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.
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.
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 6.2
Breadth/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
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 3 2 9 / 1 1 2 log 2 075 . 0 cos sin 2 2 2 2 Rn SV Fn e C Fn e C e C e C R mFn mFn mFn mFn T ρ where, 1.(
WL)
i WL i( )
WL i i(
)
i m i WL i p i p i i i i i C d T B d T B d C d C d B L d B L d C d C d LCB d LCB d d C + + + + + + + + + + + + = 11 , 2 10 , 9 , 2 8 , 7 , 2 6 , 5 , 2 4 , 3 , 2 2 , 1 , 0 , 3 / / / / 10 2. 1. ( /2) b p C bm= − − or for small ships this can be presented by:
( 2.1976) 14347 . 0 − − = Cp m
3. C is a parameter for angle of entrance of the load waterline, iWL e, where
(
L B)
iCWL = e WL/
4. Approximation for wetted surface area is represented by:
3 / 1 33 / 2 0.5402 223 . 3 V L V 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.
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
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
The step by step procedures are shown below to calculate resistance in order to predict the ship power.
Calculate: 1. Frictional Resistance, RF =
( )
1/2 ρSV2(
CF(
1+k)
+Ca)
2. Wetted Surface,(
)
( )(
)
BT B WP M B M B T C A C C C C B T L S 2.38 / 3696 . 0 / 003467 . 0 2862 . 0 4425 . 0 4530 . 0 2 0.5 + + − − + + = 3. Form Factor(
)
(
)
(
)
(
)
(
)
0.6906 92497 . 0 22284 . 0 0225 . 0 1 52145 . 0 95 . 0 / / 93 . 0 1 LCB C C L B L T k P P R + − − − + = + where,LR =L(
1−CP)
+0.06 4. Correlation Factor,Ca=0.0006(
L+100)
−0.16−0.002055. Frictional Resistance Coefficient,
(
)
22 075 . 0 − = LogRn CF
6. Residuary resistance, = (m1Fn)−0.9+m2cos( Fn)−2
R Ce
R λ
( )
(
)
(
)
3 2 3 / 1 1 984388 . 6 8673 . 13 07981 . 8 / 79323 . 4 / 75254 . 1 / 0140407 . 0 P P P C C C L B L T L m − + − − + ∇ − = (0.1/ 2) 2 2 1.69385 Fn P e C m = − B L CP 0.03 / 446 . 1 − = λ7. Therefore, total resistances are,RT = RF +RR
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, ∇/
(
0.01L)
3 200 – 500 Prismatic coefficient, CP 0.55 - 0.70 Block coefficient, CB 0.42 - 0.47 Speed/length, V/√L 0.7 - 1.5Longitudinal center of buoyancy, LCB 0.50% - 0.54% aft of FP
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,S/ ∇L 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 S/ ∇L
v) Reynolds Number,
µ
ρUL
Rn=
vi) Frictional resistance coefficient,
(
)
22 075 . 0 − = LogRn CF
vii) Total resistance, R
(
C C)(
/ SV2)
2F R
T = + ρ
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, RT' =RTx correction
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
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:
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
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 F1 = f
(
Cp,B/T)
,(
Cp LCB)
fF2 = , and F3' = f
(
Cp,1/2α,L/B)
iii) Calculate F using 6 F6 =100a
(
Cm −0.875)
. The parameter ‘a’ is a function V/√L and given by Table 6.7iv) Calculate residuary resistance, ( ) 6
' 3 2 1 200 F F F F CR = + + + v) Calculate, 2/3 1 / 0935 . 0 ∆ = S S vi) Calculate, L'=1.05V/ L
vii) Calculate Froude’s skin friction correction,
(
' 4 '2 6 '3 8)
175 . 0 ' 0.0196 0.29L /10 2.77L /10 1.22L /10 SL SFC= − + − + viii) Calculate, δ1 =(
152.5xSFC)
/∆(200)1/3ix) Calculate residuary resistance for new ship, CR(new) =CR(200) +δ1
x) Calculate total resistance, ( )
L V C RT Rnew 2 ∆ =
Tables 6.7: Values parameter ‘a’
V/√L a
0.8 -0.045
0.9 -0.053
1.0 -0.031
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 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’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,ηG = 0.96-0.97 (0.97)
2. Shaft and bearing coefficient, ηS.ηB = 0.98 – machinery aft (0.98) = 0.97 – machinery amidships 3. Drive Coefficient, ηD = 0.5
Table 6.9: Resistance prediction using a various method
Resistance Prediction, Rt (kN) Speed (knots) Cedric Ridgely Nevitt’s method Chart (Average) Chart (Optimum) Holtrop & Mennen’s Van Oortmerssen’s Method 4 - - - 1.32 1.16 6 - - - 2.88 2.86 7 - - - 4.01 4.09 8 - - - 5.56 5.63 9 - - - 7.87 12.42 10 11.98 22.20 13.32 10.33 17.57 11 18.09 38.34 24.22 13.80 19.39 12 27.75 - - 23.79 36.50 12.5 - - - 50.95 51.22 13 - - - 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 3.19 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
Effective Power Against Ship Speed 0 100 200 300 400 500 600 700 800 0 2 4 6 8 10 12 14 Speed (knots) P E (H P )
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) R t (kN ) Cedric Ridgely Nevitt’s Chart (Average) Chart (Optimum) Holtrop Van Oortmerssen’s Tank test Table 6.11: Summary of result (all)
Graph 6.1: Comparison of effective power between various methods and tank test
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
Graph 6.2: Comparison of total resistance between various methods and tank test
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 be accepted.
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
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
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
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.
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.
