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.

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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:

RT = 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

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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

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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.

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Table 8.1: Model test protocol

No. of

run

Ship Speed

VS (knots)

Corresponding Model Speed, Vm

(m/s)Fn

1 3 0.4880 0.1006

2 3.5 0.5693 0.1174

3 4 0.6507 0.1341

4 4.5 0.7320 0.1509

5 5 0.8133 0.1677

6 5.5 0.8947 0.1844

7 6 0.9760 0.2012

8 8 1.3013 0.2683

9 9 1.4640 0.3018

10 10 1.6267 0.3353

11 11 1.7893 0.3689

12 12 1.9520 0.4024

13 12.5 2.0333 0.4192

14 13 2.1147 0.4359

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

Line 1957

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:

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:

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.

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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:

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CTS = CFS + CRM

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

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:

which valid for

where TF = draft at fore perpendicular

Therefore, resistance of the ship is:

where is the ship speed and is the wetted surface of the ship, and is the density

of the seawater.

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8.5 Sample of Calculation

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,

Procedure:-

1. Ship speed,

2. Model speed, where λ = model scale

3. Reynolds number (model),

80

at T=27°C, fresh water kinematics viscosity,

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

resistance coefficient,

5. Total resistance coefficient

81

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

According to ITTC frictional line, model viscous coefficient is given by

where (1+k) is the form factor which is determined at slow speed.

6. Model wave-making resistance coefficient,

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

Reynolds number (ship),

82

at T=27°C, salt water kinematics viscosity,

8. According to ITTC-1957 friction line,

Ships are equivalent to flat-plate resistance coefficient,

9. Since the model and ship have kinematics similarity, therefore

10. Total ship resistance coefficient

83

11. Model-ship correlation factor,

The ratio of

Therefore,

12. Final ship total coefficient,

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

13. Ship total resistance,

14. Effective power,

84

8.6 Model Resistance Test Result

The results of experiment are stated as follows:-

85

Table 8.2: Model resistance result for bare hull

Model

Model

Speed,

Vm (m/s)

Ship

Speed,

Vs

(knots)

Model

Resistance,

Rtm (N)

Ctm

(x10-3)

Reynolds

Number, Rn

(x106)

Froude

Number,

Fn

Cfm

(x10-3)

Cvm =

Cfm

(x10-3)

Cwm

(x10-4)

0.6507 4 1.8722 5.6410 1.8274 0.1341 4.1292 5.2511 3.8984

0.9760 6 4.6218 6.1893 2.7411 0.2012 3.8080 4.8427 13.466

1.3013 8 10.1120 7.6171 3.6548 0.2683 3.6024 4.5811 30.360

1.4640 9 17.5440 10.442 4.1116 0.3018 3.5229 4.4801 59.617

1.6267 10 23.8094 11.478 4.5685 0.3353 3.4541 4.3925 70.859

1.7893 11 32.0396 12.765 5.0253 0.3689 3.3935 4.3155 84.499

1.9520 12 46.9054 15.703 5.4822 0.4024 3.3396 4.2470 114.56

2.0333 12.5 57.8679 17.855 5.7106 0.4192 3.3148 4.2154 136.39

2.1147 13 68.2631 19.473 5.9390 0.4359 3.2912 4.1854 152.88

86

Table 8.3: Ship resistance result for bare hull

SHIP

Ship

Speed,

Vs

(knots)

Cws =

Cwm

(x10-4)

Reynolds

Number,

Rns

(x108)

Cfos =

Cvs

(x10-3)

Cts

(x10-3)

Cts final

(x10-3)

Ship

Resistance,

Rts (N)

(x103)

Pe (kW) Pe(hp)

4 3.8984 0.54639 2.2783 2.6682 3.3928 1.1556 2.3778 3.188

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

87

Table 8.4: Form factor result for bare hull

Form factor (1+k)

Model

Speed,

Vm

(m/s)

Ship

Speed,

Vs

(knots)

Model

Resistance,

Rtm (N)

Ctm

(x10-3)

Rn

(x106)Fn

Cfm

(x10-3)Fn^4/Cfm Ctm/Cfm

0 0 0 0 0 0 0 0

0.4880 3 1.0071 5.39 1.37 0.1006 4.38 0.0234 1.2309

0.5693 3.5 1.5162 5.97 1.60 0.1174 4.24 0.0447 1.4060

0.6507 4 1.7997 5.42 1.83 0.1341 4.13 0.0784 1.3132

0.7320 4.5 2.2898 5.45 2.06 0.1509 4.03 0.1286 1.3521

0.8133 5 2.9395 5.67 2.28 0.1677 3.95 0.2002 1.4359

0.8947 5.5 3.6264 5.78 2.51 0.1844 3.87 0.2987 1.4919

88

Ctm/Cfm Against Fn4/Cfm

y = -0.3788x2 + 0.8508x + 1.2717

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35

Fn4/Cfm

Ctm

/Cfm

Bare hull

Poly. (Bare hull)

Graph 8.1: Form factor for bare hull

89

Model Total Resistance Against Model Speed

0

10

20

30

40

50

60

70

80

0 0.5 1 1.5 2 2.5

Model Speed, Vm (m/s)

Mod

el T

otal

Res

ista

nce,

Rtm

(N

) Model

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

90

Ship Resistance Against Speed

0

10

20

30

40

50

60

70

0 2 4 6 8 10 12 14

Ship Speed (knots)

Ship

Tot

al Re

sistan

ce (k

N) Ship Resistance

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

91

Power (HP) Againts Speed (knots)

0

100

200

300

400

500

600

700

0 2 4 6 8 10 12 14

Ship Speed (knots)

Powe

r (Hp

)

Ship power

Graph 8.4: Ship power against ship speed for bare hull

92

Table 8.5: Model resistance result for hull form with bulb

Model

Model

Speed,

Vm (m/s)

Ship

Speed,

Vs

(knots)

Model

Resistance,

Rtm (N)

Ctm

(x10-3)

Reynolds

Number, Rn

(x106)

Froude

Number,

Fn

Cfm

(x10-3)

Cvm =

Cfm

(x10-3)

Cwm

(x10-4)

0.6507 4 2.02504 6.1016 1.8274 0.1341 4.1292 5.7091 3.9258

0.9760 6 4.69976 6.2937 2.7411 0.2012 3.8080 5.2650 10.287

1.3013 8 9.96607 7.5072 3.6548 0.2683 3.6024 4.9806 25.266

1.4640 9 15.4475 9.1940 4.1116 0.3018 3.5229 4.8708 43.232

1.6267 10 22.5416 10.867 4.5685 0.3353 3.4541 4.7756 60.916

1.7893 11 31.3811 12.503 5.0253 0.3689 3.3935 4.6919 78.112

1.9520 12 46.0709 15.424 5.4822 0.4024 3.3396 4.6173 108.07

2.0333 12.5 57.0176 17.592 5.7106 0.4192 3.3148 4.5830 130.09

2.1147 13 68.947 19.668 5.9390 0.4359 3.2912 4.5503 151.18

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Table 8.6: Ship resistance result for hull form with bulb

Ship

Ship

Speed,

Vs

(knots)

Cws =

Cwm

(x10-4)

Reynolds

Number,

Rns

(x108)

Cfos = Cvs

(x10-3)

Cts

(x10-3)

Cts final

(x10-3)

Ship

Resistance,

Rts (N)

(x103)

Pe (kW) Pe(hp)

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

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Table 8.7: Form factor result for hull form with bulb

Form factor (1+k)

Model

Speed,

Vm

(m/s)

Ship

Speed,

Vs

(knots)

Model

Resistance,

Rtm (N)

Ctm

(x10-3)

Rn

(x106)Fn

Cfm

(x10-3)Fn^4/Cfm Ctm/Cfm

0.4880 3 1.1549 6.1866 1.3705 0.1006 4.3824 0.023372 1.411685

0.5693 3.5 1.5855 6.2395 1.5990 0.1174 4.2439 0.044711 1.470215

0.6507 4 2.0250 6.1016 1.8274 0.1341 4.1292 0.078394 1.477673

0.7320 4.5 2.6795 6.3791 2.0558 0.1509 4.0319 0.128605 1.582171

0.8133 5 3.2618 6.2899 2.2842 0.1677 3.9477 0.200196 1.593328

0.8947 5.5 4.0044 6.3818 2.5127 0.1844 3.8737 0.2987 1.647457

95

Ctm/Cfm Against Fn4/Cfm

y = -2.7653x2 + 1.698x + 1.3826

0

0.3

0.6

0.9

1.2

1.5

1.8

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35

Fn4/Cfm

Ctm

/Cfm Bulb

Poly. (Bulb)

Graph 8.5: Form factor for hull with bulb

96

Model Total Resistance Against Model Speed

0

10

20

30

40

50

60

70

80

0 0.5 1 1.5 2 2.5

Model Speed (m/s)

Mod

el T

otal

Res

ista

nce,

Rtm

(N)

Model (Bulb)

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

97

Ship resistance against Ship speed

0

10

20

30

40

50

60

70

0 2 4 6 8 10 12 14

Speed (knots)

Ship

resi

stan

ce (k

N)

Ship resistance

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

98

Ship power against Ship speed

0

50

100

150

200

250

300

350

400

450

500

550

600

650

0 2 4 6 8 10 12 14

Speed (knots)

Ship

pow

er (H

p)

Ship power

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

99

100