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72

CHAPTER VIII

MODEL RESISTANCE TEST TECHNIQUES

8.1

Introduction

Resistance test techniques used in this model experiment are based on three similarities of the ship and that are, geometrical, dynamical and kinetic similarities. These three similarities are used to make sure that the flow pattern along both the model and ship are the same. The appendages of ship are also scaled in the same order as the model, but normally to be added as a percentage of the naked hull total resistance.

73

8.2

Resistance Test Calculation Concept

Through the various method of extrapolation, the model resistance test results can produce the resistance for the actual ship. The methods used to calculate resistance are firstly introduced by William Froude as an original concept of resistance calculation. In this method, the flat plate is used to consider the viscous form resistance, Rvisc.form proportional to wave resistance, RW. The sum of these two resistances is referred to as the residuary resistance, RR to give the following equations:

R T = RF + RR

Froude assumption and conditions are as follows:i)

The model is made to a scale ratio of and run over a range of corresponding speed such that VS / √LM = VM √LM

ii)

Model frictional resistance is calculated, assuming the resistance to be the same as that of a smooth flat plank of the same length and surface as the model.

iii)

Model residuary resistance is then calculated as follows RRM = RTM – RFM

iv)

Ship residuary resistance is calculated using scale ratio RRS = RRM x λ³ For the corresponding speed given by VS = VM x λ1/2

74 v)

Ship frictional resistance is calculated using a frictional coefficient to the ship length.

vi)

Finally the ship total resistance for naked hull is calculated as follows RTS = RFS – RRS

Figure 8.1: Extrapolation of model results to ship using the form factor given by Hughes

Figure 8.2: Graph of determining the form factor given by Prohaska

75 8.3

Procedure of Resistance Test

1. Firstly, the displacement of model is determined according to the full load and service condition of the ship. 2. Total displacement must be as same as calculated above when ballast weight placed into the model. 3. Before doing all the procedures above, model should be ballasted and confirmed its draft to make sure there is no trim and also to establish the location of center of gravity (LCG and VCG). 4. The center of gravity of the model must be obtained on the swing frame. 5. Then, mark the lines when it’s on stable condition. Put 200 g of weight, on bare swinging frame and mark again. 6. The model properly ballasted is then put onto the swinging frame at its location of gravity center. Then, the ballast weight is moved aft or forward until the swinging frame becomes stable to confirm the longitudinal gravity center (LCG). 7. Again, 200 g of weight was put on the swinging frame (without model) at one end and state the degrees of inclination. Make sure the model with the ballast weight having the same degrees with bare swinging frame inclination to confirm the vertical gravity center (VCG). 8. Model with full load condition then transferred into the tank to check the inclination (Taft = Tfwd) by using the water inclinometer. 9. After that, model is attached to the towing carriage. 10. The measurement of resistance is conducted in the towing tank with the different corresponding speed. 11. After finished running at one speed, the models continue to run with other speed after the water is calm. 12. Step (11) then will be repeated for four times with the difference speed. 13. This procedure is repeated when using model with bulbous bow.

76 Table 8.1: Model test protocol No. of run 1 2 3 4 5 6 7 8 9 10 11 12 13 14

8.4

Ship Speed VS (knots) 3 3.5 4 4.5 5 5.5 6 8 9 10 11 12 12.5 13

Corresponding Model Speed, Vm (m/s)

Fn

0.4880

0.1006

0.5693

0.1174

0.6507

0.1341

0.7320

0.1509

0.8133

0.1677

0.8947

0.1844

0.9760

0.2012

1.3013

0.2683

1.4640

0.3018

1.6267

0.3353

1.7893

0.3689

1.9520

0.4024

2.0333

0.4192

2.1147

0.4359

Method of Analysis Using International Towing Tank Test (ITTC) Friction Line 1957

77 The ITTC 1957 method is one of the methods used to calculate resistance and is based on Froude’s principal and based on the “ITTC 1957 model ship correlation line”. This is a popular method used to calculate the frictional resistance followed by the total resistance. In 1957, the ITTC (1959) decided that the line was given by the formula: CF =

0.075

( LogRN

− 2)

2

By adopting this as correlation line, CF is friction resistance coefficient for the ship. Figure 8.3 illustrates the ITTC 1957 method. The total resistance coefficients for the model are determined by the towing tests and from the formula:

C TM =

RTM 0.5.ρ mV m S m 2

Where RTM is the model resistance Vm is the speed of the model. Sm is the wetted surface of the model ρm is the density of the water in the towing tank.

78

Figure 8.3: Schematic representation of the ITTC 1957 method

The residuary resistance coefficients for the model is then calculated by CRM = CTM – CFM

According to the frictional resistance coefficient given by ITTC 1957 friction line, the residuary resistance coefficients for the ship at the same Froude number is the same as the model at corresponding Reynolds number. CRS = CRM

Using the ITTC 1957 model-ship correlation line as an extrapolator, the total resistance coefficients for smooth ship can be determined by: CTS = CFS + CRM

In addition, furthermore, that totals resistance coefficients for the ship is

79 CTS = CFS + CRM + CA

Where CA is incremental resistance coefficients for model ship correlation that taking into account and also the effect of the roughness of the ship. Usually, some model tanks are using the same CA coefficient for all types of ship, for example, CA= 0.0004. This value is obtained because it varies with the type and size of the ship. For a ship that use length as a parameter, the variation of the incremental resistance can be as follows:

(

C A = 0.006 LWLS + 100

)

−0.16

− 0.00205 which valid for

TF > 0.04 LWL

where TF = draft at fore perpendicular Therefore, resistance of the ship is:

(

RS = CTS 0.5.ρ S .V 2 S .S S

)

where VS is the ship speed and S S is the wetted surface of the ship, and ρS is the density of the seawater.

8.5

Sample of Calculation

80 The resistance experiment is conducted using the analysis of ITTC (1957) friction line. This example is based on 12 knots ship speed. After obtaining the model resistance from the tank test, the ship resistance can be calculated. Total model resistance, RTM = 46 .9054 N Procedure:-

1. Ship speed, VS = 12 knots = 0.5144 x12 = 6.1728 m / s

2. Model speed, VM =

=

VS

where λ = model scale

λ 6.1728 10

=1.9520 m / s

3. Reynolds number (model), Rn =

=

V M LWL M

υM 1.9520 x 2.3987 0.85409 x10 −6

= 5.4822 x10 6

at T=27°C, fresh water kinematics viscosity, υ M = 0.85409 x10 −6 m 2 / s

81 4. According to ITTC-1957 Friction Line, model is equivalent to flat-plate resistance coefficient,

C FOM =

=

0.075 [ ( log10 Rn ) − 2] 2

0.075

[log (5.4822 x10 ) − 2] 6

2

10

= 3.3396 x10 −3

5. Total resistance coefficient

CTM

=

=

RTM 0.5.ρ M .VM .S M 2

46 .9054 0.5 x996 .4 x1.9520 2 x1.5735

=1.5703 x10 −2

82 at T = 27°C, fresh water density, ρM = 996.4 kg/m

According to ITTC frictional line, model viscous coefficient is given by CVM = (1 + k )C FOM where (1+k) is the form factor which is determined at slow speed.

6. Model wave-making resistance coefficient, CTM

CWM

= (1 + k )C FOM + CWM

= (1.5703 x10 −2 ) − (1.2717 ) (3.3396 x10 −3 ) =1.1456 x10 −2

7. For ship resistance, its similar to the model calculation,

Reynolds number (ship), R N =

=

VS LWL S

υS 6.1728 x 23 .987 0.90331 x10 −6

=1.6392 x10 8

at T=27°C, salt water kinematics viscosity, υS = 0.90331 x10 −6 m 2 / s 8. According to ITTC-1957 friction line,

83

Ships are equivalent to flat-plate resistance coefficient, CVS = C FOS

C FOS =

0.075 [ ( log10 Rn ) − 2] 2

=

0.075

[log (1.6392 x10 ) − 2] 8

2

10

=1.9419 x10 −3

9. Since the model and ship have kinematics similarity, therefore CWS = CWM = 1.1456 x10 −2

10. Total ship resistance coefficient CTS

= CVS + CWS = (1.9419 +11 .456 ) x10 −3

=1.3398 x10 −2

11. Model-ship correlation factor, C A

84

The ratio of

TF 2.426 = = 0.1011 > 0.04 LWL 23 .987

(

Therefore, C A = 0.006 LWLS + 100

)

−0.16

− 0.00205

= 0.006 ( 23 .987 +100 )

−0.16

− 0.00205

= 7.2467 x10 −4

12. Final ship total coefficient, CTS

Final

= CTS +C A

= (133 .98 + 7.2467 ) x10 −4

=1.4123 x10 −2

at T = 27°C, salt water density, ρM = 1022.6 kg/m

13. Ship total resistance,

RTS

= CTS Final ( 0.5.ρ S .V 2 S .S S )

=1.4123 x10 −2 x (0.5 x1022 .6 x 6.1728

2

x157 .348 )

= 4.3294 x10 4 N

14. Effective power, PE

= RTS xVs

= 4.3294 x10 4 x6.1728 = 2.6725 x10 5 Watt

85 =

267 .25 kW 0.7457

= 358 .37 hp

8.6

Model Resistance Test Result

The results of experiment are stated as follows:-

86

Table 8.2: Model resistance result for bare hull

Model Speed, Vm (m/s)

0.6507 0.9760 1.3013 1.4640 1.6267 1.7893 1.9520 2.0333 2.1147

Ship Speed, Vs

Model

Ctm

Resistance,

Model Reynolds Number, Rn

-3

Froude

Cfm

Number,

Cvm = Cfm

Cwm

Fn

(x10-3)

1.8274

0.1341

4.1292

5.2511

3.8984

6.1893

2.7411

0.2012

3.8080

4.8427

13.466

10.1120

7.6171

3.6548

0.2683

3.6024

4.5811

30.360

9

17.5440

10.442

4.1116

0.3018

3.5229

4.4801

59.617

10

23.8094

11.478

4.5685

0.3353

3.4541

4.3925

70.859

11

32.0396

12.765

5.0253

0.3689

3.3935

4.3155

84.499

12

46.9054

15.703

5.4822

0.4024

3.3396

4.2470

114.56

12.5

57.8679

17.855

5.7106

0.4192

3.3148

4.2154

136.39

13

68.2631

19.473

5.9390

0.4359

3.2912

4.1854

152.88

Rtm (N)

(x10 )

1.8722

5.6410

6

4.6218

8

(knots) 4

(x106)

(x10-3)

(x10-4)

87

Table 8.3: Ship resistance result for bare hull

88

SHIP Ship

Cws =

Speed,

Cwm

Vs

Reynolds Number, Rns

Cfos = Cvs

Ship Cts -3

(knots)

(x10-4)

4

8

(x10-3)

(x10 )

Cts final

Resistance, Rts (N)

Pe (kW)

Pe(hp)

2.3778

3.188

-3

(x10 )

3.8984

(x10 ) 0.54639

2.2783

2.6682

3.3928

(x103) 1.1556

6

13.466

0.81958

2.1447

3.4913

4.2159

3.2310

9.9721

13.372

8

30.360

1.0928

2.0568

5.0928

5.8175

7.9260

32.617

43.739

9

59.617

1.2294

2.0224

7.9842

8.7088

15.017

69.523

93.229

10

70.859

1.3660

1.9924

9.0782

9.8029

20.869

107.35

143.953

11

84.499

1.5026

1.9658

10.416

11.140

28.696

162.37

217.742

12

114.56

1.6392

1.9419

13.398

14.123

43.294

267.25

358.376

12.5

136.39

1.7075

1.9309

15.570

16.295

54.201

348.51

467.355

13

152.88

1.7758

1.9204

17.208

17.933

64.516

431.43

578.553

89

Table 8.4: Form factor result for bare hull

Form factor (1+k) Model

Ship

Speed,

Speed,

Vm

Vs

(m/s) 0 0.4880 0.5693 0.6507 0.7320 0.8133 0.8947

(knots) 0 3 3.5 4 4.5 5 5.5

Model

Ctm

Rn

Cfm

Resistance,

Fn -3

6

Rtm (N)

(x10 )

(x10 )

0 1.0071 1.5162 1.7997 2.2898 2.9395 3.6264

0 5.39 5.97 5.42 5.45 5.67 5.78

0 1.37 1.60 1.83 2.06 2.28 2.51

Fn^4/Cfm

Ctm/Cfm

0 0.0234 0.0447 0.0784 0.1286 0.2002 0.2987

1.2309 1.4060 1.3132 1.3521 1.4359 1.4919

-3

(x10 ) 0 0.1006 0.1174 0.1341 0.1509 0.1677 0.1844

0 4.38 4.24 4.13 4.03 3.95 3.87

90

Ctm/Cfm Against Fn4/Cfm y = -0.3788x2 + 0.8508x + 1.2717

1.6 1.4

Ctm/Cfm

1.2 1 Bare hull

0.8

Poly. (Bare hull)

0.6 0.4 0.2 0 0

0.05

0.1

0.15

0.2

Fn4/Cfm

0.25

0.3

0.35

91

Graph 8.1: Form factor for bare hull

M o d e l T o ta l R e s is ta n c e A g a in s t M o d e l S p e e d 80 70 Model Total Resistance, Rtm (N)

60 50 40

M odel

30 20 10 0 0

0 .5

1

1 .5

2

M o d e l S p e e d , V m (m / s)

2 .5

92

Graph 8.2: Total resistance of model against model speed for bare hull

S h ip R e s is t a n c e A g a in s t S p e e d 70 60

Ship Total Resistance (kN)

50 40

S h ip R e sista n c e

30 20 10 0 0

2

4

6

8

10

S h i p S p e e d (k n o t s )

12

14

93

Graph 8.3: Ship resistance of model against ship speed for bare hull

P o w e r ( H P ) A g a in t s S p e e d ( k n o t s ) 700 600 500 Power (Hp)

400

S h ip p o w e r

300 200 100 0 0

2

4

6

8

10

S h ip S p e e d (k n o ts)

12

14

94

Graph 8.4: Ship power against ship speed for bare hull

Table 8.5: Model resistance result for hull form with bulb

95

Model Speed, Vm (m/s)

0.6507 0.9760 1.3013 1.4640 1.6267 1.7893 1.9520 2.0333 2.1147

Ship Speed, Vs (knots) 4

Model

Ctm

Resistance, Rtm (N)

Model Reynolds Number, Rn

-3

(x10 )

(x106)

Froude

Cfm

Number, Fn

(x10-3)

Cvm = Cfm (x10-3)

Cwm (x10-4)

2.02504

6.1016

1.8274

0.1341

4.1292

5.7091

3.9258

6

4.69976

6.2937

2.7411

0.2012

3.8080

5.2650

10.287

8

9.96607

7.5072

3.6548

0.2683

3.6024

4.9806

25.266

9

15.4475

9.1940

4.1116

0.3018

3.5229

4.8708

43.232

10

22.5416

10.867

4.5685

0.3353

3.4541

4.7756

60.916

11

31.3811

12.503

5.0253

0.3689

3.3935

4.6919

78.112

12

46.0709

15.424

5.4822

0.4024

3.3396

4.6173

108.07

12.5

57.0176

17.592

5.7106

0.4192

3.3148

4.5830

130.09

13

68.947

19.668

5.9390

0.4359

3.2912

4.5503

151.18

96

Table 8.6: Ship resistance result for hull form with bulb

97

Ship Ship

Cws =

Speed,

Cwm

Vs (knots)

Reynolds Number,

Ship Cfos = Cvs

Cts final

Rns

Resistance, Rts (N)

-3

(x10-4)

Cts

(x10 )

-3

(x10 )

Pe (kW)

Pe(hp)

-3

(x10 )

(x108)

(x103)

4

3.9258

0.54639

2.2783

2.6709

3.3956

1.1566

2.3798

3.1913

6

10.287

0.81958

2.1447

3.1734

3.8980

2.9874

9.2202

12.3643

8

25.266

1.0928

2.0568

4.5834

5.3081

7.2320

29.761

39.9094

9

43.232

1.2294

2.0224

6.3457

7.0703

12.192

56.443

75.6896

10

60.916

1.3660

1.9924

8.0840

8.8086

18.752

96.460

129.3533

11

78.112

1.5026

1.9658

9.7769

10.502

27.051

153.06

205.2589

12

108.07

1.6392

1.9419

12.749

13.473

41.302

254.95

341.8888

12.5

130.09

1.7075

1.9309

14.940

15.665

52.106

335.04

449.2879

13

151.18

1.7758

1.9204

17.038

17.763

63.905

427.35

573.0724

98

Form factor (1+k) Model

Ship

Speed,

Speed,

Vm

Vs

(m/s) 0.4880 0.5693 0.6507 0.7320 0.8133 0.8947

(knots) 3 3.5 4 4.5 5 5.5

Model

Ctm

Rn

Cfm

Resistance, Rtm (N) 1.1549 1.5855 2.0250 2.6795 3.2618 4.0044

Fn -3

(x10 ) 6.1866 6.2395 6.1016 6.3791 6.2899 6.3818

6

(x10 ) 1.3705 1.5990 1.8274 2.0558 2.2842 2.5127

Fn^4/Cfm

Ctm/Cfm

0.023372 0.044711 0.078394 0.128605 0.200196 0.2987

1.411685 1.470215 1.477673 1.582171 1.593328 1.647457

-3

(x10 ) 0.1006 0.1174 0.1341 0.1509 0.1677 0.1844

hull form with bulb

4.3824 4.2439 4.1292 4.0319 3.9477 3.8737

Table 8.7: Form factor result for

99

C tm/C fm Ag ain st F n 4/C fm y = -2 .7 6 5 32 +x 1 .6 9 8 x + 1 .3 8 2 6

1 .8

1 .5

Ctm/Cfm

1 .2

B u lb

0 .9

P o ly. (B u lb )

0 .6

0 .3

0 0

0 .0 5

0 .1

0 .1 5

0 .2

F n 4/C fm

0 .2 5

0 .3

0 .3 5

100

Graph 8.5: Form factor for hull with bulb

M o d e l T o ta l R e s is ta n ce A g a in s t M o d e l S p e ed 80

Model Total Resistance, Rtm (N)

70 60 50

M o d e l (B u lb )

40 30 20 10 0 0

0.5

1

1.5

M o d e l S p e e d (m /s )

2

2.5

101

Graph 8.6: Total resistance of model against model speed for hull form with bulb

S h ip re s is ta n c e a g a in s t S h ip s p e e d 70 60

Ship resistance (kN)

50 40 S h ip re sista n c e 30 20 10 0 0

2

4

6

8

S p e e d (k n o ts)

10

12

14

102

Graph 8.7: Ship resistance against ship speed for hull form with bulb

S h ip p o w e r a g a in s t S h ip s p e e d 650 600 550 500

Ship power (Hp)

450 400 350

S h ip p o w e r

300 250 200 150 100 50 0 0

2

4

6

8

S p e e d (k n o ts )

10

12

14

103

Graph 8.8: Ship power against ship speed for hull form with bulb

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CHAPTER VIII

MODEL RESISTANCE TEST TECHNIQUES

8.1

Introduction

Resistance test techniques used in this model experiment are based on three similarities of the ship and that are, geometrical, dynamical and kinetic similarities. These three similarities are used to make sure that the flow pattern along both the model and ship are the same. The appendages of ship are also scaled in the same order as the model, but normally to be added as a percentage of the naked hull total resistance.

73

8.2

Resistance Test Calculation Concept

Through the various method of extrapolation, the model resistance test results can produce the resistance for the actual ship. The methods used to calculate resistance are firstly introduced by William Froude as an original concept of resistance calculation. In this method, the flat plate is used to consider the viscous form resistance, Rvisc.form proportional to wave resistance, RW. The sum of these two resistances is referred to as the residuary resistance, RR to give the following equations:

R T = RF + RR

Froude assumption and conditions are as follows:i)

The model is made to a scale ratio of and run over a range of corresponding speed such that VS / √LM = VM √LM

ii)

Model frictional resistance is calculated, assuming the resistance to be the same as that of a smooth flat plank of the same length and surface as the model.

iii)

Model residuary resistance is then calculated as follows RRM = RTM – RFM

iv)

Ship residuary resistance is calculated using scale ratio RRS = RRM x λ³ For the corresponding speed given by VS = VM x λ1/2

74 v)

Ship frictional resistance is calculated using a frictional coefficient to the ship length.

vi)

Finally the ship total resistance for naked hull is calculated as follows RTS = RFS – RRS

Figure 8.1: Extrapolation of model results to ship using the form factor given by Hughes

Figure 8.2: Graph of determining the form factor given by Prohaska

75 8.3

Procedure of Resistance Test

1. Firstly, the displacement of model is determined according to the full load and service condition of the ship. 2. Total displacement must be as same as calculated above when ballast weight placed into the model. 3. Before doing all the procedures above, model should be ballasted and confirmed its draft to make sure there is no trim and also to establish the location of center of gravity (LCG and VCG). 4. The center of gravity of the model must be obtained on the swing frame. 5. Then, mark the lines when it’s on stable condition. Put 200 g of weight, on bare swinging frame and mark again. 6. The model properly ballasted is then put onto the swinging frame at its location of gravity center. Then, the ballast weight is moved aft or forward until the swinging frame becomes stable to confirm the longitudinal gravity center (LCG). 7. Again, 200 g of weight was put on the swinging frame (without model) at one end and state the degrees of inclination. Make sure the model with the ballast weight having the same degrees with bare swinging frame inclination to confirm the vertical gravity center (VCG). 8. Model with full load condition then transferred into the tank to check the inclination (Taft = Tfwd) by using the water inclinometer. 9. After that, model is attached to the towing carriage. 10. The measurement of resistance is conducted in the towing tank with the different corresponding speed. 11. After finished running at one speed, the models continue to run with other speed after the water is calm. 12. Step (11) then will be repeated for four times with the difference speed. 13. This procedure is repeated when using model with bulbous bow.

76 Table 8.1: Model test protocol No. of run 1 2 3 4 5 6 7 8 9 10 11 12 13 14

8.4

Ship Speed VS (knots) 3 3.5 4 4.5 5 5.5 6 8 9 10 11 12 12.5 13

Corresponding Model Speed, Vm (m/s)

Fn

0.4880

0.1006

0.5693

0.1174

0.6507

0.1341

0.7320

0.1509

0.8133

0.1677

0.8947

0.1844

0.9760

0.2012

1.3013

0.2683

1.4640

0.3018

1.6267

0.3353

1.7893

0.3689

1.9520

0.4024

2.0333

0.4192

2.1147

0.4359

Method of Analysis Using International Towing Tank Test (ITTC) Friction Line 1957

77 The ITTC 1957 method is one of the methods used to calculate resistance and is based on Froude’s principal and based on the “ITTC 1957 model ship correlation line”. This is a popular method used to calculate the frictional resistance followed by the total resistance. In 1957, the ITTC (1959) decided that the line was given by the formula: CF =

0.075

( LogRN

− 2)

2

By adopting this as correlation line, CF is friction resistance coefficient for the ship. Figure 8.3 illustrates the ITTC 1957 method. The total resistance coefficients for the model are determined by the towing tests and from the formula:

C TM =

RTM 0.5.ρ mV m S m 2

Where RTM is the model resistance Vm is the speed of the model. Sm is the wetted surface of the model ρm is the density of the water in the towing tank.

78

Figure 8.3: Schematic representation of the ITTC 1957 method

The residuary resistance coefficients for the model is then calculated by CRM = CTM – CFM

According to the frictional resistance coefficient given by ITTC 1957 friction line, the residuary resistance coefficients for the ship at the same Froude number is the same as the model at corresponding Reynolds number. CRS = CRM

Using the ITTC 1957 model-ship correlation line as an extrapolator, the total resistance coefficients for smooth ship can be determined by: CTS = CFS + CRM

In addition, furthermore, that totals resistance coefficients for the ship is

79 CTS = CFS + CRM + CA

Where CA is incremental resistance coefficients for model ship correlation that taking into account and also the effect of the roughness of the ship. Usually, some model tanks are using the same CA coefficient for all types of ship, for example, CA= 0.0004. This value is obtained because it varies with the type and size of the ship. For a ship that use length as a parameter, the variation of the incremental resistance can be as follows:

(

C A = 0.006 LWLS + 100

)

−0.16

− 0.00205 which valid for

TF > 0.04 LWL

where TF = draft at fore perpendicular Therefore, resistance of the ship is:

(

RS = CTS 0.5.ρ S .V 2 S .S S

)

where VS is the ship speed and S S is the wetted surface of the ship, and ρS is the density of the seawater.

8.5

Sample of Calculation

80 The resistance experiment is conducted using the analysis of ITTC (1957) friction line. This example is based on 12 knots ship speed. After obtaining the model resistance from the tank test, the ship resistance can be calculated. Total model resistance, RTM = 46 .9054 N Procedure:-

1. Ship speed, VS = 12 knots = 0.5144 x12 = 6.1728 m / s

2. Model speed, VM =

=

VS

where λ = model scale

λ 6.1728 10

=1.9520 m / s

3. Reynolds number (model), Rn =

=

V M LWL M

υM 1.9520 x 2.3987 0.85409 x10 −6

= 5.4822 x10 6

at T=27°C, fresh water kinematics viscosity, υ M = 0.85409 x10 −6 m 2 / s

81 4. According to ITTC-1957 Friction Line, model is equivalent to flat-plate resistance coefficient,

C FOM =

=

0.075 [ ( log10 Rn ) − 2] 2

0.075

[log (5.4822 x10 ) − 2] 6

2

10

= 3.3396 x10 −3

5. Total resistance coefficient

CTM

=

=

RTM 0.5.ρ M .VM .S M 2

46 .9054 0.5 x996 .4 x1.9520 2 x1.5735

=1.5703 x10 −2

82 at T = 27°C, fresh water density, ρM = 996.4 kg/m

According to ITTC frictional line, model viscous coefficient is given by CVM = (1 + k )C FOM where (1+k) is the form factor which is determined at slow speed.

6. Model wave-making resistance coefficient, CTM

CWM

= (1 + k )C FOM + CWM

= (1.5703 x10 −2 ) − (1.2717 ) (3.3396 x10 −3 ) =1.1456 x10 −2

7. For ship resistance, its similar to the model calculation,

Reynolds number (ship), R N =

=

VS LWL S

υS 6.1728 x 23 .987 0.90331 x10 −6

=1.6392 x10 8

at T=27°C, salt water kinematics viscosity, υS = 0.90331 x10 −6 m 2 / s 8. According to ITTC-1957 friction line,

83

Ships are equivalent to flat-plate resistance coefficient, CVS = C FOS

C FOS =

0.075 [ ( log10 Rn ) − 2] 2

=

0.075

[log (1.6392 x10 ) − 2] 8

2

10

=1.9419 x10 −3

9. Since the model and ship have kinematics similarity, therefore CWS = CWM = 1.1456 x10 −2

10. Total ship resistance coefficient CTS

= CVS + CWS = (1.9419 +11 .456 ) x10 −3

=1.3398 x10 −2

11. Model-ship correlation factor, C A

84

The ratio of

TF 2.426 = = 0.1011 > 0.04 LWL 23 .987

(

Therefore, C A = 0.006 LWLS + 100

)

−0.16

− 0.00205

= 0.006 ( 23 .987 +100 )

−0.16

− 0.00205

= 7.2467 x10 −4

12. Final ship total coefficient, CTS

Final

= CTS +C A

= (133 .98 + 7.2467 ) x10 −4

=1.4123 x10 −2

at T = 27°C, salt water density, ρM = 1022.6 kg/m

13. Ship total resistance,

RTS

= CTS Final ( 0.5.ρ S .V 2 S .S S )

=1.4123 x10 −2 x (0.5 x1022 .6 x 6.1728

2

x157 .348 )

= 4.3294 x10 4 N

14. Effective power, PE

= RTS xVs

= 4.3294 x10 4 x6.1728 = 2.6725 x10 5 Watt

85 =

267 .25 kW 0.7457

= 358 .37 hp

8.6

Model Resistance Test Result

The results of experiment are stated as follows:-

86

Table 8.2: Model resistance result for bare hull

Model Speed, Vm (m/s)

0.6507 0.9760 1.3013 1.4640 1.6267 1.7893 1.9520 2.0333 2.1147

Ship Speed, Vs

Model

Ctm

Resistance,

Model Reynolds Number, Rn

-3

Froude

Cfm

Number,

Cvm = Cfm

Cwm

Fn

(x10-3)

1.8274

0.1341

4.1292

5.2511

3.8984

6.1893

2.7411

0.2012

3.8080

4.8427

13.466

10.1120

7.6171

3.6548

0.2683

3.6024

4.5811

30.360

9

17.5440

10.442

4.1116

0.3018

3.5229

4.4801

59.617

10

23.8094

11.478

4.5685

0.3353

3.4541

4.3925

70.859

11

32.0396

12.765

5.0253

0.3689

3.3935

4.3155

84.499

12

46.9054

15.703

5.4822

0.4024

3.3396

4.2470

114.56

12.5

57.8679

17.855

5.7106

0.4192

3.3148

4.2154

136.39

13

68.2631

19.473

5.9390

0.4359

3.2912

4.1854

152.88

Rtm (N)

(x10 )

1.8722

5.6410

6

4.6218

8

(knots) 4

(x106)

(x10-3)

(x10-4)

87

Table 8.3: Ship resistance result for bare hull

88

SHIP Ship

Cws =

Speed,

Cwm

Vs

Reynolds Number, Rns

Cfos = Cvs

Ship Cts -3

(knots)

(x10-4)

4

8

(x10-3)

(x10 )

Cts final

Resistance, Rts (N)

Pe (kW)

Pe(hp)

2.3778

3.188

-3

(x10 )

3.8984

(x10 ) 0.54639

2.2783

2.6682

3.3928

(x103) 1.1556

6

13.466

0.81958

2.1447

3.4913

4.2159

3.2310

9.9721

13.372

8

30.360

1.0928

2.0568

5.0928

5.8175

7.9260

32.617

43.739

9

59.617

1.2294

2.0224

7.9842

8.7088

15.017

69.523

93.229

10

70.859

1.3660

1.9924

9.0782

9.8029

20.869

107.35

143.953

11

84.499

1.5026

1.9658

10.416

11.140

28.696

162.37

217.742

12

114.56

1.6392

1.9419

13.398

14.123

43.294

267.25

358.376

12.5

136.39

1.7075

1.9309

15.570

16.295

54.201

348.51

467.355

13

152.88

1.7758

1.9204

17.208

17.933

64.516

431.43

578.553

89

Table 8.4: Form factor result for bare hull

Form factor (1+k) Model

Ship

Speed,

Speed,

Vm

Vs

(m/s) 0 0.4880 0.5693 0.6507 0.7320 0.8133 0.8947

(knots) 0 3 3.5 4 4.5 5 5.5

Model

Ctm

Rn

Cfm

Resistance,

Fn -3

6

Rtm (N)

(x10 )

(x10 )

0 1.0071 1.5162 1.7997 2.2898 2.9395 3.6264

0 5.39 5.97 5.42 5.45 5.67 5.78

0 1.37 1.60 1.83 2.06 2.28 2.51

Fn^4/Cfm

Ctm/Cfm

0 0.0234 0.0447 0.0784 0.1286 0.2002 0.2987

1.2309 1.4060 1.3132 1.3521 1.4359 1.4919

-3

(x10 ) 0 0.1006 0.1174 0.1341 0.1509 0.1677 0.1844

0 4.38 4.24 4.13 4.03 3.95 3.87

90

Ctm/Cfm Against Fn4/Cfm y = -0.3788x2 + 0.8508x + 1.2717

1.6 1.4

Ctm/Cfm

1.2 1 Bare hull

0.8

Poly. (Bare hull)

0.6 0.4 0.2 0 0

0.05

0.1

0.15

0.2

Fn4/Cfm

0.25

0.3

0.35

91

Graph 8.1: Form factor for bare hull

M o d e l T o ta l R e s is ta n c e A g a in s t M o d e l S p e e d 80 70 Model Total Resistance, Rtm (N)

60 50 40

M odel

30 20 10 0 0

0 .5

1

1 .5

2

M o d e l S p e e d , V m (m / s)

2 .5

92

Graph 8.2: Total resistance of model against model speed for bare hull

S h ip R e s is t a n c e A g a in s t S p e e d 70 60

Ship Total Resistance (kN)

50 40

S h ip R e sista n c e

30 20 10 0 0

2

4

6

8

10

S h i p S p e e d (k n o t s )

12

14

93

Graph 8.3: Ship resistance of model against ship speed for bare hull

P o w e r ( H P ) A g a in t s S p e e d ( k n o t s ) 700 600 500 Power (Hp)

400

S h ip p o w e r

300 200 100 0 0

2

4

6

8

10

S h ip S p e e d (k n o ts)

12

14

94

Graph 8.4: Ship power against ship speed for bare hull

Table 8.5: Model resistance result for hull form with bulb

95

Model Speed, Vm (m/s)

0.6507 0.9760 1.3013 1.4640 1.6267 1.7893 1.9520 2.0333 2.1147

Ship Speed, Vs (knots) 4

Model

Ctm

Resistance, Rtm (N)

Model Reynolds Number, Rn

-3

(x10 )

(x106)

Froude

Cfm

Number, Fn

(x10-3)

Cvm = Cfm (x10-3)

Cwm (x10-4)

2.02504

6.1016

1.8274

0.1341

4.1292

5.7091

3.9258

6

4.69976

6.2937

2.7411

0.2012

3.8080

5.2650

10.287

8

9.96607

7.5072

3.6548

0.2683

3.6024

4.9806

25.266

9

15.4475

9.1940

4.1116

0.3018

3.5229

4.8708

43.232

10

22.5416

10.867

4.5685

0.3353

3.4541

4.7756

60.916

11

31.3811

12.503

5.0253

0.3689

3.3935

4.6919

78.112

12

46.0709

15.424

5.4822

0.4024

3.3396

4.6173

108.07

12.5

57.0176

17.592

5.7106

0.4192

3.3148

4.5830

130.09

13

68.947

19.668

5.9390

0.4359

3.2912

4.5503

151.18

96

Table 8.6: Ship resistance result for hull form with bulb

97

Ship Ship

Cws =

Speed,

Cwm

Vs (knots)

Reynolds Number,

Ship Cfos = Cvs

Cts final

Rns

Resistance, Rts (N)

-3

(x10-4)

Cts

(x10 )

-3

(x10 )

Pe (kW)

Pe(hp)

-3

(x10 )

(x108)

(x103)

4

3.9258

0.54639

2.2783

2.6709

3.3956

1.1566

2.3798

3.1913

6

10.287

0.81958

2.1447

3.1734

3.8980

2.9874

9.2202

12.3643

8

25.266

1.0928

2.0568

4.5834

5.3081

7.2320

29.761

39.9094

9

43.232

1.2294

2.0224

6.3457

7.0703

12.192

56.443

75.6896

10

60.916

1.3660

1.9924

8.0840

8.8086

18.752

96.460

129.3533

11

78.112

1.5026

1.9658

9.7769

10.502

27.051

153.06

205.2589

12

108.07

1.6392

1.9419

12.749

13.473

41.302

254.95

341.8888

12.5

130.09

1.7075

1.9309

14.940

15.665

52.106

335.04

449.2879

13

151.18

1.7758

1.9204

17.038

17.763

63.905

427.35

573.0724

98

Form factor (1+k) Model

Ship

Speed,

Speed,

Vm

Vs

(m/s) 0.4880 0.5693 0.6507 0.7320 0.8133 0.8947

(knots) 3 3.5 4 4.5 5 5.5

Model

Ctm

Rn

Cfm

Resistance, Rtm (N) 1.1549 1.5855 2.0250 2.6795 3.2618 4.0044

Fn -3

(x10 ) 6.1866 6.2395 6.1016 6.3791 6.2899 6.3818

6

(x10 ) 1.3705 1.5990 1.8274 2.0558 2.2842 2.5127

Fn^4/Cfm

Ctm/Cfm

0.023372 0.044711 0.078394 0.128605 0.200196 0.2987

1.411685 1.470215 1.477673 1.582171 1.593328 1.647457

-3

(x10 ) 0.1006 0.1174 0.1341 0.1509 0.1677 0.1844

hull form with bulb

4.3824 4.2439 4.1292 4.0319 3.9477 3.8737

Table 8.7: Form factor result for

99

C tm/C fm Ag ain st F n 4/C fm y = -2 .7 6 5 32 +x 1 .6 9 8 x + 1 .3 8 2 6

1 .8

1 .5

Ctm/Cfm

1 .2

B u lb

0 .9

P o ly. (B u lb )

0 .6

0 .3

0 0

0 .0 5

0 .1

0 .1 5

0 .2

F n 4/C fm

0 .2 5

0 .3

0 .3 5

100

Graph 8.5: Form factor for hull with bulb

M o d e l T o ta l R e s is ta n ce A g a in s t M o d e l S p e ed 80

Model Total Resistance, Rtm (N)

70 60 50

M o d e l (B u lb )

40 30 20 10 0 0

0.5

1

1.5

M o d e l S p e e d (m /s )

2

2.5

101

Graph 8.6: Total resistance of model against model speed for hull form with bulb

S h ip re s is ta n c e a g a in s t S h ip s p e e d 70 60

Ship resistance (kN)

50 40 S h ip re sista n c e 30 20 10 0 0

2

4

6

8

S p e e d (k n o ts)

10

12

14

102

Graph 8.7: Ship resistance against ship speed for hull form with bulb

S h ip p o w e r a g a in s t S h ip s p e e d 650 600 550 500

Ship power (Hp)

450 400 350

S h ip p o w e r

300 250 200 150 100 50 0 0

2

4

6

8

S p e e d (k n o ts )

10

12

14

103

Graph 8.8: Ship power against ship speed for hull form with bulb

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