The transverse stability and resistance of single step boats when planing

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FRAN

STATENS SKEPPSPROVNINGSANSTALT

(PUBLICATIONS OF THE SWEDISH STATE SHIPBUILDINO EXPERIMENTAL TANK)

Nr 25 . GOTEBORG 1953

THE TRANSVERSE STABILITY

AND RESISTANCE OF

SINGLE-STEP BOATS WHEN PLANING

BY

R. RODSTROM, HANS EDSTRAND

AND H. BRATT

GUMPERTS AB

GOTEBORG

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This paper describes some systematic model experiments which

have been carried out at the Swedish State Ship buil

d-ing E xperim ent al Tank on a fast, pland-ing, sd-ingle-step

boat having a displacement of about 35 m3.

It was intended, in the first place, to investigate the influence of

breadth variation both on the transverse statical stability under planing conditions and on the resistance. The aim was to arrive

at a relation between the breadth and the other dimensions which

would give good transverse stability together with acceptable

resist-ance. In addition, the extents to which these qualities are affected

by the height of the step and by the angle between the fore-and

after-body keel lines were investigated by systematic variation of each of these characteristics. Similarly the deadrise was also varied in two stages.

The transverse statical stability of this type of vessel under planing

conditions is only dealt with briefly in technical literature and it has, therefore, been considered appropriate to publish herein the experimental results and details of the technique employed in

ob-taining them.

The investigations and the special apparatus involvedwere planned and designed by Mr. RonsTRom, while Dr. EDSTRAND compiled and

edited this paper and Mr. BRATT assisted with the analysis of the test results.

2. Symbols and Units

Dimensions of Boat and Model

= scale ratio = length overall

La = length of after-body from step to transom

= breadth between chines at step 17 = volumetric displacement (at rest)

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= weight displacement (= wV)

H = height of step

M' = transverse rnetacentre when heeled under planin,g sonditions

0 = centre of gravity

G' centre of gravity in heeled position

K = intersection between keel line of fore-body and a vertical plan through GI and 49'

K' = intersection between the direction of the vertical component of the

resultant water force when heeled under planing conditions and the hori-zontal line through K

= angle between keel lines of fore-body and after-body (bottom angle)

= angle of heel under planing conditions

To = angle of heel under planing conditions when F 0

= rudder angle

=-- rudder angle when F = 0 Kinematic and Dynamic Symbols

= speed in general

V = boat's speed in Metric knots

= resistance

athwartship force when heeled under planing conditions

weight of water per unit volume (= 1000 kg/m3 for tank water) =- temperature of water

Dimensionless Ratios

LaIB = after-body length-breadth ratio

B IV 113 = breadth-displacement ratio

BIH = breadth-height of step ratio

R B

= resistance-displacement ratio

W V A

F4 = v/Vg 17h13 = FILOUDE number, displacement

Suffix m denotes model. The boat is referred to if no suffix is used. Units and Conversion Factors

Metric units are used throughout

1 metre = 3.281 ft. (recipr. 0.3048)

1 metric ton = 1000 kg = 0.984 British tons (recipr. 1.016)

1 metric knot = 1852 m/hour = 0.999 British knots (recipr. 1.001) For g (acceleration due to gravity) the value 9.81 m/sec.2 has been used.

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3. Models Tested

Two wooden models, Nos. 468 and 479, were used for these

in-vestigations, each having a length overall, L., of 2.86 m and a breadth between chines at the step, B., of 0.52 m. The lines of

these models are shown in Fig. 1.

The only difference between the two forms lay in the deadrise,

which was 7.5 degrees at the step in the case of Model No. 468 and

10 degrees in the case of Model No. 479. The length overall was

Lm

divided into 20 parts, the step being arranged at or Station 10.

The models were not intended to represent any particular boat or

design, but their main dimensions and lines, though somewhat

simpli-fied, may be considered generally representative of this type of

vessel.

In order to facilitate systematic variation of the height of the

step, H, and of the angle, e, between the fore-and after-body keel

lines, the fore and after halves of each model were made separately

and joined together by means of a hinge at the step. As can be

seen from Fig. 2, the adjustment of this hinge controlled the angle E, while its vertical position determined the height of the step.

Model No 468, in its original form, represented to a scale of 1:8

a boat with a displacement, V, of 35 m3. This model, however, was

L.

fitted at the after end with two removable portions each 2T) in length. The length of the after-body could thus be decreased in

relation to the other dimensions, so that in addition to the original version, No. 468, two further forms, Nos. 468-A and 468-B, were obtained using Stations 1-10 and 2-10 respectively; see Fig. 2.

In the two latter cases, the scales used in analysing the results (1:8.9 and 1:10) were chosen so that the full-scale length of after-body was the same for all three versions; thus, by also maintaining the same corresponding displacement (V = 35 ni3) in all three ver-sions, three different ratios of length of after-body to breadth were

obtained at constant displacement. This procedure, of course,

virtu-ally entailed changes in the other dimensions, for instance in the length of the fore-body, but this was not considered important be-cause, at the speeds in question, the model (and the boat) planed

to such an extent that only a small part of the fore-body immediately

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Model No. 468 Model No. 479 17 18 19 20 Stem . i0

1\

Full Length Prot/le 10 12L/ 14 16 18 20 Fig. 1.

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Variations in the draught were also necessary, but these were

considered insignificant in comparison with the changes in breadth.

Thus, as intended, the main effect of this procedure was to produce variations in the breadth of the boat at constant displacement and constant length of after-body.

Model No. 468-A (with the after-body shortened to Stations 1-10, as explained above) was Also investigated assuming a scale 1:8.

It

was intended thereby to determine the influence of the length of after-bodSr when the displacement and the other dimensions are

maintained constant.

Model No. 479 was only investigated in its original form and, in

the scale 1:8, it represented a boat of 35 m3 displacement.

For the stability tests, each of the models was fitted with a rudder

and a stabilising fin, as shown in Figs. 1 and 2. The reasons for this are discussed in Section 4 of the paper. Spray deflectors of

different forms were used in some of the stability tests. This was because, in these tests, the water tended to be drawn up the sides of the model in a manner not true to scale and this evidently had a

considerable effect on the measured results. This point is dealt with

in Section 5 of the paper.

Particulars of the various model versions are given in Table 1. The design and position of the spray deflectors are also shown in this Table.

4. Experimental Arrangements

Resistance Tests

The resistance tests were carried out in the usual manner, with

guides fitted at Stations 0 and 19. In the case of the two model

versions with shortened after-bodies, the after guide was fitted at

Stations 1 and 2 respectively, (the model scales being 1:8.9 and 1:10

respectively). The models were run naked and no special devices

were employed to stimulate turbulence.

In accordance with the general practice in tests on vessels of this type, the towing force was applied in line with the assumed pro-peller shafts. This meant that the towing wire had to be adjusted in the vertical plane at the beginning of a run, so that at each speed its direction would be at an angle of 70 with the after-body keel

line and so that, if produced, it would pass through a point 480 mm (in full scale) below the keel at Station 0. The adjustment was made

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during each run but before any recordings were taken, by raising or

lowering the point of attachment of the towing wire on the carriage dynamometer. The direction of the towing wire, as defined above, can be assumed to correspond approximately with the direction of the propeller shafts in a boat of this type and size.

Transverse Stability Tests

The arrangement of the apparatus employed in these tests is

illustrated in Figs. 2 and 3.

When in motion, the model was free to swing about a fixed datum

point and also to heel and trim. The datum point, a (Fig. 2),

consisted of a spherical ball-bearing fitted on an outrigger, b on the fore end of the model. A horizontal rod, c, was fixed to the outer ring of the ball-bearing at right angles to the direction of motion of the carriage. The other. end of this rod was connected to a dyna-mometer which, in turn,, was fixed to the carriage, and by means of the dynamometer, the athwartship forces acting on the model through the datum point, a, could be measured during a run.

The model could be given any desired initial heel by the

athwart-ship movement of a weight and the heeling angle when under way

was measured on a special heeling indicator, the principle of which

is evident in Figs. 2 and 3. The indicator consisted of a piano wire, d, attached to both ends of an athwartship beam, e. The beam was

attached to the aforementioned outrigger immediately abaft the

datum point and the wire passed over two smooth-running pulleys

f, which were mounted on a transverse frame, g, relatively high above the beam. A millimetre scale was fitted on the frame and

the amount- of heel could be read off in mm by means of a pointer, h,

attached to the piano wire. The piano wire was kept taut by means of weights, i, and the frame and pulleys were mounted on a rod, k, which rested on -a pivot, 1, attached to the carriage. The weight of the indicator system was balanced by a weight, j, at the opposite end of this rod, k. There was thus a certain amount of tension in the wire, but due to the fact that the whole system was balanced and pivoted about an athwartship aids, the extension of the wire was not affected the trim or other movements of the model. All

the transverse stability tests were, for technical reasons, carried out with initial heel to port.

Since these stability experiments were only concerned with the

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0 1 2 \N Movable Weight 0 12 14 16 18 4 6 8 Movable Hinge Fig. 2. Heeling Indicator/ Spherical Ball- Bearing 17 'Connected to To Resistance Dynamometer

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;h14 1\ 1. \\ I/IP \ Movable Weight

was fitted in order to provide the necessary directional stability and

to counteract the tendency to yaw caused by heeling. Boats of

this type often have more than one rudder and, with multiple screw propulsion, they are usually placed in the slipstream of the

pro-pellers. In this case, however, on account of the absence of

slip"-stream and the fact that only one rudder was employed, the dimen-sions of the rudder Were greater than normal. The single rudder was, in fact, designed so that it Would provide 'approximately the

same steering effect in these tests with towed models as would two normal rudders each working behind a propeller. The rudder could be set at different angles, the angle of helm being read off a graduated

scale.

Heeling Ingiccitor

Lim

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For the stability tests, the models were each fitted with a fin

under the fore-body. Such fins are generally used on boats of this type in order to counteract drift, particularly in side winds. They can be considered to have some affect on the stability, and for this reason they were fitted in these investigations. Their dimensions

were based on the information given in technical literature on

boats of this type. The rudder and fin proportions may be seen in

- Fig. 1.

The stability tests were carried out in a similar manner to the

resistance tests. The model wasP towed by a wire attached to the carriage dynamometer, the wire passing through the centre of the hole in the spherical ball-bearing. This ball-bearing was fixed in

such a position relative to the model that, as iii the case of the

resistance tests, the towing wire was at an angle of 70, to the

after-body keel line and, if produced, would pass through a point 480 mm

(in full scale) below the keel at Station 0. At the beginning of each run, the wire was adjusted so as to maintain this direction and the position- in the centre of the hole in the ball-bearing. The pulley-wheels, m and n, shown in Fig. 2 were for this purpose mounted on the frame of the resistance dynamometer, which could be raised

or lowered accordingly.

When carrying out the tests, the model was given a certain initial heel when at rest by moving a weight and a certain rudder angle, 6. Then a test would be made, taking measurements of speed, athwart. ship force and heel, the latter by means Of the heeling indicator. By investigating several possible rudder angles at each speed and initial

heel, a relationship was obtained between the rudder angle, a, the

angle of heel, 97, and the athwartship force F. The rudder angles

were chosen so that, in some of the tests, the athwartship force

changed sign. The angle cif heel for the case when the athwartship force F = 0, corresponding to a completely free model, could then be obtained by interpolation. This angle of heel is denoted by To

and the corresponding rudder angle by 60.

Fig. 3 illustrates in principle the method of using the angle of

heel, To, thus obtained to determine the statical stability of the

model (or boat) ;Under way. In Fig. 3, G. is the centre of gravity of the model in the upright Position and G. is the corresponding

centre of gravity in the heeled position. The position of G. was

determined by balancing the model before each series of experiments

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the weight and the distance moved to bring about the angle of heel.

The centres of gravity G.. and G,,' always lay in the same

trans-verse plane and at the same height above the waterplane of the

model in the upright position, since the weight was always moved

athwartships and parallel to this waterplane.

The point K. in

Fig. 3 is at the intersection between the keel line of the fore-body

and a vertical plane through G. and G. The point K. is at the

intersection between the direction of the vertical component of the resultant water forces when heeled under planing conditions, and a horizontal line through K..

For equilibrium in the heeled position when under way, the

vertical component of the water forces must act through G.' and

must be equal in magnitude and opposite in direction to the weight zl.

The magnitude of distance K.K.' then becomes a measure of the transverse stability of the model at different values of the angle of

heel, To.

The centre of gravity G, of the boat has also been considered in model scale in Fig. 3. The height of G above K was assumed to be 1.5 m (in full scale), this value being considered typical of boats

of this type and size.

Then, by subtracting the distance KG

sin

To from KK', the righting arm GG, was determined and

this- be regarded as a measure of the transverse stability of

the oat. _A1944,1,

In connection with Fig. 3, it should be pointed out that the

distances Um0, Knz,K.' etc have been considerably exaggerated for reasons of clarity. The diagram is thus not to scale and is only

intended to illustrate the principle involved.

5. Test Results

The different experimental series and their numbers can be identi-fied with the aid of Table 1.

The results of all the tests are given in tabular form in the Ap-pendices at the end of the paper; Appendix 1 contains the results of the resistance tests and Appendix 2 the results of the stability investigations. The figure numbers given in the tables indicate that the values in question are illustrated graphically in the diagram of

that number. Furthermore, the appropriate experimental series

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Table 1

Series Nos.

(The Series Nos. are marked with 0 on the Figures)

Spray Deflectors (in Model Scale) Measurements in mm

CI

1) Stations 10-16 2) Stations 10-16 3) Stations 10-16 4) Stations 10-16 5) Stations 11 - 16 Unit Model No 468 468-A 468-B 479 Model Scale (1: a)

-

1:8 1:8 1:8.9 1:10 1:8 Displacement, V m3 35 35 35 35 35

Breadth between Chines at Step, B m 4.19 4.19 4.66 5.24 4.19

B/I71/3

-

1.28 . 1.28 1.42 1.60 1.28 Length of After-Body, La m 11.45 10.31 11.45 11.45 11.45 LaIll

-

2.73 2.46 2.46 2.19 2.73 Height of Step, H m 0.24 0.42 0.60 0.42 0.40 0.45 0.24 0.42 0.60 BIH

-

17.46 9.98 6.98 9.98 11.65 11.64 17.46 9.98 6.98 Resistance Tests 2 degrees 2 1 » 6 1 13 24 27 16 18

Angle, E, between keel lines 0 * 8 5 3 11 23 26 22 14 17

of fore- and after-body

-1

» 9 7 4 12 25 20 15 19

-2

* 10 21

I 1 degrees 384) ₃₀ ₄₅

0 b 33 28 31 40 44 29 32

Angle, c, between keel lines 0 » 341) 41) 462)

of fore- and after-body 0 * 352) 42)

» 36) ₄₃₂₎

0

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14

In addition to the model resistance and model speed, Appendix 1 includes the trim changes measured during the tests, the

correspond-ing full-scale speed and the temperature of the tank water. The

calculated values of r-7 and Fn, are also given.

Wm v m

The tables in Appendix 2 include values of the height of the centre

of gravity

of the model above the

keel, Kmam, which was

determined, as mentioned previously, by balancing the model before

each series of tests. They also give values of the applied initial

shift.of centre of gravity, G.G.' , the resulting angle of heel, To

(when the athwartship force F 0), the corresponding rudder angle,

60, and the temperature of the tank water. In addition, Appendix 2

includes values of corresponding full-scale speed, values of the

distance KIV converted to full scale and values of Fnr.

It should be noted that the values of (p0 and 60 given in Appendix 2

are not actual measured values, as mentioned in Section 4 above. Generally, two runs were made at the same speed and initial heel but with different rudder angles; these rudder angles were chosen

as close to each other as possible, while at the same time producing

a change in the sign of the athwartship force. The measured values of angle of heel, 99, and athwartship force, F, were then plotted as

functions of the rudder angle, 6. By this means, the angle of heel, To,

corresponding to the rudder angle, 60, which would produce an athwartship force F = 0 was obtained, as mentioned previously, by

direct interpolation. For technical reasons, it was not always possible to obtain exactly the same carriage speed for the two interdependent

runs; the differences, however, were so small that the errors arising therefrom were considered to be within the limits of accuracy of

the measurements in general. Resistance Tests

Some representative results from resistance tests are shown in

R.

Figs.

4-8, where the

resistance-displacement ratio is Wvm plotted as a function of the Froude number Fnr. By this means,

the values in the diagrams become comparable with one another

even in those cases where values from experiments in different

scales (1:8, 18.9 and 1:10) are shown together. A scale of correspond-ing ship speed for a displacement 17 35 m3 has been included for comparison in each of the figures.

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0.2

E

cc E

Resistance Tests

Influence of Deadrise

Model No. 468 0 o Deadrise: 7.5 degrees' 0113 1.28, Li8= 2.73, Model No. 479 0 d Deadrise: 10 degrees! 8/N =9.98, = 0 degrees

2 3 V Fnr I/TF-77-! 1 lo 20 30 40 50 60

Corresp. Ship Speed, Vs , in knots at p = 35 m3

Fig. 4.

Fig. 4 illustrates the effect of variations in the deadrise when the breadth, length of after-body, height of step and bottom angle are constant. The model with the least deadrise, No. 468, shows the

lowest resistance. The subsequent comparisons are therefore limited to Model No. 468.

The effect of breadth variation at constant length of after-body,

height of step and bottom angle is shown in Fig. 5. In this diagram,

the results from Series 1 have been included for comparison in the

form of a curve, since this series covered the whole speed range from

10 to 60 knots. The spots, through which this curve was drawn

are shown in Fig. 8.

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Resistance :Tests Influence of Breadth 1/3 ₆ _degrees 0 El a a 2 3 4 F_np- v Vgi f/.3 1 1 1 1 1 10 20 30 40 50 60

Corresp. Ship Speed, V5 , in knots at !735.m3

Fig. 5.

For technical reasons, the height of the step was not quite the

same in Series 5, 23 and 26, the results of which are compared in Fig. 5. The vertical position of the hinge (see Section 3), which connected the fore-body of the model to the after-body, could not be varied by such small amounts as those required by the adoption of the different scales. The differences in the full scale height of

step, as given in Table 1, are however so small that they can be

neglected in the comparison in question.

From the comparison between series 5, 23 and 26 in Fig. 5, it is

5 Model No. 468 1.28, L./8.2.73, 8/H.6.98, Model No. 468-4 0 13/17V3 1.28, a B/P'- 1.42, a B/171/3 1.60, B 2.73, B/H -9.98 2.46,01-11.65 e 0 degrees 1../B2.19,B/H 11.64 Model No. 468-8 El 071/3 -1.6o,1./8.2.19,8/H*11.64 e degrees

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2

Resistance Tests Influence of Length of After-Body

Model No. 468 0 0 La/ 8=2.73 I

8/p'/ =1.28, B/H= 9.98, 6 = 0 degrees

Model No. 468-A 0 La/B=2.46

o 2 3 F v nP ./ V9P 1/3 i 1 1 1 1 I 10 20 30 40 50 60

Corresp. Ship Speed, Vs, in knots at /7 = 35 17.13

Fig. 6.

evident that the resistance is decreased by an increase in the breadth.

However, at the greatest breadth (Series 26) the model could not

be run above a speed corresponding to about 40 knots on account

of porpoising. For this reason the results from Series 27 are also shown in Fig. 5. In the latter series, the bottom angle, _{s, was} some-what greater than in Series 26 and this eliminated the _porpoising at higher speeds; on the other hand the resistance _{was considerably} increased, particularly at the highest speeds. It is, however, evident

from Fig. 5 that increasing the breadth-displacement _{ratio, B/171/3,} from 1.28 to 1.42, i. e. increasing the beam from 4.19 m to 4.66 m when V = 35 m3, has the effect of decreasing the resistance.

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02

E cc E

0

Model No. 468

Influence of Height of Step

®

B/H,. 6.98 B/H 9.98 B/r/j. 1.28, La/B 2.73, B. 0 degrees

0

a 8/11 17.46 Resistance Tests 4 5 Fig. 7.

Figs. 6 and 7 illustrate the influence on the resistance of variations in the length of the after-body and the height of the steprespectively.

According to Fig. 6, a decrease in the length of after-bodyclearly has the effect of increasing the resistance.

Fig. 7 indicates that, of the different step heights investigated,

the mean value, corresponding to BIH = 9.98. (H = 0.42 m when

V = 35 m3), gives the lowest resistance, although the resistance seems to be comparatively slightly affected evAn by considerable

alterations in the height of the step. The aforementioneddisregard

6

0 10 20 .30. 40 50 60

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0.2

0.1

Resistance Tests

Influence of Angle between Keel Lines of.Fore- and After-Body

2 3

F

vgp I/3

I

-10 20 30 40 SO 60

Corresp. Ship Speed, Vs , in knots at 17 =35 m3

Fig. 8.

of the much smaller variations in the height of the step between

Series 5, 23 and 26 in Fig. 5 therefore appears permissible.

Finally, in Fig. 8, a comparison is made between the results ob-tained with different bottom angles, e. Angles of about 0 degrees appear to be most satisfactory from a resistance point of view, up to the speeds where they give rise to porpoising, as was the case in Series 26 over about 40 knots and with Series 3 above about 55

knots (See the Tables in Appendix 1).

'd cf 6 (Id dY d d a d d

40"----/

Model No. 468 Model No.468-8{@

0

d a d 0 5-2 5. 1 5-0 5.-1 5. 5.0 8/71/3 8/171/3. 1.60, La/ 2.73, 8/H-6.98 L0/B.2.19,8/H 11.64_ 5 6 V

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20

1-0--

37.3 knots, Fe= 3.387 Model No 468 0 _d Vs 466 knots, Fnr 4231 a.Vs 37.4 knots, F51. j.396 Model No.479 Vi 46.6 knots, 4231 200

Influence of Deadrtse, 17 =35 m3

100 3I rz...

c)

2 2

2 4

Heeling Angle,

n,

in degrees Fig. 9. B/P 7= 1.28 La/B =2.73 B/i1= 9.98 = 0 degrees 6

Some representative results from stability tests are shown in Figs. 9-14. In these diagrams, the values of Kr (in boat scale)

calculated from the results of tests at different speeds are shown plotted to a base of angle of heel, To. A curve of KG sin To has

also been plotted in Figs. 9-14, after assuming a value of 1.5 m

for KG. The vertical distance between the various spots and this

curve, KK' KG sin 99, is then a measure of the stability of the

boat in the heeled position; see also Section 4 and Fig. 3. In order to make these results more generally applicable, a scale expressing the righting arm in dimensionless form has been included in Figs.

9-14.

Fig. 9 illustrates the effect of variation in the deadrise on the

transverse stability. - Within the limits of variation investigated, however, the deadrise does not apparently influence the transverse

stability.

The effect of breadth variation is shown in Fig. 10. On account

of the decrease in stability at high speed, it was not possible to

make tests with the narrowest model at the highest speeds. An

in-crease in the breadth within the limits investigated clearly improved

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Model No. 468-8

400

300

-S 200

100

Influence of Breadth, =35 m3

V, 3Z3 knots, Fo, a 3.387

Model No. 468 0 8/171/3 = 1.28, La /8 2.73, 8/H a 9.98

ce V, a 46.6 knots, Fnp. 4.231

Model No. 468-A (40)

V, -46.8 knots, Fnr a 4.2501.8 .,0 42 1,15 .54.7 knots, F,a4.967 /V a 1 L /8 2 46 8/H -11.65 a . ' 1 { V, a 48.1 knots, 4.368 _B/P0 .1.60, La/8.2.19, 8/H a 11.64 V, = 54.9 knots, F4..4.985 5 4 3 2 2 4 6 10

Heeling Angle,ro, in degrees

Fig. 1:0.

the resistance point of view (Fig. 5) and from the stability aspect, the most satisfactory form is that with the greatest breadth.

As may be seen from Figs. 11 and 12, the variations in the length

of after-body and the height of the step, which were investigated in these tests, evidently have no effect on the transverse stability.

However, Model No. 468, with which Fig. 12 is concerned, was only tested with two different heights of step, namely those corresponding

to BIH= 9.98 and BIH = 17.46 (H= 0.42 m and 0.24 m

respect-ively when V = 35 m3). Stability tests were also carried out with Model No. 479 with heights of step corresponding to BIH = 6.98

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200 100 Model No. 468 200 -E /00 0 0

Transverse, Stability Tests

Influence of Length of After-Body, 0.35 M3

2 4

Heeling Angle,n , in degrees

Fig. 11.

Influence of Height of Step, 17=35m3

(9, y37.3 knots, Fo, 3.387, B/ H .9.98 B/P". 1.28

La/B.2.73 Vs . 37.6 knots, Fnr 3.414, 8/Hl7.46J 0 degrees 0

-_ o .\.

Model No. 468

®

V, 37;3 knots, F0.3.387, L0/82.73 8/r/3.1.28

8/H.9.98

Model No. 468-A 0 of V,. 37.6 knots, Fo.. 3.4/4, La Al. 2.46 _{. 0 degrees}

0 2 4 6

Heeling Angle,ro, in degrees

Fig. 12. 6 5 4 3 YI

22

1 0 6 5 4

22

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Influence of Angle between Keel Lines of Fore- and After- Body,

= 35 m3 300 . a

7

_ _ m) 15 f 46.9 knots,Fnp 4.259

01 I

e. degrees 8/V"s.1.60 Model No. 468-8{ E 0 degrees L0/8 2.19 8/H H.64

°

{ 0 vs .55.0 knots, F.4.994 Vs. 48.I knots, Fne 4.368 Vs= 54.9 knots, Fnr 4.985

2 4 6 8

Heeling Angle, re , in degrees Fig. 13.

are referred to as Series 32 and 29 respectively in Table 1 and

Appendix 2. Even the results obtained with the greatest height of

step in the latter case showed no apparent difference. Thus the

length of after-body corresponding to LalB = 2.73 (La= 11.45 m

for V = 35 m3) and the height of step corresponding to BIH --= 998-(H. 0.42 m at the same displacement), which were found to be the most satisfactory from the resistance point of view (Figs 6 and 7),

would also be considered acceptable on the basis of stability in the

light of the comparisons shown in Figs. 11 and 12.

The effect of variation of bottom angle, E, has only been investig-ated to a limited degree and the results are illustrinvestig-ated in Fig. 13.

Fig. 14 indicates that the spray deflectors shown in Table 1

produced an improvement in the stability. The reason for this

would appear to be that the water spray, which is displaced mainly in a transverse direction at the step, impinges more strongly on the lowered side of the boat than on the raised side. The forces acting

200 E .c 100 9 7 6 5 4 3 2

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24

Influence of Spray Deflectors, V35m3

V. =373 knots F=3.387)

el No. 468

67,-A 1 -,...- 3 f,

'<211. 1 cr V5= 46.6 knots; pne 4.23/I

(..;-6

Vs =45.7 knots, F=4241

.V2Y 1_,___ V, =55 knots, Fa=4.994

o v5=46.7 knots, Fnp=4241

0 {

d vs= 54.9 knots, f-nr4.985 (.;.z IV--- Vs =47.2 knots, Fa= 4.286 ''''''9 t--=-V--- Vs =54.8 knots, F0=4.976 C? Vs. 4Z0 knots, Fnp= 4.268

0

1 85` V5=54.6 knots, Fnp=4.958 1 S vs =46.8 knots, Fnp= 4.250

°

dt, vs= 546 knots, Fnp=4.958 No Spray Deflector Spray Deflector No.1

8//70=

Spray Deflector No.2

La/8 =2.73

8/H =9.98

Spray Deflector No.3

I

e=0 degrees

Spray Deflector No.4 Spray Deflector No.5

' 1.28 _ _ _ _

/a!

'

si,

...

Pi

V

cl o o 15 l''l

pr."-0 2 4 6 a /0 12

Heeling Angle, 500, in degrees Fig. 14.

on the boat due to the spray are thus largely vertical in direction

and are greatest on the lowered side, so that the angle of heel is

decreased and the stability is increased. Alternative 3, which has the most marked spray deflection qualities, appeared to have also the greatest stabilising effect.

Mod .c 400 -300 200 J00 0 13 12 11 10 9 8 7 6 5 3 2 0

(25)

The experiments showed that the highest speeds referred to in Figs. 9-14 were in the region of the maximum from stability considerations.

Speed appeared to have great effect on the etability; see Series 34 and 36 (Fig. 14) and Series 40 (Fig. 10). The stability clearly

deteriorated with increasing speed.

In the stability tests, the rudder was always in such a position

that the rudder force increased the angle of heel. This would imply

that when greater rudder angles are used in steering the boat, a

deterioration in the stability is to be anticipated. It should also be

pointed out that in the case of the longest model without spray

deflectors, it was not generally possible to make the athwartship

force F = 0 at the higher speeds by increasing the rudder angle.

The corresponding boat, therefore, could not be held on a straight

course, but would describe a circular course.

In the cases when the fore-body waterline intersected the chine

forward of the step on the raised side of the model when underway,

good stability was observed as a rule. If, however, the waterline

intersected the step within the chine, the stability was generally

reduced. In the former instance, spray was apparently ejected in the usual way mainly in a transverse direction from the raised side

of the boat. In the latter case, on the other hand, the spray was

thrown aft in a longitudinal direction and impinged on the bottom abaft the step; under these conditions the spray evidently exerts an

upward force on this area of the bottom and this produces an in-crease in the angle of heel and the stability is reduced.

6. Conclusions

The results obtained from the various forms seem to indicate

generally that those forms which are satisfactory from a resistance

point of view also have relatively good stability qualities. Of the values investigated in these experiments, the breadth of 4.66 m,

the length of after-body of 11.45 m, the height of step of 0.40 m

and the bottom angle of zero would appear from both aspects to be the best values of these dimensions for a boat of this type.

Since stability experiments in particular take rather a long time

to carry out, the whole investigation had to be limited, not least

for reasons of cost. Otherwise it might have been possible to extend

the programme to include a model with a further increased bottom

angle. From seaworthiness considerations this could be regarded as

(26)

26

7. Acknowledgement

The authors wish to express their sincere thanks to Dr. H. F.

NoRrsTktom, the Director of the Swedish State

Ship-building Experimental Tank, for the interest he has

shown in these experiments and for his invaluable advice.

Thanks are also due to the staff of the Tank for all their assistance and to Mr. P. D. FRASER-SMITH who translated the paper from the

(27)

(28)

Resistance Tests

Raising is denoted by + and sinking by

-Model porpoising Model rolling

Model No. 468

Change of Model Trim Rnz

t vn, 14, F n r At Stn. 19 At Stn. 0 wm . 17"1 °C misec. kg mm mm

-

knots Series No. 1 (Figs. 5, 8) 1) 1) 1.819 4.72 + 5 - 8.5 0.069 0.908 10.0 3.621 ' 9.48 + 78 -17 0.139 1.808 19.9 1 5.468 9.70 + 84 +23 0.142 2.730 30.13) e., II 6.932 8.200 9.05 8.81 + 92 +100 +45 +60 0.132 0.129. 3.461 4.094 38.1 45.1 L. 9.100 8.70 + 98 +65 0.127 4.544 50.0 9.960 8.99 +101 +70 0.132 4.973 54.82) 16.8 10.88 9.49 +111 +80 0.139 5.432 59.82) Series No. co (Fig. 8) II e 5.422 9.93 + 69 +32 0.145 2.707 29.83) 6.860 10.05 + 63 +5 0.147 3.425 37.7 8.136 10.23 + 72 +65 0.150 4.062 44.7 9.080 10.26 + 74 +70 0.150 4.534 49.9 9.936 10.63 + 75 ₊₇₇ 0.156 4.961 54.6 10.28 10.90 + 77 +80 0.159 5.133 56.5 10.94 10.81 + 78 +85 0.158 5.462 60.2 1 Series No. 3 (Figs. 7', 8) to co ao co o 6 1 11 2 17.0 5.422 9.61 +107 +23 0.141 2.707 29.8 L . 6.894 9.06 +114 +40 0.133 3.442 37.9 8.104 8.76 +118 +50 0.128 4.046 44.6 1 8.970 8.80 +121 +58 0.129 4.479 49.3 9.926 9.62 +122 +72 0.141 4.956 54.62)

(29)

Resistance Tests

-Model porpoising

Model No. 468

Change of Model Trim Rm

.t vm Rm Env At Stn. 19 At Stn. 0 wm 1724 °C m/see. kg mm mm

-

knots Series No. 4 . _{(Fig. 8)} 1) 1) 5.430 9.97 +115.5 +21 0.146 2.711 29.9 6.898 11.28 +118 +24 0.165 3.444 37.9 8.204 10.28 +130 +36 0.150 4.096 45.1 9.050 10.61 +136 +45 0.155 4.519 49.82) In m 17.0 Series No. II (Figs. 4, 5, 6, 7) 5.422 9.27 +105 + 8 0.136 2.707 29.8 6.838 8.91 +106 +28 0.130 3.414 37.6 8.112 8.69 +102 +40 0.127 4.050 44.6 9.022 8.59 +102 +49 0.126 4.505 49.6 9.956 8.72 +102 +56 0.128 4.971 54.7 II d 10.82 9.53 + 98 +60 0.139 5.402 59.5 Series No. 5.422 9.41 + 92 +11 0.138 2.707 29.8 6.922 9.20 + 87 +33 0.135 3.456 38.1 8.134 9.23 + 85 +50 0.135 4.061 44.7 1 9.050 9.40 + 81 +54 0.138 4.519 49.8 9.930 9.70 + 80 +62 0.142 4.958 54.6 , 8 17.2 _10.85 _9.95 _{+ 80} ₊₆₉ _0.146 _5.417 _59.7 1 6 II Series No. I ;5! . 5.412 9.48 +125 + 6 0.139 2.702 29.8 ' 8.092 8.84 +122 +37 0.130 4.040 44.5 8.970 8.76 +125 +45 0.128 4.479 49.32) 10.07 9.67 +124 +50 0.141 5.028 55.42)

(30)

Resistance Tests

Model porpOising Disturbed run

Model No. 468

t v,n 14,

Change of Model Trim Rff,

Pr, pr V At Stn. 19 At Stn. 0 win . 17"1 -°C in/sec. kg mm mm

-

knots Series No. 8 (Fig. 7) 1) 1) 5.410 9.02 +118 -12 0.132 2.701 29.7. 8.122 9.38 + 96 +23 0.137 4.055 44.7 1 _9.158 _9.58 _{+ 90} ₊₃₇ _0.140 _4.573 _50.3 co _11.19 _10.04 _{+ 84} ₊₅₄ _0.147 _5.587 _61.5 II Series No. 9 L. co 16.5 5.420 9.19 +131 -18 0.134 2.706 29.8 II 8.102 9.09 +115 +24 0.133 4.045 44.5 9.082 9.27 +107 +32 0.136 4.535 49.9 co co co 10.87 10.48 + 99 +45 0.153 5.427 59.8 cD o cir Series No. 10 II ' 5.438 9.61 +133 -19 0.141 2.715 29.9 L. _8.204 _9.12 ₊₁₂₉ ₊₂₂ _0.133 _4.096 _45.1 9.004 9.32 +122 +27 0.136 4.496 49.53) 10.91 11.30 +120 +43 0.165 5.447 60.02)

(31)

Resistance Tests

--Model porpoising 2) Model rolling

Model No. 468-A

t vm Rm

Change of Model Trim

R772, Fnr V At Stn. 19 At Stn. 1 WM . VM °C misee. kg mm 1 mm

-

knots Series No. 11 (Fig. 6) 1 1) 1) .,, co II 5.428 8.120 9.67 8.82 +108 +126 + 6 +37 0.141 0.129 2.710 4.054 29.83) 44.6 D, 8.966 -:-;10.9 ' 8.73 --Z1-10.4 +127 --:.;-_ +130 +44 +55 ::-.... 0.128 :'..-_ 0.15 4.477 ::::-5.4 49.3 602) GO II Series No. 12 16.5 5.414 9.77 +128 0 0.143 2.703 29.8 1 _8.176 _10.30 ₊₁₄₄ ₊₂₀ _0.151 _4.082 _45.0 co co 9.050 10.35 +144 +25 0.151 4.519 49.82) Series No. 13 .6 II 5 5.386 9.89 + 88 + 8.5 0.145 2.689 29.63) D. 8.080 9.42 +101 +40 0.138 4.034 44.4 9.036 9.29 +103 +50 0.136 4.512 49.7 10.85 9.53 +102 +57 0.139 5.417 59.72)

(32)

3

Resistance Tests

--Model porpoising Model rolling

Model No. 479

Change of Model Trim Bm

g Vm Rm F n v At Stn. 19 At Stn. 0 WM . 17M °C m/sec. kg mm 111/11

-

_knots Series No. 14 (Fig. 4) 1) 1) 5.422 9.26 + 96 +10 0.135 2.707 29.8 8.178 8.94 + 95 +45 0.131 4.083 45.0 9.160 8.94 + 96 +53 0.131 4.574 50.42) La co 10.94 9.63 + 97 +59 0.141 5.462 60.1 II _{Series No. 15} L. 15.4 5.480 9.28 +112

+ 9'

0.136 2.736 30.1 8.228 8.85 +119 +43 . 0.129 4.108 45.2 ao 9.250 9.12 +118 +45 0.133 4.619 50.92) Series No. 16 II tS 5.486 9.44 + 80 +16 0.138 2.739 30.2 8.214 10.33 + 71 +50 0.151 4.101 45.2 9.306 10.68 + 70 ₊₆₂ 0.156 4.646 51.2 10.94 11.73 + 68 ₊₇₀ 0.172 5.462 60.1 OD CO OD Series No. 17 OD 0 d II 15.2 5.450 9.54 + 92 +27 0.140 2.721 30.03) L. _9.1948.204 _9.038.87 +111₊₁₁₆ +53 0.130 4.096 45.1 +57 0.132 4.591 50.52) 10.00 9.90 +117 +60 0.145 4.993 55.02) z-,:10.9 2.--._11.2 ₊₁₁₅ :Z.:H- 70 :::,-; 0.16 -7,`_-5.4 z..--:602)

(33)

Resistance Tests

-Model porpoising Model rolling Disturbed run

Model No. 479

Change of Model Trim Rn,

t vm An FnV V At Stn. 19 At Stn. 0 wm- PM °C m sec. kg mm mm

-

knots ' Series No. 18 1) 1) 5.476 9.69 + 73 +30 0.142 2.734 30.13) 8.170 9.24 + 88 +58 0.135 4.079 44.9 9.074 9.18 + 90 +64 0.134 4.531 49.9 10.77 9.96 + 96 +72 0.146 5.377 59.22) I 15.2 co Series No. 19 II L. 5.474 9.59 +109 +25 0.140 2.733 30.13) 8.186 9.23 +128 +47 0.135 4.087 45.0 9.200 10.04 +135 +50 0.147 4.594 50.62) 9.910 11.01 +135 +61 0.161 4.948 54.52) oo ii Series No. 20 25 5.476 9.14 +123 -13 0.134 2.734 30.1 8.120 9.21 +107 +25 0.135 4.054 44.6 9.114 9.42 +103 +34 0.138 4.551 50.1 1 . 10.87 11.20 +107 +46 0.164 5.427 59.84) Series No. 21 CO oo co c: 0 15.1 _5.464 _9.38 ₊₁₃₅ _-13 _0.137 2.728 30.0 II 8.158 9.28 +121 +23 0.136 4.073 44.9 E _9.130 _10.19 ₊₁₁₇ _0.149 4.559 50.22) L. .+35 Series No. 22 5.428 9.06 +111

- 7

0.133 2.710 29.8 8.170 9.70 + 92 +32 0.142 4.079 44.9 9.218 10.34 + 85 +43 0.151 4.603 50.7 10.90 11.54 + 75 +55 0.169 5.442 59.9

(34)

Resistance Tests

-Model porpoising

Model No. 468-A

Change of Model Trim Bin

t vn, F n p V At Stn. 19 At Stn. 1 win . 17"1 °C m/see. kg mm mm

-

knots Series No. 23 (Fig. 5) .h 2) 1) 5.196 6.28 + 92 +14.5 0.126 2.735 30.1 Vi _7.790 _6.07 + 83 _+39.5 0.122 4.100 45.1 II 8.680 6.17 + 81 +40 0.124 4.568 50.3 L. _9.420 _6.26 _{+ 80} ₊₄₆ _0.126 _4.958 _54.6 ci? 10.27 6.6 7:-...-0.13 5.405 59.52)

CID _{Series No. 24}

II tS 13.5 5.145 6.47 + 78 +16.5 0.130 2.708 29.8 7.756 6.85 + 60 +44 0.137 4.082 44.9 1 rz co = ,14 o 8.664 10.32 7.29 8.08 + 59 + 57 +50.5 +52 0.146 0.162 4.560 5.431 50.2 59.8 c; Series No. 25 II 'A L. 5.110 6.43 +108 +19 0.129 2.689 29.6 7.724 6.08 +100 +31 0.122 4.065 44.8 8.582 6.58 +100 +34 0.132 4.517 49.72)

(35)

Resistance Tests

1) Raising is denoted by + and sinking by Model No. 468-B Change of Model Trim Em

t .V Em Fn r

At Stn. 19 At Stn. 2 wm .17m

°C rn/sec. kg mm mm knots

e:, Series No. 26

nz _{(Figs. 5, 8)} II IL. 1) 1)

6

4.890 4.19 --I-- 91 +20 0.120 2.730 _'30.1 ii 6.916 4.11 ± 85 +28.5 0.117 3.861 42.5

Series No. 27

. 6 .;^ 13.3 E o o to en (Figs. 5, 8) 0 6 4.882 4.44 ± 67 d-23 0.127 2.725 30.0 II 6.904 4.68 ± 57 +34 0.134 3.854 42.4 S 8.080 4.85 ± 52 . +40 0.139 4.511 49.7 L. _9.010 _5.66 _{+ 55} ₊₄₄ _0.162 _5.030 _55.4

(36)

(37)

1) Model porpoising

Model Range Boat Range

t 1 Km Gm1G'm _Soo

1 6o K K' V F, 17

°C 1 1 degrees degrees mm knots

-Series No 28, Model No. 468 (Figs. 9, 10, 11, 12, 14) 3.7 2.5 2.5 92 37.3 3.387 181.4 7.3 4.6- 4.5 174 37.2 3.378 3.7 2.1 1.5 83 46.6 4.231 1 15.1 lo co II

Series No. 29, Model No. 479 (Fig. 9)

3.7 2.5 2.5 02 37.2 3.378

180.6 7.3 4.4 4.5 169 37.5 3.405

3.7 2.0 1.5 80 46.6 4.231

co

Series No. 30, Model No. 468-A

II 7.3 6.7 1.5 219 37.3 3.387

15.0 172.3

7.3 7.2 1 232 46.7 4.241

Series No. 31, Model No. 468-A (Fig. 11

178.8 7.3 4.9 0.5 182 37.6 3.414 Series No. 32, Model No. 479

..5 co co 7.3 4.9 16 193 37.5 3.405 00 CD 14.6 7.6 17.5 323 37.7 3.423 c'

°

15.1 195.7 3.7 1.8 2 77 46.6 4.231 II e 7.3 7.1 20 251 46.41) 4.213

L. Series No. 33, Model No. 468 (Fig. 12)

(38)

1) Model porpoising

Transverse Stability Tests Model No. 468

I

t

KG

GM Gra To 6o K IC V Fnr

°C mm mm degriies degrees mm idiots

-Series No. 34 . (Fig. 14) 14.8 _7.3 4.4 " 2 170 46.6 4.231 14.6 10.8 16 388 46.7 4.241 1 7.3 9.1 2 289 54.9 4.985 uc. cn 14.6 12.3 14.5 424 z-.-_551) 5.0 II _{Series No. 35} L. (Fig. 4) 14.9 182.2 1.5 144 46.7 4.241 7.3 9.9 2 309 54.9 4.985 Series No. 36 (Fig. 14) 7.3 3.6 1.5 150 47.1 4.277 II 14.6 8.5 3.5 331 47.2 4.286 i3 _7.3 _5.7 ₁ ₂₀₂ _54.6 _4.958 14.6 8.8 0.5 339 54.9 4.985 Series No. 37 (Fig. 14) 13.8 _181.1 7.3 7.3 3.4 7.3 1.5 0.5 143 243 47.0 54.6 4.268 4.958 1 tn co ez © Series No. 38 172.3 7.3 4.7 I 1.5 171 46.7 4.241 II Series No. 39 L. (Fig. 14) 7.3 3.0 1 134 46.8 4.250 181.1 7.3 4.4 1.5 170 49.7 4.512 7.3 9.7 2 -303 54.6 4.958

(39)

Transverse Stability Tests Model No. 468-A

t Km Gml Gm, Grini _(Po _do K K' V Fn r

oc _mm _mm

degrees degrees mm knots

- Series No. 40 (Fig. 10) 6.6 5.1 4 215 46.8 4.250 1 197.8 _6.6 8.7 2.5 323 54.6 4.958 II 3.3 1.9 1.5 86 46.7 4.241 187.8 3.3 6.2 2 209 54.8 4.976 en oi 13.5 Series No. 41 200.6 13.1 8.2 4.5 370 47.0 4.268 II 13.1 8.8 2.5 389 54.4 4.940 Series No. 42 197.5 13.1 7.4 5 342 47.1 4.277 1 ot oo 13.1 8.0 1 359 54.7 4.967 = ..14 o Series No. 43 6 II _3.3 _1.6 _1.5 ₇₅ _46.7 _4.241 a 13.7 C:. 6.6 3.4 2.5 156 46.6 4.231 187.7 13.1 6.6 4 309 46.6 4.231 3.3 5.8 2 198 54.7 4.967 6.6 6.5 2 248 54.8 4.976 198.7 13.1 9.2 13.5 2.5 398 54.7 4.967

(40)

Transverse Stability Tests Model No. 468-B

t Kni,Gm Grz Gm To ao K le V Fn r

°C mm mm degrees degrees mm knots

-Series No. 44 un en (Fig. 10, 13) 156.7 11.7 5.8 2.5 275 48.1 4.368 II 11.7 6.4 1 992 54.9 4.985 1. Series No. 45 o (Fig. 13)

'

13.3 II 11.7 4.3 2 226 46.9 4.259 d _145.0 _5.9 6.2 2.5 214 55.0 4.994 11.7 7.1 2.5 295 54.9 4.985 1 _{Series No. 46} © © kn en 0 d 11.75.9 5.3 5.2 2.5 1.5 261 200 46.5 54.9 4.222 4.985 II 11.7 6.4 1 289 - 54.8 4.976 F. 1. 156.0 2.9 3.7 2.5 130 46.7 4.241 13.7 5.9 4.4 2.5 178 46.4 4.213 2.9 4.0 1.5 137 55.1 5.003

(41)

Appendix 1

Page Introduction . . .

. ... . ..

. . 3

Symbols and Units 3

Models Tested ₅ Experimental Arrangements Test Results 12 Conclusions ₂₅ Acknowledgement ₂₆ 27 Appendix 2

...

37'