The Mean Wave, Wind and Current Forces on Offshore Structures and Their Role in the Design of Mooring Systems

Deift University of Techneioy

PAPER OFFSHORE TECHNOLOGY CONFERHNCE

5ip HyromecbanIcs Laborory

_NUER

_{O T C}

_{1 7 41}

6200 North Central Expressway

LIbra Dallas, Texas 75206

Mekelweg 2 229 CD Deift

THIS IS A PREPRTh TO CORRECTION 31 15 7 - Fc: :i 15 7

lAb s trac t

The mean forces induced by waves, wind and current on tankers, barges and other structures, are very important for the selection of an appropriateassive or active positioning System. In the presen paper tools are given for the

deterrina-tion of these forces, especially for

tanker shaped bodies, taking

ìnto

ac-count

the

main ìnfluene of

water

depth.

The way in which the estimation

of

the

mean forces has to be used

fora

pre-liminary design of a mooring system will be dealt with.

Introduction

The problem of designing an adequate

mooring

or

anchoring system for floating

offshore structures is rather complicated not at least due to the non-linear nature

The Mean Wave, Wind and Current Forces on

Offshore Structures and Their Role in the

Design of Mooring Systems

By

G F M. emery and G va rtmersse, Netherlands ship Model sìn

© Copyigbt 1973

Aninean Initut of Mining, Meta1IurgicaI. andPetrolcum Engincer, Inc.

-OffshoreTechnoio' Conference on-beiali'-of the American Institute of Minthg, Met1 lurgical, and PetroleumEngineers, Inc., American Association of Petroleum Geologists, American Inst±tute of Chemical Engineers, American Society cf Civil Engineers, American Society of Mechanical .&gineers, Institute of Electrical and Electronics Engineers, Inc., Marine Technolo Society, Society of

Exploration GeopIsicists, and Socity of aval Architects & Marine Engineers.

Th&s paper was prepared for presentation at the FÍth Annual Offzbore Tecbnlo Cciference held in Houston Tex., April 29-May 2, 1973. Permission to copy is restricted

toan abstmct of

not more than 300 words. Illustrations may not be copied. Such use of' an abstract should cor-tain conspicuous acknowledgment of where and by whom the paper is presented.

of the problem. It is a problem of dyna-inics and the moored stictur may be

regarded as a mass-spring systain. The total load, exerted by the environment, consists of the oscillating wave for.c and of forces, which vary at a frequen

much lower than the wave

frequency:: tha

wini, current and wave rif t foLces..

when designing an anchor system, three

aspects of these

very

slowly varying

-forces are of importance.

I. As will be illustratedat the end of

this

paper the almost steady wind,

current and wave

drift forces are

_o

significant for the

fina].

determina'-tion cf the diameter of the anchar

lines. This is

due

to the f at

that

the main purpose of ananchøtit

sys-tem is

to

hold the structure on an

average pösition. Basicly the

force

required

for

this statio keepi1i

.

r,V

WIND AND CURRENT FORCES _{OTC 17}

oscillating wave, wind and current

forces on the structure.

The almost steady wind, _{current and}

wave drift forces cause _{a shift of the}

neutral position of the moored object,

around which the oscillation _{due to}

waves occurs. Since the _relationship

between the horizontal displacement of the anchored structure and the restor

ing force of the anchor _{system. is}

almost always non-linear, _{the shift. of}

the neutral position _{causes a change}

in the spring rate,. _{and consequently}

in the dynaxaic _{response.However,}

generaly the natural frequency of the horizontal motion of the anchored structure is considerably smaller than

the wave frequency, also _{after an}

in-crease of the spring constnnt _{due to}

the mear shift of the structure, but

this has to be checked _{for each}

spe-cial design. Therefore _{it is very}

im-portant to study this effect of the wind, current and wave drift forces in

an early stage of the design, _{to be}

sure that resonance at the _wave

fre-quency will be avoided.

Since the wind, current and wave drift forces are slowly fluctuating forces,

the risk exists that _{resonance occurs}

at the very low frequencies, _{at which}

these forces oscillate. _Lowfrequency

oscillations in the horizontal _plane

have been observed in model

experi-ments as well as at full _{scale. The}

naiure of this phenonenon _{is not yet}

fully understood, hut in general it

can be attrthuted to the slowly

vary-ing wae drift for.e as a result of the varying wave height in irregular sear. Attention has to be paid to the

dynamic forces due _{to wind gusts,}

while the variation in the current velocity occurs at a much too low

frequency to be of _importance.

The first two aspects _{discussed here,}

have to be taken into _{account during thE}

preliminary desiçn, and _{will be of-}

sig-nificant impor'cance for this design.. For

this aspect the wind, _{current and wave}

drift may be regarded _{as steady}

phenom-ena, inducing only constant _{forces. For.}

the investigation of _{the.... dynamic.. charac}

ter of especially the wave: drift force'

and--its effect on the _{dyrmic. responsÇ..}

of the anchored object, _{model tests}

are still indispensable.

.

Figure 1 shows _{a flow diagram, depicting}

a possible design _{process for an anchor}

system. In general, the proce _{will hav}

to be repeated foì: _{a numb3r of different}

conditions, For a drill _{rig, for .Lnstavlce}

the anchor system must ie strong enough

to -withstand the _{extreme loads in the}

survival condition, _{wriile for the maximuir}

operational wave condition _{the motion of}

the rig may not _{exceed a certain value.}

In a certain condition, _{it my be}

neces-sary to consider various _combin,tion

of

wave, current and wind _directions.

Ir. this paper we will _{deal with the de}

termination of the steady _{forces, mainly}

on tanker hulls. The _{nature cf the wind,}

current and wave drift,_{forces will be}

briefly discussed and data will be given

for an estimate of these _{forces. The}

problem of the choice of the design

an-vironmental conditions will be left out of consideration. An example how to use

these data for the _{design of an anchor}

Description of steady forces and moments

Wind forces and current forces are

fre-quently presented as being composed of a

drag force, in the direction ef. the flow, and a lift force, perpendicular to the flow direction. However, when describing the dynamic behavìour of a floating ob-ject, the equationsof motion are usually related to a structure bound system of coordinates, with its origin in the mid-ship section of the structure. Therefore it is convenient to describethesteady forc2s as a longitudinal and a transverse

component pplving in the midship sedtion

and a moment around the vertical axis. Figure 2 shows a sketch in which the sign cf the forces and moment, and the direc-tion of wind, waves or current are

defin-ed.

The force due to wind

Like all environmental phenomena, wind has a stochastic nature which greatly de-pends on time and location. It is usually characterized by fairly large fluctua-tions in velocity and direction. It is common meteorological practice to give the wind velocity in terms of the aveiage over a certain interval of time, varying from i to 60 minute.s or more. The varia-tion in mean velocity is very slow com-pared with the wave period. The fluctua-tioris around the mean value wIll impose dynamic forces on the structure, but in generi]. these aerodynamic thrces may be neglected in comparison with the hydrody-namic forces, when considering the dyna-mic behaviour of the floating bocy.

Therefore, we will consider the wind

ve-locity as a steady value, both in

magni-tude and direction, resulting _in

con-stant forces and a concon-stant moment act-ing on the structure.

The role which wind plays in the deter-mination of the environmental conditions of floating structures is twofold:

- On the part of the structure exposed. to the air, wind forces are exerted due to the stream of air aro'.nd the various parts. For the det'rmination

'àf these forces information is

requir-ed about the local Winds only.

- The forces exertd by the wind on the water surf are cause disturbances of th

still water level, thus generating waves and current, which induce forces ori the submerged part of the structure. To determine this effect of the wind, information is required about the wind

and storm -conditions in a muc larger

area

The wave and current generating character of tIe wind will be left out of

consider-ation. The effects of wavei and currents

will be dealt with seperately.

Local winds are gener;.y .efiried in

terms of the average vclocit' and average

direction related to a certain height above the still water ie'el. The standard height above the water surf;'e for which

generally the wind velocity data are

given amounts to 10 met-es or 30 feet. A

number of exrirical and theoretical fc-mula3 is available in literature to de-termine the wind velocity at other heights. An adeu.te veridcai distribu-tion of the wind speed is represented by

(see ref. (i))

V (Z)

= 1/7

V(10) li0,

I-172

_{THE MEAN WAVE, WIND AND CURRENT FORCES}

in which

v(Z) = wind speed at height Z above the water surface

v(lO)= wind speed at 10 metres height above the water surface

The total force and moment experienced by an object exposed to wind, is partly of viscous origin (pressure drag) and partly due to potential effects (lift

force and moment). For blunt bodies, the wind force may be regarded as independen of the Reynolds number and proportional to the square of the wind velocity.

Wind load data for tankers

w C_xw

=a +

a cosnc O n w C = b

sinmx

yw n n 1 = _{b sin nc} nw n n= i

From the harmonic analysis it was found that a fifth order representation of the wind data is sufficiently accurate for preliminary design purposes.

In Table II through IV the Fourier coef-ficients are given for the longitudinal and transverse force, and the yawing mo-ment, for a nwnber of tankers. Particu-lars of the tankers are listed in Table I, where also the reference numbers are given of the publications, from which the data'werc taken. Figure 3 shows, as an example, the measured wind forces and moment together with the Fourier approxi mation, for one of the tankers.

The wind load on other structures

OTC 1741

The wind forces and moments on other types of structures, as for instance floating semi-submersible platforms, can be approximated by dividing the struc-ture in a number of components, all with a more or lesseleinentary geometry, and estimating the wind force on each ele-ment. For a lot of simple geometrical

forms-such as spheres, flat plates and cylinders of various cross sectional shapes, the drag and lift coefficients are given in literature. Reference is made of the publications of Hoerner (6)

and Delany and Sorensen (7).

The total wind load on the structure is then found by adding the contributions of all the component parts.

The forces and moment exerted by wind on tankers can be calculated from:

= a

v2

C(a)

. _AT

N =½p V

C

(a) .A .L

Y _{= ½p} V C (a) . A w a w2 yw L w a w nw L in which

= steady longitudinal wind force = steady.transverse wind fcrce = steady yaw wind moment

= density of air v,

windvlocity

wind direction

-= exposedtransverse area exposed lateral area AL

L = length of the ship

C_x', C- and C_yw are coefficients,

de-nw

pending on the angle of incidence of the

wind.

In literature the results of wind tunnel

experiments are given for various types

of vessels. From several papers the wind data on tanker hulls were collected, and

the force and moment coefficients _C

xw

C and C _{were expanded in Fourier}

yw nw

series as a function of the angle of

The force due to current

There are several independent phenomena responsible for the occurrence of cur-rent: the ocean circulation system,

resulting in a steady current, the cycli cal change in lunar and solar gravity, causing tidal currents, wind and differ-ences in density. The steady velocity at

the water surface due to wind amounts to about 3 percent of the wind velocity (at

30 ft height). Tidal currents are of main importance in areas-of restricted water depth and can attain values up to

10 knots. However, these extreme velo-cities are rare. A 2 or 3 knots tidal current speed is common. The prediction of the magnitude of tidal currents is a special sience. Some predictors take not less than 60 parameters into account in their prediction procedure.

Although for floating structures the surface currents will be the governing ones, the vertical current distribution may also be of imortance, especially for the case of restricted water depth. For the design of an anchor system of a floating structure the designer is espe-cially interested in the probability that a particular extreme current velo-city will be exceeded during a certain period of time. Observations obtained from current speed measurements are in-dispensable for that purpose. It may be usefull to split up the total measured current in two or more components, for instance in a tidal and a non-tidal com-ponent, since the direction of the vari-ous components will be different, in general. The variation in velocity and direction of the current is very slow, and current may therefore be considered

as a steady phenomenon.

The forces and moment exerted by current on a floating object is composed of the

following parts:

- A viscous part, due to friction be-tween the structure and the fluid, and due to5pressure drag. For blunt bodle3 the frictional force may be neglected,

sinc it-is small compared to the

vis-cous presure drag.

- Apotential part, with a component due to Ì ciculation around the obj ect., and an other component dueto the f re water surface (wave resistance) . In most cases, the latter component is small in comparison with the f irt.

Current load data for tankérs

The forces and moment exerted by curren.t on a tanker hull can be described by:

X _{= ½} V 2 C (a) . A c w c xc TS Y _{= ½} V C (a) A C W c yc LS N ₌ p V ' C (a) A . L C W c nc in which

X = steady longitudinal current force

= steady transverse current force = steady yaw current moment

= density of water

V = current velocity

a = angle of incidence

= submerged transverse area = submerged lateral area = L x T

L = length of the ship

T = draft of the ship

C , C and C are coefficients, de.

XC yc nc

pending on the current direction.

At the N.S.M.B., the current loads have been measured on several tanker models of different size. From the results the

coefficients C , C and C were

cal-xc yc nc

culated. For flow in the longitudinal

direction a tanker hull is a rather sien

der body, and consequently _{consists the}

longitudinal force mainly of frictional

resistance. The total longitudinal _force

was very small for the relatively low

current speed, and could therefore not

be measured very accurately. _Moreover,

extrapolation to full scale _dimensions

is difficult, since the longitudinal

force is affected by scale effect:.

For mooring problems, the longitudinal

current force will hardly be of

impor-tance. An estimate of its magnitude can

be made by calculating _{the flat plate}

frictional resistance: x _{= (} 0.075 _½ 2 c (log R

-

2)2)

_{w c} n cos a Cos a in which V cos a c

R_n = the Reynolds number =

y _{= kinematic viscosity of water}

S _{= the wetted surface}

Extrapolation of the transverse _{forc an}

yaw moment to prototype values _{is no pro}

blem. For flow in the _transverse

direc-tion the tanker i _{a blunt body, and}

since the bie

_{diusIs small, flow}

5eparation ocus in the _{model in the}

axne wayas in the prototype. Therefore,

bhe transverse force. _{coefficient and the}

iaw moment coefficient _{are independent of}

:he Reynolds number,

rhe-coefficients for the transverse forc

and the yaw moment were expanded i.n a

Fourier series: as was done for the wind

Load coefficients:

= b

sinna

n=l n

nc b sin na

The average value of the Fourier

coeffi-cients for the fifth order Fourier

se-ries, are given in Table V. These

re-sults apply to deep water. For shallow

water, the current force and rroment

coef-ficients have to be multiplied by a

coef-ficient, which is jiven in Figure 4 on a

base of the water depth-draft ratio. _In

the data, given i.n Table V, the influenc of the free water surface is included.

This influence, however, depnds on the

water depth and on the Froude number,

and consequently changes if the curr3nt

velocity or the tanker dimensions cI'ang' For the condition to which these data

apply, deep water and a prototype

cur-rent speed in the order of 3 knots, the

effect of the free water surface is very

sm.11. For a case of a small underkeel

clearance and a current direction of 90

degrees damming up of the water at the

weather-side and a lowering of the ater

level at the lee side of the ship occurs

The current load on other structures

The current load on other types of float

ing

structures

can

be estiLated

in.

the

saine way:as.-was described for the wind load in a previous section.

Wave drift forces

A structure floating in _{waves eprience.}

forces and moments which _{can be}

deter-mined if the velocity potential _{of the}

water motion around the structure _is

known. By integrating the _{component of}

the pressure in a particular direction over the hull of the structure, the

force component in this direction can be

calculated. The pressure can be obtained

VV i' t1LLJ L. Li £\.rLLik'4 .L . L) LXL. i

from the Bernoulli equation for non- _{(2-dimensional case;} no diffraction) in in which p = pressure p= atmospheric pressure = velocity potential g = acceleration of gravity V = velocity of water motion

()2

(3)2

2

Wave drift load data for_{- tankers}

in the theory of periodic ship's mction

ogawa (9) applied Maruo' _{theory on a}

in waves the velocity _{term ½ p V2 is}

ne-I

captive series 60 model _(block

coeffi-w

I

glected, sinco it has only _{a second}

or-cient 0.70) in beam and _{hvi guatring}

der influence on the _oci1latory

beha-waves and he shows that

viour. However, it is this _{term which is}

= ½Pg

2 n2 a

ar

responsible for the steady _{drift force,}

in which Representing the velocity potential by a

a = direction of waves relative to ship

periodic function proportionEil

_tothe

He calculated th _{amplitude of the}

re-amplitude _{Ca of the incident wave}

flected and scattered wave using th strip theory for two wave directions (90

.

sinùt

a a

and 1200) relative to the captiv _vessel

in which = frequencyof waves it follows that

/

= ½ C 2 sin2ut ₊ a _3x ay -'

By taking the average value of the pres-2î

sure during one period _{(T = -) it will}

be clear that all periodic terms vanish

and only the velocity _{term ½PwV2 gives}

a contribution. Consequently the steady

drift force on _{a structure in waves is}

proportional to the square of the height of the incident wave. Maruo (8) shows

that the lateral drift _{force Y per unit}

length on an infinitely long cylinder

= amolitude of wave reflected _a'ìd

ar

scattered by the body

He also indicates that the _{amplitude of}

this wave is proportional _{to the}

rela-tive motion between the oscillating cy-linder and the wave.

and found a reasonable agreeaent with

the measured results. _{For the 1am wave.}

diction Lhe reulis given

_{b' Ogawa for}

the captive vessel are compered in 5 withthe experimental values of tne

wave drift force ona free flûittn

ves-sel having a smaller block coefficidnt

ofO.60.Ïn this Figure the _{drift force}

is given in a non-dimensional way by 2.

dividing the force by

_pg

.

. L and

taking the square root.

(Ca amplitude

öf incident wave).

This non-dimensional drift force coeffi-cient /

R=\/

Yd

V

C . L

is plotted to a base of non-dimensional wave length k.T, in which:

steady flow:

beam seas satisfies:

2 _{'d =}

pg

P = Po + Pwt

_{_PgZ ±}

_½P V

in which

k = = wave number À = wave length

All results apply to deep water. As

il-lustrated in Fig. 5 the drift force _on

the free floating vessel corresponds

quite well with the force on an

infinite-ly long flat vertical plate (see (io))

with a draftequal to the vessel's _draft

and over a length that equals _{the length}

of the vessel between perpendiculars.

The drift force on the restrained _vessel

in deep water can be compared quite well

with the results given of _theoretical

calculations conducted by Mei and Black

(ii) for a rectangular _{captive cylinder}

extrapolated to the same beam over draft

ratio (B/T = 2.5) as the vessel has and

to deep water. This indicates that _the

influence of diffraction due _{to the}

re-stricted length/beam ratio of the vessel

probably may be neglected.

The considerable larger drift _{force on}

the captive rectangular cylinder

rela-tive to the flat plate demonstrates _the

important effect of the beam or the

bot-tom of the vessel and consequently

_{of th}

relative vertical motion between the

ob-ject and the wave motion. _{The rather good}

agreement between the free floating

ves-sel and the vertical plate _{seems to}

indi-cate that the drift force contributed _by

the relativeheave motion _{of the vessel is}

small in this particular _{case. The}

in-fluence of the water _{depth-draft ratio is}

indicated in Figure 6, where some results

are given of measurements carried _{out at}

the N.S.M.B. on a series 60 model, block

0.80, beam/draft ratio 2.5, length/beam

ratio 7. From this figure _{it will be}

clear that in deep water _{the drift force}

in beam waves on the block _{0.80 vessel}

corresponds also reasonably well with the

force on a vertical plate. However, _at

the very reduced water depth of 1.1

times the draft of the vessel, _{very high}

drift forces are measured for _wave

fre-quencies near the natural frequency _of

the roll motion. This may be _explained

by the much higher roll damping _(the

damping coefficient is approx. 3 times

larger) at this water depth, _{which means}

that the roll generated _{waves are higher}

and consequently the steady _{drift force}

too.

For an approximation of the _{lateral drif}

force in deep water in regul ar waves the following expression may be used:

= ½P C . R2 . L . sin2 a

in which

= amplitude of incident wave

R _{= drift force coefficient for a verti}

cal plate with draft T. R is a furLc

tion of the dimensionless wave

length kT

a _{= wave direction}

For the determination of the mean drift

force or the resistance in _{head waves}

reference is made to the method describ&

by Gerritsma and Beukelman (12). This

method is based on the determination of

of the radiated _{energy by calculating thC}

amplitude of the waves generated by the

relative vertical motion between ship and

waves. In case of a rather flat bow also

the influence of the relative surge mo-'

tion has to be taken into account as is

shown in (13).

The wave drift force on other struCt

Up to now only the drift force on ship

shaped bodies have been dealt with. For the drift force on semi submersible

TC 1741

type structures no data are available on this moment. Probably the best way to es-timate the drift force is to split up the construction in elements consisting of circular or rectangular cylinders and to estimate the drift force on each element

separately. In (14) data are given for

the drift force on a restrained vertical cylinder.

wave drift force in irregular waves when the drift force on a structure is known as a function of the wave frequency either from calculations or model tests, the lateral mean drift force in irregular waves, described by a particular wave spectrum, can be determined from:

= . L

.

f

S(w)

. ½P2

dw

As an empeiical approximation for ship shaped bodies the following expression may be used for an irregular sea

describ-ed by a narrow spectrum:

1

.2

=

--

Ç 1/3

R2()

. L sin c

in which

1/3 = significant wave height

(crest-trough)

= drift force coefficient for flat

plate for w = = mean wave

fre-quency

Design of the anchor system

If the steady force on a structure in a

particular sea state is known and the lay-out of the anchor system has been se-lected the minimum thickness of the

an-chor lines is determined by the mean

ex-ternal force as will be illustrated below.

R()

G.F.M. REMERY AND C. VAN CQRTMRRSSFN I-177

Suppose the anchor system has to satisfy the following criteria

The maximum allowable excursion x max of the structure from its initial un-loaded equilibrium position is given as a certain percentage of the water depth.

The maximum allowable tension in the anchor lines may not exceed a certain percentage of the breaking strength. The thickness of the anchor chains is proportional to the weight per unit

length (specific weight). The minimum weight required will be attained when the pretension in the anchor lines is such that at an excursion which equals the maximum allowable excursion also the maximum allowable load in the heaviest

loaded anchor line is attained.

From the non-dimensional catenary cha-racteristics the tension in the line T o divided by w.ha and the angle e between the line and the horizontal plane, both measured at the attachment point of the line to the structure, can be determined

as a function of the excursion X/h of

the structure.

w = submerged weight of anchor line per

unit length

= height of attachment point above bottom

Since the breaking strength of a parti--cular type of anchor line is proportion-al to the specific weight w, the excur-sion of the structure can be determined at which the tension To/w.ha equals the maximum allowable tension. Then the re-quired pretension angle e can be read of

at an excursion which is x smaller.

max

The usual non-linear relationship be-tween the excursion of the structure and the horizontal load FH/Wha required for that excursion can be calculated for the

I-173

selected pretension.

Subtracting the maximum expected f

luctu-ating motion from the maximum _allowable

excursion x _{gives the excursion}

of th max

structure which can be allowed _{as a}

re-suit of the _{mean force}

due to wind,

waves and current. _{The total}

horizontal

force FH' _{= FH/W.h at this excursion}

can be read of. Then the minimum

required submerged weight of the

anchor lines has to satisf F

F' .h

_H

a

The above

described procedure will be

illustrated by _{means of an example.}

Example

Question

Determine the minimum weight of

the anchor lines of an

anchor-ing system

for a turret mooring cf a drilling

vessel having _the

following main _dimensions:

length 150 m

beam

_26m

draft

_8m

wind exposed _{transverse area}

= 750 ni2 displacement = 17500 metric tons

water depth = _{70 m}

The design has to be based _{on a sea state}

described by a Pierson-Moskowitz

spectrum with a significant

wave height of 4.5 ni

and a mean

period of 8 sec. The maximum

wind speed is _{40 knots,}

the current speed 2 knots. The

maximum allowable excursion

is 9% of the water depth. _{The forces}

in

the lines _{may not exceed}

50% of the breaking strength.

Although the _{vessel is}

equiped with bow _{and stern}

thrusters to

control the _{heading, since}

the turret _is

located amidships,

the anchor system has

to be designed for the combined _action

THE MEAN WAVE, _{WIND AND CURRENT}

FORCES

OTC 17

of beam _{wave, wind and}

current. The system consists of 8

anchor legs equall

distributed over the circumference _of

the turret. _{From model test}

data on

si-milar shìps the _{maximum oscillatory}

ex-cursion of the _{vessel is estimated}

to

be approximately4.35 _{ni being 7% of the}

height ha of the _{attachment points of}

the anchor chains above the bottom. Solution

The mean force on the vessel _determined

according the data

given in this paper are as follows:

due to a 40 _{knots beam wind}

17 ton

due to a 2 _{knots beam}

current _{49 ton}

due to 4.5 ni significant _height

waves

48 ton Total

114 ton From the

characteristics of the catenary it can be

determined that _{the anchor legS}

have to consist _{of approx. 500}

ni _{(8 x h)}

anchor chain (U-3 _{quality) or 1050}

ni (17

x h) steelwire _{(h = water}

depth-draft = 62 ni) _{in order to}

be sure that _the

tan-gent of the line at the anchor _coincides

with the bottom

at a tension which equal half the breaking

strength.

The pretension angle G, required _to

ob-tain a tension

which equals half _the

breaking strength _{at the iaximum}

allow-able excursion _{of 9% of the}

height ha!

amounts to the _{following values}

for _{500 ni U-3 quality}

stud link chain:

e _{= 26.2 degrees} pret. for 1050 ni _steelwire: e _{= 10.7} de-pret. grees. The non-dimensional relationships be-tween the excursion

of the vessel and th

horizontal force _{required have been}

cal-culated for both

types of anchor lines. For U-3 stud link

OTC 1741 k p po

t

w X

shown in Fig. 6. At an excursion of 9% of the height hai the tension in the heaviest loaded anchor line attaines half the breaking strength Tb

for U-3 quality chain Tb 4000 x w

for steelwire T 17500 x w

ob r

T

inkg

obr

w in kg.m

Subtracting the maximum expected oscil-latory excursion from the maximum allow-able excursion leads to an excursion of 2% of the height hai that may be allowed as a result of the mean force of 108 ton on the vessel. The dimensionless

hori-zontal load on the system corresponding to this 2% excursion amounts to:

for U-3 chain _8.7

for steelwire 59.1

The resulting minimum required submerged weight of the anchor lines is given in Table VI. The corresponding approximate

diameters of the lines are also

mention-ed in Table VI.

The method described here has to be

adapted for each special case. However,

the example illustrates _{clearly the}

im-portant role which the mean force may

play for the determination of the anchor system. Nomenclature a , b Fourier coefficients n _n h h a depth of water

height of attachment point of anchor line above bottom wave number = 27r/X

pressure

atmospheric pressure t jme

submerged weight of anchor line excursion

maximum allowable excursion of structure

x, y, z right handed system of coordi-nates

z _{vertical coordinate, upward po}

itive

lateral area above water surfa submerged lateral area

transverse area above water sui face

submerged transverse area breadth of ship

yaw wind moment coefficient yaw current moment coefficient

longitudinal wind force coeffi-cient

longitudinal current force coef ficient

transverse wind fcrce coef fi-cient

transverse current force coeff cient

total mean load on anchored structure

horizontal load on anchor

sys-t em

yaw current moment yaw wind moment

non-dimensional drift forcé coefficient

draf t of ship

-tension in anchor line velocity of water motion wind velocity

current velocity

longitudinal current force longitudinal wind force transverse current force transverse drift force

mean transverse drift force in irregular waves AL ALS ATS B C nw C nc C xw cxc C yw C yo F FH N C N w R T T o V V w V C X C X w y c

o p re t pw w w List of references Bretschneider, C.L. "Wave and wind loads"

Section 12 of Handbook of ocean and underwater engineering, Mc Graw-Hill Book Company, New York (1969).

"Research investigation _{for the}

im-provement of ship _{mooring methods"}

B.S.R.A. Report NS.

_256.

Wagner, B. "Windkrfte an

Qeberwasserachiffen"

Schiff und Hafen, _{Heft 12/1967.}

4 _{Aage, C.}

"Wind coefficients _{for nine ship}

models"

Report No. A-3 of the Hydro- and

Aero-dynamics Laboratory,

Denmark, May 1971 Gould, R.W.F.

"Measurements of the wind forces on a

series of models _{of merchant}

ships"

N.P.L. Aero Report

_1233,

April 1967. Hoerner, Dr.Ing. S.F.

"Fluid-dynamic drag"

Published by the author _{in 1965.}

Delany, N.K. and _{Sorensen, N.E.}

"Low speed drag of cylinders _of

va-rious shapes"

NACA, Technical _{Note 3038.}

Maruo, H.

"The drift of _{a body floating}

on waves'

J. of ship research _(Dec.

1960) Vo1.

Ogawa, A.

"The drifting _{force and moment}

on

ship in oblique _{regular waves"}

Publication no. 31. _{Delft Shipbuild}

nc

Laboratory. I.S.P. _{Vol. 14, no. 149'}

January

1967.

Wehausen, J.V. and _{Laitone, E.V.}

"Handbuch der Physik"

1960,

section 17, Berlin: Springer-Verlag.

Mei, C.C. and _{Black, J.L.}

"Scattering of surface waves"

J. Fluid Mech.

₍₁₉₆₉₎

Vol. 38, Part 3.

Gerritsma, Prof.Ir. _{.3. and}

Beukelman, W.

"Analysis of the resistance increase in waves of a fast cargo ship"

I.S.P. Vol. 19,

Sept. 1972 no. 217.

Remery, G.F.M. and _{Hermans, A.J.}

"The slow drift

oscillations of a

moored object in _{random seas"}

Society of Petroleum _{Engineers Journal}

(1972) Vol. 12,

no. 3.

Oortmerssen, G. van

"The interaction between a vertical

cylinder and regular _waves"

Symposium on "Offshore

HydrodynaflhiC5

in Wageningen. _August

_1971.

Publication no. 375 _{of the N.S.M.B.}

Y _{mean transverse wind}

force w

a _{angle of incidence}

Ca amplitude of incident _wave

Car amplitude of reflected _and

scat-tered wave

ç 1/3 significant wave height

o _{angle between anchor}

line and

horizontal plane at the

attach-ment point to the _structure

pretension angle = angle O for _T0

is equal to pretension velocity potential density of air density of water wave frequency

mean wave frequency of _an

TABLE 5 - COEFFICTRNTS FOR THE

TRANSVERSE FORCE AND lAW

1NT ON TASI'.RS DUE TO

CURRENT FORCE FOR THE LOANED CONDITION IN DEEP WATER

transverse ya

force cornent

TABLE 1 - DATA OF TA20S

TARER 3 - COEFFICj.UDDS FOR THE TRANSVERSE FORCE ON

TANS DUE TO WIND

TABLE 2 - COEFFICTS FOR TER LO1$OIrIrDTRAL FORCE ON TA000BS DUE

TO WIND

TABLE ¿4 - COEFFICTRRTS FOR THE lAW FOMENT 014 TAN1S DIJE TO WIND

TABLE 6 - TER 4D1UM RUIREN SUBNERGED WEIGWC PaID THE

APPROXIWTE DIAMETERS OF THE ANCR LINES

Ship

No.

Type Length Conutton Data tako

froc ref.

1 bridge anridsh. - loaded 2

2 - ballast 2

3 bridge aft - loaded 2

-4 - ballast 2

5 bridge ainidsh. 225 m. loaded 3

6 ballast 3

7 bridge aft loaded 3

8 ballast 3 S 172 rn. loaded 4 10 - 150 n. loaded 5 11 - ballast 5 Ship NO. a a1 a2 a, a4 a5 1 - 0.131 0.738 - 0.056 0.059 0.108 - 0.001 2 - 0.079 0.615 - 0.104 0.085 0.076 0.025 3 - 0.028 i 0.799 - 0.077 - 0.054 0.018 - 0.018 4 0.014 0.732 - 0.055 - 0.017 - 0.018 - 0.058 - 0.074 3.050 0.017 - 0.062 0.080 - 0.110 6 - 0.0550.748 0.018 - 0.012 0.015 - 0.151 7 - 0.038 0.630 0.031 0.012 0.021 - 0.072 8 - 0.039 0.646 0.034 0.024 - 0.031 - 0.090 9 - 0.042 0.487 - 0.072 0.109 0.075 - 0.047 10 - 0.075 0.711 - 0.082 0.043 0.064 - 0.038 11 - 0.051 0.577 - 0.058 0.051 0.062 0006 Ship No. b1 b2 b3 -b4 b5 1 0.785 0.039 0.003 0.034 - 0.019 2 0.880 0.004 0.003 - 0.004 - 0.003 3 0.697 0.03e 0.018 0.028 - 0.023 4 0.785 0.014 0.014 0.015 -0.020 5 0.707 - 0.013 0.026 0.007 - 0.Q44 6 2.731 - 0.014 0.016 0.001 - 0.025 7 0.718 0.032 0.010 - 0.001 - 0.040 8 0.735 0.003 0.004 - 0.005 - 0.017 9 0.764 0.037 0.052 0.016 - 0.003 10 0.819 0.051 0.023 0.032 - 0.032 11 0.879 0.026 0.014 0.031 - 0.029 Ship b1 b2 b3 b4 b5 1 - 0.0451 - 0.0617 - 0.0110 - 0.0110 - 0.0000 2 - 0.0338 - 0.0800 - 0.0080 - 0.0096 - 0.003.3 3 - 0.0765 - 0.0571 - 0.0166 - 0.0146 0.0021 4 - 0.0524 - 0.0738 - 0.0175 - 0.0089 - 0.0021 5 - 0.0216 - 0.0531 - 0.0063 - 0.0073 0.0024 6 - 0.0059 - 0.0730 - 0.0035 - 0.0017 - 0.0013 7 - 0.0526 - 0.0596 - 0.0111 - 0.0113 0.0099 8 - 0.0335 - 0.0722 - 0.0090 - 0.0047 0.0067 9 0.1025 - 0.0721 - 0.0345 - 0.0127 - 0.0022 10 - 0.0881 - 0.0681 - 0.0202 - 0.0145 0.0039 11 - 0.0644 - 0.0726 - 0.0244 - 0.0076 0.0024 submerged weight per meter leneth

diameter

U-3 stud link chain steelwire 211 kg 31.2 kg 107 rem 4 92 mn a 3 1/4 5/5W 0.908 - 0.0252 0.000 - 0.0904 b3 - 0.116 0.0032 b4 0.000 0.0109 - 0.033 0.0011

SELECT NEXT DESIGN CONDITION ADAPT ANCHOR SYSTEM FOR WORST CONDITION no no

[ OBTAIN ENVIRONMENTAL DATA

ESTABLISH DESIRED WORKABILITY J

DETERMINE OPERATIONAL ENVIRONMENTAL CONDITIONS

DETERMINE DESIGN CRITERIA

SELECT DESIGN CONDITION

WITH RESPECT TO:

WAVE WIND ,CURRENT DIRECTION LOADING CONDITION

WATER DEPTH etc.

CALCULATE STEADY FORCES DUE TO WINOWAVESCURRENT

ESTIMATE DYNAMIC BEHAVIOUR OF STRUCTURE WITH RESPECT

TO MOTIONS S DE SIG N FOR OPERATIONAL CONDITIONS' ye s DETERMINE DIMENSIONS AND PRETENSIONS OF

VARIOUS ANCh)R SYSTEMS

SELECT A PROPER ANCHOR SYSTEM DESIGN FOR SURVIVAL CONDITIONS? yes H AVE ALL CONDITIONS BEEN CHECKED yes CHECK DYNAMIC BEHAVIOUR

IN IRREGULAR SEA CONDITIONS BY MODEL TEST

no

no

Fig. i - The design of an anchor system.

DETERMINE SURVIVAL ENVIRONMENTAL CONOtTIO. CHECK AND/OR ADAPT ANCHOR SYSTEM FINALIZE DESIGN

1.0 0.5 o 0,5 -1.0

Fie. 3 - Comparison of the Fourier approximation

with measurements of the

wind load on the tanker.

area AL area 4Ls

Fig. 2 - Description of forces and osDaenta.

o -C

I

Q. u O

3

J Z2 Lu cc cc u _L)

00

DRECTION OF WIND,WAVES OR CURRENT

area AT

Fig.

- The influence of the water depth on the

current load on a tanker.

FOURIER MEASUREMENTS APPROXIMATION L e Cxw a. 50 100 50 200 - WINO DIRECTION 2 3 WATER OEPTN ORAr t

00 1.2 0.8 R 0.4 o k.T

Fig. 6 - _{Influence of water depth}

on the drift torce coefficient.

DRJFTFORCE COEFFICIENT R» Yd

DEEP. WATER V

VPwL

k.T

Fig. 5 - Drift force

coefficient in beam waves.

100 75 Ö 4 O -J -J 4 z o 50 O z O z 25

FHIWha H0RIZONTAL LOAD

To/w.ha = TENSION INHEAVIEST

LOADED LINE MAXIMUM ALLOWABLE EXCURS 0H Xmx MAXIMUM EXPECTED OSCILLATING MOTION B LEGS EACI- LEG: 0Ø U-3 OUALIT'f S1. LINI< CHAIN

/

/

EXCURSION

DUE TO MEAN LOAD

0.05 0.10 EXCURSION X/I'a

Fig. 7 - Ch&racteristtc _{of the eight_leg ancF a1.e'.}

** I I I I

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I, B/T PLATE O CYLINDER 2.5 B070 CAPTIVE 2.5 6OC80.60 FREE 2.5 VERTICAL SERIES 60-C SERIES

iRECTANGULAR

L OGAWA LALANGAS RECTANGULAR CYLINDER £ VERTICAL PLATE MEASUREMENTS ON A SERIES 60 MODEL IN BEAM WAVES

C _{0.80 ; L/B 7; 8/Te}

2.5

O

WATER DEPTH 4_{x DRAFT} ..

FLAT PLATE (theory)

R

1/2 Pg2L

o

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0.2 _{04 06} 08 tO 0.5 ₁₀ 1.5