chapter viii model resistance test techniques
TRANSCRIPT
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),
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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
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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),
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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
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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,
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8.6 Model Resistance Test Result
The results of experiment are stated as follows:-
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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100