TECHNISCHE UNIVERSITEIT Laboratorium voor ScheepShYdrOmeCta1 Archief Mekelweg 2, 2628 CD Deift Tel.: 015- 788873 - Fax 015- 781836
SEAKEEPING PERFORMANCE ASSESSMENT OF SHIPS
Tuomo Karppinen and Timo Aitta
TECHNICAL RESEARCH CENTRE
OF FINLAND
SHIP LABORATORY
Espoo 1986
nstm
br changing course. Amethod. for overall evaivatioñ.of seakeeping performance based on the percentage of timó of operation is
presented! On the basis of data. in the literature numerical values for operability limiting critéria are suggested. Resùits of
theoretical seakeeping performance predictions for Series 60 vessels are expressed.
Ç UNTE NTS
Page
ÑONENCLATURE 3
INTRODUCtION 5
DEFINITIONS 7
PERFORMANCE OF SHIPS IN ROUGH WEATHER N GENERAL 8
PREDICTION OF SEAKEEPING PERFORMANCE INDICES
General 1.5
Ship Response to Irregular Seas 17
Operability 21
Sustained Sea Speed 26
Percentage of Time of Operation. 28
Required Speed Reduction . 30
Seakeepin Perforiaance Effectivenéss. . 33
SEAKEEPING CRITERIA Vertical Acceleration . 35 Slamiing - .45 eck Wetness - 52 Lateral Acceleration 57 Roll 59 Pitch 65 Propeller Emergence 65 Special Criteria 65
THEORETICAL SAKEEPING PERFORMANCE PREDICTIONS
Vessels and Predictions 67
Wave Data . 69
Results . 70.
CUNCLUSIOUS
NOMENCLATURE
B Beam
D Draft
d Local draft
E Long-term performance effectiveness
e Performance effectiveness
F Freeboard
Fn Froude number
Joint frequency distribution Qf wave height and period Frequency distribution of ship speed
f Frequency distribution
of
headingAcceleration due to gravity
9r rms relative motion for unit significant wave height
rms relative velocity for unit significant wave height Root mean squàre response for Uiit significant wave height
H Significant wave height
h Overall operability limiting significant wave height
h&
Operability limiting H5 due to deck wetness Operability linPting H due to slarnmingh Operability limiting H with regard to Ship response x
L Length
ni. jth niornent of wave spectrum
-m Mean square relative vertical motion
or
ra Mean square relativé vértical velocity
orv
Iii Area under response spectrum
pOX
Probability of not exceeding the opérational limit
dw Maximum allowable probability of deck wetness
P0 Overailpercentage of operability
4
ilaxitnum allowable slamming probability
Maximum allowable exceedance probability for ship response Distribution
of
wave observationsFrequency response function
S Sea state
Wave spectral density
Spectral density of ship response
T Characteristic wave period
Mean period
t Time
V Ship speed
Mean speed
Critical re-entry velocity
V Maxiinuri ship speed in calm water
max
x Ship response
x Ship respOnse amplitude
X Critical value
of
ship responsePhasé angle X
Snip headin9 to waves ( 1800 for head seas) Root mean square value
of
ship responseaxcr Critical rms value Of ship response
w Incident wave frequency
We Frequency of encounter
Integration limit
max
in danger owing to the violent wave-induced motions of the ship. As
a consequence of the speed reduction the ship is perhaps no longer able to keep to the time-table. Hayy rolling or green water washing the. decks may prevent essential work on exposed areas of the ship, or vertical ¡notion of the flight deck may prevent helicopter landings and jeopardize the execution Of the mission of the ship. Vertical accelerations may cause symptoms of seasickness in people onboard thus reducing the comfort of the passengers and the working
efficiency of the crew. Deperding on the iission
of
the ship, all these ship motion effects may contribute to the degradation of the ship performance in a seaway as compared to cairn sea performance.It has become a routine to compute or measuië by model tests ship motions in waves, but response. arnplitud operators or significánt motion values aloné give littlé indication whether a new dsi:gn will be a good seakeeper. The practical evaluation of ship seakeeping performance requires an index for measuring the seakeepin.g
performance as weil as standards or norms for judging the index
value. Since the effect of the seaway is to degrade the mission performance of the ship, the seakeeping performance index should measure the ability of the ship to carry out its function in varying environmental conditions. Exçisting ships, set the standards of
reference against which to compare the seakeeping performance of new designs. Before the numerical value of the seakeeping performance index can be predicted, criteria for acceptable levels of ship
motions, critical from the point of view of ship operations, must be
Among the first to pay attention to the seakeeping performance of snips and not only to ship motions in waves was Lewis (1955). In the sixties efforts mainly concentrated on refining theoretical methods for predicting wave-induced motions of ships, and few studies on seakeeping performance were published. Modern times in seakeeping performance research, auch involved with naval ships, may be
considered to have started with the monograph prepared by St.Oenis (1976) although, for instance, an interesting paper on seakeeping criteria by Hadler and Sarchin (1973) was published a few years earlier. A rêcent general review on the status of
commercial seaKeepirig research has been produced by Lewis (1982).
Procedures for predicting seakeeping performance indices of ships have been presented by Hainlin and Compton (1970), St.Denis (1976), Chilò and Sartori (1979), Johnson et al (1979), bales (1981), Hosöda et al. (1933) and Kin and Nakamura (1984). Values of limiting criteria with regard to ship responses for reducing speed or changing course are considered by Aertssen (1968), Conolly (1974), Höffman (1976), Lloyd and Andrew (1977), Olson (1978), Andrew and Lloyd (1981) and Lewis
(1982). At the moment no generally accepted set of criteria for an acceptable level of ship notions in waves exist although for instance the U.S. Navy seens to have its own standard seakeeping criteria for surface ships (Comstock et al. 1982). Wo scales for evaluating the overall seakeeping performance of ships have been established.
This paper, a literature review on seakeeping indices and criteria supplemented with theoretical resûlts, is based on the work carried out so far in the first part project of the Nordic seakeeping
project "Skibes søegenskaber". The aim of the part project is to uefine criteria for seakeeping performance evaluation of ships and to establish guidelines for seakeeping merit rating. Since the third part project carried out by MARINTEK is concerned with ship
propulsion in waves, this aspect of seakeeping performance is only given little áttention here.
_4-._
DEFINITIONS
The key terms of this stUdy, "seakeeping performanc&" and
"enviroriniental operability", have approximately the same meaning and are usually used in the same context. For naval ships Comstock& Keane (1980) define seakeeping performance shOrtly as "ability to execute mission in a seá environment. Accotding to Hdler &
Sarchin (1.973) operability i.s "the ability of the crew to operaté the ship with all of its mechanical equipment so as to carry out the assigned mission in the ocean environment iii which the ship is expected to function".
While "seakindliness" and llhabttabilityÍ are part of se.akèeping performance, "seaworthiness" has to be distinguished from seakeepi.ng performance. By Comstock & Keane (1980) seaworthiness is "ability to survive in an extreme sea environment". Hoffman (1976) considers seawOrthiness t bè a mOre generalized term that reflects the capability of the ship to survive all hazards at sea such as collision, grounding, fïrè as wèll s heavy- weather effécts. In any case, seaworthiness is out of the scope of this study.
While seaWorthinéss deals with extremes, seakindliness usualh' réfers to the less violent ship responses due tO wind and waves. A seakind ship has in a seaway easy motions, dry dècks, no propeller racing or 1amjing (Lewis, 1967). Habitability is concerned with providing the crew with an environment in rough seas that permits them tO function effectively and providing the passengers an environment where they can enjoy the trip. The main concerns here are discomfort,
seasickness and accidents due to wave-induced motions of the ship. A recent study On how to minimize the adverse ship motion effects on the crew onboard naval ships has been made by Iiittner & Guignard
8
PERFORi1ANCE OF SHIPS IN ROUGH WEATHER IN GENERAL
One difficulty in overall evaluation of seakeepin,g performance of ships is to find a suitable measure of merit. For merchant ships an absolute uieasure of merit should reflect the profitearning ability of the ship, How to include the many profit and cost factors in a single seakeeping performance index is, however, at the moment beyòn.d
the state of the art. Therefore it has often been suggested that seakeeping performance of merchant ships could simply be measured by their ability to máintain speed in heavy weather. The sustained
sea speed reflects the ability of a merchant ship to fulfil its function, i.e. to deliver cargo and passengers safely and precisely from port to port, regardless of sea conditions.
The percentage of time of operation in the environmental, conditions the shjp is likely to encounter in its lifetime or over a long-term interval has been a seakeeping performance index suitable for naval
ships. This operational time is the oppösite to the downtime,. which
has often been used in perfòrmance comparisons of offshore vessels. Operational time may also be a suitable measure of merit for supply ships, support ships,. ocean research vessels, factory ships, fishing vessels and för other ships whose function requires operation at different speeds. Prediction of both the long-term average speed in a seaway and the. operational time requires knowledge f the ship speed reduction due to weather.
The speed loss in a seaway consists of (1) involuntary speed loss due to added resistance and loss of propulsive efficiency caused by wind,, waves and ship motions and of (2) voluntary speed reduction at the
discretion of the ship's master. Power is throttled, course is
changed or both are executed by order of the captain if the safety of the ship or cargo is indanger or habitability of ship personnel or passengers is significantly reduced. The main concerns of the captain are here (1) excessive vertiçal and lateral accelerations, (2) slamming, (3) screw racing, (4) deck wetness and (5) rolling.
Only for deck cargo.
2 Only for operations on opn lower decks.
ShIp subsystem Slam Deck
wetn
Vert. acc.
Lat. acc.
Roll Pitch Vert. motion Vert. vel. Rel. mot. Shiphull Propulsion machinery Ship equipment Cargo Personnel effectiveness Passenger comfort Special operations helicopter spnar lifting x x x X2 x x X x x X X x X x X x X x X x X X x X X x X x
10
Table 1 shows a surnnary on the significance of various ship responses from the point of view of the different subsystems of the ship.
In the full-loaded condition in head seas - particularly on fast ships - deck wetness is especially harmful while slamming and racing are problems with a light draft (Aertssen, 1977). According to older log-book data (Lewis, 1967) rolling has been the most frequent cause of course change. Also a recent seakeeping questionnaire (Wahl, 1979) shows that un container ships the speed reduction is ordered in the first place as a result of extreie rolling motion. A second important cause of slow-down is deck wetness and a third is sidm1111 fly.
In the beginning of the seventies the unanimous opinion of a small group of commanding officers of the U.S. Wavy destroyer-type ships was that the order of priority for ship performance in a seaway were roll control, reduction of deck wetness , and slamming (Hadler&
.Sarcbin, 1973). Answers to a recent questionnaire (Kehoe et al. 19d3) distributed to commanding officers of the U.S. Navy frigates, destroyers and cruisers indicate almost universally that speed is reduced Iecause of slamming. The change of opinion may be attributed to the efforts of the U.S. Navy to improve the seakeeping performance of naval surface coribatants (for a review, see Comstock & Keane,
198(J). Also IIeyerhoff (1978) stresses the importance of
slaming as
a reason for speed reduction on destroyers and frigates.
The decision to slow down or change .course depends on the subjective judgernent of the captain. Conolly (1974) refers to the psychological effects of heavy slamming insisting the captain to slow down. This subjective reaction depends on the character and probably even on the state of mind of the ship's master. Aertssen (1977) speaks of a daring captain anxious to follow the schedule. and of a relief master on his ship. Aertssen (1968) agrees that much depends on the
captain's personal feeling, but he. adds that thefèeling always has a technical basis. Masters react to ship motions or to visual
Severlty of deck wetness is judged by the frequency of green water on deck, while slamming is generally d'etected by the resulting whipping vibration of the hull girder (Lloyd & Andrew, 197?, Hadler & Sarchin, 1973, and Meyerhoff, 1978).
Thus, it will never be possible to find a set of exact, universal limiting criteria with regard to ship responses that would precisely define the conditions under which ship's masters redüce speed or change course. At best it is possible to derive numerical values fOr
the limiting criteria that are in agreement with most observations on actual service performance of ships in rough seas. Perhaps one
should consider the criteria in probabilistic terras: so and so many per cent of' ship's riiasters reduce speed if the response x exceeds the
value y. If' the levels of'the numerical criteria in the set are in
balance with each other, the criteria set can be used for eva)uating, on a comparative basis, the seakeeping performance of different
designs, and
for
revealing in the design phase possible problems in the seakeeping qualities of the ship.Lloyd and Andrew (1977) propose that limiting criteria for reducing speed should be related to physical phenomena actuallyexperiencecj by the captain, crew and passengers, and limiting values should be
derived from the apparent service performance of existing ships. This makes sense, but unfortunately little published information exists on actual service performance of ships in rough seas. Many of the limiting criteria appearing in the literature are partly based on personal opinion and partly on data on the behaviour of a few ships and actions taken by their masters in limiting envronmental
condi tions.
A most notable source of full-scale performance data is the
seakeeping trials conducted by Professor 'ti. Aertssen of University of
Ghermt in Belgium. As cän be seen in Table 2, which summarizes limiting criteria found in the literature, many of the criteria are based on Aertssen's observations. An important newer, less
well-Table 2.
SUMMARY OF SEAKEEPING. CRITERIA FN LITERATURE
continues
Reference
Slam
D.W. V.Acc.
Criteria L.Acc. Roll Pitch Special Ship types
Based on
Adams & Beverly (1984) Aertssefl (1966,1968,1.969, and 1977) and Aertssen & Sluys (1972) Andrew & Lloyd (1981) Andrew et al. (1984) Bales (1981). Bales & Ciesi.owski. (1981) Bales et al. (1982) Bau et al.
(1981)
Chilo & Sartorl (1979) Chryssostomldis (1972) Comstock et al. (1980) Comstock et al. (1982) ComStock & Keane (1980)
x x x x x X X X X X x x x x x x X X X X X X x x x x x x X X X X X x x X x x x x x x X X x x x x X X -x . x x x . X x
Surface effect ship Merchant ships Naval ships and merchant
h1ipS
Frigat& Naval ships Naval shps Naval. ship.s Me.rchant ships. Naval ships Seri.es 60 FF-1052 destroyers Air capable ships Naval ships
U.S. Navy criteria Full-scale seakeeping trials Seakeeping trials of two frigates.
.
U.S. Navy criteria U.S. Navy criteria U.S. Navy c.rite.ria Ochi & hotter (1974) Recent studies ('Ochi&Motter,
1974)
Drewry (1966) and Loukakis
(1970)
Table 2.
Continuation.
Reference
Siam
D.W. V.Acc.
Criteria :L.Acc. Roll Pitch Special Ship types
Conoil'y (1974) Ferdjnände & De Lembre
(1970)
Giannotti et al.
(1977)
Hadler et al. (1974) Hóffman (1976) Johnson et. al. (1979) Journée & Meijers (1980) Kehoe et al. (1983) Kim & N'akamura (1984) Ki.tazawa et al. (1975) Landsburg & Cruickshank
(197:6) x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x .x x x x x x .x x x x x x x
Destroyers Car-ferry Merchant ships Catamaran USNS Hayes Merchant ships Cruiser Merchant ships Frigates, destroyers and cruisers Container ship S175
Based on Seakeepin.g trials by Aertssen .(1966a) and Biedsoe et ai. (1960). Baitis 'et al. (1984.) and Hosoda et ai. '(1983') U.S. Navy criteria Aertssen (1966a), Aertssen (1968) and Aertssen &
van
Sluys '(1972) :Ochi & Itotter (1973), Aertssen & van Sluys (1972), own experience U.S. Navy criterlá Questionnaire to ship's masters onboard' commercial ships in service U.S. Navy criteria
Table 2.
Continuation.
Criteria
Reference
Slam
D .W. V.Acc. L.. Acc. Roll P i.
tc h Special.. Ship types
Lloyd & Andrew(1977)
X
X
'X
Naval ships and' merchant ships
Lloyd & Hanson (1985) McCreight & Stahl (1985.)
X X
X
X
x
Naval ships (heil'- copter Qperations), Naval shiips
0,chi & Motter (1974)
Merchant ships
Oison (1978)
X
Naval ships., mono 'hulls' and SWATH
Schaffer et al. (1983)
X
X
Destroyers
Wahl & Andersson (1974)
X
Cargo carriers,, reefers
Wahl (1979) X Container ships Walden 8 Grundmann (1985)' X X Naval ships Yamamoto (1984) 'X Bulk' ca.Priers
known source of information on the level f ship responses at. th mOment of reducing speed or changing course is the seakeeping
questionnaires conducted onboard Swedish merchant ships by Wahl. and Andersson (1974) and by Wahl (1979).
PREDICTION OF SEAKEEPING PERFORMANCE INDICES
General
In the following a procedure which can be used for the assessment of seakeeping performance of ships is outlined. The procedure can be adapted to evaluating the seakeeping performance of different ship types With different missions,, settin.g requirements on the seakeeping qualities of the ship. The procedure Outlined can equally well be applied both to basic seakeeping iiodel test data and tÒ results of theoretical computer calculations.
For the basic seakeeping performance measure the percentage of time ofoperation has been chosen. If only voluntary speed reductions due to excessive ship motions are considered, this operation index can be computed for all ships in head seas on the basjs of the frequency vesponse functions and phases of heave, pitch and vertical relative mOtion. Thi:s becomes evident in Figure 1, whi.ch shows the dependence óf the ship- responses appearing in the most important limiting
criteria on the basic ship motion components. If the added
resistance and the propulsion effIciency in waves are known too, the effect of involuntary speed reduction can be incorporated in the séakeeping performance. measure. When the percentage of operation has been determined for several speeds up to the maximum calm water speed, the average annual or seasonal speed can be predicted. Also the maximum speed in a seaway due to motion consideration can be estimated. The calculation of the seakeeping performance
effectiveness as defined by Hosoda and Kunitake (1985) can bé carried out as part of the procedure..
bASIC MOTIONS Wave Lel Heave Pitch Sway Rol i
r
Yaw / , / /b'
...-/
\
DE RI VEE) RE SP OÑSE S 16 Rel. mOtion *I'
iel.vel. Ve.rt. vel. *Wot in head seas
Only out of centerplane
Depends on section where Considered
Figure 1. The relation between basic
motion components and the most important operability limiting criteria with regard to ship responses. CRITERIA WITH REGARE) TO PrOp. emergence Slamming*
1
Deck wetn. *Ivrt.motion*J
tVert. motioiVert. vel.*
Vert. acc.*
f 1V-t.
acc.*
Lat. acc. - - - - t. acc.
Roll
LPitch
In deriving the formulas for predicting the seakeeping performance of ships it has been assumed that the linear superposition principle and the Rayleigh distributiOn çan be applied. The peak values of ship response to waves follow the iayleigh distribution if the following cond1tions are satisfied: (a) Random sea is steady-state Gaussian
(normal) process with zero mean, (b) response to waves is linear, and (c) spectrum is narrow-banded. The validity of the Rayleigh
probability law up to surprisingly violent ship motions has bêen verified in numerous correlation studies both on the full- and model-scale.
In principle all possible speed and heading combinations can be included in the procedure. However, at other headings than head or following seas (assuming long-crested waves,) many of the limiting' criteria depend on the roll motion as can be seen in Figure 1 Roll
response of most ships is non-linear at resonance, and this makes questionable the appi ication of the linear superposition principle and the use of the Rayleigh distribution for predicting the
short-term statistics pf ship response amplitudes. Cloe tO the roll axis the dependency of the critical ship respQnses on roll may be. minor., and can perhaps be disregarded, though often roll as such is one of the most important operability limiting responses.
Ship Response
rrgvlas
Applying the linear superposition principle and assuiing the irregular waves to be unidirectional, the spectral density of the ship response to waves, S (w), can be føuñd from:
5(w)
= [R(w)
]2 S(w),
where w is the Wave, or absolute circular frequency,
S(w),Is
the wave spectral density and Rx(w) is the frequency response function,In (2), w. is the frequency of encounter
related to the wave frequency y:
= w -
(w2/g) V COS.. ( 4)
Here. g is the acceleration
due to gravity. Ship heading to
waves, p.,
has been defined in Figure
2,
and V is thé steadyforward speed of the ship. Différent frequency
response functions are obtained for different ship speeds and headings.
This can be indicated by writing the frequency response function in the
form R(w;V,p.).
The mean square value of the ship response in irregular
seas. is obtained as the area under the response spectrum function:
w-max
C E
= ¿
S.(w)dw, ( 5)where is the standard
deviation, or root mean square about the mean, anciw
refers to the maximum limit in the numerical max
i nteyration.
18
i.e. the amplitudé of the ship response
ina regular wave of unit
aiplitude and frequency w.
Here the ship response can be any of the liiìar responses of the ship to
waves, for instance, heave., pitch, relative vertical motion, vertical velocity
or acceleration. With the amplitude of the incident regular
wave given by Cand the ship response expressed as
x = x COs( t
a e x
the frequency response funct10
is obtained by:
- 18 Degrees Cotresponds Io H.d Wayss
90 Degree. Corresponds to Starbosid Beam Wives
-
O D.Qró.s Correipónds to Fó1$o*4ng WivósRoot iDean square amplitude
Average ampi i tudë
Average of highest 1/3 amplitudes Average of highest 1/lo amplitudes
l.00a
l.25y 2.00 Prob x > l.25a 0.458 Prob x > 2 0.135 Prob x > 2.SSa 0.039 ProD x > 2.l46c 0.1Prob x> 3.O35a
0.01 Prob X > 3.717c 0.001Most probable extreme value in N succeeding oscillations:
x
= c / ¿
ln N' max x in 50 oscillations 2.8Qa max loo 3.03c, 200 3.25e 500 3.53crProb[x>x
J 0.63 max AP FP- SURGE ¿3 - HEAVE PITCH
¿7 - SWAY ¿4 - ROU. YAW
Figure 2. Description of ship heading and motion componènts..
table 3. SHORT-TERM STATISTICS ON THE BASIS OF
with
À = 173 and
B = 691/T
where the significant wave height, H5, çan be factóred out and the spectrum may be written in the form:
S() = H f(w;T
1 7)
Here T is a characteristic
wave period defined. in the ISSC-spetru,n
as the mean period:
-i
= 2rc
(ni/rn1)20
The wave spectrum S(w)
is here defined by an analytical spectral density function such as the ISSC-spectrurn (Price & Bishop, 1974, p. 160) S(w) =(A/w5) exp(_B/wk) ( 6) = jf.
wS(w)
nd.
oThe significant wave height is defined by
=4p.
o with w max C 9) (10)Substituting first ( 7) for S(w) in ( 1) and then the expression
obtained for in ( b) yièlds:
(J)
max
02=H2f
[R(X
S0
XH
[g(T;V)]2
where g(T;V.) is the root mean square response for unit significant wave height as a functiOn of characteristic wave period with ship speed V and heading as parameters.
With the response root mean square known, short-term statistics of the responsecan be predicted by the Rayleigh distribution:
P[X>x] = eXp(_x2/2rn0). (12)
Table 3 gives a summary of the most important statistical values that can be derived froiii the Rayleigh distributiOn.
dperability
If the funçtions have been determined, the operabilitylimiting significant-wave heights for different types of criteria with regard to linear ship responses can easily be found.
For a criterion defihed äs à maximum allowable root mean square
value,
xcr' usually for instance by acceleràtionsand angular motions, the lifliiting significant wave height, h, is given by:
h(T;V,.L) = 'xcr /g(T;V.t).
(3)
22
An alternative way to express the limiting criterion with regard: to responsex is to define a inaxiÌnum allowable probability for exceéding
a critical value such as 1g, or the maximum roll
angle for safe footing. By the Rayleigh distribution
the probability of exceeding is given by
-x2 /2m P[x >
Xcr] = e cr ox
Where is the prespécified maximum
allowable exceedance probability
and rn has been defined
in (5).
When (11) is substituted for m in ox
ox (14), the limiting significant wave height can be solved from the resulting expression, and is obtained thus:
X
cr h(T;V,.) =
g(T;v,)/(_ lfl P)Ç)
As can be seen, (15) is equivalent to setting the maximum permissible
root riean square value, to:
CXc =
XII (-2 in
(16)The criterion with regard to deckwetness is most conveniently expressed in 'terms of
the
maxiium permissible probability,Pd:
Prob(Deck wetness) = or
< (17)
where F is the effective freeboard at the section considered, and m or is the' mean square relative
vertiçai motion at the same section. By (15) the limiting significantwave
height with regard to deck wetness can be expressed in thé form:
hdW(T;V,IL) = F gr(T;V)I (-2 in P ') dw (15)
(18)
, (14)where g
is the root mean square valUe of relative vertical motion
for unit significant wave height as a function of characteristic
waveperiod with ship speed and heading as parameters.
Thé slamming criterion is cprveniefltly defined in the
saine form as
the criter9on for deck wetness.
By the Rayleigh distHbution the
prObability of a slam becomes (Ochi, 1964):
Prob(Slam)
e_21'2ffor +V2/2rn)
s.'
(19)
where d is local draft, V
is the critical re_entry velocity and m
çr
or
and m
are the mean square relative -motion and relative velocity,
orv
respectively, at the section examined.
It follows froni (19) for the
limfting significant wave height with regard
to slaÍming:
h5(T;V,)
=./(
- )[d
V2 +2 in
P g(20)
wherePS
is the naximum permissible slamming probability and
g andrv
are, respectively, the root mean square. relative motion and
relative velocity for unit significant wave height.
When the limiting significant, wave heights have been determined
with
regard to
ll critical responses as a function of characteristic
waveperiod, the h(T) curves can be plotted at
a particular speed and
heading on a wave scatter diagram_(Figure 3) expressing the joint
probabilities of Occurrence for H5 and T in the operation
area of the.
ship.
The Operational boundary of the ship on the H-T-plane is
obtained by taking the lowest of the limiting significant
waveheights at each characteristic wave period.
In mathematical terms:
10,0 2L1 -24 121 78 956 0 000 0 009 23.895 0 001 13.244 0.008 5.992 0.010 2141 0.000 0.875 0.000 0. 0 2 0.149 0.001 4 0.378 0.000 24 121 28947 23 894 13.236 5.992 2.141 0.875 44 0.1 ' 0.378
i -
0001 001g 0076 0.109 0157 0.068 0.048 .032 0.007 24120 28978 23818 13.127 5.825 2073 0826 0.212 0.371 0000 0009 0.038 0091 0.054 0.035 0012 0.004...
0.002 2e 919 2;J4:.I
.01A o...4 â:...
:..
74 119 - -. i .), ., - ,-. . 0.134 0.368 240 24 107.
0.147 0.198 0.132 0.356 0010 V p !.T.
Ef.. -
00 . 0.008 0.000 0.001 74.097 g-
28626 23098 0619 0.187 0129 0.355 0135,I
0.343 . . . 0003 0.001 0.001 24 063 28 491 22.755 g 24055 4. rt .567 0.587 0.182 0.127 0354 o 019 ,i.!it.
, 0.046 020 0.002 0.003 0.002 24 036 . ... . O ' 0 180 0.124 0.352 0079.!.
.. 0.17 0.032 0.017 0.006 23e57 2 . ".26 1215 0.394 0.148 0 107 0.346 o os o. . W.. 0.697 0.259 0086 0.004 0.002 237522692 %14 3129
0066CELL-WISE APPROXIMATION 0151 1376 0.863 0289 TO LIMITING CONTOURSL.
23601 ' 6546 7266 0 667 0.228 0083 0.102 0.342 o 348 . . 1 900 0.831 0.166 0.061 0 027 0001 0.002-
23 253 23.553 12814 4646 1435 0.501 0167 0056 0.340 0 710 4 152 4 806 I 992 0616 0 22S 0046 0009 . 0003 22 543 19401 WETNESS LIMIT 0819 0216 0121 0047 0.33! iSIS 6469 AT STATION 2 0381 0118 0032 0006.
0021-
21028 '2932 3668 1160 0438 0158 0089 0041 . 0316 5 134 8334 2505 0 710 0 306 0 108 0045 0071.
0.021 ib 594 4 598 1163 0 390 0 132 0050 0.044 0020 0.065 0.295 8643 3015 0899 027/ 0108 0.03! 0035 0014 004.4 0074 7260 0683 0264 0113 0024 0013 0009 0006 0041 0221 4437 0571 01/6 006.4 0.014 000! 0006 0004 0006 0205-
223 0112 0088 004g 0010 0006 0003 0002 0035 0016 2823 0112 0088 0049 0010 0006 0003 0002 0035 0016 7'/ I I I I I I I I I I I I I I I I o S 6 9 IO 11 12 13 14 15 16 17 8 19 20 21 22 23MODAL WAVE PERIOD (iecl
Figure 3.
Operabi1itylirniting significant Wave height with regard to slamming and deck wetness superimposed on a wave scatter diagram (Bales, 1981). g 8. 8. 7. 6 E 6 5.5 w > 5.0 3.5 3.0 7.0 1.5 10 05 00
The probability of significant wave height not exceeding the
operability limiting value h in each wave period class can either be deterÑtfled by direct countiñg from the wave scatter diagram or from the Weibuil distribution by assuming that this distribütion has been fitted to the wave data in each wave period class. if the
Weibull distribution is used, the prQbabllity of significant wave height not exceeding the operational limit height in a particular wave period range is given by:
h(T)-H
y = Prob{H <h(T)} = i - expH0
O)
],
(22)where H represents the lower limit of observed significant wave height for a specific period range and y and H are parametrers to be determined by the fit.
The percentage operability in the specified envirOnment at the particular speed and heading can finàllV be dêtermined
by:
= E P(T.;V,)Q(T.),
3 3 3
where Q is thepercentage of wave observations in the period range with central period I. The foregoing procedure can be repeated fOr
evera1 headings at each speed il only the corresponding respbnse ämplitude operators are known. Then the percentage operability bècomes the weighted theati over ail fleadings and speeds:
P0(Ocean. area) E E
kl
IVk)Pô(Vk,).
(24)
Here.f is the frequency distribution of speed and f is the conditional frequency distribution of heading given ship speed.
Both frequency distributions are to be defined in accordance with the misSion profile of the ship! The procedure can easily be extended tO iiclude several ocean areas with different wave climates.
Sustained Sea Speed.
In a specific sea area at a given heading the operability index (23) is a function of ship speed only and expresses the probability
of this speed being able to be maintained over a longer period of
time. Thus, the derivative dP/dV is the so-called probability density function and the average speed can be determined by (Chilò &
Sartori, 1979): V dP' fV [-_-.] dV., O dV
where V is the maximum speed öf the ship in calm
water. max
\
So far only volUntary speed reductions due to intolerable ship
motions nave been considered in predicting the seakeeping performance of a ship. However, it would be. possible to
incorporate in the foregoing procedure, and in the operability index po, the effect of speed loss due to added resistance and reduction of propulsion
efficiency in waves. This involves thé prediction of the shaft horse power required to operate the. ship at a specifIc speed as a function of significant. wave height
n each wave period range by the procedure presented by Faltinsen et al. (1980) or Yamamoto et al. (1984), for
instance.. The operability_limiting
significant wave height due to rnaxir!1umengine output can then be determined as illustrated in Figure
4. The limiting wave height due to engine power, together with
the limiting wave heights with regard to ship motions,
can be plotted on a wave scatter diagram and included in
the determination of the
operational boundary by (21) at the given speed. In this way the mean anhual or seasonal speed determined
by (25) includes both the voluntary and involuntary speed redüctions.
An alternative way to determine the mean speed or the sustained sea speed is to predict first the maximum speed of the ship in each sea
2.6
S HP
MAXIMUM ENGINE OUTPUT
SIGNIFICANT WAVE HEIGHT
Figure 4' Limiting significant wave height with regard to maxiwum
engine output at a particular characteristic wave period.
Table 4. Required operational capabilities an associated motion limits.
IMIT ING
EIGHT
Rel: Johnson et ai. (1979)
- 0JIR0D 0R41IG64L c.'eAeILrrlEs 6MO A5IMEO CT1 LYI4OTS
Mi,.iao R.gutrId Oub.y.t.a 3.O.y.t..Mett s.pms. Liait.
Lr.. 0pr11.OWI -, -. C.p.41ilty
-
.! ¡ ; .1 MOB - P.pi.ntshaãt 0 30 5 30 20 .nd Strike-- 0 IO 3 . .2 øo1 X 5 3 D.y/BILht X 6 3 6.5 MOB ContInuo.. 1 30 5 30 20 rrina.».n o io 3 .4 .2 OPI enoept 0 30 3 R.pi k Hio I Lialt.d OPS X 30 5 30 20 X 10 3 . .2 X 30 3 MOB 5p.i..biIXty X 30 5 30 20 - 0 15 5 1.0 .5 - . . _3P 3 -¡3W M.Ì, OPS - X 30 5 30 20 SOW -- 0 10 3 .4 .2 X 30 3 - . X 6-LOW Soe.r Dea. 0 30 5 30 20
D.t.ctlâ O lO 3 .4 - .2 - X 30 LAW D.ek-6Zeant.d i - 30 5 30 20 -$0W D.t.ci.ion, Tr.cking,4 X X IO 30 3 -3 .4 .2 V..poe. Firing
28
state appearing in the wave climatology of the operational area of the ship. This is done by reducing the attainable 'speed due to maximum engine output until every motion criterion is satisfied. In order to obtain the mean speed, the maximum speeds in each sea state are weighted by the probability of occurrence of the sea state, and the average of the weighted speeds is computed. In each sea state several headings can be considered. Then the maximum speed in a sea state becomes the average in which the speeds at each heading are weighted according to the mission profile of the ship.
Percentage of Time o,f Operation
Thouyh Bales (1981) uses a method basically similar to the method presented in the previous chapters in optimizing the freeboard of naval combatants, the "standard" method for assessment of seakeeping performance of naval vessel in the U.S. seems to be the procedure presented by Johnson ét al. (1979). Thè seakeeping performance index used by Johnson et al. expresses the percentage of time the ship is capable of certain operatións on a given sea area. In determining the value of the Seakeeping Performance Index (SPI) all speed and heading combinations can be weighted according to their importance. This PI rias been used in several comparisons of naval ship
operability. Examples are, the studies by Bales &
Cieslowskj (1981), Comstock et al. (1982) and McCreight& Stahl (1985).
In predicting the SPI the Required Operational Capability (ROC) of the vessel is defined in terms of ship motion limits as for example in Table 4. There may be several RÖCs, such as Anti-Air Warfare (AÄW), Antisubmarine Warfare (ASW) and Mobility (MOB), with different degrees of importance. The SPI is then the weighted mean of the
PERFORMANCE CRITERIA SHIP RESPONSEIEVENT
ROLL (DEGREES) PITCH (DEGREES)
BOW WETNESSES (PER
HOUR)
SLAMS (PER HOUR)
FULL
PERFOANCE
/
Figure 5. Development of Seakeeping Operating Envelopes, Comstock et al. (1980).
...
SOE FOR SPEED/HEADING
GIVEN ROC TIME PROFILE
SEAKEEPING OPERATING ENVELOPES
Figure 6. Development of Seakeeping Performane Indices (SPIs), Keane & Sandberg (1984).
r
0.1
X X-5 1 L
SEA STATE ROC RELATIVE
FREQUENCY IMPORTANCE
0F OCCURRENCE
5 3
30
/
The Seakeeping Performance Index for a prespecified ROC in a given operation area is computed by developing first Seakeeping Operating Envelopes (Figure 5) fOr each sea condition, or for each cmbination of characteristic wave height and period. The Seakeeping Operating Envelope (SOE) presents in a speed polar format the speed heading combinations at which a certain operation is possible, i.e. ship responses do not exceed the prespecified seakeeping criteria. From the SUE the Operability. Index (UI) is computed, this expressing the percentage of time of operation in the given sea state. In Figure 5, 01 is the ratio of the non-shaded area (operable) to the total area of the circle, in per cent,assuming all speeds and headings equally probable. In order to obtain the SPI each UI is weighted according to the probability of occurrence of the sea condition and the average of the weighted OIS is computed as shown in Figure 6.
In visualizing seakeeping performance, in addition to the Operating Envelopes, Olson (1978) also uses Seakeeping Contours (SC), Figure 7. Seakeeping Contours are expressed on the same speed polar base as the SUE, but SCs are three-dimensional and the height of the contour reflects the maximum significant wave height, at the particular speed and heading, that the ship can accept without exceeding any of the specified seakeeping criteria.
Required Spe Reduction
Predïction of the Seakeeping Performançe Index of Johnson et al. (1979) involves the computation of the maximum speed of the ship in a
seaway. A part of the process is the evaluation of the speed reduction to restrict the ship motiòns tO within the maximum acceptable limits. The required speed reduction can easily be estimated by the fonnula given by Naito et ai.. (1980), if the mean square response, rn0, is known as a function of ship speed. The forrìula is derived in the following way.
figure 7. A Seakeeping Coñour (SC) expresses on the vertical sçle the maximum significant wave height, here i féet, that the ship can accept without exceeding any of the operability criteria. The base of the SC is a speed polar plane (Olson, 1978).
1oo
V,
V) uJz
Ui
>
L)
taJ LL u-.LJJ
J
=
20 4O 60 80NUMBER OF OCCURRENCES PER HOUR
Figure 8. Degradation of ship hull effectiveness due to slaming and deck wetness according to Hosbda e.t a].(1985).
In (11) it can be seen that rn
is a function of sea state, S; ship speed, V; and heading, :
m = F(S,v,).
(26)
Assuming that. the changes
in sea state, speed and heading are small with respect to an èquilibriurn condition the
higher order terms in a Taylor series expansion f F may be neglected,
and a small, change in the mean square response can be expressed
as:
If the limiting
criterion has been defined in probabilistic erms as in (14), the relation between the critical
'notion parameter, x, and
rim is given by: ox and 32 Orn ox (27) (29) (31) X = 2 n P)'. (28)
When the ship
response x.exceeds the critical value,
X,
the speed arid/or heading of the
ship should be changed so that the response will be reduced by thé amount
ôxx
-X,..Cr
On. the other hand, the reduction (29) in
terms of the Corresponding reduction in
m
can.be determined by differentiating (28) with respect to m . This gives:
ox dx /(- in P) '11;--' (30) Ox = 6m
in p)
ox 2 ma oxSubstituting (27) for ôm0 in (31) and assüming that sea state and heading remain cónstaflt yields
o
oF
= - aV
oV,From (32) the following formúla is finally obtained for the requ,ired speed reduction: ax X oF /'(__in
2m
ox$çjng Perfoae Effectiveness
Hosoda et ai. (1983, 1984 and 1985) apply methods of reliability engineering and introduce the concept of mission effectiveness in the quantitative evaluation of seakeeping performance of ships. They assume that the effectiveness Of the sh'p system is equal to 100 % in calm sea. In rough seas the missiOn effectiveness measures the rate at which the mission
of
the ship can be accomplished fn relatiOn tocalm seas.
-In evaluating the mission effectiveness, the ship system Hosoda et al. consider salvage missions by patrol boats - is divided into séries and parallel subsystems. Examples of series subsystems are hull structure and main engine. If either of them fails, the ship sysiem no longer has the capability required by the mission.
Personnel, radar and communications are examples of parallel subsystems.
The degradation Of the performance effectiveness f each subsystem of the ship due to wave-induced motions is expressed as function of statistical response valües as shown in Figures 8, 16 and 17.
(32)
34
In a given sea state (defined by H
and T) the performance effectiveness of each subsystem, e., is estimated
from the performance degradation curves on basis of statistical
response values, which can easily be determined by
using the unit
rms-functions g(T;V,) defined in (11). The total performance
effectiveness of a series system is given by
n
e =n
Si1
and of a parallel system by
m
- ri (1 - e.),
j=1 J
where n and rn are the
number of components in a series and in a parallel subsystem, respectively.
The short-terrnmissjon effectiveness as a function of significant wave height and characteristic wave periód, e(H5,T),at a prticu1ar
speed and héading is obtained by applying both
equations (34) and (35) and their combinations. In the same way the
mission effectiveness can be predicted for several
speed-heading combinations, and the mission effectiveness in each sea state is obtained
as a weighted mean, the weights being determined
in accordance with the probability of occurrence of each speed-heading
combination.
The long-term seakeeping
performance éffectiveness can be estimated by:
E(Ocean area) = Ê f (H ,T)e (H 1)
k s
ks
where
k is the long-term joint frequency distribution of wave height and period'in the operation area, and ek is the mission effectiveness
SEAKEEPING CRITERIA
Vertical Acceleration
Though ships passenger vessels perhaps excluded -do not often reduce speed or change course solely as a result of high vertical accelerations, much more reliable full-scale data is available on vertical accelerations in rough seas than on the frequency of
slamming ôr deck wetness. On the basis of the published data, it is easier to set a relatively reliable criterion for the level of
vertical acceleration that well-experienced navigators seem to accept than to find criteria covering slamming and deck wetness, the. primary reasons for a manoeuvre to reduce ship motions. The vertical
acceleration criterion determined thus reflects the overall level of vertical motionsof the ship in weather conditions where slamming or deck wetness iiiay be critical, and does not necessarily define the limit of acceptable vertical acceleration from the point of view of safety of the ship, crew and cargo. The. vertical acceleration
riterion can then be utilized in finding realistic li'midng criteria for slamming and deck wetness.
Figure 9 shows data found in the literature on the maximum vertical acceleration measured at the forward perpendicular of merchant ships in service 'The. ships appearing in Figure 9 and the sources of data are given in Table 5. The maximum vertical acceleration has been expressed as a fûnction of ship length between perpendiculars since there seems tb be a tendency for masters, on larger ships to permit a lower level of vertical acceleration than masters on shorter ships.
Most of the data in Figure 9 i from to sources: Westin (1977) and Lindemann et al. (1977). Westin (1977) sunmarizes data of earlier fùll-scale meaurements on container ships presented in the
literature. me vertical acceleration valüe given by Westin is in mOst cases the maximum peak' value observed in a long-term study of'
lo
:k
E
L. 10D
Q
Iv o_. cri 0,2 1O oL
U 'J,w
>
o. 4,. o HOFF1&N(19)
o o o 36OCHI & MOTTER 11974)
o
200
LENGTH BTW PP
[mJFigure 9. Data on the maximum boq of merchant ships in
Table 5. Main particulars
vertical acceleration measured at the
service and some liffliting criteria.
of ships included i Figure 9.
Ship Type Le nqth Be am Draft Reference [mJ [m] [m} Boston Cöntajner Antónja Johnson America Maru 'I Japan Ace i' t4ihon 'I Atlantic Saga I' Dart Europe
Hodakasan tlarù
1inr
Roi baudoin car-ferry
151.2 157.2 1:7 5.0 175.0 257,6 208.8 218.0 145 .1 110.6 21.8 25.15 25.0 25.2 32.2 30.5 .19.6 15.2 i O 1 9.5 9.7 11.6 9.3 9.1 8.5 3.5 Westin (1977) I' I, II Wahl (1979) Aertssen & van Sluys (1972) Hanaoka
et
al. (1963) Ferdinande & "A" Contai ne r obo "C" tank "0" car-carrier 259 310 311 157 DeLembre (1970) Lindemann et ai. (1977) 'Iseveral voyages. In Figure 9 the maximum peak value has been
converted to the maximum root mean squae vaue by assuming that the maximum is equal to the most probable extreme value in 200 succesive pitches, i.e. maximum = 3.255a in accordance with Table 3. This relatiOn seems to hold on the average quite well in cases where both the maximum and the root mean square are given.
The vertical acceleration data by Lindemann et al. (1977) originates from long-term full-scale riesurements with hull surveillance systems on four cargo ships.. Lindemann et al. present their results in terms of a non-dimènsional Rayleigh parameter from which the root mean square value can be determined. The data has been recorded in 15 instances. of speed reduction (change of course) due to extreme ship motions. Ten of the 15 recordings were made on the. 157-raetres-lpng car-carrier. According to Lindemann et al. the slow-down was not necessarily due to severe vertical accelerations but probably more often due to heavy slamming or green water on deck.
Figure 9 has been completed with a scale for the probability of
exceeding one g according to the Rayleigh distribution and with a few operational limits from Table 6, which gives a summary of vertical acceleration criteria appearing in the literature. The data in Figure 9 seems to confirm, the limiting criteria suggested by
Aertssen (1968).. It is significaht that most of the full-scale data i.n the figure has been recOrded after Aertssen wrOte his SNAME paper. It can also be seen that the data measured on the car-carrier
(Lindemann et al. 1977) agrees Well with the critical value of 048g root mean square recommended by Ferdinande and De Lembre (1970) on the basis Of the thorough measurements on the. car-ferry m.s. ROI BAUDOIN in serVice. The operational limit recommended by Hoffman
(1976) is partly based on experience with hull surveillance systems installed on large ships such as LASH ITALIA, while Ochi & Motter
(1974) considér a Mariner-hull 161 metres in length. Both Hoffman and Ochi & Motter refer to Aertssen's seakeeping trials in
Table 6.
LIMITING CRITERIA WITH
REGARD TO VERTIC/L
ACCELERATION
Reference
Andrew & Lloyd (1981) Bales (1981), Wa}den 8 Grundman (1985) Chi lo & Sartori (1979), Bau et al. (1981) Chryssostomidis (1972) Comstock & Keane (1980), Schaffer et al. (1983), Adams & Beverly (1984), McCreight & Stahl (1985) Conolly (1974)
Criteri on
subjective motion magnitude < 12 sign.
s.d.
0.55 g
sign. s.a. 0.4 g av. 1/10 < i g sign. s.a. 0.4 g
rs0.32 g
= i g/673 sec = i g/132 pitches Corresponding rms. valueStation
Ship types
0.125 g 0.225 g 0.25 g 0.35 g
bow bow bow bow
Large tanker and bulk
carrier
General cargo. iiner Cross-channel ship Trawler
0.275 g 0.175 g 0.125 g
bow bow b ow weighted mean over L
Merchant ship 125
rn
in length
Merchänt ship 190m in length Merchant ship 260 m in length Naval Ships
0.275 g
FP
Naval ships
0.2 g
FP
Naval ships, merchant ships
0.392 g
cargo spaces
Merchant ships
0.2 g
bridge
Naval ships, surface effect ship
032 g
0.2L abaft FP Destroyers As given in Reference Aertsser, (1968) sign. s..a. 0.25 g sign. s.a. 0.45 g sign.s.d.
0.5 gsign. s.a. 0.7 g sign.
s.d.
0.55 g
sign. s.a. 0.35
g
Table 6. Continuation Reference Criterion Station As given in Reference Correspôndi ng rms value Giannotti et al. (1977
)
Hoffman (19i6) rm 0.15 g maximum 0.5 g or 0.15 g any location Irms 0.15 gQ5 g
bow Kitazawa et al. (1975) Prob. (ampi .>0.8g}Kim & Nakamura '(1984)
0.001 0.215 g f.P Lewis (1955) Prob. {ampl.>O.4g} 0.158 g working reas < 0.04
Lloyd & Andrew (1977)
subjective motion magnitude < 15 weighted mean over L
Ochi & Motter (1974)
Prob. .{sign. s.a. > 0.4 g
.< 0.07
0.2 g
bow
Prob. {sig. s.a.
0.4 g} < 0.03 0.2 g bow Oison (1978) MSI = 20 % 0.1 g creW spaces Schmltke (1981) t'ms 0.2 g 0.2 g b rid ge Yamamoto (1984)
Prob. (ampi .>O.5g}
0.204 g
FP
< 0.05 Prob. (ampi .>O.4g}
0.163 g
bridge
40
Thus, the data in Figure 9 and Table 6 indicates that the vertical acceleration criteria recommended by Aertssen (1968) are still valid and may be used for comparing the seakeeping performance of ordinary cargo ships such as general cargo liners, container ships, tankers and bulk carriers. The limiting criteria with regard to the vertical acceleration at the forward perpenqicular are for different ship
lengths approximately as follows:
Length btw. Criterion pe.rp. at FP 100 m 0.25g 150 w U.20g 200 m 0.15g 250 m 0.125g
FOr car-carriers around 150 metres in length a suitable criterion with regard to the vertical acceleration at FP seems to be about
0.. 175g root mean square.
The criterion has been defined at the forward perpendicular since. most of the comparable., full-scale data and. criteria in the literature
concerns the vertiçal acceleration at FP. However, it might have been more logical to define the criterion at the bridge, where the decisioñ to slow down is made. Figure 10 shows for some Series 60 hulls the vertical acceleration at O.75L abaft of the FP, or
approximately at the bridge, corresponding to 0.2g root mean square at the EP. he results have been taken from the Seakeeping Tables of Loukakis & ChryssostoinidiS (1975) and are expressed as a function of wave period corresponding to the spectrum peak1 or modal period. As
can be seen, the personnel on the bridge are exposed to an
acceleratthn of u.lg root mean square, approximately, when at the sai1e time the vertical acceleration at the forward perpendicular is
(MODAL PERIOO)/iC
Figure IO. Vertical acceleration rms O.75L abàft of the FP when the vertical acceleration at the FP is O.2g roes. Series 60 vessels.
42
Tne U.S. Navy surface ship criterion with regard to vertical
acceleration, 0.2g root mean square, has been defined at the bridge.
This value is well in agreement with the observations of Andrew and
Lloyd (1981) during the seakeeping trials of the british frigates
LEANDER and TRIBAL when the root mean square bridge vertical
acceleration was close to 0.15g on most of the runs.
According to
Andrew and Lloyd "... the motions were sufficiently severe to curtail
normal daily activities of the crew and it wOuld have been
impractical to drive the ships at these speeds into head seas for
very long."
According to Conolly (1974) a root mean square vertical
acceleration of 0.32g ".. would impose impossible conditions
... to
live and work ...' for a protracted period.
The U.S. Navy criterion
is well suited for displacement type naval vessels, while the
criterion for cargo ships at the
ridge could perhaps be slightly
lower, of the magnitude 0.1 to U.lSg root mean
square.
From the point of view of people unused to ship motions these
vertical acceleration levels are high.
According to the
International Standard 2631 Addendum 2 "Evaluation of exposure to
whole-body vibration in the frequency range 0.1 to 0.63 Hz" the
severe discomfort boundary in the frequency range 0.1 to 0.315 Hz for
an exposure period of two hours is 0.5 m/s2, 1.0 m/s2 for an exposûre
of half an hour.
These vertical acceleration magnitudes cause
syîiptoins of hiotion sckness in about lu % of unacclimatized seated or
standing men.
This has been verified for instance by Goto (1983)
amongst students of a merchant marine school on training voyage.s at
sea and by Lawther and Griffin (1985) amongst passengers on a
cross-channel ferry.
Above 0.315 Hz the equivalent acceleration in
the ISO standard increases by the rate of 10 dB per octave, thus
following the results of licCauley et al. (1976) obtained with healthy
male students in laboratory conditions using
a motion generator
(Figure 11).
Results of McCauley et al. indicate that human beings
are most sensitive to motion sickness when the frequency of
so 'o 30 V)
z
20 10 5 4 s 0.4, 0,3 0.' o1 0.0 S GaTO Ii
I O.1 0,2 0.3 0,5 1,0 FREQ [Hz)6010 (83)
O IAWTHER g GPF FIN (198S) a 0,333 Hz g MCAIIEY (1976) 0,167 Hz JFigure 11. Motion Sickness Incidence (MSI) predictedby the formula of McCauley' et al (1976), International Standard 2631 Add. 2 for haif-tiour dnd two-hour exposure periods and Goto's (19U3) proposal
for
a Standard.Figure 12. MSI ratio auIÖnst people unused to ship motions according to experimental data.
1,5 05
VT. ACC. rms [mis2)
o44
McCauley et al. (1976) found alsothat the Motion Sickness Incidence (riSI) ratio, or the percentage of people vomiting, was independent of roll and pitch motions, when they were superimposed on thé vertical accelerations. Later this was confirmed by Lawthe.r and
Griffin
(1985). They Observed that the vomiting incidence amongst the
passengers correlated well with the root mean square vertical acceleration. The motion in the five other degrees of freedòm had only a small effect on the vomiting incidence.
Above the acceleration level of 0.5 rn/s2 the MSI ratio increases steeply with increasing acceleration as can be seen in Figure 12.
It
can also be seen that the results by Goto (1983) and Lawther & Griffin (1985) agree well, while the data of O'Hanlon & McCauley
(1974) from experiments with the motion generator predict a lówer MSI
räio. Lawther and Griffin point out that their data indicates the
acceleration magnitude about 0.1 rn/s2 root mean square is the lower treshold below which voraiting is unlikely to take place.
The effect of acclimatization on the motion sickness incidence, ratio onboarcl during a long voyage is considerable. Goto (1.983) observed that the MSI ratio decreases by nearly the same rate each day if the acceleration level remains approximately constant. The rate of
decrease is about 0.6.
Thus,if the MSI ratio on the. first day at
sea is :50 %, on the third day the ratio has decreased to about. 18 % assuming that the acceleration level has remained approximately constant. both Goto (1983) and McCauley et al. (1976)
give empirical formulas for estimating the MSI ratio as a function of vertical root mean square acçeleration for exposure periods longer than about two
hours, i,e. for estimating the asymptotic value of the MSI ratio. In 00th stuciies it was observed that individuals who did not vomit during the first two hours of exposure rarely did so during
subsequent prolonged exposure.
On the basis of the information available on the motion sickness incidence amongst unaccliinatized human beings it seems Well founded
to use a limiting acceleration
of O.05groot mean square in the
passenger spaces for comparing the
seakeeping performance of
passenger vesséls on shorter routes.
For cruise ships this
acceleration level may bê too high.
An acceleration magnitude of
about O.Ulg to Q.02g woul.d perhaps form a better limiting
criterion.
Slamming
Before limiting criteria with regard to slamming can be considered
it
has'to be agreed what is called a slam. Should every
impact be called
a slam, or only the severe ones?
According to Aertssen (1968), only
a blow which incidentàlly might cause a ship's master to slow down is
called a slajii..
A more precise definition of slamming is given in
terms o
the slam-induced whippin.g stress in the maindeck
amidships.
The impact. is called a slam if the midship whipping stress
exceeds'19.6 HN/rn2 (2 kp/inm2)
ina ship 225 liietres in length built of mild
steel and 29.5 MN/rn2 (3 k'p/mm2) in a high tensile steel ship
(Aertssen,
1977).This treshold value can oe scaled up and down
according to ship length squared.
Hoffman (1976)suggests treshold
values of
24.55 MN/rn2 and 15.7N/rn2 for a heavy slam and for a
milder slam,, respectively.
This definition of a slam is difficult to
apply in model tests and inconvenient to use in theoretical
predictions.
The most frequently used defintion of a slam is that of Oçhi
(1964).He uses the vertical velocity of the bow
relative to the wave surface
in defining a slam.
According to Ochi the impact is called a slam if
the foreship at 0.15L abaft of FP emerges from water and
the relative
velocity at the station exceeds a critical value of
V
=0.093/jE'
(37)
c,r
i.e. 3.66 m/s (12 fps) for a ship 158.6 m
(520fU in length with a
46
was derived by considering results of slamming model tests of six different models, including a LIBERTY, a 1ARINER and a V-form high-speed craft. Ochi (1964) points out that his critical re-entry velocity is the miniauri velocity which causes a slam.
In contrast to Aertssen's definition of a slam, in Ochi's criterion every impact on the bottom is called a slam. This different
defInition of a slam explains the observation by Aertssen (1968,) that a satisfactory correlation between the slamming frequency predicted by Ochi's (1964) theory and the results of the mv,JORDAENS seakeeping trials (Aertssen, 1966a) was obtained by using O.143/[' as the
critical velocity.
The formula for the critical re-entry velocity suggested by Conolly (1974) takes into account in a crude way the susceptibility of the underwater hull shape forward to slamming. Conolly's critical re-entry velocity 'can be expressed in the form:
V = 4.56
1
D/k (38)where [J is draft and k is given by'
k = (cot p)2 (39)
with p defined as the deadrise angle of an equivalent wedge at the section U.2L abaft of the FP, where slamming is examined. The p-angle is shown in Figure 13. Conolly's formula for the critical re-entry velocity in general gives significantly higher treshold values than Ochi's formula (3) as can be seen in Figure 14.
In the literature the seakeeping criteria with regard to slaming expressed as the maximum permissible probability vary from O.Q1 to 0.05 approximately, as is evident from Tables 7 and 8. With both merchant ships and naval combatants the criterion of 3 slams in 100 pitch oscillations at 0.15L abaft of the FP with Ochi"s definitjon of
10 s o 0.03 E E E C E 50 loo 150 200 LENGTH 1ml Section shape -0:02 OOL 0-06 000
INotf widlh)/(Mozimum beoin)
FigUre 13. Definition of deadrieag-1e of an equivalent wedge
adcording tO Cönolly (1974).
Figure 14. Critical re-entry velocities V calculated by the
formuis presented byAertssen -(1968), Ochi (].964) and Conolly (1974). Aetssen and Ochi examine slamming at the sectionO.15L abat of the FP and Conollyat O.2L abaft of the FP.
MWS = Midshij whipping stress. in MN/rn
'Tàble 7.
LIMITING CRITERIA WITH
REGARD TO SLAMMING. ÑERCÑANT SHIPS. Criterion Station Definition Ship types Re ference
In terms of critical prob.
As given in Reference abaft of FP 0.01 1/100 pitches O.2L Ochi's Merchant ships Chryssòstomidis (1972) .0..01 Prob.<0 .01 0.1SL Ochi's
Contai ner ship
Kitazawa et al. (1975) Kim & Nakamura (1984)
0.01 1/15 min. MWS>24. 5.5 Merchan.t ships Hoffman (1976) 0.02 2/15 min. MWS>15.7 Merchant ships Hoffman (1976) 0.02 .02 Bulk carriers Yamarnoto (1984) 0.03 Prob.<0,03 O.i 5L Ochi's Merchant ships
Ochi & Motter (1974) Journée & Meljèrs (1980) Bau et ai. (1981)
O .03
3/100 pitches
MWS>19.6
Large tankers, bikers
Aertssen (1968)
0.04
4/100 pitches
MWS>51,9
General cargo liners
Aertssen (.1968) 0.05 5/100 pitches MWS>3.9 Cross-channel 0.06 6/100 pitches 0..9g decel. Small trawlers Aertssen (1968) 0.06 6/100 pitches Ochi's Tankers
Table 8.
LIMITINGCRITERIA WITH REGARD TO SLAMMING.
Criterion
Station abaft of FP
Definitlon
Ship types
'In terms of 'critical prob.
As given in Reference 0.003125 1/320 pitches. 0.2L Conolly's Destroyers 0.015 0.03 10/1 hour 20/1, hour Frame '25, O.15L
FF-1032 destroyers Naval s:hips
0.03 Prob.<0.03 O.15L ' Ochi's Frigates 0.03 3/100 pitches , 0.15L ' Ochi's Naval ships 0.03 0.04 Prob.<3% Prob.<0.04 ' '0.15L 0.i5L ' Ochi's Destroyer , Frigates 0.05
5/100 pitches Whipping acc.
bow ' average Ochi's Catamaran ampi., < 0.18g -over L -'Naval ships
50
a slam has been the most widely used. Critical slamming
probabilities suggested by Aertssen (1968) are in general somewhat higher than the values used in recent studies. However, Aertssèn's criteria, seeti to oe quite well in agreement with later full-scale observations. On the large container ship DART EUROPE the peed of the vessel was adjusted so that the slamming probability was less than 5 % (Aértssen & van Sluys, 1972). On a fruit carrier 125.4 metres in length, 4slarns per 100 pitch oscillations were considered critical (Aertssen, 1977).
In the answers to the Swedish seaworthiness questionnaire by Wahl (1979) on container ships the number of slams in five minutes
at the moment of slowing down varied from one to five with an average of ¿ per 5-minute period. This corresponds to a slamming probability of U.U5 to 0.06. In a similar questionnaire carried out earlier
(Wahl & Andersson, 1974) the average results, one slam in 7 minutes
(Prob. 0.0?) by cargo ships and one slam in 9 minutes (Prob.
Ü.u1b) oy refrigerated cargo liners, were considerably lower than in the 1979 study. Wahl does. not provide any explanation for the
di fferênce.
Kehoe et al. (1933) distributed a seakeeping questionnaire to commanding officers of 185 U.s. Navy frigates, destroyers and
cruisers. The results indicate that speed is reduced if the slamning frequency is 6 to 20 slams in one hour, or the slamming probability is0.01 to 0.03, respectively. In practice speed is reduced after 2...4 consecutive heavy impacts. Hadler and Sarchin (1973) obtained
similar statements in an interview with six commanding officers of U.S. Navy destroyer-type ships, who all said that they would reduce speed if they had two slams in three or four successive waves. This iiay be the situation which typically precedes the decision to slow
down. Thc seakeeping trials with the Dutch destroyer "Ba
(Bledsoe et al. 1960) andwith the British frigate TRIBAL (Añdrew & Lloyd, 1981) were abandoned after the ship had suffered a succession of very heavy
slams. Earlier during the trial runs TRI8AL had sustained a slamming
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