Comparison of seakeeping prediction methods for different ships

(1)

Report No. 42O

LABORATORIUM VOOR

SCHEEPSBOUWKUNDE

TECHNISCHE HOGESCHOOL DELFT

COMPARISON OF SEAKREPING PREDICTION METHODS FOR DIFFERENT SHIPS

by

W. Beukelman

$

L

I

(2)

CONTENTS.

Summary.

introduction.

Ships considered.

Calculation procedures.

4.

1.. Smith effect foi bulbous ctions.T

Calciflated parameters.

Discussion and comparison of results.

'1. Conclusions.

8Nothenálature,.

References.

Tables and Figures.

(3)

1. SUMMARY.

Four different procedures to determine the added mass and damping have been used to predict the seakeeping performance for different ship-types with an increasing length,

block-coefficient and biflb

Only vertical motions have been consi.derd for the case of head waves..

If the close-fit procedures are accepted.as,a reference,, it appears that besides a MIT bulb-form transformation Ta]iso., and for many cases with slight preference an adaptive

Lewis-transforination, suitable for bulbous sections., may be applied for the pre-dictioP of seakeeping qualities.

(4)

2.. INTRODUCT]0N.

For the calculation of added' mass and damping of the 'ship-sections the following

procedures have been used:

1. _{the close-fit mapping method for a good approximation of the cross-section (1,2)}

an a4aptive Lewis-transformation of the cross section to the unit circle with

a special application for bulb6Is sections. For normal Lewis-transformation

see (3,).

the Frank close-fit method' with a distribution of pulsating sources: along the contour of the cross-sections (5,6,11).

14. _{the MIT bulb-form transformation specially for bulbous sections combined with} _a

flormai(iinsfôrmatio)for the other cross-sectons (14).

After the calculation of the sectional added mass and damping as denoted above the

seakeeping performance in regulai' and irregular waves, has been determind in the same way and according to Korvin-Kroukovky's strip theory as modified b'Gerritsma e.a. in It should be remarked, that a version has been used in which nq symmetrical terms for the added mass cross coupling coefficients were present. This version is ieferred

to in

(8)

as the old method.

The following parameters have been determined:

the, heaving and pitching motion,, the vertical wave bending moment at the midship

sectiOn, the added resistance( rin waves, the phenomena of slaing and

ship-ping in standard irregular séa.

These caIulations have been applied for five ships with different lengths,

block-coefficients and buibsizes.

It was the intention to show the differences in the final results because of the

(5)

3. SHIPS CONSIDERED.

As denoted before the calculations have been carried out for five ships with

in-creasing length, blockcOefficient and bulb. These ships are the following ones:

the ijell-knowri 60 series hull form with C =

the "SA. van der Stel", a -fast cargo-ship with a small bulb (.1%) (9)

bhe "Atlantic rown"., a containership with a circular bulb of moderatésize

(9. 5%) (ip)

. the "Davidson A Destroyer' withan exreme1y bulbous fore-ship (35%)

(ii)

5.

the "Macoma" a tanker with a bulb of 6.9% (12)

For the principal ship data see table I and for the offsets see tables -6'.

It should' be remaiked, that the MTTbulbform transformation could bn'ly be' applied

for t'he"tiantic' Crom" and the"Daidson A Destroyer". The integrated weight-dis-tribution has also been presented in tables 2-6 for the different ships except for

the "Atlantic Crown" In this case the integrated weight-distribution was unknown

For the motions f this ship has. been made use of an estimated diusof inertia.

The block coefficient varied from CB = -54O until 'C,B .850, while the ship length

varied from L = llTm until L. '3i0m.

For all.ships the full-load condition only has 'been taken)into account..

The calculations, have originally been made for two ship speeds., but the tendency

proved to be the same for both these speeds, so that in the figures the

esü1tsför

one speed only have been presented.

(6)

c_3.=

6.

I. _{CALCULATION PROCEDURES.}

In the close-fit mapping rocedure the ship section is conformally mapped to the unit

circle and a distribution of multipoles is used, for the solution. The mapping is done ly the following transformation formula:

N

_,1'zrv-4)

z

2n-I

wher.e 'N = maximum index number of the transformation coefficient.

The number N used for the ships considered is 'shown in table 1. The mapping under consideration is rather accurate.. A good descript:ion of the transformation procedure has been presented y De Jong in (2). The' computer results'iió'r added mass and damping have proved to agree very well with experimental results (i).. For this _{reason the}

results of the close-fit procedure are accepted as a reference to check the accuracy

more or less of the Other methods.

The iewis-transformation is obtained by using N = 2 for

_(ID

which results into.:

Z'.

4 -

+.

3 (2)

The half-beam to draft ratio. and the, sectional area coef'ficient _{are presented as} follows.:

i+-,J

2T

__'3

2 2.

_-ri.cL1-',

From (3)' ma' be derived:

.J. =

(

4 4

Substituti' of

₍₅₎

in

R)

'delivers the following equation:

+c2

0 iwhich

Ei.",.. (!

(1)(HD_)2

(7)

The solution of

(6)

rêsiits into:

-F! ±

From the. di.scriminait of

(8)

it isobvious, that the condition holds:

ci'

If

HØZ.,4

then.:

k-.1'

T

4j

With (12).' it value:'for c'

From (1:0) and (11) -followS:

(

4)2

H0#4

can be shown, that c1 in (fl- is increasing with

6

and sO the minimum

The limits for the coefficient c1 are

and for a3, if only the positive root of

(8)

is taken into account:

--

3-33

The limits for -a1- are to determine with -(-5), (10) and (ii-)..

if then

and if

-I-L> I

then

0 ,> cx

)

('3)

and if

HD>4

then:

The maximum values for the area coefficient may be evaluated' for each H0 with condition (9) and delivers the relation:

.od&I

(iiç

I

(8)

--The minimum value of this range may be obtained by

dG

0

achieved for H0 = 1.and so with

₍₁₇₎

_{the result is}

ax

4.(z

which shows,. that this minimum value is

(is)

The maximum values for the area coefficient _{are shown in figure 1} _for _{H0>1 and}

110<1.

Small values of the sectional _{area coefficie±-it may cause reentrant forms, but this}

will only occur for very fine sections.This. _{effecton the final results may be}

neglected or can easily be avoided as denoted in (13,14).

The beam of a section should not be too small. For bulbous sections the half-beam should not beimaller than 1% of the maximum half-half-beam of the shi.

If for a section condition (17) _{can not be fulfilled the adaptive procedure will}

be so, that half-beam and _{area are kept constant, while the draught will be}

in-creased to such a value, that condition (17) is _{satisfied. From this procedure}

follows the minimum new draught.

T

_-

.ç

. _.

For numeri!l reasons T should be increased up to i.0075T.

This procedure as described above is called the adaptive Le is-transformation _and.

will be specially required for bulbous sections, _{although the fit is not accurate.}

Generally speaking the representation of the section _{by the Lewis-transformation is}

rather poor, but this fit is not the main-target _{of the transformation.}

It should be noted, that, the use of this adaptive Lewis-transformation is restricted.

to vertical motions only.

The Frank close-fit method is based _{upon the determination of the velocity potential}

obtained for a distribution of _{source singularities over the submerged ship section.}

The sources which satisfy the linearized free-surface _{condition and the kinematic}

boundary condition on the surface of the section-cylinder have to be infinite in

number to obtain a continuous _{source distribution. Frank (5) came to an approximation}

by using a finite source distribution in such a way, that a constant strength _was

consi/dered for some straight segments replacing the original section. The

hydro-dynamic pressures are obtained from the potential by means of the linearized

Ber-noulli equation _{Integration of thesepressures} _{over tke submerged seet1oncy1inder}

,de14'v-ers the hytho-dynamiorep _{The accurac'y cf thac1ut-Ton de.pendaon}

the chosen number of source segments. This 'number of' segments has been denoted in table 1 _for the ships considered. The hydrodyxiamic

forces represented as 'added mass and damping 8.

(9)

zç

in which A and B are transformation coefficients.

The half-beam to draught ratio and the sectional area coefficient are related to

the coefficients.A and B in the next way:

H

₀

-2

LH1,

The MIT bulb-forms are used in (14) for seätions with

.) and

(5> 1.2

and claim to afford a rather good fit of the section.

For

our

_{calculation of added mass and damping of the bulbous ship sections according}

to the MIT bulb-form transformation use has been made of the Subroutine

_Bulb

in (14).

The determination of the motions and other parameters have been performed with the

same seakeeping computer-program "TRIAL" of the Shipbuilding Laboratory of the Delft

University of Tedhnology as described in (114), so that differences in the final results

may only arise from differences in the sectional added mass and damping.

14.1. _{Smith-effect for bulbous sections.}

For the calculation of the sectional wave forces and -moments an effective draught

is used in ('i) and

(8)

at which draught these forces and moments are supposed to

act. In general this effective draught T may be found for each section by using

a sufficient number of waterlines as shown in figure 2 and so it holds, that:

e

-

y

I

+ I

Ayje

.. ...

IJ

=

.

The general expression for each section becOmes:

9.

have been calculated with a computer program described and presented in (6).

The MIT bulb-form transformation developed by Demanche and presented in 4) by

Loukatls is just as the Lewis-transformation based on the sectional half-beam to draught ratio and the sectional area coefficient and also oharacterized as a two-parameter transfo]mation.

The mapping funôtion of the MIT

bul

-form is presented as

(2o)

(24)

(10)

T

=

0

from which the effective: draught I _{may be solved,.}

If for a section y is increasing continuously with z,, expression (2)) may be written as:

_kT

After partial integration is obtained:

0 Y

_.kT

_z

YW

e

(y/_kJy

'1z)

Yw

If one keeps in mind., that z 0 for y

y and

4'

-

kT

e

=

from which follows

HJ

yw

r

_kz

0 - kz

(2)

the resfit looks as

(2)

T-

e(fkZ)

cz)

-T

This expression for

T

is analog to the one used in (7), but one shoild keep in miid,

that this expression is only valid for a normal ship section where y is increasing

continuously with z. For bulbous ections the general expression (21) should be used.

it is almost needless to remark, that the described I

ma b

used for vertical wave

(11)

5. WLCULATED PABAIvIETERS.

First of all the response functions have been calculated _{for the heaving and pitching}

motion, the added resistance in waves and the _{wave bending moment at the}

midship-section. The last one has not been determindfor he "Atlantic Crown" _{because of the}

lack of the weight distribution. All these parameters have been _{plotted on base of}

the root of the ship-length 'wavelength ratio as follows:,

zot, /c.,c,

for heave /

int11efigures3-7-1T-i5-i9

for pitch

/k'

_.1,

for the added resistance in waves _{in the figures} ₁₄

_-

_{8 - 12} _-

_{16. -}

₂₀

V

(W)

for the wave bending, moment at the midship 'section in th figures 14 -

'8 - 16 -

20' in which:

1w

heave amplitude pitch 'aiñplitude wave amplitude

wave height (twice the wave amplitude) added resistance in waves.

2T/

= wave number

wave length

maximum wave slope density of water

acceleration of gravity

ship length between perpendiculars breadth.

Afterwards the significant values have been. determined for the parameters considered

in different wave spectra according to the general expression of Pierson

Moreover the number per hour of shipping and slamming has been _{calculated. All these}

(12)

for the significant heave amplitude Zay3 for the significant pitch amplitude &ry for the increased effective power

for the significant wave bending moment amplitude

for the number per hour of shipping.

for the number per hour of slamming

j

12. in the figures

5 -

₉ -13 - 17 - 21 in figures 6 10 -18 - 22

The differences in sectional damping and added mass are neglectabie for the greater

part. of the investigated ships, 'except for section 20 of the "Atlanti _{Crown" and} section 16 - 20 o.f the "Davidson A Destroyer". In view of this phenomenon and because

of the fact, that the MIT bulb-form transformation could only be applied _{for both}

the mentioned ships the sectional damping and added _{mass have been shown in the next}

figures' for the denoted cases only:

"Atlantic Crown" for

UY =.7 (A/L'4.Ji)

_{the added mass and damping on base of}

sh±p-sections in the fig.ues 23 and 2)4 respectively;

for section 20 the added mass and damping _{on base of frequency}

in'hefigures, 2.5 and 26respe'tively.

"Davidsèn A Destr.oyer" for.

_{l.2o (Yt4'the added}

_{mass and damping on base of}

ship-sections inthe figures 2 and 28 respectively;

for section 16, 11', _{i8 and 19 the added mass and damping on}

(13)

6. DISCUSSION AJ1D COARISON OF THE RESULTS.

Generally the differences between the results appear to be very small both for the regular and irregular waves. The most sensitive parameters are besides the sectional

damping and added mass the resistance increase in waves and the wave bending moment.

FOr tie Todd 60 with CB = .10 and the "S.A. van der Stel" the results are almost identical, which means that for normal ships without or with a small bulb no dif-ferences in motions, added i'esitance and wave bending moment may be expected in consequence of the method considered to determine the sectional added mass and

damping i.c. the close-fit mapping method, the Frank close-fit method and the

Lewis-form transLewis-formation. For the "Atlantic Crown", a ship with a deeply submerged circular bulb of normal size for this type the differences are negligible.

The MITbulb-form transformation could only be applied for section 20 of this ship and so the small differences in the final results between MIT bulb-form- and the Lewis-transformation can only be caused by the difference in sectional &amping and

added mass of section 20. See figure 25 and 26.

From these figures it is clear, that the sectional added mass shows rather high values for the adaptive Lewis-transformation in the case of a deeply submerged circular bulb. Nevertheless the influence from this on the motion and resLstance

parameters is very small and for practical purposes negligible.

The "Davidson A Destroyer" has extreme bulbous sections in the forward part of the

ship and the MIT bulb-form transfrmation could be applied. or the sections 16 - 20.

A comparison of the results of the methods considered shows, that MIT bulb-form

transformation results viate rather strongly from both the close-fit methods,

al-though for practical use the differences remain yet small..

The differences are thainIy caused by too: high values for the sectional damping in the

case of.the MIT bulb-form transformation compared with the resuls, of the other

methods. See figure 26 - 36.

The results of the adaptive Lewis-transfoiation method for sectiona damping and

added mass are closer to the close-fit methods than those of the MIT bulb-form-trans-formation. Consequently the same tendency can be shown for the motions, added

resistance and wave bending moment in spite of a more correct representation of the

section contour in the case of the MIT bulb-form transformation.

(14)

CONCLUSIONS..

For prediction. øf the seakeeping performance of usual ship types the method of

determining sectional added mass and 'daping is noj so important. No significant difference appeared to be for all investigated ship types between the mapping-and Frank cicse-fit method. If these procedtes are considered to be. a reference, it has been' shown, that for extremely bulbousections the results of the adaptive

Lewis-transformation are closer to this reference than those of the. MIT

bulb-form transbulb-formation with an exception or deeply submerged circular sections

(15)

8.

NOMENCLATURE.

A Sectional area; coefficient of MIT bulbforrn transformation. an Transformation coefficient with index number n.

B Beam of ship; coefficient of MIT bulb-form traisformatibn.

C.B Block coefficient.

CM Wave bending moment coefficient. -.

cn Parameter for Lewis-transformation. g Acceleration of gravity.

'Half-beam to draught ratio.

k Wave number.

k Longitudinal radius of inertia. L, I Ship length between perpendicu.ars.

Ship length on the wate line. Wave bending moment 'amplitude.

,ba1/3 Significant wave bending moment amplitude.

rn' Sectional added mass.

Maximum index umber of the transformatibn. coefficients.

Sectional damping.

PEAW Added effective power' in waves. RAW Added resistance in waves. T Draught of ship.

Effective draught for Smith-effeut.

x,y,z Right hand coordinate system fixed to ship.

Half width of designed aterline.

z Heave displacement,, mapping function. Za Heave amplitude.

Significant heave amplitude.

A Wave length.

w Circular wave frequency.

wJ

Circular frequency of encounter. Density of water.

Sectional area coefficient..

(16)

16.

Pitch amplitude.

Significant pitch amplitude.

Instntaneous wave elevation; denoted reference, plane for transformation. Wave amplitude.

Significant wave amplitude.

(17)

9.

REFERENCES.

Porter, W.R.,

Pressure distribution, added mass and damping coefficients for cylinders

oscillating in a free suf'ace.

University of California, Institute of Engineering Research, Series

82, 1960.

Jong, B.. de,

Computation of the hydrodynamic coefficients of oscillating cylinders..

Shipbuilding Laboratory, Dëlft University of Technology, report

17.

Netherlands Ship Research Centre TNO, repor.t no. i1i5',

_1913.

Tasai., F.,

On the damping force and added mass of ships heaing and p±tching.

Journal of Zosen Kiokai, 105, July

1959, 147_56,

.TTans.lated by Wen-ChinLin

edited by W.R. Porte.r, University of California, Institute ôf Engineering Research, Be.rkiey, Calif. Series no. 82., issue no.

P5., July P960.

14 _{Loukakis, Theodore A.,}

Computer aided pPediction of seakeeping performance in ship design. MIT, report no. 70-3, August 19.10.

Frank, W.,

Oscillation of cylinders in or below the free surface of deep fluids.

NRSDC report 2375, October

_1967.

Bedel, J..W.; Lee, C.M...,

Numerial calculation of the added mass and damping coefficients of cylinders

oscillating in or below a free surface.

NRSDC report

3551,

March

191.

1. Gerritsma, J,.; Beukelman, W.,

Analysis of the modified strip theory for the alculation of ship motions and

wave bending moments.

International Shipbuilding Progress, vol.

14,

no.

_156,

_1.967.

(18)

Cerritsma, J; Beukelmax, W; Glansdorp, 'C.C,

The 'effect 'of beam on thehydro'dynamic characteristics of ship hulls. Office. of Naval Research 19714..

Gerritsma, J., Beukeiman, W..,

nalysis of the resistance increase of a fast cargo hi].

international Shipbuilding Progress, vol.

_19,

no.

211, 1972.

hO. BeUkelman,, W., Bu'ften'hek, M.,

Full scale measurements and predicted seakeeping' performance of the container-ship "tlantic Crown't.

International Shipbuilding Progress, vol 1 no. 2143, 19'7)4.

Ii. Frank,, W, Salvesen, N.,

The Frank close-fit ship-motion computer program. NRSDCreport no.. 3289, June _197O.

Glansdorp,, C.C.,. Pijfers, J..G.,L., " . .

The effedt of design modifications of' the, atiira1 course. stability o' full tanker models'.

Shipbuilding Laboratory, Deift University of Technology, report no. 235'..

Von Kerczek, C'., Tuck, E.O.,

The representation of ship hulls by confbrmal mapping functions.

Journal of Ship Research, vol. 13, no; 14,

_1969.

14 Beukelman, W., Bi,jlsma, E..F.,

Description of a program to.. calculate the behaviour' of a ship in a seaway (named: TRIAL)

Shipbuilding 'LaboratOry, Delft University of Te.chnolbgy, report no.

_383.

18'..

(19)

Tab_ - DATA OF SHIPS.

SHIP A.RACTISTIC (full

scale)

Lengt

btween perpendiculars Lp

Lengt

on the waterline L.

Bread hB

j

Draiigt .

Volum-

o displacement

Block oeficient CB

Water.labe area

Longi

udilnal

moment of inertia

Of wa eläne

LOB fir

rd. of

centr

o effort of waterplane

forwa4'd

bf L/2

Perce tae of

bulb

Todd 60

.70

- "Van

e. Stel"

"Atlantic

Crom"

"Davidson

c-DestrOyer"

"Macoma" (ni)

i)

152.50

196.00

116.77

310.00

(m) 123.96 154.68

203.04

116.77

318.05

(m) 17.42 22.82

?8.Q0

12.45

47.16

(m)

6.97

9.14

8.15

4.26

18.90 (m3)

10324

17910

26061 3345.

24994

.-00

_.563

.540

.850

(in2) i6io

2428

3976

1074

13257

(m4)

_1425054

_2816396

_8173499

₉₅₂₇₅₁

90514506

(m)

.59

- 1.68

1.80 + 2.01 -

8.74

(ui)

-

2.55 - 4.30

-

5.97

10.95

.

-

6.76

0

4.4 _9.5

35.0

. 6. k /L Maxim coe

ff

Ma±im

Frank

Freeb.ard

index

number

of transformation

cint fo: close-fit mapping

humbér of sOurces

emeiit

for

close-fit method at FPP for shipping

(00

19 9

5.454

.2190 19 12 15.000

.2556

19 28 12.400

.2554

31 21 5.130 .2709 .9.100

(20)

Dimensions in meter.,

T4'0

1 2 3 14 ₅ ₆ 7 8 9 10 '0 0 .1514

.517

1.2148

231'0

₃₅₇₂

.14.733 5.7140 6.1451 6.713

6.713

0.581

.0

_.565

_1.550

_2.765

14.165

5.515

6.650

7.1420

_7.915

_8.076

_8.100

1.161

0

.680

_1.895

3.280

14.770

6.190

7.265

7.960

8.375

8.5214 8.5140 1.7142 0

.773

2.129 _3.710

5.257 6.6714 7.708

8.325

8.595

8.682

8.690

3.14814' ₀

_.932

_2.7314 _14.6141

_6.321

_7.558

_8.333

_8.6146 _8.708

_8.708

5.226

0 1.1428 _3.701

_5.729

7.1814

8o72

8.5314 8:.7o8

-6.968

_.775

3.2014 5.3)47 :6.861

7.811

8.368

8.629

8.708

8.708 IP.ii

12 13 114 ₁₅ 16 ₁₇ 18 19 20 0

6.713 6.00

6.3014

5.572

14.337 2.9314 1.6014

.671

.1714 0

0.581

8.. 100

8.100 _7.855

7.260

6.335

5.105

3.700

2.330 .895

0 1.161 8.5140 8.5140

8.310

7.855

7.050

5.880

14.390 2.7145

_1.195

0'

1 7142

8 690

8/690) 8 55jY8 186

71439[ (

₂₉₂

148O) 3O14

₁ ₃₇₃ ₀

314814

_8..o8

_8.708

_8.656

_'8.1455

_7.872

_6.7714

_5.216

3.387

1.5141 0,

5.226 -

-

8.6.90 8.5314

8o11

6.983

5.1459 3.51414 .1.602 0

6.968'

8.708

8.108

8.708

8.577

8.1:142

7.201 _5.703

3.71414

1.690

Tabje .2. Todd 6o

_{= .70}

'O'diliate number Weigth froth FPP to ordinate Ordinate number

/Th

c

)

Weight from FPP to ordinate ton 0 _10356.14,9 11 14635.05 1

10327.17

12 _14013.66 2

_9958.92

13

_3058.83

(3

_9337.08

'114 2558.146 14 86314.07 15 _2369.146 5 .

8071.18

16 18o3.6'1 6 _79114.75 17

1068.30

7

7391.27

18 14114.76 8

_6525.91

₁₉

_39.70

9

583.90

20,(FPP) o 10

_5296.57

(21)

Table 3. "VAN DE STEL"

Or di nate Weight from Ordinate Weight from

number FPP to ordinate number FPP to ordinate

10

_8512.50

Dimensions in meter.

7. il00

1 2 3 14 ₅ 6 7 8 10 0 0 0

.195

.350

.960

1.9140

3.i85

14.660

6.205

7.1400

7.655.

.1r3.5 0 0

.515

1.230 2325

3.750

5.255

6.820 8.l60

9.1145

9.325

.871 OS 0

.700

1.635

2.98.5 14.590

6.300.

7.880

9.135 9950

10.090

1.3014 0 0

.825

1.9115 3.14140

5.150 _6.905

8.505

9.710

10.1400 10.510.

2.613

0

.060

ll'80

2.735

14.600 :6.1455

8.280 Q9.71.5

10.680

11.1145

11.225

3.919

0

.125

1.615

3.560

5.615

7.585

9.260

10.14145 11.1145. 11.1410 11.1410

5.225

0 .1145

2.275

14.5145.

6.655

8.570

10.005

10.900

11.1410

-6.531

0 .5.60

3.225

5.680 _7.700

9.365

10.550

11.200

11.1410

-

-7.88

0

1.870

14.51:0

6.825

8.670

10.025

10.9145

11.350

11.1410

-

-9.11414 .9140 3.1475

5.880 _7.915

9.1470 10.5)45

11.200

11.395

11.1410 11.11:1.0 11.1410 T."/ORD.11 1.2 13 11t 15 16 17 18 19 20 no. 0

6.855.

s.14so

3.925

2.525

1.905

1.375 .965

.625

.290

0' .1435 _8.7140 _7.6145

_6.170

_14.715.

_3.510

_2.650

1.995 _1.515

1.280 _.995

.871

9.580

8.615.

7.210

5.725

14.335

3.260

2.1470

1.915

1.585

1.380

1.306

10.0145.

9.120

7.730 .6.265

14.8o

3.610 2715

2.1:00

1.700

1.500

2.613

10.795

9.960

8.750

7.295

5.735

14.265

3.050

2.155 i.56o

1.110

3.919

11.130

l0.)4)40

9.365

7J9S35

_6.310

14.680

3.200

2.0140

1.075 _.390

5..2251 o.25. .tO..7140. (9.. 715. .8425

6.765

5.010 Iti .910

.765

.o6o

-6.531

11-320

1'09OJaJ05 885o 7.190

5.3140

3.500

1.870

.6855 0

7838

11.370

11.100

10.360 _9.205

6io

_5.705

_3.750

_.1..970

_.755

.. 0. 11414 11.1410 11.2.00

_10.580

9.520

8.010

6.1140 14.160

2.330. .990

.075

ton ton 0

17931.00

.

ii

710lL00

1:71478.25 12 55146.63: 2. 17287.50. 13 14362.50

I68rrT.75

114

3695.63

14

16068:00

15 21497.13 5

15313.88

16

1213.75

6 .1143145.13 17 8o5. 38

12899.00

18 1491.13 8

11552.63

19 3142.88 9

10016.25

20

25.00

(22)

Dimensions in meter. Table 14 1 "ATLANTiC(OR0WN" distributi:on 5 6 8

9)10

T.0RD.0f\\

2 No weight 3 11 U .ii@j: .140. .110 .140 .110 .IiO. .85.

.3.90

6.83

8.93

10.00 .388

.Ii1

.140 .1411 .81

1.66

3.31

5.118

7.75

9.71

11.06

11.68 .776

.110 .51 1.21

2.62

.11.65

6.89

9.01

10.69

11.85

12.35

1.165

.14 .110

.63

1.69

3.55

573 7.9b

9.8

11.117 12.1111

_12.79

2.329 .6J

.110

1.16

3.12

5.60

7.86

9.98

11.61

_12.78

13.113

13.62

3.11911

.ç50)

_.52

2.03

14.59

7.25

9.51: 11.31

12.63

13.118

13.86

13.95

11.659

.52

.97

3.22

6.06

8.72 io.i6

12.28

13.31

13.86

111.00 111.00 5.8211

.57j

i..86

'7.56

9.98

11.73 1293

13.10

111.o®

-6.988

.67

3.37

6.1111

9.02

_11.07 _12.115

13.36

13.89

i14.00

l53

2.14.2 5.117

8.21

10.32 11.9T 13.011 13.70

13.99'

1i1t.00 111.00 111.00 T,/ORD:. 11 112 13 . 114 15 16 17 18 19 . 20 'KJno'. 0

9.28

7.67

5.62

3.147 _1.70

_.59

.. 02 0 0 0

.388.

11.111

9.88

8.211

6.22 tt.3

_2.77

i:Ji.6

1.35

1.35 .776

11.91

10.75

9.16

7.26

531

3.57

2.07

1.80

1!.80 1.80

i.i6

12.38 11,32

9:.81

_.96

6.01

11.11 2.118

2.13

2.329

13.31

12.145

11.09

9..311 7.314

5.26

3.35 2.50'

2.50

3.11914

_13.76

13.09.

11.89

10.21

8.22

6.10

11.01

2.30

11.65,9

13.96

13.116 1:2.38

10.82

8.88

6.12

11.511

2.62

1.36

.8211 i11.00.

13.67

12.73

11.28

_9.39

_7.2)4 11.99

2.97

1.29

.214

6.988

111.00.

13.79

13.00

11.65

9.79

7.66

5.39

3.31

1.51 0

8.153

114.00

13.89

13.21

11.95

10.18

8.01

5.81

3.67

1.75

.20

(23)

Table

_5.

"DAVIDSON A DESThOYER"

Ordinate eigh't from dinate. .eight from

Dimensions in meijer. T.4bRD.0 c2no-. 1- 2 3 14 ₅

.6

7 8. ₉ 10 0 0 0) 0- 0 0 0 . 13 -.13 .5.14

.81

.203

0 0 0 0 0 0

.39

-L56

1.89

1.95

.1406 0 0 0 0 0- o .814 1.70

2.13

2.148

2.67 .609

0. 0 0 0 0 .19

1.30) 2.11

2.61

_2.97

_3.1.7

1.217

0 0. -0 0

.32

-1.i

2.62 _3.29

3.714 14.05 -)4.25

1.826

0 0 -0

.57

2.114

3.26

3.80

14.36 14.68 14.88

5.07

2.14314 0 0.

.93

2.66

3.83

14.91.

5.21

_5.143

5.58

5.68

3.0143 0

1.38

3.55

_14.56

5.06-

_5.38

5.62

5.82 _5.92

_6.02

_6.o6

3.651

2.11

14.20 14.83

5.31 _5.56

_5.78

_5.93

_6.09

6.i6

6.20

14.260

3.68

14.1414

_-5.05

5.149

5.72

5.90

6.00 _-6.11

6.20 6;22

6.22

TJ0RD. 11 12 13 114 _1-5 i?6 ₁₇

i8

₁₉

₂₀

-0

.81

_.Th

(.8i

.81

_O5 0

.203

1.95

1.80

1.141 0 .1406

2.67

2.67 _2.67

_2.67

_2..67

_2.67

_2.62

_2.33

_1.82

0-.609

3.17

3.03

2.69

2.06

0

1.217

14.25 14.;25

(25

14.25 14.25 14.03

3.69

322

2.35

0

1.826 _5.07

50-1 14.97 14.814 14.62 14.29

3.83

3.23

2.29

0 2.14314

5.62

15.t15

5.32

5.00

14.56 14.03

3.55

2.82

1.89

0 3.0143

.5.9)4

5.72

5.37

14.82 14.27

_3.53

2.82

2.05

1.28

0

3.651 6.o6

_5.79

_5.25

14.8

3.90

3.10

2.32

1.59 .93

0 14.2-60

6.13

5.76

5.20

14.117

_3.76

_2.92

_2.11

1.142

_.80

0 ton ton 0 314147.141 11

1578.60.

1

3355.25

12

1358.66

2

_3259.146

₁₃ _1-1141.72 3

_3139.20

114

932.53

14

2997.146

1-5

738.70--5 28314.214

i6

i_56o-.

2-3 6

26149.55

_39T.13

7 21411.3.314

i8

2149. 39 8 2226.141 19 117.01 9

2009.147

20 TO

'i792. 53

(24)

Table 6 "MACMA"

Qdinate

Weight from .

0rdiñte

Weight from

Dimensions in meter. 0 ton 231499)4 11 ton

112191

1 23109)4 12 995)40 2

223883

13

86889

3

213365

114

7'I37

14 _2007149 ₁₅

₆₁₅₈₆

5

188098

16 148935 6 17514146 . 17 362814. 7

162795

18

₂₃₇₀₃

8 15011414 19

₁₁₅₈₉

9 i37)49.3

20

. 0 10 12148142 T/ORD..

_'no'.

'0 1' 2 3 14 5 6 '7 8 9 10 0 0

1.10

3.76

7.214

11.38

16.00

20.12

20.55

0.9

0 '

2.21

6.26

10.914

15.60

19.146

22.10 '22.89

22.89

22.89 '1.8

' 0

2.67

7.143 12.141

17.03

20.58

22.82

23.145 23.145 23.:145 23.145

2.700

0

2.98

8.25 _13.50

_18.09

21.36

23.22

23.58

23.58 s,)400 .0

3.61 io.0o

_i5.8i

20.10

22.68 _23.58

-

-8.10o

0 14.31

_11.57

_17.147

21.32

23.31 -

-

-10.800

.0

5.60

13.28

18.82 _22.13'

_23.57

-

-13.500

0

8.26 _15.08

_19.93

22.68

23.58 -

-

-i62oo ,(.57

11.30 i6.8. 20.85

23.0.5

23.58 -

-

.

-t8.9oo

7.114.

13.36 18.19'

21.52

23.28 '23.58

23.58

23.58 TJ0..

11 12 13 114 ₁₅ ₁₆ '

vi

18 19 '20. 0

2.55 2055

20.55

20.140

16.0)4

_7,63

5.26 .900.

22.89 22.,8

22.89 2?.89

2..89

22.89

22.60 _18.90

_11.05

2.63

1.800 23.145 .23.145

23.145 23.145 23.145 23.145

23.16

19.95 _12.39

3.37 '2700

23.58 23.58

23.58

23.142

20.59 _13.28

_3.85

5.1400

_'

-

23.58

21.57

114.79

_3.96

8.108 -

,-

-

-,

-

21.95

15.140

2.15 10.800'

-

-'

'

-

22.1.2

15.60

_.148 13'. 500

-'

-

22.214

_15.72

0 116.200

-

.'

-

'

-

22.31 ' 15.92

0

18.90023.58 23.58

235'8

2.58 23.58' 23.8 258 22.Ø "T69 ...

(25)

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