Lighters and seagoing barges and the design of yaw controlling units

2nd International Tug Conference

organised by Ship & Boat International

3/f1/

Day 1

Paper No 3

LIGHTERS AND SEAGOING BARGES AND THE DESIGN OF YAW CONTROLLING UNITS

Captain Dipl.-Ing. JOCHIM E. BRIX : Chief of the Shipmanoeuvring and Ship Trials Division, Hamburg Shipmodel Basin (HSVA)

SYNOPSIS: This paper presents some new aspects of the hydrodynamic properties of skegs or

fins and the optimum arrangement of these devices at the barge stern. The well-known method

of skeg-stabilised course-keeping of the towed barge is supplemented by a simple model

testing procedure and a method of evaluating the results obtained. Thus information is provided

about the stabilising qualities by means of a "'damping factor- D and a circular frequency v of

the damped or undamped yawing motion.

After discussing some of the existing literature on this matter, the results of model tests on

several new barges are presented, conducted with various types of skegs, bow rudder and

centreline skegs with activated rudders. Finally the hydrodynamic forces on both the hull and

the appendages are given. Free-flow characteristics are investigated for several types of skegs.

It is shown that the drag/lift ratio of the skeg can be considered as a characteristic

hydrodynamic value for skeg positioning. From these tests it appears that an approximately

optimum skeg is possible if the direction of flow in way of skegs is known.

I. GENERAL REMARKS ABOUT COURSE INSTABILITY OF TOWED VESSELS

WHEN towing a vessel- -known for course stable behaviour in

the

self-propelled conditionwithout rudder

action, heavy

yawing motions will appear, endangering the whole tow unit and shipping in the vicinity as well. These yawing motions will also rapidly reduce the towing speed or make the whole towing procedure completely impossible. This well-known phenomenon

appeared once more after the Second World War, when a number of freighters, put out of commission, had to be towed to the scrap yard.

The inclination for self-excited yawing motions of increasing

amplitudes in a towed vessel becomes worse with :

increasing LID ratio; increasing draught T;

\cry short or very long hawser; shifting the hawser's attachment aft:

trim by the head.

1.1 Influence of draught and L/B ratio

Dawson (Ref. I) reports the disadvantage of high length/beam ratios L/B on the coursekeeping ability of a towed vessel. This information is supported by very interesting results of towing trials with a pontoon of Lift 2.0 which was to be considered course stable. From this it appears that free-running vessels

be-have contrarily to towed vessels with regard to the influence of the

L/B ratio on the course stability. Self-propelled vessels of high LIB ratios are known for good coursekeeping qualities whereas those of small L/B ratios are subject to course instability and heavy yawing motions.

At the same time Dawson (Ref. I) refers to the influence of

increase of draught, whichlike trim by the headhas also

proved to be a disadvantage for the coursekeeping qualities of a

free-running vessel.

1.2 The influence of the length and arrangement of the hawser A necessary and adequate criterion of course stability is derived

from theoretical investigationsthough based on

linearised

equations of motion for a towed bodyby Strandhagen,

Schoenherr and Kobayashi (Ref. 2) and by use of the so-called Routh's discriminant (known since 1877). This criterion is

expressed in five inequality conditions (e.g. see (Ref. 2) page 38,

equations 5, 6).

lithe hydrodynamic derivates are known, the course steadiness

of a towed vessel can be investigated by means of this criterion. Compared with this, the method of judging coursekeeping qualities, described in paragraph 4, gives comparative results of

the course stabilising qualities in an easier way.

The theoretical investigations, quoted above, lead to the conclusion, however, that course instability is to be expected when moderate or long lengths of hawser are used. On the other hand it is known from American and Canadian barge shipping that some of the barges towed at short hawsers are prone to instability but become course stable when towed on long tow-ropes. The same behaviour has been proved by results of model

tests, carried out in the HSVA, and by observations made by

Ben ford (Ref. 7).

Peters (Ref. 3) refers to the importance of the point of attack of

the hawser on the towed ship, which must be located ahead of the

centre of effort of the hydrodynamic cross force in order to attain a course-correcting steering moment from the transverse com-ponent of the towrope pull. Since the hydrodynamic cross force attacks near the bow when the drift angles are small and moves

aftquickly first and more slowly laterwith increased drift

angles (see Fig. 27) the point of attack of the towrope is to be

positioned as far forward as practically possible.

In many cases instead of a single-point attachment the hawser

is connected to the barge by means of a horizontal bridle of about 1.5B (B beam of the barge) leg length, which improves the

course steadiness. This recommendation is given by Dawson (Ref.

1) and Baler (Ref. 4). A disadvantage of this practice appears when one bridle leg breakes. In such a case the towed vessel will follow the tug as if being towed on an eccentric rope attachment under a drift angle of about 8 deg. and with a considerable trans-verse shift. The towing connection will be extremely stressed by external forces in this state and the safety of the tow is not guaranteed.

A short hawser of 600-ft. (I83-m.) length, a normal one of 1.200-ft. (365-m.) length and a long sea-hawser of 1,800 1.200-ft. (549 in.) are used on U.S. seagoing barge shipping.

1.3. Influence of trim

Taggart (Ref. 5) and other authors describe the tendency to course instability of a towed vessel trimmed by the head. Trim by the stern is reported to have a stabilising effect. This is easy to understand in view of the fact that the centre of effort of the resulting hydrodynamic cross force moves aft with an increased trim by the stern. Its influence on course stability together with

the hawser's point of attack is mentioned in paragraph 1.2.

A3-1

2. FORMS OF BOW AND STERN OF INLAND AND

SEAGOING BARGES

Out of a number of former publications the following refers top the paper of Dawson (Ref. I) quoted before, to the compre-hensive analysis by Taggart (Ref. of a "fleet" of 10 different barges (at the disposal of the U.S. Army after the Second World War) and to the paper of Benford (Ref. 7). The opinions of these authors differ in certain points so that the new tests and service

results may be a useful contribution. 2.1. Stern shape

Since firm design principles have gradually developed with regard to the bow, greater attention should he paid, according to Sanford (Ref. 7), to the design of the stern if skeg stabilising is

intended. Conventional ship sterns are not suitable for the fitting of

course stabilising skegs (see paragraph 3). Square-shaped aft

bodies have a natural course stability due to the high resistance at

the stern involved. The total resistance of a typical barge stern is, however, considerably lower when equipped with skegs of optimum efficiency.

This point of view has been taken into account for the majority of all existing barges, except for those employed in integrated pushed units or as pontoon-like lighters for special purposes. Thus, once more, Dawson (Ref. I) recommends the conception of a barge with raked stern of low hull resistance and a set of skegs

causing an increase of resistance, which usually amounts to 20 to 30 per cent of the barge resistance.

(a) The rake of the stern of seagoing barges is 14 deg. for

high-speed units (9 to 12 knots) and 22.5 deg. for medium-high-speed units according to Dawson (Ref. 1). The results given in that paper

indicate that a smaller stern rake favourably affects the resistance in spite of the deeper immersion of the transom.

Taggart (Ref. 6) recommends optimum stern rakes of 30 deg. after having evaluated the results obtained with 10 barges of different shapes of section and of different form parameters.

Benford (Ref. 7) judges the stern rake under the aspect of the skeg efficiency. According to him too high a rake would have an unfavourable influence by disturbing the local flow around the

skegs due to separation.

Fig. 1 Skeg forces on straight progress of barge

1 1 4

06

ITO

v

Dawson recommends that the bilge radius be small in the midship range and as large as possible within the range of the

stem rake in order to keep the resistance low.

The same author recommends drawing the transition from the even bottom to the stern rake not in a sharp knuckle but in a large bottom radius. Taggart (Ref. 6) supports this opinion, probably because of the suggested high rake of 30 deg. Contrary to the opinion communicated in (a) . . . (c) Taggart (Ref. 5)

refers in his discussion to (Ref. I) to the primary importance of the character of the sectional area curve concluding that the influence of the stern rake, the enlarged bilge radius and the bottom radius will disappear if this curve is kept constant.

According to the unanimous opinion of all above-quoted references the waterlines of the aft body should have square characteristicsexcept for the bilge radiusin order to enable a suitable skeg arrangement. This question will be discussed in

paragraph 3.

t 2.2. Bow forms

The conventional fore body design (partly with a bulb) is some-times chosen for reasons of seakeeping quality (with respect to "slamming"). The usual barge, however, is built in chine con-struction with single or double chine for manufacturing reasons (and with good results in resistance), their hull plating being curved in only one direction (see Williamson: discussion to (Ref. I), with lines plan added, Baier (Ref. 4). Taggart (Ref. 6) with

lines plan of a seagoing barge or extremely low resistance). U.S. barges of higher speed generally show spherical fore body

plating. From there the so-called spoon-bow was developed with two-directional plating curvature, which is generally con-sidered to be the optimum bow form. \According to tests, recently

carried out in the HSVA, this bow form improves also the

propulsive efficiency of self-propelled crafts of low L/13 ratios. Benford (Ref. 7) calls attention to the proper influence of this bow form with regard to yaw sensitivity as the spoon-bow does not enable the setting-up of yaw promoting suction fields at small course deflection (see Fig. 27 of an oblique-towing test). This is also valid for the self-propelled barge, as shown during the manoeuvring tests with the vessel mentioned above.

Fig. 2 Skeg forces at w =15 deg. course deflection of barge

1,4

N IC

6)

Lstb

3. DESIGN OF ANTI-YAW DEVICE

From the "Principles of Naval Architecture" and from the above discussed references the unanimous opinion emerges that an increase of resistance aft improves the course stability in the

towed condition. This view is confirmed by the course stabilising influence of chains, ropes and anchors dragged over the stern of

the towed vessel as described by Benford (Ref. 7).

The stabilising quality of sets of skegs is generally interpreted under the same aspect of resistance increment. Benford (Ref. 7),

however, demonstrates with two types of skegs the hydrodynamic forces acting on a twin set of skegs on a straight course and under

oblique flow which produce a course-correcting steering moment. He refers to the importance of a high cross force to resistance

ratio as characteristic value for an optimum skeg.

The model tests described in the latter paragraphs of this paper

support Benford's opinion and will show that the hydrodynamic cross forces of skegs are of main interest for course stabilisation, although the resistance component contributes to the course stabilising steering moment.

The flow direction in way of skegs normally is 7 to II deg. inward under the raked sterns. This direction of flow can be determined in a model test by means of a metal flag connected to a nearly frictionless pivoted vertical axis. Numerous tests have shown that the influence of speed on the direction of flow is very small. Fig. 1 shows the hydrofoil forces on a pair of skegs posi-tioned parallel to the centre line of a barge running on straight course. The skegs are attacked by the local flow at an angle a (deg.). The lift forces L (kp) are of equal amount and opposite direction, whereas the drag components D (kp) are parallel. The hydrodynamic cross forces C (kp) and the resistance com-ponents W (kp) in longitudinal direction are obtained via the resulting forces R (kp).

The cross forces are balanced when the barge is moving straight ahead and the skeg resistance, mentioned in paragraph 2.1., appears which is composed of the components W (kp) and the frictional resistance. Fig. 2 demonstrates the corresponding

forces appearing when the barge is proceeding under a drift angle corresponding to ty = 15 deg. course deflection to starboard.

The cross forces Cpar, and Cstb. (kp) of the skegs and the re-sistance components Wpor, and W. produce a course-correcting moment. An effective stabilising skeg must react in the manner described already at a slight drift angle. Consequently a high-lift gradient dC Lid a may be claimed to be a property of an optimum skeg, which should be fitted in a zone of undisturbed flow and

minimum wake as far aft and outboard as possible. 3.1. Stabilising skegs and their arrangement

Plane fixed skegs

The lateral area of this type of skegs extends, in general, over

the whole lateral area under the raked stern and has, therefore, in most cases triangular shape. In many cases the fore triangle tip is

cut away so that a trapezoidal shape appears. Dawson (Ref. I) measured the increases of resistance due to this type on an oil barge and reported these to be 31.3 per cent (8 knots) and 24.4 per cent (12 knots) for an angle of 7i deg. between skegs and barge centre line. The author considers skegs of a parallel arrangement to be ineffective. This opinion is contradicted by satisfactory results obtained with skegs of this type in parallel

position (see paragraph 5.3., skegs A, B, C and Figs. 41, 42). Fixed knuckle skegs

This type, developed by Baler, also called "Dravo-skeg" "Michigan-skeg", or "GTC-skeg", has also trapezoidal shape. The aft third of the total length forms an outward angle of 20 to

25 deg. with the forward leading part. The leading part is generally

fitted parallel to the local direction of the flow (Benford (Ref. 7),

Dawson (Ref. 1)). Dawson reports the increase of resistance to be

25.5 per cent for the oil barge mentioned under (a), fitted with these skegs. An exact answer to the question of the stabilising ability of this type of skeg could not be found in the pertinent literature owing to the fact that the behaviour of the vessels was

only visually observed.

Curved fixed skegs

In his summary Dawson (Ref. I) comes to the conclusion thatconsidering the skeg types described under (a) and (b) and their respective resistance behavioura skeg of curved profile might produce satisfactory stabilising qualities at lowest skeg resistance. Benford (Ref. 7) on the contrary rejects curved

skegs.

Plane fixed skegs with adjustable rudder (flap)

This combination allows adjustments in the necessary stabili-sing efficiency with respect to loading condition and/or pushing/

towing service.

Fixed skegs of the types (a) and (c) are suitable basic forms for the leading part. Benford (Ref. 7) refers in detail to this kind of stabilisation, which is frequently used in the U.S. barge traffic.

Single fixed skeg

This skeg, fitted in the centre-line plane, was found to be inefficient (Dawson (Ref. 1), Taggart (Ref. 6) and Benford (Ref. 7)). Considering the hydrodynamic forces on a set of twin

skegs, shown in Figs. and 2, the inefficiency of a single skeg is

easy to understand.

Retractable single skeg

According to Dawson (Ref. I and Benford (Ref. 7) a stabilising

effect can be observed when the fin is drawn out under the base line in the undisturbed flow. This skeg is, therefore, not suitable for shallow water shipping.

Centre rudder

Centre rudders, activated either by hand or by the hawser, are

ineffective. All authors agree on this (see also paragraph 6.5.).

Bow rudder

According to Benford (Ref. 7) the remarks given under (g) are also valid for a bow rudder operated in similar manner.

Further types of skegs

Many other skeg variations are known from the pertinent literature but in principle they can be classified under one of the types described above. Skegs of types (a) and (b) are often seen with so-called fish-tails at the trailing edges. Skeg forms of

com-plicated designfor instance with vertical slotsor groups of

fins have been built in several cases (e.g. the so-called "herring-bone skeg"). All these special constructions are prone to the danger of deformation in case of grounding, loading and dis-charging.

Arrangement of skegs

Searching for the optimum position of a set of skegs, systematic

model tests should be done in order to compare the resistance qualities with the stabilising qualities. From Benford (Ref. 7) we learn with regard to model-ship correlation that the yawing behaviour is reproduced exactly in model tests. However there are

uncertainties about the resistance due to separation and eddy-formation of the appendages at the low Reynolds numbers in the model test. If, however, comparative tests are carried out with

different skegs and skeg arrangements, the respective increments of resistancerelative to the hare hullcan render valuable aid in the search for the optimum skeg and its optimum position. If required to reduce the testwork to a minimum, at least the flow direction y (deg.) in way of the skeg position should be deter-mined, as in paragraph 7.5. of this paper the approximate opti-mum angle of attack eta (deg.) against the local direction of flow

will be given for various types of skegs usually employed.

High rake should be omitted, as discussed above, for reasons of

resistance and its disadvantageous influence on the stabilising

efficiency of the skegs.

The deck-line should be rectangular in order to enable a skeg

position as far outboard as possible.

A3-3

(e)

20

20

Direction of progress

Fig. 3

Damped yawing motion, D < 1

Direction of progress

Fig. 4

Immediately damped yawing motion, D < 1

20

10

"Course

10

D-<0

20

Direction of progress

Fig. 5 Negative damping, D <0

Course

D<1

4. METHOD OF EVALUATING MODEL TEST RESULTS, THE DAMPING FACTOR D

Figs. 3, 4 and 5 show strip-chart records of the coursekeeping behaviour of a towed barge as a function of the time t (sec.). Fig. 3 indicates that here only a small damping effect is present to reduce the yawing motions induced by a course alteration or a

similar cause. Fig. 4, on the other hand, shows the high stabilising

effect exerted by another skeg position of different type. Fig. 5

shows negative damping. i.e. increasing yawing motions.

For the ease of judging the stabilising efficiency of a tested type

of skeg the theory of the free damped oscillation is used: With the damping factor D and the amplitudes qi1 and wit of one yawing cycle the logarithmic decrement is defined:

I

1,\1

sin -, arctan

)

or D _..2

₄₂

The natural logarithm of the quotient of two yawing oscilla-tions can be calculated from the record of the course angle w(t) obtained from a self-recording gyro compass installed in the towed model.

The damping factor D () according to equations (2) or (3) yields:

0 undamped oscillation (see Fig. 25);

0 < D

I damped oscillation (see Fig. 3);

1 oscillation with optimum damping (see Fig. 4);

< 0 increasing oscillation (increase of yawing

amplitudes) (see Fig. 5). The circular frequency v (1/sec.) of a damped yawing oscilla-tion is:

y 21t

T w D2 (4)

where

v ti /sec.) circular frequency of the damped oscillation, w ( /sec.) circular frequency of the undamped oscillation,

T (sec.) period for one complete yawing cycle.

Hence it follows that an optimum stabilising skeg has the following properties:

I. D 2. v

-0

(5)

If a damping factor D 1 is attained a yawing motion will be

damped immediately, Ie., the towed barge will return to straight

course without any further oscillation. When the

circular frequency fends to small values a smooth extinction will take place.

The period T (sec.) of a yawing motion is about T 100 to 200 sec. for hopper barges, T - 300 to 400 sec. for seagoing barges of

medium slit: and T 600 to 7(X) sec. and more for large units.

A towed

vessel has an individual characteristic circular

frequency v ( l/sec.) of the yawing motion, keeping hawser length,

speed and displacement constant. It is only slightly influenced by

modifications of the skeg system.

A remarkable increase of the circular frequency y, however,

was observed in numerous model tests with: the decrease of displacement; ( b) the increase of towing speed;

the decrease of the hawser length.

5. THE SEAGOING "NEPTUN" CARRIER "HERA"

The publication of the results of comprehensive model tests is done with the kind authorisation of Messrs. Howaldtswerke-Deutsche Werft AG., Werk Kiel, steel construction department.

Furthermore I was obliged to Messrs. Bergnings och Dykeri-AB. Neptun, Stockholm, for the photographs reproduced in Figs. 6

and 7.

r.7

111;111rh0111H111111.11iffil

-NE

Fig. 6 The seagoing barge "Hera

MCPYUN CARRIER

Mo.".

Fig. 7 The seagoing barge "Hera"

The self-unloading method (dumping procedure) of this barge

was described in the HA NSA special issue for the S.T.G. meeting

in 1969, of which a corrected reprint is available from the HSVA.

5.1. General data

Mission description: seagoing timber barge with self-unloading equipment of the "dumping" type,

also deployable as salvage barge or oil

lighter.

Length o.a. LOA 107.65 m. (354 ft.)

Length b.p. Lpp 105.00 m. (344.5 ft.)

Beam moulded 24.00 m. (78.7 ft.)

Depth, loading deck, 7.00 m. (23.0 ft.)

Designed draught 5.35 m. (17.6 ft.)

Displacement hereby 11,473 cu. m.

Useful deck load-length 93.80 m. (308 ft.)

Safe deck load max. 6 Mp/sq. m.

Volume of the "tipping" tanks 2 each 1,340 cu. m.

Symbol of classification TOO A4 E2

"Lighter"

Deadweight carrying capacity about 9,000 tons

Deck cranes 3 electric-hydraulic Hagglunds

cranes, load 12 Mp.

Length of hawser 200 m. (656 ft.) with a vertical

bridle of 16m. (52.5 ft.) length

Crew none

5.2. Bow and stern forms, stabilising skegs Bow shape: Spoon-bow, (see par. 2.2.). Stern shape: Barge stern with large varying bilge

radius (see par. 2.1. (b). Stern rake: 18 deg. (see par. 2.1. (a).

Bottom radius: large (see par. 2.1. (c).

Aft body water lines: square characteristic (see par. 2.1. (d). Fig. 8 shows the body plan with two stern

variations, of which form 2 finally has been built for Hera, form 1 for the latter

Juno.

A3-5

2 . D In 41i )4/ 4 In =. D2 1 2

-I-=

=

=

. is J-I '

Stabilising skegs : fixed knuckle skegs (sec par. 3.1. (b).

Shape and position are outlined in Fig. II

(skeg K from the model tests described in paragraph 5.3.), (skeg B having been applied for Juno).

5.3. MODEL TESTS FOR THE SEAGOING BARGE

"HERA"

The model tests included resistance tests

with two stern

variations and eight different types of stabilising skegsone of' which at three different positions. They were carried out according

to Froude's law at the designed draught of T 5.35 in. (17.6 ft.) on deep water. While the resistance tests carried out by Fritsch (Ref. 8) covered the speed range of 9 to II knots, the stabilising tests were made at a corresponding speed of 10 knots with the towing gear arranged as described in paragraph 5.1. A self-recording gyro compass installed in the model delivered con-tinuous records of the yawing motion of the barge after an initial

deflection off course. These records have been evaluated using the method described in paragraph 4.

When scaling the results to ship size the 1TTC-57 correlation line was used with an allowance of 0.00025 for the fully-welded hull. The flow direction at half skeg length was found to be con-sistently 7 to 7.5 deg. directed inward within the speed range of 6

to 10 knots.

Fig. 8 Body plan "Hera"

C4'.4

Stern I

0

i.1'680 a, en_..._.1680 enrn

to,v,1/2,

4

Stern 1

Both of the stern variations shown in Fig. 8 in the aft body plan. They differ in the size of bilge radii within the stern rake

Fig.

and in the bottom radiuswhich has been omitted in variation 1. The skegs A. B, and C are shown in Fig. 9. They are triangular fixed (see par. 3.1. (a) ) of different profiles which are arranged parallel to the centre line and to the inner edge of the bilge

tan-gent line. Each skeg has a lateral area of As 32.9 sq. m. 5.86

per cent of Lpp. T. The results were obtained with the stern form

I.

Ven,

ZOO am, 2630 ..nni

I to,g0,7,

Stern 2

5 skeg G sheg H s keg I

These skegs were tested in combination with the stern form 2. The fixed knuckle skeg K (see par. 3.1. (b)) was also tested with the stern form 2. The angle between its leading part and the centre line is 12 deg. The skeg area amounts to As = 28.0 sq. m.

-= 5.0 per cent of Lop . _{T. Shape and position of this skeg are}

shown in Fig. 12. Outboard s

Sire (position as ske e

Fig. 10

''Vell` ask, _{Stern 1}

mac rnm 1 268o men

sheg D skeg E

skeg F

Skegs D, E and F are also triangular fixed skegs. Two of them, however, E and F, have a tapered, knuckled trailing edge. They are fitted at an angle of 5 deg. relative to the centre line, thus being attacked by the flow at an angle of 2.0 to 2.5 deg. from outward. In particular, they have the following lateral areas:

Skeg D: 25.0 sq. m. 4.45 per cent of Lop . T Skeg E: 34.4 sq., nv. 6.12 per cent of Lop T Skeg F: 33.4 sq. in. = 5.94 per cent of Lpp

. T

These skegs and their positions are represented in Fig. 10. Skeg G is a trapezoidal, curved fixed skeg (see par. 3.1. (c)) with a lateral area of As 30.5 sq. m. 5.45 per cent of Lpp . T. The skegs H and I differ from skeg G only in the position as

shown in Fig. II.

Fig. 11 Sh.PCa slog C skeg A skeg 8

=

=

a

. 2

CWL

Fig., 2

SO

---70

0

ro,,ent_ple 5terr7 2

Sireq K .:4$0 0680 men tonge,t ;brae S keg A C Pe/th

Fig. 13 Resistance diagram "Hera"

The results of Fritsch's resistance tests are plotted in Fig. II They clearly demonstrate the increment of resistance due to the

different types and positions of the skegs. The model used for the tests was 5 m. (16.4 ft.) in length and, therefore, the results especially those of the bare hullarc to be considered reliable. It is surprising that identical values are obtained with the two different stern forms since the influence of the bottom radius and of the complex varying bilge radii seems to be smaller than the

accuracy of the measuring technique. This agrees with the opinion

of Taggart given in paragraph 2.1. (a). The results of the course stabilising tests are given in table 1 which also shows the respec-tive values of the relarespec-tive resistance increment AR (per cent) due

to the individual types of skegs at a speed of 10 knots.

In paragraph 3.1. Benford's opinion about model-ship correla-tion of barge model tests has been stated. Due to the higher loss of momentum in the model wake at low Reynolds numbers the skeg resistances represented by the values :-.R are to be

con-sidered lower for the full-scale vessel.

Simple fixed skegs of the types A-C, arranged in parallel position, guarantee an optimum stabilising effect at a relatively small increase of resistance, as can be seen by comparing the stabilising characteristics given in table 1. This fact is remarkable for it disagrees with the experience of Dawson (Ref.

1)re-tt Speed v rif 171

ported in paragraph 3.1.(a)probably because of the aft body forms which were in use at the time when his results were obtained (up to 1950).

6. THE SEAGOING BARGE "ISLAND FORESTER" The results of extensive tests reported in this paragraph refer to a seagoing timber barge, whose lines are similar to those of the Neptun, the carrier Hera (see par. 5) but of considerably higher displacement'. The barge was recently put into service and belongs to a large fleet of similar vessels being employed in different trades in the Canadian offshore traffic. The publication of data listed in paragraphs 6.1. and 6.2. and of the model test results given in paragraph 6.3. was kindly authorised by the designers Messrs. Robert Allan Ltd., Naval Architects and Marine Engineers, and by the owners, Messrs. Island Tug and Barge Ltd., both of Vancouver B.C., Canada. They supplied also

the photographs of the barge in service shown in Figs. 14 and 15.

Fig,. 14 Seagoing barge "Island Forester", fully loaded

Fig. 15 "Island Forester" discharging (dumping procedure)

43-7

TABLET

Draught T 5.35 m., Speed v= 10 knots, Smooth water values

Damping Circular Relative resistance

Aft body Type factor frequency increments

shape of skeg

D ()

v (1/sec.) R (per cent)

Stern form 1 A +0.233 0.022 194 Stern form 1 B +0.233 0.021 22.7 Stern form 1 C +0.248 0.020 22.7 Stern form 1 D

0.122

0.022 12.0 Stern form 1 E +0.207 0.021 44.0 Stern form 1 F +0.123 0.021 32.5 Stern form 2 G

0.068

0.022 6.6 Stern form 2 H +0.209 0.019 47 6 Stern form 2 I +0.387 0.019 102.6 Stern form 2 K +0.090 0.021 24.8 01141

6.1. General data Mission: Length o.a. Length b.p. Beam moulded Draught (loaded) Displacement loaded Crew Service speed

Model scale ratio

Length of hawser

6.2. Bow and stern for Bow shape:

Stern shape:

Stern rake: Bottom radius:

Aft body water lines:

Stabilising skegs:

Fig. 17

frame spacing

knim*M

2

Seagoing timber barge with self-unloading equipment of the "dumping"

type (see Fig. 15).

LOA 452 ft. 3 in. (137.86 m.) Lpp 441 ft. 0 in. (134.42 m.) 96 ft. 0 in. (29.26m.) T1 20 ft. 0 in. (6.10 m.)

20,704 long tons (21,036 metric tons) none 9.0 knots /4 800 ft. (243.84m.) with a vertical bridle ms, stabilising skegs spoon-bow (see par. 2.2.)

barge stern with a large varying bilge radius (see par. 2.1.(b)) 16.5 deg. (see par. 2.1. (a)) large (see par. 2.1.(c))

square characteristic (see par. 2.1.(d)) Fig. 16 shows the body plan

curved fixed skegs A with moveable rudder (flap), flap setting Rr 10 deg. at skeg position 3 (see Figs. 17 and 18 and par. 3.1.(d))

Skeg A

6.3. Model tests for determination of optimum stabilising skegs The model tests included resistance tests and tracking tests with

two types of skegs. Skeg A, a quadrangular, curved fixed skeg

with moveable rudder (flap) was tested in three different positions and with several flap settings, whereas skeg B, a triangular, plane fixed skeg, was examined in two positions. The tests were carried

out in accordance with Froude's law and in smooth and deep

water at a designed draught Ti = 6.10 m. (20.00 ft.) The resistance tests of Fritsch (Ref. 9) covered the speed range around the service speed of 9.0 knots, and the tank values obtained were extrapolated to full scale ship according to the ITTC-57 correla-tion line with an allowance for the fully-welded hull of 0.00025.

The tracking tests were made in the same manner as described in

paragraph 5.3. at a speed corresponding to 9.0 knots. The yaw angle records were evaluated using the method explained in paragraph 4.

Figs. 17 and 18 show the curved fixed skeg A (see par. 3.1.(d))

and its different positions. The lateral area of this skeg including

flap is As 43.5 sq. m. 5.31 per cent of Lpp . T.

Skeg B is a triangular, plane fixed skeg (see par. 3.1.(a) and par.

5.3., skegs A, B. and C) of constant cross section with a lateral area of As = 53.0 sq. m. 6.46 per cent of Lpp . T1 . It was

tested in a position parallel to the centre line as well as turned outboard by 8 deg. Skeg B is shown in Fig. 19. Positions, where

flow direction tests were made for skegs A and B according to the method described in paragraph 3, are marked in Fig. 18. They are shown at mid-length of each skeg. The flow direction is 10 deg. at

the forward position (for skeg B) and 10.5 deg. at the aft position (for skeg A) inwardly directed and independent of speed within

the range of 6 to 10 knots.

Fig. 16 Body plan "Island Forester"

'frilL --_ ---_,.---__________ ---._ 1 1 I , I I, i ---1 leara

TN

chic 4,

_

10,0/ 0 1 4 5 6 7 Block coefficient at A1 CB 0,857

Ballast draught T2 8 ft. 6 in. (2.59 m.) Ballast displacement

_Az

8,000 long tons (8,128 metric

tons)

=

L

Fig. 1.9 30 25 20 15 '10 5 0 3

Sireg_B_

Fig. 20 Resistance diagram "Island Forester" LT r 101605' Mp

.

35

bore hull

position of streamline vests

017

stregks B.

8 dep. re/ to CIL sAegs A, posit,on .j al

-

days shags A, position 3, X= -25 degs "

r.tv,

The results of F itsch's resistance tests are plotted in Fig. 20, the unit LT employed in this diagram corresponds to 1.01605 Mp.

The skeg resistance values are rather high as was already shown in the resistance curves from the Hera tests given in Fig. 13. Figs. 20

and 21 confirm the sensitive increases in resistance caused by

relatively small changes in the skeg system.

Fig. 21 shows the results of the resistance and tracking tests with skegs A fitted in position 2 at 9.0 knots speed but with various flap settings So, where positive angles SR indicate an

outward setting of the flaps.

Optimum stabilising efficiency D is attained at a flap setting of 8R = ± 10 deg. (outward). The skeg resistance is very high, being AR = 76.7 per cent, and tends to higher amounts with increasing flap angles although the damping factor D diminishes. Using small negative flap settings the stabilising efficiency strongly decreases since the flap is located in the dead water

behind the fixed skeg.

4

5

6 7

₈

_i

b .

The lowest resistance was found at 5R --- 25 deg., being 22.15 LT. It is, however, still higher than Ro = 15.9 LT of the bare hull, i.e., a relative increment of 39.3 per cent.

For this reason the skegs A were tested in a modified position, '3, with a somewhat lower resistance (see Fig. 20) since an improvement in stabilising efficiency could be observed in this position at a flap setting of 6R = 10 deg. this was chosen for the full scale construction.

Fig. 22 shows a wave profile photograph at 9.0 knots speed corresponding to a Fronde number of Fn = 0.128.

The characteristic values D (-) and v (1/sec.) obtained from the

tracking tests are listed in table 2, together with the corresponding

values AR (per cent) of the increment in resistance relative to the

resistance of the bare hull.

The following conclusions may be drawn from the results of the

tests described in paragraphs 5 and 6:

Fig. 21 _{Skeg A. position 2, speed v = 9.0 knots: damping} factor D (-) and resistance Ro (LT) at different flap Roo on settings SR (deg.)

35 JO 25 20 0 _{flap angle ce} 3T0' 20 b.

-r

.1 10' 20' SO'

-I-A3-9

, ' 6;76 . _. 6 ..,

,

10' Or 1 IreV Skeg A I Fig. 18 skegs A, 2, -25 degs 7 skegs 6, v

-mmr._=en

Fig. 22 Wave profile, FIFE 0.128, v = 9.0 knots

TABLE 2

Draught T = 6.1`0 m.,

Speed v = 9.0 knots,

Smooth water values

Relative resistance increments AR (per cent)

- - -

_{57.9 66.7 76.7 87.4 98.1} . 45.9 -40.3 . -39.3 44.7 35.2 32.1 7 29.6 35.9 _117.0 0 0 50 F

23 Yawing period T (sec.), D (-)i and vt(1/sec.)iversus

length of hawser (m) 100 150 200 250 _

-towline length Imt

Skeg

Position

Flap _angle

on (deg.)

Damping factor

D (-)

Circular _{frequency v (/ /sec.)}

,,A 1. 0.046 0.017 A 1 +10 0.061 0.017 A

/

+15 0.095

aoth

A 1 +20 0.144 0.018 A 2 0 0.248 0.015 A 2

+5

0.274 0.014 A 2 ..-+10 0.296 0.014 A 2 +15 0.262 0.014 A 1 +20 0,215 0.015 A 2

-10

0.144 0.013 A 2

-20

0.188 0.015 A 2

-25

0.183 0.016 A. 3 o 0.215 0.014 A a

-10

0.296 0.013 3

-15

0.227 0.014 A 3

-20

0.156 0.014 B parallel turned 0.106 0.015 8 outboard by 8 deg 0.221 0.015 025 0,20 015 0,05 109

-A

-

-(a) Influence of skeg position

It was recommended in paragraph 3, that the skegs be ar-ranged as far outboard as possible. A comparison of the damping factors given in table 2 for skegs A in positions I and 2 strongly confirms this recommendation, position 2 being shifted parallel outboard by 2.4 m. At a flap setting of oR = - 5 deg., for instance, the damping factor is D = 0.046 in the inboard position

and D --- 0.274 in the outboard position. At 8R ;

20

deg.-and consequently high skeg resistance - D 0.144 in the inboard position as compared with D 0.215 in the outboard position. The circular frequency v follows thc same trend viewing its values in both positions and the properties D and v of an optimum skeg, given in paragraph 4.

(h) Influence of displacement

In paragraph 1.1. it was pointed out that course stability will decrease with increasing displacement. In order to prove this, a comparison can he made between the damping factors obtained with skegs A. B, and C of Hera and those determined for skegs B

in parallel position on the Island Forester. The values are given in

the following table.

Hera

Skeg area

Skeg (per cent Lap

(-)

(1/sec ) (per cent)

D -; 0.233 found for Hera is to be compared with D 0.106 for Island Forester while the values of resistance increment differ remarkably too.

The circular frequency v of the yawing motion was found to be v 0.019 to 0.022 for the Hera ( 11,473 cu. m.) and v 0.013 to 0.018 for the Island Forester ( = 20,523 cu. m.). This confirms the statement that the circular frequency v of yawing motion will increase, i.e. tend to improve stability, if the dis-placement is reduced (sec par. 4.).

6.4. Influence of the length of hawser on the course stability

In paragraph 1.2. the discrepancy existing between theoreti-cally derived influence of the hawser length on the coursekeeping stability and results known from practice on the other hand was

discussed. Fig. 24

centreline shag with moveable rudder

For this reason the barge model of Island Forester with the fixed skegs B in parallel position was tested on the fully-loaded draught Ti - 6.10 m. (20.00 ft.) at a corresponding speed of 9.0 knots with various tow rope lengths. The yawing motions w(t) recorded after a deflection off the straight course were analysed

according to the method described in paragraph 4.

The results of these tests, i.e. the damping factor D (-), the period T (sec.) and the circular frequency v (1/sec.) of the yawing motion, are represented as a function of the tow rope length in Fig. 23. The measured points at the tow rope length of 243.83 m. marked by framed symbols are taken from previous tests with the same configuration. The good agreement with the

results from new tests discussed in this paragraph proves the good repeatability of model test results.

Fig. 23 indicates that in the range of the hawser lengths tested the course stability is steadily increasing with higher tow rope length. The damping factor D becomes less and the circular frequency v gets higher values when the tow rope is shortened. These results clearly confirm the service results known from Canadian and American barges as well as the observations made

by Benford (Ref. 7).

6.5. Tracking tests with a fixed centre line skeg and activated rudder

The unsatisfactory stabilising efficiency of a single fixed skeg fitted in the midship plane was mentioned in paragraph 3.1.(e). The inefficiency of a centre rudder operated by the tow rope was

described too (see par. 3.1

Fig. 24 shows a combination of a fixed centre-line skeg with a moveable rudder which operated by the hawser via the helm in a transmission ratio of i 2. If e is the angle between the hawser and the centre line the rudder angle is sR = 2c. The total lateral area of the skeg-rudder combination corresponds to one skeg of

the type A with:

As = 43.5 sq. in. ---- 5.31 per cent of Lpp . T1.

The tests with this configuration were carried out on the fully-loaded draught Ti - 6.10 m. (20.00 ft.) at 9.0 knots corresponding speed and a hawser length of 800 ft. (244 m.). The skeg-rudder combination can be easily changed into a single fixed skeg by blocking the rudder in the amidship position. Fig. 25 represents the graphs of the yawing motions 111(t) obtained from this test. Immediately after starting the towing procedure the barge takes up a remarkable yawing motion of constant circular frequency v and constart amplitudes i of yaw angle.

In this condition the damping factor D 0. Blocking of the

rudder causes a severe change in the period of the yawing motion

but no stability whatsoever. The circular frequency v amounts nearly to those values obtained with the skcgs A in the inboard

position I (see table 2).

Table 3 gives the characteristic stability values D (-) and v (1/sec.) for the yawing motions recorded in Fig. 25.

4

5

A3-11

A 5.86 +0.233 0.022 19.4 5.86 +0.233 0.021 22.7 5.86 4-0.248 0 020 22.7 Island Forester Skeg area

Skeg _{(per cent trip} T1)

_(-)

(1/sec.) (per cent)

6.46 +0106 0.015 35.9

=

R . .

=

:WL

Fig. 25A Yawing motion obtained with fixed centre line skeg

ge

E3b.

300-

20°-

10°- 10°-

_20°-

_300-

9th

Gierschwingung

(t) be! fester Miltelflosse

326s

Geschwindigheit v = 9 kr/

Schleppleinenlange

800 ft

Richtung des Beivegungsvorganges

Fig. 258 Yawing motion obtained with fixed centre line skeg and moveable rudder

326 s

Gierschwingung

710(1) bei fester Mittelflosse ant bowel Ruder

7t, Bb _{40°- 300-}

20°-I

10°-\

\

\

i

804 s

I

224 s

10'-224 s

224 s

\

20°-\

/

\

\

\

40.

_Stb

Geschwindigked v=9 lip

Schlepplernenldnge 800 ft

Richtung des Beivegungsvorganges

TABLE 3

Draught T1 = 6.10 m Speed v = 9.0 knots. Smooth water values

Fig. 26

If the moments N (No) and the cross forces Cr (Co) are measured after (before) fitting the skegs, the cross force difference AC and its centre of effort xt,c relative to the main section is obtained from:

Ct Co

xec

NI No_Co AN_AC (7)

A two-component measuring device, shown in Fig. 28, was used for measuring the cross Forces C. The calibration of the measuring

Skeg/rudder configuration centre skeg with moveable rudder

centre fixed skeg

Damping factor

()

'0 B.0119

The results given above confirm the general opinion that a stabilising efficiency is hardly to be expected from devices of this type. The yaw angle graphsespecially that of the tests with a fixed centre-line skegdemonstrate, however, the presence of non-linear components neglected in the usual linearisations and

simplified equations of motion (see (Ref. 2)).

6.6. Oblique-towing tests at various inflow angles to investigate the amount and the centre of effort of the skeg cross force

The hydrodynamic forces of a set of skegs were described in

paragraph 3. Figs. I and 2 show the cross forces C of the skegs in

straight ahead motion and after deflecting the barge by an angle

respectively.

If these interpretations are correct, a difference of cross force PC (Mp.) must appear when stabilising skegs are fitted to a barge being towed under an oblique angle of flow. The centre of effort X c of this cross force difference must be located within the length of the skegs. In order to prove the existence of this cross force difference and its centre of effort, oblique-towing tests were carried out with :he model of the barge Island Forester on the fully loaded draught T, 6.10 m. (20.00 ft.) at 9.00 knots

cor-responding speed.

During these tests the moment N (mMp.) about a vertical axis in the midship section and the hydrodynamic cross force C (Mp.) were measured as a function of the drift angle p (deg.) with both bare model and model fitted with skegs B in parallel

arrange-ment.

Relative to the midship section the centres of effort xc (m) of the total cross force C (Mp.) are calculated from the measured

values of the moment N by means of the equation:

xc (m) =

C 1(6)

with sign conventions as shown in Fig. 26.

414

Circular frequency v (1/sec.) 0.028

equipment and the recording instruments was carried out im-mediately before the test (with the model attached) by means of weights in the midship section plane (for C) and at the lever arm 2 m. abaft (for N).

yttrium rbro-- or

...Ft, ell raw, ler t ro

kern& rEr al arort

." 7244 2,1111 toa aa Sc so so 40 0' r ,OPPI err.* 0.16. .444,4 !Verb& 4s 4C .4' 10 .0 20 10 0 ,0 20 SO 40 50 60 :0 80 SO /00fir a .72 74; xr, xa, !ml re, It

Fig. 27 Diagram of cross forces and corresponding centres

of effort

Fig. 27 shows the results of these oblique-towing tests, i.e. the cross forces C and their centres of effort xc with the angle of inflow as parameter. From this diagram the following can be concluded:

IC

(a) Barge without skegs

The centre of effort xco of the hydrodynamic cross force is located before the vessel at drift angles up to about 0 -- 15 deg.

This phenomenon is physically possible only if cross forces act on the vessel before and behind the midship section in opposite direction. The vessel is course unstable since even a small yawing

motion will be reinforced by the hydrodynamic moment N due to Co and xco (see par. 1.2. and Peters' contribution about

tow-line attachment relating to cross force).

Bargewith skegs B in parallel position

The total hydrodynamic cross force C1 has attained higher amounts and its centres of effort xci are located near the midship section plane already at small drift angles p. According to the characteristic stability values of these skcgs listed in table 2, in

this condition the barge is course stable. (a) Hydrodynamic cross forces of skegs

The cross forces AC of the skegs and their centres of effort xpc calculated according to equations (7) are also plotted in Fig. 27. The dimensions of the barge shown in the diagram indicate that the centres of effort x4c are within the length of the skegs for drift angles 0 4.5 deg. This proves the interpreta-tion of the skeg performance, as given in paragraph 3, to be correct.

7. SKEG CHARACTERISTICS AND EFFECTIVE CONFIGURATIONS

In paragraph 6.6. results were given of oblique-towing tests carried out with the model of the log carrier Island Forester, both, before and after fitting a set of plane fixed skegs. The

hydro-dynamic centres of effort x ac of the cross force differences AC obtained after fitting skegs were found to be located within the skeg plane. Therefore superposability of the hydrodynamic forces of the barge and of the stabilising skeg forces could be concludedat least for the tested stem form with a flat bottom and a constant stern rake.

The interpretation of skeg action given in paragraph 3, and the superposability of skeg forces may be regarded as proven only if

A3-13

C" 0.20"

PLC'

"rat e ro...-t a,,

no 41* s e hr.

". e

C,

D

the hydrodynamic forces C on the skegsdctermined in a fret= running test without the hullequal the forces as determined in the oblique-towing test. Since this proof is deduced in the follow-ing, the problem of skeg stabilisation may he approached largely from the angle of their free-running qualities thus enabling im-mediate comparison of different skegs and determination of their optimum arrangement.

7.1. Determination of the skeg characteristics

Fig. 28 shows a sketch of the measuring device applied already for the oblique-rowing tests described in paragraph 6.6. The connecting element t,it) for the model has been fastened to the bending-and torsion-proof traverse a) which is clamped firmly to the towing carriage.

This is done by means of a centring device and four socket-head

cap screws, which lead through elongated holes and enable a continuous variation of the drift angle. This connecting element is equipped with transducers for cross force, resistance and torque. The base of the measuring apparatus consists of two floating parts which allow model tests in trimmed or inclined conditions

as well. For the free-running skeg tests this proven apparatus was

extended by the supplementary element cri) which consists of a connecting plate to ®, a steel tube and a 'large circular spill plate

Fig. 28

Measuring device for oblique-towing and

free-running tests _gratzated Scgt_../ fair

\3-14

griltargie affingd .1 tarsier,' crosilance and rearsiVlat_metera_ (stean; gauges)

santrional erotica ,,in2

_free flow ?est

under which the skegs were fitted. The calibration of the instru-mentation was done as described in paragraph 6,6. In order to eliminate uncertainties in the resistance measurement all of the skcgs were tested at model speeds v (m/sec.) corresponding to a supercritical Reynolds number:

V .

106 (--) (if)

where

v (sq. in./sec.) cinematic viscosity of water

c, (m.) = mean chord length of profile

After recalibration at the end of the tests the cross forces C and the longitudinal resistance W of the apparatus without skeg were determined and subtracted from the measured values. In

this paragraph the angle of attack a (deg.) is the angle between the

direction of inflow and either the centre line of the leading part (skegs II and IV) or the centre line itself (skeg Ill) or the tangent to the centre line at the leading edge*) (skeg I). The rudder angle Bs (deg.) at the fixed skeg IV with moveable rudder is the angle between the centre lines of the fixed skeg and the rudder

respec-tively.

29, 'Sketch of hydrofoil forces

Fig. 29 shows the hydrofoil forces acting on a skeg underan

angle of attack a (deg.). When the cross forces C (kp) and the longitudinal component W (kp) of the resistance are known, the hydrodynamic lift L (kp) and drag D (kp) in aco-ordinate _system oriented in the direction of flow a are calculated by_{means of the} transformations:

L C. cos a . sin

D = C

. sin a W . cos a ₍₉₎

These quantities are given in non-dimensional' form as cross

force coefficients Cc (), lift coefficients CL () and

drag coefficients CD () by:

where

v i(rn./sce.) =t velocity

_of

inflow

1 . C Cc

2.tL

CL

fr. V2

As 2

. D

Ct) p . v2

. As

1

0

traverse for constraint to

towing carriage

/rim . - .

--W-sin

Fig. . . .

Fig. 31 Plane fixed skeg with adjustable flap

CN/L

(kpirsec.2 )

m.4 = mass density of water As (m.2) - lateral area of the skeg 7.2. The forces on the skegs tested. both, free-running and

fitted to the barge (proof of the principle of superposition)

The plane fixed skeg tested in connection with the bargemodel

of the island Forester (see par. 6.6.) was tested free-running using the method described in paragraph 7.1. The cross force coefficients

Cc were calculated by means of equation 10a using the valuesof the cross forces C measured under various angles of attack. On the other hand, the cross force differences . C that appeared at

different drift angles after fitting the skegs are known from the results of the oblique-towing tests. When the cross force coeffi-cients C...c of these differences are calculated in analogy to equation 10a fallowing for the fact that during the oblique-towing tests a pair of the skegs was in action) the principleof superposition is established if Cc C. c. since it was already shown in paragraph 6.6., Fig. 27, that the centres of

effort x.ç of

the cross force differences AC due to the fitting of the skegs were located within the skeg plane.

Fig. 30 shows the non-dimensional cross force coefficients Cc of

the free-running skeg and Cz..c of the cross force difference for the total system barge and skegs. This diagram indicates the following:

both cross forces have the same qualitative tendency to increase with the angle of inflow a or the drift angle

(h) the free-running coefficients are about 20 to 25 per cent higher than those of the skeg fitted to the barge. This quantitative difference is easily explained: since the skegs are not attacked with the ship speed v but with the speed vA v (1 w) behind the shipthus allowing for the waketheir cross force is lower than that of the free-running skeg. Therefore, when

non-dimen-sional cross force coefficients are calculated based on speeds v. the

cross force coefficient of skegs fitted to the barge is apparently smaller.

When the inflow velocity VA of the fitted skegs is determined

under these assumptions from the cross force coefficients Cc and

C c on the basis of cross force equality, then:

C r

vA

=

"cc

v = 0.89

. v to 0.92 . v

and hence a local wake fraction in way of the skegs of:

w = 8 to I

I per cent

This local wake value can be considered as quite normal for aft bodies of this kind. Hence, following the inductive procedure of interpretation and proof of skeg action described in paragraphs 3. 6.6. and 7.2., thesuperposition ofskeg fineson the

hydrody-namic forces of the barge is seen to be admissible when barges with square waterlinecharacteristics undostraight rake are considered. The limiting curve of cross force coefficients for thin, flat plates

;tangreof_/o7e Cc C-1 CAc

2,0

0,5 0

o skeg HI free flow values

skeg II coefficients Cjc of

cross force difference obtained from oblique toying lest

0 5 10 15 20

angle of attack cc !deg 7 at free flow, test

drift angle /3 [dog) of barge with slregs

Fig. 30 Diagram to prove the principle of superposition of high aspect ratio, calculated theoretically according to: Cc = .

2rc . sin a . cos

it =it .

sin 2a is also plotted in Fig. 30.

As is well known, the lift gradient dC, /daand consequently the cross force gradient dCc/dadecreases at lower aspect ratios A. With these low aspect ratios we are generally confronted in ship rudder designs and skeg stabilisation (A = b2/A5; As rudder/

skeg area: h rudderiskeg height). 7.3. Particulars of the skeg types tested

The free-running characteristics have been investigated for three skegs I, II, Ill (already known from the resistance and course stabilising tests) and for a fixed skeg IV with moveable

rudder (flap). The particulars of these skegs are listed below:

5

6

A3-1 5

- -r

0

2

=

=

tc

8

Skeg 1:

curved fixed skeg (see par. 3.1.(c)).

Hera

skeg G

(see Fig. 11) Island Forester

skeg A

at SR - 0 deg.

(Figs. 17, IS).

Skeg II: plane knuckle skeg (see par. 3.1 .( h)), Hera skeg K

(see par. 5.3.,

Fig. II).

The angle between leading

and trailing part is 8 25 deg.

'Skeg III: plane fixed skeg (see par. 3.1.(a)), Heraskcgs A, B,

C, (see par. 5.3., Fig. 9) and

Island Forester skeg B (see par. 6.3., Fig. 19).

'Skeg IV: fixed skeg

with moveable rudder (flap) (see par.

3.1.(d)) Fig. 31 shows this skeg, which is often used when seagoing barges are pushed with the rudder in zero position (see par. 7.6. for data on some seagoing

barges).

7.4. Skeg characteristics, the significance of the drag/lift ratio of

the skeg

The experimental determination of skeg characteristics was

described in paragraph 7.1. A representation of these important

hydrodynamic quantities as a function of the angle of attack u

(deg.) is possible when the lift and drag coefficients CL

() and

CD ()

of the skegs are known from the equations 10b and 10c.

Among other information, the lift gradient dCL/da (sec par. 3)

can he taken from these diagrams for various skeg types which are

fitted at an angle of attack

(10

(deg.) relative to the local flow

direction (see par. 3.1.: positioning of stabilising skegs)

and

when

the barge is yawingare attacked additionally by the drift

angle Ii. i.e. actually at an angle a = uo L13.

Plotting the lift coefficient CL versus the drag coefficient CD

produces the well-known polar curves of hydrofoils

CL (CD)

which have been drawn for the different skeg types tested using

tile angle of attack a as parameter.

Much more informative is the quotient of the drag and

lift

coefficients given as a function of the angle of attack. the so-called

drag/lift ratio c.

'CD

8(a)

=

CL

The test results reported in this paragraph and in the following

show that a skeg must already have a positive lift coefficient

CL(u0) 0 el 2a)

when

the barge is moving straight ahead. Thus fitting the skcg

ander an angle of attack uo (deg.) the economic requirement of

he lowest possible resistance coefficient

CD(ao) - 0 (12b)

'cadsby combination with (12a) to the skeg drag/lift ratio

CD

indin the optimum case of minimum

resistance td:

Co

no)

mm.

Formally, it

follows from the minimum condition (I2c) by

lifferentiation that:

dCD CD

dCL

For the minimum of the drag/lift ratio. These considerations

lo not yet give an indication of

the mosteffective configuration,

,e.suitable angles ofattack au(deg.) relative to the direction of

low in way of the skegs. This matter will be taken up in paragraph

.5. Fig. 32 shows the lift coefficientsCL

() Of the curved fixed

keg I. the plane knuckle skeg II and the plane fixed skeg

ersus the angle of attack (deg.). Fig. 33 gives the corresponding

uantities for the fixed skeg IV with moveable rudder. Due to the

urved centre lineof skegI, to the knuckled fixed part of skeg II.

nd to the rudder setting of skeg IV, a lilt already appears when

(12c)

(13)

the angle of attack a. is still zero. All of the four skegs prove to be

equivalent with regard to the lift gradient dCL/da (see Par. 3).

Fig. 32 Lift coefficients CL (-),skegs I, II, ill; Rn = 106

Fig. 33 Lift coefficients CI_ (-), slceg IV; Rn = 106

CL C-1 1,5

05

5

10 15 ₂₀ 25

angle of attack ce [deg]

Fig. 34 Drag coefficients CD (-), skegs 1,11,111; Rn = 106

Imerkie slreg I Iregff r 1,5 -:----1 1

/

/

-41( ! I

7

1 i I '

1--.

,0'1 , 1 1 plane guar:map/or A 0-7.0.---. tarred padranyulor ...-s---, plane tmango/or ..rs I I I I 1

II

1

/

0.5

/

Ca 1' -1

I\s.

1 I ...

/

/

.---.-- fgafenizquadranp quadrangula It p/Ineraivmpla, Aaaronswa angular a . 0----.---. curked 6.--7-0 Irons -20 -15 -10 -5 0 5 10 15 20 25 30 ,55 40

angle of Oatha: lacy1

5 10 15 20 25 30 35 40

angle of oeco,tt lay!

-20 -15 -10

-5 /0

)

>

=

=

=

mib u

The drag coefficients CD () for the four types of skegs are plotted in Figs. 34 and 35.

Fig. 35 Drag coefficients CD (- ), skeg IV; Rn = 106

The polar curves for the four skeg types tested are shown in

Figs. 36 and 37, for reasons of completeness, although there is not much information to be gained from them with regard to the appropriate design and positioning of skegs.

Fig. 36 Polar curves skegs I, II, Ill: Rn = 106

-to

plane pao'rangular knuckle she;

1

-5°

0--0 0

ClitTeCi

padrarvedor sire;

plane tramplar slog'

0 0,5 co 1%7 1,0

The possibility of relating the hydrodynamic properties of stabilising skegs to the drag/lift ratio e (a) has been discussed in the previous part of this paragraph. According to (12c) the minimum of the drag/lift ratio function, its amount and angle of

attack u (um in) are significant for optimum skeg positioning.

_

Fig. 39 (opposite) Diagram of drag/lift ratio, skeg IV; Rn = 106

Fig. 37 Polar curves skeg IV; Rn 106 CL

-a51

Fig. 38 Diagram of drag/lift ratio, skegs1,11,111; Rn = 106

-ct;- 40° 4-30*

-5 0 5 10 15

angle of attack a [deg 1

20

A3-17

-CI L:72 1,0 I I 0----0--0 I I I

plane guadrangatar knuckle

correct quadrangular Meg/ alone triangator slreg,E

shegi" , 1 0,8 co- -0

/

\--\

061

par-111WAS

04

asp_

Kai

-, J -15 -10 -5 0 5 70 15 20 25 50 35 40

angle of attack ct faeg

-10 -5 0 5 10 15

angle of eater

a !deg]

20 25 (-1 Z5

15

414

I

-15 -10

I

-15 25 0,5 0

Figs. 38 and 39 give the curves of drag/lift ratios( versus the angle of attack for the skegs examined. The minima of the drag/ lift ratio appear at different angles of attack a (cm") depending on the foil curvature and flap set ting 8R. The drag/lift ratio curve has a pole at zero lift angle a (CL = 0) and a steady and increasing

tendency at higher angles of attack.

From equation 13 the remarkable fact was obtained that for

the minimum of drag/lift ratio the quotient of drag and lift

gradients (dCD/clu)/(dCL/da) dCD/dCL, equals the amount of the drag/lift ratio c = CD/CL. The gradients were determined

according to the principle of the divided' differences.

Fig. 40 Drag/tdt ratio diagram according to equation (13) plane quadrangular knuckle Meg curved quadrangular shag I

alone inangaar shag III

approx. approx. approx. approx. service speed length of

TABLE 4

Amounts and angles of attack at the minima of drag/lift 'ratio

curved fixed skeg I: Emin = 0.148 at cr 3.0 deg.

plane fixed knuckle skeg II Ernin = 0.216 at = 6.0 deg.

plane fixed skeg

Ill:

Emin = 0.305 at u = +11.0 deg.

r P

10. deg. Thus, consulting equation (12c) for comparing skeg properties, this skeg presents itself as a favourable one.

Indeed. numerous U.S. barges are equipped with stabilising skegs

whose leading parts have been titled parallel to the local flow direction (en 0 deg.) with flap settings of SR 0 deg. in the push unit and of 8R 10 to 30 deg. when towed. Higher flap angles could be avoided if the leading part were fitted under a small angle of attack (see Fig. 43 and compare barges "X" and -11"). Unfortunately, the drag/lift

ratio does not provide a

satisfactory criterion for the choice of optimum skegs since, e.g. the plane fixed skegs of high drag/lift ratios would obviously be judged to be too unfavourable as shown by the stabilising charac-teristics and the relative resistance increment values available for Hera (see Fig. 41). However, the drag/lift ratio is a valuable aid in

the selection of suitable angles of attack a() for the skegs, as will be shown in paragraph 7.5,

15. Suitable angles of attack for skeg configurations

Using any type of skegwhether for reasons of manufacturing or from considerations of providing adjustable stabilisation for the pushing as well as for the towing conditionthe next question is, how to arrange it in the most efficient way. General remarks were made in paragraph 3. The assumption that the plane fixed skeg, for instance, would be positioned best at an angle of attack of no 0 deg. since the condition LICLJda > 0 is fulfilled, is invalid for it does not meet the condition ( I 2a) CL (an) > 0.

For the same reason a fixed centre skeg is ineffective (compare par. 3.1 (c) and 6.5.).

Moreover, the investigations show thataccording to the

equation (124an operation of the skeg at its minimum of drag/

'lilt ratio cannot be generalised for all types of skegs. Since, on the

other hand, suitable angles of attack of the stabilising skegs are located in the vicinity of the minimum of the drag/lift ratio the significance of this function is demonstrated.

Since the stabilising characteristicsespecially Dand the

local flow directions are known from tracking tests, it suggests itself that the angle of attack ao be traced in the corresponding diagram of drag/lift ratios and its influence on the change of .drag/lift ratio and stability characteristics be studied.

and bow bulb moveable flap

.-,-,

CL w 40 il dc/dc

IM

ii

rag

ral

pi

0.8

061IPiUV

e

III

4

II =II

lEll

a.

alittil

Mission displacement (cu. m.) Lpp (m.) beam (m.) draught (m.) (knots) Stern shape bow shape type of skeg hawser (m.)

containers 23,600 255 32 4.60' 10 "Fletcher" spoon-bow -Wingwall" 570

aragonite 50,000 1'89 29 10:60 10 raked stern spoon-bow fixed skegs with

moveable flap

phosphate 23,400. 431 24.4 8.60 1,0 to 14 raked stern spoon-tow plane, fixed

skegs

i'y 556

bulk cargo 23,300 1'28 24.4 ,,, 8.60 10 to 1.4 latEed stern spoon-lbow plane, fixed

knuckle skegs

550

bulk cargo 35,000 165 25.9 19.65 10 to' 14 "Fletcher" spoon-bow ''Wingwall" 550

bauxite 44,500 1,89 26% 10.70 10 parabolic V-section fixed skegs with 245

5 -se -5 0 5 10 15 20 25 30 35 40

angle al &lath a (dog]

Fig. 40' shows the drag/lift ratio diagram of Fig. 38 with the functions dCo/dCL for the skegs I, II, and Ill plotted additionally. The intersection points of these curves with those of the drag/lift ratio functions are located in the drag/lift ratio minima. The amounts emir, and the corresponding angles of attack a (cm in) are listed in table 4.

From this table it appears that of all stabilising skegs 'tested the

skeg IV attains the lowest drag/lift ratio at a flap setting of SR =

flap setting Sn= 0 deg: emir, = 0.260 at a = + 6.5 deg. flap setting SR = 4-10 deg. Emir, = 0.098 at a = 0 deg.

plane fixed skeg flap setting OR = +20 deg. emir, = 0.14o at = 3.5 deg

with moveable flap flap setting 6R +30 deg. Cm i n= 0.230 at u -w- 4.0 deg.

flap setting SR -= +40 deg. crnin = 0.360 at a= 4.0 deg. =

u

550

IV: a