Weerstand en Voortstuwing, deel 1 en 2

Weerstand en voortstuwing

Prof.dr.ki. J.D. van Manen

,Deel I - %.

INHOUDSOPGAVE deel I en II

Hoofdstuk I

Extrapolatiediagram

(II)

Inleiding

(II) 1.1 "Some applications of the three-dimensional

extrapolation of ship frictional resistance"

by Ir. A.J.W. Lap

(I)

1.2 "A statistical analysis of performance test

results" by Ir. J. Holtrop

1.3 "Statistical data for the extrapolation of

model performance tests" by J. Holtrop

Hoofdstuk II

Golfmakende weerstand

2.1 Minimale weerstand

(II) 2.2 "The N.S.M.B. - 40 years of scientific

in-dustrial service in marine technology" by

Prof.Dr.Ir. J.D. van Manen

(II) 2.3 "Methodical series experiments on cylindrical

bows" by Ir. J.J. Muntjewerf

Hoofdstuk III

_{Weerstandsberekening met behulp van bekende}

resultaten van soortgelijke schepen

(II)

Inleiding

(II) 3.1 "Diagrams for determining the resistance of

single-screw ships" by Ir. A.J.W. Lap

(II) 3.2 "Extended diagrams for determining

_the

resis-tance and required power for single-screw

ships" by W.H. auf 'm Keller

(II) 3.3 "A power prediction method and

_{its application}

to small ships" by Ir. G. van Oortmerssen

(I)

_{3.4 "A statistical power prediction method" by}

J. Holtrop and G.G.J. Mennen

(I)

_{3.5 "Resistance prediction of small,}

high-speed

displacement vessels: state-of-the-art"

_by

Dr. P. van Oossanen

2

Hoofdstuk IV

Systelatische schroefseriediagrammen

(II)

Inleiding

(II) 4.1 "The Wageningen B-screw series" by Prof.Dr.Ir.

W.P.A. van Lammeren, Prof.Dr.Ir. J.D. van Manen

and Dr.Ir. M.W.C. Oosterveld

(I)

4.2 "Further computer-analyzed data of the

Wageningen B-screw series" by M.W.C. Oosterveld

and P. van Oossanen

Hoofdstuk V

Toelichting op het gebruik van

schroefserie-diagrammen

(I)

5.2 "Representation of propeller characteristics

suitable for preliminary ship design studies"

by M.W.C. Oosterveld and P. van Oossanen

Hoofdstuk VI

Het "schroef met straalbuis" systeem

(I)

6.1 "Open-water test series with propellers in

nozzles" by Dr.Ir. J.D. van Manen

(I)

6.2 "Recent research on propellers in nozzles"

by Dr.Ir. J.D. van Manen

(I)

6.5 "Analysis of ducted-propeller design" by

J.D. van Manen and M.W.C. Oosterveld

(I)

6.7 "Ducted propeller characteristics" by

Dr.Ir. M.W.C. Oosterveld

Hoofdstuk VII

Cavitatie

(I)

7.3 "Cavitation scale effects" by G. Kuiper

Hoofdstuk VIII

Het ongelijkmatige snelheidsveld; wisselende

krachten opgewekt door de voortstuwer

(I)

8.3 "Some hydrodynamic considerations of

propeller-induced ship vibrations" by

S. Hylarides

Hoofdstuk I

EXTRAPOLATIEDIAGRAM

Publication No. 540 of the N.S.M.B.

Reprinted from

INTERNATIONAL SHIPBUILDING PROGRESS

SHIPBUILDING AND MARINE ENGINEERING MONTHLY Rotterdam - The Netherlands

Vol. 24 - No. 270 - February 1977

5

22

A STATISTICAL ANALYSIS OF PERFORMANCE TEST RESULTS

by

Ir. J. Holtrop

1. Introduction

A statistical evaluation of model and trial test re-sults, selected from the archives of the Netherlands

Ship Model Basin, was carried out using multiple

re-gression analysis methods. The objective of this study

was to develop a numerical description of the ship's

resistance, the propulsion properties and the scale

effects between the models and the full size. The most

important applications of the obtained results are the

determination of the required propulsive power

with-out doing specific model tests and further the

refine-ment of the extrapolation method by which model

test results are scaled up.

The evaluation was performed by applying

mul-tiple regression analysis to the results of 1707 resistan-ce measurements, 1287 _{propulsion measurements}

carried out with 147 ship models and the results_{of 82}

trial measurements made on board 46 _{new ships. This}

material has been used partially in a previous study

[ 1], while most of the mentioned full-scale

measure-ments were involved in an extensive model-ship

cor-relation study initiated and co-ordinated by the

Per-formance Committee of the International Towing

Tank Conference [2]

. A survey of the parameter

ranges and ship types is given in Table I.

*) Netherlands Ship Model Basin, Wageningen, The Netherlands.

A STATISTICAL ANALYSIS OF PERFORMANCE TEST RESULTS

by Ir. J. Holtrop*)

Table 1

Parameter ranges for different ship types 2. Resistance prediction

In order to make the resistance prediction valid for

ships and models of different size, the resistance com-ponents have to be expressed as dimensionless

quan-tities depending on their respective scaling parameter. This dependency varies from model to model owing to

differences in hull form. Applied to components of viscous and wave making origin, disregarding

inter-action, we can thus express each component

non-dimensionally as a function of the scaling parameter

and the hull form:

Rv Rw

A = f1

(Re, form) and A _{=f2 (Fn'} form)

Here, R. is the Reynolds number and F. the Froude

number, while Rv /A and Rw /A are the specific resis-tances of viscous and wave-making character

respect-ively. Normally, the viscous resistance is deterrnined

from a flat plate friction formula which is _corrected

for the effect of the ship form. This additional form

resistance is in most cases expressed

_{as a fraction of}

the resistance of the flat plate ofequal length

_and

wetted surface at the same speed as the actual ship.

This adaptation of the original Froude method _as

pro-posed by Hughes is generally referred to as the form

factor method. Another component, which can be

con-sidered of a viscous origin in most cases, is the

resist-ance of the appendages. It is known that the

appen-Type of ship

F.

max.

C, L/B Number

single screw of shipstwin screw

min. max.

min. max. model f

scal

le model

scalefull

Tankers, bulkcarriers 0.24 0.73 0.85 5.1 7.1 48 13 3 2 General cargo 0.30

0.58 0.72

5.3 8.0 21 17 3 2 Fishing . vessels, tugs 0.38

0.55 0.65

3.9 6.3 35 3 2 Container ships, frigates 0.45 0.55 0.67 6.0 9.5 6 18 1 Various 0.30

0.56 0.75

6.0 7.3 7 6 3 3 Total _{117 36} 30 10

(5.

2

dage resistance is under-estimated in general when

only the wetted surface of the appendages is added to the equivalent flat plate surface. This under-estimation can be explained by the fact that appendages pierce

to some extent through the boundary layer of the hull, have a short length en hence a high specific re-sistance. In the present analysis the resistance of the appendages was calculated separately, using the flat

plate friction formula with the Reynolds number

based on a virtual appendage length. This virtual length equals the length of the streamline over the ap-pendages if the appendage is more or less outside the boundary layer of the hull. When this virtual length equals the ship length, the resistance contribution of the appendage is the same as if it were part of the hull surface. This approach is valid only in the case that the local boundary layer of the appendage is turbulent and no flow separation occurs. From series of model resistance tests, in which the appendage configuration was varied systematically, several values of the

vir-tual appendage length were determined. Average values

for this virtual length are given in Table 2. The total viscous resistance of a ship model with appendages and a form factor 1 + k can be written as:

Rv = 'hp V2 CF (1

+k)Swith

p the water density, V the speed, CF the coef-ficient of frictional resistance and St. / the total wetted surface of both the hull and the appendages. The form factor 1 + k can be divided into the form factor of thé single hull form 1 + k/ and a coefficient k2 describing the contribution of the appendage resistance:

1 + k = 1 +k1 + (k2 )Sapp/Stot

The appendage factor 1 + k2 is presented in Figure I as a function of the virtual appendage length Lapp

Throughout the analysis all plate friction coefficients CF were calculated from the ITTC-1957 formula:

CF 0.075

- (log R. 2)2

Table 2

Virtual appendage length

The wetted surface, without appendages, was correlat-ed with the hull-form parameters and the following formula, having a standard deviation of a = 2.1 per

cent, was deduced:

S = L(2T+B)VCm 10.5303368+0.6321359CB

0.360327(Cm 0.5)-0.0013553L/T1

In this formula L is the length on the waterline, B is the moulded breadth, T is the moulded draught, Ca is the block coefficient based on the waterline length and Cm is the midship section coefficient.

The form fáctors could be obtained in the case of 91 resistance tests with a reasonable reliability from a numerical or graphical evaluation of:

1 + k = lim (R/RF ) Fa. 0

This procedure is based on the assumptions that the boundary layer is turbulent in all measured points and that the Froude-dependent resistance components vanish at low Froude numbers. The 91 form factors

RESISTANCE OF APPENDAGES UPPER SCALE 10 0 001 002 aos 004 005 006 007 WS 009 01 0 0 0.2 0.3 04 05 06 07 08 09 LApp IL

Figure 1. Appendage resistance as a function of the virtual

ap-pendage length.

3.0

25

20

15

Appendage configuration _{LaPP /L}

rudder single screw 0.1 0.5

rudders twin screw _0.03

rudders+shaft brackets twin screw 0.01

rudders+shaft bossings twin screw 0.02

stabilizer fins _0.01

bilge keels _0.20

thus determined were corrected for appendage

re-sistance when necessary and were correlated with the form parameters. By means of regression analysis the following formula was derived having a standard

de-viation of a = 4.6 per cent

k 0.93 + mu 0.22284 (B/LR )0.92497

(0.95-cp)-0.521448 . (1 Cp +0.0225 Icb)0-6906

In this formula Cp is the prismatic coefficient based on the waterline length. LR is the length of the run

and is approximated by:

LR = LI 1-Cp+0.06Cp.lcb/(4Cp -1) I

In the formulae lcb is the position of the centre of

buoyancy forward of 0.5L given as a percentage of

the waterline length L.

With regard to the resistance components that

de-pend on the Froude number, practically the

same

procedure as followed in the previous analysis [I]

,

was applied. The equations are based on a simple

wave-malcing theory, originally derived by Havelock

[3]:

m.F-2/9 m.F-2

Rw = c1 e n +e " c2+c3cos(XF,7 2) I

In this equation c1, c2, c3, X and m are coefficients

which depend on the hull form. This expression

des-cribes the wave-making resistance of two pressure

dis-turbances of infinite width with the first term

as a correction to account for the induction of the diverg-ing waves. The distance between the centres of the disturbances XL can be regarded as the wave-making

length. The interaction between the transverse waves,

accounted for by the cosine term, results into the

typical humps and hollows on the resistance curves.

By an analysis of 31 experimental resistance curves,

the wave-making length could be related to the

pris-matic coefficient Cp and the length-breadth ratio_by:

X = 1.446.Ç - 0.03L/B

For practical use as regression and prediction formula the wave-making equation was simplified to:

Rw-2

m,F..4-m2 ncos(XF

= c.e " A

From the regression analysis the following expressions were derived for the coefficients c, d, m1 and m2:

C = co6 (B/ L) 2.984. (N-0.7439 c1.2655 '14 WL d

= -0.9

m1 = -4.8507B/L-8.1768Cp +14.034C/2, -7.0682 2 m2 = -0.4468e-0.1 "F

In these expressions the waterplane coefficient Cw the prismatic coefficient Cp and the Froude number are based on the length on the waterline. Application

of this prediction formula for the wave-making

resist-ance in combination with the given formula for the

form factor to the basic material resulted in a standard

deviation of 6.9 per cent of total model resistance

values.

3. Prediction of the delivered power

When the resistance is known the power delivered

to the propeller PD can be predicted from an estimated

propulsive efficiency np. The propulsive efficiency is

generally sub-divided into the propulsion factors w, t,

R ando:

nD = PE/Pu fo7lR

Here w is the effective wake fraction, t is the thrust

deduction fraction, defined as t = 1-R/T, no is the

open-water propeller efficiency and nR is the relative-rotative efficiency. Throughout this study the effective

wake w is based on thrust identity which means that

the advance coefficient J, defined as V(1-w)/nD, is

determined from Kr = Kr

o(J). In these definitions KT and K10 are the thrust coefficients for the behind

and the open-water condition respectively with:

KT

-p n2 D4

Further, the torque coefficient KQ is definedas:

KQ - Q

75.PD

p n2 D5 2npn3D5

Similarly,

_{the open-water torque coefficient}

KQo exists and no and nR are definedas:

nCro

n° 2n_KQ and nit = KQ./KQ 0

From the results of model propulsion tests, together

with the measured characteristics of 77

propeller

models, the values of w, t and nR were computed. It

is generally known that the effective wake is composed

of both a viscous fraction w, and

_{a potential wake}

fraction wp. For this reason the effective _{wake was}

correlated with both a characteristic boundary _layer

variable as well as geometrical parameters. As

boun-dary layer parameter the quantity D, with:

D-L(CT - Cw ) 011.11

G

was used. In this definition D is the propeller diameter, L is the waterline length and CT and Cw are the coef-ficients of total and wave-making resistance. The para-meter Dv was obtained by considering the propeller to be placed at the trailing edge of a flat plate with length L and having equal viscous resistance as the

ac-tual hull forrn. From an integration of the velocity

over the screw disk it followed that the nominal wake is directly depending on Dv, provided the velocity in the boundary layer follows a n-th power law and the propeller radius is less than the boundary layer thick-ness. Although the latter condition is not always

ful-filled, especially not at the full scale, Dv proved to be significant in the regression analysis. For single-screw configurations the following prediction formula for the effective wake was obtained:

w= 0.177714B2/(LL.Cp)2-0.577076B/L +0.404422Cp +7.65 I 22/Dv2

This formula is based on 1176 model values and 68 values derived from trial test measurements with a standard deviation of a = 0.048. In a similar way a prediction formula for twin-screw ships with a stan-dard deviation of a = 0.041 was determined:

w = 0.4141383q 0.2125848Cp+5.768516/Dv2 The thrust deduction t and the relative-rotative

ef-ficiency 77R were also correlated with the hull-form and propeller parameters but as no Reynolds scale

ef-fects are assumed to be present on both these two

pro-pulsion factors in modern analysis methods, the boun: dary layer parameter Dv was not considered in the sta-tistical analysis. For single-screw configurations the formula

t = 0.088775+0.2992778Cp 0.2355184CP +0.04302q+0.0355997B2/(LL.Cp

with a standard deviation a = 0.037 and for

twin-screw ships the prediction formula:

t 0.0994+0.125 B/ LR

with a = 0.06 were deduced. With respect to the latter formula the remark is made that fortwin-screw ships

with open-stern arrangement the thrust deduction can

be up to 0.07 lower than :ndicated by _{the formula.} Also smaller wake fractions can be expected _{for this} class of ships. For the relativelrotative _{efficiency with} a 3 per cent standard deviation were found:

nit = 0.9922-0.05908AE /A.+0.07424Cp_A

(single screw) and

= 0.9737+0.11136Cp A 0.06325P/D (twin screw)

In these formulae AE/A. is the propeller blade-area ratio, P/D is the pitch-diameter ratio of the propeller and Cp A is the prismatic coefficient of the afterbody, approximated by:

Cp A = Cp 0.0225 lcb

It is noted here that the influence of the propeller par-ticulars is not considered to reflect a physical phenom-enon. The last propulsion factor that has to be predict-ed is the open-water propeller efficiency rio. However, for practical purposes the open-water characteristics of most propellers can be approximated fairly well by those of a B-series screw. Polynomials for the thrust and torque characteristics of this extensive propeller series are given in [4]. Using the prediction formulae a standard error of 8.6 per cent for single screw and 7.8 per cent for twin-screw configurations has to be considered for the propulsive efficiency nD.

4. Scale effects between model and ship

The numerical model for the powering

characteris-tics as described in the previous sections is based

main-ly on the results of model tests and direct application to full-scale ships would lead to unrealistic results. In present day extrapolation and correlation methods scale effects are considered to be present at the resis-tance, the effective wake and the propeller

characteris-tics, while the thrust deduction and the

relative-rotative efficiency are considered equal for model and ship and independent of the propeller load. The cor-relation analysis from which the scale effects have been

derived was carried out along the following lines:

the trial test results were corrected for deviating

draught, water depth, wind force above number 2 Beaufort, deviating propeller pitch and sea water

temperature,

a friction loss of 1 per cent in the stern tube was

as-sumed,

the open-water torque and thrust coefficients were

determined using 77Ft and the model open-water

characteristics corrected for the proper Reynolds

number and average full-scale blade roughness,

the full-scale effective wake, based on thrust iden-tity and the resistance were determined,

comparison with the model values for the wake and

the resistance then yielded the scale effects.

From this correlation analysis it was found that the resistance components as described so far, cover only

about ninety per cent of the actual resistance of new

built ships under trial condition. The additional

re-sistance that accounts for this discrepancy is generally referred to as the incremental resistance or correlation allowance with:

R= Ry+Rw+1/2pV2 CA S_tot

and is partially due to the roughness of the hull plating and the air resistance. Besides, systematic effects, aris-ing from the model testaris-ing technique and inaccuracies

in the applied extrapolation method are considered to contribute to the correlation allowance. Based on 82 measurements made on board 46 new built ships the statistical CA -formula

CA = (1 .8+260/L)0.000 1

with a standard deviation a = 0.00025 was derived.

There appeared no obvious difference between the

CA -values for single and twin-screw ships. In Figure 2 the CA -values are given on a base of the ship's length. In this diagram the height of the columns corresponds

with the maximum deviation found between the

re-MODEL - SHIP CORRELATION ALLOWANCE ITTC - 57 WITH FORMFACTOR

FRICTION COSS : 1 PER CENT

0.0015AK amo ACC. TO LINDGREN

0.0010 1.14 it) §0.0005 3 a 0. 0 to - 0.0005

t

4

Figure 2. Correlation allowance CA as function of length 350 0.30 0.20 0.10 0.10 -0.10 o SINGLE SCREW L C, -Ct,

Figure 3, Viscous part effective wake fraction.

sults at different trial speeds of one or a number of sister ships. With respect to the scale effect on the ef-fective wake use can be made of the numerical

sub-division of the wake into a potential and a viscous

part. The Reynolds scale effect can then be calculated

from the prediction formulae for the viscous wake

fractions w, with

= 7.65122/D,2 (single screw)

and hence:

= 7.65122 (Crrn CTs)(CT +Crs 2Cw )L2 /D2

In a similar way for twin-screw ships the wake scale

effect can be calculated from:

Aw = 5.769 (CT. CTs)(CT.+CTs-2Cw )L2/D2

_ In Figure 3 the viscous component of the effective

wake fraction vv,

is presented as a function of the

boundary la.yer parameter D. In these diagrams both the results of trial measurements and corresponding

model tests are given. The diagrams were set up in such

a way, that the representation of the potential part of the wake by the prediction formulae was assumed to be perfect. The effective wakes detemiined from the full-scale measurements have been based on

open-WAKE SCALE EFFECT FRICTION LOSS 1 PER CENT

AK° ACC TO LINDGREN

10 15

150 200 250 300

SHIP'S LENGTH Cm)

water characteristics that have been corrected for aver-age blade roughness and Reynolds effects according to

the method proposed by Lindgren [5]. The scale

ef-fect on the propeller characteristics was investigated

by applying three different methods for propeller

scale effects: - AKT = AICQ = 0,

- Reynolds effect according to B-series polynomials, - Lindgren's method.

For each of these methods the effective wake on the

full-scale was calculated and compared with the sta-tistical curve in Figure 3 as determined from model experiments. From these calculations it appeared that

if no scale effect is considered to be present at all,

the effective wake is somewhat overestimated when

the prediction formulae are used and the full-scale

calculated wake fractions fall well below the curves in

Figure 3. Contrarily, when the Reynolds effect on the propeller characteristics is considered by using the B-series polynomials [4] the full-scale effective wake

fractions were too high when compared with the

statis-tical lines.

A probable explanation is that blade roughness, which is not considered in the B-series polynomials, playsan important role in the propeller performance. It turned out that Lindgren's method, accounting for both Rey-nolds and roughness effects, yielded wake fractions

that well complied with the statistical lines as can be

seen from Figure 3. It is noted that the scale effects

should be employed only in their specific combination,

because of the mutual dependency and relation to the

method of determining the resistance components.

In order to check the accuracy of the presented for-mulae for resistance, propulsion factors and scale

ef-fects combined as a power prediction method the

powering characteristics of 49 ships were estimated.

The computations resulted in a standard deviation

be-tween calculated and measured power values of a =

8.83 per cent and a standard deviation between

pre-dicted and observed propeller rotative speed of

a =

3.08 p...r cent. Compared with the power prediction from model tests, where standard deviations of the sarne magnitude are obtained [2], the accuracy of the presented statistical power calculation looks surpris-ingly good. It is likely, however, that as most of the full scale test data have been used also in the deriva-tion of the presented formulae, less promising values

for the accuracy will be found when the method is ap-plied to more general cases.

Conclusions

The numerical description of the resistance and

pro-pulsion properties can be considered to be useful for the estimation of the required propulsive power of a ship in early stage design. However, a more critical assessment of the accuracy of the presented method for power prediction is desired. With the presented method scale effects can be determined that have to

be applied when the performance properties are

predicted from model experiments. Especially in view

of the evaluation of model test results the derived

system of correlation factors will be gradually

im-proved and implemented in the facilities of the

Neth-erlands Ship Model Basin.

References

Holtrop, .1., "Evaluation of performance model tests and the

power prediction from model test statistics", IV

Inter-national Symposium on Ship Automation, Genova, Novem-ber 1974.

Report of the Performance Committee, 14th Intemational

Towing Tank Conference, Ottawa 1975.

Havelock, T.H., "Ship resistance, the wave making properties

of certain travelling pressure disturbances", Proc. of the

Royal Society, A, Vol. 89.

Oosterveld, M.W.C. and Oossanen, P. van, "Representation

of propeller characteristics suitable for preliminary ship

design studies", International Conference on Computer Ap-plications in Shipbuilding, Tokyo, 1973.

S. Lindgren, H., "Ship model correlation method based on

theoretical considerations", 13th International Towing Tank Conference, Berlin and Hamburg, 1972.

1

STATISTICAL DATA FOR THE EXTRAPOLATION OF MODEL PERFORMANCE TESTS

by

J. Holtrop

Publication No. 588 of the N.S.M.B.

Reprinted from

INTERNATIONAL SHIPBUILDING PROGRESS

SHIPBUILDING AND MARINE ENGINEERING MONTHLY Rotterdam - The Netherlands

Introduction

In view of an adequate extrapolation of model per-formance test results a statistical analysis of results of towing tank experiments and full-size speed trials has

been made. This analysis covers not only the derivation

of the correlation factors that account for the scale

effects that are present in the model-test results, but also the separation of the resistance into components

of different origin with emphasis on the determination

of the form factor from either low-speed resistance measurements or from a statistical formula. Some of these results have been published in a previous paper [1]. In that article, however, the extrapolation method

has not been described in detail.

Analysis of resistance tests

The extrapolation method employs a separation of

viscous and wave-making resistance components using

the form-factor concept. According to this method the form resistance is expressed as a fraction of the resist-ance of a flat plate having the same length and wetted surface as the ship and moving with the ship's speed.

With this adaptation of the original Froude method the

total viscous resistance of a ship model can be written

as:

Rv = V2 CF (1 +k)S

with p the mass density of water, V the speed, l+k the form factor, Cp the coefficient of frictional resistance

and S the total wetted surface. In the method the

plate-friction coefficients are

calzulated from the

ITTC-1957 formula:

C 0.075

F (log Rn 2)2

in which the Reynolds number Rn is based

on the

length on the waterline.

From low speed resistance measurements the form factor 1 +k can be determined provided the boundary

layer is turbulent during the measurements and

_the

Froude-dependent resistance components vanish at low Froude numbers.

For the form-factor determination the method

pro-posed by Prohaska is often followed. This method is

equivalent to the determination of l+k by means of a

curve-fitting process in which as regression equation

*) Netherlands Ship Model Basin, Wageningen, The Netherlands.

is used:

R = (l+k)RF +c.V6

It has been observed that in many cases, especially for models having a bulbous bow, at ballast draught the exponent 6 is not appropriate. Therefore, the use of regression formulae of a more general type for the

determination of the form factor can be useful.

In several cases reliable form factors have been

ob-tained using the formula: R = (l+k)RF+

c( V Vo )"

with

= 0.1

In the application of this formula the exponent n is

systematically varied.

Another regression formula that can be employed

for the determination of the form factor is:

R = (l+k)RF+c.exp( m/ .

F;°.9)

in which Fn is the Froude number. The coefficient mi

is a function of the length-breadth ratio and the

pris-matic coefficient:

m/ = 4.8507B/L 8.1768Cp +14.034C1 +

7.0682q,

The formula for the coefficient m1 has been derived

from the resistance curves of more than 100 ship

models.

A statistical analysis, in which form factors deter-mined by means of the last mentioned method were

compared with those derived from Prohaska's method,

revealed that the method employing an exponential representation of the wave-making resistance has to

be preferred.

A statistical support of the determination of the

form factor from low speed measurements is often de-sired. In that case the following approximative formula

with a standard deviation of a = 4.6 per cent can be

used:

+k 0.93 + (r/L)0.22284 (B/LR )0.92497

(0.95 Cp )-0.521448 ( Cp + 0.0225 lcb) 0.6906

T = average moulded draught L = length on waterline

B = moulded breadth

--- /NMI

STATISTICAL DATA FOR THE EXTRAPOLATION OF MODEL PERFORMANCE TESTS

by

LR = length of the run

Cp = prismatic coefficient based on the waterline

length

lcb = position of the centre of buoyancy forward

of 0.5L as a percentage of L.

The length of the run LR is approximated by:

LR = L(1 Cp + 0.06C Jcb/(4Cp 1))

On the full size the total resistance Rs is considered

to be composed of the viscous resistance, a

com-ponent associated with the induction

of waves

0.0015

0.0010

CA

0.0005

and the model-ship correlation resistance RA . The cor-relation resistance is defined as:

RA = thpV2 SCA

The model-ship correlation allowance CA was de-termined from the analysis of 106 full-size speed-trial

measurements made on board 53 new-built ships.

In Figure 1 the obtained CA values are given as a

function of the ship's length. The height of the

co-lumns corresponds with

the maximum deviation

found between the results at different trial speeds of

one ship or a number of sister ships. An average value

100 _{200 300}

SHIP LENGTH IN METRES

of CA is given by the statistically determined formula

with a standard deviation of o = 0.00021: CA = 0.00675(L + 1 00)- 33 - 0.00064

From the test results there appeared no obvious

difference between the CA -values of single and twin-screw ships.

It appeared that for full ships at ballast draught

CA -values are approximately 0.0001 higher. A possible

reason for this difference c innot be solely the greater air resistance of the ships in ballast condition. A more probable explanation can be given if the wake of the breaking bow wave interacts with the relatively thick boundary layer on the hull on model scale. According to this assumption the difference in CA value will be

present only if in full-load condition breaking is absent whereas it is supposed to occur at the ballast draught.

3. Analysis of the effective wake

The wake fraction is assumed to be composed of

both a viscous fraction wv and a potential wake frac-tion w. For this reason the effective wake fracfrac-tions,

determined from model propulsion tests as well

as

full-size trial

_{measurements, were correlated with}

both a characteristic boundary-layer variable as well as

geometrical parameters. As boundary-layer parameter the quantity

D =

L(C-

)

was used. In this definition, D is the propeller

dia-meter, L is the waterline length and CT and Cw are

coefficients of total and wave-making resistance. The

parameter Ds, was obtained by considering the

propel-ler to be placed at the trailing edge ofa flat plate with length L and having the same viscous resistance as the

actual hull form. From an integration of the velocity over the screw disk it followed that the wake fraction

is directly dependent on D, provided the

propeller

radius is less than the boundary-layer thickness. Al-though the latter condition is not always fulfilled,

es-pecially not at the full size, Dv proved to be significant in the regression analysis. For single-screw

configurat-ions the following prediction formula for the

effect-ive wake was obtained with a standard deviation ofa = 0.041:

w = 0.177714B2/(L- L.Cp )2- 0.57707613/L+

+0.404422Cp + 7.65122/Dv2

In a similar way a prediction formula for_twin-screw

ships with a standard deviation of a = 0.041 was de-terrnined :

w= 0.4141383Cii - 0.2125848Cp + 5.769/Dv2

The Reynolds scale effect on the wake fraction can

be determined using the following prediction formulas for the viscous wake fraction:

= 7.65122/D! (single screw),

= 5.769/Dv2 (twin crew).

The scale effect on the wake, w, can be calculated

from

W= 7.65122(CT. - CTs) (C.T. + CTs - 2Cw )L2/D2

(single screw)

w= 5.769 (CT.CTs )( CTm + CTs 2C.1v ) L2 /D2 (twin screw)

In Figure 2 the viscous component of the effective

wake fraction wv is presented as a function of the

boundary-layer parameter D. In these diagrams both the results of trial measurements and corresponding

model tests are given. The effective wakes determined

from the full-size measurements have been based on

open-water characteristics which have been corrected for average blade roughness and Reynolds effects ac-cording to the method proposed by Lindgren [2]. The blade roughness, however, has been put equal to 30 pm instead of 50 pm in accordance with correlation

studies carried out by the ITTC in a later stage.

4. Outline of the extrapolation method

In a model propulsion test the propeller thrust T,

the torque Q and the residuary towing force F that

acts on the mcidel are measured for a number of

speeds. From these measured values, the resistance and

the open-water characteristics of the propeller model,

the propulsion factors are determined. The thrust-deduction fraction is definedas:

t = 1 + (F - Rm )/T,

The wake fraction wm is determined using thrust identity which means that the advance coefficient J,

defined as V(1-w)/nD, is determined from KT _{= KTo'}

in which KT and KT° are the thrust coefficients_for

the behind and open-water condition _{respectively, n}

the number of revolutions of the propeller and Dthe

propeller diameter. The open-water efficiency no and

the relative-rotative efficiency nit are defined as:

"(To

=- and nR = K(10/KQ

KQo

in which the torque coefficient is given by:

KQ = Q

2 r.,5

p n u

wV 0.20 0.10 o -0.10 o 0.10 0.20 .111111

the wake fraction, being 6w, is considered

_present,

whereas the thrust deduction and the_{relative-rotative}

efficiency are assumed to be equal for model and ship. The analysis of the model test results proceeds along the following lines:

from the resistance test the full-size _{resistance is}

determined:

= ( R.

FD )X3ps/pm

in which FD is the scale effect on resistance with:

L (CT Cw )

Figure 2. Viscous part effective wake fraction.

FD = 1/2pm V.2 Sm 1 (1+k) (CFm _{CFs ) CA 1}

ii _{the scale effect on the wake is estimated and the}

full-size wake fraction is determined:

W8 = w 6w

_m

iii _{the full-size propeller load is calculated from:}

( KT/12 (1-0 (l_ws)2vs2Ds2p, 0.30 _{SINGLE SCREW} TWIN SCREW WV 0.10 10 15 ₂₀

a

-iv the open-wat,n- characteristics are corrected for

Reynolds and blade-roughness scale effects using

the method proposed by Lindgren [21.

interpolation in the full-size open-water curves

with ( /J2 )s yields Js and KQ0s.

vi

_{the full-size rate of rotation of the propeller is}

calculated from:

ns = Vs (1 ws )/.JsDs

vii the power delivered to the propeller is determined

from:

27rp sn: Ds5 PD

nR

viii the power supplied to the shafting system

is

assumed to be 1 per cent more in view of friction

losses in the stern tube:

PS = PD /0.99

5. Final remarks

With the presented method scale effects on ship

performance can be determined. The method can be applied when the performance properties of a ship are to be predicted from model experiments. The derived system of correlation factors will be refined further.

More specific attention will be paid to the relation

between the propeller loading and the propulsion

factors.

Other fields for investigation are the scale effects on the form factor and other resistance components.

The method is employed in the facilities of the

Nether-lands Ship Model Basin and will be used more and

more for standard application.

References

I. Holtrop, J., "A statistical analysis of performance test results", International Shipbuilding Progress, Vol. 24, No.

270, February 1977.

2. Lindgren, H., "Ship model correlation method based on theoretical considerations", 13th International Towing Tank Conference, Berlin and Hamburg, 1972.

HoofdstUk III

WEERSTANDBEREKENING

met behulp van bekende resultaten

A STATISTICAL POWER PREDICTION METHOD

by

J. Holtrop and G.G.J. Mennen

Publication No. 603 of the N.S.M.B.

Reprinted from

INTERNATIONAL SHIPBUILDING PROGRESS

SHIPBUILDING ANP MARINE ENGINEERING MONTHLY Rott, rdam - The Netherlands

-Introduction

In a previous paper, [11, a numerical representation

of resistance properties and propulsion factors was

presented that could be used for statistical

perfor-mance prediction of ships. After more than a year of

experience several fields

for improvement of the

derived prediction method can be indicated:

the formula for the wave-making resistance does not

include the influence of a bulbous bow; this implies

that especially the resistance of ships with large

bul-bous bows is over-estiinated by the original

for-mula.

the resistance of fast naval ships appeared not to be

represented accurately enough by the statistical

formula; more in particular the wave-making

resist-ance of ships with a large waterplane-area

coef-ficient is over-estimated by the previous formula.

it 'appeared that the accuracy of the formula for the thrust deduction fraction for slender single-screw

ships is insufficient.

the wake fraction and the model-ship correlation

allowance

are not properly represented by the

formulas for full ships at ballast draught.

Focussed on the above-mentioned points for

im-provement of the prediction method a new statistical analysis was made. The presented revised formulas for statistical power prediction are based on more ex-perimental results than the original equations given in

[ I

1-Re-analysis of resistance data

The total resistance of a ship is generally subdivided

into components of different origin. In the numerical

representation of the total resistance the following

aimponents were considered: - equivalent flat plate resistance;

- form resistance of the hull;

- viscous drag of appendages;

wave-making and wave-breaking resistance; resistance of a (not fully immersed) bulbous bow; model-ship correlation allowance.

In the present statistical study each component was

expressed as a function of the speed and hull form

parameters. The numerical constants in the regression

equations were obtained from random model test

data.

*) Netherlands Ship Model Basin, Wageningen. The Netherlands.

A STATISTICAL POWER PREDICTION METHOD by

J. Holtrop and G.G.J. Mennen*

The first, second and third mentioned component

were described using the form-factor concept:

Rv = V2p V2 Cis ( 1 +k)Stot

in which p

is the mass density of the water, V the

speed, CF the

coefficient of frictional

resistance,

(l+k) the form factor and Stnt the projected wetted

surface including that of the appendages.

The coefficient of frictional

resistance was

deter-mined using the ITTC-1957 formula:

C7F = 0.075

(logRn 2)2

with the Reynolds number Rn based on the waterline length L. The form factor (1+k) can be divided into the form factor of the single hull ( l+ki ) and a

con-tribution of the appendage resistance (1+k2):

1 +k = 1 +lc/ + 1 ( 1 +k2 )( 1 +lc 1) ISapp /Stot

In Table 1 tentative values of (1 +k2) are given.

Table 1

Appendage factor 1 + k2

The form factor for the bare hull (1+k ) can be

ap-proximated by the formula:

H-k1 = 0.93 +(m)0.22284(B/LR )0.92497

0.95 _CI, )-0.52144_{8(1 Cp +0.0/25} 16)0.6906

In this formula T is the average moulded draught,

L is the lengtl. on the waterline, Cp is the prismatic coefficient and Icb is the longitudinal position of the centre of buoyancy ibrward of 0.5L as a percentage of the waterline length L. LR is the length of the run

and is approximated by:

LR /L = 1 Cp +0.06Cp Icb/(4Cp I)

Appendage configuration

rudder - single screw 1.1 - 1.5

rudders - twin screw 2.2

rudders + shaft brackets - twin screw 2.7

rudders + shaft bossings - twin screw 2.4

stabilizer fins 2.8

bilge keels 1.4

The projected wetted surface of the bare hull was

correlated with the data of 191 ship models. The

following statistical formula involving a standard deviation of a = 1.8 per cent was deduced:

S = L(2T+B)V-CT4 (0.453+0.4425CD -0.2862; + -0.003467B/T+0.3696Cwp )+2.38ABT /CB

In this formula Cm is the midship-section coefficient. L the length of the waterline, T the average moulded

draught, B the breadth, CB the block coefficient,

C_WP the waterplane coefficient and ABT is the

trans-verse sectional area of the bulb.

The wave-making and wave-breaking resistance

com-ponents were described using the following represen-tation for the dependency on the speed:

Rw

= c c2exp 1 miFdn +m2 cos(XFn-2 )

In this equation, in which R/

is the

Froude-num-ber dependent resistance per unit displacement and Fn

the Froude number based on the waterline length.

The coefficients c1, c2, ml, d, m2 and X are functions

of the hull form.

The coefficient X can be determined from: X = 1.446Cp -0.03L/B

From a regression analysis using the

above-mention-ed equation for the wave-making resistance with the exponent

d = -0.9

the following formulas for the coefficients cl, c2, m1

and m2 were derived:

= 2223105(B/L)3.78613 (T/B)"°796'7961 (90_0.5(2)-1.37565

c2 = exp(-1.89

)

mi = 0.0140407L/T-1.75254VI/3/ L-4.79323B/L+ -8.07981CF +13.8673q, -6.984388q, m2 = -1.69385q,exp(-0.1/F2n.)

The coefficient c3, that accounts for the reduction of the wave resistance due to the action of a bulbous

bow, is defined as:

c3 = 0.56AN / I BT(0.56.VABT+T1: -hB -0.25NTAT11.) I

In the above given formulas 0.5a is the angle of' the

waterline at the bow in degrees with reference to the

centre plane neglecting the local shape at the stem, V is the displacement volume. ABT is the transverse area of

the bulbous bow, ho is the position of the

centre of

area ABT above the base and T1, is the draught on the

forward perpendicular. The halt* angle of

entrance can be approximated by:

-

'25

-0.5a = 125.67B/L-162.25q+234.32C1+

+0.155087 (lcb+ 6.8(TA -TI.)3

With respect to the resistance of a bulbous bow

which is close to the water surface a tentative formula

was deduced using the results of only a few model

tests. From inspection of these test results it was con-cluded that the relation to the speed could be

repre-sented well by:

RB = C Fn3i /(1+Fn2i

In which Fni is the Froude number based on the

im-mersion:

Fni = V/Vg i+0.15V2 with

i = TF -hs -0.25.TAETT In the definitions above:

V = speed

g = acceleration due to gravity

TF = draught forward

hB = position of centre of area ABT above base

ABT = transverse area of the bulb at the position

where the still water plane intersects the

stem.

As a measure for the emergence of the bulbous bow

from the still water surface the coefficient

pit was

introduced with:

pB = 0.56Nritir; /(TF-1.5hB )

It appeared that the resistance of

a bulbous bow

could be described fairly well according to:

R = 0.11 exp ( -3

p-B2 ) _{p g/(1+Frii )}

With respect to the model-ship correlation resistance

RA it was observed that the correlation allowance _CA

With

CA _{= RA i( Y2P}

V2Stot)

for full ships in ballast condition is about 0.0001 high-er than at the loaded draught.

A possible explanation for this difference can be

found in the interaction of the wake of the _breaking

bow wave with the relatively thick boundary

_{layer on}

the hull on inodel scale.

According to this explanation the difference in CA

value will be present only if in fully loaded condition

wave breaking is absent, whereas it

_{is supposed to}

occur at the ballast draught. Based on the results of

108 measurements made during the speed _{trials of 54}

new ships the following formula for CA having

a standard deviation of o = 0.0002 was deduced:

CA = 0.006(Ls + 100)-0.16 _0.00205

+ 0.003./ Ls / Lm C c2 (0.04 c4 )

with c4 = TF /Ls

if Te /Ls.< 0.04 or

=0.04 if

/Ls > 0.04 .

In this formula Ls is the length on the waterline of the ship. Lm the similar value for the ship model, CB the

block coefficient and TF the draught forward. The

coefficient c2 accounts for the influence of a bulbous bow on the wave-breaking resistance. For calculating full-size resistance values for ideal trial conditions the above given formula can be used employing a typical model length of Ls,/.= 7.5 metres.

Application of the

afore-mentioned statistical

re-sistance formulas showed a standard deviation of 5.9

per cent of the total model resistance values.

3. Statistical data for propulsion factors

New formulas for the thrust deduction fraction, the

effective wake fraction and the relative rotative

ef-ficiency were derived for single-screw ships. The thrust deduction fraction, defined by

t= 1 R/T ,

in which R is the total resistance and T the propeller thrust, can be approximated by:

t = 0.001979L/ (B B Cp )+1.0585B/ L-0.00524 +

0.1418D2/(BT)

In this formula B is the moulded breadth, T the aver-age moulded draught, D the propeller diameter and

Ce the prismatic coefficient.

For the effective wake fraction based on thrust

identity the following formula was derived:

w=

BSCv 10.0661875 1.21756Cv

DTA k TA .

D(1C)/

B 0.09726 +0.11434

L(1 Ce )

0.95Ce

0.95

In

_{this formula Cv is the viscous resistance}

coef-ficient, determined from:

Cv ( I +k)CF + CA

S is the total wetted surface, TA is the draught aft and D is the propeller diameter. The above-mentioned

for-mula has been derived from the results of model

ex-periments and speed trials. The full-size wake frac-tions were determined using the following calculation

procedure:

a. The measured trial speed, rotation rate and shaft

power were corrected for ideal trials conditions: - no wind, waves and swell

+ 0.24558

-

deep sea water of 15 degrees centigrade and a

mass density of 1025 kg/m3 - a clean hull and propeller

The open water torque coefficient was determined from these values assuming a shafting efficiency of ns = 0.99 and using the relative-rotative efficiency

from the model test.

The open-water characteristics

of the propeller

were determined from the results of the open-water test with the model propeller by correcting for the proper Reynolds number and the average full-size blade roughness according to the method proposed

by Lindgren, 12] .

The effective wake fraction then followed from:

w= 1lnD/V

in which J is the advance coefficient, n the rotation

rate of the propeller and V the speed.

The relative-rotative efficiency

can be

approx-imated by

nR = 0.9922-0.05908AL /A0 +0.07424CpA

In this formula AE ¡A0

is the expanded blade area

ratio and CpA

is

the prismatic coefficient of the

afterbody. CpA can be approximated by:

CpA = Cp 0.0225 leb

With respect to twin-screw ships only tentative

formulas are presented:

w = 0.3095 CB +1 OCv CB 0.23D/VT3T

= 0.325 CB 0.1885D/1F-3T

nR = 0.9737+0.111 (Cp 0.0225 Icb)-0.06325P/D In these formulas Cv is the viscous resistance

coef-ficient, D is the propeller diameter and P/D is the

pitch-diameter ratio.

4. Application in preliminary ship design

The numerical description of the resistance

com-ponents and propulsion factors can be used for the

determination of the propulsive power of ships in the preliminary design stage. In this stage the efficiency of the propeller has to be estimated. To this purpose a propeller can be designed using the characteristics of

e.g. the B-series propellers. Polynomials for the thrust and torque coefficient of this extensive propeller series

are given in [3]. The calculation procedure for deter-mining the required power proceeds along the follow-ing lines:

-

for the

_{design speed the resistance components} described in Section 2 are determined.

-

for a practical range of p..opeller diameters the

thrust deduction and Om tIfective wake fraction

are calculated.

- the required thrust is determined from the resistance

and the thrust deduction.

- the blade area ratio is estimated.

-

for a practical range of rotation rates the pitch

ratio as well as open-water thrust and torque

coef-ficient are determined from the polynomials given in

[3].

- the

scale effects on the propeller characteristics

are determined from the method described in [2] .

- the shaft power is calculated for each combination

of propeller diameter and rotation rate using the

statistical formula for the relative-rotative efficiency and a shafting efficiency of ns = 0.99.

that combination of rotation rate and propeller

diameter is chosen that yields the lowest power;

further optimization of the propeller diameter and rotation rate, employing e.g. the embedded search

technique can then be carried out.

5. Final remarks

The presented formulas for the resistance and pro-pulsion properties constitute an appreciable

improve-ment with respect to the previously given formulas

in [ 1] . Especially, the incorporation of the influence

of a bulbous bow in the numerical description of the

resistance is considered important.

Apart from the application in preliminary ship

design, where the presented method can be used for parameter studies, the method is also of importance

for the determination of the required propulsive power

from model experiments. The given formulas for the

model-ship correlation allowance and the effective

wake, from which the wake scale effect can be easily deduced, can be employed in the extrapolation from

model test results to full-size values.

References

Holtrop, J., "A statisticalanalysis of performance .test

results", International Shipbuilding Progress, Vol. 24, No.

270, February 1977.

Lindgren, H., "Ship model correlation based on theoretical

considerations",13th International Towing Tank Conference, Berlin and Hamburg, 1972.

Oosterveld, M.W.C. and Oossanen, P. van, "Representation

of propeller characteristics suitable ,for preliminary ship

design studies", International Conference on Computer

RES=ANCE PR2D:CTION OF SMAL-,.. HIGH-SPEED DISPLACEMENT _"CSSELS: STATC-OF-THE-ART

by

Dr. PETER VAN OOSSANEN research scientist Netherlands Ship Model Basin

Wageningen, The Netherlands

SUMMARY

In preliminary ship design studies it is frequently _{necessary to} estimate the calm water resistance characteristics _{of various hull forms} prior to carrying out model tests. For such estimations, use is gene-rally made of results of well-known methodical model experiments such as Taylor's Standard Series, Series 60, and others, _{to determine the} effect of specific hull form parameters on resistance. For small, high-speed displacement vessels designed _{to operate in the speed range} corresponding'to Froude number values of 0.4 _{to 1.1 (equivalent to a} range in V//l, of 1.34 to 3.70), these well-known _{methodical series} results are inadequate due to the limited _{speed range coveted.} Alterna-tive methods must then be used. In _{this paper, all available and reliable} data for the prediction of the resistance of small, high-speed vessels, designed to operate in the _{displacement mode, are presented. Included} are the results of restricted and less _{well-known methodical series} and averaged results of tests with _{a large number of non-systematic} models, in both graphical and numerical form. Some basic considera-tions on how and when each of the presented methods can be applied _are also presented.

1. INTRODUCTION

Methods for the prediction of the hydrodynamic resistance of ships are used in preliminary ship design studies when the influence of displacement, length and hull _{form on speed and power have to be} determined. Model tests are usually only _{carried out once these first} design considerations have resulted in a more-or-less definite-design. The aim of this paper is to compile all useful data on the resistance of high-speed, round bilge displacement vessels to facilitate prelimi-nary design studies on the effect of hull _{dimensions and hull form on} ship speed and required power for this kind of vessel.

For most ships approximate

resistance predictions can be carried out by means of methods based on well-known methodical series experi-ments such as Taylor's Standard

Series, Series 60, etc. These methods present the results of resistance tests with models constituting a

systematic series whereby it is possible _{to identify the effect on} resistance of various hull form parameters. The hull form _parameters which are usually adopted in _{an extensive series are the} length-displacement ratio L/V1/3(or A/(0.01L)3)

or the length-breadth ratio L/B, the breadth-draught

ratio B/T, and either the block coefficient CB or the prismatic coefficient Cp. Most methodical series _experiments cover a speed range which is not sufficient _{for application to}

high-speed displacement vessels, at high-speeds in excess of a Froude number value of 0.4 (equivalent _{to V/iL = 1.34). Some less extensive} methodical series experiments, _{however, are available for}

this purpose, in addition to a number of numerical methods. These _{methods are} presen-ted in the main part of this

paper. The presentation of the original results of'some of the graphical methods have been _{re-arranged for the} sake of wanting to obtain one particular presentation _{throughout this} paper, a presentation which

a particularly straight forward manner.

2. BASIC CONSIDERATIONS

The type of ship addressed in this paper is that which is designed to operate at speeds below which fully developed planing is possible. Fully developed planing is possible at speeds in excess of a Froude number value of about 1.1 (equivalent to V/iI, = 3.70), if a hard-chine type of hull form with flat underwater sections is adopted. At speeds below this value of the Froude number no hydrodynamic advantages in adopting a hard-chine type of hull form exist. Both the resistance and the seakeeping behaviour of a round-bilge type of hull form are then generally superior. For this reason, ships which operate in a dominantly displacement mode, below the above-mentioned speed value, are designed as round-bilge hulls. At speeds in excess of the speed at which the primary resistance hump occurs (at a FroUde number value of about 0.5), these hull forms experience some lift due to the action of dynamic forces which increases as speed is increased. The significant decrease in wetted surface due to the bow being lifted clear of the water,

such as occurs with hard-chine forms, does not occur, however. In the context of this paper, the term high speed is meant to indicate speeds in excess of a Froude number value of about 0.4

(equivalent to V/VL = 1.34) This definition of high speed finds its origin in the fact that the wave-making resistance becomes significant at this Froude number value, requiring a more slender hull form in order to keep the power of the required prime mover within acCeptable limits. Some combinations of length and speed, resulting in the above-mentioned values of the Froude number, are given in Table 1.

Table 1. Ship length and ship speed values leading to Froude number values of 0.4 and 1.1.

Unfortunately, in presenting the results of model _{resistance tests,} different formats are used by different authorities. _{No normalized} procedure exists because of specific advantages of certain presenta-tions in certain cases. When presenting the _{results of tests of a} systematic model series, for general use, it

is

_{advantageous to adopt} a format in which residual resistance values _{are used rather than} total resistance values. To justify this _{statement it is necessary to} consider the fact that the resistance of a ship is composed of viscous and non-viscous components. The frictional resistance RF is dependent on the Reynolds number while the non-viscous or residual resistance RR, mainly consisting of wave resistance, is dependent on the Froude

number, i.e. RT = RF (Rn) + RR (Fn) (I) Ship length in metres Ship length in feet

Ship speed in knots for Fn = 0.4 (V/A, = 1.34)

Ship speed in knots for F = 1.1 (V/L = 3.70) n 5 16.40 5.45 14.98 10 32.81 7.70 21.19 20 65.62 10.90 29.97 40 131.23 15.41 42.38 60 196.85 18,87 51.91 80 262.47 21.79 59.94 100 328.08 24.36 67.02 200 656.17 34.33 94.78

So

4

It follows that if the total resistance were to be adopted in presen-ting the results of a systematic model series for (eneral use, it would be necessary to incorporate the Reynolds number and the Froude number as independent variables (or separate speed and length or Froude number and length variables). This constitutes a particular handicap when presenting the results graphically.

In Eq. 1, the frictional resistance is assumed to be dependent on the wetted surfdce S, the square of the ship speed V, the mass density of water p and the coefficient of friction CF as follows:

RF = p V2 S

CF (2)

In this equation, CF is dependent on the value of the Reynolds number Rn. This formula is used to estimate the frictional resistance for the model (to determine the residual resistance from the measured total

resistance) and for the ship (to determine the total resistance from the residual resistance). The residual resistance of the

_model,

when expres-sed as a fraction of the displacement weight, is equal to the residual resistance of the ship when model tests are carried out at full-scale values of the Froude number (rather than at full-scale values of the Reynolds ntimber).

During the last years, alternative formulas have been _developed for the frictional resistance RF. These are based on the knowledge that the frictional resistance is influenced by the _{three-dimensional form of} the vessel. In assuming that the frictional _{resistance of a ship is} equal to that cf a _{flat plate with an equivalent area of wetted surface,} the frictional resistance is underestimated leading .to an overesti-mation of the residual resistance. Considerable uncertainty about the value of this form effect exists, however. This _{practice has not been} incorporated in this paper, primarily because this _{would entail a new} analysis of the results of methodical model _{series which do not} incorpo-rate the influence of this form effect. In _{some cases a re-analysis is} not possible because of lack of inforMation concerning the measured values of the total resistance of the models (in some cases these values have not been published). On using the Same _{friction formulation as was} originally used in arriving at the published residual resistance values, however, and on using a realistic value of _{the model-ship correlation} factor CA, no serious errors need occur on using a two-dimensional frictional resistance formulation. The actual procedure for calculating the resistance and effective power of a proposed design, to be used in the context of the results given in the main part of this paper, is as follows. The total resistance is calculated from the following equation:

RT=

h p SV2 (CF + CA) + RR A

(3)

A

in which _{p = mass density of salt water (= 1025.8 kg/m3}

for salt water and 1000 kg/m3 for fresh water);

S = wetted surface in m2; V = ship speed in m/sec.;

CF= flat plate friction _{coefficient for which the same} formu-lation should be adopted as was used in the analysis of the methodical model series;

CA= model-ship correlation _{factor accounting for the effect} RR of hull roughness, etc.

= residual resistance divided by _{displacement weight. This}

non-dimensional entity is to be determined from graphs or numerical formulations given in sections 3 and 4 of

0.075

C =

F

(log10Rn

St

G = displacement weight. In defining RR/A to be a non-dimensional entity, it is necessary to express A in the

same dimension-as R. In the SI (Systéme International

d'Unit6s) system of Units, force and weight are expressed in Newtons (N). Hence A snould here be expressed in N or 1r:410-Newton (kN). If V is the volume of displacement in m', then li=pgs7

= 10.064 7kN.

Only two different formulations for the frictional resistance coefficient Cr are used in the results presented in this paper -the 1947 ATTC- (Schoenherr) formulation and -the 1957 ITTC formulation. These are as follows:

0.242//CF = log10 (Rn.CF)

-

1947 ATTC .(4)

1957 ITTC

The value of the Reynolds number is determined from:

R = VL

11

-V

(5)

CF values according to these formulations can be determined from Table2.

Table 2. Values of CF according to 1947 ATTC and 1957 ITTC lines.

(6) Rn -CF x 103 according to 1947 ATTC line CF x 103 according to 1957 ITTC line lx106 4.409 4.688 2 3.872 4.054 3 3.600 3.741 4 3.423 3.541 5 3.294 3.397 6 3.193 3.285 7 3.112 _3.195 8 3.044 3.120 9 2.985 3.056 lx107 2.934 3.000 2 2.628 2.669 3 2.470 2.500 4 2.365 2.390 5 2.289 2.309 6 2.229 2.246 7 2.180 2.195 8 2.138 2.162 9 8 2.103 2.115 lx10 2.072 2.083 2

1.884

1.889

3 1.784 1.788 4 1.719 1.721 5 1.670 1.671 6 1.632 0 1.632 7 1.600 1.601 8 1.574 1.574 9 9 1.551 1.551 lx10 1.531 1.531

where V = ship speed in m/sec.;

L = waterline length in metros;

y = kinematic viscosity of salt water (= 1.18831 x 10-6 m2/sec. at 15°C).

The modal-ship correlation allowance factor CA, accounting for the effect on resistance of structural roughness (plate seams, welds,rivets, paint rouhness) and some allowance to give a realistic prediction, is primarily a function of the length cf the subject vessel. Typical values are given in Table 3.

Table 3. Typical values of the model-ship correlation. factor _CA.

On having determined the total ship resistance -for a certain ship speed, the effectiVe power follows from:

PE

= RT.V

(7)

where _{PE.is in Watt (W), RT is in Newton and V in m/sec. or in} kilo-Watt (kW) when RT is in' kN and V in m/sec. Conversion _to horse power follows from 1 HP (metric) = 735.5 W or 0.7355 kW, while 1 HP (British) = 745.3 W or 0.7453 kW.

Besides being dependent on Froude number, the residual resistance is, of course, also dependent on the hull form. _{The most important hull} form parameter intbis regard is the length-displacement ratio. The length-displacement ratio used throughout this paper is the entity L/V1/3, with L in metres and V in m3. The relation of this parameter with other commonly-used length-displacement _{(or displacement-length)} ratios is as follows:

30.57

(A/(0.01L)3 )1/3

where,in A/(0.01L)3, A is the displacement in tons of 2240 lbs and L the waterline length in feet.

L/V1/3 - 10

(V/(0.1L)3)1/3

where VA0.1L)3 is non-dimensional.

The speed parameter used in this paper in presenting residual resistance values of methodical _{model series is the volumetric Froude} number Fri, defined as:

F =

nV

777

gV

where V is the ship speed in m/sec.,

g the acceleration due to gravity (= 9.81 m/sec.2) and V the volume of displacement in m3. This speed

-

'3

-Waterline length in metres CA 12.5 0.00060 25.0 0.00055 50.0 0.00045 100.0 0.00035

parameter allows a better comparison of residual resistance values for ships of different lengtn-f_isplacement ratio, such as occur in methodi-cal model series. The relation of this parameter with other

commonly-used speed parameters is as follows:

V F.11V = . Fn where Fn = V and FnV = 0.2975 v/v113 V (12)

where,in V/iL, V is the ship speed in knots and L is the waterline length in feet. All other dimensions of V, L, g and V in Eqs. 10 and 11 are in metric (SI) units.

The wetted surface of systuvAtic hull, forms is often expressed as S = C V2/3 or S = CS iVL where C, is a constant for a particular hull

Si-.--.

form. In this paper, S = Cs 1/GL is used. To facilitate adopting the alternative expression, use can be made of the following kelation.

S

2/3

V

S

1/3

vTL-3. RESISTANCE PREDICTION BY METHODICAL SERIES DATA 3.1. Nordstrom Series

In 1936,'Nordstrom [1]* published the results of tests carried out at the Royal Institute of Technology in Stockholm with 14 different round bilge models, 5 of which were tested at more than 1 draught. Three of these models, each tested at 3 different draughts, form a small systematic series.

The results of resistance tests with these models, carried out in calm water, were originally analyzed with Froude's frictional

resistance coefficients. Even though no turbulence stimulating devices were adopted, subsequent analyses of the results have not revealed

low enough resistance values to suspect significant influence of laminar flow.

The results obtained by Nordstrom are now only rarely used, with the exception of the results for the small systematic series. As originally presented, the results are only useful for a full-scale displacement range of between

10 and 30

mi. A more applicable presen-tation of these results is given in Fig. 1, in which the residual resistance-displacement weight ratio RR/A is given as a function of the length-displacement ratio L/VI/3 and the volumetric Froude number Friv The residual resistance values in Fig. 1 are based on a re-analysis carried out by De Groot [2j using the 1947 ATTC friction line with

CA = 0.

*numbers in brackets designate references listed at end of paper.