47059117 resistance prediction
TRANSCRIPT
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.
43
6.2 Van Oortmerssen’s Method
This method is useful for estimating the resistance of small ships such as
trawlers and tugs. In this method, the derivation of formula by G. Van Ootmerssen is
based on the resistance and propulsion of a ship as a function of the Froude number
and Reynolds number. The constraint of this formula, also based on other general
parameters for small ships such as trawlers and tugs that are collected from random
tank data. The method was developed through a regression analysis of data from 93
models of tugs and trawlers obtained by the MARIN. Besides, few assumptions were
made for predicting resistance and powering of small craft such as follows:
1. According to the Figure 6.1 there are positive and negative pressure
peak distributions for the hull surface. For the ship hull scope, there
are high pressure at the bow and stern, while in the middle it becomes
a low pressure.
Figure 6.1: Pressure distribution around a ship hull
2. Small ship can be said to have a certain characteristics such as the
absence of a parallel middle body, so the regions of low pressure and
the wave system of fore and after shoulder coincide and consequently
the pressure distribution is illustrated as in figure 6.2.
44
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 LimitationsLength of water line, LWL 8 to 80 mVolume,∇ 5 to 3000 m³Length/Breadth, L/B 3 to 6.2Breadth/Draft, B/T 1.9 to 4.0Prismatic coefficient, CP 0.50 to 0.73Midship coefficient, Cm 0.70 to 0.97Longitudinal center of buoyancy, LCB -7% L to 2.8% L½ entrance angle, ½ ie 10º to 46ºSpeed/length, V/√L 0 to 1.79Froude number, Fn 0 to 0.50
45
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
24
232
9/11
2l o g2
0 7 5.0
c o s
s i n2
222
R n
S V
F neC
F neCeCeCRm F n
m F nm F nm F n
T
ρ
where,
1.( ) ( ) ( ) miiiWLiWLiWLi
WLipipiiiii
CdTBdTBdCdCdBLd
BLdCdCdLCBdLCBddC
++++++
++++++=
11,2
10,9,2
8,7,2
6,
5,2
4,3,2
2,1,0,3
///
/10
2.( )2/
1.b
pCbm −−= or for small ships this can be presented by:
( )1976.214347.0 −−= pCm
3. WLC is a parameter for angle of entrance of the load waterline, ie, where
46
( )BLiC WLeWL /=
4. Approximation for wetted surface area is represented by:
3/133/2 5402.0223.3 VLVS 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.
Table 6.2: Allowance for frictional resistance
Table 6.3: Values of regression coefficient
i 1 2 3 4di,0 79.32134 6714.88397 -908.44371 3012.14549di,1 -0.09287 19.83000 2.52704 2.71437di,2 -0.00209 2.66997 -0.35794 0.25521di,3 -246.46896 -19662.02400 755.186600 -9198.80840di4 187.13664 14099.90400 -48.93952 6886.60416di,5 -1.42893 137.33613 -9.86873 -159.92694di,6 0.11898 -13.36938 -0.77652 16.23621di,7 0.15727 -4.49852 3.79020 -0.82014di,8 -0.00064 0.02100 -0.01879 0.00225di,9 -2.52862 216.44923 -9.24399 236.37970di,10 0.50619 -35.07602 1.28571 -44.17820di,11 1.62851 -128.72535 250.64910 207.25580
Allowance for ∆ CF
Roughness of hull 0.00035Steering resistance 0.00004Bilge Keel Resistance 0.00004Air resistance 0.00008
47
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/TMin 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
48
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
The step by step procedures are shown below to calculate resistance in order
to predict the ship power.
Calculate:
1. Frictional Resistance, ( ) ( )( )CakCSVR FF ++= 12/1 2ρ
2. Wetted Surface,
( ) ( )
( ) BB TW P
MBM CA
CTB
CCCBTLS /3 8.2
3 6 9 6.0/0 0 3 4 6 7.0
2 8 6 2.04 4 2 5.04 5 3 0.02 5.0 +
+
−−++=
3. Form Factor
( ) ( ) ( ) ( )( ) 6906.0
92497.022284.0
0225.0152145.0
95.0//93.01
LCBC
CLBLTk
P
PR
+−
−−+=+
where, ( ) 06.01 +−= PR CLL
49
4. Correlation Factor, ( ) 00205.01000006.0 16.0 −+= −LCa
5. Frictional Resistance Coefficient, ( ) 22
075.0
−=
LogRnCF
6. Residuary resistance, ( ) ( ) 22
9.01 cos −− += FnmFnm
R CeR λ
where,
( )( ) ( )32
3/11
984388.68673.13
07981.8/79323.4/75254.1/0140407.0
PP
P
CC
CLBLTLm
−+
−−+∇−=
( )2/1.022 69385.1 Fn
P eCm −=
BLCP /03.0446.1 −=λ
7. Therefore, total resistances are, RFT RRR +=
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
50
Parameter LimitationsLength/Breadth, L/B 3.2 –5 .0Breadth/Draft , B/T 2.0 - 3.5Vulome/length, ( )301.0/ L∇ 200 – 500
Prismatic coefficient, CP 0.55 - 0.70Block coefficient, CB 0.42 - 0.47Speed/length, V/√L 0.7 - 1.5Longitudinal center of buoyancy, LCB 0.50% - 0.54% aft of FP½ entrance angle , ½ α˚e 7.0˚ - 37.4˚
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 ∆/(0.01L) 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, µρUL
Rn =
vi) Frictional resistance coefficient, ( ) 22
075.0
−=
LogRnCF
vii) Total resistance, ( ) ( ) 22/ SVCCR FRT ρ+=
51
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, xRR TT =' correction
factor
6.5 DJ. Doust’s Method
DJ. Doust’s Method is used for calculating resistance based on the resistance
tests 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
Parameter LimitationsLength/Breadth, L/B 4.4 – 5.8Breadth/Draft, B/T 2.0 – 2.6Midship coefficient, CM 0.81 – 0.91Prismatic coefficient, CP 0.6 – 0.7Longitudinal center of buoyancy, LCB 0% - 6% aft of midship½ entrance angle, ½ α˚e 5˚ - 30˚
52
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.
ii) Determine three factors used to calculate residuary resistance using
graph given. These three factors are ( )TBCpfF /,1 = ,
( )LCBCpfF ,2 = and ( )BLCpfF /,2/1,'3
α=
iii) Calculate 6F using ( ).875.01006 −= mCaF The parameter ‘a’ is a
function V/√L and given by Table 6.7
iv) Calculate residuary resistance, ( ) 6'
321200 FFFFCR +++=
v) Calculate, 3/21/0935.0 ∆= SS
vi) Calculate, LVL /05.1'=
vii) Calculate Froude’s skin friction correction,
( )83'62'4'175.0' 10/22.110/77.210/29.00196.0 LLLSLSFC +−+= −
viii) Calculate, ( ) ( )3/1
2001 /5.152 ∆= SFCxδ
ix) Calculate residuary resistance for new ship, ( ) ( ) 1200 δ+= RnewR CC
x) Calculate total resistance, ( )
L
VCR newR
T
2∆=
Tables 6.7: Values parameter ‘a ’
V/√L a0.8 -0.045
53
0.9 -0.053
1.0 -0.031
1.1 -0.035
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 also
has limitations on the usage of this graph, they are:
Table 6.8: Limitation of Diagram method
Parameter LimitationLength (m) 10 – 70 m
Beam (m) 0 – 10 m
Displacement (m³) 0 – 3000
Engine in SHP (hp) 0 – 1500
Speed (knots) 7 – 13.5
54
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’s
Method and Diagram method. The diagram and Cedric Ridgely Nevitt’s method are
applied by calculation based on the graph while the Van Oortmerssen’s and Holtrop
& Mennen’s method were calculated by Maxsurf program. The prediction of
resistance will be compared with tank test result. The assumption on the coefficient
is stated below.
Assumption of coefficient:
1. Gearing coefficient, Gη = 0.96-0.97 (0.97)
2. Shaft and bearing coefficient, BS ηη . = 0.98 – machinery aft (0.98)
= 0.97 – machinery amidships
3. Drive Coefficient, Dη = 0.5
Table 6.9: Resistance prediction using a various method
55
Effe ctive P ow e r Aga inst S h ip S pe e d
0
100
200
300
400
500
600
700
800
0 2 4 6 8 10 12 14
S pe e d (knots)
PE
(HP
)
Cedric Ridgely Nevit t’s
Chart (A verage)
Chart (O pt im um )
Holtrop
V an O ortm ers sen’s
Tank Test
Table 6.10: Effective power prediction, PE
Table 6.11: Summary of result (all)
Resistance Prediction, Rt (kN)Speed
(knots)
Cedric Ridgely
Nevitt’s method
Chart
(Average)
Chart
(Optimum)
Holtrop &
Mennen’s
Van Oortmerssen’s
Method4 - - - 1.32 1.166 - - - 2.88 2.867 - - - 4.01 4.098 - - - 5.56 5.639 - - - 7.87 12.4210 11.98 22.20 13.32 10.33 17.5711 18.09 38.34 24.22 13.80 19.3912 27.75 - - 23.79 36.50
12.5 - - - 50.95 51.2213 - - - 78.14 67.95
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 3.196 - - - 11.935 11.8557 - - - 19.36 19.7658 - - - 30.7 31.0959 - - - 48.89 77.1110 82.61 153.12 91.88 71.26 121.1811 137.28 290.94 183.75 104.68 147.1512 229.74 - - 196.92 302.17
12.5 - - - 439.32 441.6513 - - - 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 0
6 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
56
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 RidgelyNevitt’s
Chart(Average)
Chart(Optimum)
Holtrop
VanOortmerssen’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
6.8 Discussion on prediction result
57
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 be
accepted.
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 the
lower percentage difference on the prediction value. Therefore Van Oortmerssen’s
method is suitable because the hull characteristics are covered by this method.
6.8.2 Holtrop and Mennen’s method
58
Generally, Holtrop and Mennen’s method is suitable for a small vessel and
this 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.
6.8.3 Cedric Ridgely Nevitt’s Method
59
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.
60