Systematic resistance and propulsion tests with models of single screw full oil tanker

7. I

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B.S.R.Â. TRANSLATION _{NO. 2154f.}

Systematic Resistance and Propulsion _{Tests with}

Models of

Single-Screw PuJl Oil Tanker

IC. Tsuchida

and others

.hip Research

Institute, Ministry of Transportation, November, 1964..

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-fr CONTENTS Page SUMMARY ₁ PkEFACE ₂ MODEL ₂ 2.1. CB - series ₂ 2.2. L/B - series ₃ 2.3. B/d - series ₃ MODEL PROPELLER

₄

TEST CONDTIONS, etc. _¿4.

ANALYSIS AND PRESENTATION

5

5.1. Resistance ₅

5.2. Self propulsion ₆

USE OF DIAGRAMS ₉

EXAMPLE OF POWER ESTIMATION ₁₁

NOTATIONS ₁₃

REFERENCES

14 TABLES AND DIAGRAMS

Systematic. Resistance and _{Propulsion Tests with Models}

of Single-Screw Full Oil _Tankers

by

Kiyoshi Tsuchida', Koichi Yokoo', Atsuo

_Yaaki

xx)

x)

Shigeo Moriyana _{and Seizo Ohashi}

S UVNARY

This paper deals with the results of systematic resistance

and propulsion experiments _{carried out with models of}

single-screw full oil tankers. The models form a related family de-signated as UT series. The resistance and propulsion tests

were carried out on 35 models, _{ranging from 0,7e to 0Lf}

in

block coefficient, from _{6,17 to}

in length-beam ratio and from 2,16 to 3,06 in beam-draft ratio under three load condi-tions. The results of resistance tests are given as contours

of residuary resistance coefficieni. The results ¿f

propul-sion tests are given as contours of wake fraction, _thrust

deduction fraction and relative rotative _{efficiency. Within}

the limits of fullness and proportions covered by _{the series,}

the results given in the paper will enable the designer _to

make _{. close estimate of the EH? and the SHP}

of any desired

ship, if the principal dimensions of a hull and a propeller _were

given. In addition, it will _{be possible to}

determine quickly

the effects of any variation in dimensions _{and machinery}

characteristics in the course of a design study. An example

of such an estimate _{is given in the paper.}

x) Ship Hull Form Research Division xx) Ship Propulsion Division

,.-

-2-PRE FAC E

For about 10 years the Ship Propulsion Division, Ship

Research Inst., has been carrying out series of systematic

model tests of large tankers. In view of _{new developments,}

both in size and form, in the current way of building tankers,

similar tests are scheduled to be carried out _{in the future.}

However, in this report all test results analysed up-to-date are sunmaerized. These data can be used for basic design of

super-tankers.

2. _MODEL

As shown in table 1 a total of _{35 models are provided}

with various block-coefficients and ratios between principal dimensions. Lpp is kept constant (=6,00 m).

Except for the _{wooden models, underlined in.. the column}

giving model numbers in table 1, all models are of the parafine

type.

The models are grouped into different series as indicated by the reference column of the table. Most models are taken from contract test series.

The models derived from the parent types _{are grouped}

into the following series.

2.1. _Cß-zeries

With due consideration to the changing ratio of _CB

b/b' = l-p

1.-P'

(See Cp-Curve, and Body-plan

_{page l)}

However, both end parts, fore and aft, are properly

faired--- up.

2.2. _{1,,/B -series}

The dimensions are determined in proportion to L/B, where

complete geometric analogy is maintained _{for each frame section.}

2.3. ß/d -series

Each frame section is proportioned vertically _{in respect}

to draft change. To meet a practical _{demand of bilge circle,}

the elliptic contour, which will be the _{result of this}

con-struction, is replaced by a circular arc, which closely approxi-mates the elliptic contour.

The different values of CB, L/B and B/d can be seen in fig. 1. Model M.S. No 1321 is chosen as a representative one

of the series.

Datas are given as follows:

fige 2. Bodyplan and stem & stern contour fig. 3. Prismatic curve (Cp-curve)

fig. .4. Stern frame & rudder

tab. 2. Principal particulars

As shown in fig. 2, the stem is of an ordinary shape, having no bulbouc Thracteristics.

r 3

The contour of each frame section in the bodyplan wasdeter-mined in such a way as to satisfy the following relation:

¿4.

3. MODEL PROPELLER

The model propeller, M.P. No. ¿f7 was used in this test.

Drawing and principal particulars are given in fig. ₅ and. the

characteristic curve in fig. 6.

C

Fig. _{14. shows the propeller in position on the ship.}

¿f. TEST CONDITIONS, ETC.

The following three load conditions are considered in

this test:

Full load (even keel)

Half load (65% of the displacement at full load condition, with i % - Lpp trim by the stern)

Ballast (414. % of the displacement at full load condition, with 2 % - Lpp trim by the stern)

All tests have been carried out with appendages (except for bilge keels) attached to the model when measuring resistance and selfpropulsion parameters. Turbulance stimulator was

pro-vided by trapezoidal studs, each i mm. high, placed vertically

in one row at station No. 9. The distance between the studs

were lO mm.

Schoenherr's method was adopted as a standard formula for calculating frictional resistance. Accordingly corrections were made in selfpropulsion-tests, asswning a ship length

Lpp = 190,50 in, and a roughness correction coeff. Cf. = O,

I

equal for model and ship.

Wake distribution was measured round the propeller and analysed for some of the models in full 1öd eondition.c.

-5-5.

ANALYSIS AND PRSENTATION

5.1.

esistance

Residuary resistance coeff. rR is calculated from the

test data according to the formula (1), given below, and is presented as Contour Curves shown in diagrams 7-50. In the

s-diagrams 7-50 the parameters, _LIB and Cß are used as abscissa

and ordinate, respectively. The calculation of frictional re-sistance is based on the Schoenherrs formula.

2/3

2

rR

RR/p.y . V

Where, RR = RR

çi= displacement (n3)

y = velocity

p = water density (kg _{sec2! m4)}

R = total resistance, model (kg)

frictional resistance, model, according to Schoenherr (Kg) residuary resistance

The details of the diagrams 7-20 are:

x) F =

(1)

Diararnad

_{Condition E/d Froude}

_number,

FX

7-14 full load

2,46

0,14; 0,16; 0,17;

-O,l;.1

15-22

2,76

0,19; 0,20; 0,21; 0,22;

23-29

half load.

2,46

_{0,14; 0,16; 0,l; 0,19;}

30-36

2,76

0,20; 0,21; 0,22;

37-43

2,46

ballast do.

44-50

2,76

between rR and LIB of full load conditions at varying CB,

where F and B/d are taken as parameters. In diagram 55 and

i56 the values rR are plotted against

with Cß as parameter for two values of L/B.B/d = 2,76 is kept constant and the

Isame

loading condition (full load) is applied in the two

dia-gr&m.

5.2. ,elf tropulsipn

IFrom the test results, the values (l-wT), (l-t) and TR are

obtained. These parameters are shown in diagrams 57-59. These diagrams show the influence of CB and L/B on the parameters above. A study was also made on the influence of Bld on the

parameters. No significant indication could be reached on the

present basic models results.

Several contour curves are drawn for the above mentioned parameters, using L/B as abscissa, and CB as ordinate. However,

attention must be paid to the Fraude number, F _{0,16, which}

was applied to these models throughout. Therefore the following

remarks must be observed when using the diagrams _{6o - 65.}

According to the test results, it can be assumed that

TiR are nearly independent of F-numbers, ranging

from 0,lL. to 0,22, and stay constant throughout, whereas (l-wT) varies slightly.

-6

The imfluence of the parameters CB, LIB etc. on _{rR 1}

shown in diagrams 51-56. Diagrams 51-5L1. give the relations

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I 5.2.2.Ca.lculation of w2

Since (1-wT) is the value obtained by the so called thrust identity method, a transformation can be made to determine the wake fraction (WQ) defined by the torque identity method. For this purpose the following approximate formula can be used.

l_WQ _{= (1-wT)(l+_o,7}

(6)

5.2.3.Scale effect

-7-Giving denotes

16

and 20 to the value (1-wT) corresponding

to F = 0,16 and 0,20, respectively, the value of (1_wT) can

be approximately calculated by the following formulas:

Full load condition:

Ballast condition:

(lwT)2o = (l-wT

of the factor (1-wT).

/

1-t

The value of -

. also depends on F, simply because

lWT

Since the values in the diagrams

_60-65

are related only

to the models, allowance must be made for the scale effect.

(1-t) and are practically independent of the scale effect, which is not the case of (l-wT) cr (l_wQ).

(5)

(lwT)2o

(l-wT)

l6/°'9

(3)

Half load condition:

(l-wT)20 =

(l-wT)l6/0955

(Lt)

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5.2.l+.Chane of popel1er data

As the model results pertains only to self-propulsion

tests with 4-blade model propeller, _{as shown previously in}

fig. 5, reservation must be made for correcting the value

- of (1-w), when the propeller diameter relative the hull

dimen-sions differ exeedingly from the test case.

6. _{E 0F DIAGRAMS}

The influence of CB _{LIB, Bid, load conditions arid speed}

etc. on resistance and self-propulsion characteristics of superlarge type vessels can be derived from previously

men-tioned diagrrnns. The presented diagrams _{can be used for}

esti-mating effective horsepowers (EHP) _{as well as delivered}

horse-powers (DHP). An example of power estimating is given _below.

6.1. _{The residuary resistance coeff. r. for a given ship}

will be read off from the diagrams 7-50 for each F - number.

Actual parameters of the ship _{CB L/B etc. must be known.}

Forthe values of B/d between 2,14.6 and 2,76, _{a linear}

interpolation method can be applied.

6.2. _{The frictional resistance coefficient CF can be calculated}

for the ship at each F _{- number by using the Schoenherr's}

formula. The proper roughness correction _{factor CF is then}

2 (ni)

9)

For different F _{- numbers the residuary resistance}

(RR)

and _{the frictional resistance (R')}

can be calculated by the

following formu.la:;

RR = rR p

(7)

= (CF+ C)

p Sv2

(e.)

V:

dicplacement of the ship (ni3)

v : speed at the respective

F - nu.mbex's (n/s)

S : wetted surface area of the ship including _{bilge keels}

CF: frictional resistance coeff. _{(calculated according}

to the Schoenherr method) _{for the Reynold#s numbers}

corresponding to the respective Froude numbers.

C: roughness correction _{coeff. for the ship}

p: water density

Unless the wetted surface area, S, is _{known, it can be}

estiìnted by the formula _{(9). Wetted surface}

area cf bilge keels

must then be adcicd.

V

S'=aLd+-S _{: wetted surface area without bilge keels}

L : Lpp (ni)

d _{: mean draft}

: displacement (ni3)

a : coeff. l,l _{---- full load condition}

1,76 ---- half load condition 1,75 ---- ballast condition

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-The screw efficiency in _{open water, r must be determined}

for the ship from the characteristic _{diagram. The propulsive}

coeff. r for the ship can then be obtained by thé formula.

'R

0

(ii)

1-w3: the alternative values between

(l-wT) and .1-w0) for the ship.

The delivered horsepower (DHP) _{for a certain number}

can be calculated by the formula

DHP-'1 ₍₁₂₎

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6.3.

_{The total resistance R can be obtained by R = RR + RF.}

Consequently the effective horsepower (EHP) at a given F' _{- nu.mb}

I

will be.

EH?

(io)

6.14.. _{The self-propulsion parameters for the model can be}

ob-tained by using diagram

_60-65

_{for CBJ LIB, B/d etc. of the}

given ship.

6.5.

_{The parameter (lwT), which is believed to be greatly}

in-fluenced by the scale effect has _{to be redesigned to the}

ac-tual value of the ship. If (i_wQ) _{is wanted instead of}

(l-wT),

calculation can be made according to the formula (6).

6.6.

_{Correction must be made for the value (l-w), if the}

rela-tion between propeller diameter _{and hull dimensions differ}

from that of the test _case.

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6.7.

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EHP and SHP can be

calculated for different F

- numbers

at a certain

load

condition. The diagram curves of

SHP and

EHP can

then

be

drawn as

in

example

of power estimation shown

in diagram 66.

The above mentioned method can be applied

to ships

fairly

similar

to

the basic one given in table i and fig. 1. However,

this method of power

estimating is not reoriended on ships

considerably deviating from the presented test series.

EXAMPLE OF POWER ESTIMATION

According to the presented method of calculations, power estimation can be made for a tanker having the following data: Hull

Ordinary stem and stern.

Maine Engine

l,0OO SHP, 110 rpm (fitted astern) Pro2elier

Au-type,

5 blade, non-controllable,

LL :

221,60 m Lpp : 217,00 n B :

31,OOm

d : ll,14.9m CB : 0,796 n 10b : 1,50 D :

6,60 m

H/D :

0,764 n

aE : 0,610 n

12

-¿ CF = -0,002 (Obtained by Schoenherrs method)

1-wc,

- 1,20

For tank test results compared to the calculated values see table 3 and diagram 66. DIagram 66 shows a very good agree--. ment.

n

g

:

Acceleration of gravity

Lpp, L :

Length between perpendiculars

L

DWL :

Design load waterline length

R :

Total resistance

RF :

Frictional resistance

R :

Reynolds number

Residuary resistance

rF

Frictional resistance coeff.

rR

:

Residuary resistance coeff.

S :

Wetted surface area

S'

:

Wetted surface area without bilge keels

F :

Pro.de nt±iber

13

-NOTATIONS

a

Coeff.

B

Breadth

CB

Block coeff.

:

Draft

t

Thr.ust reduction coeff.

V

Velocity

:

Wake fraction, model

:

Wake fraction, ship

WQ :

Wake fraction according to the Torque Identity Method

WT :

Wake fraction accorciing to the Thrust Identity Method

T) :

Propulsive coeff.

110 :

Screw efficiency in open water

:

Relative rotative efficiency of the screw

Çt :

Displacement

1cb

:

Position of the centre of bouyancy

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9. REFERENC ES

A Yasal'i, et.al:

Comparison of wake-fraction between thrust identity method and torque identity method

Tech.' Res. memo. No.

_{4.3 (7/1964)}

_{and No. 5}

_(3/1963)

A Yasaki, et. al:

Approxim.te correction method of wake-fraction between

iidel1 and ship fitted with single _screw.

Tech. Res. Men'o. No. _13.3

_(7/1962)

K Yokoo.,

Ari investigation into Ship _{Model Correlation (in English)}

Min. of Trans. Japan Rep. No

_{45 (10/1961)}

¿f. T. P. Oßrien.,

The design ôf marine _{screw propellers}

15

-Table 1. List of models

'17f.

1_1

r

f' x)

The Ship Research Association of Japan

M.S. No. _{CB L/B B/d Reference Contractor}

987' 0,78 7,34 2,46 C series _Mitsul-Zosen 988' 0,80 B 989v 0,82 " 'I 990v' _0,84 " 1125 0,78 _{6,983 2,59 B series Mitsui-Zosen} 1126' 0,80 7,163 2,525 1127« _{0,84 7,519 2,406} 118e 0,80 7,00 _{2,46 Ç/L3 series} ( 41) 1189 " 7,20 1190 7,60 1321 ti ₇₃₄ ti _{Same as M.988}

1322 0,82 _{7,00 2,46 V/i3 series SRAJ (SR 4)}

1323 7,20 1324 ti _7,34 " _{Same as M.989} 1325 7,60 1152 / 0,80 _{7,839 2,16 B series} 1153 6,935 2,76 1154' 0,82 7,839 2,1 1155k 6,935 2,76 1506 0,80 6,75 2,76 L/B, B/d series Hitachi-Zosen 1507 0,82 " 1508 0,80 6,50 1509 0,82 II 1548 0,84 6,50 1549 0,84 6,25 1550 0,82 " 1564 0,82 _{6,75 2,46} 1565 0,80 " " 1566 0,82 6,17 3,06 1567 0,80 " 1551 0,84 6,50 2,46 _{L/B, B/d serieMitsui-Zosen} 1552 0,82 6,25 ' " 6,50 Kawaso.kiHeavy 1555 0,80 6,25 2,76 , industry

No. r Coeff.

rRr

(actual ship) 'Ç7(m3)

_61,40

Ç72/3 _1,559 VS Cm/sed) 7,46 RR (kg) 1,393xt09 CF 1,470x163 "-0,2x10 CFS l,270x1f3 S (m ) RF (kg) R (kg) .EHP V (knots)

lWT

f(l-wT) (1 W C

-16-Table ,3. EamD1e of

_{power_eiation.}

In this example _{a full loaded condition for}

F = 0,16 is considered n

-R1'6

R(th2,76)

rR 0,796 = 0,796 B/d = 2,70

V=

L x B x d- x _CB

V =F\jL

_.gJ"=3,i305

S n _DwL R L

V Iv,

_{vl,l7 x}

10_6 (15°C) n OwL s

Schoenherr's resistance coeff.

c

from fig. 63

1WTS

(1-wT)1 x 1,20

from fig. 63

xx) from propeller diagram, taken from

Thrust Method (see next page)

DHP

2

sec /m

i

9,47

S = aLD + _{without bilge keels}

36,370 Ftp = _{p Sv2 CFS}

64,930

R=+

6,45e

EHP = Rv/75 =(jixÇ'/75

Valu e _Remarks 0,16 0,00295 from fig. _{; L/B = 7,0; CB} 0,00320 from fig. 16; L/B = 7,0; 0,00025 0,00020 _{rR 4 X}

0,3'

0,00315 1,032

lWTS

o,646 1-t _0,792 fl0 0,565 71 _0,714 DHP _9,045 14,5 _{1,944 y 1,944 x} 0,574 from fig. 60

-0,036 correction for propeller _diameter

from Harvald's diagram

o 53

_{(l_wT)1}

2,560

= _Vs2

17

-xx) In the case of _{beeing calculated by torque method it}

is necessary to get value,

_{(1wQs) =}

which in the present _{case yields: iWQS =}

_0,675;

=

C.

A.?

Cp - Curve

8ody

_P(an.

I Pattern of Ceometorical Variation of Model Proportions

66 ComparIson of Results of Tank Teat and Estimation by the Present Method

4 .1

pIS1(ATb (V1

5

MP. No. 487

I4tL 6P NO IZt

.2 Body Pian, Stem & Stern Contour (M.S. No.1321)

;: :.:r

Th.!

4 Stern Fr&me & Rudder (M.S. No. 1321)

,

II..

A irni

IW

_'i

O J - - -- L._ J_

--

_O (J CI 0? 0) 04 05 06 0-T o. q o J

6 _{Characteristic Curve öl M.?. No. 487}

1JI

:WjIii

..

__J!i1I1I1,

1

::

.

WUVI 1MW ar

A _-t -. ETR 2//O i. .210

-

H ATO -4A'A 77O C2.ff" -_,,_.,.-#__ .

_.11114wa41

íiIIffA

iYJtWÀi

ii/172J

wii,iigi

VaV

X

-0-

Il

r1

3 PrismaticCurve of M.S. No. 1321 Table .2 M.S. No. 1321 Lp.'. (m) 6.000 LDL (m) 6.150 B Cm) 0.8172 d Cm) 0.3318

,

(m') 1.3017

L,lB

7.342 Bld 2.463 f(LppX10) 6. 027 C, 0. 800 Cr 0. &8 Ci 0.990 ¿a (%) 1.53 50 75.

Ffl-0i4

rL1

0.84 0.83 0.82 79 0.78 0.77 -2.46 84 ä3 £2 79 .78 077

7 Contours of Residuary Resistance Coefficieit

8 Contours of Residuary Resistance Coefficient

-r

-

---A,

7.6 7.4 7.2 68 70 YB O.? 64 66

L r

L-L

CB

9 Contours of Residuary Retistance Coefficieni

FmO.i8 OMit 0.83 0.82 OE8 i 0.80 0.7 0.78 0.77 62 Á

10 _{Conioura of Residuary Resistance Coefficient}

0.84 0.83 0.82 0.81 CB 0.80 o.7q 0.78 0.77 ¿6 6.8 70 _{72 7.4 76} L,6

11 Contours of Residuary Resistance Coefficient

0.84 0.83 OE8 I Cs 0.80 078 0.77 F'n-0.2f _____.__p.w. .,

-5/d-2.46 0.84. 0.83 0.82 0.81 CB 0MO 0.79 0.78 0.77 62 6.4 ₆₆

_%7O

_{72 74. 76}

13 _{Contours of Residuary Resistance Coefficient}

Q.77 _0.77

6.2 6.4 6.6 6.8 7.0

VB 72 74 76

M 14 Contours of Residuary Resistance Coefficient

ln,'O.2? _{)u t t. j=2.4 6} 0.84 _0.84 0.83 _-0.83 082 _0.82 0.81 _0.81 CB 0.80 _0.80 0.79 _0.79 0.78 ₀₇₈

0.84 c 0.83 0.82 0.8I o 0.60 o.7q 0.78 0.77 6.8 7.0

½

72 74 76

15 Contours of Residuary Resistance Coefficient

16 Contours nf Residuary Resistance Coefficient

0.84 0.63 0.62 0.81 CB 0.80 O.7q 0.78 0.77 0.84 0.63 0,82 0.81 Cb 8M 0.7 0.78 0.77 0M 0.63 O ô2 0.81 CB 0.80 O.7R 0.78 0.77 Fn-0.14 'Fu U %-2.76 6.6 64 62 -0.16 _{fuLL /d-2.76} 2 6.4 66 6.8 70 72 _{7.4 7.6}

L L 0.84 0.83 0.52 0.6 f Cb 060 o.7q 0.78 0.77 62 6.4 66 66 70 72 L/ 74 76 0.84 0.83 0.82 OSI

c

0.60 07q O.7 0.77

17 Contours of Residuary Resistance Coefficient

0.84 0.83 0.52

c

O51 0.60 o.7q 0.78 0. to

Fufl

18 Contourb of Residuary Resistance Coefficient

O.4 0.84 0.83 0.82 0.8, C8 0.80 o.7q 0.75 0.77

19 Contours of Residuary Resistance Coefficient

0.83 .8 70 L, 72 74 7.6 0 83 0.82 0.8I CB 0MO 0.7q 0.78 0.77

20 Contours of Residuary Resistance _Coefficient

Tu11 «-2.76

&2 64

8L/570 72 74 7.6

}- 0.20

'Ful 1.. _S/d2.76

0.83 0.82 0.6 f CB 0.80 C.7q 0.78 0.77 Fn=Q.2 f £2 £4 £6 Tu 1.1. 68 70 LIB 9a= Z76 72 74 76 0.54 0.83 0.52 0.6 c 0.80 0.7q 0.78 0.77

21 Contours of Residuary Resistance Coefficient

Contours of Residuary Resistance Coefficient

Fn0.27

_L276

084 Q _Q3 G 87 ₈₂ Q 8i _{os t} c a so _{o so} ,

----GT _am

arr

₀₇₇ 62 64 66

6870

72 74 7.6

23 _{Contours of Residuary Resistance Coefficient} Fn O 16 O-84 O. 83 0.8 0.8 f Cr 0.80 0.78 O-lT

H.lf

81a- 2.46 O. 1-6.2 6.4 6.6 68 7.0 7.2 7.4 T-6 0.53 82 08f Ca 0.80 0.7Q 0.78 0.77

.24 Contoura of Residuary _{Resistance Coefficient}

FnO-14

_B/d2.46

84

0.6 0.84 0.83 0.8 _0.82 0.51 0.8 Cr 08. _0.80Cr Q.Tq Q.7. 0.77 Q.7 °° 0.7 6.2 6.4 6.6 6.8 7.0 7. 7.4 7.6

Hf

2.45 .84 -o:Tr

'

I 36 6-8 7.0 L,,8 7.2 T.4 7.6 O. 63 0 82 0 81 C, 0-80 0:78 OTT

25 Contours of Residuary Resistance Coefficient

vn - o. tq 0.8 0.63 a 0.81 C8 0.80 0. 7q O. T8 O.7T 6.2 6.4

H1+

7.2 - 2.46 84 7.4 7.6 0.83 0.82 081 C' 0.80 .7-q O-76 0.77

26 Contours of Residuary Resistance Coefficient

ø.)-_____.

;4di$*i.

_.-

--38 6. 64 6.6 6.6 6-8 710 7'8

0.8 0. C O.T 0.7 0.7 62 6.4 O-84 O 8: 0.8 0.8 C. 0. 8 0.7 0.7 Fn 0.20 0. 07 HALL. 6.6 66 7.0 YB 5/d 0.84

27 Contours of Residuary Resistance Coefficient

28 Contours of Residuary Resistance Coefficient

0-83 0.82 0.81 C8 0.80 o. 7q 0.78 0.7r Z.46 0.84 083 0.82' O-el C 0.80 ON 0.78 0-Tr

.

*

dØilil

!IilIPIl!1I

di

T. 7.4 7.6

F- on

H41f 6.8 7.0 Ya 62 64 6.6 7.? 7.4

F - 0.??

0.84 0.63 0.82 6.2 6.4 66 68

Helf

7.0 7.2 8 P.46 0.84 0.83 082 0.81 Ca 0.80 o. rq 0.78 4 OTT

74

7.

29 Contours of Residuary Resistance Coefficient

31 _{Contours cf Residuary Resistance Coefficient} a84

Fnfl18

62 6.4 41 % -276 0.8.4 û83 082 0.81 CB 0.50 0.71 Q.7 77 66 &8 7.0 72 74 7.7

I. L r

F o.iq

_Htf

L-T

ais? ... l_-Í uyq F

t1

am .. 6.2 6 - 2,76 Q84

i.

063 08? O. BI ca 0.80 ON .078 83 082 ON 078 077.

33 Contours of Residuary Resistance Coefficient

Fn-O 20 H.1-F

r-/ 776

34 _{Contours of Residuary Resistance Coefficient}

.04 C) 3 08 06? Le 0.bO i. (líq 0.78 - 0'17 7-7 - 0.77 74 76 6.6 68 70 7.2 6h L/b7° 7.2 '(.b

35 Contours of Residuary Retistance Coefficient

I I

37 Contours of Residuary Resistance Coeffkient

FTt 0.16

a&6

Btt

- 2.6

U.0

6.2 64 66 68 70 7.2 74 76

38 Contours of Residuary Resistance Coefficient

Fn.01L

BItst

'U

83

.82 0Ml Cs O.. 0.83 Q2 081 Q., .. .4

AUI

iiFdUU

... a7q 07; A

Vd

ilS

0.77 62 6. 66 66L

_/8

hiO 7.2 7.4 7.6 Q83 '83 Q82 0.82 Q81 08 Cs 080 080 ay.

U

0.78

__u

r.77

Fn.OEf8 084 agi Cs a80 a 083 082 Q 7 078 62 64 66 68 7.0 72 ¼ - 2.46 034 0.83 a82 ß.8o 0. 7q ¿278 077 74 7.6 39 _{Contours of Residuary Resistance Coefficient}

Fn0.!q

at1ast 8%246 0.84. O. 84. 083 082 agi Cl aso 7q 78 77

40 Contours of Residuary Resistance Coefficient

68 70 7.2 7.4. 7.6

% -2.46 0.84 C5 U 8Q 079 Q7: _iTS 07 _0.77 62 64 6.6 6.8 70 7.2 7. 7.6 VB 0.83 O. $2 081 CB 080

41 _{Contour, of Residuary Resistance CoeffIcient}

083 Q 2 cisl CB as. 0.7 ci n 0.77 6.2 64 6.6 6.f 7.0 4,, 0.f4 o23 0.81 078 077

42 Contours of Residuary Resistance Coefficient

72 T4 7.6 Fn -0.2'( Rai 1.,1; Fn-O.20 B&((a.st 084 083 08

1

I

I

I

I Fn 0.22 034 a 83 032 03f CB c'8o

Rl la .-r

-2.46 014 e 78 0.77 62 64 6-6 6 70 72 7.4 76 0.83 0.82 Ce 30

43 Contours of Residuary Resistance Coefficient

R,11 s1 A' 6.2 6.4 6.6 68 70 4'R -276 72 71 76 024 023 0.7q 0.77

0J7 I

.

1 Rid1 ¶1

27

014 0.r3 z.t ci 'o 79 77 77

45 Contours of Residuary Resistance Coefficient

0.83 02.2 a i ce 020 0.79 OiT

au

62

Rai lat

a

- F

U l.a.: I Wd -27i 014 .6 6. 70 72 74 76

¼

46 Contours of Residuary Resistance Coefficient a73 o.g.t ci OL 0 0.73 77 2 6.4 C6 67 70 VB 7.2 74

7'

En -0.1 0.84 0.7-r

R Ilai

9i 2.76 s 2 64 66 68 70 7.2 VB 84 33 87 o 8i G a o o.7q 0. 7 077

47 _{Contours of Residuary Resistance Coefficient}

48 Contours of Residuary Resistance Coefficient

I Fn -(121 0.34 0.TT .1 _a 62 64 GB

flail

63 70 72 74 'd _2.76 54 76

49 _{Contours of Residuziry Resistance Coefficient}

50 Contours of Residuary Resistance Coefficient

53 052 osi CI

80

0.7 77 Fn 0.72 a34 G77 62 O4 0.33 082 o f C 30 aiq 78 77 H11 2 7 64 66 65 70 7.2 74 ₇₆

51 _{Effect of L/B and Bld on Residuary}

Resistance Coefficient (C.'=O. 78)

Effect of LIB and Bld on Residuary Resistance Coefficient (C,O.80)

11

111F:

_MMM

r

r

M__ rri

53 Effect of LIB and Bld on Residuary

Resistance Coefficient (Cs=O. 82)

oo

ua.M_R.I.uRIa

I,

MUMMIMIMMIIMUM0

uU.UUaauIUuaUa

Uu_MuuaaUUMaU1012

---u---

1.010

MUUUURRiÏáái.

aauIii

uauuaauììlu

UMUMUMUMUMUMU

54 _{Effect of L/B and Bld on Residuary}

Resistance Coefficient (C,-'O. 84)

Fu t

- T6

°MMURMRMUIUMUIUM

612UUUUMIUUUIUUUU

UMUUUIMIUMUUUM

II0 UUUUUUU....

40

UMUMUMUIMUMUMU

II..

UU.UUUUI.aUUU.

a..

:auuu

00

-s----_.,v,

_{---- ,r.____}

----2 4 U 6.7 70 72 7.4 7 Fu 1. t

-746

--276 62 64 66 6.3 ZO 7.2 74 76

F.&tt

iiaiai

Ial..'..

mua'..".

a.,a...ua

a a..

u.uIIauua uI

.,I.a,.mIa.

_uaui.aaaa.a.

aaaasaIIuI4.

aaaaaaaraaai

jIII

aauáaaauuaaaa

H

W6

7 00

Cil 020 O)t 027 FA

55 Effect of Cs ori Residuary Resistance Coefficient

r:

_{u: i:::..}

a.auaa,a uhu

a.a'ua...a...

aauuaauaaaua

aaaaaaaaiaaaa

. aaaaamaaa...

....aauuuua#

_ahaa

_raaa

E;iI'uu

uul$ auaua.

.57 Effect of LIB and C1 _{on Iwy}

ne o $T O ois ao 021 o F6 54 Effect of C on Residuary Resistance Coeffkknt -k6. at .-tt 06 03 4 o'

I,

o' 04 04 os I LS 06 05 0.6 o, 74 74 r.

r1

1

__1

-iamIluii

-- H

aaamaaaauiu

$$IIRRRhh

a

_!

aaauauuaaaaaua

auiaaamaaa

_a

Z5 F, I I 276 72 64 6 (I _7.0 e

ei J_. _{- --4.-._} 07

171 0*0 Z 04

2 04 06 6.8

Effect of LIB and C, on 'jR

Effect of LIB and C, on 1t

0.8 0.7 l-t 0.8 c-7 o! 07 171 G. 8*? 4

C..

Io

'z

64 66 .I 70 7.2 7m 7.0 72 '4 7.6

081! Ce F vL

:----'7-

;.1oß4

r-°L- -í.T'

'

I --

-

_- -r ---

'-1) ")9

o7q_..-/I

GT8

y//

X7'710Tb

07

-2 C4 084 07-q GT

-L i

J 62 4 8 70 07T -T? 74 T

.61 Contours of 1 ur and _{(Half Load Condition)}

I

w7-of1 W, and

I _WT 7)1? (Full Load Condition)

Cunt ou rs

70

-s

62 Contours of i--wi and rp (Ballast Condition)

A

.64 Cni(ours of - t and (Half Lead Condition)

6S Cou(.urs o f I i ;n.d iji: C8 e.. F -OE!6

Hi1f

oz 53

ri.iivarnsia

:7 g

i4IUI&ui

C8 e., Q . e Q

1111 'ir

Q 62 64 66 6.5 V8 70 7? 7.4 76