passing ship flory

7/25/2019 Passing Ship Flory

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A METHOD FOR ESTIMATING PASSING SHIP FORCES

John F. Flory

Tension Technology International, Inc.

4 Tower Lane, Morristown, NJ 07960973-267-0871 ; [email protected]

INTRODUCTION

As a moving ship passes another ship, it exerts forces and moments on that ship. This

passing ship phenomenon is of particular concern in the design and analysis of ship mooringsystems alongside ship fairways and channels.

This paper uses results from several published model tests and analytical studies to develop a

method for estimating the forces and moments induced by the passing ship on the moored ship.Published results of earlier studies were difficult to interpret and apply. The new method is easy

to use and provides good estimates of the forces and moments imposed by passing ships.

BACKGROUND

Esso Research and Engineering Co. (ER&E), now Exxon Mobil Research and EngineeringCo., conducted several studies of the effects of passing ships on moored ships. Those studies

were conducted by others; I advised and vetted the studies and thus am familiar with the methods

and the results. Several papers published by others give some of the results of those studies.

Recently I used those published results to develop a method of predicting passing ship effects,which is presented in this paper.

Lean and Price

In 1969, ER&E conducted a model test program at the Hydraulics Research Station,Wallingford, UK in order to investigate passing ship problems experienced at an Esso terminal.

Some of the results of that test program were published by Lean and Price (1977). The moored

model represented a 250,000 dwt tanker. Models representing 17,000, 80,000, and 210,000 dwttankers were towed as various separation distances and speeds. Moored tanker motions and

mooring line loads were measured.

Lean and Price concluded that the mooring load was proportional to the square of the speedof the passing ship when the mooring lines were properly pretensioned and thus ... small

reductions in speed can produce significant reductions in mooring loads.

Prior to conducting those model tests, ER&E had developed a mooring analysis computerprogram based on simple force = mass x acceleration calculations, accounting only for dampingand added mass. An attempt to validate that computer program using the results of the passing

ship model tests made it apparent that the program did not accurately model ship dynamic

response. ER&E then abandoned the simple model and began developing a more sophisticatedcomputational model.


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Remery

In order to gather further information on passing ship effects, ER&E then conducted another

model test program, at the Netherlands Ship Model Basin (NSMB) in Wageningen, the

Netherlands. NSMB is now Maritime Research Institute Netherlands (MARIN). The mooredship modeled a 100,000 dwt tanker. The passing ships were models of 30,000, 110,000, and

160,000 dwt tankers. Three passing speeds and four separation distances were modeled,

although not for all ship sizes.Some of the results of that program were published by Remery (1974). Like Lean and Price,

Remery concluded ... that the forces and moments on the captive ship were proportional to the

square of the speed of the passing tanker. Remery also observed that ... the lowest mooringforces occurred when the ship was fully restrained. Lower mooring forces could only be attained

for a very soft mooring system, but very large motions would have then have to be accepted.

Remery also observed that plotting the measured forces and moments to a base of theposition of the passing ship relative to the moored ship shows that the character of the curves is

similar for the various sizes and passing distances of the sailing {passing} ship. Thischaracteristic allows time histories of forces and moments to be plotted with knowledge of only

the peak forces and moments, as will be demonstrated later in this paper.Remerys paper provided a number of such plots of forces and moments on the moored ship

against the position of the passing ship. These data plots are the bases for much of the analysis

reported in the present paper.

Muga and Fang

The NSMB model test results provided ER&E with some data for the analysis of mooring

systems subjected to passing ship effects. But a more general method of predicting passing shipforces and moments for various ship sizes and other parameters was needed as input to the

mooring analysis computer program then being developed. ER&E then developed a method for

calculating passing ship forces and moments. A paper describing that method was published byMuga and Fang (1975).

The Muga and Fang calculation method gives good agreement with the results of the NSMB

model tests. However, the method requires a special computer program, and thus it is not

suitable for general use.Like Remery, Muga and Fang observed ... the time pattern (or phase relations) of the

occurrence of the peaks and the sequences of the loadings are very similar. This suggests that

each loading function can be described by a single value of the ordinate, perhaps the maximum.They also observed ... the time pattern of the loading functions as predicted by theory are all

very similar to each other and to their corresponding experimental cases.

THE PASSING SHIP PHENOMENON

As a ship moving through a waterway passes a moored ship, it exerts time-varying forces andmoments on the moored ship. These forces and moments are caused in part by the waves

produced by the moving ship. But the principal cause is the movement of water around the

passing ship which exerts a Bernoulli effect suction on the moored ship.


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Conventions Used in This Paper

The nomenclature and conventions used in this paper are illustrated in Figure 1. These

conventions are the same as used by Remery.

The separation distance is measured between the sides of the two ships as they pass.The passing ship position is related to the distance between the two ships transverse

centerlines, measured along the path of the passing ship at a particular time. This position is

expressed as a ratio of that distance to the characteristic length, which is the average of the twoships lengths. That is:

1

whereLc = Characteristic Length

Lm

= Length of Moored Ship

Lp = Length of Passing Ship

The ships lengths used should be length between perpendiculars. Using overall length willresult in a distortion of the position graph and thus the time scale, but it will have little effect on

the calculated maximum forces.

The sign conventions for the forces and moments are shown in Figure 1. Positivelongitudinal force is toward the approaching passing ship (and thus opposite to the direction of

travel). Positive lateral force is toward the passing ship (and away from the pier). Positive

moment tends to turn the end of the moored ship which is closest to the approaching ship awayfrom that approaching ship.

Passing Ship Force and Moment Diagrams

Figure 2 shows plots of typical patterns of longitudinal force, lateral force, and momentproduced on the moored ship. The horizontal axis marks the position of the passing ship relative

to the moored ship, expressed as a ratio to the characteristic length, explained above. In each

plot, the vertical axis is scaled relative to the peak respective force or moment, thus making the

values dimensionaless.These force and moment vs. position graphs have been derived from Remerys published

figures. When Remerys longitudinal force, lateral force, and moment figures are

nondimensionallized in this manner, the respective plots for the various tanker sizes andseparation differences become essentially the same, allowing one set of graphs to represent all

cases.

Later I present empirical formulae for calculating the peak longitudinal force, lateral force,and moment, based on separation distance and relative tanker size. These peak values can be

used with the respective nondimensionallized graphs in Figure 2 to produce graphs of forces and

moment against passing ship position.Then, with knowledge of the ships lengths, and the speed of the passing ship, graphs of

respective forces and moment against time can be created.

Narration of the Passing Ship Phenomena

2

pm

c

LLL

+=


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Figure 3 illustrates successive positions of a passing ship relative to a moored ship andindicates the respective force and moment directions. In the following narration, the bow of the

moored ship points toward the approaching passing ship. Thus positive moment pushes the bow

away from the passing ship.

The influence of the passing ship is first felt when it is about -2 characteristic lengths away.Small negative longitudinal and lateral forces are first felt at about that relative position. When

the passing ship is about -1 characteristic length away, there is a peak negative lateral force. In

this position, the passing shops bow comes in line with the bow of the moored ship.The bow of the passing ship reaches the midpoint of the moored ship at 0.5 characteristic

length. At about this position, the longitudinal force reaches a positive peak, and the moment

reaches a negative peak, as shown in Figure 2. There is a strong tendency to draw the mooredship along the pier toward the approach direction and to draw its bow away from the pier. The

lateral force is essentially zero at this position.

When the two ships are side-by-side, the longitudinal force and the moment both dropessentially to zero. This is fortunate, because the peak positive lateral force occurs at this

position, tending to draw the ship away from the pier. This may seem counterintuitive, but theflow of water flowing from ahead to behind the passing ship produces a Bernoulli suction effect.

As the passing ship moves on, essentially a mirror image of the above effects takes place.At about +0.5 characteristic length, the longitudinal force reaches a negative peak and the

moment reaches a positive peak. These tend to draw the moored ships stern off the pier and to

push the moored ship in the direction along which the passing ship is traveling. Fortunately, thelateral force drops almost to zero by this point. However, because ship response lags behind the

applied force, the ship may still be drawn away from the pier at this time, permitting it to surge

along the pier without the restraining frictional effects of the fenders.When the passing ships stern is in line with the moored ships stern, there is a small negative

lateral force and a small negative moment tending to push the moored ship against the pier. Bythe time the passing ship has traveled one ship length beyond the moored ship, the applied forces

and moment drop to zero. However, because of the ship response lag force and also because of

mooring system dynamics, the moored ship may still be moving at this time.

Principal Features of the Passing Ship Phenomena

Typical graphs of passing-ship-induced surge and sway force and yaw moment vs. position show the following:

Longitudinal Force (surge) maximum positive longitudinal force occurs at a position of about -0.5 maximum negative longitudinal force occurs at about 0.4 magnitudes of positive and negative longitudinal forces are about equal zero longitudinal force occurs at about 0

Lateral Force (sway) maximum positive lateral force occurs at about 0 maximum negative lateral force occurs at about -0.9 the zero lateral forces occur essentially coincidentally with the maximum longitudinal forces

Moment


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maximum negative moment occurs at about same time as maximum positive longitudinal force maximum positive moment occurs at about same time as maximum negative longitudinal force magnitude of maximum negative moment is greater than that of maximum positive moment moment at time of maximum lateral force is nearly zero.

THE PASSING SHIP FORCE AND MOMENT EQUATIONS

Remery published plots of forces and moment for three passing ship sizes. The ratios of the passing ship to

moored ship sizes (expressed in dwt) were 0.3, 1.1, and 1.6. Remery published data for separation ratios of 0.12,0.23, 0.47, and 0.78.

Through regression analyses of Remerys published data, I developed empirical formulae for estimating passing

ship forces and moments. Figure 4 compares the estimates made by those formulae for the ship size ratios of 0.3,1.1, and 1.6 with Remarys data. In almost all cases, the empirical formulae agree with Remerys data within 5%.

The Lateral Force Factor and Longitudinal Force Factor are the respective forces (in metric

ton) divided by the square of passing ship velocity (in knots). The Moment Factor is the moment(in ton meter) divided by the square of passing ship velocity.

Following are the empirical formulae.

Longitudinal Force:

2

Lateral Force:

3

Moment:

4

where:Fx

max = Maximum Longitudinal Force, metric ton

Fymax

= Maximum Lateral Force, metric tonM

max = Maximum Moment, metric ton meter

V = Passing Ship velocity, knotsDR = Displacement Ratio, Passing Ship / Moored ShipSR = Separation Ratio, Distance Between Ships / Characteristic Vessel Length

The results of the equations may become negative at large separation distances, but negative

values should be ignored. The equations are expressed in metric ton (1 metric ton = 9.8 kN) topreserve the relationship with Remerys data.

Scaling of Dimensions and Forces

The above equations are based on the ER&E model test results reported by Remery, in which

( ) ( ){ } ( )[ ]06.0lnln28.071.0ln134.0171.02max ++= SRDRDRVFx

( ) ( ){ } ( )[ ]SRDReVFy DR lnln93.141.425.2168.12max +=

( ) ( ){ } ( )[ ]06.0lnln4.519.171651.247.02max += + SRDReVM DR


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Fruode law scaling was used to model a moored 100,000 dwt tanker with a length between

perpendiculars of 257 m. The above equations are based on non-dimensional length ratios andthus input does not need to be scaled.

But if the actual moored ship differs substantially from that modelled length, the passing ship

velocity and the resulting forces and moments used in the equations should be scaled

appropriately.By Froude law scaling,

5

whereVe = Equation Velocity, knotsLe = Equation Length, metersVa = Actual Velocity, knotsLa = Actual Length, meters

g = Gravity

The ship on which the equations are based was 257 m long. Accordingly, the velocity of the

actual passing ship should be scaled by the following equation to obtain the equation velocity.

6

By Fruoude law scaling, forces scale in proportion to the cube of length. Thus the forces

calculated by the equations should be scaled as follows to obtain the actual longitudinal and

lateral forces:

7

where:Fe = Equation ForceFa = Actual Force

Likewise, the moment obtained by the above equation should be scaled as follows to obtainthe actual moment:

8

where:Me= Equation MomentMa= Actual Moment

a

a

e

e

Lg

V

Lg

V=

a

a

a

e

aeL

V

L

LVV

16==

38

3

1089.5 aee

aea LF

L

LFF =

=

410

4

103.2 aee

a

ea LML

L

MM

=

=


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Effect of Underkeel Clearance

The model tests reported by Remery were run with an underkeel clearance to draft ratio

(UKCDR) of 1.15. But the ER&E model tests included other UKCDR .

The theoretical analyses of passing ship effects developed by Muga and Fang were based on

zero underkeel clearances for both ships. Muga and Fang then utilized the model test results todevelop adjustment factors.

The following is quoted from Muga and Fang. ... the results of a large number of tests can

be presented on a single graph as shown in Fig. 16 [of Muga and Fang], where the effects ofseparation distance, passing ship speeds, different ship combinations, underkeel clearances of

either passing or fixed ships are all included and taken into account at once. In Fig. 16, values of

the non-dimensional force (or moment) ratios appear as straight lines as indicated on the semi-logarithmic graph. ... only those tests where the current is zero appear in Fig. 16.

According to Muga and Fang, the minimum water depth / draft ratio can be either that for

the fixed vessel or the passing vessel ...I performed regression analyses on the data in Muga and Fangs Fig. 16 to develop empirical

equations for the several UKCDR coefficient lines. These equations are adjusted to correspondwith the respective surge, sway, or yaw coefficient at a UKCDR of 1.15, the ratio used in

Remerys tests.The following UKCDR coefficient equations were thus derived:

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where:

UKCDR = ratio of water depth to draft of moored vessel.

Cx = adjustment to be applied to surge force , Fx

Cy = adjustment to be applied to sway force, Fy

Cm = adjustment to be applied to moments, M

For example, if the water depth is 20 m, the draft of the moored ship is 18 m and that of the

passing ship is 15 m, then the UKCDR = 0.10 [(20-18)/20]. For this case, Cx= 1.032, Cy=1.118 and Cm= 1.121.

These coefficients are based on a UKCDR of 0.15 and can be used to adjust the results of the

respective equations 2, 3 and 4 to other UKCDRs . They may be used with Remerys published

data or with other appropriate data obtained at a UKCDR of 0.15, but they should not be used toadjust data or calculations based on other UKCDR .

( )0.0955 0.6367UKCDRxC e

=

( )0.5157 3.438UKCDRyC e

=

( )0.343 2.288UKCDRmC e

=


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DISCUSSION

This paper presents a set of empirical equations for estimating the peak forces and momentproduced by a passing ship and applied to a moored ship. These equations might appear to be

complex, but they can easily be programmed on a computer. The values predicted by these

equations agree closely with the results of model tests.These equations may be used for the analysis of mooring systems. A static mooring analysis

based on peak forces and moments can serve as a preliminary check. If a static analysis shows

that the moored ship moves completely off the fenders or too far along the pier or if mooring lineloads are too high, then passing ship effects may pose a problem at the mooring. A dynamic

mooring analysis can then be conducted. With knowledge of the passing ships speed, the forceand moment vs. position graphs given in this paper can then be used to develop force and

moment time histories for use in dynamic mooring analysis.

Adequate mooring line pretension has been shown to be very important in minimizing ship

motions and mooring line loads in model tests and computer analyses. Line pretensions shouldbe accurately represented and not overestimated in the mooring analysis.

The passing ship forces and moments vary with the square of the velocity of the passing ship.

This has been demonstrated in model tests and analyses and is shown in these equations. Thusthe speed of passing ships should be strictly controlled in the vicinity of critical moorings.

Several published papers give contradictory advice on the effects of current on these forces

and moments. The conservative approach is to use the passing ship velocity relative to the waterwhen the ship is moving against the current and to use the ship velocity relative to the channel

floor when the ship is moving with the current. Further research is needed on this issue.

The equations for passing ship forces and moments given in this paper only apply to caseswhere the path of the passing ship is essentially parallel to the longitudinal axis of the moored

ship. The model tests and analyses on which the equations are based represented an essentially

infinite waterway. The effects may be different in a confined waterway or with the moored ship

alongside a sloping or vertical wall. Further research is needed on this issue.____

Note:I intend to publish another paper to compare the results of these equations with those of other

published calculation methods and to discuss other aspects of passing ship effects. Page count

limitations precluded including these in this paper.____

References:

Lean, G.H. and W.A. Price, The Effect of Passing Vessels on a Moored Ship , Dock and Harbour

Authority, London, Nov. 1997, pps 275-277

Muga, B.J. and S.T. Fang, Passing Ship Effects from Theory and Experiment, OTC 2368,Proceedingsof 1975 Offshore Technology Conference, Offshore Technology Conference, Richardson, TX, 1975

Remery, G.F.M., Mooring Forces Induced by Passing Ships, OTC 2066,Proceedings of 1974 Offshore

Technology Conference, Offshore Technology Conference, Richardson, TX, 1974

1/26/2000


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Figure 1 Nomenclature and Conventions Used in this Paper

Passing Direction

Moored Ship

+FyLateralForce

Lm

+ FxLongitudinal

Force

+MMoment

SDSeparationDistance

PassingShip

Length Ratio, LR = Lp/ Lm

Lp

Separation Ratio, SR = SD /LC

Characteristic Length, LC= ( Lm+ Lp) / 2

Position P = PD / Lc

PDPath Distance


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Figure 2 Nondimensional Passing Ship Position vs. Force and Moment Graphs

-1.00

-0.80

-0.60

-0.40

-0.200.00

0.20

0.40

0.60

0.80

1.00

-2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0

Passing Ship Position, Characteristic Lengths

NormalizedLong

itudinal(Surge)

For

ce

-1.00

-0.80

-0.60

-0.40

-0.20

0.00

0.20

0.40

0.600.80

1.00

-2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0


NormalizedLateral(Sway)Force

-1.00

-0.80

-0.60

-0.40

-0.20

0.00

0.20

0.40

0.60

0.80

1.00

-2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0


No

rmalized(Yaw)Moment


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One-Ship Length Separation:

First influence.Small negative longitudinal

and lateral forces and smallpositive yaw moment begin.

Bow-to-Bow:

Greatest negative lateral force.

Small negative lateral force.

Small positive moment.

Almost Bow-to-Midship:

Greatest positive longitudinal force.Greatest negative moment.

Essentially zero lateral force

Side-by-Side:

Greatest positive lateral force.

Essentially zero longitudinal force.

Essentially zero moment.

Almost Stern-to-Midship:Small positive longitudinal force.

Greatest positive moment.

Essentially zero lateral force.

Stern-to-Stern:Small negative lateral force.

Small negative moment

Longitudinal force drops

essentially to zero.

Figure 3 Narrative of Passing Ship Forces and Moments During Passage

Passing Ship

Moored Ship

L

2 L

Passing Ship

Moored ShipL

Passing Sh ip

Moored Ship0.4 L

Passing Ship

Moored Ship

Passing Ship

Moored Sh ip

0.4 L

Passing Ship

Moored ShipL


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Figure 4 Equation Estimated Values Compared With Remery Model Test Values

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Separation Distance Ratio

LongitudinalForce/V^2

1.6 Ship Size Ratio

1.1

0.3

0.00

2.00

4.00

6.00

8.00

10.00

12.00

14.00

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1


LateralFo

rce/V^2

1.6 Ship Size Ratio

1.1

0.3

0

100

200

300

400

500

600

700

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1


Moment/V^2

1.6 Ship Size Ratio

1.1

0.3

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