Shock phenomena on a trawler

SHOCK PHENOMENA ON A

TRAWLER

by V. FERDINANDE

u in iii a rv

Shock phenomena on a trawler, sailing in rough head seas, are described. An explanation of

these shocks is attempted Lv means of a theory on wedges in the process of being immersed. The values of acceleration peak magnitudes, measurod on board by means of an accelerometer

in the foi'eship, are compared with the results of theoretical calculations.

mtrI) (III Iion.

in January and February 1962, full-scale trials

were carried out on the trawler 'Belgian Lady',

which was fishing in the neighbourhood of Iceland.

A report of the measurements on hoard is given in Ref. 1. From accelerometers p! aced fore and aft, records were obtained out of which the nature of

some shock phenomena during bad weather and

in head or bow seas \vRS reflected in the

irregu-larities, superposed on the low cycle oscillations.

The ship, sailing in waves of a considerable

height, endured shocks, which instantly teminded the author of the 'slam ming -etfect' formerly

en-countered onageneral cargo ship [Ref. 2]. There were no straingages attached to the deck of this ship, but both acceleration records often revealed

the existence of a hull vibration, just after the

appearance ot' a peak in the fore accelerometer

diagram. The occurrence of an acceleration peak

in the foreship, followed by a hull vibration would indeed indicate slam ming, foilowing the criteria

given by Szebehely and 'Judd in Ref. 3. Flowever,

the nature of the peak and the fact that at the in-stant of the shock, the foreship apparently was already in the water, convinced the author that

this shock phenomenon was quite different from

the classical slamming of the forehottom on the water surface. It even seemed to differ from the

'slamming' of a destroyer, which is caused by

the building-up of hydrodynamic pressures on the flared bow, resulting in vibrations of a high

am-plitude in the slender hull girder, [Ref.4. It is

shown further that classical slamming also

oc-curred, but its effect was very moderate, and much less spectacular than the other shocks.

Laboratory of Naval ArchkCtUra. Stato Univereity of Ghent, Belgium.

Asan explanation of such shock phenomena on this trawler was not readily at hand, a theoretical

study seemed opportune. The theoretical results \vill be compared with the experimentally

mea-sureci values.

Description of hoek phenomena and

circurn-stances on board ni the trawler Rrlgian LadY.

The experimentist is aware of the fact that

visual observations and the interpretation of what is felt on board of a ship in bad weather can often

be erroneous and misleading. Nevertheless, the

author thinks foil owing statements concerning the

behaviour of the trawler in head seas, can be

made.

- Inahigh sea,the shocks mostly occurred while the ship was encountering waves of rather moder-ate height.

- These environmental waves were very steep. - An observer staying aft felt himself rising

be-fore the shock occurred.

- At the instant of a severe shock, he and all loose objects were lifted upwards and thrown forwards.

An observer in the engine room, near the midship,

Icl the feeling of being shifted forwards.

- At this same instant, an observer on the bridge

could seethatthe ship was in a pitched-clown po-sition, and had the impression that the part of the ship in front of the bridge lay deep in the water.

He heard a short 'crack',which seened to come

from amidships though this could be erroneous.

No considerable amount ot green water on the

deck was noticed in head seas. This does not

the forecastle deck. hut the breakwater on this

deck seemed to be efficient; moreover the strong

wind immediately Irrinsformed the overflowing

green water to a spray. Damage to equipment or

loss of fishiii gear was never noticed. The usual

'drvness'of the deck in head seas was confirmed

by the ci'ew. Not all fishing vessels however

de-serve this reputation. It is assumed, that during

the two voyages the deck was struck only once by

a mass of green water; (thecircumstancesare

described in the following statement).

The shock was felt first. Maybe less than a

second later,a huge spray,starting at the bows,

hit the bridge and made visibility nil for a moment.

- The severest shocks were followed by a hull

vibration, which didn't seem to be important

however. It faded away quickly.

During the forty days at sea, mostly in bad

weather, only one severe vibration was noticed.

It occurred in a heavy sea, the ship was 'hove to'

but a few seconds just before the phenomenon,

the motions happened to be quite moderate. The

accelerometer records fore and aft suddenly re-vealed a vibration of an anusual amplitude. The

records arc shown on Fig. 1. The corresponding wave record shows that the trawler encountered

a high and extremely steep wave,probahly having

ahrcakingcrest. It is assumed, considering the

small pitch angle at the moment the bow faced the

steep wave crest, this crest overflowed the ship

and a considerable mass of green water was

thrown on the deck and the bridge. Moreover the

direction of the acceleration peaks indicates an

impact aft of the vessel. This impact of green

C,4AT NO " O T LItSfl I STR IJI4 1JTS

TI

_'

/L

t '

1 i[i

- t ' r L 4

-L\i

k._L.L.

L_L..

Figure 1. Recordofaccelerationsforeandaft atthe

mo-ment of a vibration of exceptional severity.

water may be considered as highly exceptional

on this ship and diilers in nature from all the

shock phenomena discussed in the following study. The ship was equipped with several instruments

for the measurement of engine power, ship speed, vind speed and direction, ship motions, accele

-rations and environmental wave height. These

instruments 'crc described in Ref. 1. For the

interpretation of the shock phenomena described

here, the following instrumentation was

especi-ally helpful.

- Theaeceleromctcrs fore and aft; their signals were recorded by means of two synchronized

carrier amplifiers and a two-channel

oscillo-graph.

- The Tucker shipborne wave recorder.

The statements mentioned above were, as a

whole, confirmed by the analysis of the records.

What is more, the fore accelerometer records

showed peaks in the negative direction (negative,

meaning directed downwards) at the moment of

a shock. This is in the opposite sense of slamming

acceleration peaks on an ordinary cargo in

bal-last condition.

Sometimes, such an acceleration peak was

preceded by a sudden deceleration, without the

appearance of a peak however. This deceleration was usually followed by a high-frequency

oscilla-tion of small amplitude in the diagram. It is apparent that this last phenomenon has some

characteristics of a classical slam, the emerged

bottom hitting the wave surface. The lack of any

flat bottom area and the high deadrise angles of

the fore-bottom prevent serious slamming on this ship however.

Surging of the vessel was not recorded, but one

could see on the dial of the log, that the ship slowed down rapidly after any severe shock.

Theoretical study of the Immersion of a

wedge.

The cause of the shocks on the trawler 'Belgian

Lady' seems to be the penetration of the fore -body

into the water. As the fore-body sections of this

trawler have a V-form, an approach by

strip-theory can be based on the study of a triangular wedge, penetrating the water surface. This

(Schwarz -Christoffel transformation) to tackle the problem, it differs from earlier StLIdiCS on the same subject, mostly dealing with the

calcu-lation of hydrodvnamic pressures on the floats of landing waterplanes. In the present case, the

results will only be applied to wedges with large

dcadrisc angles. So compressibility of the water or other physical effects making the use of

po-tential theory inadequate in the case of very small

cleadrise angles, could be ignored. Even the

in-fluence of spray-root effects might be considered

as being less important.

The flow around a wedge, penetrating the water

at a constant velocity U, is assumed to be

equi-valent to the lower half plane of the infinite, two-dimensional flow with vertical velocity U at infi-nity around a lozenge-shaped, expanding prism. The piling-up of the water was calculated in Ref.

5 and represented by m -=

.-

, (where c and

respectively are the length ? the wedge side to

the risen water surface and to the undisturbed

water level). A high entrance velocity was as-sumed, to compensate for the fact that gravity

influence was neglected. For the range of deadrise angles concerning the foreship of this trawler,

the calculated values are given here:

(deg) = 40 50 60 70 80

m = 1,49 1,45 1,40 1,33 1,23

These values are higher than those found by other

authors.

The calculation of this piling-up also implied the determination of the wave rise profile. It is

Figure 2. Planes of the Schwarz-Christoffel transfor-mation.

level is equal to the section of the wave rise above this level.

Further in Ref. 5, the pressure distribution

on the side AB of the wedge (Fig.2) was calculated.

Itis opportune however, for the further

investi-gations, to know the hydrodynamic velocities and

pressures in the neighbourhood of AB. A more

general procedure therefore was necessary, using the complex potential

W =(p-l-k=U

(1)

and the general mapping function

2

/ (_c)

-c

The hydrodynamic pressure in an arbitrary point is given by

= -

+ -oo \J2

at. at 2 2

where V is the modulus of the complex velocity

u + iv , given by the expression

= U -

iv =Ve

(4)

where is the angle with the x-axis.

By relation (1),one can write

U -

iv

_e(2;12)1_*,U

(5) From the real part u and the imaginary part v,

V can be calculated.

a(p

is the real part of

i.Some transforma-tions, similar to those in Ref. 5, lead to the ex-pression

-_1..L(2_( .ç2_C2p_/(

_ç2

atL

'TI:

I'

/

/ \C')

-C'

(6)

or, with a transformation of the integral, and

calling ' =

Z =

-e

*2

dJ c'U

The convenience of using (6) or (7) depends on

the region one is working in.

A similar procedure as in Ref. 5 shows that e(p(-oo) _mU2

at

On the side AB of the wedge, in particular, one finds then for the pressure the expression (54) o Ref. 5. or using (7) and calling

'&

__i

S and k

Zr.:

P _2mkI S

jsi[_'2

d}

2m

(12)2(1)

+ 1 (9)

The values of k are calculated in Ref. 3.

On the line ( - oc , A), the pressure can be

e-valuated by the expression:

r

cxt

P

-

2mkI I ₍₂

'( 'E'-11f/

½U2 '

\Jf1\

2/

/

(.2

)

-

(i) J.t+i

(10)

To find the pressure in a point on the line BD,

one will find that this line corresponds with the

axis O1)in the -plane. Soon BD, _4, =0. In (6) has to be replaced by ii) The value of the line

integral of this complexanalytic function is inde-pendant of the path followed, avoiding though the

singular point B' by a quarter of a circular path with an infinite small radius .. It can be shown

however that the line integral along this quarter of a circle is infinite. Therefore, expression (7) appears to be more useful, since in

/12)1

_{d (11)}

where

t:5=h'

= o

when

I E approaches zero.

Formula (7) becomes, when 7' =

(8)

Finally, the hydrodynamic pressure in a point of

BD has the rather simple expression:

p

_2m(1)lt_2m.(

1

752)2(I-)

_{+ 1} ,/2pUz_ \

Il

(18)

As an example, the hydrodynamic pressure

distributions on these three lines are given for 60 degrees on figure 3. It is noticed that the unsteadiness of the flow makes the rate of pres-suredecreaseon the line (A, -00) much smaller

than in the case of a permanent flow. On the line

BD, by unsteadiness, the pressure become

posi-tive, except in the immediate neighbourhood of B.

These positive pressures have a small relative

value.

a(P(oo) ri2 ₍₁₄₎

at.

-The components of the velocity are

(15) (16) U =

_U(a1

_cosa

and

v =

_U(i-21)1_

3ifl so V

=u(1j1_

(17) aw_de'

U i/'2+1)'cos

ct k 712 .2 ____

' d

-ra

1 1l2+1 -T mk (12)

(

1)3r.sinxj

.S(P

_{and since} dc'

-The real part is

_di

--

--

mU22+1)1_

(13)

When 1 approaches infinity, it can be shown that also

r

IA

A

20 16 1 I6 1 1 I

i1

Figure 3. Distributions of hydrodynamic pressures for a wedge with a deadrise angle _{60 degrees.}

\u,fl('rcaI calenlation of ihc hydrodvula,nj(.

)rcuJe in an arbitrary point of the fluid.

First, the relation given by the general mapping

function

z

- e

ought to be tabulated by means of a numerical method. This will make it possibic to trace the potential and stream tines of the flow in the z

-plane. One is especially interested in the region near the water surface and the calculations will be restricted to this region.

Ix

/''+l'

The line integral can be split up/ + /

-I

where the values of

₄

are already known by

for-mer calculations and x in functions of _{is given}

in Ref. 5. For the calculation of

)'-

(20)

following symbols are used

B=2'1

A-i

B

c=i+

. D=

2 2 2 2

(A-i) +B

(A-i) +B

Then = C + Di, which can be brought to the

ie

form Re where n =I2 +D2 and e = Arctan D

C

EtIF

(19) C .1 10 (3: 60 deg .2 .4 .6 .1 1.0 1.2 ₁₄ 1.1 1.6 1.2 SCALE FOR POSITIVE VALUES

4 -10

.9S .99 .01 .02 .03 .04 .05 SCALE FOR NEGATIVE VALUES

if

E = P

cOs(i -) e

and

F=Rsjn(i-)e

To map the equipotential line p = (a constant)

from the _{-plane into the z-plane, one gives this}

constant value to ' and consecutive values to BvSimpson's rule, the integral can be evaluated for consecutive points in the z -plane.After trivial transformations the following expression is found:

--= f

+ k(/Edi.sinc +/Fd??'. co)

(21)

For ?'=oo

, the lincç= U''(= constant) in the

z-plane is parallel to BD or =0, and at a dis-tance d. As for 17=00,

dz=-e"d

(22)

the complex form of the _{segment d is given by} the relation

-= -e''

and the absolute value of the distance of the a-symptote of the equipotential line _{to the}

line (p=O can be written under the form:

c (23)

The equipotential and streamlines in the neigh-bourhood of the free water surface _{are traced for}

deadrise angles _{40, 50 and 60 degrees on} figure4a, 4b and 4c. 'l'hc profile of the piled-up water surface is traced on these same figures.

0

11'

+ I

k(-/Edr'.

_{cos. +/Fdr?'. SInc)}

N N N N N N undisturbed w LiVe1 N N N N

N,

-z

Figure 4a. Figure 4b. "0 0 : - .1 --.2 'N N N N N 4Odeg

undisturbed

wit iTeviC

I.

(6O deg

Figure4. _{Equipotential and streamlines around a wedge.}

FornumericaIcomputationof, it is advan-

_{By combination of formula (5) and its inversed}

tageous to use formula (7). If one calls form one can write:

I (24)

V +

T2 =_tj{(ECO5a-Fsincx) +(Esin

which was calculated earlier, and

+ Fcos)

i] (31)

If

K=-Icos/Fd.

(25)

G=-Ecos+Fsjn

₍₃₂₎ 0 and

L

= I sin

_Edo'

(26)

H =-E sin-Fcos

33 0 then then 2

v2-

U2 ₍₃₄₎ G2+ H2

)

d =K + i

L

(27)

So, the numerical value of the specific _pressure in any point of the fluid is:

Figure 4c.

MJ<E+LF

LL

E2+F2

N=-;-

(29)

d'=M+iN

P 2mk (28)

riii-(

_'M)-2rn

G2+H2 + (30) (35)

since only the real part of (30) has to be taken

into account.

In figure 5, p _{is given for different}

values of 'versus . Froiri this representation

one can conclude that the pressures do not

dimin-ish fast with distance in the immediate neigh-bourhood of the side of the wedge.

If

4 3 2 2 0 1.2 .8 .4 0 .4 .8 1.2 1.6 2.0 .4 .8 1.2 1.6 1' 20

watersurfaceisequalto the vertical induced ve-locity in the corresponding point situated above on the line BD (figure 2). This also implies the assumption of similarity of the pressure fields

respectively under the line BD and under the

pro-file of the piled-up water surface. It is shown

that the decrease of the hydrodynamic pressure relative to the distance is small near the sides

of the wedge. The validity of the above mentioned

assumption will be accepted for present purposes in this region.

The entrance velocity U was assumed to he high. With a relatively small entrance velocity, gravitation prevents the full development of the wave riseas calculated. In order to have an idea

of the entrance velocity required for full wave

rise a following simplified criterion could be cho-sen: at the point E of figure 2 the hydrodynamic

pressure should not be less than the static pres-sure corresponding to BE,

where BE

(i sin3) C

(36)

This condition can be written as: BE (37) if p, weight density ' and BE are expressed in metres and kilograms, or

U>4.43(m1

sI)Y2( p

\-Ya

Ct/2

\Y2PU)

(38)

where U is in metres per second and c in metres.

Figure 7 shows these values of U versus c for = 40, 50 and 60 degrees. c will be the length of the side of any immersed foreship section. It will be seen that in the case of the trawler these

required values of U can be reached.

Figure6 allows one to determine the pressure Hvdrodynamic forces and added mass.

in an arbitrary point of the fluid in an easier way.

Stream mode! and free water surface.

It is assumed [Ref. 51 that the stream model of

the uniform infinite flow U around the

lozenge-shaped prism, expanding upwards at a rate of mU,

simulates the flow around the wedge, penetrating the water surface,taking account of the piling-up

of water. This Imp] tes that the velocity on the free

In Ref. 5. the resultant of the hydrodynamic pressures on the sides of the wedge while being immersed was evaluated by measuring the area under the curves of pressure distribution, given on figure 11 of this reference. Only the area of

positive pressures was taken into account and the

area of negative pressures neglected. It was

as-sumed that the effect of these negative pressures

would actually be very small, since it was

be-lieved that there isa natural tendency to annulate

40dsg P (: 50 deg r cuL (60deg .2 .4 .6 .8 17' ₁₀

Figure 5. }-lydrodynamic pressures for constant values of .

0 3

$

.4

-

.2 - .1 0 .4 .6 .8 1.0 71.2 .2 .4 U(m.s,c)

Figure 6. Hydrodynamic pressure lines.

12 B 6 4 2 0 .6 .8 ?'l.O .2 .4 .6 .87'l.O

wii

11

'JIM',

A 0'

iIiiIiLII1

A4MIA

Ir

1 {1MutJ

'1

I1

70

1!

1

I>suI

_Ju,

/!4300

deg

i/A

IA

rcA'7-

-(,

40 deg SO deg 60 deg

0 .2 .4 .6

.1 X/

0 .2 .4 .6 .8 1

Figure 9. PartIal pressure values due to the Induced Figure 8. Partial pressure values due to the time rate

velocity. of change of the potential.

0

2 4 s i tO 12 14 clint IS

Figure 7. Required entrance velocities versus c. 10

6

4

2

excessive underpressurcs. Beside the length over which these negative hydi'oclynamic

pres-sures occur, near the spray-root, is seen to be

small.

It micht be opportune to take full account of the negative pressures here of which the effect on the

final resultant then can be noted by comparison with the figures given in Ref. 5. The actual re-sultantofhydrodynamic pressures is believed to lie in between. For that purpose, the area under

the curves representing the partial values of due respectively to the time rate of '/2P U

change of the potential, and to the induced velo-city have to be evaluated. These curves are shown

on figure 8 and figure 9 for different deacirise arigles.Whenapproaches unity,that is near the

spray-root, both partial pressures tend to infinity.

While for the first one no difficulties arose to

evaluate a sufficiently accurate value of the area,

an approximation method had to be used in the

case of the pressure partdue to the induced velo-cities u. It was proved however that for

sufficient-ly small values of ' , or in the neighbourhood

of-=1

I

0 C()2(

2--1

CL

x(3

2$i

2cr. CL n k

(i-) 3-Z

(39)

Including the term of the stagnation pressure, the (negative) resultant of 'steady-state'

pressur-es was found.

The vertical component of the hydrodynamic force will be called F for the steady-state , and F"fortl-ieunsteady--state force, due to the

change of the potential. The total vertical hydrodyna

-mic force component, acting on a water surface

piercing (half) wedge is

F = F' + F" = cp.cos

where p is the average pressure, and where a negative sign is attributed to F' and a positive

sign to F". F is always positive. Only one side of the wedge is considered here.

The entrance velocity 15 being constant, the

added mass ma can be given by

-

ft

ftin

mCL-TJ- _2Um

Corresponding with the two terms of F:

ma = m_a m _a (43)

so the added mass is represented here as com-posed of a positive part m"a and a negative part

m'a.

Most authors derive the concept of added mass from the kinetic energy of the fluid, set in motion

by the body. Green's 'first identity' leads to the expression of this kinetic energy, in the case of

a steady flow

K =p/pds

(44)

in which the symbol 'n' is related to the

perpen-dicular on the boundary of the body. For the case of the wedge, one accepts the configuration of

po-tential and streamlines around a body.

consist-ing of the wetted part and its image, or the

lozenge-shaped prism, moving with the constant velocity 15 through the infinite fluid, initially at rest. Only

the fluid and its kinetic energy under the line of symmetry, BD (figure 2), where (9=0, is taken into account. It is easily shown, that the line in-tegral in (44) has a value, different from zero, only over the wetted side of the wedge. In the pseudostationary, in fact unsteady flow around the wedge, at a time t, the configuration of the potential and streamlines is considered as being

the same as in the above mentioned corresponding flow model. The added mass is then derived from

K =m

U2 (45)

2 a

In the co-ordinate axes Axy of figure 2, being fixed

to the body, which is moving at the constant speed U, the velocity potential is given by:

(PU-1Jxsinj3+Uy cos +Ucsin (46)

The fluid at infinity is at rest and there (p=O. On

(40) the side of the wedge, y =0 and also:

(48) (42) _{This value, and thus the added mass according}

to (45), can be calculated numerically without any

= Ucos (47)

A convenient transformation of ( shows that:

fPdc=kc2U2cos3/"1. "

_C'C

1 k j C

problem of accuracy. It is stated here that this value otadded mass is exactly the formerly

cal-c ul ated

F'c sin

13

m a -

₂

2(J m

(49) of formula (43).

The other, negative term nl'a in (43) is related

to the often called'steady-state' force F':

F'csin

There is a fixed relationship between F', through the values of the velocities u on AB (axes Axv of

figure 2), and the values of the velocities u' on line ED in the axes T3Xi, I hese velocities u built

U the wave rise, from the instant t = o the keel of the wedge touched the 'water surface till a

cer-tain time t at which the instantaneous picture of

the wetted wedge side and the surrounding fluid

is investigated. The time history of crossing the instantaneous line BD by the fluid particules at velocities u' suggests the existence, at the time t, of an additional momentum of the fluid under the piled-up water surface. To this momentum, an added mass m'a is related.

A clear relationship can be found by means of

the impulse -momentum principle. In figure 2, the axes BXY, and the line 0'OO' at infinity are fixed to the moving prismatic body. The case of permanent flow is considcrcd here. 1-lence the flow pattern stays unchanged between the lines O'OO"andBY. Fromt = o tot, the mass that has

flowed through BY is:

y=oo

pct/

u'dY/c=pct/ {U+(.-i)U]dY/c

° ₀

(51)

In the same lapse of time, a mass flowed through

0 00 , which will be written under the form =0o

pUtc cos

+pct./

Ud'/c

0

'I'hcse two masses being equal, the following re-lation results from (51) and (52)

(52)

4

3

2

The values of - are calculated for several dead-riseangles and are represented by the curves on

figure 10. Relation (53) can be verified by

mesuring the area under the curves.One caii get a-r9undl the difficulty in the vicinity of B, where

= oo, by means of the following approximation formula

1 2(1-') _I

-Yc

0

valid for small values of Y/c

By similar considerations of momentum through BY and 0 00 , and taking account of

relation (53), one finds that the chatige of momen-tum, over the timet, from 0'OO" to BY is expres-sed by the lefthand side of the following impulse-momentum equation:

pctU2cos

+pcW2/A1l)2dY/c

_=(F'+F0)t

In the impulse F't + l'0t, F is the resultant of the pressures on the line BD

Y/C:OO

F=cp

d'1/c

_P

'/U21tJ'

-1

Writing (--)2-1under the

_{form (}

U,

-U o0

Fo=4pcU2/

(-)2dk-0 (56) (57) 2 U' 1) +2(--1): pcU2cos (58) U (3 30 dig.

/Q

50 70

d46°

.2 .4 .1 Yi- .1 = cos (53)

ma

(50)

I)etk ol a triaiitilar %%'e(lgr ('ct For convenience, in this two-dimensional ap-proach, a wedge section of unit length is

consi-dered. M is the mass of the wedge and z the

dis-tance of the keel under the level of the undisturbed

water surface.

(M+ma) z + mz = Fe (61)

encloses external forces.

For the wedge, penetrating the water at con-stant speed, the first term is zero and the second

,.

, i.e. the time rate of change of momentum

of the added mass, is equivalent to the

hydro-dynamic force F, evaluated in the present work. At the instant the piled-up water surface cros-ses the decklinc, the rate of change of potential drops to zero, and so does the partial force F" in F. In other words, a decrease m"a of added

mass suddenly occurs and theoretically, only the

negative added mass m'a is left. This disconti-nuity is assumed to have an effect only during a very little fraction of time, being immediately disturbed by other physical effects.

Restoring buoyancy forces and damping forces,

represented in F of (61) are assumed to stay constant during the small fraction of time , in

which the change of hydrodvnamic force takes place. This discontinuous change having taken place, the change of acceleration a is derived from the relation (61):

F"

ta=

_{M + m}

a

If for some reason the entrance velocity U is

maintained after the discontinuity, the change of

acceleration is recorded on a diagram versus

time as a peak, with depth a.

Reasoning in terms of added mass,it was stated

that a classical slam is caused by a sudden

in-crease in time of the momentum of added mass. In the present case however the shock phenome-non, associated to the acceleration peak, is caused by a sudden decrease of the momentum of added

mass. In a way of speaking, one could call this shock a 'negative slam'.

While the concept of added mass is quite

oppor-tune for use in the calculations of ship motions, it is seen however that a direct study of hydro-dynamic pressure variations is more suitable for the investigation of these discontinuous

pheno-mena.

(62)

Calculation of 1114' IIlagIIItU(Ie (II aleeieratioII

1)eak at Ihe how Of a traw icr.

Using the results of this theory on the immer-sion of wedges, an attempt is made here to

calcu-late the magnitude of acceleration peaks for the

trawler 'Belgian Lady', sailing at a certain speed in a known sea state.

In order to compare with distinctly measured

values, a special trial run was chosen for the analysis. For this trial run the helmsman was

asked to maintain the ship on a straight course, perpencliculartothe wave crests, and full power was ordered.

The characteristics of the ship and the known data, used in the analysis, are given in Table I.

Table I

The sea state was J3caufort 8, the relative wind

velocity was 42 knots at a relative direction of

0 degrees, and the average of the 10 percent

highestwaves was 9.6 metres. The spectrum of

this head sea is given in Ref. 1 under observation

no. 5.

The location of the used instruments was as follows: pickup wave recorder: 14 m from AP,

stern accelerometer: 1 m behind FP, bow acce-lerometer: 1 m behind AP. The ten minutes long bow acceleration record shows 40 peaks, ranging

fromo,lgto2,8g. Three samples are shown on

fig. 13. The bow and stern acceleration records are synchronized. By numerical integration of these records,diagrams of vertical velocity were obtained. The same procedure applied to these

velocity diagrams furnished a time history of the vertical displacement at the same places as well. The instant of each acceleration peak at the bow

could be mapped on the simultaneous wave record.

It is necessary to derive the instantaneous profile

from this time history of wave displacement at

Lo. a. (metres) 50, 00

Lpp (metres) 45, 00

B (metres) 8,60

T aft,above keel (metres) 4,40

T Iore,above keel (metres) 2,66

i (metric tons) 648

Cb= 0,475

Longitudinal radius of gyration ki= 0, 23OLpp

Centre of buoyancy, from A P (metres) 21,70

Freeboard, at FP (metres) 4,75

;4

1LR4I _{\ \ :}

J / 4:OW. DWI ACCCLII*ION At OW

fr:. /

*

-.

Wi

L\ \.L \ \ ' I

7;!-RvP/

I ACCELRA1iOtlATSTEM .1

-17 7 +. w nwii. AcCA1Io,i *isow

BOW tIP

_2

cw 3cwt

BOW UP

Figure 13. Samples of bow acceleration record in a rough head sea.

a moving point. The average ship speed is known,

but surge is neglected. The apparent periods of wave encounter can he measured on the record

but the celerity of the different wave crests and troughs in this irregular sea is an uncertain

fac-tor. it is known that the celerity of irregular waves

is smaller than its value derived from the troch-oidal wave theory and probably higher than the group velocity, which has half this value. It was suggested by oceanographers that the average

apparent wave length _2 91

"-r 7c

Iii ,.9 I I 'I I '. I.

(63)

where T = average apparent period.

As it was noticed that the acceleration peaks mostly occurred when encountering waves of

rather average height, it was decided here to

ac-cept a celerity.

(64)

where is the celerity of a trochoiclal wave,

corresponding with the measured period of en-counter. These gradually varying periods, attri-buted to successive points on the wave record, are evaluated in function of the time distances

between neighbouring crests and troughs. Hence, following relation is accepted here:

Te-

_O,83V+Vs (65)

where Te = period of encounter, (sec.)

= apparent wave length, (metres)

V = ship speed, (metres per sec.)

KnowingAfora certain, on the record estimated value of Te, a distance per time unit, at which the wave height is read off on the wave record,

is derived, and hence, an instantaneous picture

of the wave profile, with the position of the ship

on it, is obtained. Figure 14 shows for different cases, which have been numbered, the position

of the shipat the moment of an acceleration peak

on the estimated profile. This wave profile is

indeed only a rough estimation, because of an-other serious shortcoming in this method. The presumed instantaneous wave height at the bow

iscierived from the wave height picked up by the

wave recorder (14 m from the AP), a couple of seconds later. However, in this lapse of time,

a trough can be deepend, or a crest grown up, or

both partially leveled already. A scattering of

the final results of the present computation

method might be mainly due to the difficulty of tracing the actual wave profile.

The profile of the trawler on figure 14 includes

the deckline of the forecastle and the bulwark behind, which strokes fluently with this deck. The calm-water line is indicated, so the

calcu-lated vertical displacement, relative to the known quiet-waterlevel is shown.

As the vertical velocity of the wave at the lo-cation of the bow can roughly be estimated by

measuring the wave slope there, the vertical

relative velocity of the fluid at the bow can f in-ally be calculated. 'Ihe speed of the ship and the relative vertical velocity are the components of the resultant relative velocity of the fluid with respect to the forcsliip hull. It is assumed that surging of the vessel is cmpensated by the hori-zontal component of the orbital velocity of the

wave particules.

Because of the inclination of the resultant re-lative velocity, one has to consider the

corres-ponding hull sections wider this same inclination, dificring in this respect from the usual procedure

of strip-theory.

It is noticed on thc diagrams that at the instant

of a shock the vertical velocity was not varying

fast, so the assumption of a constant entrance

velocity does not seem to he a serious drawback. Furthermore, the different inclined foreship

see-tioiis maintained an outspoken character of a triangular wedge section. The sections of the

foreship of the 'B&gian Lady' at equidistant in-tervals,overadistatlCe of interest to this study,

were traced for different inclination angles £,

where £ =90 degrees means perpendicular to the

waterline, asfora uSLial striptheory. The

dead-rise angles for the different cross sections at

different inclination lay between following values:

Figure 14. Wave profile and position of the ship at the instant of a shock. 200 z 160 120 80 40 0 30 45° 1045 2000 1600 1 200 800 400

Figure 15. Hydrodynamic force IF", Its vertical com-ponent and moment with respect to the midship, and its horizontal component for different inclination angles in the case of the 'Belgian Lady'. (full foredeck-line im-mersion). tons ton.m C

V

0 60°

?5 .

U in m.sei'

Mc

hal = 1 x and = + 'a ,,

Fv

M + Ma

where 1 distance from fore accelerometer to centre of buoyancy = 22,30 metres,

= moment of. F" with respect to the

centre of buoyancy,

M = mass of the ship=66.05 Tonm see2,

I = longitudinal moment of inertia of the

ship = 7075 Ton m see2,

Ma = added mass,

'a = longitudinal added moment of inertia. All units are metric tons, metres and seconds.

The added mass for the whole ship was

evalu-ated by numerical integration over the length of the added mass per unit length, calculated for equidistant, vertical cross sections. Those cal-culations are based on sectional inertia coef I

cients c' , according to Prohaska, as function

of the ratio B/H and section coefficients 6 (x) = B H The sectional draft H is measured, for

each case, from the upperside of the keel to the instantaneous wave profile. However, as the in-stantofa discontinuity is considered, a negative added mass m'a, as calculated earlier, has also to be taken into account for the cross sections at the bow. It is difficult to foresee what length of

the deckline in the foreship is simultaneously

immersed. By estimation, in the area of station

8, the plots of added mass, according to Prohaska,

are forced to join the negative added mass values

bya continuous curve. At station 8, the mean of

both values was chosen, The used distribution of added mass over the ship's length for the 7

posi-tions of the ship on the wave, considered here above, are given on figure 16. This procedure might seem to be rather crude, and the results,

especially for the longitudinal added moments of

inertia, less accurate. However, it is believed

that the effect on the final result of such inaccu-racy is small, because of the overweighting in-fluence of the factor relative velocity.

For the 7 shock phenomena, investigated here. the important factors and resulting magnitude of

acceleration peaks near the FP is given in table II. These results and the measured values of the

magnitude of acceleration peaks, are represented on figure 17. The occurrence of two consecutive distinct peaks on the acceleration diagram might

be due to partial consecutive immersions of the

deckline. The corresponding magnitudes are

added. E (degrees) ' (degrees) 30

4

- 68 45 49

-72

GO 48.5 - 68 75 52

-70

90 49

-72

Actually, the entrance velocity is different for

each cross section, depending on the angular

pitch velocity. An investigation on the effect of higher velocities around the most forward

sec-tions with the smallest deadrise angles and of the

lower velocities in the more extended region of the sections with highest deadrise angles seems

to justify the introduction of one overall relative

velocity,as calculated at the location of the fore

accelerometer. Moreover, the length of the region in question is relatively small. On the other hand,

it is seen that in general at the moment of a shock, the vertical velocity at the bow is not only

compo-sed of the angular pitch velocity, but also of a

considerable downwards heave velocity.

Fromfigurell, the force F", which is consi-dered here as the drop of hydrodvnaniic force, is derived for each section at a given inclination angle. Furthermore, its vertical component and

moment with respect to the midship, and its

horizontal component is evaluated. A numerical integration overthe length of the foreship allows one to evaluate the total vertical component and its moment to the midship M", and the hori-zontal component Fj' of the hycirodynamic force

IF", vanishing at the instant of an acceleration

peak.

The results for this trawler are given in the

form of graphs on figure 15. The magnitude of the vertical acceleration peak in the foreship is derived from the equations of motion, and

%IIitiuiiaI and ennellidilig

reiitark.

The scatter in the plotting of measured magni-tudc of acceleration peaksaround the rather

con-tinuous curve through the plots ot calculated

values on figure 17 might be clue to several

mac-curaCicS,aS mentioned above. It is also not sure

that in each case the deckline was actually

im-mersed over the length assumed in this compu-tation. This might be a reason why some of the

values of I ,(thus also M and Aa) in Table II

apparently are too high for the actual motions and position on the wave of the ship.

Further-more, a roll angle may change the presumed

conditionS. Except for no 7 and no 38. the plots

of the mcasu red acceleration peaks however seem

to have a similar trend as the calculated curve.

On figure 14 it can be seen that br every case

the ship lies on the descending slope of the wave,

is heaving down and pitching into the oncoming

wave. Only the profile of the wave Is shown, but

the water surface near the hull is actually higher,

first, by the existence of a bow wave, of whieh

the height was estimated to be 1,2 m,according

to Tasaki's formula for effective freeboard, [Ref.

1 and secondly, by the

hydrodynamiC piling-up

of the wftcr surface, which is assumed to reach the deckline of the foreship at the instant of an

acceleration peak. It is emphasized that an

ob-server on the briclge,distinctly feeling the shock,

did not notice any green water falling on the deck

at that moment.

ThecomponefltFl suggests the simultaneous

existence of a sudden acceleration in the longi-tudinaldirection of the ship too. Since no

accel-erometer was mounted in this sense,and the added mass in this directionpoorly known, no calculated

values are given here.

Since the described shock phenomena would

find their source indiscontiiiuOUspressure varia

-tions, reactions of the surrounding fluid are to

he expected. These effects have also to be taken

in consideration to complete the picture of a

shock.

On figure 13, the deceleration just before the

how acceleration peak no 9, no 26 and no 38

in-jcatesaslamming, with moderate effect, of the

shipbottomonthe\V3.ter. The position of the ship

onthcwaveatthatm0me1td5 shown on figure 14.

Though the shocks were felt aft, the

accelera-tion record over there is less clear for inter-pretation. At the stern the term

ta" has tobe

0

Figure 17. Measured andcalculated magnitude of accele -ration peaks at the bow of the 'Belgian Lady'.

substracted I roin ta', makinga much smaller than in the iorcship. The flexibility of the hull

and the existanco of a longitudinal acceleration

might further disturb theaccelerogram.

Never-theless,at the instant of a shock, the downwards

directed acceleration due to themotion had a value already near 1 g, so consequencesof small super-posed acceleration peaks or whipping were

spec-tacular sometimes. Life in the accomodationS

became difficult, foodstoreS were overthrown,

and damage to instruments and auxiliary machin-ery at that time might be attributed to these severe working conditions.

For large vesselS , where the proportion of

discontinuous hydroclynamic force variations to

the mass is much smaller, these shocks are of

less importance. For

smaller vessels with a

highly flared bow, the same phenomena might

have serious effects. Thepresent theory suggests to moderate this flare, asfar as other seaworthi

-ness qualities do not become affected.

Ackno\vledgementSTheexPel'iments on board of

the trawler 'Belgian Lady' were carried out by

the Laboratory of Naval Architecture (Director

Prof. C. Aertsscn) of the State University of Ghcnt

and sponsored by Centre Beige de RechercheS Navales. Brussels. E + CALCULATED MEASURED 38 4 Ui 0

z

/ 0

4

Ui -J Ui_____ C-, 4

0

26 9 0 0

/9

/

26/ oO 38o

-C,

/

25

/

o _// / VELOCITY A"25 AT a 0

THE BOW m.sec 4

2

RELATIVE

7/

4-, 2 4 6 8 5 4 3 2

formance and seakeeping trials on two

conventio-nal trawlers'. Transactions North - East Coast Institution of Engineers and Shipbuilders, 1964. Ferdinande:'MOdel tests in regular and irregular waves

at the Davidson Laboratory', appendix of:

Aertssen :'Service Performance and Scakecping Trials r onm.v. Lukuga'. R.I.N.A. 1963.

Szcbehely and Todd: 'Ship slamming in head seas', David W. Taylor Model Basin, report 913, 1955.

Korvin Kroukovsky : 'Theory of seakeeping',

S.N.A.M.E., 1961.

Fcrdinande:'Theoretical considerations on the pene-tration of a wedge into the water', International Shipbuilding Progress, April 1966.

Bisplinghoff and Doherty: 'A two-dimensional study

of the impact of wedges on a waler surface',

Massachusetts Insitute of Technology, 1950. Tasaki: 'Model experiments in waves', p. 155,

Re-search on seakeeping qualities of Ships in Japan, Volume 8, 1963, The Society of NavalArchitects