06 5.644 4.128 1.517 1.220 0.3277 0.00467 0.01737

2 0.35 1.387 184.24 2.14E+06 6.145 4.001 2.144 1.807 0.6306 0.00898 0.02574

3 0.40 1.585 259.33 2.44E+06 6.622 3.896 2.726 2.544 1.0473 0.01491 0.03623

4 0.45 1.783 338.28 2.75E+06 6.826 3.807 3.019 3.319 1.4677 0.02090 0.04726

5 0.50 1.981 415.82 3.05E+06 6.796 3.730 3.066 4.079 1.8406 0.02621 0.05809

6 0.55 2.179 490.59 3.36E+06 6.626 3.662 2.965 4.813 2.1533 0.03066 0.06854

7 0.60 2.377 563.47 3.66E+06 6.395 3.601 2.794 5.528 2.4149 0.03439 0.07872

8 0.65 2.575 636.24 3.97E+06 6.153 3.547 2.606 6.241 2.6434 0.03764 0.08888

9 0.70 2.773 710.67 4.27E+06 5.926 3.498 2.428 6.972 2.8566 0.04068 0.09928

10 0.75 2.971 787.99 4.58E+06 5.724 3.453 2.271 7.730 3.0667 0.04367 0.11009

11 0.80 3.169 868.73 4.88E+06 5.546 3.412 2.134 8.522 3.2795 0.04670 0.12136

12 0.85 3.368 952.97 5.19E+06 5.389 3.374 2.015 9.349 3.4960 0.04979 0.13313

13 0.90 3.566 1041.00 5.49E+06 5.251 3.339 1.912 10.212 3.7193 0.05297 0.14543

14 0.95 3.764 1134.32 5.80E+06 5.135 3.306 1.830 11.128 3.9645 0.05646 0.15847

15 1.00 3.962 1237.09 6.10E+06 5.055 3.275 1.780 12.136 4.2726 0.06085 0.17283

74




3 CF 10

3 CR RT RR RR/ RT/


1 0.30 1.189 288.77 1.72E+06 6.596 4.182 2.414 2.833 1.0366 0.00417 0.01139

2 0.35 1.387 580.99 2.00E+06 9.750 4.053 5.697 5.699 3.3301 0.01339 0.02292

3 0.40 1.585 1022.18 2.29E+06 13.134 3.946 9.188 10.028 7.0147 0.02821 0.04033

4 0.45 1.783 1507.38 2.57E+06 15.303 3.855 11.448 14.787 11.0622 0.04449 0.05948

5 0.50 1.981 1964.14 2.86E+06 16.151 3.776 12.375 19.268 14.7631 0.05938 0.07750

6 0.55 2.179 2350.24 3.15E+06 15.972 3.707 12.265 23.056 17.7045 0.07121 0.09273

7 0.60 2.377 2650.37 3.43E+06 15.135 3.646 11.489 26.000 19.7372 0.07939 0.10458

8 0.65 2.575 2871.80 3.72E+06 13.974 3.590 10.383 28.172 20.9335 0.08420 0.11331

9 0.70 2.773 3039.08 4.01E+06 12.750 3.540 9.210 29.813 21.5351 0.08662 0.11991

10 0.75 2.971 3187.70 4.29E+06 11.650 3.495 8.155 31.271 21.8908 0.08805 0.12578

11 0.80 3.169 3356.79 4.58E+06 10.783 3.453 7.330 32.930 22.3851 0.09004 0.13245

12 0.85 3.368 3580.74 4.86E+06 10.189 3.414 6.774 35.127 23.3561 0.09394 0.14129

13 0.90 3.566 3879.91 5.15E+06 9.847 3.378 6.469 38.062 25.0041 0.10057 0.15309

14 0.95 3.764 4250.26 5.44E+06 9.682 3.345 6.337 41.695 27.2900 0.10976 0.16770

15 1.00 3.962 4652.03 5.72E+06 9.564 3.314 6.250 45.636 29.8242 0.11996 0.18356


3 CF 10

3 CR RT RR RR/ RT/


1 0.30 1.189 162.20 1.72E+06 6.324 4.182 2.142 1.591 0.5388 0.00543 0.01602

2 0.35 1.387 249.32 2.00E+06 7.142 4.053 3.089 2.446 1.0577 0.01065 0.02463

3 0.40 1.585 359.58 2.29E+06 7.886 3.946 3.940 3.527 1.7624 0.01775 0.03552

4 0.45 1.783 476.39 2.57E+06 8.255 3.855 4.400 4.673 2.4910 0.02508 0.04706

5 0.50 1.981 589.61 2.86E+06 8.276 3.776 4.500 5.784 3.1448 0.03167 0.05824

6 0.55 2.179 694.39 3.15E+06 8.055 3.707 4.348 6.812 3.6769 0.03703 0.06859

7 0.60 2.377 790.03 3.43E+06 7.701 3.646 4.055 7.750 4.0812 0.04110 0.07804

8 0.65 2.575 878.85 3.72E+06 7.299 3.590 3.709 8.621 4.3807 0.04411 0.08682

9 0.70 2.773 965.01 4.01E+06 6.911 3.540 3.371 9.467 4.6170 0.04649 0.09533

10 0.75 2.971 1053.40 4.29E+06 6.572 3.495 3.077 10.334 4.8384 0.04872 0.10406

11 0.80 3.169 1148.49 4.58E+06 6.297 3.453 2.844 11.267 5.0890 0.05125 0.11345

12 0.85 3.368 1253.16 4.86E+06 6.087 3.414 2.672 12.293 5.3976 0.05435 0.12379

13 0.90 3.566 1367.57 5.15E+06 5.925 3.378 2.546 13.416 5.7661 0.05806 0.13510

14 0.95 3.764 1488.04 5.44E+06 5.786 3.345 2.441 14.598 6.1587 0.06202 0.14700

15 1.00 3.962 1605.87 5.72E+06 5.635 3.314 2.322 15.754 6.4902 0.06536 0.15864

75




3 CF 10

3 CR RT RR RR/ RT/


1 0.30 1.189 526.79 1.76E+06 10.210 4.160 6.050 5.168 3.0622 0.00770 0.01300

2 0.35 1.387 784.55 2.06E+06 11.172 4.032 7.140 7.696 4.9187 0.01237 0.01936

3 0.40 1.585 1301.71 2.35E+06 14.191 3.926 10.266 12.770 9.2373 0.02324 0.03212

4 0.45 1.783 2325.13 2.64E+06 20.029 3.835 16.193 22.810 18.4417 0.04639 0.05738

5 0.50 1.981 4101.68 2.94E+06 28.619 3.757 24.862 40.237 34.9549 0.08793 0.10122

6 0.55 2.179 4958.50 3.23E+06 28.593 3.689 24.904 48.643 42.3678 0.10658 0.12236

7 0.60 2.377 5480.40 3.52E+06 26.555 3.628 22.927 53.763 46.4185 0.11677 0.13524

8 0.65 2.575 5753.48 3.82E+06 23.754 3.573 20.181 56.442 47.9527 0.12063 0.14198

9 0.70 2.773 5956.38 4.11E+06 21.204 3.523 17.681 58.432 48.7237 0.12257 0.14699

10 0.75 2.971 6161.16 4.40E+06 19.106 3.478 15.628 60.441 49.4395 0.12437 0.15204

11 0.80 3.169 6384.57 4.70E+06 17.401 3.436 13.965 62.633 50.2651 0.12644 0.15755

12 0.85 3.368 6639.24 4.99E+06 16.029 3.398 12.632 65.131 51.3252 0.12911 0.16384

13 0.90 3.566 6984.89 5.29E+06 15.042 3.362 11.680 68.522 53.2064 0.13384 0.17237

14 0.95 3.764 7579.59 5.58E+06 14.650 3.329 11.321 74.356 57.4598 0.14454 0.18704

15 1.00 3.962 8730.93 5.87E+06 15.230 3.298 11.932 85.650 67.1037 0.16880 0.21546


3 CF 10

3 CR RT RR RR/ RT/


1 0.30 1.189 582.59 1.83E+06 10.731 4.128 6.603 5.715 3.5167 0.00700 0.01138

2 0.35 1.387 876.05 2.14E+06 11.855 4.001 7.854 8.594 5.6935 0.01134 0.01711

3 0.40 1.585 1414.06 2.44E+06 14.651 3.896 10.755 13.872 10.1829 0.02027 0.02762

4 0.45 1.783 2768.48 2.75E+06 22.664 3.807 18.857 27.159 22.5969 0.04499 0.05407

5 0.50 1.981 4399.76 3.05E+06 29.174 3.730 25.445 43.162 37.6440 0.07495 0.08594

6 0.55 2.179 4615.35 3.36E+06 25.292 3.662 21.631 45.277 38.7219 0.07710 0.09015

7 0.60 2.377 4886.75 3.66E+06 22.502 3.601 18.901 47.939 40.2670 0.08017 0.09545

8 0.65 2.575 5168.22 3.97E+06 20.278 3.547 16.731 50.700 41.8319 0.08329 0.10095

9 0.70 2.773 5354.93 4.27E+06 18.116 3.498 14.618 52.532 42.3892 0.08440 0.10459

10 0.75 2.971 5585.53 4.58E+06 16.461 3.453 13.008 54.794 43.2999 0.08621 0.10910

11 0.80 3.169 5775.84 4.88E+06 14.961 3.412 11.549 56.661 43.7391 0.08709 0.11282

12 0.85 3.368 5921.20 5.19E+06 13.586 3.374 10.212 58.087 43.6618 0.08693 0.11566

13 0.90 3.566 6028.67 5.49E+06 12.338 3.339 9.000 59.141 43.1380 0.08589 0.11775

14 0.95 3.764 6087.28 5.80E+06 11.181 3.306 7.875 59.716 42.0608 0.08375 0.11890

15 1.00 3.962 6086.05 6.10E+06 10.089 3.275 6.814 59.704 40.3231 0.08029 0.11888

76




3 CF 10

3 CR RT RR RR/ RT/


1 0.30 1.189 179.60 1.86E+06 6.668 4.113 2.555 1.762 0.6751 0.00537 0.01403

2 0.35 1.387 295.48 2.17E+06 8.060 3.987 4.073 2.899 1.4647 0.01166 0.02308

3 0.40 1.585 452.38 2.48E+06 9.448 3.883 5.565 4.438 2.6141 0.02081 0.03533

4 0.45 1.783 620.01 2.79E+06 10.231 3.794 6.437 6.082 3.8269 0.03047 0.04842

5 0.50 1.981 779.48 3.10E+06 10.419 3.717 6.702 7.647 4.9187 0.03916 0.06088

6 0.55 2.179 921.31 3.41E+06 10.177 3.649 6.528 9.038 5.7972 0.04615 0.07196

7 0.60 2.377 1043.44 3.73E+06 9.685 3.589 6.096 10.236 6.4427 0.05129 0.08149

8 0.65 2.575 1149.19 4.04E+06 9.089 3.535 5.554 11.274 6.8885 0.05484 0.08975

9 0.70 2.773 1245.30 4.35E+06 8.492 3.486 5.006 12.216 7.2010 0.05733 0.09726

10 0.75 2.971 1339.88 4.66E+06 7.960 3.442 4.518 13.144 7.4604 0.05940 0.10465

11 0.80 3.169 1440.44 4.97E+06 7.521 3.401 4.120 14.131 7.7408 0.06163 0.11250

12 0.85 3.368 1551.87 5.28E+06 7.177 3.363 3.814 15.224 8.0905 0.06441 0.12120

13 0.90 3.566 1674.45 5.59E+06 6.908 3.328 3.580 16.426 8.5125 0.06777 0.13078

14 0.95 3.764 1801.82 5.90E+06 6.671 3.295 3.376 17.676 8.9449 0.07121 0.14072

15 1.00 3.962 1919.01 6.21E+06 6.412 3.265 3.148 18.826 9.2410 0.07357 0.14988


3 CF 10

3 CR RT RR RR/ RT/


1 0.30 1.189 127.12 1.95E+06 5.625 4.077 1.548 1.247 0.3433 0.00437 0.01589

2 0.35 1.387 195.37 2.27E+06 6.352 3.953 2.399 1.917 0.7239 0.00922 0.02442

3 0.40 1.585 281.97 2.59E+06 7.019 3.850 3.169 2.766 1.2490 0.01591 0.03524

4 0.45 1.783 374.57 2.92E+06 7.367 3.762 3.605 3.675 1.7982 0.02291 0.04681

5 0.50 1.981 465.51 3.24E+06 7.416 3.686 3.730 4.567 2.2969 0.02926 0.05817

6 0.55 2.179 551.04 3.57E+06 7.255 3.619 3.636 5.406 2.7090 0.03451 0.06886

7 0.60 2.377 630.43 3.89E+06 6.974 3.560 3.415 6.185 3.0279 0.03857 0.07878

8 0.65 2.575 705.24 4.22E+06 6.648 3.506 3.141 6.918 3.2692 0.04165 0.08813

9 0.70 2.773 778.41 4.54E+06 6.327 3.458 2.869 7.636 3.4623 0.04411 0.09728

10 0.75 2.971 853.50 4.86E+06 6.043 3.414 2.629 8.373 3.6425 0.04640 0.10666

11 0.80 3.169 933.86 5.19E+06 5.811 3.374 2.438 9.161 3.8428 0.04895 0.11670

12 0.85 3.368 1021.76 5.51E+06 5.632 3.336 2.296 10.024 4.0861 0.05205 0.12769

13 0.90 3.566 1117.66 5.84E+06 5.495 3.302 2.194 10.964 4.3769 0.05576 0.13967

14 0.95 3.764 1219.31 6.16E+06 5.381 3.269 2.111 11.961 4.6936 0.05979 0.15238

15 1.00 3.962 1320.94 6.48E+06 5.261 3.239 2.022 12.958 4.9799 0.06344 0.16508

77




3 CF 10

3 CR RT RR RR/ RT/


1 0.30 1.189 439.06 1.92E+06 9.670 4.087 5.583 4.307 2.4869 0.00792 0.01372

2 0.35 1.387 635.38 2.24E+06 10.282 3.962 6.320 6.233 3.8311 0.01220 0.01985

3 0.40 1.585 1042.72 2.56E+06 12.919 3.859 9.060 10.229 7.1738 0.02285 0.03258

4 0.45 1.783 1861.08 2.88E+06 18.218 3.771 14.448 18.257 14.4786 0.04611 0.05815

5 0.50 1.981 2946.70 3.20E+06 23.365 3.694 19.671 28.907 24.3365 0.07751 0.09207

6 0.55 2.179 3458.98 3.52E+06 22.667 3.627 19.039 33.933 28.5023 0.09078 0.10807

7 0.60 2.377 3798.86 3.84E+06 20.918 3.568 17.350 37.267 30.9104 0.09845 0.11869

8 0.65 2.575 4017.69 4.17E+06 18.850 3.514 15.336 39.414 32.0654 0.10213 0.12553

9 0.70 2.773 4166.81 4.49E+06 16.857 3.466 13.391 40.876 32.4719 0.10342 0.13019

10 0.75 2.971 4297.58 4.81E+06 15.145 3.422 11.723 42.159 32.6343 0.10394 0.13427

11 0.80 3.169 4482.23 5.13E+06 13.883 3.381 10.502 43.971 33.2620 0.10594 0.14004

12 0.85 3.368 4685.22 5.45E+06 12.855 3.344 9.511 45.962 34.0070 0.10831 0.14639

13 0.90 3.566 4933.33 5.77E+06 12.073 3.309 8.764 48.396 35.1324 0.11189 0.15414

14 0.95 3.764 5233.91 6.09E+06 11.496 3.276 8.220 51.345 36.7111 0.11692 0.16353

15 1.00 3.962 5594.32 6.41E+06 11.090 3.246 7.843 54.880 38.8158 0.12363 0.17479


3 CF 10

3 CR RT RR RR/ RT/


1 0.30 1.189 154.66 1.85E+06 6.392 4.117 2.275 1.517 0.5399 0.00559 0.01571

2 0.35 1.387 240.96 2.16E+06 7.316 3.991 3.325 2.364 1.0743 0.01112 0.02447

3 0.40 1.585 349.29 2.47E+06 8.120 3.887 4.234 3.426 1.7865 0.01850 0.03547

4 0.45 1.783 464.26 2.78E+06 8.528 3.798 4.730 4.554 2.5262 0.02615 0.04715

5 0.50 1.981 576.37 3.09E+06 8.576 3.721 4.855 5.654 3.2011 0.03314 0.05854

6 0.55 2.179 680.94 3.40E+06 8.373 3.653 4.720 6.680 3.7658 0.03899 0.06916

7 0.60 2.377 777.12 3.71E+06 8.029 3.593 4.437 7.624 4.2124 0.04361 0.07893

8 0.65 2.575 866.79 4.02E+06 7.631 3.539 4.092 8.503 4.5602 0.04721 0.08803

9 0.70 2.773 953.58 4.32E+06 7.239 3.490 3.749 9.355 4.8449 0.05016 0.09685

10 0.75 2.971 1041.79 4.63E+06 6.889 3.445 3.444 10.220 5.1093 0.05290 0.10581

11 0.80 3.169 1135.36 4.94E+06 6.599 3.404 3.195 11.138 5.3923 0.05583 0.11531

12 0.85 3.368 1236.84 5.25E+06 6.368 3.366 3.002 12.133 5.7193 0.05921 0.12562

13 0.90 3.566 1346.33 5.56E+06 6.183 3.331 2.852 13.208 6.0917 0.06307 0.13674

14 0.95 3.764 1460.46 5.87E+06 6.019 3.298 2.721 14.327 6.4766 0.06705 0.14833

15 1.00 3.962 1571.35 6.18E+06 5.845 3.268 2.577 15.415 6.7969 0.07037 0.15959

78




3 CF 10

3 CR RT RR RR/ RT/


1 0.30 1.189 173.19 1.84E+06 5.496 4.122 1.374 1.699 0.4248 0.00274 0.01097

2 0.35 1.387 330.07 2.15E+06 7.695 3.995 3.700 3.238 1.5568 0.01005 0.02091

3 0.40 1.585 556.85 2.46E+06 9.939 3.890 6.049 5.463 3.3245 0.02147 0.03528

4 0.45 1.783 801.48 2.77E+06 11.303 3.801 7.502 7.863 5.2183 0.03370 0.05078

5 0.50 1.981 1030.86 3.07E+06 11.776 3.724 8.052 10.113 6.9146 0.04466 0.06531

6 0.55 2.179 1227.68 3.38E+06 11.590 3.656 7.934 12.044 8.2442 0.05324 0.07778

7 0.60 2.377 1387.25 3.69E+06 11.005 3.596 7.409 13.609 9.1618 0.05917 0.08789

8 0.65 2.575 1514.30 4.00E+06 10.236 3.542 6.694 14.855 9.7147 0.06274 0.09594

9 0.70 2.773 1619.86 4.30E+06 9.441 3.493 5.948 15.891 10.0115 0.06466 0.10263

10 0.75 2.971 1718.07 4.61E+06 8.723 3.448 5.274 16.854 10.1915 0.06582 0.10885

11 0.80 3.169 1822.99 4.92E+06 8.135 3.407 4.727 17.884 10.3931 0.06712 0.11550

12 0.85 3.368 1945.47 5.23E+06 7.690 3.369 4.321 19.085 10.7231 0.06925 0.12326

13 0.90 3.566 2089.94 5.53E+06 7.368 3.334 4.034 20.502 11.2255 0.07250 0.13241

14 0.95 3.764 2251.27 5.84E+06 7.124 3.301 3.822 22.085 11.8504 0.07653 0.14263

15 1.00 3.962 2411.60 6.15E+06 6.887 3.271 3.616 23.658 12.4229 0.08023 0.15279


3 CF 10

3 CR RT RR RR/ RT/


1 0.30 1.189 198.71 1.85E+06 6.593 4.117 2.475 1.949 0.7319 0.00525 0.01399

2 0.35 1.387 338.90 2.16E+06 8.261 3.991 4.270 3.325 1.7183 0.01233 0.02386

3 0.40 1.585 533.02 2.47E+06 9.948 3.887 6.061 5.229 3.1860 0.02286 0.03753

4 0.45 1.783 741.49 2.78E+06 10.934 3.798 7.136 7.274 4.7476 0.03407 0.05220

5 0.50 1.981 939.03 3.09E+06 11.216 3.721 7.495 9.212 6.1561 0.04418 0.06611

6 0.55 2.179 1112.35 3.40E+06 10.980 3.653 7.327 10.912 7.2818 0.05226 0.07831

7 0.60 2.377 1257.69 3.71E+06 10.432 3.593 6.839 12.338 8.0888 0.05805 0.08855

8 0.65 2.575 1378.54 4.02E+06 9.743 3.539 6.204 13.523 8.6116 0.06180 0.09705

9 0.70 2.773 1483.14 4.32E+06 9.038 3.490 5.548 14.550 8.9319 0.06410 0.10442

10 0.75 2.971 1582.19 4.63E+06 8.399 3.445 4.954 15.521 9.1549 0.06570 0.11139

11 0.80 3.169 1686.39 4.94E+06 7.868 3.404 4.464 16.544 9.3862 0.06736 0.11873

12 0.85 3.368 1804.13 5.25E+06 7.456 3.366 4.090 17.698 9.7085 0.06967 0.12702

13 0.90 3.566 1939.03 5.56E+06 7.148 3.331 3.817 19.022 10.1577 0.07290 0.13651

14 0.95 3.764 2087.61 5.87E+06 6.907 3.298 3.609 20.479 10.7001 0.07679 0.14697

15 1.00 3.962 2236.90 6.18E+06 6.679 3.268 3.412 21.944 11.2086 0.08044 0.15748

79

Appendix 6: SKLAD Series Experiment Results

Table 37: SKLAD Series hull parameters

Model L/B B/T CB L/∇1/3

Cs L S

1 6.00 4.00 0.35 7.438 8.035 4.557 3.016

2 4.00 4.00 0.35 5.676 7.019 3.478 2.635

3 8.00 4.00 0.35 9.010 8.844 5.520 3.320

4 6.00 3.00 0.35 6.757 7.288 4.140 2.736

5 6.00 5.00 0.35 8.012 8.821 4.909 3.311

6 4.00 3.00 0.35 5.157 6.366 3.160 2.390

7 4.00 5.00 0.35 6.114 7.706 3.746 2.893

8 8.00 3.00 0.35 8.186 8.021 5.016 3.011

9 8.00 5.00 0.35 9.706 9.706 5.947 3.644

10 6.00 4.00 0.45 6.840 7.260 4.191 2.725

11 4.00 4.00 0.45 5.220 6.343 3.198 2.381

12 8.00 4.00 0.45 8.286 7.991 5.077 3.000

13 6.00 3.00 0.45 6.214 6.580 3.807 2.470

14 6.00 5.00 0.45 7.368 7.983 4.514 2.997

15 4.00 3.00 0.45 4.743 5.748 2.906 2.158

16 4.00 5.00 0.45 5.623 6.974 3.445 2.618

17 8.00 3.00 0.45 7.528 7.243 4.612 2.719

18 8.00 5.00 0.45 8.926 8.787 5.469 3.299

19 6.00 4.00 0.55 6.397 6.784 3.919 2.547

20 4.00 4.00 0.55 4.882 5.920 2.991 2.222

21 8.00 4.00 0.55 7.750 7.459 4.748 2.800

22 6.00 3.00 0.55 5.812 6.163 3.561 2.314

23 6.00 5.00 0.55 6.891 7.432 4.222 2.790

24 4.00 3.00 0.55 4.436 5.384 2.718 2.021

25 4.00 5.00 0.55 5.259 6.493 3.222 2.437

26 8.00 3.00 0.55 7.041 6.783 4.314 2.546

27 8.00 5.00 0.55 8.348 8.180 5.115 3.071

80

Table 38: SKLAD Series Experiment Results for Fn=1.00


Number Fn V Rn 103CF 10

3CR 10

3CT

RT RF RR RT/ RR/

m/s N N N

1 0.37 2.45 9.40E+06 3.032 3.539 6.571 59.562 27.487 32.075 0.02640 0.01422

2 0.42 2.45 7.18E+06 3.181 10.183 13.364 105.824 25.186 80.637 0.04690 0.03574

3 0.33 2.45 1.14E+07 2.933 0.872 3.805 37.969 29.266 8.702 0.01683 0.00386

4 0.38 2.45 8.54E+06 3.084 6.460 9.544 78.468 25.355 53.113 0.03478 0.02354

5 0.35 2.45 1.01E+07 2.993 2.435 5.428 54.017 29.788 24.230 0.02394 0.01074

6 0.44 2.45 6.52E+06 3.236 14.751 17.987 129.179 23.240 105.939 0.05725 0.04695

7 0.40 2.45 7.73E+06 3.139 7.175 10.314 89.668 27.288 62.380 0.03974 0.02765

8 0.35 2.45 1.03E+07 2.982 2.553 5.535 50.084 26.985 23.099 0.02220 0.01024

9 0.32 2.45 1.23E+07 2.896 0.884 3.780 41.391 31.712 9.679 0.01834 0.00429

10 0.38 2.45 8.65E+06 3.077 6.207 9.285 76.045 25.203 50.842 0.03370 0.02253

11 0.44 2.45 6.60E+06 3.229 12.415 15.644 111.946 23.106 88.841 0.04961 0.03937

12 0.35 2.45 1.05E+07 2.976 3.930 6.906 62.257 26.828 35.429 0.02759 0.01570

13 0.40 2.45 7.86E+06 3.130 8.448 11.578 85.943 23.233 62.710 0.03809 0.02779

14 0.37 2.45 9.32E+06 3.037 5.507 8.544 76.950 27.354 49.596 0.03410 0.02198

15 0.46 2.45 6.00E+06 3.285 16.887 20.173 130.813 21.304 109.508 0.05798 0.04853

16 0.42 2.45 7.11E+06 3.186 9.598 12.784 100.580 25.067 75.513 0.04458 0.03347

17 0.36 2.45 9.52E+06 3.026 4.949 7.975 65.162 24.726 40.437 0.02888 0.01792

18 0.33 2.45 1.13E+07 2.938 3.535 6.473 64.170 29.124 35.046 0.02844 0.01553

19 0.40 2.45 8.09E+06 3.114 8.901 12.015 91.954 23.831 68.123 0.04075 0.03019

20 0.45 2.45 6.17E+06 3.268 16.969 20.237 135.155 21.827 113.327 0.05990 0.05023

21 0.36 2.45 9.80E+06 3.011 5.907 8.917 75.039 25.334 49.705 0.03326 0.02203

22 0.41 2.45 7.35E+06 3.167 11.421 14.588 101.427 22.021 79.406 0.04495 0.03519

23 0.38 2.45 8.71E+06 3.073 7.748 10.821 90.731 25.767 64.964 0.04021 0.02879

24 0.47 2.45 5.61E+06 3.326 22.365 25.691 156.045 20.200 135.845 0.06916 0.06021

25 0.44 2.45 6.65E+06 3.225 13.495 16.720 122.473 23.620 98.853 0.05428 0.04381

26 0.38 2.45 8.90E+06 3.062 7.033 10.095 77.248 23.428 53.821 0.03424 0.02385

27 0.35 2.45 1.06E+07 2.972 4.255 7.227 66.697 27.427 39.270 0.02956 0.01740


3CR 10

3CT

RT RF RR RT/ RR/

m/s N N N

1 0.46 3.06 1.18E+07 2.917 4.719 7.636 108.157 41.322 66.835 0.04794 0.02962

2 0.52 3.06 8.97E+06 3.057 12.305 15.362 190.073 37.829 152.244 0.08424 0.06748

3 0.42 3.06 1.42E+07 2.824 1.713 4.537 70.725 44.025 26.700 0.03135 0.01183

4 0.48 3.06 1.07E+07 2.966 8.332 11.298 145.143 38.105 107.039 0.06433 0.04744

5 0.44 3.06 1.27E+07 2.881 3.399 6.279 97.639 44.792 52.847 0.04327 0.02342

6 0.55 3.06 8.15E+06 3.110 17.612 20.721 232.527 34.894 197.633 0.10306 0.08759

7 0.51 3.06 9.66E+06 3.018 9.359 12.377 168.127 40.995 127.132 0.07451 0.05635

8 0.44 3.06 1.29E+07 2.870 3.987 6.857 96.950 40.581 56.369 0.04297 0.02498

9 0.40 3.06 1.53E+07 2.789 1.553 4.342 74.281 47.715 26.565 0.03292 0.01177

10 0.48 3.06 1.08E+07 2.960 6.381 9.341 119.544 37.878 81.665 0.05298 0.03619

11 0.55 3.06 8.25E+06 3.103 13.948 17.050 190.641 34.693 155.947 0.08449 0.06912

12 0.43 3.06 1.31E+07 2.864 3.505 6.369 89.713 40.346 49.367 0.03976 0.02188

13 0.50 3.06 9.82E+06 3.009 9.878 12.888 149.483 34.906 114.576 0.06625 0.05078

14 0.46 3.06 1.16E+07 2.922 5.280 8.202 115.415 41.121 74.294 0.05115 0.03293

15 0.57 3.06 7.50E+06 3.156 20.197 23.353 236.621 31.978 204.643 0.10487 0.09070

16 0.53 3.06 8.89E+06 3.062 10.751 13.813 169.811 37.648 132.163 0.07526 0.05857

17 0.46 3.06 1.19E+07 2.911 5.258 8.170 104.310 37.172 67.138 0.04623 0.02976

18 0.42 3.06 1.41E+07 2.828 2.865 5.694 88.188 43.810 44.378 0.03909 0.01967

19 0.49 3.06 1.01E+07 2.994 9.018 12.012 143.646 35.807 107.838 0.06366 0.04779

20 0.57 3.06 7.72E+06 3.140 18.856 21.996 229.538 32.766 196.772 0.10173 0.08721

21 0.45 3.06 1.22E+07 2.897 5.349 8.246 108.425 38.091 70.334 0.04805 0.03117

22 0.52 3.06 9.19E+06 3.045 13.754 16.799 182.502 33.078 149.424 0.08089 0.06623

23 0.48 3.06 1.09E+07 2.956 7.116 10.072 131.949 38.726 93.222 0.05848 0.04132

24 0.59 3.06 7.01E+06 3.194 27.744 30.938 293.621 30.313 263.308 0.13013 0.11670

25 0.55 3.06 8.31E+06 3.099 14.125 17.224 197.138 35.467 161.671 0.08737 0.07165

26 0.47 3.06 1.11E+07 2.945 7.387 10.332 123.542 35.213 88.328 0.05475 0.03915

27 0.43 3.06 1.32E+07 2.861 3.506 6.367 91.804 41.248 50.556 0.04069 0.02241

81




3CR 10

3CT

RT RF RR RT/ RR/

m/s N N N

1 0.55 3.68 1.41E+07 2.828 4.699 7.527 153.517 57.688 95.829 0.06804 0.04247

2 0.63 3.68 1.08E+07 2.962 10.124 13.086 233.151 52.773 180.379 0.10333 0.07994

3 0.50 3.68 1.71E+07 2.739 2.719 5.459 122.539 61.491 61.048 0.05431 0.02706

4 0.58 3.68 1.28E+07 2.875 7.365 10.240 189.429 53.183 136.246 0.08396 0.06038

5 0.53 3.68 1.52E+07 2.793 3.306 6.099 136.571 62.544 74.027 0.06053 0.03281

6 0.66 3.68 9.78E+06 3.012 13.577 16.588 268.050 48.665 219.385 0.11880 0.09723

7 0.61 3.68 1.16E+07 2.924 8.294 11.219 219.439 57.201 162.237 0.09726 0.07190

8 0.52 3.68 1.55E+07 2.783 3.879 6.662 135.645 56.668 78.977 0.06012 0.03500

9 0.48 3.68 1.84E+07 2.706 2.409 5.115 126.014 66.659 59.355 0.05585 0.02631

10 0.57 3.68 1.30E+07 2.869 5.233 8.102 149.304 52.868 96.435 0.06617 0.04274

11 0.66 3.68 9.90E+06 3.005 10.147 13.153 211.765 48.387 163.378 0.09385 0.07241

12 0.52 3.68 1.57E+07 2.778 3.141 5.919 120.058 56.341 63.717 0.05321 0.02824

13 0.60 3.68 1.18E+07 2.916 7.783 10.699 178.698 48.708 129.990 0.07920 0.05761

14 0.55 3.68 1.40E+07 2.833 4.431 7.264 147.194 57.406 89.788 0.06524 0.03979

15 0.69 3.68 8.99E+06 3.056 14.304 17.360 253.284 44.588 208.696 0.11226 0.09249

16 0.63 3.68 1.07E+07 2.967 8.513 11.479 203.212 52.519 150.693 0.09006 0.06679

17 0.55 3.68 1.43E+07 2.823 4.362 7.185 132.096 51.896 80.200 0.05855 0.03554

18 0.50 3.68 1.69E+07 2.743 2.381 5.125 114.300 61.190 53.110 0.05066 0.02354

19 0.59 3.68 1.21E+07 2.902 6.936 9.838 169.414 49.969 119.445 0.07508 0.05294

20 0.68 3.68 9.26E+06 3.041 12.992 16.033 240.924 45.690 195.233 0.10678 0.08653

21 0.54 3.68 1.47E+07 2.809 4.492 7.301 138.229 53.183 85.046 0.06126 0.03769

22 0.62 3.68 1.10E+07 2.950 10.495 13.445 210.337 46.148 164.189 0.09322 0.07277

23 0.57 3.68 1.31E+07 2.865 5.984 8.849 166.936 54.053 112.884 0.07399 0.05003

24 0.71 3.68 8.41E+06 3.092 19.443 22.535 307.970 42.259 265.712 0.13649 0.11776

25 0.65 3.68 9.97E+06 3.001 10.430 13.431 221.361 49.467 171.894 0.09811 0.07618

26 0.57 3.68 1.34E+07 2.855 6.292 9.147 157.491 49.153 108.338 0.06980 0.04802

27 0.52 3.68 1.58E+07 2.774 2.873 5.647 117.262 57.602 59.660 0.05197 0.02644


3CR 10

3CT

RT RF RR RT/ RR/

m/s N N N

1 0.64 4.29 1.65E+07 2.756 3.489 6.245 173.363 76.517 96.846 0.07683 0.04292

2 0.73 4.29 1.26E+07 2.885 7.815 10.699 259.463 69.956 189.508 0.11499 0.08399

3 0.58 4.29 1.99E+07 2.670 1.527 4.197 128.254 81.595 46.658 0.05684 0.02068

4 0.67 4.29 1.49E+07 2.801 5.670 8.471 213.306 70.527 142.779 0.09454 0.06328

5 0.62 4.29 1.77E+07 2.723 2.752 5.475 166.845 82.972 83.873 0.07395 0.03717

6 0.77 4.29 1.14E+07 2.932 10.490 13.423 295.221 64.497 230.725 0.13084 0.10226

7 0.71 4.29 1.35E+07 2.849 6.442 9.291 247.355 75.839 171.516 0.10963 0.07602

8 0.61 4.29 1.81E+07 2.713 2.819 5.531 153.289 75.179 78.110 0.06794 0.03462

9 0.56 4.29 2.15E+07 2.638 1.911 4.549 152.556 88.466 64.090 0.06761 0.02840

10 0.67 4.29 1.51E+07 2.795 3.965 6.760 169.565 70.112 99.454 0.07515 0.04408

11 0.77 4.29 1.15E+07 2.926 7.471 10.397 227.845 64.130 163.715 0.10098 0.07256

12 0.61 4.29 1.83E+07 2.707 2.506 5.214 143.938 74.748 69.190 0.06379 0.03067

13 0.70 4.29 1.37E+07 2.841 5.805 8.645 196.538 64.580 131.958 0.08711 0.05848

14 0.64 4.29 1.63E+07 2.761 3.288 6.049 166.831 76.142 90.689 0.07394 0.04019

15 0.80 4.29 1.05E+07 2.975 10.292 13.267 263.462 59.081 204.380 0.11677 0.09058

16 0.74 4.29 1.24E+07 2.889 6.250 9.139 220.214 69.618 150.596 0.09760 0.06674

17 0.64 4.29 1.67E+07 2.751 3.439 6.190 154.888 68.837 86.051 0.06865 0.03814

18 0.59 4.29 1.97E+07 2.674 2.014 4.688 142.329 81.194 61.135 0.06308 0.02710

19 0.69 4.29 1.42E+07 2.827 5.265 8.092 189.669 66.257 123.412 0.08406 0.05470

20 0.79 4.29 1.08E+07 2.960 9.876 12.836 262.537 60.546 201.990 0.11636 0.08952

21 0.63 4.29 1.71E+07 2.738 3.533 6.270 161.591 70.548 91.042 0.07162 0.04035

22 0.73 4.29 1.29E+07 2.873 7.782 10.655 226.871 61.177 165.694 0.10055 0.07344

23 0.67 4.29 1.52E+07 2.792 4.132 6.924 177.777 71.684 106.093 0.07879 0.04702

24 0.83 4.29 9.81E+06 3.010 14.320 17.330 322.360 55.986 266.374 0.14287 0.11806

25 0.76 4.29 1.16E+07 2.923 7.801 10.724 240.573 65.563 175.010 0.10662 0.07757

26 0.66 4.29 1.56E+07 2.782 4.486 7.268 170.318 65.188 105.130 0.07549 0.04659

27 0.61 4.29 1.85E+07 2.704 2.223 4.927 139.256 76.422 62.833 0.06172 0.02785

82




3CR 10

3CT

RT RF RR RT/ RR/

m/s N N N

1 0.64 4.29 1.65E+07 2.756 2.986 5.743 159.423 76.517 82.906 0.07066 0.03674

2 0.73 4.29 1.26E+07 2.885 6.635 9.519 230.845 69.956 160.890 0.10231 0.07131

3 0.58 4.29 1.99E+07 2.670 1.659 4.329 132.291 81.595 50.695 0.05863 0.02247

4 0.67 4.29 1.49E+07 2.801 4.440 7.241 182.321 70.527 111.795 0.08081 0.04955

5 0.62 4.29 1.77E+07 2.723 2.208 4.931 150.267 82.972 67.295 0.06660 0.02983

6 0.77 4.29 1.14E+07 2.932 8.583 11.516 253.281 64.497 188.784 0.11226 0.08367

7 0.71 4.29 1.35E+07 2.849 5.408 8.257 219.824 75.839 143.985 0.09743 0.06381

8 0.61 4.29 1.81E+07 2.713 2.261 4.974 137.827 75.179 62.648 0.06109 0.02777

9 0.56 4.29 2.15E+07 2.638 1.412 4.050 135.811 88.466 47.345 0.06019 0.02098

10 0.67 4.29 1.51E+07 2.795 3.048 5.843 146.559 70.112 76.447 0.06496 0.03388

11 0.77 4.29 1.15E+07 2.926 5.846 8.772 192.234 64.130 128.104 0.08520 0.05678

12 0.61 4.29 1.83E+07 2.707 2.013 4.721 130.338 74.748 55.590 0.05777 0.02464

13 0.70 4.29 1.37E+07 2.841 4.375 7.216 164.038 64.580 99.458 0.07270 0.04408

14 0.64 4.29 1.63E+07 2.761 2.505 5.266 145.236 76.142 69.094 0.06437 0.03062

15 0.80 4.29 1.05E+07 2.975 8.095 11.070 219.840 59.081 160.758 0.09743 0.07125

16 0.74 4.29 1.24E+07 2.889 4.649 7.539 181.641 69.618 112.023 0.08050 0.04965

17 0.64 4.29 1.67E+07 2.751 2.509 5.260 131.623 68.837 62.786 0.05834 0.02783

18 0.59 4.29 1.97E+07 2.674 1.533 4.208 127.737 81.194 46.543 0.05661 0.02063

19 0.69 4.29 1.42E+07 2.827 3.951 6.778 158.862 66.257 92.606 0.07041 0.04104

20 0.79 4.29 1.08E+07 2.960 7.310 10.270 210.056 60.546 149.509 0.09310 0.06626

21 0.63 4.29 1.71E+07 2.738 2.587 5.324 137.208 70.548 66.660 0.06081 0.02954

22 0.73 4.29 1.29E+07 2.873 6.122 8.996 191.542 61.177 130.365 0.08489 0.05778

23 0.67 4.29 1.52E+07 2.792 3.063 5.855 150.344 71.684 78.660 0.06663 0.03486

24 0.83 4.29 9.81E+06 3.010 11.102 14.112 262.501 55.986 206.514 0.11634 0.09153

25 0.76 4.29 1.16E+07 2.923 5.252 8.174 183.379 65.563 117.816 0.08127 0.05222

26 0.66 4.29 1.56E+07 2.782 3.516 6.298 147.586 65.188 82.397 0.06541 0.03652

27 0.61 4.29 1.85E+07 2.704 1.719 4.424 125.018 76.422 48.596 0.05541 0.02154


3CR 10

3CT

RT RF RR RT/ RR/

m/s N N N

1 0.83 5.52 2.12E+07 2.644 2.373 5.018 230.272 121.356 108.916 0.10206 0.04827

2 0.94 5.52 1.61E+07 2.765 5.707 8.472 339.631 110.845 228.786 0.15053 0.10140

3 0.75 5.52 2.56E+07 2.564 1.179 3.743 189.041 129.493 59.547 0.08378 0.02639

4 0.87 5.52 1.92E+07 2.686 3.771 6.458 268.799 111.818 156.981 0.11913 0.06957

5 0.79 5.52 2.28E+07 2.613 1.921 4.534 228.413 131.626 96.786 0.10123 0.04290

6 0.99 5.52 1.47E+07 2.810 7.669 10.479 381.006 102.160 278.846 0.16886 0.12359

7 0.91 5.52 1.74E+07 2.731 4.636 7.368 324.253 120.199 204.054 0.14371 0.09044

8 0.79 5.52 2.33E+07 2.604 1.906 4.509 206.571 119.273 87.298 0.09155 0.03869

9 0.72 5.52 2.76E+07 2.533 1.031 3.564 197.573 140.432 57.142 0.08757 0.02533

10 0.86 5.52 1.95E+07 2.681 2.475 5.156 213.807 111.165 102.642 0.09476 0.04549

11 0.98 5.52 1.48E+07 2.804 4.761 7.565 274.049 101.583 172.466 0.12146 0.07644

12 0.78 5.52 2.36E+07 2.599 1.705 4.303 196.389 118.594 77.795 0.08704 0.03448

13 0.90 5.52 1.77E+07 2.724 3.547 6.271 235.662 102.360 133.302 0.10445 0.05908

14 0.83 5.52 2.10E+07 2.649 2.212 4.860 221.586 120.757 100.829 0.09821 0.04469

15 1.03 5.52 1.35E+07 2.850 6.618 9.468 310.805 93.554 217.251 0.13775 0.09629

16 0.95 5.52 1.60E+07 2.769 3.860 6.629 264.053 110.307 153.746 0.11703 0.06814

17 0.82 5.52 2.14E+07 2.639 2.123 4.762 196.998 109.180 87.818 0.08731 0.03892

18 0.75 5.52 2.54E+07 2.568 1.287 3.855 193.438 128.853 64.586 0.08573 0.02862

19 0.89 5.52 1.82E+07 2.711 3.218 5.929 229.712 105.028 124.683 0.10181 0.05526

20 1.02 5.52 1.39E+07 2.836 6.056 8.892 300.638 95.884 204.754 0.13324 0.09075

21 0.81 5.52 2.20E+07 2.627 2.142 4.769 203.159 111.905 91.254 0.09004 0.04044

22 0.93 5.52 1.65E+07 2.754 4.804 7.559 266.051 96.943 169.107 0.11791 0.07495

23 0.86 5.52 1.96E+07 2.678 2.492 5.170 219.438 113.660 105.777 0.09726 0.04688

24 1.07 5.52 1.26E+07 2.882 8.814 11.697 359.669 88.631 271.038 0.15941 0.12012

25 0.98 5.52 1.50E+07 2.801 4.503 7.304 270.849 103.855 166.994 0.12004 0.07401

26 0.85 5.52 2.00E+07 2.668 2.622 5.291 204.963 103.369 101.594 0.09084 0.04503

27 0.78 5.52 2.37E+07 2.595 1.242 3.837 179.271 121.253 58.019 0.07945 0.02571

83




3CR 10

3CT

RT RF RR RT/ RR/

m/s N N N

1 0.92 6.13 2.35E+07 2.600 2.158 4.757 269.518 147.280 122.238 0.11945 0.05418

2 1.05 6.13 1.79E+07 2.717 5.427 8.145 403.078 134.472 268.606 0.17865 0.11905

3 0.83 6.13 2.85E+07 2.521 0.889 3.410 212.616 157.197 55.418 0.09423 0.02456

4 0.96 6.13 2.14E+07 2.640 3.381 6.022 309.432 135.687 173.745 0.13714 0.07700

5 0.88 6.13 2.53E+07 2.569 1.879 4.447 276.605 159.761 116.843 0.12259 0.05179

6 1.10 6.13 1.63E+07 2.761 7.290 10.050 451.119 123.918 327.201 0.19994 0.14502

7 1.01 6.13 1.93E+07 2.684 4.381 7.065 383.874 145.836 238.038 0.17013 0.10550

8 0.87 6.13 2.59E+07 2.560 1.723 4.283 242.221 144.772 97.449 0.10735 0.04319

9 0.80 6.13 3.07E+07 2.491 0.832 3.323 227.437 170.493 56.944 0.10080 0.02524

10 0.96 6.13 2.16E+07 2.635 1.921 4.557 233.256 134.897 98.359 0.10338 0.04359

11 1.09 6.13 1.65E+07 2.755 4.062 6.817 304.892 123.221 181.671 0.13513 0.08052

12 0.87 6.13 2.62E+07 2.555 1.494 4.049 228.110 143.950 84.161 0.10110 0.03730

13 1.00 6.13 1.96E+07 2.677 2.732 5.409 250.952 124.195 126.757 0.11122 0.05618

14 0.92 6.13 2.33E+07 2.604 1.709 4.313 242.741 146.551 96.190 0.10758 0.04263

15 1.15 6.13 1.50E+07 2.800 5.779 8.579 347.697 113.465 234.232 0.15410 0.10381

16 1.05 6.13 1.78E+07 2.721 3.118 5.840 287.164 133.817 153.347 0.12727 0.06796

17 0.91 6.13 2.38E+07 2.595 1.746 4.341 221.685 132.505 89.180 0.09825 0.03952

18 0.84 6.13 2.82E+07 2.525 1.231 3.755 232.662 156.417 76.245 0.10312 0.03379

19 0.99 6.13 2.02E+07 2.664 2.779 5.443 260.362 127.438 132.924 0.11539 0.05891

20 1.13 6.13 1.54E+07 2.786 5.420 8.206 342.525 116.296 226.229 0.15181 0.10027

21 0.90 6.13 2.45E+07 2.582 1.674 4.257 223.876 135.818 88.058 0.09922 0.03903

22 1.04 6.13 1.84E+07 2.707 4.201 6.907 300.161 117.612 182.550 0.13303 0.08091

23 0.95 6.13 2.18E+07 2.632 2.100 4.732 247.979 137.926 110.053 0.10991 0.04878

24 1.19 6.13 1.40E+07 2.831 8.094 10.926 414.766 107.484 307.283 0.18383 0.13619

25 1.09 6.13 1.66E+07 2.752 3.810 6.562 300.429 125.979 174.450 0.13315 0.07732

26 0.94 6.13 2.23E+07 2.623 2.269 4.892 233.966 125.442 108.524 0.10369 0.04810

27 0.87 6.13 2.64E+07 2.552 0.999 3.551 204.802 147.178 57.624 0.09077 0.02554


3CR 10

3CT

RT RF RR RT/ RR/

m/s N N N

1 0.92 6.13 2.35E+07 2.600 2.158 4.757 269.518 147.280 122.238 0.11945 0.05418

2 1.05 6.13 1.79E+07 2.717 5.427 8.145 403.078 134.472 268.606 0.17865 0.11905

3 0.83 6.13 2.85E+07 2.521 0.889 3.410 212.616 157.197 55.418 0.09423 0.02456

4 0.96 6.13 2.14E+07 2.640 3.381 6.022 309.432 135.687 173.745 0.13714 0.07700

5 0.88 6.13 2.53E+07 2.569 1.879 4.447 276.605 159.761 116.843 0.12259 0.05179

6 1.10 6.13 1.63E+07 2.761 7.290 10.050 451.119 123.918 327.201 0.19994 0.14502

7 1.01 6.13 1.93E+07 2.684 4.381 7.065 383.874 145.836 238.038 0.17013 0.10550

8 0.87 6.13 2.59E+07 2.560 1.723 4.283 242.221 144.772 97.449 0.10735 0.04319

9 0.80 6.13 3.07E+07 2.491 0.832 3.323 227.437 170.493 56.944 0.10080 0.02524

10 0.96 6.13 2.16E+07 2.635 1.921 4.557 233.256 134.897 98.359 0.10338 0.04359

11 1.09 6.13 1.65E+07 2.755 4.062 6.817 304.892 123.221 181.671 0.13513 0.08052

12 0.87 6.13 2.62E+07 2.555 1.494 4.049 228.110 143.950 84.161 0.10110 0.03730

13 1.00 6.13 1.96E+07 2.677 2.732 5.409 250.952 124.195 126.757 0.11122 0.05618

14 0.92 6.13 2.33E+07 2.604 1.709 4.313 242.741 146.551 96.190 0.10758 0.04263

15 1.15 6.13 1.50E+07 2.800 5.779 8.579 347.697 113.465 234.232 0.15410 0.10381

16 1.05 6.13 1.78E+07 2.721 3.118 5.840 287.164 133.817 153.347 0.12727 0.06796

17 0.91 6.13 2.38E+07 2.595 1.746 4.341 221.685 132.505 89.180 0.09825 0.03952

18 0.84 6.13 2.82E+07 2.525 1.231 3.755 232.662 156.417 76.245 0.10312 0.03379

19 0.99 6.13 2.02E+07 2.664 2.779 5.443 260.362 127.438 132.924 0.11539 0.05891

20 1.13 6.13 1.54E+07 2.786 5.420 8.206 342.525 116.296 226.229 0.15181 0.10027

21 0.90 6.13 2.45E+07 2.582 1.674 4.257 223.876 135.818 88.058 0.09922 0.03903

22 1.04 6.13 1.84E+07 2.707 4.201 6.907 300.161 117.612 182.550 0.13303 0.08091

23 0.95 6.13 2.18E+07 2.632 2.100 4.732 247.979 137.926 110.053 0.10991 0.04878

24 1.19 6.13 1.40E+07 2.831 8.094 10.926 414.766 107.484 307.283 0.18383 0.13619

25 1.09 6.13 1.66E+07 2.752 3.810 6.562 300.429 125.979 174.450 0.13315 0.07732

26 0.94 6.13 2.23E+07 2.623 2.269 4.892 233.966 125.442 108.524 0.10369 0.04810

27 0.87 6.13 2.64E+07 2.552 0.999 3.551 204.802 147.178 57.624 0.09077 0.02554

84



3CR 10

3CT

RT RF RR RT/ RR/

m/s N N N

1 0.92 6.13 2.35E+07 2.600 1.887 4.487 254.197 147.280 106.917 0.11266 0.04739

2 1.05 6.13 1.79E+07 2.717 4.883 7.600 376.112 134.472 241.640 0.16669 0.10710

3 0.83 6.13 2.85E+07 2.521 0.614 3.135 195.485 157.197 38.288 0.08664 0.01697

4 0.96 6.13 2.14E+07 2.640 3.233 5.873 301.801 135.687 166.114 0.13376 0.07362

5 0.88 6.13 2.53E+07 2.569 1.671 4.239 263.664 159.761 103.903 0.11686 0.04605

6 1.10 6.13 1.63E+07 2.761 7.001 9.761 438.156 123.918 314.237 0.19419 0.13927

7 1.01 6.13 1.93E+07 2.684 3.932 6.616 359.494 145.836 213.658 0.15933 0.09469

8 0.87 6.13 2.59E+07 2.560 1.512 4.072 230.305 144.772 85.534 0.10207 0.03791

9 0.80 6.13 3.07E+07 2.491 0.697 3.188 218.169 170.493 47.676 0.09669 0.02113

10 0.96 6.13 2.16E+07 2.635 1.311 3.946 202.018 134.897 67.121 0.08953 0.02975

11 1.09 6.13 1.65E+07 2.755 3.069 5.825 260.498 123.221 137.277 0.11545 0.06084

12 0.87 6.13 2.62E+07 2.555 0.989 3.544 199.698 143.950 55.748 0.08851 0.02471

13 1.00 6.13 1.96E+07 2.677 2.140 4.817 223.502 124.195 99.307 0.09906 0.04401

14 0.92 6.13 2.33E+07 2.604 1.012 3.616 203.514 146.551 56.963 0.09020 0.02525

15 1.15 6.13 1.50E+07 2.800 4.781 7.581 307.249 113.465 193.783 0.13617 0.08589

16 1.05 6.13 1.78E+07 2.721 2.347 5.068 249.217 133.817 115.400 0.11045 0.05115

17 0.91 6.13 2.38E+07 2.595 1.256 3.850 196.637 132.505 64.132 0.08715 0.02842

18 0.84 6.13 2.82E+07 2.525 0.595 3.120 193.284 156.417 36.867 0.08566 0.01634

19 0.99 6.13 2.02E+07 2.664 2.571 5.235 250.428 127.438 122.990 0.11099 0.05451

20 1.13 6.13 1.54E+07 2.786 4.673 7.459 311.360 116.296 195.064 0.13800 0.08645

21 0.90 6.13 2.45E+07 2.582 1.593 4.175 219.596 135.818 83.778 0.09733 0.03713

22 1.04 6.13 1.84E+07 2.707 3.625 6.332 275.139 117.612 157.528 0.12194 0.06982

23 0.95 6.13 2.18E+07 2.632 1.798 4.430 232.141 137.926 94.215 0.10289 0.04176

24 1.19 6.13 1.40E+07 2.831 6.734 9.565 363.110 107.484 255.627 0.16093 0.11329

25 1.09 6.13 1.66E+07 2.752 3.639 6.390 292.562 125.979 166.583 0.12966 0.07383

26 0.94 6.13 2.23E+07 2.623 1.922 4.545 217.364 125.442 91.923 0.09634 0.04074

27 0.87 6.13 2.64E+07 2.552 0.581 3.133 180.706 147.178 33.528 0.08009 0.01486

85

Appendix 7: S-NPL SeriesExperiment Results

Table 47: S-NPL Series Hull Parameters

Table 48: S-NPL Series Experiment Results for Model 3b

Model L (m) L/B B/T L/1/3

(m3) CB CP CM

WSA (m2)

LCB(% from

midship) 1+k

3b 1.6 7.00 2.00 6.27 0.0166 0.397 0.693 0.565 0.434 -6.4 1.45

4a 1.6 10.40 1.50 7.40 0.0101 0.397 0.693 0.565 0.348 -6.4 1.30

4b 1.6 9.00 2.00 7.41 0.0101 0.397 0.693 0.565 0.338 -6.4 1.30

4c 1.6 8.00 2.50 7.39 0.0101 0.397 0.693 0.565 0.340 -6.4 1.30

5a 1.6 12.80 1.50 8.51 0.0066 0.397 0.693 0.565 0.282 -6.4 1.28

5b 1.6 11.00 2.00 8.50 0.0067 0.397 0.693 0.565 0.276 -6.4 1.26

5c 1.6 9.90 2.50 8.49 0.0067 0.397 0.693 0.565 0.277 -6.4 1.26

6a 1.6 15.10 1.50 9.50 0.0048 0.397 0.693 0.565 0.240 -6.4 1.22

6b 1.6 13.10 2.00 9.50 0.0048 0.397 0.693 0.565 0.233 -6.4 1.22

6c 1.6 11.70 2.50 9.50 0.0048 0.397 0.693 0.565 0.234 -6.4 1.22

Fn Fn V 103CT RT 10

3CWP Rn 10

3CF 10

3CR RF RR RR/ RT/

m/s N N N

0.20 0.50 0.79 7.553 1.029 0.076 1.11E+06 4.582 2.971 0.624 0.405 0.02435 0.06190

0.25 0.63 0.99 7.880 1.677 0.259 1.39E+06 4.370 3.510 0.930 0.747 0.04495 0.10091

0.30 0.75 1.19 8.016 2.456 0.722 1.67E+06 4.208 3.808 1.289 1.167 0.07022 0.14782

0.35 0.88 1.39 8.878 3.703 1.199 1.94E+06 4.078 4.800 1.701 2.002 0.12049 0.22284

0.40 1.00 1.58 9.590 5.224 1.633 2.22E+06 3.970 5.620 2.163 3.062 0.18426 0.31440

0.45 1.13 1.78 11.913 8.214 3.530 2.50E+06 3.878 8.035 2.674 5.540 0.33340 0.49430

0.50 1.25 1.98 12.836 10.926 5.229 2.78E+06 3.798 9.038 3.233 7.693 0.46296 0.65753

0.55 1.38 2.18 12.271 12.639 6.393 3.06E+06 3.728 8.543 3.840 8.799 0.52949 0.76059

0.60 1.50 2.38 11.292 13.841 6.067 3.33E+06 3.666 7.626 4.494 9.347 0.56249 0.83295

0.65 1.63 2.57 10.347 14.885 5.175 3.61E+06 3.611 6.736 5.194 9.691 0.58316 0.89574

0.70 1.75 2.77 9.514 15.873 4.474 3.89E+06 3.560 5.954 5.940 9.933 0.59776 0.95522

0.75 1.88 2.97 8.897 17.040 4.024 4.17E+06 3.514 5.383 6.731 10.309 0.62040 1.02544

0.80 2.00 3.17 8.383 18.268 3.484 4.44E+06 3.472 4.911 7.566 10.702 0.64401 1.09932

0.85 2.13 3.37 7.917 19.476 2.838 4.72E+06 3.433 4.484 8.445 11.031 0.66382 1.17204

0.90 2.25 3.57 7.498 20.679 2.253 5.00E+06 3.397 4.101 9.368 11.311 0.68067 1.24444

0.95 2.38 3.76 7.148 21.965 1.711 5.28E+06 3.363 3.785 10.334 11.631 0.69991 1.32183

1.00 2.50 3.96 6.910 23.528 1.282 5.55E+06 3.332 3.578 11.344 12.184 0.73322 1.41586

86

Table 49: S-NPL Series Experiment Results for Model 4a


Table 51: S-NPL Series Experiment Results for Model 4c

Fn Fn V 103CT RT 10

3CWP Rn 10

3CF 10

3CR RF RR RR/ RT/

m/s N N N

0.20 0.54 0.79 6.49 0.709 0.039 1.11E+06 4.582 1.909 0.500 0.208 0.02062 0.07013

0.25 0.68 0.99 6.84 1.166 0.265 1.39E+06 4.370 2.465 0.746 0.421 0.04161 0.11538

0.30 0.82 1.19 7.48 1.838 0.632 1.67E+06 4.208 3.273 1.034 0.804 0.07956 0.18186

0.35 0.95 1.39 7.66 2.563 0.849 1.94E+06 4.078 3.585 1.364 1.199 0.11863 0.25355

0.40 1.09 1.58 8.07 3.525 1.256 2.22E+06 3.970 4.099 1.734 1.791 0.17716 0.34871

0.45 1.22 1.78 9.18 5.077 2.143 2.50E+06 3.878 5.305 2.144 2.933 0.29017 0.50227

0.50 1.36 1.98 9.32 6.364 2.846 2.78E+06 3.798 5.526 2.592 3.772 0.37312 0.62960

0.55 1.50 2.18 8.81 7.279 2.836 3.06E+06 3.728 5.086 3.079 4.200 0.41551 0.72015

0.60 1.63 2.38 8.10 7.959 2.551 3.33E+06 3.666 4.432 3.604 4.356 0.43091 0.78742

0.65 1.77 2.57 7.54 8.692 2.337 3.61E+06 3.611 3.924 4.165 4.527 0.44783 0.85987

0.70 1.90 2.77 7.04 9.414 2.061 3.89E+06 3.560 3.477 4.763 4.651 0.46014 0.93134

0.75 2.04 2.97 6.64 10.200 1.883 4.17E+06 3.514 3.128 5.397 4.803 0.47521 1.00913

0.80 2.18 3.17 6.38 11.141 1.764 4.44E+06 3.472 2.904 6.067 5.074 0.50200 1.10218

0.85 2.31 3.37 6.14 12.109 1.649 4.72E+06 3.433 2.706 6.772 5.338 0.52807 1.19801

0.90 2.45 3.57 5.94 13.138 1.434 5.00E+06 3.397 2.544 7.512 5.626 0.55662 1.29978

0.95 2.58 3.76 5.76 14.195 1.263 5.28E+06 3.363 2.398 8.287 5.908 0.58453 1.40433

1.00 2.72 3.96 5.60 15.300 1.087 5.55E+06 3.332 2.272 9.096 6.204 0.61378 1.51364

Fn Fn V 103CT RT 10

3CWP Rn 10

3CF 10

3CR RF RR RR/ RT/

m/s N N N

0.20 0.54 0.79 7.20 0.763 0.049 1.11E+06 4.582 2.614 0.486 0.277 0.02754 0.07582

0.25 0.68 0.99 7.00 1.160 0.295 1.39E+06 4.370 2.629 0.724 0.436 0.04327 0.11522

0.30 0.82 1.19 7.74 1.847 0.605 1.67E+06 4.208 3.532 1.004 0.843 0.08373 0.18349

0.35 0.95 1.39 7.84 2.547 0.868 1.94E+06 4.078 3.763 1.325 1.222 0.12143 0.25301

0.40 1.09 1.58 8.49 3.602 1.183 2.22E+06 3.970 4.519 1.684 1.917 0.19047 0.35777

0.45 1.22 1.78 9.28 4.983 2.587 2.50E+06 3.878 5.402 2.082 2.901 0.28815 0.49499

0.50 1.36 1.98 9.19 6.090 3.376 2.78E+06 3.798 5.389 2.518 3.572 0.35485 0.60497

0.55 1.50 2.18 8.59 6.893 3.186 3.06E+06 3.728 4.865 2.991 3.902 0.38760 0.68469

0.60 1.63 2.38 7.94 7.582 2.749 3.33E+06 3.666 4.276 3.500 4.082 0.40543 0.75310

0.65 1.77 2.57 7.40 8.288 2.508 3.61E+06 3.611 3.787 4.045 4.243 0.42148 0.82331

0.70 1.91 2.77 6.95 9.036 2.406 3.89E+06 3.560 3.394 4.626 4.410 0.43802 0.89754

0.75 2.04 2.97 6.61 9.862 2.175 4.17E+06 3.514 3.098 5.242 4.621 0.45898 0.97966

0.80 2.18 3.17 6.32 10.726 1.885 4.44E+06 3.472 2.848 5.892 4.833 0.48012 1.06542

0.85 2.31 3.37 6.08 11.648 1.584 4.72E+06 3.433 2.647 6.577 5.071 0.50375 1.15708

0.90 2.45 3.57 5.87 12.612 1.338 5.00E+06 3.397 2.475 7.296 5.316 0.52810 1.25283

0.95 2.59 3.76 5.72 13.699 1.172 5.28E+06 3.363 2.361 8.048 5.650 0.56124 1.36072

1.00 2.72 3.96 5.68 15.056 1.134 5.55E+06 3.332 2.346 8.834 6.222 0.61805 1.49561

Fn Fn V 103CT RT 10

3CWP Rn 10

3CF 10

3CR RF RR RR/ RT/

m/s N N N

0.20 0.54 0.79 6.75 0.720 0.000 1.11E+06 4.582 2.169 0.489 0.231 0.02280 0.07097

0.25 0.68 0.99 6.88 1.146 0.310 1.39E+06 4.370 2.506 0.729 0.418 0.04116 0.11295

0.30 0.82 1.19 7.20 1.727 0.654 1.67E+06 4.208 2.987 1.010 0.717 0.07066 0.17019

0.35 0.95 1.39 7.43 2.427 0.962 1.94E+06 4.078 3.348 1.332 1.094 0.10780 0.23909

0.40 1.09 1.58 8.34 3.559 1.483 2.22E+06 3.970 4.370 1.694 1.865 0.18379 0.35071

0.45 1.22 1.78 9.40 5.078 2.810 2.50E+06 3.878 5.524 2.095 2.984 0.29401 0.50039

0.50 1.36 1.98 9.31 6.208 3.206 2.78E+06 3.798 5.512 2.533 3.676 0.36215 0.61172

0.55 1.50 2.18 8.75 7.059 3.373 3.06E+06 3.728 5.021 3.008 4.051 0.39915 0.69558

0.60 1.63 2.38 8.14 7.816 3.097 3.33E+06 3.666 4.473 3.521 4.295 0.42318 0.77008

0.65 1.77 2.57 7.61 8.571 2.721 3.61E+06 3.611 3.994 4.069 4.501 0.44353 0.84448

0.70 1.90 2.77 7.19 9.400 2.548 3.89E+06 3.560 3.632 4.653 4.747 0.46771 0.92621

0.75 2.04 2.97 6.87 10.314 2.324 4.17E+06 3.514 3.360 5.273 5.041 0.49670 1.01624

0.80 2.17 3.17 6.59 11.252 2.058 4.44E+06 3.472 3.119 5.927 5.325 0.52464 1.10865

0.85 2.31 3.37 6.36 12.247 1.846 4.72E+06 3.433 2.922 6.616 5.631 0.55486 1.20675

0.90 2.45 3.57 6.14 13.266 1.633 5.00E+06 3.397 2.743 7.339 5.927 0.58399 1.30712

0.95 2.58 3.76 5.97 14.362 1.455 5.28E+06 3.363 2.603 8.096 6.266 0.61740 1.41512

1.00 2.72 3.96 5.81 15.506 1.278 5.55E+06 3.332 2.481 8.887 6.619 0.65217 1.52779

87




Fn Fn V 103CT RT 10

3CWP Rn 10

3CF 10

3CR RF RR RR/ RT/

m/s N N N

0.20 0.58 0.79 6.44 0.570 0.094 1.11E+06 4.582 1.854 0.406 0.164 0.02468 0.08570

0.25 0.73 0.99 6.86 0.948 0.281 1.39E+06 4.370 2.487 0.604 0.344 0.05173 0.14266

0.30 0.88 1.19 7.22 1.437 0.532 1.67E+06 4.208 3.007 0.838 0.599 0.09009 0.21616

0.35 1.02 1.39 7.34 1.989 0.647 1.94E+06 4.078 3.262 1.105 0.884 0.13303 0.29931

0.40 1.17 1.58 7.64 2.706 0.931 2.22E+06 3.970 3.674 1.405 1.301 0.19571 0.40713

0.45 1.31 1.78 7.98 3.576 1.534 2.50E+06 3.878 4.104 1.737 1.839 0.27666 0.53805

0.50 1.46 1.98 7.68 4.249 1.783 2.78E+06 3.798 3.884 2.101 2.148 0.32320 0.63930

0.55 1.60 2.18 7.17 4.797 1.728 3.06E+06 3.728 3.440 2.495 2.302 0.34635 0.72179

0.60 1.75 2.38 6.73 5.359 1.557 3.33E+06 3.666 3.063 2.920 2.439 0.36701 0.80638

0.65 1.90 2.57 6.35 5.934 1.401 3.61E+06 3.611 2.737 3.375 2.559 0.38498 0.89280

0.70 2.04 2.77 6.02 6.527 1.261 3.89E+06 3.560 2.461 3.860 2.668 0.40137 0.98209

0.75 2.19 2.97 5.79 7.209 1.148 4.17E+06 3.514 2.279 4.373 2.836 0.42669 1.08471

0.80 2.33 3.17 5.61 7.940 1.043 4.44E+06 3.472 2.136 4.916 3.024 0.45507 1.19475

0.85 2.48 3.37 5.47 8.748 0.970 4.72E+06 3.433 2.040 5.487 3.261 0.49064 1.31629

0.90 2.63 3.57 5.33 9.544 0.893 5.00E+06 3.397 1.929 6.087 3.457 0.52018 1.43607

0.95 2.77 3.76 5.23 10.449 0.809 5.28E+06 3.363 1.870 6.715 3.734 0.56176 1.57212

1.00 2.92 3.96 5.15 11.398 0.745 5.55E+06 3.332 1.820 7.371 4.027 0.60598 1.71500

Fn Fn V 103CT RT 10

3CWP Rn 10

3CF 10

3CR RF RR RR/ RT/

m/s N N N

0.20 0.58 0.79 5.99 0.519 0.017 1.11E+06 4.582 1.405 0.397 0.122 0.01824 0.07775

0.25 0.73 0.99 6.73 0.911 0.302 1.39E+06 4.370 2.363 0.591 0.320 0.04794 0.13662

0.30 0.87 1.19 6.84 1.333 0.404 1.67E+06 4.208 2.632 0.820 0.513 0.07690 0.19986

0.35 1.02 1.39 6.97 1.848 0.617 1.94E+06 4.078 2.890 1.082 0.767 0.11495 0.27712

0.40 1.17 1.58 7.48 2.592 1.036 2.22E+06 3.970 3.513 1.375 1.217 0.18250 0.38870

0.45 1.31 1.78 7.57 3.319 1.383 2.50E+06 3.878 3.691 1.700 1.619 0.24267 0.49760

0.50 1.46 1.98 7.32 3.961 1.708 2.78E+06 3.798 3.519 2.056 1.905 0.28559 0.59387

0.55 1.60 2.18 6.85 4.489 1.658 3.06E+06 3.728 3.126 2.442 2.047 0.30695 0.67311

0.60 1.75 2.38 6.52 5.080 1.570 3.33E+06 3.666 2.851 2.858 2.222 0.33316 0.76167

0.65 1.90 2.57 6.21 5.680 1.430 3.61E+06 3.611 2.598 3.303 2.377 0.35639 0.85166

0.70 2.04 2.77 5.85 6.202 1.316 3.89E+06 3.560 2.285 3.777 2.424 0.36345 0.92982

0.75 2.19 2.97 5.67 6.905 1.225 4.17E+06 3.514 2.155 4.280 2.624 0.39349 1.03525

0.80 2.33 3.17 5.48 7.597 0.987 4.44E+06 3.472 2.010 4.811 2.785 0.41764 1.13903

0.85 2.48 3.37 5.37 8.403 1.105 4.72E+06 3.433 1.938 5.371 3.032 0.45458 1.25982

0.90 2.62 3.57 5.23 9.168 0.971 5.00E+06 3.397 1.830 5.958 3.210 0.48128 1.37453

0.95 2.77 3.76 5.22 10.191 0.877 5.28E+06 3.363 1.852 6.572 3.619 0.54260 1.52798

1.00 2.92 3.96 5.14 11.119 0.824 5.55E+06 3.332 1.803 7.214 3.905 0.58548 1.66708

Fn Fn V 103CT RT 10

3CWP Rn 10

3CF 10

3CR RF RR RR/ RT/

m/s N N N

0.20 0.58 0.79 7.10 0.617 0.013 1.11E+06 4.582 2.517 0.398 0.219 0.03269 0.09220

0.25 0.73 0.99 7.13 0.968 0.298 1.39E+06 4.370 2.755 0.594 0.374 0.05590 0.14458

0.30 0.87 1.19 7.22 1.412 0.598 1.67E+06 4.208 3.010 0.823 0.589 0.08796 0.21092

0.35 1.02 1.39 7.35 1.957 0.760 1.94E+06 4.078 3.272 1.086 0.871 0.13015 0.29233

0.40 1.17 1.58 7.66 2.662 1.187 2.22E+06 3.970 3.686 1.380 1.282 0.19151 0.39772

0.45 1.31 1.78 7.77 3.418 1.769 2.50E+06 3.878 3.890 1.706 1.712 0.25578 0.51073

0.50 1.46 1.98 7.42 4.031 2.003 2.78E+06 3.798 3.621 2.064 1.967 0.29389 0.60220

0.55 1.60 2.18 6.96 4.575 1.896 3.06E+06 3.728 3.232 2.451 2.124 0.31738 0.68358

0.60 1.75 2.38 6.71 5.253 1.802 3.33E+06 3.666 3.048 2.868 2.384 0.35621 0.78476

0.65 1.89 2.57 6.30 5.780 1.629 3.61E+06 3.611 2.684 3.315 2.465 0.36822 0.86353

0.70 2.04 2.77 5.98 6.365 1.561 3.89E+06 3.560 2.417 3.791 2.573 0.38448 0.95090

0.75 2.19 2.97 5.72 6.991 1.338 4.17E+06 3.514 2.205 4.296 2.695 0.40266 1.04447

0.80 2.33 3.17 5.55 7.715 1.213 4.44E+06 3.472 2.075 4.829 2.886 0.43118 1.15263

0.85 2.48 3.37 5.34 8.378 1.121 4.72E+06 3.433 1.903 5.390 2.988 0.44641 1.25172

0.90 2.62 3.57 5.26 9.259 1.001 5.00E+06 3.397 1.863 5.979 3.280 0.49000 1.38333

0.95 2.77 3.76 5.28 10.352 0.939 5.28E+06 3.363 1.915 6.596 3.756 0.56111 1.54657

1.00 2.91 3.96 5.12 11.118 0.816 5.55E+06 3.332 1.784 7.240 3.878 0.57936 1.66106

88




Fn Fn V 103CT RT 10

3CWP Rn 10

3CF 10

3CR RF RR RR/ RT/

m/s N N N

0.20 0.62 0.79 6.50 0.489 0.000 1.11E+06 4.582 1.917 0.345 0.144 0.03022 0.10246

0.25 0.77 0.99 6.63 0.780 0.184 1.39E+06 4.370 2.257 0.514 0.266 0.05559 0.16324

0.30 0.92 1.19 6.65 1.127 0.439 1.67E+06 4.208 2.443 0.713 0.414 0.08666 0.23592

0.35 1.08 1.39 6.61 1.523 0.577 1.94E+06 4.078 2.527 0.941 0.583 0.12202 0.31889

0.40 1.23 1.58 6.69 2.016 0.739 2.22E+06 3.970 2.723 1.196 0.820 0.17174 0.42206

0.45 1.39 1.78 6.67 2.545 0.998 2.50E+06 3.878 2.796 1.479 1.066 0.22317 0.53265

0.50 1.54 1.98 6.46 3.039 1.264 2.78E+06 3.798 2.658 1.788 1.251 0.26187 0.63612

0.55 1.70 2.18 6.16 3.510 1.181 3.06E+06 3.728 2.435 2.124 1.387 0.29025 0.73477

0.60 1.85 2.38 5.91 4.007 1.045 3.33E+06 3.666 2.246 2.485 1.522 0.31861 0.83882

0.65 2.00 2.57 5.72 4.552 0.872 3.61E+06 3.611 2.111 2.872 1.680 0.35156 0.95281

0.70 2.16 2.77 5.48 5.053 0.755 3.89E+06 3.560 1.917 3.285 1.768 0.37016 1.05772

0.75 2.31 2.97 5.30 5.608 0.748 4.17E+06 3.514 1.781 3.722 1.886 0.39479 1.17387

0.80 2.47 3.17 5.11 6.152 0.698 4.44E+06 3.472 1.633 4.184 1.968 0.41191 1.28768

0.85 2.62 3.37 4.98 6.771 0.659 4.72E+06 3.433 1.544 4.670 2.100 0.43967 1.41722

0.90 2.77 3.57 4.88 7.435 0.598 5.00E+06 3.397 1.478 5.181 2.254 0.47190 1.55630

0.95 2.93 3.76 4.89 8.311 0.768 5.28E+06 3.363 1.528 5.715 2.596 0.54347 1.73971

1.00 3.08 3.96 4.85 9.138 0.964 5.55E+06 3.332 1.521 6.273 2.865 0.59962 1.91268

Fn Fn V 103CT RT 10

3CWP Rn 10

3CF 10

3CR RF RR RR/ RT/

m/s N N N

0.20 0.62 0.79 6.34 0.463 0.032 1.11E+06 4.582 1.755 0.335 0.128 0.02686 0.09699

0.25 0.77 0.99 6.51 0.743 0.182 1.39E+06 4.370 2.136 0.499 0.244 0.05107 0.15559

0.30 0.92 1.19 6.46 1.063 0.437 1.67E+06 4.208 2.255 0.692 0.371 0.07766 0.22256

0.35 1.08 1.39 6.23 1.395 0.557 1.94E+06 4.078 2.150 0.913 0.482 0.10079 0.29192

0.40 1.23 1.58 6.61 1.933 0.828 2.22E+06 3.970 2.638 1.161 0.772 0.16153 0.40455

0.45 1.39 1.78 6.57 2.433 1.156 2.50E+06 3.878 2.695 1.435 0.998 0.20884 0.50929

0.50 1.54 1.98 6.31 2.883 1.221 2.78E+06 3.798 2.510 1.736 1.147 0.24007 0.60341

0.55 1.70 2.18 6.07 3.355 1.185 3.06E+06 3.728 2.339 2.062 1.293 0.27067 0.70223

0.60 1.85 2.38 5.75 3.785 1.105 3.33E+06 3.666 2.085 2.413 1.372 0.28714 0.79218

0.65 2.00 2.57 5.51 4.256 0.953 3.61E+06 3.611 1.900 2.789 1.468 0.30720 0.89091

0.70 2.16 2.77 5.31 4.754 0.845 3.89E+06 3.560 1.748 3.189 1.565 0.32768 0.99519

0.75 2.31 2.97 5.17 5.316 0.758 4.17E+06 3.514 1.656 3.613 1.703 0.35637 1.11273

0.80 2.47 3.17 5.05 5.904 0.716 4.44E+06 3.472 1.575 4.062 1.843 0.38570 1.23592

0.85 2.62 3.37 4.96 6.551 0.764 4.72E+06 3.433 1.527 4.534 2.017 0.42215 1.37119

0.90 2.77 3.57 4.92 7.285 0.727 5.00E+06 3.397 1.523 5.029 2.255 0.47209 1.52485

0.95 2.93 3.76 4.85 7.993 0.719 5.28E+06 3.363 1.482 5.548 2.445 0.51173 1.67309

1.00 3.08 3.96 4.76 8.697 0.750 5.55E+06 3.332 1.426 6.090 2.607 0.54578 1.82055

Fn Fn V 103CT RT 10

3CWP Rn 10

3CF 10

3CR RF RR RR/ RT/

m/s N N N

0.20 0.62 0.79 6.47 0.475 0.093 1.11E+06 4.582 1.884 0.336 0.138 0.02896 0.09939

0.25 0.77 0.99 6.76 0.776 0.327 1.39E+06 4.370 2.394 0.501 0.275 0.05749 0.16245

0.30 0.92 1.19 6.79 1.122 0.574 1.67E+06 4.208 2.581 0.695 0.426 0.08926 0.23479

0.35 1.08 1.39 6.74 1.516 0.742 1.94E+06 4.078 2.665 0.917 0.599 0.12547 0.31741

0.40 1.23 1.58 6.75 1.984 0.923 2.22E+06 3.970 2.784 1.166 0.818 0.17120 0.41526

0.45 1.39 1.78 6.69 2.488 1.194 2.50E+06 3.878 2.815 1.442 1.047 0.21907 0.52081

0.50 1.54 1.98 6.42 2.948 1.418 2.78E+06 3.798 2.626 1.743 1.205 0.25225 0.61714

0.55 1.70 2.18 6.12 3.400 1.347 3.06E+06 3.728 2.394 2.071 1.329 0.27823 0.71163

0.60 1.85 2.38 5.84 3.862 1.122 3.33E+06 3.666 2.178 2.423 1.439 0.30124 0.80844

0.65 2.00 2.57 5.62 4.357 0.930 3.61E+06 3.611 2.006 2.801 1.556 0.32573 0.91194

0.70 2.16 2.77 5.43 4.881 0.862 3.89E+06 3.560 1.866 3.203 1.678 0.35130 1.02168

0.75 2.31 2.97 5.27 5.440 0.808 4.17E+06 3.514 1.754 3.629 1.811 0.37908 1.13869

0.80 2.47 3.17 5.15 6.056 0.755 4.44E+06 3.472 1.682 4.079 1.976 0.41367 1.26754

0.85 2.62 3.37 5.07 6.719 0.720 4.72E+06 3.433 1.633 4.553 2.166 0.45339 1.40650

0.90 2.77 3.57 4.97 7.383 0.702 5.00E+06 3.397 1.568 5.051 2.332 0.48812 1.54540

0.95 2.93 3.76 4.99 8.269 0.692 5.28E+06 3.363 1.628 5.572 2.697 0.56456 1.73090

1.00 3.08 3.96 5.00 9.185 0.681 5.55E+06 3.332 1.671 6.116 3.068 0.64227 1.92251

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RE-EVALUATION OF RESISTANCE PREDICTION FOR HIGH-SPEED