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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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.

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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 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

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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/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

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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

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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

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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

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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

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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