Random impact loads due to ship slamming in rough seas

5 N1. 1972

ARCHI

EF

RANDOM IMPACT LOADS DUE TO SHIP SLANNING

IN ROUGH SEAS

by

Mickel K. Ochi

David Taylor Model Basin U. S. Navy

To be presented at the First Conference on

Ship Vibration Acoustics and Vibration Laboratory, David Taylor Model Basin and

Davidson Laboratory January 1965.

Lab

y.

Scheepsbouwkunde

Technische Hogeschool

Deift

z.

4i

Onderafkin. .r-'

TABLE 0F CONTENTS.

Page

INTRODUCTION

...i

OUTLINE OF IMPACT LOADS DUE TO SLAMMING i

Ship Slamming and Hydrodynamic Impact Loads i

Frequency of Occurrence of Impact ., 3

Magnitude of Impact Load

...,

Probability Distribution 4

Distribution of Impact Loads Along Ship Length 4

METHOD FOR ESTIMATING MAGNITUDE OF RANDOM IMPACT LOADS 7

Probability of Occurrence of Impact 7

9

Probability Density Function of Impact Load IO

Magnitude of landom Impact Load 12

Summary of Estimation Method 13

CONCLUSIONS

...øÖ..o.o

INTRODUCTION

Vibration experienced by a ship may usually be attributed to

either mechanical or hydrodynamic unbalanced forces. The unbalanced

force caused by the main engine is a typical example of the former,

while that induced by the propeller is an example of the latter. Besides vibrations caused by these unbalanced forces, a ship also experiences vibrations induced by an impact type force applied to the

hull. A typical example of this type of vibration ïs that due to

slamming. A significant difference between main engine or propeller

induced vibration and that due to slamming is that the former is periodic

while the latter is aperiodic. Hence, the-vibration of the former type

continues indefinìte:Ly, while that of the latter type occurs at random

and diminishes with time. We may distinguish these two types of

vibration as steady-state and transient.

The difficulty in evaluating the exciting force for te tran-sient type vibration is that its magnitude randomly varies with every

impact. Hence, in order to estimate the magnitude of the exciting force

a statistical approach is required.

The purpose of this paper is to discuss the frequency of occur-rence and magritude of random impact loads associated with ship slamming at sea as a typical example of an exciting force which causes the transient

vibrations. Part i. of the paper outlines the various properties of impact

loads due to slanmi:í.ng obtained from model experiments, and Part 2 discusses

a method forestimating the frequency and magnitude of impact load.

i OUTLINE OF IMPACT LOADS DUE TO SLAMMING

1.1 Ship Slamming and Hydrodynamic Impact Loads

Ship slamming is always accompanied by a hydrodynamic pressure on

the forward bottom, and this pressure excites -vibrations in the bottom

plating as weil as in the hull girder. As mentioned earlier, the magnitude

of the hydrodynamic impact load varies randomly when slams occur, It

varies from one wave encounter to the next and is dependent upon the severity of the sean sip speed, course angle, etc. Not only is the magnitude of impact random but so also is the time interval between

impacts. Sämetimes impacts may be applied successivel.y to the ship

bottom resulting in vibrations being super:imposed on those produced

by earlier impacts. Thus, we must consider both-frequency of

occur-rence of impact and its magnitude.

Prior to discussing these problems in detail, it may be well to give some general properties of the impact loads associated with

slamming.

[il

The impact load is of the triangu]. ar type and

its duration is approximately 0.08 to 0.12 sec for a 520ft vessel.

Maximum impact loads do not always occur simuianeous1y at the various locations along the ship bottom but

instead, the pressure travels either forward or aft.ward

with changing magnitude. The traveling time from

Station 2 (10 aft of FP) to Station 5 (25 aft of FP)

or viceversa is approximately 0.15 to 0.30 sec for a 520ft vessel. Quite often, however, impact pressures are applied over the ships bottom almost sïmuftaneously,

and this is certainly t.he severest case.

The domain of ship bottom where impact loads are applied ìs a function of sea, ship speed, loading condition, and

course angle. However, the domain forward of 3tation 6

is the area of prime consideration, since the chance of impact beyond this domain is unlikely in a practical

operation of the ship.

:L.2 Frequency of Occurrence of Impact

The frequency of occurrence of impact at a location of 0.1 L aft of the forward perpendicular (Station 2) will be considered first, since

experimental results have shown -that whenever impact pressure is applied

at this location1 deceleration is always apparent on the acceleration record, and slauìng can be considered to have occurred. _{When pressure}

is applied near., the forefoot only1 neither deceleration nor hull shudder

usually take place1 since the breadth of the flat bottom is too small to

generate a force large enough to cause hull shudder.

Figure 1. shows the probabilíty of occurrence of impact per cycle

of wave encounter in various sea states and at various ship speeds

obtained in tests conducted on a MARINER mode:[. _{Figure 2 shows the pr.oba'}

bility for various loading conditions and for various _{course angles jn a}

moderate Sea State 7. As can be seen in these figures, the probability

of impact increases significantly with increase of (a) sea severity and

(b) ship speed1and decreases with increase of (c) loading condition and

(d) course angle. A consistent tendency is observed for other locations

along the ship length.

Figure 3 shows the effect of ship speed on the probability of

impact at various locations along the ship length1 hiÏe Figure 4 shows

the effect of course angle. It is clear from these figures that the

probability of impact at the ship!s forward portion is much higher thn

that at the locations farther aft.

It is noted that1 although an impact will be applied at the

for-ward part of ship bottom more frequently than at locations farther aft1 the magnitude of this pressure is not necessarily higher than that at

other thcations, The present discussion concerns only the frequency

of impact and not the severity of the. impact.

Formulae to compute the probability of _{occurrence of impact for} a given condition will be shown in Part 2 of thïs paper.

1.3 Magnitude of Impact Loads

1.3.1 Probability Distribution

Since the magritude of impact load varies randomly from one slam

to another, a statistical approach is required. In other word the

probability law which governs the impact must be established.

It is a we1L known fact that ship motions follow the Rayleigh

probability i.as. But, what probability, law is applied to impact loads

associated with slamming? In order to establish the probability law

the following condItions obtained through model experiments will be

used. These are,

Impact load associated wi.th slamming is approximately

proportional to the square of the relative ve:Locity between wave and ship bow.

Relative velocity follows the Rayleigh probability law.

Ther exists critical relative velocity below which

slamming does not occur,

By taking these three conditions into account, it was found

that the impact. load associated fth slamming follows the truncated

exponential probability aw.[2l The probability density function will

be given in Section 2.3.

Figures 5 and 6 show comparisons between the theoretical probability

density function and experimental his togram for various course angles and

for various loading conditions, respectively. These figures pertain to

the impact loads observed at Station 2 of the RINER in a moderate

Sea State 7, at a 110 knot ship peed. Figure 7 shows another example

of a comparison including the averages of the 1/3 and i/io highest pres

sures. Although some discrepancy between theory and experiment a're seen

in these figures, the agreement between them is satIactory, in generali.

1.3,2 Distrìbut;on of Impact Loads Along Shi.p Lengt.h

In the preceding section, the probability distribution of impact

provides a valuable, tool for estimating the probability of occurrence

of a certain magnitude of impact load at a specific location on the ship's

bottom, _{However, it does not provide information concerning the pressure}

distribution along the ship length. The pressure distribution aLong the

shìp length i'.s very important since it has a direct relationship to hull

response

As was mentioned in Sectior 1.1, the impact load during a slam travels either forward or aftwards along the ship bottom with changing

magnitude Also, quite often impact loads are applied over the ship's

bottom almost simultaneously. _{These cases occur randomly from cycle to}

cycle, and depend entirely on the phase between wave and ship bow motion

at the instant of impact. For our purpose, however, it may be appropriate

to assume that all maximum loads are applied simultaneously to the ship's

bottom since this represents the severest case,

Figure 8 shows some typical examples of the impact pressure

distribution along the ship length obtained in a severe Sea State 7 at

various ship speeds for the MARINER, As can be seen in the figure, the

shape of the distribution changes from cycle to cycle. _{Particularly, at} high speeds, the highest pressure is sometimes observed _{near Station 2}

and sometimes farther aft, The latter case is, of course, more severe

for the ship hull than the former, since there i.s a significant increase

in flat bottom with incrasi.ng distance from the forward perpendicular. Since the shape of the distribution changes from cycle to cycle, the envelopes of the distribution curves may be drawn for each speed. These

envelopes indicate the maximum impact Load at the various locations observed

during 30 minutes operation of the ship, and provide valuable _information

concerning where a:Long the ship's length the highest pressures occurS These

curves are compUed and shown in Figure 9 as a function of ship speed.

It i clear from the figure that the location of highest pressure

on the keeL line shifts toward midship with increasing ship speed. _That

is, the location is about 0,13 L aft of the forward per.pendicular for

:Low speeds and shifts to 020 L aft of the forward perpendicular' with

increasing ship speed It can also be seen from the figure how significantly

the magnitude as weil as the range of application of impact increases with increasing ship speed. The figure may give the impression that more

severe Lmpact might be expected at higher speeds. However., this may not

be t.he case. If the ship could be operated at much higher speeds. then it

may be.. found that the impact loads would be reduced, since it is to be

expected that. ship motions will, be reduced at very high speeds.

In order to obtain the effect of sea state on the severity of

.s1amming Figure 10 was prepared, In this figure, ship speed was 10

knots for ail except Sea State 8 where the speed was 7.5 knots, It is

evident that. the impact load is drastically reduced with decreasing severity of the sea.

Thus far the probability distribution of impact load and the distribution of the loads iong the ship length have been discussed. It

is noted here that the discussions pertain to the magnitude of impact if

an impact occurs i.e., the conditional probability. The probability of

occurrence of a certain magnitude of impact is then the product of two probabilities; The one being the occurrence of impact, the other being

the magnitude of Ímpact.

Figure ii shows an example of this join probability obtained in model tests on the MARINEP for a iO knot ship speed in a moderate Sea

State 7. The figure can be 'read as foilows _{In a given moderate Sea State 7,}

the probabilit.y of occurrence of impact loads (per cycle of wave encounter')

greater than 50 psi for example, is 0.055, 0.045 and 0,010 at Stations 2,

3, and 4, respectively. The figure may givean impression that no impact

greater than 100 psi would occur at any locations along the ship length

irrespective of how ong tLme the shi.p operates ïn the given condition.

However, this is not true. The joint probability shown in Figure 11 was

constructed from test results observed in a .30 minute operation. Suppose

the ship li operate.d continuousl.y fo'r a long time, there is a chance t.hat

impacts greater than 100 ps:i may appear, _{This problem can be solved by}

using the estimation method

givén

2 METHOD FOR. ESTIMATING MAGNITUDES OF RAISDOM IMPACT LOADS

2.1 Probability of Occurrence of impact

In order to estimate the magnitude of random impact loads, it is nec.ssary to obtain the joint probability of (1) Probability of

occur-rence of impact, and (2) Probability that the impact load exceeds a

certain magnitude when impact occurs.

The DJabìlity of occurrence of impact atan arbitrary location

along the ship length can be computed by the following foi.mula

/ 2 ..

1H1

--\\ I\4

Ptob {lmpact} = e

where, H. Draft at location considered

Threshold velocity

2o Twice the variance of relative motion between

ri ri

wave and ship bow at location considered

2?= Twice the variance of relative velocity between

r.

wave and ship bow at location considered

it should be noted that the parameters, H, R', and R.., all refer

i ri ri

to a specific location for which the probability is considered.

The following discussion will be given concerning the various

parameters involved i..Equation (1). Threshold velocit.,

The threshold velocity . the critical reiatïve velocity between

wave and ship beIc which slamming impact does not. occur, i.e., the minimum velocity which causes .slaLng impact. _{The requirement of}

threshold velocity for slïng impact was suggested by Szebeheiy sometime

ago [3], however an evidence to prove its reality was left until recently when model experiments were conducted in irregular waves [21. This is

shown in Figure 12. It shows the relationship between relative velocity

and impact load measured in irregu1r waves at Station 2 of the MARINER. As can be seen in the figure. no impact is observed for a relative veLocity

less than 12 ft/sec (converted to full scale. 52OE-ft vessel).

The following two questions arise (1) Is the threshold velocity

the same for a ship of different form? (2) Can the same value of the

threshold velocity be taken for computations of the probabilities at 1oca

tions far from the ship bow such as Station 4 and 5. To answer the first

question, the magnitude v.f threshold velocity was evaluated on five different

[45]

ship forms and the results are tabulated in Table . For convenience,

the values have been converted to those for a 52Oft ship for comparison

with the MARINER, As can be seen in the table, the magnitude of the thres

hold velocity are nearly consistent with an average of :L2 ft/sec. To

answer the second question, Figure 13 was prepred. The figure shows a

comparison between predicted and observed probabilities of occurrence of

impart at various locations along ship length for the MARINER. The curves

pertain to a ship speed of 10 knots in mild, moderate, and severe Sea State 7.

In the computation of probabilities, the same thereshol.d velocity of 12 ft/sec

was used for ali locations. As can be seen in the figure, the agreement

between pred:Lcted and observed probability of occurrence of impact is

satisfactory except that near Station 4 for a moderate Sea State 7. Thus,

wïth our present knowledge, it is considered to be appropriate to take

12 ft/sec as the threshold velocity associated with slamming impact for: a

52OE-ft ship. For a ship of different length, the above value should be

modified according to the Froude scaling law.

Paramete:rs R' and E

ri ri

The most accurate method of obtaining the variances of relative motion and velocity between wave and ship bow is to measure the reiative motion in gu1ar waves by f.xing an immersion sensing element at several

Locations along the ship Length and obtain the response amplitude operators.

Then by applying the superposition principle, the area under the spectrum of the relative moton is twice the variance required for computation.

The variance of the relative velocity can be obtained simpJ.y from the spectrum of the relative motions

Another method to obtain the variances of relative motïon and velocity is by caluiatïons using the experimentally obtained pitch, heave, and phase Lags between wave and these motions.

2.2 Number of Impact per Unit Time

The problem of how many times an impact occurs t a specific

Location along the ship length for a certain period of ship operation is an interesting subject/to consider. The number of occurrences of impact

per unit time is statlst:icaily correlated with the probability of occurrence of impact under the following conditions

The random variable must have a narrow-band spectrum and a

normal dlst.ribut:ion with zero mean,

Then the expected frequency c must be equal to

If these conditions are satisfied, then we have,

Prob Impact

where, N, Number of impact per un:it time

Expected frequency

Fo:r our present problem, the relative motion between wave and

ship bow can be considered as a random variable having a normal distribution

with zero mean, This was confirmed during the experiments. it may also

be stated that although the spectrum of relative motion is not a sharp

narrow-band spectrum as is observed in a strongly resonant vibratory system, the relative motion may be considered as a narrow-band random variable.

In order to support this statement, Table 2 was prepared. Table 2 shows

a comparison between the expected frequencies and the rnes of significant energy i.n the observed spectra at Station 2 of the MARINEL From the table,

it can be seen that the expected frequencies at Station 2 lie in the domains

of significant energy in the observed spectra. Thus, the number of

occur-rences of impact per unit time at a specific location is given by the

following formula: / ₂

'-1

r

-\j-)2

RAJ

It i.s noted that the same formula for slamming was derived by

Tick by a different approach

_16L

2.3 Probability Density Function of Impact Loads

In this section, a discussion will be given on the conditional probability of impact loada namely, the probability density function of

impact load when impact occurs.

Impact load applied to a ship's forward bottom when slauuuing occurs

follows a truncated exponential probability law 2I. That is

2C

-= 2C'

(4)

i i

where p = Impact

load

2C2

Threshol.d pressure

=

Relative veiocîty

Threshold relative velocity

C = Constant

The constant C involved in the above equation is the factor

which gives the-telationship between impact load and impact velocity, and depends entirely upon the section form considered. For a given ship therefore

the coefficient should be determined through model experiments in regular

waves.

The probability that an impact load will exceed a certain specified

magnitude, _{Po is given by}

-

2C0

)

Prob

The averages of the oriethird highest, p113, and one-tenth highest,

Pi/ip ,

.z f

?3= ZCt 2JO)

2C(

33OR)

2.4 Magnitude of Random Impact Loads

On the basis of the discussion given in the three preceding sections, a method of estimating the magnitude of random impact load

will be given. Let us consïde:r the following practical problem: How

many times will a pressure greater than 50 psi occur during 30 minutes

operation of the ship? The answer to this question can be obtained by

multiplying Equations (3) and (5), by 30 minutes. As an example, we will consider the Station 2 of the MARINER, for a ship speed of 10 knots

in head seas of moderate Sea State 7. In this case, we have H. 17.08 ft,

r, 12 ftísec, R' 505 ft2,

E.

* _{ri ri}

= 12.4 psi, and Po = .50 psi. Then, from Equation (3), 60 impacts in

30 minutes operation is expected. Also from Equation (5), the probability

of an impact load greater than 50 psi is 0.158 when impact occurs. Thus, impacts greater than 50 psi will occur 9.5 times (say 1.0 times) in 30

minutes. While, actuaLly 11 occurrences were observed during the experiments.

Figure 1.4 shows an exampie of a comparison between the predicted

and observed number of impact load greater than Po

pSi

Next, let us estimate the magnitude of the largest impact load expected to occur just once uring T minutes (or hours) operation. The

estimated load may be used as a criterion for design purposes, since a ship must withstand such impact although i.t occurs only once in the opera

tion. It is noted that the estimation of an exact magnitude of largest

impact :Load is not possible; however, the estimation of the lower limit

of the mag!itude can be made. Since we expect this load to occur only

once in T minutes (or hours), we have from Equations (2) and (5),

e=

Thu s

=

2CR'

_T-

_z)

The above formula can be read as follwos A large impact load no less than Po given by Eoation (9) will occur once in T minutes (or

hours) operat.ion of the ship. An example of the application to the

MARINER is shown in Figure 15. The figure pertains to a location of

Station 2 of the MARINER for light draft9 10 knot speed9 in moderate Sea

State 7. It can be seen from the figure that an impact load of no Less

than 144 psi will appear once in 5 hours operation of the ship., and an impact of no Less than :L.58w1.l:L occur if the ship continues the operation

for 10 hours. For a 30 minute operation. an impact of no less than 96

psi is expected; while actua:Lly a maximum ìmpact of 91 psi was observed

once during the model experiment as i marked in the figure.

2.5 Summary of Estimation Method

In Summary9 in order to estimate statistically the frequency of occurrences and magnitude of impact load associated with slamming for a given ship9 the following approach will be most appropriate at the

present time. That i.S3

(i) Conduct model experiments at various ship speeds in regular waves,

and obtain pitch and heave motions and phase lags between wave, pitch,

and heave. At the same time the coefficient 2C should be determined at

several locations near the ship bow, Thic can be done by installation

of pressure gage3..

(2) Compute the response amplitude operators o.f relative motiond

velocity between wave and shi.p bow, and evaÏ,uate the variances for the

desired sea state and ship speed by applying the superposition technique. With these reparattons the following information can be obtained for the desired sea state and ship speed:

13

Probability of occurrence of impact per cycle of wave

encounter from Equation (1)

Njmbe:r of occurrences of impact per unit time from Equation (3) The probability density function of impact :Load from Equation (4) Averages of 1/3 and i/lO highest impact. loads from Equations (6)

and (7) respectively

The iower limit of the maximum impact load which is expected to occur one during T minutes (or hours) operation of the

ship from Equation (9).

These impact loads are of the triangular type and their duration is of the order of 0.08 to 0,12 sec for a 520-ft vessel (See Section 1.1).

For a ship of different lengths the Froude scaling law should be

used in converting the appropriate duration.

CONCLUS IONS

Various properties of impact loads associated with ship slamming

are outlined in Part 1 based on the results obtained from model experiments.

Part 2 dìcussed a method for estimating the frequency and magnitude of

impact load from the statistical poïnt of view. 0f particular importance

for _{ship design are the probability of occurrence of impact and the lower}

limit of the maximum impact load which is expected to occur once during

T minutes (or hours) operation of the ship. The formulae to estimate these characteristics are given in the paper.

REFERENCES

i. Ochi, "Extreme Behavipr of a Ship in Rough Seas Slamming

and Shipping of Green Water," Annual Meeting of the Society of Naval Architects & Marine Engineers (1964)

Ochi, M.K., "Predic.tion of Occurrence and Severity of Ship Slamming

at Sea" Fifth Symposium of Naval Hydrodynamics, Office of Naval Research, U.S.A. and Skipsmodelltanken, Norway (1964)

Szebehely, V.G0 and Todd, M.A., "Ship lamming in Head Sear," David Taylor Model Basin Report 913 (1955)

Ochi, K., "Model Experiments on Shi.p Strength and Slamming in Regular

Waves," Transactions, Society of Naval Architects and Marine Engineers,

Vol 66 (1958)

Szebehely, V.G. and Lum, S,M., "Model. Experiments on Slamming of a

Liberty Ship in Head Seas," David Taylor Model Basin Report 914 (1955)

Tick, L.J,, "Certain Probabilities Associated with Bow Submergence and Ship Slamming in Irregular Seas," Journal of Ship Research, Voi 2,

No. 1 (1958)

Table i _{Threshold velocity for various types of ships}

Values are converted to those for a 520-ft vessel

Sea

severe 7

7

Moderate

Expected frequency for narrow-band Gaussian process, / R./ R

0.71 _{0.68 to 0.78}

Domain of the significant energy in the observed Spectrum

Type of ship _{Cargo(U-Forni)}

Cargo(V-Forin) LIBERTY MARINER High Speed Craft (V-Form)

Block coefficient _{0.741 0.741}

0.733 0.624 0.4 79

braft _Light

Light Light Light Oesign

Waves _Regular

Regular Regular Irregular Regular

X/ L 1.00 1.00 _0.91

Severe 1.50

Sea State 7

h / X _1/30

1/30 1/16.7 1 / 34

Ship Speed (Knots) _{10.4 11.9}

10 _{10.0 18.4}

(Estimated)

Location where the 0.053 L 0.093 L FP _{0.10 L 0.1 L}

threshold velocity is evaluated

aft of F? aft of F? aft of FP aft of F?

Threshold velocity (ft/sec) 14.0 11.9 10 to 14.3 12.0 11.8 Reference [4f [4) [5] _{E il Unpublished} 0.69 0.65 to 0.75 Mild 7 _{0. 72} 0.68 to 0.75

Table 2 _{Comparison between expected}

frequency and

domain of significant _{energy in the spectrum}

(MARINER, light draft,

Ships Speed in Knots

Figure 2

Probability of occurrence of

impact per cycle of wave

encounter for various loading conditions and for various course angles

(MARINER, Station 2, moderate Sea State 7, ship speed 10 knots)

Station

Figure 1

Probability of occurrence of

impact per cycle of wave encounter in head seas (MARINER, Station 2,

light draft)

Figure 3

Probability of occurrence of impact along ship bottom in head seas

(MARINER, severe ea State 7)

g o' S... 7 '40 Q6 SHIP SPEED IS Kot* Q4 Io KnOss S Knot, u OKnotn 8 6 4

Figure 5 _{amp1c histogram and} the predicted probability density

functions for impact _load

observed at 3.10 L aft Of FL'

for various course angles

(MAREhR, moderate iCO 3tntc 7,

si-tip speed 10 knots, 1iht draft)

9

Figure 4

Probability of occurrence of iiaoact at Stations 2,3, and -+ for various course angles

(MARINfR, light draft, moderate

iCa _{State 7, si-tip speed 10}

k n o t s)

COURSE ANGLE HEAD SEA P [saJo33o

25 DEGREES 45 DEGREES 20 40 60 80 Pressure in PSI Pob r$on] 0 298 P,ob :052 lOO 20

4 O £ (ID 4 cJ C o o e 6 4 2

LOADING CONDITION LIGHT _{Prb [SIo,]o333}

MODERATE

FULL

Prob [SiooJ O.i98

Prob [5ro.] :OOee

ìre

Compari Son between experimentally

obtained histogram of impact load and prediced probability density

function (NARLER, Station 2,

moderate Sea State 7, light draft,

ship speed 10 knots)

o

Pressure ir, PSI

Figure 6

Sample histogram and the predicted

probability density functions f

impact load observed at 0.10 L aft of F2 for various loading

conditions

(MAR1NiR, moderate Sea State 7, ship speed 10 knots, head seas)

Avero9. of Averoge of I/O Highest i/IO Highest

o PSI In PSI Predicted 55.4 79.9 Measured 51.6 76 2 Ep.rImerit Pressure in PSI O loo

8

Station

p'i2urc 9

Envelopes of maximum _impact

loads experienced alone, the length(MARINER, lizht draft,

severe ea .tate 7)

2

2

50

Fioure ?

Pressure distribution alon shin

lenoth for typical slams _observed

Euri no 30 mi njt e o)erat i on i n a

severe ea _{tatc 7 C'L-\RI.R,}

li4ht draft) 3*8P SPUD 5 KNOTS - at S4om IO KNOTS S.vrssl Sóni

/'/

_I

1%

240

2

4C

Staflon

Figure 10

nvelopes of maximum impact loads

experienced along the _{ship length}

(MARtNER, liht draft, 10 knots

speed except 7.5 knots for _Sea

State 8) p 0.35 0.30 025 020 OiS 0.1 0 0.05 o Sso Stats e Ssno'. i

I

\

Probability that impact loads exceed

a _{iveri magnitude (iARINER, liht draft,}

60 4 Ç) C Q-I0 e 6 20 Relative Velocity Thmhod Wlo& t2 Ft/S.c. Figure 12

Impact pressure on the keel plate _{as a function}

of impact velocity

(MI\RINR, _{tation 2, 1iht draft, shin speed}

10 knots, moderate ea state 7)

II

UI

q .

.4

.f_

p.r.

S

V.

05 04 0. 0 7 6 io o Ob se r Pr ed e t ed

_\IJ

Secere 7 Moderate 7

Maid 7 JJ!

p-,

_/

I.

\

_\

Probability of occurrence of impact

at various locations along ship

length (MARINER, light draft, ship speed 10 knots)

0 20 40 60 80 00 20

Impact Load p in psi

Figure 14

Comparison between predicted and observed

number of impacts _{which exceed a certain}

magnitude (MARINER, Station 2, light

draft, _{ship speed 10 knots,}

moderate :ea .tate 7) 5 AI! o o E o Q, o E 40 30 20 0.3 o o 0.2

" ₆ D C o 4 ixI 8 6 4 2 x10 8 4 2 20 Hrs 2 FIrs. 0 - IO Hrs. - 5 FIrs. - I Hr. - 5Mm. 40

I

Figure 15 Lower limit of maximum load as

a function of ship operation time

(MARINER, Station 2, light draft, ship speed

10 knots, moderate 3ea tate 7)

E 2 I-X I 8 30 Min 6 - IO Min 200 80 120 60