18104299 chapter vi resistance prediction
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CHAPTER VI
RESISTANCE PREDICTION
6.1 Introduction
Nowadays there are many techniques which can be used in determining ship
resistance. There are four methods which are:
i) Model Experiments
ii) Standard Series Of Experiments
iii) Statistical Methods
iv)
Diagrams
Model experiment method is the most widely used and applied among others
since it uses models with similar characteristic of the ship and applicable to any
kinds of ships. Meanwhile the other three methods can be used for prediction only
because they have limitation and can be used only for a ship that has similar
particulars to such group. In this project, only five methods are chosen. These
methods are Van Ootmerssen’s Method, Holtrop’s & Mennen’s Method, Cedric
Ridgely Nevitt’s Method, DJ Doust’s Method and Diagram method.
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Figure 6.2: Wave system at fore and aft shoulder
3. The summation of viscous resistance and wave-making resistance
representing the components of the total resistance.
The range of parameters for the coefficients of the basic expression is as
follow:
Table 6.1: Limitations for Van Oortmerssen’s Method
Parameter Limitations
Length of water line, LWL 8 to 80 m
Volume, 5 to 3000 m³
Length/Breadth, L/B 3 to 6.2Breadth/Draft, B/T 1.9 to 4.0
Prismatic coefficient, CP 0.50 to 0.73
Midship coefficient, Cm 0.70 to 0.97
Longitudinal center of buoyancy, LCB -7% L to 2.8% L
½ entrance angle, ½ ie 10º to 46º
Speed/length, V/√L 0 to 1.79
Froude number, Fn 0 to 0.50
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Van Oortmerssen’s suggested that the final form of the resistance equation is
represented by the summation of viscous resistance and wave-making resistance as
follow:
2
2
2
4
2
32
9/1
1
2log2
075.0
cos
sin2
222
Rn
SV
FneC
FneC eC eC R
mFn
mFnmFnmFn
T
where,
1. miiiWLiWLiWLi
WLi pi piiiii
C d T Bd T Bd C d C d B Ld
B Ld C d C d LCBd LCBd d C
11,
2
10,9,
2
8,7,
2
6,
5,
2
4,3,
2
2,1,0,
3
///
/10
2. 2/
1. b
pC bm or for small ships this can be presented by:
1976.214347.0
pC m
3. WLC is a parameter for angle of entrance of the load waterline, i e, where
B LiC WLeWL /
4. Approximation for wetted surface area is represented by:
3/133/2 5402.0223.3 V LV S WL
Table 6.2 below shows an allowance for frictional resistance and table 5.3
shows the values of regression coefficient given by Van Oortmerssen’s.
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Table 6.2: Allowance for frictional resistance
Table 6.3: Values of regression coefficient
i 1 2 3 4
di,0 79.32134 6714.88397 -908.44371 3012.14549
di,1 -0.09287 19.83000 2.52704 2.71437
di,2 -0.00209 2.66997 -0.35794 0.25521
di,3 -246.46896 -19662.02400 755.186600 -9198.80840
di4 187.13664 14099.90400 -48.93952 6886.60416
di,5 -1.42893 137.33613 -9.86873 -159.92694
di,6 0.11898 -13.36938 -0.77652 16.23621
di,7 0.15727 -4.49852 3.79020 -0.82014
di,8 -0.00064 0.02100 -0.01879 0.00225
di,9 -2.52862 216.44923 -9.24399 236.37970
di,10 0.50619 -35.07602 1.28571 -44.17820
di,11 1.62851 -128.72535 250.64910 207.25580
Allowance for ∆ CF
Roughness of hull 0.00035
Steering resistance 0.00004
Bilge Keel Resistance 0.00004
Air resistance 0.00008
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6.3 Holtrop’s & Mennen’s Method
This resistance prediction method is one of the techniques widely
used in prediction of resistance of displacement and semi-displacement vessels. Like
all methods, however, this technique is limited to a suitable range of hull form
parameters. This algorithm is designed for predicting the resistance of tankers,
general cargo ships, fishing vessels, tugs, container ships and frigates. The
algorithms implements are based upon hydrodynamic theory with coefficients
obtained from the regression analysis of the results of 334 ship model tests.
In their approach to establishing their formulas, Holtrop and Mennen
assumed that the non-dimensional coefficient represents the components of
resistance for a hull form. It might be represented by appropriate geometrical
parameters, thus enabling each component to be expressed as a non-dimensional
function of the sealing and the hull form. The range of parameters for which the
coefficients of the basic expressions are valid is shown as following:
Table 6.4: Limitation for Holtrop and Mennen’s method
Ship type Max
Froude
no.
Cp L/B B/T
Min Max Min Max Min Max
Tankers, bulk carries 0.24 0.73 0.85 5.1 7.1 2.4 3.2
Trawlers, coasters, tugs 0.38 0.55 0.65 3.9 6.3 2.1 3.0
Containerships, destroyer types 0.45 0.55 0.67 6.0 9.5 3.0 4.0
Cargo liners 0.30 0.56 0.75 5.3 8.0 2.4 4.0
RORO ships, car ferries 0.35 0.55 0.67 5.3 8.0 3.2 4.0
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The step by step procedures are shown below to calculate resistance in order
to predict the ship power.
Calculate:
1. Frictional Resistance, Cak C SV R F F 12/1 2
2. Wetted Surface,
B BT WP
M B
M C AC T B
C C C BT LS /38.2
3696.0/003467.0
2862.04425.04530.02
5.0
3. Form Factor
6906.0
92497.022284.0
0225.0152145.0
95.0//93.01
LCBC
C L B LT k
P
P R
where, 06.01 P R C L L
4. Correlation Factor, 00205.01000006.0 16.0 LCa
5. Frictional Resistance Coefficient, 22
075.0
LogRn
C F
6. Residuary resistance, 22
9.01 cos
Fnm Fnm R Ce R
where,
32
3/1
1
984388.68673.13
07981.8/79323.4/75254.1/0140407.0
P P
P
C C
C L B LT Lm
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2/1.022 69385.1
Fn
P eC m
B LC P /03.0446.1
7. Therefore, total resistances are, R F T R R R
6.4 Cedric Ridgely Nevitt’s Method
This method is developed for a model test with trawler hull forms having
large volumes for their length. In this method it covers a range of prismatic
coefficients from 0.55 to 0.70 and displacement-length ratios from 200 to 500, their
residuary resistance contours and wetted surface coefficients have been plotted in
order to make resistance estimates possible at speed-length ratios from 0.7 to 1.5.
The changing of beam-draft ratio also takes into account the effect on total
resistance.
Table 6.5: Limitations for Cedric Ridgely Nevitt’s method
Parameter Limitations
Length/Breadth, L/B 3.2 – 5 .0
Breadth/Draft , B/T 2.0 - 3.5
Vulome/length, 301.0/ L 200 – 500
Prismatic coefficient, CP 0.55 - 0.70
Block coefficient, CB 0.42 - 0.47
Speed/length, V/√L 0.7 - 1.5
Longitudinal center of buoyancy, LCB 0.50% - 0.54% aft of FP
½ entrance angle , ½ α˚e 7.0˚ - 37.4˚
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This method is applicable to fishing vessels, tugs, fireboats, icebreakers,
oceanographic ships, yachts and other short and beamy ships falling outside the
range of the Taylor Series or Series 60. Procedures of calculating ship resistances
using this method are as follows:
Calculate:
i) Parameter of V/L for every speed.
ii) Parameter of ∆/(0.01 L) ³
Residuary resistance coefficient CR then can be determined from the
graph ∆ / (0.01L ) ³ against prismatic CP at every V/L.
iii) Parameter of B/T ratio
The wetted surface coefficient, LS / value can be determined from
the graph of wetted surface coefficient against prismatic coefficient Cp and
calculated B/T ratio
iv) The wetted surface area from the wetted surface coefficient LS /
v) Reynolds Number,
UL Rn
vi) Frictional resistance coefficient, 22
075.0
LogRn
C F
vii)
Total resistance, 22/ SV C C R F RT
After all parameters are calculated, correction needs to be carried out with the total
resistance according to the B/T ratio. The correction can be determined from the
graph B/T correction factor against V/L.
viii)
Calculate the real total resistance coefficient, x R R T T '
correction
factor
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6.5 DJ. Doust’s Method
DJ. Doust’s Method is used for calculating resistance based on the resistancetests of about 130 trawler models carried out at the National Laboratory in
Teddington, England. The results of the tests were transformed into a trawler
standard length, between perpendiculars, of 61m (200ft). (Fyson J. 1985) There are
sixs parameters used in the early stage of design. Those parameters are L/B, B/T, CM,
CP, LCB and ½ α˚e.
Tables 6.6: Limitations for DJ Doust’s Method
This method is relevant to be used in predicting the resistance for fishing
vessels. However, correction needs to be taken into consideration for the ships have
different length compared to the standard ship length (200ft). Procedures of
calculation for DJ Doust’s Method are as follows:
i)
Calculate the parameter required to determine factors used to calculate
residuary resistance for the ship having standard length, 200 ft. These
parameters are L/B, B/T and V/√L.
Parameter Limitations
Length/Breadth, L/B 4.4 – 5.8
Breadth/Draft, B/T 2.0 – 2.6
Midship coefficient, CM 0.81 – 0.91
Prismatic coefficient, CP 0.6 – 0.7
Longitudinal center of buoyancy, LCB 0% - 6% aft of midship
½ entrance angle, ½ α˚e 5˚ - 30˚
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ii) Determine three factors used to calculate residuary resistance using
graph given. These three factors are T BCp f F /,1 ,
LCBCp f F ,2 and B LCp f F /,2/1,'
3
iii)
Calculate 6 F using .875.01006 mC a F The parameter ‘a’ is a
function V/√L and given by Table 6.7
iv) Calculate residuary resistance, 6'
321200 F F F F C R
v) Calculate,3/2
1/0935.0 S S
vi)
Calculate, LV L /05.1'
vii) Calculate Froude’s skin friction correction,
8
3'6
2'4'
175.0' 10/22.110/77.210/29.00196.0 L L LSLSFC
viii)
Calculate, 3/1
2001 /5.152 SFC x
ix) Calculate residuary resistance for new ship, 1200 Rnew R C C
x) Calculate total resistance,
L
V C R
new R
T
2
Tables 6.7: Values parameter ‘a ’
V/√L a
0.8 -0.045
0.9 -0.053
1.0 -0.031
1.1 -0.035
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6.6 Diagram Method
This method represents the usage of a given chart to obtain the necessary
power of the vessel. It’s also one of the method used to compare the result with the
other method. Usually the values are taken directly from the chart and will be used as
comparison with the other. This chart shows the curves for displacement and beam of
a typical fishing vessel from 10 to 70m length (33 to 230 ft). (Appendix C) The solid
line in this chart is for the optimum vessel and indicates how the necessary engine
power can be reduced if the hull shape is favorably designed. (Fyson J. 1985) Dotted
lines show the corresponding curve for average fishing vessels. Nevertheless, it alsohas limitations on the usage of this graph, they are:
Table 6.8: Limitation of Diagram method
Parameter Limitation
Length (m) 10 – 70 m
Beam (m) 0 – 10 m
Displacement (m³) 0 – 3000
Engine in SHP (hp) 0 – 1500
Speed (knots) 7 – 13.5
6.7 Resistance prediction of trawler
The predictions on this trawler are done only by four methods. For all the
techniques above, the method suitable for this trawler specifications are Van
Oortmerssen’s Method, Holtrop and Mennen’s Method, Cedric Ridgely Nevitt’sMethod and Diagram method. The diagram and Cedric Ridgely Nevitt’s method are
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Table 6.10: Effective power prediction, PE
Table 6.11: Summary of result (all)
Power Prediction, PE (kW)
Speed
(knots)
Cedric
Ridgely
Nevitt’s
method
Chart
(Average)
Chart
(Optimum)
Holtrop &
Mennen’s
Method
Van
Oortmerssen’s
Method
4 - - - 3.655 3.19
6 - - - 11.935 11.855
7 - - - 19.36 19.765
8 - - - 30.7 31.095
9 - - - 48.89 77.11
10 82.61 153.12 91.88 71.26 121.18
11 137.28 290.94 183.75 104.68 147.15
12 229.74 - - 196.92 302.17
12.5 - - - 439.32 441.65
13 - - - 700.735 609.37
Differences (%)
Speed
(knots)
Towing
tank (Hp)
Cedric
Ridgely
Nevitt’s
method
Chart
(Average)
Chart
(Optimum)
Holtrop
&
Mennen’s
Method
Van
Oortmerssen’s
Method
4 6.71 - - - 14.61 06 28.14 - - - 10.73 11.34
8 92.03 - - - 29.81 28.95
9 196.15 - - - 47.56 17.29
10 302.87 42.62 6.37 36.18 50.52 15.96
11 458.12 36.96 33.61 15.61 51.93 32.42
12 754.00 35.9 - - 45.1 15.93
12.5 983.29 - - - 6 5.5
13 1217.24 - - - 21.11 5.33
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Effective Power Against Ship Speed
0
100
200
300
400
500
600
700
800
0 2 4 6 8 10 12 14
Speed (knots)
PE
(HP)
Cedric Ridgely Nevitt’s
Chart (Average)
Chart (Optimum)
Holtrop
Van Oortmerssen’s
Tank Test
Total Resistance Against Ship Speed
0
10
20
30
40
50
60
70
80
90
0 2 4 6 8 10 12 14
Speed (knots)
Rt(kN)
Cedric Ridgely
Nevitt’s
Chart
(Average)
Chart
(Optimum)
Holtrop
Van
Oortmerssen’s
Tank test
Graph 6.1: Comparison of effective power between various methods and tank test
Graph 6.2: Comparison of total resistance between various methods and tank test
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6.8 Discussion on prediction result
The prediction of resistance for trawler hull form shows an acceptable value
compared to the towing tank test result. All methods showed that resistance will
increase gradually with increasing speed. In a certain speed, there is no result on that
value. This condition occurs because parameter of the vessel can only measure at that
certain speed. If the value is higher than the particular speed, the resistance cannot be
measured, but its enough to see the comparison between the resistance test and
prediction value. The comparison can be clearly seen on Graph 6.2. Differences on
percentage are not to significant comparing to the tank test result and it still can beaccepted.
6.8.1 Van Oortmerssen’s method
Usually, the Van Oortmerssen’s methods are useful for estimating the
resistance of small ships such as trawlers and tugs. In general, Malaysian fishing
vessels are short and beamy whilst their draught is relatively low. These kinds of
vessel are normally located in shallow river estuaries. These factors will result in a
relatively low breadth-draught ratio and block coefficient. According to the Graph
6.2, the results of the tank test are nearly close to this method. It’s also shows thelower percentage difference on the prediction value. Therefore Van Oortmerssen’s
method is suitable because the hull characteristics are covered by this method.
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6.8.2 Holtrop and Mennen’s method
Generally, Holtrop and Mennen’s method is suitable for a small vessel andthis algorithm is designed for predicting the resistance of fishing vessels and tugs.
However, with this method, there are still errors exist in the final result. Therefore,
all the factors below are considered to determine the degree of uncertain parameter:
i) Increasing in Froude number which will create a greater residuary
resistance (wave making resistance, eddy resistance, breaking waves
and shoulder wave) is a common phenomenon in small ships. As a
result, errors in total resistance increase.
ii) Small vessels are easily influenced by environmental condition such
as wind and current during operational.
iii) For smaller ship, the form size and ship type have a great difference.
This method is only limited to the Froude number below 0.5, (Fn < 0.5) and
also valid for TF / LWL > 0.04. There is correlation allowance factor in model ship
that will affect some 15% difference in the total resistance and the effective power.
This method is also limited to hull form resembling the average ship described by the
main dimension and form coefficients used in the method. Graph 6.2 shows the
difference is slightly large value but according to the Table 6.11, after 12 knots, the
percentage will reduce. The critical range of speed between 8 to 11 knots shows the
dissimilarity is because of the above reason.
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6.8.3 Cedric Ridgely Nevitt’s Method
In this method, the resistances are base on the limitation of the parameter.
The acceptable speed that can be used by these methods are from 7 to 13 knots.
Referring to the calculation, this method also used the displacement-length ratio for
measuring the residuary resistance from the chart. The error occurs when
determining the residuary resistance and the correction factor of breadth-depth ratio
from the graph given. The actual value cannot acquire because the prediction is only
limited to a certain value. Therefore, an affected of residuary resistance also affect
the total resistance of the ship.
6.8.4 Diagram method
This method can be used for preliminary design of new fishing vessel based
on the requirement of that new vessel. In this analysis, the shaft horse power value
can be used use for reference to design new ship. Based on the Graph 6.2, the tank
test curve is in the middle of the optimum and average value. Therefore, it is on the
range of selected engine power and can be accepted for the preliminary design.