924025
TEC H:N'ISCHE H 0G ESCHOOL DELFT
AFOELING DER MARITIEME TECÑNIEKLABORATORIUM VOOR SCHEEPSHYDROMECHANICA
,-SHIP SPEED AT SEA
Prof..ir. J. GerritsrnaRapportno. 261-P
1971
Publikatie in "Schip en Werf".
Deift University of Technology Ship Hydromechanics Laboratory Mekelweg 2
2628 CD DELFT
The Netherlands
SHIP SPEED AT SEA
InfroductionAn important application of the theory of ship motions and propulsive performance in waves is the prediction of sustained sea speed or speed loss in a given seaway. During the last few years considerable progress has been imiade with regard to i/le
calculation of seakeepi,ig qualities of ships, bolli regarding
,iio-¡jolis aiid power require,nenls, but this k,iowledge is hardly used
in flic actual design procedure. From a /iydro,nechanical point of view the hull forni of a ship is based for 1/ic greater part on still waler performance, rat/icr i/ian on the ship behaviour in a seaway.
¡t is true 1/Ial the empirical ship design methods include know!-edge of the seakeeping qualities and I/us knowlknow!-edge is actually
used by the naval architect. However, 1/le use of emperical knowledge may not lead to 1/le best result iii all cases and is
certainly a risk when extrapolation is necessary to extreme iiui1 dimensions and very high speeds. Furthermore a quantitative or even a qualitative judgement based on analytical methods could be a powerful tool for i/ic designer.
The present analytical knowledge of i/ic seakeeping qualities of ships is noi coin plete, bitt in many Cases calculations based oit
theory und fu,,dai,u'niul experinu'nms l?11V 1w us4'(l for 1/u' (0111-parison of different design.ç ivii/i respect io their motions and
11w performance in waves.
¡n this paper sommie factors affeciimig ship speed at sea will be discussed f mug u practical pain t of view and gaps in our pres('ul knowledge will be pointed ozi:.
The speed loss due to weather
On certain ship routes a considerable spced loss due to weather conditions can occur. It is known that ship length and ship speed
which define more or less the natural period of pitch, are im-portant parameters in this respect. An illustrative example of
speed loss as a function of Beaufort number and relative weather direction is shown in Figure 1. In this case 15% speed loss was
found in a B6 head sea condition on the North Atlantic, corre-sponding with an 80 % power increase in comparison with the still water condition at the same ship speed. On this particular
:°
10
56 o
by Prof. Ir. J. Gerritsma*)
*) Delft Shipbuilding Laboratory. Paper Symposium "The Applica-tion of ShipmoApplica-tion Research to Design", The University
South-ampton, 1970. :15 C s C o w w e10 w w
45
BALLAST CONDITION LOADED CONDITN
çt%
HEAD SEAS BOWSEAS BEAM SEAS QUATERING FOLLOWING'I
U m SEAS W SEAS 10° °° 250°4&, 270e 290 y 330°-i,
30°--
-I
MV. LUBUMBASHI L,1466m C2 eQ7OIr
R-Iv
Summary of causes of speed loss at sea
In light and moderate sea conditions the ship's speed is limited by the available power, the increased resistance due to waves, the wind resistance and the decreased propulsive performance. The
lower propulsive efficiency results from the higher propeller
loading and the non-stationary flow phenomena, due to the ship
motions, which affect the hull- and propeller efficiency.
In more severe sea conditions the motions of the ship can be a cause of deck wetness and danger of deck cargo, propeller racing and slamming. These phenomena can force the captain and the master to reduce the ship's speed to avoid danger to the ship and the engine. Such decisions are based on personal judgement and 8 different risk factors will be accepted by different captains. The human factors are difficult to determine but a statistical analysis
of full scale performance data as carried out by Aertssen [6] is
most helpful in this respect.
In the following chapters the various causes for speed loss will be considered in some detail.
0 2.5 50 0 2.5 50
OBSERVED WAVE HEIGHT in m
Fig. 2. Average sustained sea speed of Victory ships
ship route B6 is exceeded in 45 % of the time in summer and in
70 % of the time during winter.
The analysis has been based on carefully conducted full scale
t g.m Is at sea I I I. l)LIt Ii Iso st at ist ¡ca I tlit n I ronì Iugtnoks have been
used for similar studies and have shown the same tendency 12, 3, 4, 51. Figure 2 shows the speed loss of Victory ships in
ballast and loaded conditions on the sante route, as derived from logbook entries. Nearly 4000 observations were used to deter-iìdne the curves in Figure 2.
These figures stress the importance of speed loss in actual sea
conditioiis. Especially in comparison with the usual shipmodcl propulsion experiments in still water, where improvements in
power of a few percent nrc considered to be important, the speed
loss and power increase in a seaway look impressive, at least from a technical point of view.
It should be realised that the curves in Figure 1 and 2 are the averages of a large number of data points, which have a
con-siderable scatter. This scatter is due to the fact that the Beaufort
number is not adequate to describe the sea conditions in
suffi-cient detail. This is a drawback for instance in ship routing pro-cedures, where similar curves are used to determine an optimal
track in predicted or reported wave conditions. In actual cases
the speed loss may differ considerably from these average values.
The importance of the speed loss problem from an economic
point of view should be considered on the basis of overall
opera-tion costs. The treatment in this paper is restricted to technical
considerations.
1 2 3 4 5 6 7
BEAUFORT -Fig. I. Relation loss of speed - Weal lier Beaufort
n y he he 1er 3.1. Added resktance
The steady component of the resistance of a ship moving in Waves is larger than its still water value at the same forward speed. This is due to various factors, such as the disturbance of the incoming waves by reflection effects and by the generation
of waves radiating from the oscillating ship.
Havelock [71 suggested that the increased resistance in waves Is mainly due to the phase difference between the heaving- and pitching motions and the wave excitation forces. In particular for resonance conditions of the heaving and pitching motions, when large relative motions of the bow are observed, the added
resistance is large as has been shown by model experiments and by observations at sea. It may be concluded that these ship
motions and the resistance increase are closely related.
Krcitner [81 explained the added resistance by wave reflection effects only, but Havelock showed that his estimation was in
error. Maruo included reflection as one of the causes of
mercas-cd resistance in a linearized theory [9] He mentioned the
dilfi-culty that added wave resistance is a higher order quantity,
which is usually omitted in the linearized theory, but he sug-gested that careful examination of the terms which should be taken into account should lead to a solution for this problem. According to Havelock the average value of the longitudinal
wave force, resulting from integration of the wave pressure over
the time dependent immersed volume of the ship, is a good
estimate of the increased resistance in a regular wave train.
Assuming that the ship does not influence the pressure distri-bution in the wave, it is found that:
- RA JI, =
(z0F,, sine p + O0M sine
(1)where k is the wave number, z3 and E are the heave and pitch amplitudes, F0 and M are the wave exciting force and moment
amplitudes, CzF and M are the phase angles between motion and wave excitation forces.
Figure 3 shows a comparison between the calculated added
resistance and the corresponding experimental values for a C = 0.70 Series Sixty Model [lO]. The model experiments were carried out by Sibul [11].
Considering the rather crude assumptions on which formula
(I) is based, the agreement is satisfactory, except for the
smallest wave length when the speed is well above the design speed of the ship. There the ship motions are negliglible and the resistance increase is mainly due to reflection which is not included in the calculation.
Abkowitz reported one experiment with a restrained model in a regular wave train to measure reflection resistance [12]. The experiment confirmed that this effect is small. Similar
experi-ments are carried out at Delit with a model of a very fast
container ship. Preliminary results confirm Abkowitz' results. lt is not surprising that for slender ships, such as destroyers and fast cargoliners, a close agreement between formula (1) and the
nwasured average wave resistance is found. This may not be the
case for ships having large angles of entrance of the waterlines,
such as coasters and large tankers. In agreement with these
experimental data Maruo's theory predicts a small reflection
resistance.
o
O 01 0.2 03 0.4
Fn
Fig. 3. Measured and calculated resistance in regular waves
S. en W. - 38e Jaargang no. 3 - 1971
j
2.0j
to -nj
2 3.0 2.0 1.0 O O 3.0 2.0 1.0 O Fn.=0.15 EXPERIMENT: Nokamura Sibut CALCULATION: .' Moru&s formuto . . Modified Maruos f.I
En. =0.20 -fr- v. Fn.=0.25 0.5 1.0 5X/12.O 2.5Fig. 4. Measured and calculated resistance increase coefficients
A detailed experimental analysis of Maruo's theory was carried out by Nakamura et al [13]. Figure 4 shows the measured and
calculated added resistance, again for the CR = 0.70 Serie3
Sixty Model. The comparison with Sibuls experimental values
indicates that the differences betweeen two sets of
experi-ments are of the same order as the differences between calcu-lation and experiment. In Figure 5 the calculated total resistance increase is compared with the part which is due to reflection
according to the formula:
®DHH Opp4 © OHPC Çp,CO5E, ® OHPSC0t0snE, © OHC e COS L, ® OHS ,SlflC, 'n S n-. I
--2
'n..-©II I I ®OPC,COSE. 3 I,/
® Op4 Sin L Sn.-,I.
I I -. 1.0 1.8 2.0Fig. 5. Co,nponents of resistance increase coefficients
57 HAVELOCK
-o.--e
--MODEL L 2 758m C.o7o SIXTY SIBUL ---a-
--SERIES o.r4w
rL al es s. ic al ng the nd tnd he 'sisJis
be(n w 3 o w o w 3 o u. o w u, 4 w (J z 4 w z 3 0.75 0.50 OE25
dependent on ship tyl)C afid ship speed. Low wind resistance superstructures must be effective to reduce the power increase
¡ri adverse weather.
Added resistance due to wind can be estimated from windtunnel
model tests. A recent ad(lition to the literature on this subject Was reporled by Wagner who gives tite results for len widely different ship types, ranging from a hydrofoilcraft to a large
tanker [18]. lt is of interest to note that in many cases the highest wind resistance was found when the relative wind
direc-tion was approximately 30 degrees off the bow.
Heading control in waves can be another source of increased
resistance because of rudder action and the corresponding
yawing motion of the ship. Automatic pilots have the reputation to be
reliable instruments but in rough seas the weather
adjustment may set up a sustained yawing motion as shown by
yawing recordings.
According to Motora, as quoted by Nomoto [19] a resistance increase of 10 to 20 % may be found in some cases. Also for
large tankers a considerable resistance increase due to low
frequency yawing motions is reported by Nomoto [201. These
ships have a relatively low yaw damping and frequently a poorly
damped yawing motion under automatic course keeping control is observed. The increased resistance is
mainly duc to the
resistant component of the centrifugal force caused by yawing.
The forced oscillation methods, now available, enable the deterniation of the hydrodynamic derivatives of the ship in yawing and swaying motion. Also the wave forces and moments
can be determined with restrained models in waves. This infor-mation should be used to design the characteristics of the
auto-matie control of ships and analog studies could be made to
optimize the auto pilot. This procedure is used with success for the design of depth control of submarines.
Experiments with supertanker models in oblique waves have
shown relatively large leeway angles at small wave length ratios.
These may be explained by wave reflection effects on the sides of the ship, which cause relatively large steady components of drifting forces and moments. The leeway angles are a cause of
increased resistance.
Ogawa calculated the reflection effect at various angles of inci-dence and he found a good agreement between calculation and
model experiment [21].
3.2. Propulsive efficiency in waves
In Figure 7 the relation between the loss of propulsion efficiency and weather is given for a cargo ship in head waves on the North
Atlantic [i]. The important decrease of the propulsive
perform-ance is caused by the resistperform-ance increase and by the
non-stationary effects which result from the seaway and the
corre-sponding motions. The increased power requirement in waves can be estiniated from the total resistance, including wave and wind effects. Also model propulsion experiments in more or
less realistic sea spectra could be carried out to determine the
power - speed relation. Extensive resistance and propulsion
experiments with a model of the HollandAmerica Line's liner
Mausdan, (C1 = 0.65) have been carried out at Delft. For
the range of variables considered in the tests it was found that
the mean increases of thrust, torque, revolutions and power were z
F
r
a. u. o 'n u, o O MV. LUBUMBASHI LB,lB.Sm CB O.7O7N
2 3 L 5 BEAurosiFig. 7. Relaiio,j loss of propulsive efficiency - Weather Beaufort
2 Fi8 pr apj co' Fij Th be sp (2) shi n C Fi L.14E.1 C O69 fly..JORDAENS m p-u w u. u.
/!//'>
p-o w u. u. w w 3 58 s. O 1, 5 6 7 8 WEATHER,REAUFORT -Fig. 6. Ratio increase of poner (tile to waves lo ¡ola! increasedue to weather
= R.1ji/og-(B2/L)
D111,
+
-F D,i,a0p0 COSC Oz -f- Sifle (-Iz(2)
+ DIIC.q, Cost2 f D,1,, jtip, + Dp,ip,, COSeH
-I--Dj5p0 Siflff& + D
where = z,,1,,. ij',, =
The authors conclude that pitching is the main cause of
resist-ance increase in waves in the case of low speed but heaving
has a larger effect for higher speeds. As indicated by the term D, the reflection is small when compared with the total resistance increase. These conclusions fully agree with Maruo's analysis of a rather slender ship like mathematical shipform (LI B
8 C = 0.533) [9]. and with similar work bij Nakamura en
Shintana for three other mathematical forms [14].
From (1) and (2) it follows that the resistance increase varies as the squared wave amplitude. Than the nican resistance in-crease in a given wave spectrum S is found from:
OD
R4t,' = 2 f
R.i(a,)
s
(oj,,)dc,j,, (3) where o.i is the frequency of encounter. The increased resistanceoperatorR.111 can be obtained from model tests in regular waves
or from calculations according to formula (I).
However, model tests do not confirm completely the validity of
the squared wave amplitude theory. A detailed experimental analysis by Sibul showed that the exponent of ¿ may vary between 1.1 and 2.5 with a mean value of about 1.8. A
super-position according to equation (3), using experimental resistance
increase operators resulted in 20 % tot 30 % less resistance than
the directly measured resistance increase in the same wave
spectrum [11]. Although in [15] no serious deviation of the
squared law has been found for a C 0.65 cargo liner, a more
systematic investigation into the merits of equation (3) for con-ditions which are of practical interest, is clearly necessary. In this respect it is mentioned that resistance increase
experi-ments are very sensitive for wall effects; the ratio of model
length to tank width in relation to speed should be considered
carefully [16].
The added resistance due to wind in adverse weather conditions should not be neglected. This is clearly denionstrated by Figure 6 taken from [6] in which the ratio of extra power due to waves and due to wind is plotted on a base of Beaufort number for a cargo ship. According to Tasaki [17] the ratio increase of power
due to waves to total increase due to weather is not much
aAWpg23/RAW
LA
C 5 10 0.5 410 F'15- o EXPERIMENT IN WAVE SPECTRLRI CALCULATION o o 0.5 1.0
- A/L
TAW tAW'2B3/L:j\
1.5Fig. 8. Mean increase of resistance, thrust, torque, revolutions and power in regular waves
proportional to the increase in resistance. They were also
approximately proportional to the squared wave amplitude at
constant ship speed and constant wave length as shown in Figure 8.
The experimental torque and r.p.m. response operators have - been used to predict the mean power and .mean r.p.m. in two
specified wave spectra, using a superposition similar to equation
(2). Direct propulsion experiments in these wave spectra have shown a very good agreement in a large speed range with the
EXPERIMENT IN STILL WATEff
NUMBERS NEAR SPOTS INDICATE NUMBER OF OBSERVATIONS ON WHICH AVERAGE IS BAS9.
1) SHIP SPEED FROM OBSERVED /
9 SERVICE DATA
/
148'
I,,
,
8.
(2)CALCULAS...INC REASE OF POW IN WAVES FOR SPEEDS s GIVEN BY CURVE (1) INCREASE IN HORSEPOWER (METRIC)
5000 4000 3000 2000 1000 1 2 3 4 5
SIGNIFICANT OR OBSERVED WAVE HEIGHT IN M.
Fig. 10. Comparison of calculated increase of power in waves wit h service peri onu unce data
predicted values using the superposition princip!e. see Figure
9. For the actual ship a prediction of the increase in power
correlated satisfactory with statistical full scale data. The ob-served wave height at sea was assumed to be equivalent to the average one-third highest waves of a Neuman spectrum
formu-lation and propulsion response operators obtained from the model tests were used in the superposition procedure. see Figure 10.
The behaviour of the propeller and the propelling machinery as well as the interaction between ship and propeller in a seaway
influence the propulsive efficiency. Particularly in extreme
con-ditions emergence of the propeller decreases the efficiency due to loss effective blade area, aeration and cavitation.
For the stationary case the influence of the propeller immersion on thrust and torque was studied amongst others by Gutsche [22]. Similar tests with oscillating propellers could be carried
out to analyse the non-stationary effects in extreme conditions.
Very little is known abotit the propeller efficiency in the time dependent wake of a pitching and heaving ship in moderate and severe sea conditions. A propulsion experiment in regular head waves with a C11 = 0.70 Series Sixty Model, has been reported
recently by Nakamura et al [I 31. Hull efficiency JII relative
rotative efficiency , propulsive efficiency , and propeller
efficiency in open water , were determined under the
assump-tion that the mean characteristics of the propeller in waves are identical with those in still water. The effective wake factor W.
the relative efficiency and the propeller efficiency of the
pitching, heaving and surging ship model were obtained from the resistance, thrust, torque, r.p.m. and mean speed of advance in waves using the open propeller characteristics in still water. Figure 11 shows that the selfpropulsion factors obtained in this
way vary considerably with the wave length ratio especially in a
region close to 2/L 1. 1.2- Fn.015 Fn.0.20 - Fn.025 1.1
----0.45 1,0 1,5 20 X/i 05 IN WAVES 1:0i
A/i.Fig. 11. Self-pro pulsion factors in regular head it'aves
18 I-o 17z 16
o-15o-I
h 12 11 11, IN SIlL!.. WATER 0.5 1.0 1.5 20 A/i. -59 o EXPERIMENT IN WAVE CALCULATION SPECTRUM 11/
I
EXPERIMENT IN STILL WATER
i_tlt
1-t
.-1_..----r__I,_.,
0.5 -1. It.1-W 5 075 10 1.25 V - rn/sec.Fig. 9. Comparison of neasured and calculated Increases of power
and rct'olnilons In Irrcg,thir waves Speclrwn I : Significant wave height - 2.7 n:
Spectrum Il: Significant wave heIght -4.1 n,
8. en W. - 38e jaargang no. 3 - 1971
0 05 1.0 15 A/L 1.25 10 rn/sec. 0.75 MODEISCALE 1:65 20 15 I0 b 20 15 2 t. 50 40
a-Fn. = 0.214Ship length 60 50 25
o
50 F- -z w 25 o 50 25 300 it <SHIP LENGTH < 350ft. 8.7h2 OBSERVATIONS CHANGE OF COURSE AND SPEED33 OBSERVATIONS
HH-nnHH
CHANGE OF COURSE 50 OBSERVATIONS SPEED RFDUCTIO 122 OBSERVATIONS0- - -
U)Z WZ OWZ ZLuO ZU) U) C Z W- - u
0 U) W WLiJ z Z023
I- F-U)4Z-
X -. L mu 4 4 X o 0 4 () 00. U)0+
0 Z U) Wo o z24
> w U)-
-ZU U)W o Fig. 12. Reasonsfor changing course and speedTABLE I Observations with change of course and/or speed reduction
Combined speed- Speed reduction Total
Speed reduction Change of course reduction + change and/or change number of
of course of course observations
50 25
¡o
I-z
w U w Q. O 50 25 CHANGE OF COURSF 50 87 OBSERVATIONS SPEED REDUCTION 338 OBSERVATIONS- -
- _ . .
W W 0W CflCZ W z zwz Zuo z
w wuj z Z OZ i.- I-U) Ç - u mu-0. 4
4 <Z o 1 0 4 X o,o
4 + w0U) 002
U) U) Wo 0. 0.0 OU) Q. 0...i U) oFig. 13. Reasons for changing course and speed
4
r',
z
o
number percentage number percentage number percentage number percentage
300'-350' 123 1.4 74 0.8 36 0.4 233 2.7 8742 Ea > 40W-450' uJ 343 2.6 147 1.1 100 0.8 590 4.5 13082 We 500'-550' 133 1.0 28 0.2 36 0.3 197 1.5 13433 Th < 600'-750' the ca
o
car To 30cv-350' 44 1.1 50 1.3 17 0.4 111 2.8 3925 pr -. 40W-450' 269 4.2 108 1.7 53 0.8 430 6.7 6353 3. X 50W-550'o
69 2.2 16 0.5 17 0.5 99 3.2 As 1er 3062 foi 600'-750' los chi ¡ncz
It 300'-350'o
32 4.7 2 0.3 3 0.4 37 5.5 674 raishi 400'-450'z
50W-550'z
18 16 0.6 0.6 8 3 0.2 0.1 9 0 0.3 0 35 19 1.1 0.7 T1 3174 sIa sh cxl 2868 be 600'-750 Va shi I H 1111+11+1!!
LOOft<SHIP LENGTH 4 50ft 13.082 OBSERVATIONS ÇHANGE OF COURSE AND SPEED93 OBSERVATIONS
S. en W. - 38e Jaargang no. 3 1971
TABLE Il Change of course and/or speed reduction on the North Atlantic
Speed reduction Change of course
The varying vertical flow component due to ship motions and the orbital velocities in the wave influence the conditions for
cavitation and aeration. In particular rather extreme phenomena can be expected when the propeller blades cut the watersurface.
To study these effects sophisticated experiments with oscillating propellers in a free surface water tunnel could be carried out. 3.3. Effects of ship motions
As stated before, slamming, deck wetness, racing of the propel-ler, large accelerations and motion amplitudes can be a reason for power reduction, which often results in considerable speed loss. Also a change of course is sometimes used to avoid syn-- chronism for one of the motiön components and this may
increase the travel distance.
It is important to note that in these cases the ship motions,
rather than the lack of power limit the sustained sea speed of a
ship.
The relative importance and the frequency of occurrence of
slamming, wetness and the other speed limiting phenomena is shown by statistical analysis of ship's log data. For this purpose extensive data have been collected from Dutch merchant ships
between 1959 and 1964 [4, 5]. A total of 60,000 visual obser-vations, each consisting of 35 items, was obtained from 243
ships. The statistical analysis gives an indication of the reasons
O
SHIP LENGTH >500 ft. 13.433 OBSERVATIONS CHANGE OF COURSE AND SPEED
36 OBSERVATIONS SPEED REDUCTION 50 129 OBSERVATIONS 25 O Wz (J O Q (J + z -J -J O W Jr Z Z WO O O (J-J-, W W > W (n n WW Z
-<ZH
Fig. 14. Reasons for changing course and speed
Combined speed reduction + change of course Speed reduction and/or change of course Total number of observations - SPEED, KNOTS
Fig. 15. Power 'ers. speeI of m.v. "Jordoens" in head and followi, g seas, medium loaded conditioll
for power reduction and their frequency of occurrence. Figures 12, 13, 14 and Tables 1, II and III give the results of the analy-sis. In most cases a combination of causes of speed reduction had been given and therefore the sum of the percentages in the
Figures 12, 13 and 14 exceeds lOO %.
The figures show that large pitching amplitudes with associated phenomena like wetness, slamming and danger to deckload are important factors for speed loss. Screw racing is most frequent for ship lengths between 400 ft and 450 ft, whereas rolling is an
important reason for change of course when L < 400 ft. For
L > 500 ft slamming and pitching combined with rolling is most
frequent as a cause of voluntary power reduction and change
of course.
Table I shows that speed reduction and change of course ic most frequent on the North Atlantic for ship lengths between 400 and 500 ft. On the Indian Ocean somewhat smaller ships
arc influenced by the seaway probably because of the smaller average wave length.
Table II shows the influence of prevailing winds on the North
Atlantic route: westbound ships do sail more in head seas than eastbound ships. Therefore speed reduction and/or change of
course has the highest frequency of occurrence on the
west-bound route.
The influence of the draught forward on the frequency of
course change and speed reduction is shown in Table III for
Victory ships.
As regards cargo ships as analysed by Aertssen 16] shipping of water in the fully loaded condition is the main reason for power reduction. The decision depends on personal insight and
expe-rience in handling the ship and therefore contains subjective
elements. Also teohnical reasons and absolute dimensions play
a role in this respect: the captain of a tanker or an ore carrier will accept a frequency of shipping water of IO to 12 per 100
oscillations, whereas on a general cargo ship he will restrict this number to5 or7[23].
In a medium loaded condition racing of the propeller and
wetness can be reasons for slowing down and in the ballast
condition racing is critical in a heavy seaway. In this case the
61
I
,.-,
pRhf9' - ' .' -4OQ " -. -- N°of 5t3m5 per 100 N° of Emergences of ter per loo OscILLOscittatioi),'' Propet-(. tions s. Stut. B..i.tt WIV& 44 M.te 5 5 7 7.3 3.5 5.3 12 o o in ii 17 1 iL 1' 16 17 11
number percentage number percentage number percentage number percentage
East bound 102 1.6 89 1.4 25 0.4 216 3.3 6540 West bound 277 4.1 85 1.2 62 0.9 424 6.2 6800
I
II 1111 + Il + Ill
CHANGE OF COURSE 18 OBSERVATIONSflH
nfl
50 25 o 50 z W 25 W Q-O 8000 a7000 6O00 5000 ¿000 3000 2000 100Draft
forward speed reduction change of course
(m)
TABLE Ill Change of cotrse and/or speed reduction of Victory ships
Head seas
chief engineer has to indicate when conditions are harmful for
the engine. The quality of the speed governor is said to have
influence on this decision.
Due to the large freeboard wetness is limited in the ballast
condition but slamming may be dangerous for the ship's struc-ture, because of whipping stresses and local hydrodynamic
im-pact forces. For other ship types the relative importance of
slamming, wetness and racing may be different.
An example of Aerssen's analysis of propulsive performance in waves is given in Figure 15. Iso weather curves for the relation: power-speed, as well as curves for constant number of slams and propeller emergence are given up to B7. In addition zones of spray and green water are indicated in the diagram and higher and lower limits of speed-power relations are suggested. The slams were defined by the magnitude of the whipping stresses. When these exceeded 60 kg/cm2 the corresponding hydrodyna-mic force produced a slam. According to Aertssen this limit is
valid for ships of 150 m. in length.
For large tankers and ore carriers a higher limit could be chosen. Another criterion may be the deceleration at the bow which nay reach a value of 0.5 g for a severe slam. A more direct criterion is the dynamic pressure on the bottom of the fore body which is
approximately I kg/cm2 for a slam. Theseare not limiting
values: in a heavy sea much higher values are found. Impact
pressures seldom exceed 5 kg/cm2 in the case-of cargo ships, but higher values were reported from destroyer trial
measure-ments [24].
Modern ships with longitudinal framing in the bottom suffer less
from bottom damage by slamming than older types with trans-verse framing. In some cases of fast cargo ships with the
com-nianding bridge aft, it appeared difficult to detect slamming and only after the journey considerable damage was observed [25]. Simple slam detection devices are considered necessary to warn the captain in time against slamming.
In Figure 1 5 a 25 % decrease of torque was used to define a critical threshold value for propeller emergence.
Below the lower limit of power the ship stays dry and there is no slamming. At the higher limit of power the ship may have 4
slams per 100 oscillations. As already mentioned, the diagram -depends strongly on the ship's dimensions and the sea route. Criteria for speed reduction depend only to a certain extent on
the personal view of captains.
Large pitch and roll amplitudes as well as large accelerations can be causes for speed reduction. In particular rolling may be a reason for course changing to avoid resonance conditions as shown for instance in the Figure 12. Large rolling motions do not
only occur at resonance, but also under certain conditions in longitudinal following waves. In such waves the restoring roll moment is a time dependent quantity and instable regions with large rolling angles may occur at wp/w = 4, 1, 14 ect, where,
w is the natural roll frequency and (O is the frequency of
encounter [26].
Large heel angles are also reported from fast slender cargo ships in following seas, when the frequency of wave encounter is very
small. When the wave length is approximately equal to the ship length the restoring moment on a wave crest can be very small due to reduction of the metacentric radius. In a wave trough an
increase of the restoring moment is observed.
Figure 16 shows the influence on the calculated restoring heel
moment, assuming static conditions.
u I-(n o X
4
number percentage number percentage number percentage number percentage
2.40-4.50 15 13.4 O O 2 1.8 17 15.2 112 4.50-6.00 33 6.4 0.2 lo 1.9 44 8.5 518 6.00-7.20 11 4.0 5 1.8 6 2.2 22 8.1 273 7.20-8.70 15 2.4 7 1.2 7 (.2 29 5.0 580 Bow seas 2.40-4.50 2 2.1 1.1 o o 3 3.2 95 4.50-600 12 2.3 8 1.5 0.8 24 4.6 519 6 00-7.20 2 0.7 9 3.2 0.4 12 4.3 281 7.20-8.70 6 1.4 8 1.9 5 1.2 19 4.4 431 Beam seas 2.40-4.50 O O O O O O O O 90 4.50-6.00 2 0.5 I 0.2 0 0 3 0.7 438 6 .00-7 .20 o 0 3 1.6 0 0 3 1.6 191 7. 20-8. 70 2 0.5 9 2.3 1 0.3 12 3.0 396 Quartering seas 2.40-4.50 2 2.4 o o o o 2 2.4 85 4.50-6.00 o o 2 0.6 o O 2 0.6 340 6.00-7.20 o O 2 0.7 o o 2 0.7 285 7.20-8.70 4 0.8 12 2,3 1 0.2 17 3.3 518 Following seas 2.40-4.50 1 2.7 0 O o o 1 2.7 37 4.50-6.00 o o 0.6 O O 1 0.6 164 6.00-7.20 o o i 0.8 O o 1 0.8 126 7.20-8. 70 6 2.3 3 1.2 5 1.9 14 5.4 259 62 14. I Il III I -.1-- li -f- Ill
combined speed speed reduction
reduction + and/or total number
change of course change of course of observations
4. Th sus m H del th the co ha Te an kn sp kn AI wa re H th As fo co ra bu rat mii pr Shi cw uni dis Fo tar Lu abi mi In ta of In nit in5 wa se th cf ex of ca M ab
160 80 4 n u I-In o X 4 O 80o 20 1.0 60 80
HEEL ANGLE degrees
Fig. 16. Restoring lice! ?nomc,It in a wave Static cotul ion
4. Influence of ship forni, ship dimensions and weight distribution on sustained sea speed.
The few examples given above indicate that an increase of
sListained sea speed is primarily a problem of reducing the ship motions rather than increasing the power.
Hull forni, weight distribution and ship dimensions can be determined with an eye on optimizing the seakeeping qualities of - the ship. A striking example is given by Aertssen who compared
the Victory ship Tervaete and the Lukuga, both in ballast condition. The Lukuga has a V shaped bow [23]. The ships
have approximately the same length and blockcoefficient. The Tervaetehas 8500 h.p. against 6500 h.p. for the Lukuga
and the corresponding still water speeds are I 7.5 knots and I 6.5
knots. In a Beaufort 7 head sea condition the Lukuga has a speed of 11.5 knots whereas the Tervaete slows down to 9 knots.
Also bulbous bows, which are benificial for the speed in still water, can be a cause of slamming and consequently speed
reduction results in some cases.
Hull form and weight distribution can be chosen in relation to
the expected sea conditions to avoid large motion amplitudes. As an extreme example, floating drilling platforms are designed
for very large natural periods of motion to avoid synchronous conditions at sea. Another more or less extreme example is a radically shaped destroyer hull form having a very outspoken
bulbous fore body as designed and tested by the Davidson Labo-ratory 127]. Although the considered hull form was designed for
minimum wave resistance in still water, the pitching motion
proved to be very small in comparison to conventional designs. Ship cross sections for minimum wave excitation have been
dis-cussed by Motora [28] and Bessho [29] and the behaviour of
unusual ship forms designed for 40 to 50 knots with 3000 tons displacement has been discussed by Uram and Numata in [30]. For non-radical ship forms the shape of the fore body is impor-tant as was shown for instance by the comparison of the
Lukuga and the Tervuete. V shaped fore bodies are
favour-able but extreme flare must be avoided, to prevent hydrodyna-mie impact forces.
In view of wetness also the ratio of freeboard to length is impor-tant; it should be chosen as a function of the expected shipment of water, as can be estimated f rm model tests or calculations.
In general ship length is a most important factor for the
mag-nitude of the ship motions in a seaway. This is shown for
instance by Table L Large motion amplitudes occur when the
wave excitation forces are large at rcsonañce conditions. In head
scis this is the case when VL> 0.75 anti the natural period of
l L.: : ::
p-
c ece. Ti
effect of ship length is demonstrated in Figure 17, where, as an example, the significant bow acceleration is given as a function of ship length and Froude number for head seas with a signifi-cant wave height of 3.1 meter [31].
Model experiments have shown that a small gyradius is favour-¡tule to reduce pitch motions [321. A decrease of the 'gyradius
II. en W. - 38e jaargang no. 3 - 1971
results in dryer decks forward but the vertical acceleration at the
bow is larger. For a 15,000 tons displacement ship in head
waves, Swaan [331 found that a high length-draught ratio results in smaller motion amplitudes. Increasing the length by reducing the blockcoefficient does not give an improvement. The length-beam ratio does not have a large effect.
5. l'redlction of sustained sea speed
As stated above the determination of sustained sea speed depends
for a large part on the prediction of the ship motions in a seaway and the associated phenomena like slamming, wetness and pro-peller racing. In this respect two subjects are important:
the determination of the ship motions and the conditions
leading to slamming etc.
the criteria with regard to the number of slams, the wetness and the racing of the propeller, which lead to power reduction.
Frequency response operators for ship motions due to waves may be obtained from strip theory calculations or from ship
model tests in regular or irregular waves. In many cases the cal-culation is sufficiently accurate for practical purposes regarding longitudinal waves. The superposition principle enables the cal-culation of the variance of the motions, velocities and
acceler-ations at any station along the length of the ship for specified wave spectra.
For most of the practical applications it may be assumed that the
motion amplitudes and the corresponding derived quantities. follow the Rayleigh distribution law.
For instance: the probability that the pitch amplitude (9,, exceeds a given value (9 is given by:
P E EI, f9,,.. ] = exp (_(9(,2/2Ili(,() (4) where m,,0 is the variance of the pitch angles.
The vertical relative displacement of any point of the deck sides, with respect to the water surface is an important quantity in the calculation of the probability of shipping water.
Assuming that the wave is not disturbed by the ship, the relative immersion of a station x in longitudinal waves is given by:
(5) where is the wave elevation, z is the heaving motion and (9 is
the pitching angle.
In defining the frequency response function of the immersion
s(x) the following notation is used:
0.8 o a' z O.6 C) u, 0.2 SIXTY SERIES CB .0.70 rn L.300m 260m 01 220m 0.2 t. .45 190m 0.3 63 - L =152.50m C =056 7WAVE TROUGH -GM =1.37m CALM WATER
4J\
[WAVE CREST MIDSHIPS-
2/'LI/2O
17. D ini el,sion!ess significant ho;' accelera lion
Fig. d n a o 4 e. n a ot in 11 th re of
iy
lip all ali el+
) = H2
exp i(E2+ wet) =
H5exp ioj5,t:k=kCOSUCI + e) = lu
exp ¡(Euz +w5J) - Hexp
costw,t + kx)
= exp
i(kx+
wit) =
Hexp
64 (6) kir' f 20 1: 3.5 KNOTS =7m f 855m (design) 1Om
PO.O5 FOR SHIIWING OREEN WATER AXINUM SPEED ITHOUT POWER REDUCTION 2 5
f
\\
12.5 PERCENTING OF WA1 ER AT STATION 20 - 18 I
I I
-4 5 6 7
OBSERVED OR SIGNIFICANT WAVE HEIGHT In m.
Fig. 19. Rough waler speed und probability of bow wetness
-Victory ship
reduced when this value was exceeded. The results show the importance of a large freeboard.
Figure 19 shows a correlation of bow wetness calculations and the actual sustained speed of a Victory ship [34]. In these cal-culations the average observed wave height corresponds to the
calculated mean of the one third highest waves and the observed wave period corresponds to the calculated mean period of a
PiersonMoskowitz wave spectrum formulation for
fully developed waves.Figure 19 shows that in very bad weather the ship slows down to 4.5 knots to arrive at a condition where water is shipped in about five out of hundred oscillations.
The prediction of slamming and related phenomena such as
whipping stresses and decelerations of motion should be based
on fundamental knowledge of the hydrodynamics of bodies
entering the free surface of a fluid.
However, at present only solutions for simplified cases are
available, for instance a flat plate falling on an undisturbed
water surface. In this case entrapped air and the compressibi-lity of air have to be included in the analysis to get agreement with the experimental values [36]. For blunt bodies the air
velocities at the entry of the water surface may be sufficiently subsonic to treat the air as imcompressjble [37]. For practical
purposes the general three dimensional problem of an arbi-trarily shaped forebody of a ship entering the wavy water surface as a result of heaving and pitching motions ina seaway
has not been solved.
Consequently an empirical approach is used for the prediction of the occurrence of slamming in a seaway. To this end the con-(litions leading to slamming have been studied by means of
model tests and full scale experiments. Slams have been detected, and more or less defined, by pressure measurements in the bottom of the ship or by the resulting whipping stresses and
deceleration peaks in the motion. The values of the pressures, stresses and decelerations defining a slam, depend on the size of the ship as has been mentioned already in chapter 3. The conditions leading to a slam can be restrictedto bow
emer-gence and a certain minimum value of the relative bow velocity at the re-entrance of the water. From various sources the mag-nitude of this threshold velocity has been evaluated by Ochiand a mean value of 3.5 m/s for a ship length of 150 meter has been obtained [381. The impact load will be thegreater the more
this threshold value is exceeded. The influence of ship speed on the threshold velocity has been studied with modeltests for one particular cargo ship form by Ferdinande [39]. He
con-cluded that the threshold velocity for slamming does not have a strict minimum value;
it has to be regarded as a rather
artificial concept. A similar study has been carried out by Tasai for a very full tanker in ballast condition [40].The experiments show that the minimum or threshold velocity decreases with increasing speed. Assuming that the conditions leading to slamming are known, the probability P of bow
emer-gence is given by the Rayleigh distribution: P[s, H] exp
(H2/2m)
where m,5 is Ihe variance of Ilse relative 1mw ciliergence.
where the subscripts "a" denote amplitudes.
Thus:
s
=
- H + kx Hr.j:)e:p ¿Wetor (7)
s ¿ H5exp 1w01 = H8 exp i(E
+ wt)
where H is the complex amplitude of the immersion s(x).
For a given wave spectrum S the variance of s(x) is given by:
OD
,n08(x)
=
J'
1H5(0,x) 12S(0)e)d(i)p (8)The probability P that the immersion exceeds the effective
free-board f0 is given by:
P [s
fe] = exp (fe2/
2m08) (9) In the vicinity of the ship the incident wave profile is affected by wave reflection and wave excitation of the oscillating ship. In particular at the bow these dynamic phenomena may increasethe immersion amplitude and empirical corrections can be
useful. In addition the form of the forebody of the ship above
the designed waterline has an important effect on wetness, which
is difficult to include in empirical corrections. Detailed investi-gations are necessary to find a reliable basis for the statistical
prediction of wetness in a seaway when extreme forebody shapes
are considered.
Formula 9 may be used to design sheerlines which have a
uniform probability of wetI1ss along the length of the ship in a given seaway. Such calculations have been carried out by van
Sluys [34J.
To estimate the speed loss due to wetnessonehas to accept the
criterion that power will be reduced when the probability of
shipping water exceeds a certain value. Such criteria should be based on practical experience at sea although they will contain subjective elements, because of the human factors involved in the problem.
For comparison of different ship designs a fixed number of wetness occurrences per hundred oscillations may by used.
Figure 18 shows the result of a calculation of the sustained sea
speed for a tanker [35]. The critical probability for shipping
green water was tanken as 5 % and power was assumed to be
10 20
WIIIOSPEED rn/sec.
u i i i i i
123
4 5 6 7 8BEAUFORT SCALE
Fig. 18. Calculateil sustained sea-speed of a tanker
(190.5 in X 27.2 in X 11.1 in) P = 0.05 for chipping green water
F a a C 1 t I f C
r
o.
Fig. 20. Probability of clamming in sea sIate 7; V = IO knots
Likewise the probability that the relative bow velocity s5 exceeds
the threshold value s is given by:
P[i5 ?
= exp
(_;.2/2fl10;)-where m05 is the variance of the relative bow, velocity.
Assuming that bow emergence and relative bow velocity arc statistically independent events, the joint probability gives the probability of a slam, thus:
P[slam] = exp(H2/ 2m08 + 2/ 2m0»
The frequency of occurrence follows from:
N = (m0/,r08)} exp(H2/2m,,5 + *2/2mo»
Figure 20 shows the probability of bow emergence, the prob-ability of exceeding the threshold value of the relative velocity and the probability of slamming as a function of the loading condition of the ship, as calculated by Ochi. From this figure
it is evident that there is a high probability of exceeding the
threshold value of the relative velocity in this particular case.
However, slamming only occurs if the scond condition is also fulfilled, therefore a muoh lower probability for the occurrence
of slamming results. 150 loo
i
o. WAVE HEETHT VO L 50-w e 'o-3Q.. 20-o g a (Lo HAASDAN 10 15CORRESPONDING SHIP SPEED KNOTS
Fig. 21. Torque fluctuation in regular waves
A reasonable correlation has been found between prediction and model test results in irregular waves. The maximum speed under these conditions can be defined as that speed at which the
probability of slamming has some prescribed value.
In this way a diagram similar to Figure 18 can be constructed for the determination of the sustained sea speed, when slam-ming is the limiting factor.
There are several uncertainties in such an analysis but the
procedure may be useful for design purposes when comparing
different designs.
Propeller racing is also an important reason to reduce power in
a seaway. The time dependent immersion of the propeller causes
a widely variable propeller loading. Although r.p.m. governors greatly reduce possible damage to the propelling machinery due to excessive turning rates large torque and thrust fluctuations
must be kept within bounds.
Figure 2! gives the torque variations at constant r.p.m. derived from model tests in regular waves [41].
Comparable full scale values have been found in a seaway during the Nissei Marit trials [42], as shown in Figure 22. For the
determination of sustained sea speed a limiting value of 25 %
of the torque variation has been adopted by Aertssen in the
analysis of full scale trials [6].
For a theoretical calculation of the maximum sea speed the
corresponding propeller emergence must be known. However
the relation between propeller emergence and torque decrease is
not available, for in this respect there is a lack of experimental
data.
The calculation of the propeller emergence from the ship's
motion and the waves must include the wave disturbance by the presence of the ship. Neglecting these effects Fukuda adopted 1/3 of the propeller diameter as a critical value of emergence for comparison purposes, assuming that racing occurs when the
propeller emergence exceeds this value [43].
The probability of propeller racing is found from a Rayleigh distribution, when the variance of the propeller emergence Is
known. The maximum ship speed in a seaway can be determined
when a criterion for the acceptable amount of propeller racing is adopted.
20
14 be based on full scale expeience with comparable ships, but it
must be kept in mind that they always contain subjective ele. ments due to human judgement of the behaviour of the ship.
65 6 5 2 (si. NISSEI MARU o SMOOTH SLIGHT A MODERATE RATHER + ROUGH xIIIGH + ROUGH + + + + X X X X + 4 X A X ++ .4+A £ A A 25 50 75 loo
LOADING CONDITION PERCENT
4 6 8 10 12
SHIP SPEED u-KNOTS
Fig. 22. Torque fluctuation of tile "Nissei Maru" at sea
S. en W. - 38e jaargang no. 3 - 1971
1.1 1.2 rn/SIC. 0.6 0.7 0.8 0.9 1.0 MOOELSPEED V -o o
Aerissen, G., Further sea trials on the Lubumbashi, TINA 1957.
Lewis, E. V. and Morrison M., Preliminary analysis of Moore -Mc Cormack log dala SNAME Btlletin, vol. 9, no. 3- 1954. Bonebakker, J. W., Analysis of model experiments, trials and
service performance data on a single screw tanker, Trans. N.E.C.
1954.
Wahab, R. and St jjnman, J. J., Observations made on board Dutch ships, Netherlands Ship Model Basin, Report
67-161-NO 1967.
Tan Setig Cje, Observations made on board of Dutch merchant ships mt. Shipbuilding Progress 1969.
.4er:sse,,, G., Service performance and seakeeping trials on m.v. Jordaens TINA 1966.
llar clock, T. H., Notes on the theory of heaving and pitching, TINA 1945.
Kreilner, J., Heave, pitch and resistance of ships in a seaway, TINA 1939.
Mamo, H., The excess resistance of a ship in rouh seas. Int.
Shipbuilding Progress 1957.
Moeyes, G., Snelheidsvermindering in zeegang. Student Thesis,
Department of Naval Architecture. University of Technology
Delft, 1968.
Sibul, O. J., Increase of ship resistance in waves. College of
En-gineering, University of California. Report NA-67-2-1967. Abkowitz, M. A., Vassilopoulos, L. A., Sellers, F. ¡1., Recent developments in seakeeping research and its application to
design. SNAME 1966.
Nakamura, S., Hosoda, R., Shintapia, A., Propulsive performance
of a Series Sixty C = 0.70 ship model in regular head waves.
Discussion to the Seakeeping Committee Report. 12th Interna-tional Towing Tank Conference 1969.
Nakainura, S. and S/,iniana, A., On ship motions and resistance increase of mathematical ship forms in regular waves. Journal of the Society of Naval Architects of Japan, 1965.
Gerriisma, J., Bosch, r. d. J. J., Beukelman, W., Propulsion in
regular and irregular waves. Int. Shipbuilding Progress 1961. Gerrits,na, J., Seaworthiness tests with three geometrical similar ship models. Proceedings Symposium on the behaviour of ships in a seaway. Wageningen 1957.
Tasaki, R., Discussion of the Seakeeping Committee Report.
12th International Towing Tank Conference.
Wagner, B., Windkräfte an Uberwasserschiffe. Jahrbuch Schiff-bautechnische Gesellschaft 1967.
Nomo fo, K., Directional Stability of Automatically steered ships with particular reference to their bad performance in rough sea. Tecnology reports of the Osaka University, vol. 10, no. 431, 1960. Nomoto, K. and Motorama, T., Loss of propulsion power caused
by yawing with particular reference to automatic steering. Jour-nal Society of Naval Architects of Japan 1966. BSRA
Trans-lation 2610.
Ogawa, A., The drifting force and moment on a ship in oblique
regular waves. mt. Shipbuilding Progress 1966.
NIEUWE UITGAVEN
Analyse, dee! 2 door drs. N. P. Zwikker en J. B. Ham. Uitgare W. Versluys NJ"., Am-sterdain-Anewerpen, 166 blz., 79 fIguren, prifs geb. f 25,-, a/in. 24,5 X ¡6 X 1,4 cm.
Het eerste dee! van dit leerboek over onder.
werpen van de hogere wiskunde werd be-sproken in Schip en Werf nr. 8 van 17 april
1970 blz. 163.
Voor dit tweede deel kan in hei algemeen worden verwezen naar hetgeen over deel i is vermeld. Het behandelt differentiaalver.
gelijkingen, onderwerpen uit de
differn-tiaalmeetkunde, functies van meer dan één veranderlijke machtreeksen, rekenen met
complexe getallen en Fourierreeksen. In een
slothoofdstuk worden enkele toepassingen gegeven.
Bu de meeste paragrafen is een aantal
vraagstukken gevoegd. Totaal zijn dit er 135, 66
References
waarvan de antwoorden achterin het bock
staan vermeld.
Prof. ir. J. H. Krietemeijer
Catalogua voor de scheepvaart
Van de Catalogus voor de Scheepvaart is
onlangs dc 3e editie verschenen.
Dit naslagwerk is voorzien van een index en registers, waardoor men snel kan zien welke firma of onderneming een bepaald
artikel, speciaal voor de scheepvaart en
scheepsbouwindustrie, kan leyeren.
Dit keurig verzorgde boekwerk is een uit-gave van Uitgeverij Mouton & Co. N.y. te
Den Haag.
ONTYANGEN KALENDERS
Van onderstaande firma's ontvingen wij kalenders:
Canadian Pacific Ships, Canada
Gutsche, F., Einfluss der Tauchung auf Schub und Wirkungsgrad von Schlffspropellern. Schlffbtttitcchnischen Herbstlagung 1967,
Rostock.
Aertssen, G., Discussion of the Seakeeping Committee Report. 12th International Towing Tank Conference 1969.
Bledsoc, M., ¡Jii,scc',,iaker, O., Cu,,,,njns, W., Seakeeping trials on three Dutch destroyers. Soc. of Naval Architects and Marine
Engineers 1960.
Goodrich, G. J., Private communication 1968.
Grigi:, O., Rolischwingungen, Stabilität und Sicherheit im
See-gang Schiffstechnik 1952.
Breslin, J. P. and Eng, K., Resistance and seakeeping
perfor-mance of new high speed destroyer designs. Davidson Labors-tory Report No. 1082, 1965.
Motora, S., On wave excitation free ship forms. Trans. Soc.
Naval Architects Japan, 1965.
Bessho, M., On the wave free distribution in the oscillation
problem of the ship. Trans. Soc. Naval Architects Japan, 1965.
Ura,ii, E. M. and Nun,ata, E., Behaviour of unusual shipforms.
Fifth Symposium on Naval Hydrodynamics 1966.
Moeyes, G., Student Thesis. Department of Naval Architecture. University of Technology Delft 1968.
Swaan, W. A . and R,jken, H., Speed loss at sea as a function of longitudinal weight distribution. Int. Shipbuilding Progress 1964.
Swan,,, W. A., The influence of principal dimensions on ship
behaviour in irregular waves. mt. Shipbuilding Progress 1961.
Sluys van, M. F., Vertical ship motions and deck wetness. SNAME 1969.
Tasaki, R., On shipment of water in head seas. 10th ITTC Lon-don 1963.
Verlzagen, J. H. G., The Impact of a flat plate on a water
sur-face. Journal of Ship Research 1967.
Greenberg, M. D., Prediction of ship slamming loads: on the
water impact of a circular cylinder. Therm. Advanced Research Inc. 1967.
Oc/ii, M. K., Prediction of occurrence and severity of ship
slam-ming at sea. Fifth Symposium on Naval Hydrodynamics ONR 1969.
Ferdinande, V., Analysis of slamming phenomena on a model of
a cargo ship in irregular waves. Laboratory of Naval
Architec-ture. University of Gent 1968.
Tasai, F., On the deck wetness and slamming of full ship forms.
Discussion of Seakeeping Report 12th International. Towing
Tank Conference 1969.
Gerriisma, J., Propulsive performance in waves. Stevens Institute
of Technology. 4th Bi-annual Seminar Ship behaviour at sea 1962.
Investigation intc the sea-going qualities of the single screw
cargo ship "Nissei Maru" bij actual and model ship experiments. Shipbuilding Research Association of Japan 1954.
Fukuda, J., Determination of fore and after draughts of ballasted buI kcarriers associated with the criteria of slamming and propel-ler racing. 11th International Towing Tank Conference 1966.
Electrostoom N.y., Rotterdam
Esso Nederland N.y., Rotterdam
Fag Nederland N.y., Rotterdam
Van der Giessen-De Noord N.y., Krimpen
a.d. IJssel
Goud, N.y. Technisch Bureau, Rotterdam Grenco N.y., 's-Hertogenbosch
Heemaf N.y., Hengelo O. Holland Repair Service N.y. KIM, Amsterdam
Kon. Nediloyd N.y., Rotterdam
Koninklijke Nederlandsche Stoomboot Mii
Phs. van Ommeren NV., Rotterdam N.y., Amsterdam
Radio-Holland N.y., Amsterdam Shell Tankers N.y., Rotterdam
Gebrüder Sulzer A.G., Amsterdam
Wilton-Fijenoord N.y., Schiedam AGENDA'S l-Iolec N:V., Hengelo O. j. Zónta 6 tubi 23 fe! AmaI 23 fe O ron 25 fe Rotte s tua Amai 23m Oron 24m Row 35m Amsi hut elzo
NI
PE.F A. y Op de I H as of S van op S N.y Van Met H. I sen Phs. In Huit Aaii d us 0m Ingo van Venu Ben Bij I thijt ling de Ir. bed leid Ext Ge scia P. Alb S. aREPORT No. 261
FEBRUARY 1970
LABORATORIUM VOOR
SCH EEPS.BOUWKUNDE
TECHNISCHE HOGESCHOOL DELFT
SHIP SPEED AT SEA
BY
PROF. IR. J. GERRITSMA
Report No. 261
LABORATORIUM VOOR
SCHEEPSBOUWKUNDE
TECHNISCHE HOGESCHOOL DELFT
february 1910
o
SHIP SPEED AT SEA
by
The Application of Ship Motion Research to Design
University of Southampton Ship Speed at Sea Prof.Ir. J. Gerritsma Introduction.
An important application of the theory of ship motions and propusive
performance. in waves is the prediction of sustained sea speed or speed
loss in a given seaway. During the last few years considerable progress has been made with regard to the calculation of seakeeping qualities of ships, both regarding motions and power requirements, but this knowledge is hardly used in the actual design procedure. From a hydro-mechanical point of view the hull form of a ship is based for the
greater part on still water performance, rather than on the ship behaviour
in a seaway.
It is true that the empirical ship design methods include knowledge óf the seakeeping qualities and this knowledge is actually used by the naval architect. However, the use of emperical knowledge may not lead to the best result in all cases and is certainly a risk when extrapolation is necessary to extreme hull dimensions and very high speeds. Furthermore a qüantitative or even a qualitative judgement based on analytical methods could be a powerful tool .for the. designer.
The present analytical knowledge of the seakeeping qualities of ships is
not complete, but in many cases âalculations based on theory and
funda-mental experiments may be used for the comparison of different designs with respect to their motions and the performance in waves.
In this paper some factors affecting ship speed at sea will be discussed
from a practical point of view and gaps in our present knowledge will be pointed out.
The speed loss due to weather.
On certain ship routes a considerable speed loss due to weather conditions can occur. It is known that ship length and ship speed which define more or tess the natural period of pitch, are important parameters in this respect. An illustrative example of speed loss as a function of Beaufort number and relative weather direction is shown in Figure 1. In this case
15% speed loss was found in a B6 head sea condition on the North Atlantic,
corresponding with an 80% power increase in comparison with the still water condition at the same ship speed. On this particular ship route B6 is exceeded in 15% of the time in summer and in o% of the time during winter.
The analysis has been based on carefully conducted full scale trials at
sea [i],, but also statistical data from logbooks have been used for
similar studies and have shown the same tendency [2 , 3 , 14 , 5J.
Figure 2 shows he speed loss of Victory ships in ballast and loaded
conditions on the saine route, as derived from logbook entries. Nearly 14000 observations were used to determine the curves in Figure 2.
Delft Shipbuilding Laboratory
-1-These figures stress the importance of speed loss in actual sea con-ditions. Especially in comparison with the usual shipmodel propulsion experiments in still water, where improvements in power of a few percent
r.e considered to be important, the speed loss and power increase in
a seaway look impressive, at least from a technical point of view.
It should be realised that the curves in Figure 1 and 2 are the averages
ofa large numbér of data points, which have a considerable scatter. This scatter is due to the fact that the Beaufort number is not adequate to describe the sea conditions in sufficient detail. This is a drawback for instance in ship routing procedures, where similar curves are used to determine an optimal track in predicted or reported wave conditions. In actual cases the speed loss may differ considerably from these
average values.
The importance of the speed loproblemfrom an economic point of view shduld be considered on the basis of overall operation costs. The treatment in this paper is restricted to technical considerations.
3. Summary of causes of speed loss at sea.
In light and moderate sea conditions the ship's speed is limited by the
available power, the increased resistance due to waves, the wind
res-is-tance and the decreased propulsive performance. The lower propulsive efficiency results from the higher propeller loading and the
non-stationary flow phenomena, due to the ship motions, which affect the hull-and propeller efficiency.
In more severe sea conditions thé motions of the ship can be a cause of
.deck wetness and danger of deck cargo, propeller racing and slamming.
These phenmena can force the captain and the mas.ter to reduce the ship's speèd to avoid danger to the ship and the engine. Such decisions are based on personal judgement and different risk factors will be
accepted by different captains. The human factors are difficult to deter-mine but a statistical analysis of full scale performance data as carried
oút by Aertssen [6]is most helpful in this respect.
In the following chapters the various causes for speed loss will be
considered in some detail. 3.1. Added resistance.
The steady component of the resistance of a ship moving in waves is larger than its still water value at the same forward speed. This is due to various factors, such as the disturbance of the incoming waves by reflection effects and by the generation of waves radiating from the
oscillating ship.
Havelock [î] suggested that the increased resistance in waves is mainly
due to the phase difference between the heaving- and pitching motions and the wave excitation forces. In particular for resonance conditions of the heaving and pitching motions, when large relative motions of the bow are observed, the added resistance is large as has been shown by model experiments and by observations at sea. It may be concluded that
these ship motions and the resistance increase are closely related. Kreitner [8] explained the added resistance by wave reflection effects
only, but Havelock showed that his estimation was in error. Maruo included reflection as one of the causes of increased resistance in a linearized theory [9]. He mentioned the difficulty that added wave
resistance is a higher order quantity, which is usually omitted in the linearized theory, but he suggested that careful examination of the terms which should be taken into account should lead to a solution for this
-2-According to Havelock the average value of' the longitudinal wave force,
resulting from integration of the wave pressure over the time dependent immersed volume of the ship, is a good estimate of the increased
resistance in a regular wave train. Assuming that the ship does not
influence the pressure distribution in the wave, it is foufld that:
RAw_(zFsinc
ap
+OMsinc
zF
ap
0M'
where k is the wave number, z and O are the heave and. pitch amplitudes,
F and M are the wave excitiflg for'e and moment amplitudes, s
F and s M
ae the
hase angles between motion and wave excitation forces OFigure 3 shows a comparison between the calculated added resistance and
the corresponding experimental values for a CB = 0.'0 Series Sixty Model [io].
The model experiments were carried out by Sibul [i
iJ.
Considering the rather crude assumptions on which formula (i) is based, the agreement is satisfactöry, except for the smallest wave length when the speed is well above the design speed of the ship. There the ship motions are negligible and the resistance increase is mainly due to
reflection which is not included in the calculation.
Abkowitz reported one experiment with a restrained model in a regular
wave train to measure reflection resistance [12). The experiment
con-firmed that this effect is small. Similar experiments are carried out
at Deift with a model of' a very fast container ship. Preliminary results confirm Abkowitzt results.
It is not surprising that for slender ships, such as destroyers and fast
cargoliners, a close agreement between formula (i) and the measured average wave resistance is found. This may not be the case for ships having large angles of entrance of the waterlines, such as coasters and large tankers. In agreement with these experimental data Maruo's theory
predicts a small reflection resistance.
A detailed experimental analysis of Maruo's theory was carried out by
- Nakainura et al 113] . .Figure 4 shows the measured and calculated added
resistance, again for the CB = 0.70 Series Sixty Model. The comparison with Sibul's experimental values indicates that the differences between
two sets of experiments are of the saine order as the differences between
calculation and experiment. In Figure 5 the calculated total resistance increase is compared with the part which is due to reflection according
to the formula: KAW = /PgC2(B2/L) = DHH 2 + + D r cose + D iJ sine
HPcoo
OzHPsoo
Oz+ D cose + D t sine + D ip cosc + D i sins + D
Hco
zHso
zPco
0Pso
Owhere C0
Z/C,
i = 0/kC
-3-(i)
The authors conclude that pitching is the main cause of resistance
.increase
in waves in the case of low speed but heaving has a larger effect for higher speeds. As indicated by the term D, the reflection
is small when compared with the total resistance increase. These
con-clusions fully agree with Maruo's analysis of a rather slender ship like mathematical shipform (L/B = S CB = 0.533) [9] , and with similar work by Nakainura en Shintana for three other mathematical forms [i1J
From (i) and (2) it follows that the resistance increase varies as the squared wave amplitude. Than the mean resistance increase in a given wave spectrum S is fourid from:
R (w.)
=2f AWe
(w)S (w)dw
AW 2 e C e e
o Ca
where We is the frequency of encounter. The increased resistance operator RAW
2
Cations according to formula (i).
(3)
can be obtained from model tests in regular waves or from
calcula-However, model tests do not confirm completely the validity of the squared wave amplitude theory. A detailed experimental analysis by Sibul showed
that the exponent of Ca may vary between 1,1 and 2,5 with a mean value of
about 1,8. A superposition according to equation (3), using experimental
resistance increase operators resulted in 20% to 30% less resistance than the directly measured resistanceincrease in the same wave spectrum [ii].
Although in [15] no -serious deviation of the squared law has been found
for a CB = 0.65 cargo liner, a more systematic investigation into the merits of equation (3) for conditions which are of practical interest, is
clearly necessary.
In this respectit is mentioned that resistance increase experiments are very sensitive for wall effects; the ratio of model 1enth to tank width
in relation to speed should be considered carefully [16J.
The added resistance due to wind in adverse weather. conditions should
snot
in which the ratio of extra power due to waves and due to wind is plottedbe neglected. This is clearly demonstrated by Figure 6 taken from-[6]
ori a base of Beaufort number for a cargo ship. According to Tasaki [ii] the ratio increase of power due to waves to total increase dueto weather is not much dependent on ship type and ship speed. Low wind resistance
superstructures must be effective to reduce the power increase in adverse
weather.
Added resistance due to wind can be estimated from windtunnel model tests. A recent addition to the literature on this subject was reported by
Wagner who gives the results for ten widely different ship types, ranging from a hydrofoilcraft to a large tanker [18]. It is of interest to note
that in many cases the highest wind resistance was found when the relative
wind direction was approximately 30 degrees off the bow.
Heading control inwaves can be another source of increased resistance because of rudder action and the corresponding yawing motion of the ship. Automatic pilots have the reputation to be reliable instruments but in
rough seas -the weather adjustment may set up a sustained yawing motion
According to Motora, as quoted by Nomoto [19] a resistance increase of
10 to 20% may be found in some cases. Also for large tankers a considerable
resistance increase due to low frequency yawing motions is reported by
Nomoto [20] . These ships have a relatively low yaw damping and frequently
a poorly damped yawing motion under automatic course keeping control is observed. The increased resistance is mainly due to the resistant component
of the centrifugal force caused by yawing. The forced oscillation methods, now available, enable the determination of the hydrodynaimic derivatives
of the ship in yawing and swaying motion. Also the wave forces and moments
can be determined with restrained models in waves. This information sITouid
be used to design the characteristics of the automatic control of ships
and analog studies could be made to optimize the auto pilot. This procedu-re
is used with success for the design.of depth control of submarines.
Experiments with supertanker models in oblique waves have shown relatively large leeway angles at small wave length ratios. These may be explained by wave reflection effects on the sides of the ship, which cause relatively large steady components of drifting forces and moments. The leeway angles
are a cause of increased resistance.
Ogawa calculated the reflection effect at various angles of incidence and
he found a good agreement between calculation and model experiment [21] 3.2. Propulsive efficiency in waves.
In Figure 7 the relation between the loss of propulsive efficiency and weather is given for a cargo ship in head waves on the North Atlantic [i]. The important decrease of the propulsive performance is caused by the resistance increase and by the non-ètationary effects which result from the seaway and the corresponding motions. The increased power requirement in waves can be estimated from the total resistance, including wave and wind effects. Also model propulsion experiments in more or less realistic
sea spectra could be carried out to determine the power - speed relation.
Extensive resistance and propulsion experiments with a model of the Holland - America Line's liner "Maasdam" (CB =
0.65)
have been carriedout at Delft. For the range of variables considered in the tests it was found that the mean increases of thrust,torque, revolutions and power were proportional to the increase in resistance. They were also approximately proportional to the squared wave amplitude at constant ship speed and constant wave length as shown in igure 8.
The experimental torque and r.p.m. response opérators have been used to predict the mean power and mean r.p.m. in two specified wave spectra, using
a superposition s'imilar to equation (2). Direct propulsion experiments
in these wave spectra have shown a very good agreement in a large speed range with the predicted values using the superposition principle, see
Figure 9. For the actual Ship a prediction of the increase in power
corre-lated satisfactory with statistical full scale data. The observed wave hight at sea was assumed to be equivalent to the average one-third highest waves of a Neuman spectrum formulation and propulsion response operators obtained from the model tests were used in the superposition
procedure, see Figure lo.
The behaviour of. the propeller and the propelling machinery as well as
the interaction between ship and propeller in a seaway influence the
propulsive efficiency. Particularly in extreme cond-itions rnergence of
the propeller decreases the efficiency due to loss of effective blade
aiea, aeration and Cavitation.
!["A Ptolemaic Vineyard-Lease", Eric G. Turner, "Bulletin of the John Rylands Library", vol. 31, 1948, no 1 : [recenzja]](data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==)