Some tests with models of small vessels

1

MED DE:1- AN D.EN FRAN

T A T EN SKEPPSPROVNINGSANSTALT

(PUBLICATIONS OF THE, SWEDISH STATE SHIPBUILDING EXPERIMENTAL TANK)1

Nr 19 GOTEBORG 1951'

SOME TESTS WITH MODELS OF

SMALL VESSELS

BY

H. F. NORDSTROM

GUMPERTS AR GOTEBORG v

GOTEBORG 1951

I. _Preface

The present article consists of a translation of a paper in Swedish

which was published in 1936 in

Teknisk Tidskrif t,

Skeppsbyggnadskons t. The original paper

appeared at a

time when the author held an

appointment at the R o y al I

n-st it ut e of Technolog y,

Stockholm, as superintendent of

the small experimental tank there.

The article has been extended a little in addition to being translated

and it has been reprinted in this form in response to the many suggestions that the author should make the results of the

in-vestigations available to a wider public.

2. Introduction

A large amount of valuable material on the resistance properties of forms of the type usually adopted for larger ships is available in technical literature, but data on the resistance of small vessels, or boats, are less abundant. The following experimental results can perhaps fill this need to some extent.

The experiments are concerned with boats with displacements of

the order of 10 to 30 m3 (about 350 to 1 050 ft.3 or 10 to 30 tons) and with a speed of 10 to 15 knots. The experiments were carried out in the small experimental tank (60 X 3 X 1.35 m or 200x 10 x 4.5

ft.) at the Royal Institute

of Technology,

Stock-holm, with wooden models about 2 to 2.5 m (7 to 8 ft.) in length. Most of the models represent actual boats of various types; there is therefore no question of them forming a systematic series.

With regard to the results presented herein, it should be mentioned

that the models from which they were obtained were probably

altogether too small and there was a risk that these results might have been affected by the occurrence of laminar flow. However,

this possibility has of course been investigated and it can be stated that in careful trials, carried out in some cases with the actual boats,

good agreement with the model results has been established. This

4

question is also connected with the evaluation of the propulsive

efficiency.

In the following, all the data and _{parameters are expressed in}

dimensionless form. Any consistent system of units can therefore be used. In this instance, the author _{employs the systems m kg}

sec. and ft. lb. sec. _{Strict adherence to principle, when using}

dimensionless quantities, entails the practical _{inconvenience that g}

(acceleration due to gravity) and w (weight of water per unit volume)

are introduced into the dynamic parameters so that the _numerical

calculations are somewhat complicated. Tables III_{a and III b have}

therefore been worked out in order to facilitate _{such calculations.} From certain practical considerations w is used instead of (mass

per unit volume).

3.

_{Symbols and Conversion Factors}

The symbols employed in this paper are given in Table I. The m kg

_{sec. system of units has been used in all the}

calculations, but this fact is of no importance in the present case since all the results are presented in non-dimensional _form.

Ship speed and power may be expressed in the _{more commonly}

used units by means of the following factors:

m kg sec.

3 600

1 m/sec.

1 852 1.944 Metric knot (recipr. 0.5144) 1 m kg/sec. _{= 0.01333 Metric HP (recipr. 75)}

ft. lb. sec.

3 600 1 ft./sec.

6 080 0.5921 British knot (recipr. 1.689)

1 ft. lb./sec. _{= 0.001818 British HP (recipr. 550)}

The following conversion factors can be used when passing from Metric to British units:

1 in _{3.281 ft. (recipr. 0.3048)} 1 kg _{= 2.205 lb. 0.4536)} 1 m2 _{= 10.76 ft.'} 0.09290) 1 m' = 35.32 ft.3 _0.02832) 1 m/sec. _{= 3.281 ft./sec. 0.3048)}

--=

=

( ( (

1 m/sec.2 = 3.281 ft./sec.2 (recipr. 0.3048) 1 kg/m3 1 m kg/sec. 1 Metric knot 16.02) 0.1383) 1.0006) 5

(From a practical point of view 1 Metric knot = 1 Br. knot)

1 Metric HP = 0.986 Br. HP (recipr. 1.014)

The following values have been used in Table III:

g = 9.81 misec.2 = 32.19 ft./sec.2

w = 1 000 kg/m' = 62.44 lb./ft.3 (fresh water)

For other types of water, the following values can be used:

w = 1 015 kg/m' = 63.38 lb./ft.3 (Baltic Sea water)

w = 1 025 kg/m3 = 64.00 lb./ft.3 (sea water)

Table I Symbols

4.

Model Particulars and their Presentation

Figs. 1-27 show the body plans of the models and Figs. 28-34

give the sectional area curves corresponding to the waterlines shown

on the body plans. In cases where one model has been tested at

several draughts, this is indicated by a Roman figure after the model = 0.06244 lb./sec." ( » = 7.235 ft. lb./sec. ( » = 0.9994 Br. knot ( » Units Symbol Significance m kg sec. ft. lb. sec. length on waterline ft.

greatest breadth on waterline . . . ft.

draught at L/2 (without keel) . . . ft.

area of maximum immersed section xn. ft.2

volume of displacement m. ft.3

L. C. B. forward of L/2 ft.

block coefficient prismatic coefficient

speed misec. ft. /sec.

total resistance kg lb.

effective power m kg/sec. ft. lb./sec. trim angle

acceleration due to gravity misec.. ft. /sec..

weight of water per unit volume'. kg/m. lb. /ft.. L T v P g w . ..

....

. . . . . . . . . . ... ... . .1 . . .. . .. . .. .. . . . . . m m

6

number. For the purpose of this investigation, of course, one model

tested at various draughts represents as many hull forms as the

number of draughts. Models which were altered by means of an

extension of some kind are denoted with an after the model

number.

In Table II, the main data for the boat forms tested are given

in dimensionless form. It should perhaps be mentioned that not all the parameters given here are independent of one another.

Models 59 and 60 were developed from the parent form, Model

43, in the following way. All longitudinal dimensions were multiplied

by a factor a, and all transverse and vertical dimensions by 1/1/a..

The values of a adopted for Models 59 and 60 were 0.9 and 0.8

respectively. By altering the form in this manner, the displacement

remains unchanged, as also do the following coefficients and ratios: block coefficient, load waterline coefficient, maximum section

coef-ficient, prismatic coefficient and the ratios BIT and tIL. The form

of the body sections is also unaltered. On the other hand, L/17" and t/ V1'3 are altered in the proportion a, BIV13 and T/ V1'3 in the

pro-portion 1/a", 01V2' in the propro-portion 1/a and LIB in the propro-portion

a3j2. _{This method was adopted in deriving Models 59,1 and 60,1}

from Model 43,1, Models 59,11 and 60,11 from Model 43,11 and

Models 59,111 and 60,111 from Model 43,111. Resistance tests on

a series derived from a parent form in such a manner seem to give

a fairly clear indication of the influence of length upon the resistance

of boats of the type in question.

The body plans (as well as the sectional area curves) are given in

dimensionless form, the scales for the body plans being expressed as

length-unit/V". If the meter is chosen as the unit of length, then the scales give the dimensions in m of a boat with a displacement

V =1 m'. Alternatively, if the foot is taken as the unit of length, the scales give the dimensions in ft. for a displacement V

= 1 ft.'

The dimensions in m (or ft.) of a certain boat with a displacement Vrn3 (or ft.') can be obtained either by multiplying the figures read

from the scale by r,3 or by dividing the scale unit by V" and

making a new scale (the value of V" can be obtained from Tables III). If a particular unit of length is adopted, a scale system such as that shown in Fig. 1 can be constructed and from these curves

the scale for each value of V can be determined. In Fig. 1, the

scale in m for V = 18 M3 is indicated; the scale is, of course, linear.

Table II _{Model Data} Mod. No. GI) 013 100 X L. 100 X B , POO X T 1 000 X 0 , 100 X L B 100 X B T -1 000 x 6 - 1 IWO X T 1 000 X t 100 X t OL L '" 'Remarks V1/3 V1/3 V1/3 V2I3 P O 43,1 22.86 772 111 312 225 694 ___ 357 373 576 --139 --179 Round bottom 1 43,11 26.67 736. 108 -323 231 683 334 390 589 --183 --249 * * , 43,111 30.48 706 105 331 237 676 316 410 a99

203

288

* 59,1 22.86 695 117 329 250 592 357 373 576 --125

179

,Y 6 59,11 26.67 663 114 340 256 583 334 390 I 589 --165

249

* o 59,111 30.48 635 110 349 263 577 316 410 599

183

288

' * * 60,1 22.86 618 124 349 281 496 357 373 576

111

--179 * k 60,11 26.67 589 121 361 288 489 334 390 589 --146

249

* 60,11 30.48 565 117 370 296 483 316 410 599 --162 --288 o 3 23.83 723 137 344 - 275 527- r 399 293 503

166

--230 Round bottom \ 48 49 24.04 24.04 700 700 115 115 1 265 265 222 222 607 607 435 435 467 I 467 ] 644 644

181

--188 --259 --269 * *. o, 17.50 625 123 304 ' 242 510 404 430 663

267

428

* * t50,1 50,11 21.00 590 118 315 247 501 374 , 457 1 686 --282 --477 * * 30,1 -12.00 704 116 i 270 209 , 606 430 . 453 C 681

185

--263 * $ 30,11 17.50 621 106 297 221 ' 586 357 ' - 512 I 729

257

--414 4 30,111 i 21.00 584 ' 101 316 233 578 319 536 735 --273 --466 c 30ir 18.79 712 103 265 215 , 688 390 513 654 ± 23 ± 33 * 54 21.00 669 I 106 326 256 , 634 323 434 IL 584 -I-2 ± 3 i 54,t 21.55 699 105 315 250 667 333 433 572 -F163 -1-234 * * 61 21.00 668 112 303 257 596 370 441 582 -1-192 1-288 * * 62 23.40 612 119 345 270 513 346 397 606 86 ' --140 * * 63 21.44 725 117 340 221 620 343 347 623

89

--122 * * 44,f 26.67 733 127 312 240 579 406 345 568

559

--762 V-bottom 55,1 ' 20.70 .' 641 128 202 208 502 437 419 749 ---368 --573 55,11 20.30 602 121 304 217 I 499 398 452 767 --366 --608 . * 55,111 20.29 672 115 315 ' 223 499 365 484 784

306

640

.1

Displacement on which Figs. 365 are based.

-8 Table III a m - kg - see. g = 9.81 m/see.2 w 1 000 kg/ma V ma 100 x 100 X_{r71 /3} 100 X V2:3 tv

-

r2..3 2q 0:01 X 042 V78 lig V173 7.5 438 196 383 195 329 8.0 443 200 400 204 354 8.5 448 204 417 212 380 9.0 452 208 433 221 407 9.5 456 919 449 229 433 10.0 460 215 464 237 460 10.5 464 219 480 244 487 11.0 467 222 495 252 514 11.5 471 220 510 260 541 12.0 474 229 524 267 569 12.5 477 232 539 275 596 13.0 480 935 553 282 624 13.5 483 238 567 289 653 14.0 486 241 581 296 681 14.5 489 . 244 595 303 709 15.0 492 247 608 310 738 15.5 495 249 622 317 767 16.0 497 252 635 324 796 16.5 500 255 648 330 825 17.0 502 257 661 337 854 17.5 I 505 260 674 344 883 18.0 507 262 687 350 913 18.5 509 265 700 357 942 19.0 512 267 712 363 972 19.5 514 269 725 369 1 002 20.0 516 271 737 376 1 032 20.5 518 274 749 382 1 062 21.0 520 276 761 388 1 093 21.5 522 278 773 394 1 123 22.0 524 280 785 400 1 153 22.5 526 282 797 406 1 184 23.0 528 284 809 412 1 215 23.5 530 286 820 418 1 246 24.0 532 288 832 424 1 277 24.5 534 290 844 430 1 308 25.0 536 - 292 855 436 1 339 25.5 537 294 . 866 442 1 370 26.0 539 296 878 447 1402 26.5 541 298 889 453 1 433 27.0 543 300 900 459 1 465 27.5 544 302 911 464 1497 28.0 546 304 922 470 1 528 28.5 547 306 933 476 1 560 29.0 549 307 944 481 1 592 29.5 551 309 955 487 1 624 30 552 311 966 492 1656 31 555 314 987 503 1 721 32 558 318 1 008 514 1 786 33 561 321 1 029 524 1 851 34 564 324 1 050 535 1 917 35 567 327 1 070 545 1 983 w . -.

Table 111 b

ft. lb.

sec. g -= 32.19 ft./see.2 w = 62.44 lb./ft.. 9 10 x 100 x 10 x 10 x 0.001 x J7 ft.. _171/3 172/3 - v2/3w 2g ' .0/2 V 7 / 6 1 ( / ['VS 300 147 669 448 435 275 320 148 684 468 454 296 340 150 698 487 472 318 360 151 711 506 491 340 380 153 724 545 509 362 400 154 737 543 527 385 420 155 749 561 544 407 440 157 761 579 561 430 460 158 772 596 578 453 480 159 783 613 595 476 500 160 '794 630 611 499 520 161 804 647 627 522 540 162 814 663 643 546 560 163 824 679 659 570 580 164 834 696 675 593 600 165 843 711 690 617 620 166 853 727 705 641 640 167 862 743 720 666 660 167 871 758 735 690 680 168 879 773 750 714 700 169 888 788 765 739 720 " 170 896 803 779 764 740 171 905 818 794 788 760 171 913 833 808 813 780 172 921 847 822 838 800 173 928 862 836 864 820 174 936 876 850 889 840 174 944 890 864 914 860 175 951 904 877 940 880 176 958 918 891 965 900 176 965 932 904 991 920 177 973 946 917 1 017 940 178 980 960 931 1 042 960 178 986 973 944 1 068 980 179 993 987 957 1 094 1 000 179 1 000 1 000 970 1 120 1 020 180 1 007 1 013 983 1 146 1 040 181 1 013 1 027 996 1 173 1 060 181 1 020 1 040 1 008 1 199 1 080 182 1 026 1 053 1 021 1 225 1 100 182 1 032 1 066 1 034 1 252 1 120 183 1 039 1 079 1 046 1 279 1 140 183 1 045 1 091 1 059 1 305 1 160 184 1 051 1 104 1 071 1 332 1 180 184 1 057 1 117 1 083 1 359 1 200 185 1 063 1 129 1 095 1 386

-10

scale unit. Hence it follows that they can be directly compared at the same displacement. _{For the same reason the scale system} illustrated in Fig. 1 can be used for all the forms to determine the actual scale (in m) at any particular displacement.

The sectional area curves in Figs. 28-34

_{are also given in}

conjunction with dimensionless scales, viz. length-unit/17113 for the longitudinal coordinate and area-unit/1723 for the _{sectional areas.} This means that for unit displacement (1 m3 _{or 1 ft.'), the section}

intervals can be read from the abscissa scales and _{the sectional}

areas from the ordinate scales. For a displacement l7m3 (or ft.'), the data can be obtained by multiplying the figures read from the

scales by 17113 and 1723 respectively (the values of 17"_{and 17213 can}

be _{derived from Tables III). Alternatively, new scales may be}

constructed by dividing the scale units by 17" and V' 3 respectively. If a particular unit of length is adopted, scale systems similar to that

shown in Fig. 28 can be drawn _{up. The scale for V = 18 m3 is}

indicated. As in the case of the body plans, the scales _{are linear.} Figs. 28-34 are all reproduced using the _{same scale units. Hence} it follows that all the areas under the sectional area curves are the

same and equal to unit area, e. g. the area of a rectangle determined

by the lengths of the units of the two scales.

As the units for the scales in Figs. 28-34 _{are the same, it follows} that the scale systems in Fig. 28 can be employed for determining

the actual scales (in m and m2) for any value of displacement.

Finally, it may be mentioned that in _{every case the values of}

B/V1/3 and T/17113 can be read directly from Figs.

_{1-27 and the}

values of L/17" and 0/F23 from Figs. 28-34.

5.

_{Resistance Tests}

As already mentioned. the resistance tests were carried out with wooden models about 2 to 2.5 m in length. In the main tests, the models were run naked. No turbulence stimulating devices were employed.

All runs were made in smooth water and the models _{were, quite}

intentionally, tested beyond their normal speed range. The primary resistance results (in model scale) were converted to the scales of

the displacements given in Table II in the conventional manner

if

6,

Presentation of the Results in the Forint

100R v -as a function of r,74Ta , w _,,,, v2 1 g V"3 2g il

The results of the resistance tests, converted to full Scale,- are

given in dimensionless form in Figs. 36-40, The abscissa isFROUDE'S

W 2/3

number, V/Vg VIM; and the ordinate is 100 R/--- V v2. This system

2 g

of coordinates Was recommended by the

International

Conference of Tank Superintendents in

Paris in

1935.

w

It Should be mentioned that 100 PI-2g 17-0 is identical with, w

100 R1-2g r1-213

the term R in the brdinate expression represents the total

resistance; that is to say the "extended law of comparison" is

assumed to apply in this case. It is well known that this assumption

can be made for a limited range of displacement and, as already

mentioned, this investigation is

concerned with boats in the

displacement range 10-30 m3' only. The primary model scale

'results have, therefore, been converted to scales corresponding to displacements within these limits; see Table II.

Fig. 35 illustrates the errors involv ed in such a simplification when

the results refer to displacements 17 = 0.02667 (model displacement),

10, 30, and 90 ,m3. In the first case (curve 1),, the primary model-scale results are expressed directly in the form 100 R12-7-gV213 v2 as a,

function of v/Vg v1I3. In the other cases, the model results have

first been converted to the displacements mentioned before being expressed in this form.

The difference between curves 2 and 3' (10 and 30 m3) is so Small that it can be neglected from a practical point of view. The diagram

shows also that the results can be applied to vessels with

displace-ments greater than 30 m3 without a much greater degree of error,

but,, on the other hand, the errors increase more rapidly for

displacements less than 10 in'.

ri

a

Fig. 35 can be used to obtain the _{necessary corrections, when the} displacement differs from that given in Table II.

In order that the different forms _{can be directly compared at}

any given values of V and v, Vil/g 171/3 has been chosen as abscissa

instead of v/V-7,g The relationship between these _{two expressions}

is as follows:

V/Vg Vi /3 ilLiv113

The resistance (or power) of one of the tested hulls at any given

values of V and v can be determined by calculating _{g V113}

(Tables III) and reading from the corresponding curve, the value

w

of 100 R/5- V23 v2, from which R can be obtained (by using Tables

III again). _{The calculations will be simplified a little if a scale}

system similar to that shown at the bottom of Fig. 41 is used.

(When Metric units are employed, the scale system in Fig. 41 can be used for all the Figs. 36-40, as the scale units are the same as

in Fig. 41 in every case).

7.

Presentation of the Results in the Form:

10 P

as a function of trg1,2 v7,6

Vg V"

The ordinate used in Figs. 36-40 has the advantage

_{that it}

results in relatively flat curves. Furthermore, it is possible to deduce the character of the resistance function from the slope of the _curves, since a rising curve shows that the index is higher than 2 (for power

higher than 3) and a falling curve means an index less than 2. For a certain form with given values V and v, the value of R

(or P) can readily be obtained from such curves, but, on the other

hand, this method of presentation is less suitable for the _reverse

operation, i. e. to find the value of v which can be reached with a certain form at given values of V and I? (or P). In this case, it is

better to use either RI w V or P lw g112 V716

_{as ordinate. In Figs. 41}

45. the results are given in the form 10 Plw g2 V7,6 to a base of

v/l/g1713.

When using the curves in Figs. 41 45, the calculations can be facilitated by scale systems similar to those shown in Fig. _{41. For}

13

such scales, any units can be employed. Thus, in Fig. 41, the speed v is expressed both in misec. and in Metric knots and the power in

Metric HP. The scale systems are based on the following assump-tions: g = 9.81 misec.2 and w = 1 000 kg/m3 (fresh water). Corrections can readily be made for other values of g and w.

The scale systems in Fig. 41 can also be used in Figs. 42-45

since the scale units for v/l/g1713 and 10 Pfwg1/2 v716 are the same

in all the Figs. 41-45.

Figs. 46 and 47 illustrate respectively the procedure to be adopted,

when using the scale systems for a particular form, in order to

determine P at given values of V and v and to determine v atgiven

values of V and P.

When the displacement differs from that given in Table II, the

necessary corrections can be obtained by means of Fig. 35.

8.

The Effect of Various Parameters upon Resistance

and

Power Results

The data on the different hull forms and their resistances as

presented herein may afford some guidance to designers of such boats. It has been the author's intention, however, to present these

results in such a way that they could be applied more generally,

i. e. to forms similar to, but not identical with, those tested. In

order to define these new forms, it is convenient to employ the

parameters usually adopted for ship forms and, in particular, those

given in Table II. The way in which resistance and power vary

with these parameters is the matter under discussion here.

It is well known that within the range of vlirg171/3 in question,

the parameter L117" is the most important. This is shown in Fig. 48, where values of 10 Plw 01121771' read from Figs. 41-45 at constant

values of vIllg V" have been plotted to a base of L/V113. As canbe

seen, the spots fall quite regularly and mean curves can readily be drawn in. If other parameters, however, are employed as bases in similar diagrams, no such regularity is discernible and they are thus

only of secondary importance in comparison with LIP".

Attempts have been made to study the relationship between

pity g1,2v7 6 (at constant values of vIllgV1(3) and the different

para-meters, but these have been unsuccessful because the present

14

must be determined in a simpler manner for each particular case

and this can be done by studying Fig. 48 and the

_parameters

corresponding to the spots shown therein. From this point of view, Fig. 48 can be said to replace Figs. 36-45, for at given values of V and v for a certain boat, the value of P can be determined and,

conversely, it is possible to obtain the value of v which can be

reached at given values of V and P.

9.

The Effect of Draught upon Resistance and Power

A problem frequently met with in practice is to calculate the

resistance and power for a certain boat at different draughts and some of the present results can be used in studying this problem,

as Models 43, 59, 60, 50, 30 and 55 were all tested at different

draughts. Model 43, for instance, was tested at the three draughts shown in Fig. 49 and the corresponding results are given in Fig. 50 in the form 10 000 P lw g" 42 as a function ofv g Ln, where Ln is the length on the waterline at the mean draught. These results

may also be used as a guidance for other forms.

10. Trim

For want of space, a complete account of the trim results cannot

be given here.

As mentioned previously, most of the models were tested beyond

their normal speed range and, in consequence, the trim angles at the highest speeds were rather absurd. _{In many cases the trim} altered to such an extent as to limit the speed.

Examples of trim changes are given in Fig. 50, which shows the

trim angles for one and the same boat (Model 43) at different draughts,

and in Fig. 51, which gives the trim curves for different lengths

of boat (Models 43, II, 59, II and 60, II) at

one and the same

displacement.

11. _{Effect of Appendages}

All the models were tested without rudders _{or other appendages,} but, as may be observed from the body plans, _{some models were} fitted with keels.

It

quantitatively by means of ordinary model experiments. Such tests

can, however, provide some guidance for comparisons between

different types of appendages.

Fig. 52 shows the results obtained with Model 49 both in the

naked condition and also when fitted with rudders and other

appendages of different :types. These results cannot, as mentioned

above, be accepted from a quantitative point of view, but, on the other hand, they give a good qualitative picture of the effect on

the resistance produced by typical appendages.

Usually, the appendage resistance can be estimated at 5 to 7 '%

of the naked resistance in the case of single screw boats and 8 to

12 % in the case of twin screw boats. If the appendages are

properly streamlined, however, these figures can be reduced to 4 % and 7 % respectively.

Air resistance can normally be neglected, but an allowance of

1 to 2 % of the naked resistance may be considered a safe estimate of this quantity.

12,,

Shaft Power and Engine Power

Between the total effective power Pe (inclusive of appendage

resistance and air resistance and with allowance for scale effect etc.)

and the shaft power Pshaft (at the tail end of shaft), it is usual to

introduce a total propulsive efficiency thus

P, -shaft = tpr depends upon propeller efficiency wake thrust deduction

relative rotative efficiency..

Then, in order to obtain the engine power (brake power) it is

necessary to consider the shaft friction losses and therefore multiply Ps' haft by a factor of the order 1.01 to 1.02.

Very little is known about allowances for scale effect, wake or thrust deduction for boats of the type in question. In most cases, therefore, it would seem that the only possible method is to allow

16

for all the components of the propulsive efficiency and also for scale

effect in one factor. Thus the engine power

Peng. )pr.

where P effective power as calculated' from the diagrams and corrected for appendages (and also, if necessary, for displacement and type of water)

and rip, efficiency factor between engine power and calculated

effective power.

Trial trips with several of the boats dealt with in these model

tests have given values of Typr. between 0.50 and 0.55. The higher

figure obtains under favourable conditions, such as a suitable

power-speed-propeller revolutions combination giving _{a high propeller} efficiency. In doubtful cases, the figure 0.5 can be recommended.

13. Acknowledgement

The author is indebted to the authorities of the R

oy al I

n-stit ute of Te c hnolog y, Stockholm, for permitting the

relevant results to be published. The author also wishes to express

his gratitude for the grant made from Hugo H a inm

a r' s

Foundation for Maritime Research which enabled

this reprint to be made. Thanks are also due to Mr. A. 0. WARHOLM, who prepared the diagrams, and to Mr. DACRE FRASER-SMITH,

B. Sc., who has assisted the author in translating the paper from

the Swedish.

,3 :Mod . 43,1 0,1' 0,2 .0,3 0,4 -/119,41117-urth V1/3 5 0,6 47 48 0,9 10 Fig. IL: Fig. Z. Fig. 3-17

gressr-Aere--

sistarsrArArgore-ozzarriffirmirArArArmr,,

obliztvisPAT

111110MINSO71ff

UN

,,

0

18 Mod. 59,1 Wng ek-unF 0,2 0r3 0,4 05 4,7 18 0,9 t,0 Fig. 4. Mod. 59, X csif Fig. 6. 0,7 48 -,, 1.9n t hoo,;( 0,9 1,0 0 0,1 06 0 0,3 0,2 43 014 45 0,6 Fig.

to 0 0;4 0,0 Fig' "1 IMod. 60'111 Il"g 9,0 4'7 00 9V 1,0 , II t'"_eh-urar 4.3 0i4 05 cy= a 09l 90 ' 9 19 5 0 Fig. 8.

-.0,0 0 0,1 42.43 0,4 AS Fig. 10..

sum

Lngth-unit 0,1 .0 0,1 6t2 43 Is 45 46 4# 10,9_V° Mod. 3 Mod. 48 Fig. 11. a, 0,4 0,0 46 _0,7 , Pig. 12. °,6 L44901,414 V 'A aq 0,8 0,9 -ength-une 1,0 ' 0,9 1,0 0,8 2') 0,7 011 0,2

11 , .11 0, Mod. 50,1 42 t0s3 05 10,6 Fig. 13. Fig. 14. °Ingth_,, 0i8

y

7 v3d,0 /4 21 q4 E 0 0,3 0.4 016 0,7

0'4 6'0 IY0 L'O 9'0 sb tio o 6 pun- yibuI7 L '!. I 23.1 iff'oc Pow 60 e'0 Lb 90 S*0 0) c'0 40 ZT, "91 ,0

Mod. 54 2 length-un, 42 4,3 44 0,6 46 017 018 49 Fig. 19. Fig. 20. 23 Mod..5 Fig. 18.

24, Mod, 61 Fig. 22. Fig. 23. ,qt 0 01 0 y 144 013 v 018" 0,0 1,0 Fig. 2,1., 0,6

flt Fig. 24.4 beng - utir 0,9 0 al '0,3 0,31 0,4 0,$. 0,6 a, 0,8 49 1,0 I r - e Fig. 25. - 25

26 6' 4 2 .4 length-unit 01 0 Or Ore 0,,4 0,5 05 0,7 0,8 49'v 1,0 Fig.. 26.. 55,111 0.210 03 0.2 0,3 0,4 as 0,6 91 Fig. 27.

Fig. 28;. see after p. 41%,

0,7

Lonpt4-unit

0,3 Area -unit A 43,11' o _ 59,71 90,11 --4e 1/1 ---2 60 13

>---r--71I

/

,-1---, ---F 11---, 1

\

/2

1 I' I 1 I A

\

II

I 1 I I

II

I I I I I I I, I

'/

' I I 1 I I I / I I 1 I I I 1

i \

59,11 59,1I I 1;' 1 .4 1 Ij i I I \ ?s, I \ ' ,-/ I' I I, I I ' , -,,

Imismilmillamlin

,wmomimminlmotinsin

, I Fig. 2 9 *

I\

2. 1 i2 II 45,1 16 * 1 ?3, 6 len9th44h 7 16. 14 -0,2 0,1 2 16

-0,3 Area -nil VO 60,1 1-Ns

\

/zr

Fig. 30. 43,1 sgs /6 Length-unit ,4

Fig. 31.

Area -al.

03

i

TE '2!J

,0,3 :Are - unit VaP 4? 44,1 55Z 551

\

5s;ir 2 4 1+-4 8, Fig. 34. 10 55,1 12 12 12 55,12 55,2' 44,f I 16 Length- unit

a vc, .21a czi_d2P 9'0 06 o OE d c..0 .d '9E .2u rbd 6/1 A 4'1 et, 90 ,'or - 9 t, - - - _,....--;-,..-,... yet at.

AG

ENENNIIIMIll

,;-.0.-"--- riss

,

Kb / Ewa - >---, too -->-,

--

--

El

A e5e _ rio . a 00i

-

_ INIMMINIENIMININ 1110111111111111111111

rani.

Mtrellii_mem

111

low

_...,

MILMII

""ElthilliMICIIII

--ma

MI

WAN

5 E eA de 4 ,-,T t, ooc 0 C. 9

3 4 a 4 2 6 50,1 /1, .3 49 Ci8 08 10 1,2 1,4 Fig. 37. Fig_ 38'.. 100 R ?-;'-oov2 ?

Effiliiiiiilei

WE/ MM.

31,71

WIMIMMIIII

IMMIERAMII

3.,f

bilial

1 A AL 1,6 ₁₈ 20 V 1,6 1,8 V 14771i 20 4 2 0 44 08 7,2

100 P ri2/3 V2 2 54,f

OMEN,

7--63

1111111ZIOMOMM11111111111111

IIIIIIMOMOMOOMMOIMMIN

111111111111111111110

0 04 100 14 =11 0112 29 Fig. 40. 1,6 1,8 2,0 :;5 06 08 1,0 1,4 44 06 08 1,0 1,4 1,6 1,8 2,0 Fig. 39. tr9-173 6 2 0 2

640 600 550 520

WOW

mg 20 41, DISPLACEMENT I o No r V in 5 10 mj 5 .7: .wg v 2,0 480 440 36 320 280 59,15F 1,6 ,

'

rj

I

M-t2

In

60,. ENE itatv 1

0,8 -v-,400" 200 160 120 80 40 35

N.

-; _'.-",a1 111

MillEidll

0,4

ll

rani!

0

_474.

o 44

_...

06 0,8 14 16 1 8 V 30 25 Pig. tisiTrir

,- .10

-/AW

Ar-A/IPIPP%AillWg

wariariajor iarAviiim

,

/.., ,MIN 1 7/ 11117/11WAWZA I 11 rA IFA I MI 11, lb

,

,?, 2 0 IN

T211/ 511=1/if MI/AMR= III I II I IA I PM% It M WEI I I

WA .1 i'' 25 -ir r3 30 _ I i -

1

11117,11Rp/A IA

MI

HP 1,0 1,2

is 41, 4,8 04 0 I I _{10 P} V2 rm6 wg 50,y

/-7

3

sf/

2,0\ 2,0\ Fig. 43. 37 11 44 I 7 1,61 1,2 0,3 0,4 004 3 06' 08 1,2 1,4 1,6. 1,8 Fig. 42. 1,0 04 '0,6 1,2 4,4 1,6 6,8 2,0 1,0 V /,6 P 304 1,2 0,8

38 Oft 2 2 0, 0 2, 1,6 0,4 10 P wg--TFl 62 ,..., .56: ,

1

11

, ,

gAill

Al

A 10 P 55,1 - c 9 y2 v7/6

si

"Ai

pm I'

Pm

U.

0 5

IMAM

,

Pr

8 4 ₁

'

/

/

-. 10 1,2 Fig. 44. 4 ₆ 1;8 2,O V 04 06 08 10 ;2 Fig. 45. 14 1,6 1,8 2 V V;T-71P 0 0 4 1,2 0,6 08

\WWIRI INIERMIMINUNIMIMINIII

11111113116-.ft1.11,7 "Mr"

/0 Length-una 0,14 0,16 Mod. 43 0,857.0. if t/43.7. 402 _O041 0,10, (1,2 Fig. 46. Fig. 47. Fig. 49. 39 Fig. 48; see after p. 41. 6 14 1,002.1. 0,9961, L, '0 0,98

1,5 t,0 0,5 40 tan 79 0,06 0,04 0,02 WATER SURFACE

-

.

- ----.-e-,,T7F7--- FORE .1 W 1 DURING RUN 10000 P -7-72 Mod. 43 See Fig. 49 V ..., -- 50,7 -e" - --- ' --- 59,1 . '

--....,....

V 0 2 03 04 OS 0O 0,7 Fig. 50. tan 6 0,5 1,0 _{13 20} Fig. 51. 008 aos 0,04 0,02 0 -0,02

1,4 1,2 1,0 0,8 0,6 0,1 0 41 Model F = Scale: No. 49 2 4.04 m3 0 0

II

ill"

'---X

I---

_I

iii

INI

N

fi.

111/

X

1/1

Ari_ 7 8 9 10 12

Speed of vessel in knots

Fig. 52.

6

1110

DISPLACEMENT V in AO Area iyleD V 0,2 59,1 2 a CO 43,i 59,1 15 SO Length-unit 6

ErssrAuveirrrnv,,e3P-,do.P---

qpriTiffirr,

MEOW

AIWAwAwAVAPISPW

W

ms

ABWIFARIPMFW

10 4 /S II 25 Fig. 28., 30 9 33 2 6 I

-2,0 10 P iwgq2 (7" 1,0 0,5 'Fig. 48, t 1 1 t t I.:1r _t _J i :Ili I 'II Z4 -76 L 7,8 -V "8 V9,V --....=.---Ir. 60,11! 55,1.77 .30,X, 60,11 50,11 55,1 6260,1 30,17 50,1 59,111 55,/ 59,161 54 159,1 54,f 48 49 30,1 43,E 30,1 3 63 44,1 43,11 43,1 -1-171/3 5,65 5,72 5,84 5,89 5,90 6,02 6,12 6,18 6,21 6,25 6,35 6,41 6,63 6,68 6,69 6,95 6,99 7,00 ZOO 7,04 7,06 7,12 Z23 7,25 7,33 7,36 772 e VIP 7,72 17 1'15 1,24 1,06 1,23 1,10 1,28 1,14 1,12 1,06 1,17 105 1,15 .1,15 1,16 1,05 1,03 1,37 1,17 1,27 1,08 1,11 T

-171/3 0,370 0,315 0,349 0,297 0,304 0,349 0,292 0,340 0,303 0,326 0,329 0,315 0,265 0,265 0,270 0,331 0,265 0,344 0,340 0,312 0,323 0,312 o

,

_V" 0,296 0,223 0,281 0,221 0,242 0,263 0,208 0,256 0,257 0,2,56 0,250 0,250 0,222 0,222 0,209 0,237 0,215 0,275 0,221 0,240 0,231 0,225 1--4,83 4,99 4,96 5,86 5,10 5,77 5,02 5,83 5,96 6,34 5,92 6,67 6,07 6,07 6,06 6,76 6,88 5,27 6,20 5,79 6,83 6,94 3,16 3,65 3,791 3,34 3,74 3,98 3,46 3,57 3,57 4,04 3,16 4,37 3,34 3,70 3,23 3,57 3,33 4,35 4,35 4,30 3,16 3,90 3,99 3,43 4,06 3,34 3,57 0,410 4484 0,536 0,390 0,457 0,452 0,397 0,373 0,512 0,430 0,410 0,419 0,390 0,441 0,434 0,373 0,433 0,467 0,467 0,453 0,410 0,513 0,293 0,347 0,345 0,390 0,373 r 0,599 0,784 0,735 0,589 '0,686 0,767 0,606 0,576 0,729 0,663 0,599 0,749 0,589 0,582 0,584 0,576 0,572 0,644 0,644 0,681 0,599 0,654 0,503 0,623 0,568 0,589 4576 + + + + T7i 0,162 0,366 0,273 0,146 0,282 0,366 0,086 0,111 0,257 0,267 0,183 0,368 0,165 0,192 p,002 I 0,125 0,163 0,181 0,188 0,185 0,203 0,023 _ 0,166 0,089 0,559 0,183 0,139 100. + , + + _ + 2,88 6,40 4,66 2,49 4,77 6,08 1,40 1,79 4,14 4,28 2,88 5,73 2,49 2,88 0,03 1,79 2,34 2,59 2,69 2,63 2,88 0,33 2,30 1,22 7,62 2,49 1,79

I

I

:

1

i Hil

I

-

I

11111 ill

11111

1 _AIN 1 , I I , -INICIEMEM timiik.

_I

_---"'"'"

11/11/1111

.-IMO

rift

., I 1 : i Bra...

II

I I 11.71111111111111111t NMI sz../... I ;It' I $ 0-, 1 ; ; III; .11.1 , 1 LI "11 el 1, :, I 6 III; III i I t ,1 tt I I I I

gal

II I I I, 111111111111 Nal it I I °I I: II I i It -11 0

ill

-igIIIIIIIIIIIII

II

' 1 . / I

milliiill

1111

/ 1

III

0 i I 56 56 62 6,8 64 6,6 1,5 0 r 7,2 1,01 1,21 1,18 1,21 1,19 1 0,316 0,361 0,315 0,304 0,345 0,233 0,288 0,247 0,217 0,270 5,78 4,89 5,01 4,99 5,13

t

-I