Some measurements of interaction induced by surface piercing and flooded banks

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DOCU"ENTFTIE : \-\

DATUMI

NATIONAL MARITIME INSTITUTE

SOME MEASURENTS OF INTERACTION INDUCED BY SURFACE-PIERCING

AND flOODED BANKS

by

IWDAND

SUMMARY

Some measurements of interaction induced on several ship models by surface-piercing and flooded banks are presented and discussed,. Variations of the measured forces, moments and sinkages with

distance-off., speed, bank type and water depth are given and the

way in which such results may be used iti port approach channel

Introduction Experimental MethOds 2 2.1 Definitions 2 2.2 Ship Models 3 2.3 Bank Models - 4 2.3.1 Experiment Facilities 4

2.3.2 Surface-Piercing Batik Model 5

2.3.3 Flooded Bank MOdel 6

2.4 Instrumentation 6

2.4. 1 Data Collection 7

Scope of Experiment 7

Results Obtained with Surface-Piercing Banks 8

4 1 Experiments in Number 2 Towing Tank 8

4 1 1 Steady State Results Bank Parallel to Ship's Track 9

4.1.2 Transient Results 9

4 2 Experiments in the Circulating Water Channel 1.2

4.2.1 General - 12

4 2 2 Comparison with Towing Tank Results 1:3

4.2.3 Effect of Speed 16

4.2.4 Effect of Bank Slope 17

4.2.5 Effect of Advance Coefficient and Rudder Angle 18

4.2.6 Effect of Screw Bias 22

4.2.7 Effect of Yaw Angle 22

5. Results Obtained

5.1 Effect

52 Effect

5.3 Effect

with Flooded Banks of Speed

Of Hull Form

of Y/B, h/PB arid hIT

24 24 26 27 6 General Discussion 29 6.1 Channel Dimensions 29

6.11

Canals 29

6.2 Use of Results in Channel/Canal Design 30

ConcluSiOns 31

References 32

Acknowledgements 33

Noencläture

34

Appendix - A Blockage Corrector for Canals 36

Figs 1-48

Figs Al - A3

by I W DAND

PROJECT NO. 2520O1

1. Introduction

When a ship moves along a dredged channel or in a canal, its behaviour can

be affected by the proximity Of the canal or channel banks. The bank

can cause forces and moments to act on the ship which, if not corrected by the ship-handler, can cause the ship to sheer away from the bank.

The probably _{érióus consequences of such}

_{a sheer make it iortanto}

take bãrik effets' into account when considering the suitability of a

channel or canal for the. safe navigation _{o a given ship.' Measurements of}

bank. effects have been made in the _{past at NM.I andelsewhere, (ref s 1 -5)}

but the data havegenerally either reulted from studiesof vertical,

surface-piercing banks, or been of a limited ad hoc fläture.

The study described below attempts to provide additional data related to

sloping and flooded banks in whith water _{depth, vessel speed, bank slOpe.,}

batik height and hull shape are all varied. _{The results Qbãinéd can be}

used for channel design studies or for input to simulation progrems

concerned, with ship behaviour in shallow an confined waters.

This study complements that on interact ion between ships described 'in

reference 6 and forms partof a larger investigation

_{coissioned by the}

UK Department of Transport with technical guidance from the National Ports Council.

2. Experimental Method

2.1 Definitions

Experiments were conducted in both the shallow section of no. 2 towing tank and the large no. 2 circulating water channel used in the shallow water

mode.

In both facilities the same basic definitions and parameters were used. These are listed below

Axis system

A right-handed axis system was used as shown in Figure 1 with the x-axis

pointing forward, the z-axis vertically upward and the y-axis to starboard. The origin was assumed to be in the water surface amidships on the centre-plane of the ship model.

Speed and depth

Speed and depth were related as usual by the Froude Depth Number

nh where h is the water depth in the channel or canal in the

vicinity of the ship model and not over the bank, and v is the speed of

the model through the water. Distance-off, Y

0

Distance off the bank, Y , is defined as the lateral distance between the

0

centreplane of the model and the toe of the bank. Bank slope

Bank slope is defined as the slope of the bank from the toe to the

upper-most level of the bank itself. It is usually given in the form '1 in n'.

Bank height, DR

For a flooded bank, its height _DB is defined as the vertical distance

from the bed of the channel to the top of the bank as shown in Figure 1. Forces and Moments

Longitudinal (X)lateral(Y)forces and a turning moment N, (all related to midships) were measured in all experiments and non-dimensionalised

according to the following scheme to give coefficients and CN:

C =

XpBTv2

=

_YRpBTv2

CN =

NpB2Tv2

... (1)

where B is the breadth of the model

Squat

Mean sinkage and dynamic trim were measured during some of the experiments and non-dimensionalised to give mean sinkage and trim coefficients

C and C thus

S T

CS = 1OO(SFp+S,)/2L

CT =

1OO(SFp_S)/LPp

... (2) where is length between perpendiculars

S, S, are sinkages measured at the forward and

aft perpendiculars.

2.2 Ship Models

Five ship models were used in the experiments and their principal particulars

are given in Table 1. It should be noted that two of the models (numbers

5233 and 5238) form a geosim pair.

TABLE I

Model number 5233 5238 5237 5338 5098

Ship type

as Tanker as Tanker as Cargo

as Container ship

Twin screw

passenger shi

Length between perpendiculars m 3.962 1.817 1.524 3.810 6.096

Breadth, iixulded, B

w 0.506 0.232 0.217 0.544 0.723

Draught at FP, T

m 0.208 0.095 0.074 0.181 0.249

Draught at AP, TAP 0.218 ' 0.100 0.078 0.181 0.249

Dieplacnt volume V

m3 0.330 0.032 0.018 0.225 0.597

Block coefficient, CB

0.761 0.761 0.701 0.60 0.544

2.627 2.627 2.603 2.609 2.791

Wetted areacoeff.

Displacement/length coeff.

0.531 0.531 0.516 0.407 0.264

Type of stern arrangement

closed closed closed open open

No. of rudderB I I I

Rudder balanced balanced balanced spade/horn Gnomon

Rudder areai (LppTme*n) 0.0137 0.0137 0.0165 0.0151 0.0153

Mazinsim rudder angle degs ±35 +35 + 70

Number of propellers I I I 2

Propeller number U512

-

- U3 86 13461

Number of blades 4RB 4RB

4.a

3 Rh 6 UI 6 RN

Diameter, D m 0.13? 0.063

0.)58

0.111 0.131

Designed face pitch (mean)

a

0.108 0.050 0.063 0.096 0.249

Model 5233 was constructed of rigid polyurethane foam while the other models

were all made of wood. All models were self-propelled when required and

models 5233, 5338 and 5098 had rudders which could be mOved to predetermined

fixed rudder angles. The twin-screw model (5098) also had independent

motors driving each shaft thus allowing different revolutions (ahead or astern) to be set on each shaft if required..

It should be noted that the rudder arEa used in Table 1 is that of. the

moveable part of the rudder only; the area Of

fixed strüctUreuch as a

horn has been Excluded.

2.3 Bank Models and Experient Facilit

The banks were modelled in two different ways depending on both bank type and the facility in which the experiments were carried out.

2.3.1 Experiment. 'acilities

Bank effects were meaured in the shallow section of no. 2 towing tank and

the no. 2 circulating water channel. The former facility was used for

both floodEd and surface-piercing bank experiments while the latter was

used for surface-piercing bank experiments

_Only.

Number 2 Tank

The shallow section of number 2 towing tank is 90 in length an4 5.798m

wide with a water depth which may be varied from zero to 0.56m. The

flatness of th bottom was better than +3th and in the vicinity of the

tank centreline the surface ftnish gave a flatness of the Order of ±1 nm.

uber 2 CirculatingWater Channel

The large mii number 2 circulating water channel ha a working section 3.658m

wide and some 18m in length. A moveablE false floor is fitted which, when

fully raised,allows the thannel to be used as a shallow-water facility.

The shallow water capabilitmy befurther exten4ed by draining the water

in the working section to I 575m leaving about 80 mm depth of water over the

bination of running" speeds and water depth for shallow water investigations.

The advantage of using such a facility is that very long run tjmes are possible which allow the effect of the change of variOus parameters (suth

as rudder angle and propeller revolutions) to be studie4 with ease. The

'main disadvantage of it's use lies in the fact that a boundary layer grows

Over, the floor of' the channel and over any siilated baflk installed which

may 'affect the results obtained. This is discussed further below, but

does not detract from the use of results obtained in the channel on a comparative basis, one of the aims of the study 4esçribed below.

2.3.2 Surface-piercing Batik Model

'The surfacepierc'ing bank models were constructed from 3.05m x 1.22m

r.ectangilar 'sections' made from glass-reinforced plastic.. These were

laid'end-to-end on the. floor of the tank or. channel, pressure sealing on the

edges being achieved by means of closed-cell plastic foam..

The bank angle of each bank section was set to give a 1 in 4 slope, and a

steeper slope than this was achieved simply by placing suitable packing

under the supporting legs of each bank section. The supporting legs,

being hollow, were weighted when used in the towing tank to maintain the

bank sections in position and resist the large vertical and horizontal

pressure'forces imposed on them by the passage of the ship mpdel." The

'weights' consisted of heavy-duty hquse bricks.

However, when usédin the,.circulating water channel., the banks were held

firmly to the false floor by means of Veribor suction pads.deployed as

shown in Figure 4. It was also necessary to provide a streamline fairing.

at the 'leading edge' of the bank in the circulating water channel so that

undue disturbance Of the flow was avoided.' This fairing was manufactured

114

m.an4 it was some 26m in lengti, with-a bankangle from the toe of

22°.

Neither bal height or batik angle were varied throughout the

experiments.

The bank was constructed by depositing the

ilica chips i±i..approimately

the correct position to one side of the path of,themodel..and

then,moulding

to'sapeith awoodenscraper fitted tOh-front of the towing

carriage

as shown in Figure 4.

In all 'experiments only one s-ide bank was simulated and thi$ was positioned

on the, pOsitive (starboard)

side of the ship models.

The lateral distance of the model- from the bank and the ya

angle of the

model tee varied by appropriately positioning

the. strongback box-section

be

to which the fôre- gauges and model were attached.

Alternatively the

sh-ipmodel was left in position. throughout all runs

while the banks were

moved relative to the track of the model,

This was done in some of the

towing tank experiments..

2.4

Instturnentation

The instrumentation used in the experiments désribed below bore many

siilaritie

to that described in' reference 6.

In factthe meastrement

of the longitudinal force

X,

iateal forces at boW and stern

_F

and

and sinkage at bow and stern were

me'aired exactly a- in reference 6 using

modular force gauges for the forces and

linear displacement trisducers

fOr th

fore and a-ft sinkages.

(It should. be. noted thgto

sinkagemeasuremeritS were made during the

circulating water channel

experiments).

, .

Speed was rneaured in the towing tank-as-the speed

of thetowing carriage

over the ground while Water

speed in the circulating water chattel was

measured by means of a miniature rota

current meter mounted upstream

All results were integrated electronically over time periods of 20, 40 or 60 seconds depending on the type of model, the type of bank under test and the

speed of the model. For some experiments, described below in section 4.1.2,

the data was also recorded as a time history on an Alcoscript pen

recorder for subsequent digitisation (using a CETEC pencil follower) and analysis by computer.

Circulating Water Channel Experiments

All results from the circulating water channel experiments were integrated

for 60 seconds and then automatically punched on to paper tape. The

results on the tape therefore consisted of water speed, X,

F' A' shaft

revolutions for one or more shafts, air temperature at force gauges, water temperature, longitudinal and lateral positions of the model and rudder angle.

The air temperature at the force gauges was measured because of the large variations in temperature found in their vicinity (5°C to 15°C during a day was not uncommon) and the sensitivity of the inductive transducers

within the gauges to such temperature variations. Air temperature was

therefore measured when a zero reading was made and during all subsequent

'runs' until the channel was shut down and a new zero value obtained. Gauge

readings were then suitably corrected for temperature.

3. Scope of the Experiments

Before describing the results obtained it seems appropriate to indicate the

scope of the experiments. The experiments and parameters measured are

summarised in Table 2.

The range of the major parameters h/T (water depth/at-rest draught) and

h/DB (water depth/flooded bank height) are given in Figure 5 for the

flooded bank experiments where it can be seen that a reasonable area of the h/T_h/DB surface has been covered.

4.1 Experiments iii Nue 2 Tpwing Tank

The surfacing-piercing bank experiments in the towing tank involved model 5233

Only and explored two áreàs rela±ing to the study of bank effects. These were

measurement of X, Y and N at variOus speeds close to a I in 4

straight bank at one depth afid varioUs distances off. These are

referred to below as 'steady state' results..

- Study of transient va2.ués of, X, Y, N, sinkage and t-rim as a ship

approaches a bank at an oblique angle to its coue n4 as a ship

passes a gap in a bank. The first of these experiments provided data on

bank rejection, relevant among other things, to the passage of a ship

along a curved canal; the second provided information of the rapidity

with which the effect of a small change in bank geometry is registered

in the force and monts induced on the ship.

The model was not lf-propelled for either Series of tests.

Straight sloping banks

CWC I in 4

I

Straight sloping banks

VI CWC 1 in 3

Straight flooded bank -tank

VI

I

Oblique bank = tank

I

Rudder angle varied?

I

Shaft revolutions varied? VI

Suat measured tank?

'I

Drift angle vaiéd - VI

Water depth varied?

I

I

Gpeed var-ied? / ,1

I

F range - CWC

nh 0.275-0.40 0.22-0.38

0.22, 0.34

-tank

hIT range - sloping banks

- cWc. 0. 1 6 '-O .52 1.207,1.554 0.2-0.55 1 .20 0.2-0.52 0.2-0.6 1 .299 - tank 1.207 TABLE 2

4.1.1 Steady $tate Results: BarikParallel to Ship's Track

ResUlts obtained with model 5233 close to a straight 1 in 4 bank ata depth!

draught ratio of 1.207 are shown in Figure 6.

It is clear from these results that X, Y and N all vary with distance off which shows, interestingly enough, that there is a slight increase in resistance when the model is close to the bank, an effect mentioned in reference 7..

It is the effect of speed on X, Y and N that is most significant however. The forces and moments shown have been non-dimensionalised according to

equation 1; they have therefore been non-dimensionalised with respect to the

square of the speed of the model. If the forces and moments were proportional

to the square of the speed, the results shown in Figure 6 should plot as values

which are constant with Fh, varying only with Y/B. This assumption has been widely used for bank effect studies in the past (see ref. 8 for example).

It is apparent from Figure 6 that is, over the _{'nh range} in question,

sensibly constant with speed; the same cannot be said for C. and CN however,

C gradually reducing in amplitude with increasing speed while the absOlute value

of increases with increasing speed at all Y/B.

It therefore appears that both sideforce and turning moment vary with speed raised to a power greater than two, this exponent itself varying with speed This is discussed further below.

The squat results shon in Figure 6 show clearly that both mean sinkage and

dynamic trim change with both speed and distance off The variation with speed

is well-known but the increase of both mean sinkage and trim by the head as

distance off is reduced is not without interest. It appears that at Fh = 0.26

for example mean sinkage increases by 25% and dynamic trim by 47% as Y/B is

reduced from 2.125 to 0.939.

4.1.2 Transient Result

Bak a

Angleto Ship's Track

Results of the time histories of X, Y, N, mean sinkage and dynamic trim as

ndel 5233 approached a bank at an angle to its track are shown in Figure 7.

The experiments were conducted by positioning a line of surface-piercing bank

Sections acroSs the whole width Of the towing tank at angles, , of 7°, 11° or

the bank across its path, and the carriage stopped as rapidly as possible so that the model stopped as close to the bank as possible without hitting it. Measurements were made continuously up to the time of' the rapid braking of the

carriage and they are shown plotted nondimensionall.y in 'Figure 7 with _an

abscissa scale of r, the straight line distance from the PP of the model

to the point on the bank which intersects the bow profile of the model when at

rest. This value of r is then non-dimensionalised ith respect to the

length of the rnodel.

The results are not without interest, and their behaviour as the 'bank is

approached is noteworthy. It is seen that for all bank angles the longitudinal

force increases and 'the sideforce becomes positive., indicating that the model is

bodily pushed away from the bank as it approaches. The turning moment also

becomes larger, the bow being pushed away as the model gets nearer the bank.

It is noteworthy that these effects

- do not vary as the s4uare of the speed for the two values of tested

as a coarison of the appropriate plottings 'in Figure reveals. - apparently increase with increasing speed

- are more marked when a is small.

It has been suggested (ref. 3) that such effects are explained by a pressure 'cushion' which builds up between bank and ship as the bank is approached; measurements of asymmetrical wave patterns which confirm the existence of such

a pres'sure wavnear the bpw have been shown in references 3 and 4. Indirect evidence that a Similar process is at work in the present series of experiments is given by the mean sinkage and dynamic trim results shown in Figure 7 where it is seen that in all cases the dynamic trim changes from bow-down clear of the

bank to increasingly bow-up as r/L tends to zero. Tb-is effect is most

marked in the case of the dynamic trim measurements appropriate to a = 7

at F = 0.523

nh

Such a trim behaviour could be explained by positivc pressure wave at the bow which increases in size and lifts the bow as the bank is 'approached.

Furthermore, if a is small the wave would have a larger time to develop fully

as in this case the approach to the bank is more gradual.

*In this context a 'pressute wave' means a 'surface wave pattern et up beteen

ship and bank which (due to its asyetry about the ship's centreline plane)

However, in the interpretation of these results it should be borne in mind that, as the bank spanned the width of the tank, the model was effectively

advancing into a continuously narrowing tank, thereby experiencing iicteased

blockage as the bank was approached. _{This could cause the longitudinal force}

to increase as shown, but would not account for the change in. .sign of the

dynamic trim as the bank is approached _{Steps were taken to minimise this}

blockageeffectby ensuring that there was no presre.se.l at either.ed of the

hank but otily along the toe. It is probable however that some wave reflections from the bank were felt by the model probably accounting for the oscilLating

nature of the C, C, and traces for 70, 110 and 150 at Fh = 0.367.

Effect of a Gap in the ank

The sensitivity of the forces acting on a ship to the configuration of tIe

bank is shown in 'igure 8. In this case the bank model had two positions,

one (A) parallel to the track of the ship model and one (B) at _{angle, both}

separated by a gap (C).. The ship model was towed along the Ce rene Qf

the towing tank so that at point C, where the model banks were absent, bank forces and moments should arise only from the. tank walls equidistant from. the

model and should therefore cancel. Near banks A and B however, bank effects

should be felt.

The ship model was run at _{0.518 where the parallel bank A induced a}

bow-out turning moent and a rejection sideforce as shown by the force and

moment traces!. The effect of the gap C is dramatic for in this tegion both and CN drop from a high level to the expected zero value, to recover again

as bank B is approached. Changes are also apparent in resistance, mean

sinkage and dynamic trim in the vicinity of the gap.

It is noteworthy that the model moved only 16% of its length past the. end of bank A for the turning moment to reduce to zero ,which illustrates the

rapidity with whichthe ship would 'sense' changes in bank configuration.

The effect Of such a gap on ship, handling can be deduced from these results. To counter the turning moment induced by bank A the rudder would be toward the bank and the ship might have a slight yaw angle to help counter the sideforce. When the ship is at the gap C, the bank effects disappear and if the rudder

4. 2 _{Experiments in the Circulating Water Channel}

4.2.] General

The main reasons for cartying out bank effect studies in a circulating water

-channel have been mentioned above. its use allowed patetets to be varied

easily arid the flow and wave characteristics of the models to be studied more

easily than in a towing tank It has indeed been used to measure bank effects

before - see ref. 3.

Its use is however confirned to steady-state measurements with straight banks

parallel to the course of the ship model. It was necessary to ue the

cir'culating wätet channel in this way with caution; mention has already been

made of the growth Of a boundary layer over the false f loot and the model bank

giving use to .f low which accelerates along the orking .secti9n and may affect

the resultS. Further mote unsteadiness in the flow due to the 'end effect' of

the leading edge of the bank and its wave system coupled with any upstream

effects fro.the weir proted a preliminary study Of the steady state forces

and moments measured.

This study concentrated on two main effectS

- longitudiflal variations jri the flow along the bank

comarisOn o results obtained in the presence of boundary layer growth Over the: channel bottom and bank with those obtained in the absence of such effects in a towing tank.

The former effect was irives'tigated by simply placing the model at various longitudinal positions along the bank at fixed water depth, distance off and

flow speed and measuring X, Y and 'N. 'Plots of X, Y and N against longitudinal

position revealed that there was a region remote froth bank end effects at which

the forces and mOthents temairièd constant with longitudinal position. This

region was therefore assumed to have reasonable flow characteristics and it

F2

4.2.2 Comparison Lth Towing Tank Results

Results obtained for various Fli and are shown in Figure 9 Comparison

with the tank tesults shown in Figure 6 show that the overlap in Foude Depth

Number in the two facilities was unavoidably small. This was because

- the maximum Fh in the towing tank was limited due to the tendency of the

model banks. to move out of position as the model passed.

This

limitation was ignored for the parallel bank A in Figure 8 - the minimum F

h in the water channel was limited at

the water depth in question by the operating characteristics of the pump impeller,

Comparison with the tank results was further, complicated by the fact that the

blockage ratio (ratio of cross-sectional area of ship model to the waterway

cross-section area Ac) was different in the water channel compared to the tank

The appropriate ratios were, for model 5233 at hIT = 1.207wit a I ii 4 bank:

TABLE 3

-where m the blockage ratio is given b

m = B.T/Ac (3)

Three values of m in the towing tank are shown in Table 3; these arise

from the fact that to change Y0 the banks were moved laterally rather

than th hipthode1 which remained on the tank céntreline for all runs.

A correctiOn for these discrepancies in m was made using the following

blockage corrector whose derivation is given in the Appendi.

.+

2(1_B/w2)(11x12)l 2 = 0 (4) .(1-E/w2). ' _'v2) 2 Towing tank: Water channel: m 0.113 0.104 0.152 Q.090

h = water depth

F

FrOude Depth Number,

w/B = 1/(rn.h/T) _{a mean waterway width ratio}

m

= blockage ratio K.. = a correction factor 13 B = ship breadth K.. 13

It is seen that the blQckage corrector has beeP used in exactly the same manner

as the more conventional use in resistanée studies; _{it assumes that C, C}

and CN a±e all changed if e flow velocity is changed due to blockage while

the speed of the ship over the ground is unchanged. The. effect of blockage

on the free wave system of the model is ignored, which. is probably not unrEasonable provided the speed is kept low.

Values of C, C and were obtained in the ater channel at fiVe values of

Y/B as shown in Figure 9. The parameter Y01w ias chosen to indicat.e distance off for comparison with the tank tesults. where

Y/w =

Y/B.B/w

Y/B.

1/.(m.h/T) ...(5)

Such a parameter, relating distEncE off to ameanwaterwa3r width (chosen so that

wh = A) accounts for the change of waterway geometry as blockage varies.

The results of Figure 9 were therefore used to obtain c, and CN values

against Fnh by interpolation. The resultant curvEs at Y0/w values of

0.044, 0.118 and 0. 232 are plOtted in Figure 10 where they are compared with results obtained from the towing tank.

subscripts I _{an4 2 refer to values at waterways} I and 2

The Use of this corrector was as follows:

Copute F2 Using equation (4) Find C, C.2 and CN2 at P2

Correct C2, C2 and CN2 tO C. ' C

2)

etc

The tank: results have been corrected uing equation (4:) and it is seen that

at.Y/w = 0.118 and 0.044 the agreement between the curves is good with

no apparent- continuity -at Y/w.= 0.232. The values however shOw good

.cont.inuity.for-Yjw.= 0.232.-and 0.118-with poor contirnilty at YJw 0.044.

However there.was some doubt. about both tank and channel results .at Y./w

- .

- 0

0.044 due to the f-act that the rnodel was close enough .to the bank to

ground occasionally

with

one bilge.. . --

--The values have been further corrected by means of a longitudinal buoyancy

corrector as- used in wind tunnel. tests (ref. 9) and which takes some account

of the longitudina-1 velocity gradient. in the channel due to boundary

layer

effects. . The correction to the measured drag values takes the form

SR = pV(1+k. )v. &v

... (6)

x

where = displacement volume

.k longitudinal inertia coefficient

-x

av/ax =

longitudinal velocity gradient

terms of-

c,

equation

(6)

becomes -- .

- -- .

:..

7)

B.T.

vax

which was used with an assumed value of k for h/T. = 1.2. of 0.25 and yielded

the corrected water channel C values shown in Figure 10 It is seen that

in general reasonable continuity of the measurements obtained in both tank

and water channel was obtained. .

Values of computed using measured deepwaer. resistance va1ue- and an

extension of L-andwéber's method (ref. 10)- are also shown on Figure 10.

The agreement with the Y/w = 0.232 C values after correction -i-s seen to

be ver good over the range 0.2 < F < 0.35. the measured values differing

nh

from those calculated for greater 'Fh. This ]ds further support, tO the

contention that measurements made in the water channe). agreed after correctiOn

with thOe made -in the tank. The L-andweber callaion applies

in

general

to the- case of a ship on the centre-line of the canal, which in the notation

of this report

would

be

at

a Y0/ Valüe'of 0.5. 'In such - -case itis

-conceivable that the, variation of' C

with

would be les pronounced- than

-x

nh

that shOwn in, Figure 10 and better agreement wit-h the estimate at the higher

Reasonable confidence in the use of the.watr channel to in-estigate bank

effects was Obtained by the above study,. but a final check was made using

model 5238, a geosim Qf. model 5233. - The small size of. this model etèndëd

the blockage range of the water channel to include that of the tank,sô that

a reduced-scale version cf the tap.k experiments was carried out in the water

channel. In this case the vertical tank wall was represented, at an

appropriate. distanôe from the sloping bank, by a portable pressure-sealed wooden wall constructed for the purpose.

Measurements obtained with this small, model at Y/w 0.128 are shown in Figure 6 which show good agreement with t-hé.tank results f Or t-he.two speeds obtained.

Summary

The results of these preliminary investigations yielded sufficient confidence

in the use of the circulating water channel to study bank effects. It is

accepted that comparisons between tank and channel were not exhaustive, but sufficient evidence was obtained to show that the channel results were not drastically different in nature and magnitude from those obtained in the tank arid that, at the very leastuse of this facility would provide a convenient and valid meàns .o.f comparing the effect of major pareter changes.

4.2.3 'The ffect of Speed

It is clear from both Figures 9 ad 10 that indications of the variation of

and CN with speed shown in the tank results are borne out by the water

channel results. . The variation with, speed. does not follow a v2 law at

4iiy

but the lOwest speeds although: C., dOes appearto adhere to a .v2 law for a

greater speed range than

To investigate this variation further it was 'ssumed that the turning moment N

could be represented by

N

_{A(Fh, Y0')}

(8)

where the exponent n is a function 'and possibly Y/B while the

'constant' A will probably be a function of both

Values of n and A were fbund from the esured data by using a logarithmic

method. Taking logarithms of equatiOn (8) we have

ln N in A + n in v, ... (.9)

A computer program was written to fit a least squares straight line to

in N/in v data, the gradient of this line yielding n and its intercept with

the in N is giving a value of A. Data were obtained by digitising the curves

faired through the. experimental. results, values of

₄

and. n being cOmputed

at each point and plotted against

The results of this exercise applied to both tank and water channel data are

shown in Figure 11 together with the parameter L/x defined as

(Cy.Lpp)/(CN.B) ... (10)

This parameter was chosen to explore the variation of C, with CN and to. see

whether a simple relationship analogous to that in ref. 8.existed. It also

had the merit of having the value of zero when C. crossed the F. axis to

1 nh

become a rejection rather than an attraction force. This feature is notable

in Figure 9, bearing out indications from the tank experiments, and shows. that

at Fh values greater than about 0.4 the ship model was bodily rejected from

the bànk,as well as being turned away.. This is presumably due to the presence

between the bow atid. the bank of a pressure. wave which increases . its effect with

increasing speed gs mentioned above.

This explanation may accQunt for the variation of the speed exponent n

hon

in Figure 1I.which is close to 2 for F < 0.3 but thereafter rises to values

nh

in excess of 6, a feature that might be. expected if wave effects are significant. In this context it should be borne iti bind that a sloping bank differs from a vertical bank of the type considered in previous studies in that the water depth

over the bank is of, course changing in the ydirection. Effects on the wave

system of the ship might therefore be expected to be more complex than the

simple 'image' effect of .a vertical .bank. .

4.2.4 Effect of Bank Slope

The effect of barik.slope is shown in Figure. 12 where values

of C, C

and CN

Obtained with. a bank slope of 1 in 3 are coare4 with those obtained with a

bank slope of I

1n4.

In both cases the measurents were made with model

5233. It, is ie4iately apparent that the bank with the steeper slope

in away which differs from results obtained with a I in'4 bank. Th

exponent ri in equation (8) appears, for a given Y/B and Fh, to be less

for a I in 3-bank compared to a

I in 4. This is borne Out by results of t1e

analysis of ri, A and LJ shown in Figure 13 which may be compared with

Figure 11.

It is clear also from Figures 1.2 and 13 that C _{values tend to be more nearly}

constant with F wit-h the steeper bank and the- 'crossover' from attraction

nh

-to repulsion occurs at a higher Fnh vaiue

Further, it may be noted thatC- values at a given Y lB aid F are in general

X _o nh

smaller due to a I in 3 than those due to a I in 4 bank.

Finally, also shown i-n Figure 12 are iralues of C _{and CN calculated for vertical}

banks by. the method of reference 8 at the same w/B and hIT; _{it is seen that the}

1 in 3 bank values are not far removed frOm these constant values at-low F and

- - - nh

it would seem therefore that the- steeper t-he bank the more closely do Y and N

follow a v2 law. -

-- 4-.2..5 Effect-of Advance-Coefficient and Ru4der -Angle

The effect of the- proximity of a bank on the behaviour of both rudder atid propeller(s) was investigated, using-the single--screw model 5233 and the twin

screw model 5098. Both models-had a single cent-reline rudder and model 5233

was run at several Y/B values whereas model 5098 was run -at one Y/B only.

The, relevant parameter values are shown in Table 4. -

-Model h/ T Y /B 0 - 5233 - 5098 - 1.207 . 1.299 -0.298, 0.545, 0.792, 1.040 1.287 0.90 TABLE 4

-For all expe-r-iment-s the screw revolutions- n- were var-ied at --fixed rudder

- -m -

--angles thereby allowing a study of the effect of the apparent advance

coefficient J where - -

--- 'V

-J = v/ti. .D

--- ...'(ll)

-Single Screw Model

The results obtained with the single screw model are shown in Figure 14 where

and are plotted against J for fixed rudder angles S of 15° and 300

toward the bank. The parameters cSC, and CN are defined as

5C = C,(5°, Fh,nlfl, Y/B) -

C(0° F

n, Y/B)

= CN(, Fh,fl,

Y/B) - CN(0°, F

_{nh m}

, n , Y₀

IB)

As shown in the Figure the results for both 5C,1. and lie on two well-defined

curves for the two rudder angles used. There is no obvious variation with

Y/B suggesting that it is appropriate to add linearly the sideforce and

turning moment due to rudder angle to those induced by the bank to obtain the

total sideforce and turning moment acting on the ship model. No obvious effect

of the bank on the force and moment induced by the rudder of a single screw ship

is indicated even though one

YIB

value was used in which the bilge of the model

was very close to the bank. This finditg has applications in the mathematical

modelling of ship-bank interaction and suggests that for this case at least interdependence effects are negligible.

The effect of J is however shown to be large and the greatly enhanced sideforce

and turning moments at low show the advantages to be gained by increasing the flow over the rudder with increased screw revolutions at a given speed.

Twin Screw Model

The twin-screw model 5098 had its maximum rudder angle increased from the usual

value of 350 port or starboard to 700. This enabled the effectiveness of such

large rudder angles to be assessed for low-speed shallow water manoeuvring situations.

The twin-screw ship with a single centreline rudder is unusual in that for most

manoeuvres the rudder blade is not situated in the screw race. The significant

parameter in this context is the angle 5 which is the rudder angle at which

the trailing edge of the rudder just touches the edge of the 'geometrical'

screw race. For the model in question this angle was just under 280.

In the experimants, measurements were made of longitudinal force, sideforce and

turning moment acting on the model at zero yaw under the following influences:

Propellers stopped, ru4der at fixed angles from 70° port to 70° starboard. Propellers running at ship self-propulsion point, rudder at fixed angles

from 700 port to 700 starboard.

Rudder fixed amidships, port screw revolutions increased in increments to full ahead while starboard screw revolutions maintained constant.

As for (3) but rudder at 35° to starboard.

Rudder fixed amidships, starboard screw revolutions reduced in increments to full astern.

As for (5) but with rudder at, 35° to starboard.

In all experiments the caflal bank was to starboard as usual at a value

of 0 90 The results obtained are shown in Figures 15 and 16

From Figure 15 it is clear that the effect of. the screw,race on initial turning

moment. is negligible for -20° <' +20° where & is defined as positive to

star-bàard.. This range of rudder angles is somewhat less tian .te calculated value

of suggests', so that some screw race/rudder inteaction occur before the

rudder trailing edge intersects the edge of the 'geometrical' screw race.

With the propelleis stopped, th rudder stalls at +35° and produces no further useful turning moment at lager angles.

With the propellers running' the rudder continues to produce an increasing

turning moment and sidefOrce up to = ±60°, after which both Y and N reduce

but are still some 3..7 times the maximum moment and 2.7 times the

ciim

sideforce obtained with the propellers stopped. This bears, out results given in

references 11 and 12 and shows clearly the benefit to be gained frox having all or part Of the rudder acting. in the screw race.

Resistance increases bysoê 8% with the rudder at +600 and the propellers stopped.

It is clear from Figure 16 that large turning rnoments and sideforces can be induced on the ship by a combinatipn of differential propeller revolutions and

rudder angle. It is apparent from Figure 1St-hat the batik induces the usual

negative (bOwaway) initial turning moment and small sideforce at 00.

In' order to counter this the ship handlet st induce a positive correcting

turning moment (t9ward the bank) and subsequently a &light angle of yaw to

positive turning moments in Figure 16 are likely to be of use in low-speed

rnanoeuvring.

At 6 = 0, increasing revolutions on the shaft farthest from the bank while

maintaining constant revolutions on the bther produces the required positive

(bow-in) turning moment together with a sideforce away fromthe ba±ik.

Increasing the revolutions on the shaft nearest the bank (while maintaining

revolutions on the other constant) produces an increasing bowaway taming

moment.

With 6 350 _{to starboard, increasing revolutions on either port or starboard}

shaft (while maintain.ing _{onstànt revolutions On the other) increased the}

bow-in turning moment and repulive sideforce. _{Increasing revolutions on the}

port shaf.t gives about 36% _{re bow-in turning moent than that obtained by}

increasing the :starboard shaft revolutions.

This result shows the importance of the acton of-the rudderin _{deflecting the}

scre race to produce a turning moment..

board shaft with rudder amidships induces repeating the exercise with the rudder at bow-in turning moment.

Increasing revolutions on the star-a bow-star-awstar-ay turning moment while 350

towards the bank produces a powerful

By far the 'largest sideforces and turning moments, coupled with a longitudinal force which will slow thê ship, were produced with the port screw running ahead

(at ship SP) while the starboard shaft revolutions were prOgressively reduced

until running full astern. There was a slight additional effect whn the

rudder was at 359 starboard.

There was a plateau in the turning momentand sideforce. measurements for

-1.5 < 1/J < 1 .5. In other words the starboard screw had not started to

V -- -

-'bite' astern in this range and would produce thE. same effeôt if stopped

altogether. ,

The starbard scrèwstart-ed to 'bite' at 1/J and with further inctease

- v

in astern revolutions the induced turning moment and sideforcé increased rapidly to very large values.

4.2.6 Effect of Screw Bias

An opportunity arose in the experiments with the single screw model 5233 to

measure, for both bank slopes., the screw bias at d 00, defined as:

6Cr' = C(0°

'nh %'

Y0/B) - C(0°

nh

Y/B)

tSCN' = CN(Oo _F

_{n, Y/B) - CN(O°,:Fh 0, Y/B)}

(13)

The results obtained, plotted against J are ShOwn in Figure 17, fo both the

I in 4 and! in 3 banks. The results apply to the range 0.22

< F < 0.45, and

the bank was to starboard.

The results show that for the.1 in 3 banks, a reducing J resulted

in

an

increased

while 1N'1 shows no obvious trend with J There also

appears to be evidence for some effect of.Y0JB. at a g-iven for the

I in 3 bank, both and CN' becomjng mOre negative as Y/B was reduced.

This is borne out by sOme of the 6CN' values for the 1 in 4 bank, but the trend

of the results is obscured by experimental scatter. The scatter

is

large

because both '

and CN' are small quantities derived from the difference

of two large quantities,

An interesting feature of the results shown in Figure 17 is the fact that in

general SC' is negative (ie away from the bank) for most becoming

increasingly so at low J. This negative bias force occurs together with a

negative _cN so that the bias of the right-handed screw is moving the stern toward

the bank ie to starboard. This would sugges that a C' to starboard

(ie positive) should result, but at low J. this was not the case; the

resulting Cf' away from the bank may in ths instance imply that CN' and

did not simply result from screw bias alone, but also from some Overall change in the flow and wave system while the screw was turning.

4.2.7 Effect Qf Yaw Angle . .

The final series of experiments carried out in the circulating water channel

in-vestigated the effect of a sloping Cl in 4) bank on the sideforce and ment induced

on

_a

yawed model at varioUs Y0/Ba Two series Of experiments were carried

out, one with model 5233 yawed at an.angle of 3.62° in the water channel with no bank present and the other with the bank present and the model held at the

same yaw angle and at various distances off. The distance off in this case.,

Y', is defined as the perpendicular distance of the model centreline at the

Unfortunately before a direct comparison could be made bEtween the 'with' and 'without bank' measurements some allowance had tO be made for the

additiOnal blockage introduced by the presence of the bank in t1e working

section of the water channel. o do this e4uation 4 was used in conjunction

with the projected beam of the yawed wodei.

Results are shown inFigure18 for Fnh values from 0.25 to 0.45 and various Y/B at the usual h/T of1.207. Als.b shown on this Figure are results

corrected to the bloakage in the chãnnél when the sidebank was present.

It is seen that both idefô±ce and turning meht in the presence of the

bank are larger than those obtained without the bank

It is tempting to assume that the sideforce and turning rnent on a yawed ship

in the presence of a bank can be obtained simply by the linear addition of the values obtained with a yawed ship above and bank forces and moments

obtained at zero yaw'.

To test this asstption values of C and CN at Fh values of 0.3, 0.34. 0.38

0.40 were lifted from the faired curves in Figures 18 and 9 and linear

additons carried out assUng that. the approp±-iate Y/B tO take t.ias in fact as this might allow for any extra tendency of the stern to be sucke4

toward he batik. The results are shown in Table 5.

TABLE 5 , nh

Y 'lB =1.040

-0.545

c diff _{CN diff} diff CN diff

0.3 26.0% 19.6% 28.1% 16.6%

0.34 27.4% 16.2% 27.4% 11.7%

0.38 22.1% 6.7% 13.5% 5.3%

0.40 26.0% 1.6% 12.7% 2.2%

The percentage figures in Table 5 are defined as

C diff C

(yaw+ bank)-C(bank)

+ bank) similarly for CN diff.

C (yaw

100 .. (14)

It is clear from this that a straightforward. linear addition of fOrces and moments from the separate sources is not adequate to cater for the changed

flow and wave system around a yawed ship close to a bank. It is possible

however that such an assumption might have limited application in ship

simulation work in which case the C and CN values due to the bank should be

computed at Y'/B to take some account of the low pressure region between

stern and bank causing the stern to be sucked toward the bank.

5. Results Obtained with Flooded Banks

The scope of the flooded bank experiments has already been indicated in

Figure 5 where it is shown that an area of the h/T : _h/DB

_p1a

has been

covered by radial lines in the ranges 1.1 < h/T < 2.3, 0.74 < h/DB < 4.06.

There are many gaps in this coverage, but there sufficient data to obtain

by interpolation values of bank forces and squat over a reasonable range of

design parameters. Clearly the part of the surface for which h/DB < 1 .0 relates

to surfce-pierc-ing caflal or river banks and is generally coveredby remarks made in section 4 above.

The results obtained are shown in Figures 19 to 41 which comprise values of

and CN plotted against Fh in Figures 19 to 33, values of longitudinal force

C in Figures 34 to 37 and values of mean sinkage and dynamic trim in Figures

38 to 41

5.1 Effect of Spee4

Si4eforcê

and

Turning Moment

It is clear from Figures 19 to 33 that, as with surface-piercing banks, C and CN

measured in the presence of flooded banks vary as speed raised to a power which

is not constant but changes with Fflh. This general statement does not apply

however when both h/DB and h/T are large, as in Figure 28 which shows

results obtained at one Y lB with model 5233. In this case both C and C

°

were sensibly constant over the range 0.2 < Fh < 0.46 suggesting that a v

The rest of the results have been analysed to give A, L/x and n using the method described in section 4.2.3 arid typical results are shown in Figures 42

to 44. The results in' these figures show the following:

(a)' The exponent n rises gradually from a value close to 2at the

lowest F to a value of 5 or 6 at an F of about 0.5. This may be contrasted

nh nh

with the behaviour with speed noted in th presence of a surface-piering

bank shown in Figures IF and 13 when, in the presence of higher 'blockage and a

1 in 4 barik,the exponent rose from' about 3 to abbut 7 over an Fh range from

'0.28 to 0.40 ' It would 'appear therefore that n

is sensitive both to bank

geometry and blockage (or waterway width at' a constant depth).

In Figures 42 and 44 it is seen that the variation of

n with

for each model is similar for the two'h/T, 'h/DB conditions shown. This is

not borne Out by the results in Figure 43 for model 5233; the trend is

similar, but a shift occurs as h/T is changed.

In all c'ases at the higher h/T value the Lix values are negative over

the whole 'Fnh range studied. At the lower h/T t'hey are positive for the whole

range or sho a change of sign (Figure 44). It also appears that 'in general

the change in sign of 'L/x from negative to positive occurs 'at an Fhvalue

which increases as h/T and h/DB increase.

Cd) :

might be expected at'the lower h/T and h/DB values the constant A

is in general larger for a given Fflh and Y/B compared to the larger h/T.

In general A varjes'with F

more atthe

lowerh/T.

nh

Longitudinal Force

The longitudinal drag fOrce Is seen in Figures 34 to 37 to vary roughly as the

square of the speed over

the Frane inquestion with the following exceptions:

'(a) ihen h/DB is large ' h/T 'is l and F hS greater than 0.5.

This

occurred with model '5338 as shown in Figure 37.

(b) when h/T is small and h/DB is less than unity as shown in

The results for odel 5237 do not always show clear trends and this is probably due to the very small size of the model which makes accurate and reliable measurement of resiStance difficult due to the possibility of the

presence of linar flow over the model. _{The Reynolds Numbers for this}

5 5

model ranged from 3.4 . 10 to 8.0.. 10 so that transitional or lamLnar flow,

particularly at the lower Fh values, is likely. _{Although this probably would not}

have

a serious effect on sideforce, turning moment or squat measurements, all

of which are caused predominantly .by normal pressure rather than viscous

(tangential flow) effects, it would have a profound effect on drag measurements.

Squat

It is apparent from Figures 38 to 41 that no unusual effects of speed on mean sizkage or running trim occurred in the results.

5.2 Effect of Hull Form

No results were obtained at identical hIT and h/DB values with different

hull forms, but from, the results some general 'statements can be made.

The, fine form model (5237) showed extremely large negative (bow away)

CN values, together with negative (repulsion) c values at an h/T = 1.105,

h/DB = 0.737 (Figure 19). The fuller form model (5238) in a similar situation

(hIT = 1..Q9, h/DB = 0.939) although showing reasonably large negative CN values

had. values which were positive (attaction) at low

nh changing to negative

as Fh increased (Figure 29). This type of behaviour is presumably associated with the type of pressure wave 'cushion' built up between the bow and the bank which in both of the ahove cases was surface piercing.

For the same two models' at a higher hIT the differences due to hull form

are less obvious. 'For example, model 5237 at h/T=1.671, h/DB=1.11.5 (Figure 22)

shows CN values slightly more negative at a given Y0/B than those from model

5238 at h/T 1.500 h/PB = 1.289 (Figue 32) while the C values are of a

Resistance values measured in the preSence of foodéd banks seem

ingeneral to be close to those predicted using Schlichting's. théthod of

referen:ce 13 This is shown in Figure 35 where resitance coefficients

for shallow water in the absence'of banks and calculated using deep watet resistance/speed values measured for model 5233, are seen to agree. reasonably

well with measurements made in the presence of flooded banks. This suggests

that, although the h/DB value iS undoub'tedly having so effect on resistance

(see below)thegeneräl features ofresistance due to the hull form ii

question are predictable using known methods.

Similar statements apply to the squat measurements. In Figures

38, 39 and 40 values ofmean sinkage and dynamic trim coefficients,

calculated using the method of reference hi, are shown in which it is seen that no unexpected behaviour occurs in the results due to hull form alone.

5.3 Effect of Y/B, h/DB and h/T

Distance-off, Y. lB --.

0

These experiments confirm the indications from other work at NMI and elsewhere that with flooded as with surface-piercing banks, reduction of distance off

increases turning moment, resistance and mean sinkage.. Sideforce is also

altered and shows a greater tendency to change from attraction to repulsion

with increasing speed at low Y/B.

The behaviour of running trim at small Y/B is interesting, for in some

This is perhaps caused in a similar way to the sae effect noted as model

5233 approached an oblique bank (section 4.1.2).wbe it was assumed to

be due again to the pressure wave between bow and bank. .

it .is of. some interest to note that this behaviour, is not apparent when model

.5233 was partly over.the slope of the flooded bark (Figure 39, h/T= 1.300,

1.502. 1.695. tO 2.272. Y/B = 0.218) when the rurming trim by the head

continued to increase with increasing Fflh. This would. be expected over such an

instances C is seEn to become less negatiVe (by the head) as increases

when Y/B is small (See for exaple Figure 38 at h/T 1.539, 1.671, 1.934,

Fnh range in ordinary shallow water with no banks present whidh suggests that in such a case a lesser pressure cushion exists between bow and bank.

This appears to be borne out in part by the and CN measurements in

Figures 26 to 28 when values Of CN and show no greater tendency to change

With _{'nh at}

Y/B

0.218 compared tO Y/B = 0.455.

This did not occur however when models 5237 and 5238 operated over the

bank slope at Y/B values in the region of O05 (See Figures 22, 23, 32, 38, 40)

Complications arise in this case because the h0/T (where h0 is the water depth

above the bank = hDB) is much smaller than was the case for model 5233 as

Table 6 shows:

TABLE 6

The hJT values for models 5237 and 5238 are so low that draw-down associated

with the interaction of the model wave system and the bank caused the local h to disappear teorarily so that the models were running close to a local

surface-piercing bank with consequently large C, and CN values. This was

not the case with model 5233 where the draw-down was never enough to expose

the top of the flooded bank at Y/B = 0.218.

-Water Depth and Bank Height, h/DB

Values of C, and CN at fixed values of h/T, Y/B and _{'nh are} shàwn in Figure 45. These have been obtained by cross-plotting from the model data (ignoring any hull-form effects not accounted for by the non-dimensionalisation) and show

that at a given h/T and

h' increasing h/DB reduces the bank effects.

This is not surprising and shows hOw flooded bank. effects vary from the

large canal-type effects at h/DB < 1 .0 to no effect at all a _{h/PB +}

and the banks disappear altogether.

Model h/T

hIT

5237 1.671 0.172 1.934 0.435 5233 - 1.300 0.765 1.502 0.967 5238 1.500 0.336

Similar effects are apparent when drag fOrces are considered as shown in

Figure 35 'for moaei 5233., Shown in this figure are resistance values measured (from reference 6) and calculated (ref 13) for open shallow

water. _{It is clear that for hIT =} 1 .099, h/DB 2.053 the drag values.

measured in the presence of a flooded bank depart re from the 'no bank'

values than in. the case at hIT = _{.5, h/DB} 2.808 when all results are

practically co-incident. The good agreement between measured and' predicted

shallow water resistance values is of some incidental interest

Water Depth to Draught Ratio, hIT

Only two sets of experiments allowed the effect of h/T at óOnstant Y/B and h/DB to be studied arid these were for models 5237 (Fig 23)

and 5238 (Fig 32). Results are shown in Figure 4:6 for h/DB I .29,

Y lB = 0.49 and F = 0.25 and 0.50. It is interesting to note that

o

nh

' .

increasing hIT while the height of the bank remains a constant proportion of the depth of the water, reduces the magnitude of both the sideforce 'and

turning moment acting on the ship. This indicates once again the importance

.f hIT as., a parameter, the changes in and CN presumably being due o

changes in the flow under as well as' around the model.

It should be noted that the lines drawn in Figures 45 and 46 'are simply to indicate the underlying trend of the results and are not meant to imply that the trend is necessarily linear.

6. General Discussion .

6.1 Channel Dimensions

The experiments descrjbed above dealt with a bank to one, side of the ship only. When the channel under consideration is wide, the results shown

here could be used directly. However in most cases of interest the

channels are cornparativcly narrow and some account should be taken Of this.

6.1.1 Canals

When h/DB < 1.0 the channel. becomeS a canal. In such a case there will be

a considerable increase in blockage from the effectively zero value when

h/DB > 1.0. Even a small positiVe h valuewill have a significant,

effect on resistance, lateral forces and ments, sinkage and trim as mentioned

When the channel has become a canal. however, resistance may be. estimated using the metho4 of reference 10 aüd squat could be estimated using data from

reference 15 for example. Values of and CN for canals with vertical

banks can be estimated directly from reference 8, but the data given in

section 4 above cOuld be used if the banks are sloping. In order to do

this some account should be taken of blockage using equation (4) and the

effect of the other bank. Norrbin in reference 16 and elsewhere shs that

C and CN for two banks can be estimated from data obtained for one from

C2(Y0/B) = C1(Y0/B) - C1(w/B-Y/B)

(Y/B)

_cN2(w/BY/B)

where w is the bottom width of the waterway.

this could then be used to compute C and CN for a canal.

6.1..2 Channels

It would seem from the results given above that resistance, sinkage and

trim can be estithated as a first approximation from known methods for shallow

water. Some allowance may than be made for h/DB using the experimental

results given above.. For c,,1, and CN values in the presence of two banks

direct use of equations (15) may be made without the need for blockage correction.

6.2 Use of Rsults in Channel/Canal Design

A method for the design of a canal carrying one-way traffic is outlined in

reference 17. In this reference the overall design procedure is as shown

in Figure 47 and the detailed design of the canal cross-section was con-veniently represented as a spiral as shown in Figure 48.

It would seel appropriate to adopt similar procedures for a dredged channel with flooded banks using the data described above together with the results of other investigations carried out as part of the Ship Behaviour Study.

The idrtance of proper design is discussed from an economic point of view in references 18 and 19 and it is clear that considerable savings can result from a proper balance being struck in design between the necessity to provide width and depth adequate for. safe navigation without being so wide and deep as to need excessive and unnecessary dredging.

7. Conclusions

As a result of the model investigation described above, the following main conclusions can be drawn:

Sideforce and turning moment induced by a sloping surface-piercing

or flooded bank to one side of the model did not always vary as v2. For

large hIT and h/DB a v2 law applied but at lower h/T and hIDB values, turning moment varied as speed raised to a power sometimes in excess of 5 while side

force changed from attraction to repulsion with increasing speed. This

behaviour was assumed to be due to a pressure wave between the bow of the model and the bank.

The circulating water channel can be used to study bank effects.

Linear addition of sideforce and turning moment due to the bank and those due to the rudder applies regardless of distance off.

When approaching a bank at an angle to its course a ship experiences an increasing pressure wave between bow and bank which pushes the bow away and can cause a bodily rejection from the bank.

The response of the measured drag, sideforce, turning moment and squat to a gap in the bank was very rapid.

Resistance and squat both increase as the distance between a ship and a bank is reduced.

Increasing shaft revolutions greatly adds to rudder effectiveness

for a single screw ship.

Rudder angles up to +700 were effective in a twin-screw, single rudder model provided the propellers were running.

The slope of the sideforce and turning moment curves plotted against rudder angle changed when the trailing edge of the rudder began to enter the screw race for a twin screw, single rudder model.

The sideforce and turning moments induced on a yaed módeL near a

surface-piercing bank can be obtaihed approximately by a

l'inea±.

sum of the

force aTnd moment or the yawed model and the force and moment induced by

the

bank

at the appropriate distance off.

For flooded banks, increasing:water depth to bank depth ratio h/DB, at constant hiT reduces the induqed Sidéforce and turning mOment. The same applies with an increasing h/T at conStant hIDB.

References

1.

DD

I W: 'The PhysicalCauses of Interaction and its Effects' Proceedings of the Nautical Institute Conference on Ship: Handling, Plymouth Nov 1977

2.' MOODY C G: 'The Haid1ing of Ships Through a Widened and

Asymmetrically-Deepened Section of Gaillard Cut in

the Panama Canal' report 17O5, 1964

G LJNE Ret al: ''The Performance of Model Ships in Rèstricted Channels

in Relation

to

the Desi of a Ship Canal'

report 601, 1948

KOSR J:

'uction Effect of Canal Banks

on Ship Behaviour'

Deift Hydraulics Laboratory Report 91, Sept 1971

5 NORRBIN N H:

'Bank Effects on a Ship Moving Through a Short Dredged

Channel' 1OthONR NaVal HydrodynamjcS Symposium,

MIT, June 1974

DAND I W:.

'Some Measurements of Interaction

etween Ship Models

Passing on Parallel Càurses' NI TM32,

April' 1979

GRAEWE H:

'Ship's Resistance During Canal Passage'

Quarterly Bulletin of PLANC, vol 2, No. 4, 1970, p.23

8 SCHOENNHERR K

'Data for

Estimating Bank Suction Effects in

Restricte4 Waters on Merchant Ship Hulls'

10 LANDWEBER L 'Tests of a Model in Restricted Channels' DThB report 460, May 1939

11. COMSTOCK J P (ed): 'Principles of Naval A±chitèctute' ASNA, New York,

I967 Capter 8, pp 463-606

12 DAND I W 'Hydrodynamic Aspects of Shallow Water Collisions'

'rans RINA vol 18, 1976,pp323-346

:13. ScIiLICHTING 0:

'Ship ResistancCin WàerófLiite Depth

Resistance

of Sea-Going Vessels in Shallow Water' Jahbuch dEr STG, vol 35, 1934, pp 12.7-148

DAND I W & FERGUSON AM: 'The Squat of Full Ships in Shallow Water' Trans. RINA vol 115, 1973, p.237

SJ0STQM c H: 'Effect of Shallow Watr on Speed. and Trim'

ASNE Journal April 167, pp 271-274

NORRBIN N H:. 'A Method fo the Pted:iction Qf the Manoeuvring Lane

of a Ship in a Chántiel of. Varying Width'

Syosium on Aspects of Manoevrability in Constrained Waterway.s,Delft, April1978 DAD I W & WHITE W R: 'Design qf Navigation Canals'

Syrnposi On Aspects of Navigab,Iity of Ccnstraiflt

Waterwas' Delft, ApiI 1978

STONBAM P R: 'Cost Benefit of Improving Port Entrance Channels'

Térrã et Aqua, International AssociationOf.Dtedging COmpnies, NO. 12/13, 1977, p.9

KIENITZ A: 'Economc EffeCt véness of InVeseñt itt Port Approach

channels' Terra et A4ua, tntërnatioflàl Association of

Dredging Coánies, No. 12/13, 1977, p.14

9. Acknowle4gements

The study described above was carried out as part of the Ship Behaviour Study for the UK Pepartrnet of Transport under the guidance of the National

Ports Council. Tie project officer was Dr1 W Dand who wrOte the report,

an4 the experiments were carried out by Mr G Taylor and Mr D B Hood with

10.

Nomenclature

A

_{COnstant.in N=Av1}

waterway cross-section area

B

mOUlded breadth of ship

Cx

longitudinal force coefficient =

C

sideforce. coefficient =.Y/pBTv

C1,

turning

.

ment coefficient = N/pB2Tv2

man sinkage coefficient

(S+S).1OO/2Lp

C1

dytiamic trith coefficient = (S+S)

_{. I 00/L.}

D

screw diameter

DB

bank height

Fh,.F

P-roude Depth Number v/v1

g

gravitatiohal acceleration

h

water depth

h

_{water depth Over flooded bank}

apparent advance coefficient v/n D

v

--k

_{longitudinal inertia coefficient}

correctiOn factor

length between perpendiculars

m

blockage tatio

n

exponent in NAv

n

shaft revolutions

n.

bank slope

t

aj.ght line distance from Ship PP to oblique bank

R

resistance

S

sinkags at fore and aft perpendiculars

T

meati draught

TFP, T

draughts at PP and AP

v

ship speed

w

mean waterway width

bqttom width of waterway

X, Y, N

lcngjtudinal force, sideforce and turning moment acting amidships

-

perpendicular distance from toe of bank to model ceritreline

a angle of bank to course of ship rudder angle

angle at which trailing edge of rudder just enters geometrical screw race

p water density

Appendix

A B1ocJage_ tor for canal_s

The well-known blockage correctôrs are generally Ued tO remove unwaited blockage

effects from resistance easurements bade On odel5 in a tank of finite width

and depth; their use provides results appropriate to water of infinite

width and depth. The problem posed here involves the correction of results

obtained in a canal of one blockage to results appropriate to another blockage;

the correction Ls ue to a change in width of canal at constant depth or change

in depth at constant width or a combination of the two.

The derivation of the blockage correctOr which follows is simply an extension of the well-known one-dimensional analysis of Kreitner (ref Al) also

developed by Conn (ref A2). tn Such an analysis the following asstptions

re made:.

(I) The flow can be considered as one-dimensional

(2) A ship moving at speed v in water of infinite extent experiences

a change in resistance when ving in confined water from the

increased local flOw speeds around the hull due to blockage.

In the analysis below we make the same assumptions with the modification that

a ship moving at v1 in a canal of blockage ratio m1 will experience

a changed resistance, lateral force and turning moment equivalent to

moving at a new Speed v2 itia canal of blockage ratio m2. The analysis

is carried out for a canal with vertical sides, but it has general applicability to canals of arbitrary cross section.

If a ship of breadth B and draught T is moving in a canal of width w

and depth h, as in Figure Al, we have from continuity, a5suing the.ship

to be stationary as the water streams past:

why

h-a-(w-B)hv1

where v1 is the mean local velocity at the ship

v is the undi.sturbed flow velocity

Now from Bernoulli's Equation 2 .2

-v

2g

Substituting equation A2 intO Al we have after some reduction i-.

_/-Ci-iW

F

ri-rn

F(1-B/w)ii

V1 _(l-B/w)F

where

F1 is Froude Depth Nber.=

...A3.

To correct from blockage m1 to we repeat the above analysis to obtain

a similar expression for

v2

which we call 8. We then eliminate .v to obtain

v18F1

1h1

cc

where subscripts now refer to canals I and 2 In practice it is unlikely that one-dimensional flow will give a good representation of reality unless blockage

ratios are high, so to allow for this an empirically derived correction factor

IC is included in equation A4 thus

F1 h1

8

=K

where in general K will be close to unity whenone-dimensioñàl flow applies.

Prom equation A5 and A3'and after some reduction weobtain

-P2

F

[22(1_/w2)(1_m2)]

+

21:

(I-B/w2)2

(l-BW2)

where y A5 I (l-B/w)

D-1f2(1B

h2

F1(l-B/w)

Fj2t1_m1_(14/'w'i)F'i2f21J

K.