Resistance, sinkage and trim measurements with a 1/10 scale model of an inland passenger vessel for Bangladesh

TECHNISCHE HOGESCHOOL DELFT

AFDELING DER SCHEEPSBOUW- EN SCHEEPVAARTKUNDE

LABORATORIUM VOOR SCHEEPSHYDROMECHANICA

Rapport No.

471

RESISTANCE, SINKAGE AND TRIM MEASUREMENTS WITH

A 1/10 SCALE MODEL OF AN INLAND PASSENGER VESSEL

FOR BANGLADESH.

A. Versiuls

Deift University of Technology

Ship Hydromechanics Laboratory

Meklweg 2 Delft 2208

Table 7 and 8.: Model respectIvely ship

dïsplacemetit = 9:0.

Table 9 and i.0:'Mödel respectively ship

displacement = 90.

Table 13 and 14

Model' respectively ship

displacement = 90

values for

.48 tons ard waterdepth ='

1.2"

values for

.48':'.tons a.nd water.depth = 32.8'

Contents:

page

Introduction.

1.

Attachment to. the :towing carriage.

1.

Turbulence stimulators on the model.

1.

3,. ExtrapolatiOn of the results tö full scale values.

.2.

4.. Reporting of the results.

4.

Model in test conditions.

4.

Example of the approxImation of the resistance fOr the.

5..

60' passenger launò'h.

7.. Acknowledgement.

6.

List of symbòi..

Tables.

Table i and 2: Model respectively, ship values for

-

displacement = 8.0 tons and waterdepth ='

Table 2 and 4: Model respectively ship values for

.displacement = 80 tons and wate.rdep.th =' 12'

Table 5 and 6.: Model respectively 'ship values for

displacement

80 tons and waterdepth

18'

Table Il and i.2: Model respectively ship values for

displacement '=

9.0 48 tons and watrdeph

1:8 '

values for

N

N '\

\\

N

N

\/ N

N. N

Table 15 and 16: Model respectively ship values for

displacement

100 tons and waterdepth =

6'

Table 17 and 18: Model respectively ship values for

displacement

100 tons and waterdepth = 12'

Table 19 and 2.0; Model respectively ship values for

displacement = loo tons and waterdepth = 18'

Figures.

Figure 1

:

Body plan 80' inland vessel (scale 1:25)

Figure 2. :

CF and C,r for model and ship versus

log (Rn)

Figure. 3

: Total resistance curves

Figure 4

:

_RR/v

ratio versus

V

Figure 5

:

Trimangles versus Fn..

introduction.

At thesEJ-flation'of the Dutch Advisory Team of the Design & I

spection Office B.I.W.T.A. in Bangladesh the resistance and trim

are measured of a wooden model to one-tenth scale of a 80 feet

inland passenger vessel. The tests have been carried out in the

small towing tank with speeds up to Fn = .40 with different

water-depths,and three different displacements.

All the measuring data have been reported in sheets añd the. results

are shown in figures.

-,

Ätthment...the....toing carriage.

-1-In the center of gravity G, a dynamometer has been mounted which

measure the model resistance. TO be able to obtain the trïmangle

and ,sinkag)of the model, two pot.meters A and B has been

positioned at equal distances (1.00 rn)

from the center cf gravity.

The.model was free. to heave and pitch.

--Turbulence....tIto

n the model.

The fritionai 'resistance increase due to the turbulence strips

was eliminated by performing two series of experiments.: one serie

with strips of half nominal breadth and the other serie

with

strips of full nominal breadth.

it has been supposed that the additional half strips produced an

equal resistance increase as the. first half strips, so that the

resistance without turbulence stimulators, but with turbulent

flow, could be determined.

if we.dènote:

=

model resitance with half nominal strips

m

where:'

= density of water in the tank

p

=

101.83 kgf. sec2/m' at 64° F (17.8°C)

mc.del speed (rn/sec)

('

wetted model surface

_(Sm

'= 1.38 m2)

=

model resistance with full nomi nal strips

then the resistance increase coefficient,

..R: ..R,',

m

VZ

F

=

V.

will be only slihtiy depèndnt on. the model speed Vm., since

the .res:istance increase is due to friction.

In practice c was determined as a mean value over a range of

model speeds where the measurements were most accurate and no

laminary flow phenomena wére experienced.

The model resistancecorredtèd for the frictional resistance

due tothe full nominalmstr.ïps follows, from:

A1

=

- 2C.V

2

m

-T

m

The föllowing value for C was found:

C

=

3.5 * io

kgf.sec2/m'2'

Ail the resistance measurements with 'the model were corrected' for

the strips by means of this coefficient C.

3. ExtrapolatiOn of the results to full scale values.

To 'be able to approach the frictonai resistance by calculation, 'the

wetted. surface h'ad to be known.

.v 2

mmm

/ piL

V

m

Sm

3

CF

=

frict±onal resistance coefficIent of model according

m

to ITTC formula.

.075

CFm

- log (Rflm - 2) 2

Rn

=

Reynolds number of model

m

V ..L

Rn

m m

m

_Vm

where: L

2.358 rn

m

kinematic viscosity of water in the tank

V

_{1.0632 *}

io6

_{m2/sec at 64°F}

The residuary model resistance follows from:

RR

-m

m

The full scale fraction res±tance has been 'caldulated analogous

to that of the model for the full scale conditions:

=

CF

½

V2 s

where :

P =

density of water, full scale condition

= 101 .59 kgf

sec2/mk

at 82°F. (27. 80C)

V5

=

full scale speed (in/sec)

=

full scale wetted surface

S

=

138 m2

C

= frictional resistance coeffïcient of shIp, according to

ITTC-formula

CF

Rn

Reynolds number of ship

V .L

-'íS

S

Rn

=

s V

L

=

23.58

rn

kinematic viscosity full scale condition

4

The total resistance of the full scale ship has been calculated

from:

R

=

R

+

c3 R

T

F

s s

Rm

where: a

=

model scale

a =

Reporting of the recuits.

The measured resistance, trim and sinkage of the model in different

conditions are presentèd in this report.

Three different displacements have been tested:

80 kg

90.48 kg (design displacement)

and 100 kg.

Each of this mentioned displacements have been tested in three

different water depth:

.6', 1.2' and 1.8'

(For the real ship 6', 12' and 18')

With the displacement of 90.48 kg a fourth waterdepth is tested nl.

1.00 m (3.28')

This case can be considered as unrestricted waterdepth.

From the data sheets some graphics are derived to give a

visualization of the test results. (See figures)

Model in test conditions.

S 1.304 rn2

1.380 m2

1.430

ni2

m

Displacement

=

80 kg

90.48 kg

100 kg.

Draft

=

.1202 m

.1295 m

.1395 m

G

in

= + .0452 m

+.0273 m

+.0120 ni

6. Example 'of the approximation of the resistance for the

60" passenger :i;aunc'h.

LCWL

=

17.70 m

V = 5.0 tons S =

7.7m2

V

=

8 knots (= 4.11.5 m/sec)

Waterdepth

18'

Frictional resistance coefficient, according to ITTC formula:

.075

CF

_{(log Rn -}

₂₎₂

V.LCWL

CF

=

.002128

Skin roughness coefficient

.0004

then the frictional coefficient becomes:

C

= .. 00212.8 + . 0004

=

.0:0252,8

F

(.

Frictional resistance,:

=

CF

+ ½ .p.V2S.

(p =

101.59)

=

168 kg

Residuary resistance:

Rn

5

.8630 &

io

then R

=

'50 j:o.og6

=

.48 tons

R

H!

Total resistance:

=

₊

_RR

= '648 k

R

.6845

V =

.0096

(See figure 4)

7.. Acknowledgement.

The author is indebted to mr. R.. Onnink and mr. B. Pleffers who

carried out the experiments. Further, thanks to mrs. Joke de Jager

for carefully typing this report.

List of symbols.

Subscription m

=

model scale condition

Subscription s

=

full scale condition

RF

=

RR

=

Fn

G

=

m

g

Rn

V.

s

V

a

7

frictional resistance increase coefficient,

C

=

3.5 * io

gf;'sec2

frictional resistance coefficient, according to ITTC formula

residuary resistance coefficient

total resistance coefficient

model resistance with half nominal strips

model resistance with full nominal strips

parasitic resistance of model, due to turbulence stimulators

tbtal resistance

frictional resistance

residuary resistance

Froude number, Fn

V

longitudinal center of gravity of the model

acceleratïon of gravity, g

= 9.81 in/sec2

length. of the construction waterline

LCWL

2.358 i

L

23.58rn

=

Reynolds nwnber,

displacement

wetted surface

speed

uodel scale,

c. lo

k±nema.ti.c viscosity of fresh water

1.0632 *

io._6

_m2/sec

.8431 *

io6

m2/se,c

at 6.4° F (= 17.8°C)

at 82° F (= 27.80C)

p =

density oLiresh water

=

101.83 kgf.sec2/mk

at 64° F

101.59 1gf.sec2/mk

at 82° F

C =

CF

=

CR

=

Ct

=

h

=

waterdepth

a trimang le

if O

>

O then

Zf _<

_Za

(trim by stern)

1f O

<

O then

Zf _> z

(trm by bow)

.Sk =

sinkage at G

T

= ,draft

Za

=

sinkage after

s inkage forward.

-8-)4

_za'

M

é1

Dsp1acement

80 kg

W-terdepth

.6'

(.183

m)

TABLE 1.

V rn

rn/sec

rn p V2S rn m m R -rn kg C T in Rn in log (Rn) Rm R kg .600 .360 23.828 .243 .01018 .

133'07

6.124 .00441 .00577 .138 .650 .422 27.965 .288 .01029 .144'+07 6.159 .00434 .00595 .166 .700 .490 32.435 .342 .01056 .155'+07 6.191 .00427 .00629 .204 .750 .562 37.232 .414 .01113 .166'+O7 6.221 .00421 .00692 .258 .800 .640 42.361

.92

.01162 .177'+07 6.249 .00415 .00746 .316 .850 .722 47.822 .704 .01473 .189'+07 6.275 .00410 .01063 .508 .900 .810 53.613 1:057 .01972 .200'+07 6.30O .00406 .01566. .840 .920 .846 56.023 2.064 .03684 .204'+07 6.310 .00404 .03280 1.838

nr

TABLE '2.

Rn..

log(Rn)

C,

s -s

kg

g.

1/

rn/sec

knots

1.897 3.688 3.600 .238'-i-Ó5 .531'4-08

7.725

.00269 .00846 .210'+03 t-1248 2

2 055

3 995

4 225

279'+05

575'+08

7 760

00266

00861

240'+03

1351

Î)

3 2 214 4 303 4 900 323'+05 619'+08 7 792 00264 00893

289'03

1455 4 372

46iô

5.625

.3i'O

.663'08

7.822 .00261 .00954

.354+03

.1559 5 2 530 4 917 6 400 422'+05 708'+08 7 850 00259 01005 425'-'-03 1663

389'í)

6

2 688

5 225 7 225 477'+05 752'+08 7 876 00257 01320 629'+03 1767 -41

7

2.846

5532

8.100

.535"+OS

.796'-'-08

7.901

.00255

.o12c:

.974'-i-03

.1871

378

8

2 909

5 655

8 464

559'05

814'+08

7 910

00255

03535

197'+04

1913

7475

'Ship

Displacement

80 tons

Model

Displacement

80 kg

Waterdepth

1.2!

(.366 m)

'TABLE '3

i

:flr

V m

n/sec

y

2 m p

mmm

V2S' kg' Rn

1og(n)

_CF -m

kg

1 .600 .360 23.828 .137 .00574

.33'+07

6.124 .00441

.00 133

Ó32 2

.700

.490

32.433

.187

.00575

.155'+07

6.191

.00427

.00148

.048

3 .800 .640 42.361 .249 .00588 .1-77'+07 6.249 .0041.5 .00172

.073

4

.900

.810

53.613

.326

.00607

.200'+07

6.300

.00406

.00202.

.108

5 1'000 1.000 66.189 424 .00641

.222'07

6.346 .00397 .0Ô243 1 6' 1 6

1.050

1.102

72.974

.485

.00665'

.233'+07

6..367

.00-393

.00271 1.98 7 1.100 1.210 80.089 .558 .00696 .244'+07 6..387 .00390 .00307

.246

8

1.150

1.322

87.536

.641

.00733

.255T+0

_6.407

_{.00386 .00346} 9

1.200

1.440

95.313

.747

.00784

.266'07

6.425

.ÓÓ383 00401.

.382

10

1.250

1.562

103.421

.889

.00860

.277'+07

6.443

.00380

.00480

.496

11 1.300 1.690 111.860

1120

.01002 .288'+07 6.460 .00377 .00625

.699

1:2 1.350 1.822 120o630 1.598 .01325 .299'+07 6.476 .0Ó374 .00951

1.147

13

1.400

1.960

129.731

2.424

.01869

.310'+07

.492

.00372

.014,97

1 .942

s

hip

Dïsplacement

80 tons

Waterdepth

12'

(3.66 m)

TABLE

4.

nr - in/sec knots

V2

RniT

log(Rn)

CFs i-.0004. kg gJ-1I3 1

1.897

3.688

3.600

.238'+05

.531'+08

7.725 _{;00269 .00402 .955'+02 .1248} 2 2.214 4.303. 4.900 .323'+05 .619'-'-08 7.792 .00264 _.00412 133'+03 .1455

_3405J

3 2.530 4.917 6.400 ..422'+05 .708'+08 7.850 .00259 .00431 .182'-s-03 .1663 4 2.846 3.162 5.532 6.147 8.109 10.000

.535'05

.660!+05 796'+08 .884.!.08 7.901 7.947 .00255 .00252 .00457 .00496

.24403

.327'-i-03 .1871 .2079

478,

6 3.320 6.454 11.025 .728'-i-05 .929'+08 7.968 .00251 .00522 .380'+03 .2183 --5!1.P7 3.479 6.762 12.100 .799'-i-05

.973'08

7.988 .00249 .00556

.444'-i-03

.2287

8 3.637 7.069 13.225 .873'-'-05 .102'+09 8.0Ó7 .00248

_.00594

519'-i-03 2391 5594 9 3.795 7.376 14.400 .950'+05 .106'i-09 8.Ô26 .00247 .00648 .615'+03 .2495 10 3.953 7.684 15.625 .103'+06 .111'+09

8.044

.00245

.00725

.748'-i-03

.2599-11 4.111 7.991 16.900 112'+06 .115'+09

8.061

_.00244

_.00869

_{969'+03 2703} 63 12 4.269 8.298 18.225 .120'+06 .119'+09

8.071

_.00243

_.01194

_{.144'+04 .2807} 13 4.427 8.606 19.600 .129'+06 .124'+09

8.093

_.00242

_.01739

_.2911

Displacement

80 kg

Waterdepth

1.8'

(.549

m)

TABLE 5.

nr rn/sec PrnSth kg CT Rn iog(Rn)' CF CR kg .700 .k9O 32.433 .172 .00532 .155'-i-07 6.191 .00427 .00105 .034 2 .800 .640 42.361 .227 .00536 .177'+07 6.249 .00415 .00121 .051 3 .900 .810 53.613 .296 .00551 .2OO-+O7 6.300 .00406 .00146 .Ó78 4 5 1/000 1.000 1.050 1.102 66.189 72.974 .383

.46

.00579 .00598 .222'+07 .233'+07 6.346

6367

.00397 .00393 .00182, 00205 .120 .150 6 1.100 1.210 80.089 .501 .00625 .244'+07 6.381 .00390 .00236 .189 7 1 150 1 322 87 536 575 00657 2551+07 6 407 00386 00271 237 8 1.200 1.440 95.313 .667 .00699 .266'+07 6.425 .00383 .00316 .302 9 1.250 1.562 103.421 .772 .00746 .2771+07 6.443 .00380 00366 .379 10 1.300 1.690 111.860 .892 .00798 .288'-'-O7 6.460 .00371 .00421 .471 11 1 350 1 822 120 630 1 046 00867 299'+07 6 476 00374 00493 12 1.400 1.960 1.29.731 1.219 .00940

.310'07

6.492 00372 .00568 .737 13 1.450 2.102 139.163 1,434 .01030 .322'+07 6.507 .00369 .00661 .920 14 1.500 2.250 14À.926 1.676 01126 .333'+07 6.522 .00367 .00759 1.130 15 1.550 2.402 159.020 1.871 .01177 .344'+07 6.536 .00364 .00812 1.292 16 1.600 2.560 169.445 2.327 .01373 .355'-'07 6.550 00362 .01011 1.713 17 1 650 2 722 180 201 2 790 01549 366'+07 6 563 00360 01188 2 142 1.8 1.700 2.890 191.288 3.448 .01802

.377'07

6.576 .00358 .01444 2.763 19 1.750 3.062 202.705 4.376 .02159 .388'-'-07 6..589 .00356 .01803 3.654

Model

f

TABLE .6.

Displacement

80 tons

Waterdepth.

18! (5.49 in) nr 1 2 3 V

rn/sec

2.214

2 530

2 846 V

knots

4.303

4 917

5 532 Vs2 4.900

6 400

8 100 .323'+05

422'-'-05

535'+05 Rn -619'+08

708'+08

796'+08

.log(Rn)

. 7.792

7 850

7 901

C,

+ .0.004 j. .00264

00259

00255 CT5 .00368

00380

00401 R

kg

.119'4-03

161'+03

214'+03 .1455

1663

1871

yg

.3405

3891

4378 4. 3.162 6.147 10.Ù0O .660'+05 .884'+08

7.947

.00252 .ô0434 .286'4-03 .2079 5

3 320

6 454

11 025

728'+05

929'+08

7 968

00251

00455

331'+03

2183

5107

6

3 479

6 762

12 100

799'+05

973'+08

7 988

00249

00485

387'+03

2287

5351

7 3.637

7.069.

13.225

.873'+OS

.

102'+09

8.007

.00248

.00519

.453'+03 .2391

.5594:

8 3 795 7 376 14 400 950'-'-05 106'+09 8 026 00247 00563 535'+03 2495 5837 9 3 953 7 684 15 625 103'+06 111'+09 8 044 00245 00612 631'+03 2599 608Ö ]0 4 111

7 991

16 900

112T+06

115T09

8 061

00244

00665

741'03

2703 6324 11 4 269 8 298 18

225

120+06

119'09

8 077

00243

00736

885'+03

2807

6567k

12 .

4.427

8.606

19.600

.129'+06

.124'+09

8.093

.00242

.00810

.105'+04

.2911 13 4.585 8.913 21.025 .139'+06

.i28'+09

8.108

.

.00241

.00902

.125'+04

.3015

14 4 743 9 220 22 500 148'+06 133'+09 8 123 00240 00999 148'+04 3119 15 4 902 9 528 24 025 159'+06 137'+09 8 137

00239

01052

167'+04

3223

540

16 5.060 9.835 5.600 .169'-i-0.6 .142'-I-09 8.151 .00238 .01249 .211'.-'-04

.3327

.7783,

17 5.218

10142

.27.225 .180'+06 .146'+09 8.164 .00237 .01426 .256'+04 .3431

:.8Ò26.

18 5.316

j0.450

28.900 .19.1'+O6 .15Ó!-+09 8.177 .00237 .01681 .321'+04 .3535 .8269 19 5.534 10.757 30.625 .202'+06 .155'+09 8.190 .00236 .02039 .4.12'+04 .3639 .8512

Ship

MOe

ei

Displacement

90.48 kg

Waterdepth

.6'

(.183 m)

nr

V ¡sec .600

V2

.360

pV2S

25.295 kg .203 .00804 Rn. .133'+07

log(Rn)

6.124 CF .00441 m .00363 ni .092 2. .650 .422 29.686 .258 .00869 .144'+07 6.159 .00434 .00436 .129 3 .700 .490 34.429 .326 .00946 .155'+07 6.191 .00427 .00519 .179 4 .750 .562 39.523 .417 .01055 .166'+07 6.221 .00421 .00634 .250 .5 .800 .640 44.968 .541 .01203 .177'+07 6.249 .00415 .00787 .354 6 .850 .722 50.765 .746 .01470 .189'+07 6.275 .0041Ó .01060 .538 7 .900 .810 56.913 1.235 .02.170 .200'+07 6.300 .00406 .01765 1.004

Ship

Displacement

90,48 töti.s

Watèrdepth

6.! _{(1.83 in)}

TABLE' 8.

rn/sec knots

+00O4

kg

1 L.897 3.688 3.600 .252'+05 .531'+08 7.725 00269 OO632 .159'+03 1248

.2L9J

2 2.055 3.995 4.225 .296'+Q5 ..575'+08

7760

.00266 .00702 .208'+03 .1351 3 2.214 4.303 4.900

.43'+Ó

.619!-i-08 7.792 .00264 .00783 .269'+03 .1455

33Jii?

4

2372

4.61&

5.625

.394'Ó5

.663'+08 7.822 .00261 .00895 o353'+03 1559 3-574 5 2.530 4.917 6.400 .448'+05 .7084-08 7.850 i-00259 .01046 .469'+Q3 1663 3812 6 2.688 5.225 7.225 .506'+ÓS .752'+Ó8 7.876 .00257 .01317

.66V+03

.1767

..4Ö1

' 2.846 5.5.32 8.100

.567'+ÖS

.796'+08 7.901 .00255 .02020

.i15'04

.1871 nr 'V V

pV2

. .

log(Rn)

Ç Ç .

VgLí/3

Model

pp1a.detnent

90.48 kg

Waterdepth

1.2' (.366 ni)

TABLE

.9.

nr

m

rn/sec

.600

y 2 rn

.360

.p y

mm ni

25.295

T. ni kg

.142

.00562

.133'4-07

log (Rn)

6.124

CF

.00441

CR

.0012.1

kg

.031

2 .650

422

29.686 .168 .00566 .144'+07 6.159 .00434 .00133 .039 3 .700 .490 34.429 .197 .00572 .I.55'+07 6.191

.0042.7

.00145

.050

4 .750 .562 39,523 .229 .00579 166'-F07 6.221

.00421

.00158

.063

5 .800 .640 44.968 .265 .00589 .177'+Q7 6.24.9

.00415

.00174

.078

6 .850 .722

50.765

.306 .00602

.19'+07

6.275

.00410

.00192

.097

7 .900 .810 56.913 .351 .00616 .200'+07 6.30Ó .00406 .00211 .120 8 .950 .902 63.412 .402 .00635 .2]1'-i-07 6.324

.00401

.00234

.148

9 1.000 1.000 70.263 .461 .00656 .222'+07 6.346 .00397 . .00259 .182

10

1.050. 1.102 77.465 .527 .00680 .233.'-I-07 6.36.7 .00393 .00287 .222 11 1.10.0 1.210 85.018 .607 .00714

.244'07

6.387 .00390 .00325 .276 12 1.150. 1.322 92.922 .705 .00758 .255'+07 6.407

.00386

.00372

.346

13

1.20.0 1.440. 101.178 .825 .00815 .266'+07 '6.425

_.00383

_.00432

438

14 1.250 1.562 109.785 .976 .00889 .277'+07 6.443 .00380 .00509

.559

1.5 1.300. 1.690 118.744 1.198 .01009 .-288'+07 6.460 .00377 .00632 .750 16 1.350 1.822 128.054 1.824 .01425 .299'+07 .6.476 .00374 .01050 1.345 17 1.40.0 1.960. 137.715 3.263 .02370 .310'+07 6.492 .00372 .01998 2.752

Ship

Displacement

90.48

Waterdepth

12' (3.66 iìi)

TABLE

10. nr I mlsec 1.897 knots 3.688 s 3.600

pV2 S

-Ss

s .252'+05 .531'+08 log(:Rn) 7.725 CF

+OÓ04

.00269 s .00390 kg .984'+02 .1248 yg. i13 2 2 055 3 995 4 225 296'+05

575+08

7 760 00266 00399 118'+03 135i 9ii 3 2 214 4 303 4 900 343'+05 619'+08 792 00264 00408 140'+03 1455 4 2 372 4 610 5 625 394'+05 663'+08 7 822 00261 00419 i65'-F03 i559 5 2 530 4 917 6 400 448'+05

708+08

7 850 00259 00433 194'+03 1663 ' 812. 6 2 688 5 225 7 225

506'05

752'-i-08 7 876 00257 00449 337'+03 1767

40i

7 2 846 5 532 8 100 567'+05 796'+08 7 901 00255 00466 264'+03 1871

29

8 3 004 5 839 9 025 632T+05 840'+08 7 924 00254 00487

30'+O3

1975

4527

9 3.162 6.147 iOt000 .701'+05 .884'+08 7.947 .00252 .00511 .358'+03 .2079 10 3.320 6.454 11.025 .772'-4-05 .929'+08 7.968 .00251 .00538 .415'-I-03 .2183 5öÓT, Ii 3.479 6.762 12.100 848'+O5

.973'08

7.988 .00249 .00574 .487'+03

.287

T.5242]

12 3 637 7 069 13 225

926'05

-102'-i-09 8 007 00248 00620 574'-i-03 2391 548O

13 3.795 7.376 14.400 .101'+06 .106'+09 8.026 .00247 .00679 .685'+03 .2495 14 15

3.953

4 111 7.684, 7 991 15.62 16 900 .109'+'6 118'+06 .1i1'+09 115'+09 8.044 8 061 .00245 00244 .00155 00876 .826'-i-03 104'+04 .2599 2703 / 6195 16 4 269 8 298 18 225

128'06

119'+09 8 077 00243 01293 165'+04 2807 17 4 427 8 606 19 600 137'+06

124'09

8 093 00242 02240 308'+04 2911

6672

Nodel

Displacement

90.48 kg

Waterdepth

1.8'

(.549 m)

...

.TLE....1' nr. V

m /sec

.600

y2

_m .360 S 25.295 R

T

m kg .131

c:

.00519 ;133'+07

lo,g(Rii )

6.124 C .00441 C R .0007,9

kg

020 2

.700

.490

34.429

.181

.00525

'155'+07

6.1.91

_.004127

.00098

.034 3 .800 .640 44.968 .242 .00.539

177'+07

6.249

.00415 .00124

056

4

.900

.810 56.913 .317 .00558 200'+07 6.300 .00406

.00152

.087 5

1.000

1.000

70.263 .41.3 .00.588

222-O7

6.346 00397 .00191 .134 6 1.050

1102

77.465 .471 .00608/1 233t+07 6.367 .00393 .00214

.166

7 1.100 1.210 85.018 .534 .00628 '.244'07 6.387 .00390 .00238

.202

8 1.150 1.322 92.922 .610 .00656 .255'+07 6.407 .00386

.00270

.251 9

1.200

1.440

101.178

.698 .00690 ..266'-i-07 6.425 .00383 .00307

.311

10

1.250

1.562

109.785

1805: ... .00733 ..277'+07 6.443 .00380' .00353 .387 11

1.300

1.690

118.744

.933 .00786

28807

6.460 .00377 .00408

.485

'12 '1.350 1.822 128.054 1.084 .008.47 299'+O7 6.476 .00374 .004172

.605

.13

.1.400

.1.6O

137.715

1.264 .00918 1%310'+07 6.492 .00372 .00546

.752

14

1.450.

2.10.2

147.727

1.486 .01006 322'+07 6.507 .00369 .00637 .941 15

1.500

2.50

158.09.1

1.762 .01114 333'+07 6.522 .00367 .00748

1.182

16 1.550 2.402 168.806 2.078 .01231 .344'+07 6.536 .00364 .00867

1 .463

17

1.600

2.560

179.873

.495 .0,1387 .355'+07 6.550 .00362 .01025 1.843

.18

1.650

2..722

191.290

3.014 .01576 . , ,366'+07 6.563

.0030

01215

2.325

19

1.700.

2.890

203.059

3.818 .01880 .377'+07 6.576 +00358 .01522 3.090

nr V rn/sec knots V s

Displacement

90.48

ton

Watêrdepth

18' (5.49 in) TABLE. 12.

p V.S

S

S 3S

S

(

-7, log(Rn ) s CFs

+.0004

CT s kg

C

V -I 1.897 3.688 3.600 .252'+05 .531'-'-08 7.725 .00269 .00347 .876'+02 .1248

.2'-j!

_-2 2.2 4- 4.303 4.900 .343'+05 .619'+08 7.792 .00264 .003f2- .124'+03-- 1455 3 2 530 4 917 6 400 448'+05 708'+08 7 850 00259 00383 172'+03 1663 '3812 4

2'86

5 532 8 100 567'+05 796'+08 7 901 00255 00408 231'+03 1871 5 3.162 6.147 10.000 .701'+05 .884'+08 7.947 .00252 .00443 .310'+03 .2Ó79

.'65)

6 3 320 6 454 11 025 772'+05 929'+08 7 968 00251 00465 359'+03 2183 òOLF 7

3.49

6.762 12.100 .848'+05 .973'+08 7.988 .00249 .00487 .413'+03 .2287 242 8 3 637 7 069 13 225

926'05

102'+09 8 007 00248 00518

480'03

2391 54Thò 9

3 75

7 376 14 400 I01'+06 106'+09 8 026 00247 00554 559'+03 2495 57i 10

3 93

7 684 15 625 109'+06 111'+09 8 044 00245 00598 655'+03 2599

TT

11 7.991 16.900 .118'+06 .115'-'-09 8.061 .00244 .00653 .773'-i-03 .2703 Ç'i95) 12

4 29

8 298 18 225 128'+06 119'+09 8 077 00243 00716 914'+03 2807 643Í' 13 4.4.7 8.606 19.600 .137'+06 .124'-'-09 8.093 .00242 .00788 .108T+04 .2911 14 4 585 8 913 21 025 147'+06 128'+09 8 108 00241 00878 129'+04 3015 6'910 15 4.743 9.220

22500

.158'+06 .133'+09 8.123 .00240 .00988 .156'±04 .3119

148j-16 4.902 9.528 24.025 .168'+06 .137'i-09 8.137 .00239 .01106 .186'+04 .3223 7386) 17 5 060 9 835 25 600 179'+06 142'+09 8 151 00238 01263 226'+04 3327 25 18 5.218 10.142 27.225 .191'+06 .146'+09 8.164 .00237 .01453

.27P+04

.3431 86ï' 19 5 376 10 450 28 900 202'+06 150'+09 8 177 00237 01758 356'+04 3535 8101

Ship

Model.

Displacement

90.48 kg

Waterdepth.

3.28'

(1.00 m)

TABLE

'13. y rn . rn/sec

y2

in p y 2 rn,rn in kg -' in Rn .1og(Rn) . CF in R.m in kg .700 .490 34.429 .175 .00508 .155'+07 6.191 .00427 .00081 .028 2 .800 .640 44.968 .233 .00518 .177'-b07 6.249 .00415 .00103 .046 3 .900 .810 56.913 .304 .00534 .200'+07 6.300 .00406 .00129 .073 4 1.000 1.000 70.263 .397 .00565 .222'+07 6.346 .00397 .00168 .118 5 1.050 1.102 77.465 .451 .00582 .233'+07 6.367 .00393 .00189 .. 146 6 1.100 1.210 85.018 .514 .00605 .244'+07 6.387 .00390 .00215 .183 7 1.150 1.322 92.922 o589 .00634 .255'+07 6.407 .00386 .00248 .230 8 1.200 1.440 101.178 .675 .00661 .266'+07 6.425 .00383 .00284 .287 9 1.250 1.562 109.785 .776 .00707

.27P+07

6.443 .00380 .00327 .359 IO 1.300 1.690 118.744 .894 .00753 .288'+07 6.460 .00377 .00376 .446 11 1.822 128.054 1.033 .00807 .299'+07 6.476 .00374 .00432

.554

12 1.400 1.960 137.715 1.192 .00866 .31Ö'07 6.492

.003ñ

.00494 .680 13 1.450 2.102 147.727 1.39.0 .00941 .32V+07 6.507 .00369 .00572 .845 14 .1.500 2.250 158.091 1.631 .01032

333tQ7

6.522 .00367 .00665 105'1 .15 1.550 2.402 168.806 1.896 .01123

.344'07

6.536 ' .00364 .00759 1.281 16 1.60.0 2.560 179.873 2.153 .01197 .355t+07 6.550 .00362 .00835 1.501 17 1.650 2.722 191.290 2.398 .01254 .366'+07 6.563 .00360 .00893 1.709 18 1.700 2.890 203.059 2.667 .01313'

.37V+07

6.576 .00358 .00955 1.940 I 9 1.750 3.062 215.180 2.992 .01390 .388'+07 6.589 .00356 .01034 2.226 20 1.800 3.240 227.651 3.390 .01489 .399'+07 6.601 .00354 .0-1135 2.584

Displacement

90.48 tons

Waterdepth

32.8'

(10 m) nr

mis c

y s knots

y2

s

pv2 s

SS

S Rn

log(Rn)

C +.0004 CT kg Fn 1

2.214

4 303 4 900 3431+05 619'+08 7 792 00264 00345 118'+03 1455 ₃₃₃₆ 2

2..5 0

4.917 6.400 .448'+05

.708'08

7.850 .00259 .00362 .162?+03 .1663

₃₈₁₂₎

3

2 84k

5 532

8 100

567'+05

796'+08

7 901

00255

00384

218'+03

1871 4 3 162 6 147 10 000

701'05

884'-i-08 7 947 00252 00420 294T+03 2079

₄₇₆₅

5 3 320 6 454 11 025 772'+05 929'+08 7 968 00251 00440 339'+03 2183 50Ó4 6 3 479 6 762 12 100 848'+05 973'+08 7 988 00249 00464 393'+03 2287 24 7 3 637 7 069 13 225 926'+05 102'+09 8 007 00248 00495 459T+03 2391 5489 8 3.795 7.376 14.400 .101'+06 .106'+09 8.026 .00247 .00531 .535'+03 .2495 .5719 9 3.953 7.684 15.625 .109'+06 .111'+09 8.044 .00245 .00572

.626'03

.2599 .59T7. 10 4 111 7 991 16 900 188'+06 115'-'-09 8 061 00244 00620 734'+03 2703

6i5

11 4.269. 8.298 18.225 .128'+06 .119T+09 _{8.077. .00243 .00675 .862'+03 .2807} 12 4 427 8 606 19 600 137r+06 124'+09 8 093 00242 00736 101'+04 2911 6672 13 4 585 8 913 21 025 147'-i-06 128'-i-09 8 108 00241 00813 120'+04 3015 6910 14 4.743 9.220 22.500 .158'+06. .133'+09 8.123 .00240 .00905 .143T+04 . .3119

.714

15 4 902 9 528 24 025 1681+06 13V-4-09 8 137 00239 00998 168'+04 3223

38

16 5.06 9.835 25.600 .179'+Ö6 .142'+09 8.151 . .00238

.01073

.192'+04 .3327 17 5.218 10.142 27.225 .191'-i-06

.146'09

8.164 .00237 .01131 .216'+04 .3431

¿.7863

18 5.376 10.450 28.900 .202'+06 .150'-4-09 8.177 .0023.7 .01192 .241'-f-04 .3535 .8iOL 19 5.534 10.757 30.625 .215'-'-06 .155'+09 8.190 .00236 .01270 ..272'+04 .3639 20 5.692 11.064 32.400

.227'06

.159'+09 8.202 .00235 .01370 .311'-*-04 .3743 .85Th

ìY

nr

Model

V

Dis?1acement

loo kg

Waterdepth

.6' (.183 in)

TABLE 15

V2

nr

(V

PYS

Rn5

log(Rn)

Fs _s

Vg.

T/3

Ship

D i spL ac ement

Wa.tedepth.

TABL

16.

100 tons

6'

(1.83 m)

in p

-mmm

v2s

-T;--m

kg C-T in Rn in log(Rn )

m

CF rn C R Ill -R

m

kg .360 26.211 .247 .00941

133'+07

6.124 .00441 .00500 .131 .422 30.762 .302 .00982

.144'07

6.159 .00434 .00548 .169 .490 35.676 .379 .01061 .155'-i-07 6.191 .00427 .00635 .226 .562 40.955 .500 .01221 .166'+07 6.22.1 .00421 .00800 .328 .640 46.597 .784 .01682 .177'+07 6.249 .0041.5 .01267 .590 -- +.0004 kg 3.600 .261'+05

.531'+08

7.725

.00269

.00-769

.201'+03

.1248

.2812

4.225

-.307'-'-05

575-Ö8 -

7.760

.00266

.008.14

.250'+03

.1351

.3046

4.900

.356'i-OS

.619'+08

7.792

.00264

.008-98

.319'03

.1455

.3281

5.625

.408'-i-05

.663'+08

7.822

.00261

.01061

.433'03

-1599

.3515

6.400

.465'-'-05 .708'+08

7.850

.00259

.01526

.709'+03

.1663

.3749

1 _1.897 3.688 2

2.055

3.995

3 2..21L

4.303

4

2.372

4.610

5

2.530

4.917

m

rn/sec .600 2 .650 3 .700 4 .750 5. .800

nr

m

mf sec

MoÄ1

Dispiacemetit

100 kg

Waterd.epth

1.2'

(.366 m)

j

LE

VS

í.

C Rn

1g(Rn )

C -m in in in

m

, Fm _in kg 1 2 3 4 5 6 7 8 9 10 11 .700 .800 .900 1.000 1.050 1.100 1.150 1.200 1.250 1.300 1.350 .490 .640 .810 1.000 1.102 1.210 1.322 1.440 1.562 1.690 1.822 35.676

46597

58.97.5 72.808 80.271 88.098 96.289 104.844 113.763 123.046 132.693 .216 .283 .365 .481 .561 .664 .799 .966 1.170 1.462 2.232 .00605 .00608 .00619 .00661 .00699 .00754 .00829 .00922 .01029 .Ó1188 .01682 .155'+07 17V-'-07 .200'-'-Oi .222'+07 .233'+07 .244'+07 .255'+07 .266'-i-07 .277'+Ol .288'+07 .299'+07 6.191 6.249 6.300 6.346 6.367 6.381 6.407 6.425 6.443 6.460 6.476 .00427 00415 .00406 .00397 .00393 .00390 .00386 .00383 .00380 .00377 00374 .00178 .001 9.3 .00214 .00264 .00306 .00364 .00443 .00539 .00649 .00811 .01308 ( .064 .090 .126 192 245 .321 .427 o 565 .738 998 I .736

:Ship

Displacement

100 tons

Wa1terdepth

12!

_{(3.66 m)}

E 18.

nr 2 3 4 5 6 7 8 9 10 11 m 2.214. 2.530 2.846 3.162 3.320,

3.479

3.37

3.795 3.953 4.111 4.269 V s sec knots 4.303 4.917 5.532 6.147 6.454 6.762 7.069 7.376 .684 7.991 8.298

V2

4.900 6.400 8.100 10.000 11.025 12.100 13.225 14.400 15.625 16.900 18.225 .356.'+05 .465'+05 .588'+O5

.726'05

.800'+05. .878'+05 .960'+05 .105'+06 .113'-i-06 .123?+06 .132'+06 R .6191+08 .708'+08 .796'+08 .884'408 .929'#08

.973'08

.102'+09 .106'+09 .111'-i-09 .115'+09. .119't09

log(Rn)

7.792 7.850 7.901 7.947 7.968 7.988 8.007 8.026 8.044 8.061 8.077 CF +.0004 .00264 .00259 .00255 .00252 .00251 .00249 .00248 .00247 .0O245 .00244 .00243 CT .00442 .00452 .00469 .Ó0516 .00556 .00613 .00691 .00785 .00894

.01055H

.0155i kg

.157'03

.210'+08 .276'+03 .374'+03 .445'+03 .539'-i-03 .663'+03 .821'+03 .101'+04 .129'-f-04 .205'+04 .1455 .1663 .1871 .2079 .2183 .2287 .2391 .2495

.2599

.2703 .2807 V 17 .3281 .3749 42I.8 4687 .4921 .5155 .5390 .5624 f5858 .6093 .6327

'f

-TABtE 19.

nr

y rn

rn/sec

1

.700

2 .800 3 900 4 1.000 5 1.050 6 1.100 7 1.150 8 1.200 9 1.250 JO 1.300 11 1 350 12 1 400 13 1 450 14 1.500 15 1.550 16 1.600 . 17 1.650. 18

1.7Oû'

Mödel

y2

_Ip

vs

In .490 35.616 .640 46.597 810 58 975 11000 72.808 1.102 80.271 1.210 88.098 1.322 96.289 1.440 104.844 1.562 113.763 1.690 123.046 1 822 132 693 1 960 142 705 2 102 153 080 .250 _163.819 2.402 174.922 2.560 J8639.0 2.722 198.221 2.89.0 210.416

loo kg

1.8' (.549 rn)

-rn

kg 193 .255 330 .433 .496 .571 .659 .767 .892 1.038 1 212 1 419 1 663 1.951 2.189 2.757 3..368 .4.338 00542 .00541 00560 .00595 .00618 .00648 .00684 .00732 .00784 .00843 00913 00994 01086 .01191 .01251 .01479 .01699 .02062 Rn In 155'+07 117'+O7 200'+07 .222'+07 .233'+07 ..244'+07 .255'+07 .266'+07 .277'+07 .288'4-07 299'+07

310'07

322'+07 .333'-i-07 r

.355'07

.366+07

.377'+07

log(RÌi)

6.191 6.249 6 300 6..346 6.367 6.387 6.407

6425

.443

6.460 6 476 6 492 6 507 6.522 6.536 6.550 6.563 6.576 .00427 .00415 00406 .00397 .00390 .00386 .00383

.00380

.00377 00374 00372 00369 .00367

.00364

.00362 .00360 .00358 rn .00115 .00131 .00155

.0198

.00225 .00259 .00298

.00349.

.00404 ó0466 .00539 .00623 .00717 .00824 .00887

.01117

.01339 .01703

,1t

rn .041 .061 .091 .144 .180

.28

o287 .366 .460

o514

.715 .889 1.098 1.350 1.551

2.082

2.654 3.584

Displacement

Waterdepth

11

2.214

2

_.2.5*

3 2..8416 4

.3l62

5 3.320 6 3.479 7

3.637

8 3.795 9

395B

lo

4,ii

11

4.26

12

4.427

13 4.585 1.4 1.5

4.902

16 17

5.218

18

5.37

V

W.L1

/3 4.303 4.900 .356'+05

.619'08

7.792 .00264 .00379 .13-5'+03 .14.55 .3281 4.917 6.400 .465'+05 .708'+08 7.850 .00259 .00390 .181'+03 .1663

.3149

5 532 8 100

58'+05

796'+08 7 901 00255 00410 241'+03 1871 4218 6 147 10 000 726'+05 884'+08 7 947 00252 00450 326'+03 2079 4687 6.454 11.025 o800'+Ó5 .929'+08 7.968 .00251 .00475 .380'+03 .2183 . .4921 6 762 12 100 878'+05 973'+08 7 988 00249 00508

446'03

2287 5155 7.069 13.225

.960'OS

.102'+09 8.001 .00248 .00546 .524'+03 .2391 .5390 7.376 14.400 .105'+06 .106'+09 8.026 .00247 .00596

623'03

.2495 .5624 7,684 15.625 .113'+06

.111'09

- 8.044 .00245 .00650 - .737"1-03 .2599 .5858 7.991 16.900 .123'i-06

.115+09

-8.06Ï .00244 .00710. .872'+03 .2703 .6093 8 298 18 225 132'-i-06

119t09

8 077 00243 00782 103'-'-04 2807 6327 8.606 19.600

.14V+06

.1-24'+09 8.093 .00242 .00865 .123'+04 .2911 .6561 8.913 21.025 .153'+06 .128'+09 8.108 . .00241 .00958 .146'+04 .3015

.796

9.220 22.500 .163'+06. .13-3'+09 8.123. .00240 .01064 .174'+04 .3119 t-7030 9.528. 24.025

.174'06

.137'+09 8.137 .00-239 .01126

.196'04

.3223 .7264 9.835 25.600

.186'06

.142'+09 8.151 .00238 .01355 ..252'+04 .3327 .74-99 10.142 27.225 .198'+06 .146'+09 8.164 .00237 .01576

.312'Q4

.3431 .7733 10.450 .28.900 .210'+06 .150'+09 8.177 .00-237 .01940 .4Ó7'+04 .3535 .7967 V V R

1g(Rn)

_CF

Fn

-s -s rn/sec knots +.0004 kg

Dis

lácemeht

100 tons

Wat rdepth

18' (5.4.9 m)

12

₁₃

₁₁₁

₁₅

15

'17 18 _is

₂₀

E 9 ¡I41 '1 k hP!ll: 9 E 11!111111110i110L.11iF E

lli

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]

1H011!110H11 11001101101110 ' I 1111 E 01111 II !1OPJ00011IO d LI1117 H11 1100101110111 11 101

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:::

01

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