NEDERLANDS SCHEEPSSTUDIECENTRUM TNO
NETHERLANDS SHIP RESEARCH CENTRE TNOSHIPBUILDING DEPARTMENT LEEGHWATERSTRAAT 5, DELFT
*
EFFECT OF FORWARD DRAUGHT VARIATION ON
PERFORMANCE OF FULL SHIPS IN BALLASTED CONDITION
(DE INVLOED VAN DE DIEPGANG VOOR OP HET GEDRAG IN ZEEGANG
VAN VOLLE SCHEPEN IN DE BALLAST TOESTAND)
by
M. F. VAN SLUIJS
and
IR. C. FLOKSTRA
(Netherlands Ship Model Basin)
Toenemende aandacht voor het scheepsgedrag in zeegang en de vol te houden vaart bij de gemiddeld te verwachten zeeconditie voor lijnvrachtschepen valt waar te nemeo, hetgeen geprojecteerd tegen de grote belangen die verbonden zijn aan de handhaving van strikte tijdschema's b.v. voor containerschepen zeer begrijpe-lijk is. Voor een andere groep schepen, nl. tue van VLCC's en OBO carriers. ingepast in een bepaald vervoersschema, gelden deze zelfde belangen ook.
Is het in de lijnvaart gebruikelijk de beladen diepgang als maatstaf te nemen voor het gedrag in zeegang. voor de al ge-noemde klasse van zeer volle schepen voor bulklading is de vaart in ballast een conditie die èn veel voorkomt èn waarbij, anders dan bu de beladen diepgang, bepaalde voorzorgen
ge-nomen moeten worden. Te denken valt aan het vermijden van ongewenste verschijnselen zoals het doorslaan van de schroef, het uittreden van de boeg en bet eventueel slammen.
Daarom wordt, mede in verband ter verbetering van het koers-varen, op VLCC's en OBO schepen op de reizen van afleverings-plaats naar winafleverings-plaats een relatief grote hoeveelheid ballastwater ingenomen. Omdat de te behalen snelheid in stil water bij
nomi-naal vermogen cen functie is van de waterverplaatsing (tot de
macht 2/3), is het duidelijk dat een minimum hoeveelheid ballast tijdwinst kan opleveren. wanneer tenminste bet gedrag van het
schip in de op de vaarroute gemiddeld te verwachten zeegang
redelijk goed is en de kans op ongewenste verschijnselen zoals slamming acceptabel blijft.
Het onderhavige rapport gaat dieper op deze materie in, waarbij wordt aangetoond dat afgezien van slamming, alle
groot-heden die eco maat zijn voor het scheepsgedrag in golven er
gunstiger uitzien bu kleinere ballastdiepgangen vóór.
Zoals helaas te verwachten was, geldt dit niet voor slamming, maar wel blijkt voor het onderzochte scheepstype van deze
vol-heid en verhouding van hoofdafmetingen dat verder ballasten
dan een bepaalde diepgang vòòr geen of nauwelijks effect heeft
op de grootte van de optredende drukken, terwijl het gedrag van het schip voor wat betreft zijn bewegingen zelfs siechter
dreigt te worden.
NEDERLANDS SCFIEEPSSTUDJECENTRUM TNO
lt can be observed that a growing attention exists for the ship's behaviour in a seaway and the sustained speed in average sea-conditions to be expected for cargoliners. This is very
understand-able when thinking of the great interests connected with the maintaining of regularity of sailings. For VLCC's and OBO
carriers, scheduled in a fixed transport scheme the same state-ment is valid.
Unlike the lining trade where the loaded draught usually is
taken as determinative for the ship's behaviour in a seaway, for the types of vessels mentioned above having a high block coeffi-cient, the ballast condition is one which often occurs, and this gives rise to some problems which are specific for that condition;
for instance due attention has to be given to the avoidance of
propeller racing, bow emergence and possibly slamming.
To evade above mentioned phenomena and moreover to improve the course-keeping abilities for VLCC's and OBO
carriers a relatively considerable amount of ballast water is loaded for the return voyages from refinery to loading area. The speed in still water at nominal power being a function of the displace-ment (to the power 2/3), it is evident that a minimum amount of ballast saves time, provided that the behaviour of the ship when exposed to the average sea condition to be expected on the route is reasonably good and the chance of occurrence of unwanted phenomena like slamming is acceptable.
The underlying report gives more detailed information and
shows that apart from slamming, all data concerning the ship's behaviour in waves indicate that the light ballast conditions are the favourable ones.
Unfortunately as could be expected, this holds not true for
slamming; however, it appears that for the type of ships of this block and ratio of main dimensions, a further increase of draught
at the forward perpendicular above a well defined minimum
value has little or no effect on the magnitude of pressure values, while the behaviour of the ship from the point of view of motions becomes even worse.
CONTENTS
page
Summary 7
¡ Introduction 7
2 Hull form and experimental specifications 9
3 Analyses of experimental results 10
4 Theory for predicting ship motions and pressure fluctuations 12
5 Discussion of results 14
6 Conclusions 17
References I 7
A00 Added mass coefficients
a0 Amplitude of vertical acceleration
a0113 Significant amplitude of vertical acceleration
a2 Sectional added mass coefficient a2 + Transformation coefficient
B Breadth
Bi.. Damping coefficients
b Sectional breadth
Sectional damping coefficient C C00 Restoring force coefficients
D Propeller diameter
Fn Froude number = V/gL
F. Complex amplitude of the exciting heave force g Gravitational acceleration
Polar moment of inertia
k Wave number
L Length between perpendiculars Aft waterline length
Forward waterline length
M Mass of ship
M Complex amplitude of the exciting pitch moment
m0 Area under relative motion spectrum Naw Increase of revolutions in regular waves
P Slamming pressure
Pa Low frequency pressure amplitude
F0113 Significant low frequency pressure amplitude
p Pressure
Q0 Mean torque increase in regular waves R0 Mean increase of resistance in regular waves
St(W) Wave spectral density
Amplitude of relative motion
sao Amplitude of relative motion aft at the stern sa, Amplitude of relative motion forward at the bow Sau3 Significant amplitude of relative motion
T Mean wave period
TA Draught aft
TE Eliective draught
TF Draught forward
TM Mean draught
T0 Natural heave period
Mean thrust increase in regular waves
T0 Natural pitch period
t Time
V Forward ship speed
Vr Complex amplitude of relative velocity
Real part of Vr
(x,y,z) Co-ordinate system
z I-leave motion
z0 I-leave amplitude
z0113 Significant heave amplitude
7 Real part of z,
ZXa Complex amplitude of absolute sectional motion
V Displacement volume
Heave-wave phase Pitch-wave phase Wave amplitude Wave height = 2a w1/3 Significant wave height
/t Wave length
o Pitch motion
Oa Pitch amplitude
1/3 Significant pitch amplitude
Potential function
PH Complex heave potential function
Imaginary part of ÇOg
Ç3Hr Real part of con
cow Wave potential function
W Wave frequency, circular
We Frequency of wave encounter, circular
o Mass density of water
EFFECT OF FORWARD DRAUGHT VARIATION ON
PERFORMANCE OF FULL SHIPS IN BALLASTED CONDITION
by
M. F. VAN SLUIJS and IR. C. FLOKSTRA
Summary
To investigate the effect of the draught forward on the performance in head seas of a cylindrical bow ship of 0.825 block coefficient, model tests were conducted for three ballast load conditions.
The draught forward was varied while the draught aft was kept constant.
For each condition, ship motions, stem and bottom pressures, and the propulsive quantities were established.
All measured data are correlated with theories; inì particular cases the merits of different theoretical approaches are discussed. The influence of several parameters on the choice of a forward ballast draught was considered.
i
IntroductionIn contrast to dry cargo liners and tramp ships, which
radically adjust their itinerary to suit the available
cargo, oil tankers and bulk carriers operate on regular service from which they do not depart under normal circumstances. Consequently, much attention is given to the regularity of the sailings and the maintaining of schedules.
For general purpose dry cargo ships many different
conditions of loading can be discerned; for tankers
and bulk carriers usually two loading conditions are
representative; fully loaded on their voyages from
winning spot to refinery or manufactory and ballasted in the opposite direction. Apart from their design con-dition the permissible draught for the loading condi-tion is primarily determined by the waterdepth of the approach route to the berth where the cargo has to be discharged or by the shallowness at the loading site. With respect to the ballast condition, no conclusive criteria or rules and regulations as regards draught to be selected are available. In average practice the vessels are provided with ballast tanks of sufficient capacity in such a way that a draught aft can be realized, which ensures an adequate immersion of the propeller.
The draught forward is adjusted sufficiently deep
to evade structural damage of the forward bottom, because of pressure impacts induced by excessive
motions in rough seas. These impacts are particularly of importance when the ship is trying to keep up its speed in heavy weather.
It is only a relatively short time since attention was focussed on this phenomenon. lt was not mentioned in technical literature until the 1920's, but since then reports on damage to bottom plating, caused by hydro-dynamic impacts, or synonymously by slamming, have been published in an increasing degree, see for instance
[1], [2] and [3]. An analysis of these bottom damages suggests that local loads and pressures of the order of magnitude of 7 kg/cm2, or equivalent to 100 psi, must have acted to account for the deformations [4].
Akita and Ochi [5], [6] conducted model experiments in waves on the influence of draught and trim of a ship with respect to pressure peaks on the keel at a distance
of 0.05 L from the fore perpendicular. From their
results it can be derived that, in case of head waves with lengths equal to the length of the ship, slamming takes place when
/L> TF/Lw/sa = 1/60, where = wave height
L = ship length TF = draught forward
= relative motion amplitude.
Moreover, they suggested that maximum pressures occur at shallow draught for high vessel speeds and at a deeper draught for low speeds. Trim by the stern
was always found to result
into higher pressureimpulses.
In 1967 Fukuda et al. [7] conducted theoretical
calculations for determining the draughts fore and aft of ballasted bulk carriers in rough seas with considera-tion of the criteria of slamming and propeller racing.
In their work, only the criterion of relative motion
has been handled, in combination with Ochi's relative velocity concept [8]. As demonstrated by Tasai [9]
significant discrepancies can originate when this procedure is followed, particularly when it is applied to full ships.
In view of these considerations a series of model tests was conducted in order to arrive at experimental information and data to assess a ballasted condition
8
power, yields the fastest sustained sea speed regarding the following aspects
Bottom and propeller emergence, thus bow and stern elevation relative to the waves
Low frequency and impact bottom pressures Low and high frequency stem pressures Ship motions and vertical accelerations increase ofpowering characteristics.
Io that purpose, a ship model of 0.825 block
coeffi-cient fitted with a cylindrical bow, was investigated, following the earlier investigations of various aspects of this ship type. [10], [II].
Head sea conditions were considered only in the ex-periments, since in this wave heading loss of speed, particularly voluntary speed reduction and slamming phenomena [12] are deemed to be most substantial. The effect of wave length and height, regularity as well as irregularity of the sea, upon performance was studied for three different ballast draughts forward,
while keeping the draught aft constant. In addition
Fig. 2. Profile and body plan of the model.
Table A: Model and ship specifications
to the relevant experimental data, a theoretical corce-lation with the occurring phenomena is also discussed
in this report. An example of how bow emergence
takes place is given in figure 1, showing a sequence of
attitudes of the model when proceeding in regular
waves.
2 Hull form and experimental specifications
As already mentioned for the experiments an already existing model, with a large block coefficient was used with adequate dimensions in order to meet the capacity of the Seakeeping Laboratory.
To give an idea of the vessel this model can be
thought representative for a ship of which the main dimensions and dynamic properties of both are listed in table A; for this example the model scale becomes 1:60. The lines and profile are shown in figure 2.
Three ballast conditions were studied,
a. A condition with a forward draught ratio TF/L = 0.0235, hereinafter designated Draught 1, having a
P5. STATION 19 P6-STATION 16 p7-STATION 17 P8 - STATION 16 15 14-10 R
Denomination symbol unit
Draught I Draught Il Draught 111
model ship model ship model ship
Length between perpendiculars L rn 4.0445 242.67 4.0445 242.67 4.0445 242.67
Breadth B m 0.6222 37.33 0.6222 37.33 0.6222 37.33
Draught fore TF m 0.0946 5.68 0.0630 3.78 0.03 15 1.89
Draught aft TA m 0.1523 9.14 0.1523 9.14 0.1523 9.14
Mean draught TM m 0.1235 7.41 0.1077 6.46 0.0919 5.515
Displacement volume V m3 0.2368 52,425 0.2026 44,861 0.1697 37,569
Centre of buoyancy aft of section 10 . m 0.0012 0.72 0.1056 6.34 0.2283 13.7
Centre of gravity above base m 0.1750 10.50 0.1615 9.69 0.1470 8.82
Metacentric height m 0.1392 8.35 0.1833 11.00 0.2483 14.90
Longitudinal gyradius 23.5 23.5 22.5 22.5 22.0 22.0
Natural heave period T sec 1.12 8.7 1.03 8.0 1.02 7.9
lo
displacement of 50 per cent. of the full load design condition.
A condition with a forward draught ratio TF/L = 0.0155, designated Draught IT, having a ment of about 40 per cent. of the full load
displace-ment.
A condition with a forward draught ratio TF/L = 0.0078, designated Draught III, having a displace-ment of 35 per cent. of the full load displacedisplace-ment.
The draught aft was kept constant at a draught to
ship length ratio TAIL = 0.0377, which can be assumed to be a usual value for normal ballasted oil tankers or bulk carriers.
The model was driven by a propeller, of which the main characteristics are given in table B, maintaining RPM constant at model self-propulsion point during each run in waves. In those cases no friction correction for model-ship resistance scale effect was applied this in accordance with the recommendations of the Inter-national Towing Tank Conference 1960.
Tabel B: Propeller model specifications
Prior to the tests, the model was dynamically balanced so as to meet the data as stated in table A.
All tests were conducted within a speed range of
0. 12 <V/-.JgL <0.17 with the model free in its
move-ments. Throughout the experiments the following
quantities were simultaneously recorded
Pitch angles, determined by a gyroscope equipped with a wire resistance potentiometer
Heave, at the model centre of gravity, sensed by a vertical push rod driving a potentiometer
Surge, measured by the horizontal excursion of the subcarriage for phase assessment
Vertical acceleration at f.p.,
obtained by a 2-g
Statham accelerometer
Relative motions forward and aft, along the stem and stern respectively, sensed by resistance-type probes to measure water elevation relative to the model
Bow and bottom pressures at 8 locations (locations P1 through .P8 are indicated in figure 2) measured
by Bytrex pressure transducers
Thrust and torque, measured by a strain gauge
fitted transmission dynamometer
RPM, measured by a slotted disk with photo-cell pick-up
- Model speed obtained by a tacho-generator
- Waves, sensed by a resistance-type probe located
approximately one model length ahead of the model.
The experimental programme consisted of self-propul-sion tests in waves approaching from ahead. All three ballast conditions were investigated, at various forward speeds, in regular waves with lengths varying between
AIL 0.4 and 1.5 and heights of WIL lISO, 1170 and 1 / 100 respectively.
In order to check linearity and superposition, the condition with a forward draught ratio of 0.0155 was, moreover, tested in a long-crested irregular sea,
corresponding to Beaufort 8
force on the North
Atlantic.3 Analyses of experimental results
As most of the dynamic quantities, measured in regular head waves, were dependent upon the same parameters,
i.e. forward ship speed, wave length and height, a
standard form of presentation was used for the presen-tation of ship motion characteristics.
The customary ship motions, pitch, heave, vertical
accelerations and relative motions, are shown in a
dimensionless form on base of the wave length - ship length ratio AIL. Pitch has been non-d imensionalized through dividing its amplitude by the wave slope am-plitude ka, whereas vertical accelerations are made dimensionless, the multiplication of the squared wave circular frequency and wave amplitude being used.
Heave and relative motion amplitudes are given,
divided by the wave amplitude.
Pitch and heave phase angles are defined as the lag of the wave at the centre of gravity of the model with respect to the motion amplitudes
propeller
Denomination symbol unit No. 4202
t to t ti - TIME t
Pressures, measured at the stem and at the forward
bottom in the vertical plane through the ship's
centre-line, can be split up into a high and low frequency
component and a mean value.
Propeller diameter D mm 133.3
Pitch ratio PUTRID
-
0.664Expanded blade area ratio
-
0.564Number of blades
z
-
4The low and high frequency components are reduced
into a dimensionkss number by dividing pre5sure
amplitudes by the product of specific mass density of water, gravitational acceleration and wave amplitude. Several types of pressure recordings were obtained depending on test conditions and whether emergence
and slamming occurred
Sinusoidal type, when the pick-up was continuously immersed, and no impact phenomena took place.
ZERO ATMOSPHERIC PRESSURE MEAN PRESSURE INCREASE DUE TO SPEED --ZERO ATMOSPHERIC PRESSURE IMPACT PRESSURE P PERIOD OF WAVE ENCOUNTER PRESSURE AMPLITUDE PR. PERIOD OF WAVE ENCOUNTER TIME t
The zero level stands for the sum of atmospheric pressure plus head of water at the location under consideration for zero forward speed in calm water.
Triangular type when impact pressures occur, in case the pressure pick-up emerged, at the moment of re-entrance into the water.
-Jii:j
- TIME t
Truncated sinusoidal
type for
stern pressures,when the pressure pick-up is located above the
calm water line for the model under speed. During one pitch down the pressure pick-up is only tem-porarily activated. No slamming.
PRESSURE AMPLITUDE PR ATMOSPHERIC PRESSURE -,.RIOQOF WAVE E NC OU N rE R - TIME t
Truncated sinusoidal type for stem and bottom
pressures, when pressure pick-up becomes sub-merged for the model under speed in calm water and emerges in waves whereas no impact pressures are experienced.
The zero level represents the sum of atmospheric pressure and the head of water for the static model in calm water.
Thrust, torque and RPM values in calm water were assessed from self-propelled tests including the model friction correction. The average increases of thrust, torque and RPM due to waves are defined here as the average value of the increase above the calm water value at equivalent speeds, when in both conditions no friction correction is applied.
These powering increase quantities have been non-dimensionalized by dividing their increased values by the squared wave amplitude in combination with the ship and propeller parameters
Mean increase of revolutions
NawD3LV gB2
Mean increase of thrust = T0L
QgB2
Mean increase of torque = QawL
QgB2D
All information derived from the regular wave tests is tabulated in table i through Ill (see appendix). For
a forward speed corresponding to Froude number
En = 0.145 the dimensionless quantities are also shown in the figures 5 through 22 (see also appendix).
In addition to the three series of regular wave tests, ballast condition II, with a forward draught to ship length ratio of 0.0155, was model tested over a speed range between 0.12 <vgL < 0. 17 in a long-crested irregular head sea. This information was transformed into data that apply to the full size vessel.
In the presentation of the results, the sea condition is indicated by the Beaufort number, which actually indicates wind speed. Since there is no direct relation
between wind speed and the state of the sea, this
presentation is consequently not completely correct. However, the procedure is often adopted since it is
easier to estimate wind speed than to describe the
state of the sea. As to the relation between wind and waves the data of Roll [13] were used, which are based
upon observations made on board North Atlantic
weatherships.
For present purposes a wind force Beaufort 8 sea
was considered, having an average observed wave
height of 4.85 metres and an average observed period
OOOF WAVE C
s(w) = 4.e_B1w4,
which depicts, apart from the A and B values, a
theoretical spectrum shape similar to the
Pierson-Moskowitz formulation for fully developed seas [14].
o o
Js(w)dw
T =27r°
$wso).dw
Then the coefficients A and B are related to significant wave height and mean period following
A = 172.8 113D
B = 691
The spectrum as formulated above is illustrated in
figure 4 in comparison with the one produced in the basin. u 20 u u o 10 u o 4 E 3 2 0 w in rad. sec' Fig. 4. Beaufort 8 wave spectrum.
The distribution of the instantaneous wave elevations is also shown, which is in good agreement with the normal Gaussian probability law according to which, following various oceanographers, also the actual sea elevations are distributed.
4 Theory for predicting ship motions and pressure
fluctuations
The ship motions are predicted by the use of an ordinary strip method, as described by Korvin-Kroukovsky and Jacobs [16], Gerritsma and Beukelman [17], Fukuda [18] and others. With strip theory only forces
perpen-BEAUFORT L5113 in rs In SeE. 3 1.40 5.9 4 170 61 5 2.15 6.5 6 2.90 7.2 7 375 7.8 8 485 84 9 620 90 10 7,45 95 1? 8,40 100 [o WAVE ELEVATION O .119n, MAX.. 4.86111 MAX - . 478m / -/ ' WAVE SPECTRUM
ki_
12of 8.4 seconds. The character of this sea condition is Observed wave period = further embodied by its power spectrum
05 10 15
w In ra, sec1 Fig. 3. Pierson-Moskowitz wave spectra.
When the wave energy spectrum is related to actual observations at sea, it is generally assumed that the average observed wave height equals the calculated
mean of the highest one-third of the waves w1/3
(=
significant wave height) and that the observedperiod conforms to the calculated mean period Tof
the waves. Following the recommendations of the
International Ship Structures Congress [15] the mean
wave period is based upon the first moment of the
power spectrum.
For a narrow-banded spectrum it follows that, Observed wave height =
w1/3 = (w)dw o 5.0 -50 TROUGH CREST 1.5 05 10 125 100 75 5.0 E 3 25
dicular to the longitudinal axis of the body can be
obtained, thus the force in surge direction being ne-glected. This neglect is insignificant, since actually the influence of surge on heave and pitch is small.
For the case of head waves, the equations of motions become
(M +A)ï+ B±+C2zA0Ö---B0f? CO =
= Re(F..e"»)
- A0± - B0.± - C0z + (Iry + A00)Ö + B00Ò + C006 =
= Re(Me1t)
whereB = $bdx
= Qgbdx
A0 = $axdx +B
B = JbxdxVA
tuC = C0. = g
bx dx= J ax dx
B0 = J bx dx + VA. A00 = azzx2dx + B00 = Jbx2dx C0() = QgJbx2dxIf the incoming wave is represented by
Re{oe]. the exciting forces and moments
can be written as
= Qgas
be_t*_tdx+wa$(wea::+
+ ibzz)e_«t*_tdx
= - gJ xbe
t*_ix)dX_WaJ [wxa +
+ i(xb. + Va)] ek((*_ix)dx
in which
M = mass of the ship
ry = polar mass moment of inertia
b = local breadth
t = cross sectional area divided by the local breadth a. = added mass coefficient
= damping coefficient z, O = heave and pitch motions.
The two-dimensional added mass and damping coeffi-cients can be obtained from a close fit method [19].
The pressure distribution in an ideal fluid can be
expressed by the Bernoulli equation in terms of the velocity potential
Determining the function ço in the vicinity of a freely floating body is a problem, already known from the ship motion theory. Some of the results obtained by that theory will be used for present purposes.
The first step in ship motion calculations using strip theory is the reduction of the three-dimensional prob-lem for the whole body to a two-dimensional probprob-lem for every individual cross-section. The two-dimensional problem consists of determining the fluid motion due
to a forced simple harmonic motion of the
cross-section.
in case of a forced heave motion = Re(eio)o), this
solution can be expressed as
= Re(pHe1°') (2)
Several ship motion calculation methods have been
developed by more or
less significantly different approaches. These theories make common use of the function H' while the final expression of the forces and moments acting on the body are different because of a non-unique application of formula (I). Thus to eachmethod a pressure formula corresponds, of which
three will be discussed briefly.
From the potential function (2) the two-dimensional added mass and damping coefficients are derived. The force dF/dx, acting on a part dx of the body,can be expressed in these coefficients when use is made of the relative motion hypothesis. In the ordinary strip methods, the following expression is employed
=
-
(
-
v)
(3)where
= 5adx
14
= Re[icoe(:_xO + VO aw e_kt*+ikx eit =
iWe 0e
= Re(vreit)
When the same functional relation is maintained, the ordinary strip method pressure formula results
/
\[VQff.
i
Ji = - (jWe V_,)[
We + (Pwj - YPHr+ Qgzx (4)
In case of oblique waves, also contributions of the forced sway and roll potentials must be taken into
account.
In modern ship motion calculation methods, the
forces and moments are obtained from a direct applica-tion of formula (1), after having neglected the double frequency terms. Then the pressure formula becomes/
'5\[vpH
i
+cwJ+OZxa
(5)where the functions ço, and P are expressed in a co-ordinate system, which moves with the body.
Both approximative formulas (4) and (5) of the
pressure are not satisfactory from a theoretical point of view. The potential p, has been derived, accounting only for the frequency of encounter as a forward speed effect, while the pressure functions (4) and (5) also contain other speed effects. In fact, the pressure should be chosen according to the two-dimensional case, as done by Vossers in his strip method [20]. This results into
p = - iQwcpv - iQW(p + (6)
The formulas (4), (5) and (6), describing the pressure distribution in the vicinity of a heaving and pitching body, have the same limitations as the ship motion equations. The results will, however, be more sensitive to these restrictions because of a lacking of smoothing effects. In particular, three-dimensional effects will cause large discrepancies between measured and
calculated pressures at the bow and stern of the body.
At the bow of the ship the results of foregoing
pressure formulas will most probably be incorrect. A
real three-dimensional solution of p will then be
necessary, a solution which is, however, not within easy reach in a manageable expression to date.
A case of a two-dimensional bow has been studied by Dagan and Tulin [21]. The dimensions of the bow of the ship, at present considered, allow the application
of a simplified calculation method. In this case, the pressure distribution in the vicinity of the free surface can be approximated by the static pressure distribu-tion, as known from the small wave theory
p = Qg(z()
(7)where
= the instantaneous wave elevation above the con-sidered location.
The harmonic part of this pressure is
p = QgS
where Sa = local relative motion.
Increase of resistance in waves can be calculated in many different ways. The measured resistance increase will be compared with the methods of Gerritsma [22], Havelock [23], Joosen [24] and Maruo [25], in order to establish the most accurate method applicable for this type of ship.
5 Discussion of results
All results from the experiments in regular waves are given in the tables I through. III (see appendix). For a forward speed corresponding to Fn = 0.145 measured and theoretical data are moreover shown in the figures 5 through 24 on base of the wave length ratio.
Motion, pressure and powering response curves
exhibit the usual tendencies; highest values originate when synchronism occurs in waves having a length which is nearly equal to the length of the ship.
Pitch and heave amplitudes are hardly affected by the three conditions of loading considered; generally it can be stated that amplitudes of relative motions, accelerations,
and thrust, torque and revolutions
increase, decrease considerably when the draught for-ward becomes shallower. This particularly holds true when the ship proceeds in waves longer than itself.Amplitudes of the pressures at the stem, also decrease considerably when the draught forward is decreased, except for the pressure P4 at the transition between stem and bottom where the difference in pressure between
draught Il and III is rather small. At this location
slamming can be scarcely expected as follows from figure l8c, whereas the magnitude is practically inde-pendent of the various forward draughts over the con-sidered wave length range.
Low frequency bottom pressures are generally
cannot be deemed conclusive since slamming pressures are largest for this condition. Bottom slamming
pres-sures are almost equal for ballast draught I and II
when he locations at station 18 and 19 are considered. Highest slamming pressures occur at station 19 for
the smallest draught forward; they diminish with
increasing draught in such a way that slamming will
no longer take place at station 16. Waves having a length equal to or a little shorter than the length of the ship seem to be most severe for slamming; the
peak in the slamming pressure response will shift to shorter waves when the draught forward is decreased. The position of maximum pressure on the bottom
shifts toward midships with increasing ship speed,
which also has been found by Ochi [8] for a Mariner
ship.
The results of the investigation into linearity of the ship performance and pressure quantities with wave height, conducted for ballast condition II are given in table lib. The ship motions vary linearly with wave
height, whereas the propulsion quantities are
pro-portional to the wave height squared. Low frequency pressures also vary reasonably linearly with wave height, with the exception of the pressures at positions near the free surface.
The relation between higher frequency pressure
(slamming) and wave height is apparently somewhat random; it is thought that slamming pressure at the various locations at the ship forward bottom are to a large extent affected by the observed bore, produced
by the ship's bottom at the moment of re-entrance
into the wave surface. Therefore it is felt that, for the ship form considered in this experiment, the validity of the relation that slamming pressures are propor-tional to the squared relative velocity between ship and waves, see Ochi [8], is doubtful.
This was, moreover, confirmed by additional experi-ments during which a pair of electrodes was put in the vicinity of the pressure cells in the bottom to enable the assessment of the local relative velocities between model and waves at the moment slamming phenomena were recorded.
The theoretical correlation of the model data shows that minor differences exist between calculated and measured pitch response for large wave length ratios. Since heave response correlates fairly well, it may indicate that pitch discrepancies are caused by end
effects originating from three-dimensional effects at the cylindrical bow and from the small motion
ampli-tude assumption in theory. This latter reason
is illustrated in table lib, where the influence of the wave height on the measured quantities is given. The deviation in pitch response will, as a matter offact, also be noticeable in the vertical acceleration
response forward.
As can be expected, the theoretical calculation of the relative motions according to the usual method will yield inaccurate results, since the relative motion of a certain location of the ship is determined with respect
to the undisturbed incoming wave. This procedure
leads to reasonable results in case of sharply pointed bodies. For blunt bodies, such as a cylindrical bow ship, the incoming wave is disturbed appreciably and consequently the calculated relative motions deviate strongly from those measured.
The low frequency part of the bottom pressures at
stations 19, 18, 17 and 16 has been calculated according to formulas (4), (5) and (6) from section 4. The com-mon function has thereto been expanded in a series consisting of a source function and higher order sin-gularities with coefficients, being numerically
deter-minable, following a generalisation of the method
introduced by Ursell [26]. The quantity wqI/g equals
the ratio between the dynamic and static pressure
amplitudes.
lt is shown in figure 23 for ballast draught I for the cross-section at station 18, and also for the
corre-sponding double body problem
w
w2/
b-
lI1I =I----
- ¡XI +
¿=0
where a2 + are the coefficients of the conformal trans-formation and t is the sectional draught. The difference
between the curves indicates the effect of the free
surface.
For the bottoni pressure at station 18 a comparison has been made between the model data and the results of the three pressure formulas. The results (4) and (5)
are approximately equivalent, while the data from formula (6) deviate from the measured values, in
particular at high frequencies.
Since for this type of ship, the ordinary strip method formula yields sufficiently reliable results, this method has been chosen for the correlation of the pressures at station 19, 18, 17 and 16. Calculated results and the model data are given in the figures l9b through 22b. Differences are mainly due to the non-including of three-dimensional effects in theory.
The calculation of the stem pressures falls outside of the range of the applicability of strip theory, since a real three-dimensional soluLion is required for that purpose.
Using the relative motion in formula (7), measured
i 16
aside of the stem pressure pick-ups, will lead to some discrepancies because a certain amount of dynamic swell-up is incorporated in this measurement.
Therefore a method was used in which one particular
location was taken as a reference point, where the deviation from the quasi-static pressure due to the
Smith effect is small. When the distance of this location to the free surface is known in calm water together with the measured pressure amplitude due to waves, pressures at other locations can be calculated from (7) and
:rI Pr + ¡ Qg
where /is the distance between reference location and the free surface at forward speed in calm water, while Prcf is the maximum measured pressure. In the figures 15b through 18b the pressure amplitudes thus calcu-lated are shown.
For the ballast conditions I and II the pressures P1
and P2 have been respectively chosen as reference locations. The rate of deviation between calculated and measured pressures increases with the distance below the free surface of the location considered (Smith
effect) and with increasing frequency of wave
en-counterWe, due to a domination of added mass effects. The calculated resistance increment and measured
resistance increase due to waves is given in figures 24 for ballast condition I and III, being the most extreme
conditions investigated. Large discrepancies in the
results of the various calculation methods exist with respect to the measured data, in particular when waves longer than the ship are considered. Apparently, the model test results for both loading conditions correlate best with Gerritsma's method [22]. Results of the ex-periments in irregular long-crested head seas corre-sponding to wind force Beaufort 8 are shown in table IV for ballast draught condition II.
The designation "predicted" indicates the results of calcLilations, based upon the test data in regular waves. Those designated by "measured" represent the results directly obtained from the experiments in the Beaufort 8 head sea.
Since the agreement between the directly measured values and the predicted ones is very good, it seems justified to use the regular wave test results to predict the ship behaviour and performance in irregular seas
for all three loading conditions enabling a reliable assessment of a condition which yields the most
favourable sustained sea speed. Calculated results are given in the figures 25 through 32 for the three loading
conditions considered in the experiments. Irregular wave data utilized, are presented in figure 3 (see page 12). All curves reported apply to the condition that the ship proceeds at full power, for which purpose it was assumed that 20,000 HP were installed.
Irregular ship motions, pitch, heave and vertical
accelerations at the fore perpendicular are approxi-mately equal for the three loading conditions. In seas higher than 4 metres significant, loading condition Ill becomes more favourable as regards pitching, while in very adverse weather in seas higher than 6 metres, conaition II will suffer fewer accelerations at the fore perpendicular.
With respect to bottom pressures, it can be stated that amplitudes of these quantities decrease with for-ward draught, particularly in the most forfor-ward bottom portion. Figure 32 shows the forward speed, that can be sustained by the full size ship at various conditions of loading dependent upon sea state, when maintaining an engine output of 20,000 1-IP. Only the effect of waves has been accounted for.
Also curves, indicating the 5 per cent. probability
that the bow emerges or that during 5 out of 100
oscillations propeller racing takes place, are given. The probability of bow emergence is expressed by
p = = eTE2/2m
TE OS
where
TE = effective draught
rn0 = area under relative motion spectrum
_i-
2- Sa1I3
S0113 = significant relative motion amplitude.
Propeller racing was calculated in accordance with the
proposition of Fukuda et al. [7]. Involuntary speed
loss, thus loss of speed caused by wave action and
reduced propulsive efficiency, is largest for the condi-tion with the deepest draught forward; the magnitude
with respect to the other conditions increases with the severity of the sea.
The five per cent. probability level of propeller racing is almost equal for the three conditions; if propeller racing becomes serious then the speed has to be reduced very drastically.
It most cases, however, not merely propeller racing but rather bow emergence, combined with slamming,
is the factor that limits the rough water sustained
speed. When a five per cent. probability is taken as a criterion, it is seen that in draught condition I the limit of operation are about 3 metres high waves while in condition II and Ill speed has to be reduced when 2.5 metres high waves are encountered.
For condition II speed does not have to be reduced
as radically as compared with the ship sailing in
condition I or III. lt is most likely that condition II
will become superior to condition I in waves, with a significant height greater than about 3 metres.
Therefore ballast condition 11, with a forward
draught to ship length ratio of 0.0155 seems prefer-able; the more so since slamming pressures are of the same magnitude as those for condition I. Moreover, largest slamming pressures shift to shorter waves for condition Il when compared with condition I, which
means that in this respect also condition Il will be
superior to condition I when sea conditions worsen, since maximum wave energy is then concentrated at longer waves present in the spectrum.
6 Conclusions
The experimental results show a linear dependence on
the wave height for ship motions, accelerations,
relative motions and low frequency pressures and a
squared dependence for mean thrust, torque and
revolutions increase. Slamming pressures can hardly be related to wave height.
The superposition principle appears to be valid for all ship motions, not for slamming pressures.
For full ships sailing in ballast the dependence of the slamming pressures on the relative entrance velocity squared seems to be questionable.
Predicted motions, accelerations and low frequency pressures agree reasonably well with the model mea-surements. The relative motions deviate. The static pressure hypothesis at the bow will be a sufficiently reliable approximation for prediction purposes.
Ship motion quantities decrease for large AJL ratios with the forward draught, except the slamming pressure response which shows an opposite tendency; in irreg-ular seas the different ballast conditions have almost the same seakeeping abilities. The choice of a forward draught will be mainly determined by the occurrence of slamming.
The highest speed attainable in a given sea state will decrease with increasing draught. Voluntary speed reduction is mainly determined by bow emergence, associated with slamming phenomena and propeller racing. The risk of propeller racing is almost
equiva-lent for the ballast conditions investigated. Since
propeller racing starts in relatively high seas, the
slamming criterion will be decisive, since slamming already takes place in moderate seas. In that respect,
the forward draught must not be taken too shallow
so as to avoid severe impacts which may cause bottom damage.
I
References
HANSEN, K. E., Pounding of ships and strengthening of bottoms forward. Shipbuilding and Shipping Record, 45,
1935.
BULL, F. B. and J. F. BAKER, The measurement and record-ing of the forces actrecord-ing on a ship at sea. Part I, Sea trials on a 10,000 t. deadweight cargo steamer. TINA 91, 1949. JASPER, N. H. and R. L. BROOKS, Strains and motions of
USS Essex" during storm near Cape Horn. David Taylor
Model Basin Report 1216, 1958.
0ciii, K., Model experiments on ship strength and slamming in regular waves. Transactions SNAME, Vol. 66, 1958.
AKITA, Y. and K. 0cm, Investigations on the strength of ships going in waves by model experiments, II!, on the influence of ships draughts and trims. Journal of Zosen
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FUKUDA, J., Y. ONO and G. OGATA, Determination of fore and after draughts of ballasted hulk carriers associated with
the criteria of slamming and propeller racing, Journal of
Zosen Kiokai, 33, February 1967.
OCHS, M. K., Prediction of occurrence and severity of ship slamming at sea. 5th Symposium on Naval Hydrodynamics, Bergen, Norway, 1964.
TA5AI, F., The seakeeping qualities of full ships. Reports of Research Institute for Applied Mechanics, Kyushu Univer-sity, Japan, Vol. 16, No. 55, 1968.
MUNTJEWERF, J. J., Methodical series experiments ori
cylindrical bows. Transactions RINA, Vol. 112, No. 2,
April 1970.
SLUIJS, M. F. VAN, Performance and propeller load fluctm-tions of a ship in waves. Netherlands Ship Research Centre TNO, Report No. 163 S, February 1972.
OcHI, M. K., Extreme behaviour of a ship in rough seas
- slamming and shipping of green water. Transactions
SNAME, VoI. 72, 1964.
ROLL, H. U., Die Grösse der Meereswellen in Abhängigkeit
von der Windstärke. Deutscher Wetterdienst,
Seewetter-amt, Hamburg 1954.
PIERSON. W. J. and L. MosKowiTz, A proposed spectral
form for fully developed wind seas based on similarity theory of S. A. Kitagarodskii. Journal of Geophysical
Research, Vol. 69, December 1964.
Proceedings of the International Ship Structures Congress, 20-24 July 1964. Report of Committee No. I on environ-mental conditions.
KORV!N-KROUKOVSKY. B. V. and W. R. JACOBS, Pitching and heaving motions of a ship in regular waves. Transaction SNAME, 1957.
GERRITSMA, J. and W. BEUKELMAN, Analysis of the modified
strip theory for the calculation of ship motions and wave bending moments. Netherlands Ship Research Centre
TNO, Report No. 96 S, June 1967.
FUKUDA, J., A practical method of calculating vertical ship
motions and wave loads in regular oblique waves. Inter-national Ship Structures Congress, Committee 2, August
1968.
PORTER, W. R., Pressure distribution, added mass and damping coefficients for cylinders oscillating in the free
surface. University of California, Institute of Engineering Research, Series 82, 1960.
18
VOSSERS, G., Some applications of the slender body theory in ship hydrodynamics. Thesis Delft, 1962.
DAGAN, G. and M. P. TULIN, Two-dimensional free surface gravity flow past blimt bodies. Journal of Fluid Mechanics, Vol. 51, Part 3, February 1972.
GERRITSMA, J. and W. BEUKELMAN, Analysis of the resist-ance increase in waves of a fast cargo ship. 13th International Towing Tank Conference, Hamburg, 1972.
HAVELOCK, T. I-I., The drifting force of a ship among waves. Philosophical Magazine, Vol. 33, 1942.
JoosaN, W. P. A., Added resistance of ships in waves. Sixth Symposium on Naval Hydrodynamics, Washington, 1966. MARUO, H., The excess resistance of ships in rough seas. International Shipbuilding Progress, Vol. 4, 1957.
URSELL. F., On the heaving motion of a circular cylinder on
the surface of a fluid. Quarterly Journal of Mathematical
Appendix Table 1:
Regular wave test results for draught 1
A Z Oa a
''D'1 V QL
TawL 18ia "2a "3a 1'4 P4 "Ba 5 1'Ba '8 P7 17 Fn CU2U gB22 QgB2D2 gB22 9.'î gi, Qg L L a 0.4 1/70 0.12 0.07 240 0.04 60 0.03 2.66 0.28 3.60 0.30 1.55 0.5e 1.00 1.47 1.07 0 0.94 0 0.70 0 0.17 0 0.33 0.145 0.07 215 0.04 48 0.03 2.90 0.32 5.35 0.30 1.55 0.80 1.33 1.50 1.06 0 0.89 0 0.79 0 0.18 0 0.36 0.17 0.07 198 0.04 40 0.02 3.14 0.34 7.00 0.30 1.55 1.50 1.71 1.54 1.05 0 0.83 0 0.90 0 0.17 0 0.39 0.6 0.12 0.16 115 0.08 - 38 0.09 3.20 0.30 5.50 0.42 2.80 0.96 1.63 1.87 1.20 2.1 1.23 0 1.06 0 0.35 U 0.36 0.145 0.16 90 0.07 - 63 0.09 3.25 0.31 7.30 0.46 2.85 1.28 1.72 1.84 1.12 2.0 1.21 0 1.08 0 0.36 0 0.38 0.17 0.16 65 0.06 - 82 0.08 3.54 0.32 9.40 0.50 2.95 1.96 1.93 1.85 1.20 1.9 1.21 0 1.09 0 0.37 0 0.40 0.8 0.12 0.24 78 0.26 -115 0.22 3.83 0.64 9.10 0.73 6.20 1.40 2.55 2.63 2.47 2.6 1.89 4.2 1.72 0 0.50 0 0.49 0.145 0.22 65 0.26 -125 0.22 3.90 0.63 12.00 0.84 6.40 2.00 2.47 2.64 2.42 3.! 1.90 3.9 1.64 0 0.54 0 0.50 0.17 0.20 36 0.26 -132 0.23 4.00 0.60 15.20 0.91 6.50 2.64 2.43 2.52 2.50 3.3 1.91 3.5 1.71 0 0.57 0 0.53 0.9 0.12 0.16 67 0.42 -120 0.31 4.18 0.92 12.40 0.93 8.80 2.50 2.84 2.92 2.73 2.6 2.32 5.0 2.06 1.2 0.65 0 0.145 0.17 49 0.42 -123 0.34 4.30 0.92 16.00 1.04 9.25 2.74 2.95 3.15 2.88 3.5 2.30 8.1 2.06 3.4 0.65 0 0.58 0.17 0.17 30 0.42 -130 0.38 4.34 0.89 20.00 1.13 9.50 3.36 3.12 3.41 2.79 4.4 2.29 12.6 2.06 6.1 0.68 0 0.57 1.0 0.12 0.15 32 0.55 -101 0.38 3.90 1.28 11.60 0.78 6.40 2.62 3.01 2.98 3.08 2.6 2.66 5.3 1.88 1.7 0.68 0 0.63 0.145 0.16 21 0.55 -108 0.43 4.28 1.25 17.30 0.93 7.50 3.16 3.23 3.20 3.20 3.5 2.66 8.7 1.88 8.0 0.67 0 0.64 0.17 0.18 15 0.55 -115 0.49 4.69 1.21 22.30 1.02 8.60 3.80 3.49 3.40 3.40 4.4 2.68 14.2 1.89 23.1 0.68 0 0.64 1.2 0.12 0.32 -10 0.79 - 98 0.37 3.11 1.28 7.40 0.43 3.85 1.92 2.83 2.11 2.59 2.4 2.25 4.4 1.44 0 0.50 0 0.51 0.145 0.33- 5
0.77 -100 0.41 3.20 1.31 10.30 0.53 4.4t) 2.46 2.85 2.31 2.86 3.1 2.26 5.5 1.46 0 0.53 0 0.17 0.35 2 0.76 -104 0.47 3.40 ¡.35 ¡3.30 0.63 4.75 3.04 2.88 2.63 2.92 3.3 2.26 8.1 1.47 0 0.57 0 1.5 0.12 0.57 7 1.03 - 95 0.34 2.28 0.77 4.65 0.32 2.25 1.36 2.01 1.76 2.27 0 1.87 0 1.45 0 0.43 0 0.145 0.58 9 ¡.00 - 95 0.37 2.30 0.84 5.65 0.38 2.30 1.76 2.01 1.85 2.38 0 ¡.70 0 ¡.46 0 0.45 0 0.17 0.60 10 0.99 - 95 0.42 2.34 0.92 7.00 0.44 2.50 2.30 2.01 ¡.96 2.45 0 1.51 0 1.46 0 0.48 0Tahk I la:
Regular wave test results for draught II
¿ L Io L Fo Za Ça f Oa
ka
Sia 5aa 7. a IVawD3L V QatvL T11 1,L P11 P211 P311 P40 P P50 P6 P611 P6 P716 P8a P8 W2a gB2112 gBD02 jgB7,, g11 g1 g11 otì oçi Qg11 Ya OfJaea
0.4 1/70 0.12 0.07 240 0.04 70 0.05 2.50 0.35 3.65 0.30 3.00 0.28 1.40 1.44 0.95 2.1 1.22 0 0.88 0 0.18 0 0.28 0 0.145 0.07 220 0.04 65 0.05 2.83 0.36 5.68 0.40 3.0() 0.36 1.70 1.42 0.81 2.1 1.10 0 0.90 0 0.19 0 0.31 0 0.17 0.07 208 0.04 60 0.06 3.10 0.37 7.80 0.47 3.00 0.42 2.22 1.45 0.69 2.1 0.97 0 0.93 0 0.20 0 0.31 0 0.6 0.12 0.16 121 0.10 -IO 0.12 2.68 0.30 5.50 0.41 4.05 0.56 1.76 1.80 1.01 1.6 1.57 4.7 1.22 0 0.30 0 0.38 0 0.145 0.16 ItO 0.10 -16 0.14 3.11 0.3! 7.65 0.52 4.10 0.78 2.16 1.78 0.90 2.7 1.57 3.3 1.20 0.6 0.31 0 0.40 0 0.17 0.16 98 0.09 -20 0.15 3.49 0.32 9.80 0.60 4.20 1.04 2,72 1.80 0.82 4.8 1.57 2.2 1.17 1.6 0.33 0 0.42 0 0.8 0.12 0.22 91 0.26 -80 0.22 2.88 0.80 7.40 0.55 5.30 0.82 2.14 2.08 1.80 1.3 1.84 3.9 1.70 1.8 0.46 0 0.46 0 0.145 0,20 80 0.26 -90 0.25 3.43 0.72 10.28 0.69 5.60 1.26 2.64 2.12 1.61 2.7 1.88 8.! 1.73 8.7 0.48 0 0.49 0 0.17 0.19 71 0.25 -95 0.27 3.90 0.69 13.30 0.81 6.00 1.98 3.22 2.23 1.94 3.9 1.89 16.7 ¡.76 20.0 0.49 0 0.54 0 0.9 0.12 0.15 72 0.42 -88 0.26 2.88 1.21 8.30 0.52 4,80 0.86 2.22 2.32 1.98 1.4 1.88 4.4 1.66 1.0 0.55 0 0.51 0 0.145 0.16 55 0.42 -94 0.30 3.45 1.16 11.30 0.70 5.40 1.50 2.82 2.42 2.00 2.5 1.91 9.5 1.70 5.5 0.56 0 0.55 0 0.17 0.16 42 0.42 -99 0.36 4.07 1.06 15.20 0.93 5.90 2.12 3.54 2.68 2.08 3.1 1.91 25.6 1.72 11.3 0.58 t) 0.58 0 1.0 0.12 0.16 18 0.55 -87 0.28 2.62 1.47 7.70 0.38 3.40 0.76 2.08 2.09 1.69 1.6 1.80 4.0 1.67 0.5 0.52 0 0.48 0 0.145 0.18 15 0.55 -94 0.33 3.10 1.44 10.00 0.54 4.00 1.34 2.64 2.26 1.72 2.2 1.82 7.2 1.68 1.7 0.53 0 0.48 0 0.17 0.20 13 0.55 -97 0.37 3.75 1.38 14.08 0.77 4.70 2.10 3.50 2.50 1.85 2.7 1.81 14.5 1.69 7.1 0.53 0 0.47 0 1.2 0.12 0.34 -21 0.74 -91 0.30 2.10 1.53 5.20 0.23 1.70 0.30 1.62 1.76 .47 1.4 1.44 1.1 1.30 0 0.38 0 0.36 0 0.145 0.35 -14 0.72 -93 0.35 2.40 1.49 6.70 0.33 2.30 0.62 2.12 1.83 ¡.46 1.6 1.47 0.9 1.24 0 0.40 0 0.37 0 0.17 0.36 9 0.72 -98 0.38 2.95 1.49 9.00 0.46 2.60 1.02 2.68 2.03 1.56 1.3 ¡.49 0.7 1.18 0 0.44 0 0.36 0 l.5 0,12 0.58 0 0.93 -91 0.30 ¡.60 1.04 2.75 0.17 1.00 0.06 1.40 1.44 1.20 0 1.28 0 1.04 0 0.35 0 0.30 0 0.145 0.59 0 0.92 -92 0.32 1.81 1.10 3.70 0.25 ¡.20 0.22 1.78 ¡.45 1.21 0 l.21 0 1.02 0 0.36 0 0.30 0 0.17 0.60 0 0.92 -92 0.33 2.16 1.17 4.70 0.33 1.50 0.38 2.20 1.60 1.22 0 1.15 0 0.97 0 0.36 0 0.28 0Table lIb:
Regular wave test results for draught Il
L Fn Za o', I, 'ç a s 'a s a NUWD3L V QawL TawL "la "fia "3a "Aa A4 "fia fi 6a
"
7a ? 2u gB22 gB2D'2 gB22 Qg O(ia QYa PJ1''a Qg eg 0.9 1.0 1.2 0.9 1.0 1.2 1/100 1/50 0.12 0.145 0.17 0.12 0.145 0.17 0.12 0.145 0.17 0.12 0.145 0.17 0.12 0.145 0.17 0.12 0.145 0.17 0.14 0.16 0.18 0.17 0,18 0.17 0.34 0.34 0.34 0.15 0.15 0.16 0.17 0.18 0.18 0.34 0.35 0.36 70 55 41 22 16 16 -23 -14 -11 71 58 41 22 12 14 -21 -14 -12 0.41 0.41 0.42 0.52 0.52 0.53 0.68 0.68 0.69 0.42 0,4! 0.4! 0.53 0.53 0.53 0.74 0.73 0.68 86 - 92 -102 87 94 94 - 91 - 92 - 95 - 92 - 97 - 99 - 83 - 94 - 99 94 99 98 0.26 0.31 0.33 0.28 0.32 0.36 0.30 0.35 0.39 0.25 0.29 0.34 0.27 0.31 0.37 0.30 0.33 0.37 2.85 3.47 4.02 2.63 3.41 3.75 2.10 3.08 3.00 2.80 3.29 3.80 2.57 3.33 3.75 2.15 3.03 2.9! 1.19 1.16 1.05 1.51 1.46 1.38 1.53 1.51 1.47 1.07 1.08 1.00 1.34 1.32 1.34 1.33 ¡.36 ¡.37 8.60 11.80 15.60 7.55 0.25 14.10 5.05 6.95 9.35 8.15 11.45 14.55 7.55 9.95 14.15 5.20 6.45 9.05 0.56 0.72 0.91 0.36 0.47 0.74 0.21 0.33 0.40 0.50 0.62 0.93 0.32 0.44 0.80 0.24 0.35 0.35 4.90 5.05 6.05 3.40 3.90 4.35 1,70 2.30 2.60 4.55 4.60 5.50 3.10 3.50 4.60 1.85 2.30 3.10 0.96 1.52 2.24 0.74 1.36 2.10 0.30 0.54 0.84 1.20 1.62 2.18 0.98 1.50 2.06 0.42 0.90 1.42 2.08 2.76 3.50 2.06 2.68 3.46 1.62 2.20 2.86 2.20 2.70 3.40 2.10 2.56 3.24 1.48 2.06 2.72 2.39 2.50 2.74 2.21 2.29 2.45 1.80 1.83 1.97 2.12 2.22 2.40 97 2.08 2.28 1.72 1.80 1.94 1.67 1.83 2.15 1.52 1.67 2.00 1.31 1.29 1.63 2.05 2.13 2.22 1.82 1.82 1.60 1.58 1.50 1.39 0 0 0 0 0 0 0 0 0 3.7 6.8 10.0 3.6 5.5 7.5 2.8 3.7 4.5 1.92 1.93 1.93 ¡.89 1.90 1.91 1.56 1.58 1.59 1.60 1.61 1.62 1.43 1.44 1.45 1.38 1.38 1.37 0 0 0 0 0 0 0 0 0 10.0 19.5 63.0 10.0 18.6 54.0 9.0 ¡5.8 49.5 1.63 1.63 1.62 1.55 1.58 1.60 1.38 1.35 1.32 1.58 1.57 1.56 1.48 1.46 1.43 1.16 1.10 1.00 0 0 0 0 0 0 0 0 0 9.3 16.4 32.0 6.5 14.0 25.0 2.8 11.0 17.0 0.50 0.52 0.56 0.48 0.46 0.46 0.44 0.43 0.39 0.42 0.43 0.43 0.53 0.52 0.52 0.43 0.42 0.42 0 0 0 0 0 0 0 0 0 1.0 1.5 5.5 0 0.8 4.0 0 0.5 2.0 0.49 0.51 0,52 0.41R
I
III:
Regular svave test rL-u!I,
1riiil III A L L Fn Za On
ka
aa S'fa " 'a Saa 'a tau,°3-'-' V QawL TawL "la -2a 3a '4a 4 -1'5a 5 6a 7a 7 "la a gB2,2 9gB2D,2 gB2Og, Qg4'a 'Y4a 9lla 0ga Q9'a &g, Q9'a QY,, 'c, 'g, La
0.4 1/70 0.12 0.07 240 0.04 80 0.06 2.12 0.40 3.85 0.30 2.50 0.04 0.44 1.66 2.03 2.7 1.11 5.0 1.12 0.9 0.19 0 0.29 0 0.145 0.07 224 0.04 75 0.05 2.25 0.40 5.00 0.34 2.60 0.04 0.44 1.86 1.42 3.0 1.15 3.3 1.15 1.5 0.20 0 0.31 0 0.17 0.07 214 0.04 70 0.05 2.37 0.40 6.25 0.38 2.55 0.04 0.46 2.22 0.78 3.3 1.18 2.3 1.16 2.0 0.2! 0 0.32 0 0.6 0.12 0.16 132 0.12 7 0.14 2.48 0.30 5.80 0.38 3.90 0.16 0.88 2.26 2.33 2.7 1.25 12.2 1.45 8.0 0.33 0 0.38 0 0.145 0.16 128 0.12
- 5
0.14 2.60 0.31 7.00 0.49 3.95 0.28 1.06 2.66 1.77 3.4 1.29 10.8 1.49 13.3 0.35 0 0.40 0 0.17 0.16 120 0.11 -15 0.14 2.72 0.32 8.60 0.50 4.00 0.48 1.18 3.16 1.20 4.0 1.33 6.7 1.50 16.7 0.36 0.9 0.41 0 0.8 0.12 0.20 109 0.26 -71 0.23 2.80 0.80 7.15 0.43 4.20 0.46 1.22 2.56 2.63 2.8 1.33 6.7 1.44 6.1 0.54 0 0.41 0 0.145 0.18 lOO 0.26 -81 0.24 3.00 0.72 8.30 0.57 5.30 0.64 1.66 3.06 2.41 3.6 1.35 15.0 1.46 14.0 0.56 1.6 0.43 0 0.17 0.17 89 0.25 -87 0.28 3.17 0.67 10.65 0.69 5.00 0.86 2.18 3.72 2.25 4.4 1.36 2!.! 1.48 19.3 0.57 6.4 0.44 0 0.9 0.12 0.13 75 0.43 -80 0.27 2.75 1.18 7.45 0.42 3.75 0.56 1.50 2.70 2.71 2.8 1.30 8.0 1.43 4.8 0.57 0 0.38 0 0.145 0.14 63 0.42 -88 0.3! 3.03 1.12 9.70 0.58 5.30 0.76 1.94 3.24 2.50 3.6 1.33 20.6 1.43 14.4 0.62 3.2 0.41 0 0.17 0.16 55 0.42 -92 0.35 3.28 1.08 11.75 0.72 6.25 1.00 2.46 3.96 2.37 4.2 1.38 34.4 1.46 21.5 0.63 12.0 0.42 0 1.0 0.12 0.18 5 0.55 -81 0.28 2.48 1.41 6.30 0.35 2.80 0.26 1.46 2.52 2.44 2.5 1.30 7.3 1.56 3.5 0.61 0 0.35 0 0.145 0.20 8 0.55 -86 0.33 2.8! 1.36 8.30 0.54 4.55 0.52 1.82 2.98 2.23 2.9 1.35 12.9 1.6! 8.5 0.63 2.0 0.36 0 0.17 0.21 lO 0.55 -92 0.38 3.15 1.33 10.55 0.68 5.60 0.96 2.54 3.76 2.00 3.5 1.40 19.0 1.64 11.1 0.66 7.2 0.35 0 1.2 0.12 0.35 -31 0.7! -86 0.30 2.01 1.57 4.45 0.23 1.60 0 0.94 2.16 2.20 1.5 1.31 6.2 1.36 1.5 0.44 0 0.19 0 0.145 0.37 -24 0.70 -86 0.34 2.27 1.50 5.70 0.31 2.40 0.10 1.38 2.66 1.90 2.0 1.35 7.9 1.35 2.5 0.45 0.3 0.19 0 0.17 0.38 -19 0.69 -93 0.38 2.50 1.40 7.05 0.38 3.00 0.44 1.90 3.36 1.58 2.5 1.36 10.0 1.35 8.2 0.46 1.0 0.20 0 1.5 0.12 0.59- 5
0.86 -87 0.30 1.52 1.23 2.75 0.11 0.70 0 0.76 1.96 2.12 0.7 1.18 1.0 0.97 0 0.38 0 0.14 0 0.145 0.61- 7
0.86 -89 0.32 1.69 1.12 3.70 0.12 1.00 0.04 0.90 2.40 1.76 1.1 1.19 1.7 0.97 0 0.40 0 0.14 0 0.17 0.62- 8
0.85 -90 0.34 1.90 .09 4.30 0.13 1.30 0.08 1.04 3.00 1.47 1.5 1.21 2.4 0.98 0 0.41 0 0.13 0Table 1V:
Comparison between predicted and directly measured values in BeauFort 8 head seas
20j/3 2Ö0113 2à1,3 20113 (forward) 2s0113 (aft) in m in deg. in g in m in m in tm Speed in knots measured predicted measured predicted measured predicted measured predicted measured predicted measured Tw 2F5a113 2P6a1ì3 2F70113 2F80113 in tons in kg/cm2 in kg/cm2 in kg/cm2 in kg/cm2 Speed in knots measured predicted measured predicted measured predicted measured predicted measured predicted 11.4 1.0 1.0 2.0 2.2 0.26 0.25 12.8 12.1 3.8 3.8 54 13.7 1.0 0.9 2.0 2.2 0.28 0.28 14.4 14.5 3.6 3.6 52 16.1 0.9 0.9 2.1 2.2 0.32 0.31 6.0 16.1 3.5 3.5 44 11.4 69 63 0.57 0.70 0.49 0.59 0.28 0.16 0.14 0.17 13.7 62 60 0.57 0.70 0.51 0.59 0.31 0.17 0.15 0.16 16.1 54 59 0.56 0.69 0.52 0.60 0.34 0.18 0.15 t).l7
G 100 200 o 100 200 100 0 o -100 0. I II EI DRAUGHT DRAUGHT DRAUGHT
Fn 0.145 / / -5 /7 I II 2! DRAUGHT DRAUGHT Fn 0.145 -'-'-' DRAUGHT 'r - r--/' -DRAUGHT I
'-a-..
DRAUGHT U Fn rO 145 DRAUGHT III\\
\\
' \ \ __ CALCULATED I III I III DRAUGHT MEASURED DRAUGHT DRAUGHT Fr0145 - DRAUGHT 'I u, / CALCULATED DRAUGHT I m D I UI Fn r0,145 -DRAUGHT MEA SURE DRAUGHT DRAUGHT5,
CALCULATED DRAUGHT I DRAUGHT IR Fn 0.145 MEA SU RE D DRAUGHT I DRAUGHT III /1 t'I
'I
i,'
tj
t,
-Fig. 5h. Heave response; comparison.
Fig. ob. Heave-wave phase; comparison.
Fig. 7h. Pitch response; comparison.
Fig. 5a. Heave response.
Fig. 6a. Heave-wave phase.
Fig. 7a. Pitch response. 05 10 05 10 IS X 05 IO IS X L 05 10 o 05 X lo 15 05 Io Is X 15 1.0 0.5 0 10 05 IS 1.0 0.5
Fig. 8a. Pitch-wave phase.
05
Fig. 8b.
Pitch-wave phase; comparison.
Fig. 9a. Response of vertical acceleration at F.P.
O o
Fig. lOa. Response of relative motion at the stem.
R 3 o 4 2 I D
À
\
/
DRAUGHT DRAUGHT -DRAUGHT FT :0.145 / / \\\ r I U UI DRAUGHT DRAUGHT Fn:0145 --*--. DRAUGHTDRAUGHT DRAUGHT DRAUGHT
I II m Fn :0145 / i,
j
I, /, CA LC U LAT E D I 10 I 10 DRAUGHT MEASURED DRAUGHT DRAUGHT Fn 0.145 DRAUGHT CALCULATED I 10 I W DRAUGHT MEASURED DRAUGHT DRAUGHT Fn I - DRAUGHT CALCULATED I III I lu DRAUGHTMEASURED DRAUGHT DRAU0HT
Fn :0145 DRAUGHT 05 10 05 1.0 X
Fig. 9b. Response of vertical acceleration at F.P.;
comparison.
05
lo
X
Fig. lOb. Response of relative motion at the stem;
comparison. 05 lo 15 05 10 15 À X Io 15 t-10 -20 06 0.4 o 02 o 100 o 100 -200 0.6 o 04 o 3 02 o
LU4 o X L o o U 10 DRAUGHT DRAUGHT FnrO.145 DRAUGHT I II m
DRAUGHT DRAUGHT DRAUGHT
Fri r 0.145
IL
/ /__','\-
'I\
\\ \
\ I It III DRAUGHT DRAUGHT Fn 0.145 -. DRAUGHT CALCULATED I III I DRAUGHT -DRAUGHT MEASURED DRAUGHT DRAUGHT Fri r 0.145 I DRAUGHT ---- DRAUGHT 0 Frir0.145 DRAUGHT 01Â
Fig. lia.Response of relative motion at the stern.
Fig. 12. Mean increase of thrust.
Fig. 14. Mean increase of revolutions.
15 2 10 I'- 4 :IJ o 'U 05 o o 0.5 15 05 Io l-g.
lib. Response of relative motion at the stern;
Fig. 13. Mean increase of torque.
comparison. 05 lo X 05 10 IS 05 X 1.0 rs 10 5 Is 10 o 5 o
3 2 oo o
X L
Fig.
I Sa. Response of low frequency pressure at
position P1.
o
o 3 o
X
Fig. I7a. Response of low frequency pressure at
position F3. I D IS DRAUGHT Fn O.145 ---- DRAUGHT --- DRAUGHT I
\
/
/
\
/
i-/ ,.-.' // \
, \ \ \ N. N DRAUGHT X DRAUGHT II DRAUGHT Fn O145 --*---¡IA
N
DRAUGHT I U DI Fa O.14 --- DRAUGHT ---*--- DRAUGHT \ / I / // /
// \ s. / / I/
CALCULATED DRAUGHT I D I 1 DRAUGHT DRAUGHT Fn O.145 DRAUGHT MEASURE 1rl
rl
CALCULATED DRAUGHT I I MEASURED DRAUGHT Fa '0145 CALCULATED -DRAUGHT III MEASURED DRAUGHT I DRAUGHT III Fn 0.145 //
/
Fig. 15b. Response of low frequency pressure at
Fig. 16h.
Response of low frequency pressure at
Fig. 17h.
Response of low frequency pressure at
position F1; comparison. position P2; comparison. position P3; comparison. 05 l-o 05 lo 15 X Fig. 16a.
Response of low frequency pressure at position P2.
05 Io 05 l_o X L 05 10 À L 05 lo 15
o 3 2 o
30 20 10 o
I G ID
DRAUGHT DRAUGHT DRAUGHT
Fn 0145 CALCULATED I 1G I III / DRAUGHT DRAUGHT MEASURED DRAUGHT DRAUGHT Fn O145 N. . -DRAUGHT I U 1G DRAUGHT Fn0.145 -.--.---DRAUGHT 1 CALCULATED DRAUGHT I 1G I W
DRAUGHT DRAUGHT DRAUGHT
Fn 0145 MEASURED DRAUGHT I II 1G DRAUGHT -DRAUGHT Fn0.145 -. ¡ I I' i .J
/
jI /J
/ ,-/ / / .7/
N. I fi III DRAUGHT DRAUGHT Fn 0145 ---s---DRAUGHTI
a
X X L L Fig. I 8a.Response of low frequency pressure at
Fig. 181).
Response of low frequency pressure at
Fig. 18e. Response at slamming. position P4. position P4; comparison. Fig.
I 9a. Response of low frequency pressure at
Fig. 19b. Response of low frequency pressure at
Fig. 19e. Response at slamming. station 19. station 19; comparison. 05 IO IS 05 I0 '5 05 lo IS 0.5 lo 15 05 Io 1.5 X L 05 X Io L a o
o o
Fig. 20d. Response of low frequency pressure at
station 18; comparison. 30 20 Io o DRAUGHT DRAUGHT I G UI Fo R 0.145 -. DRAUGHT I //f\S\\\\\\ / "f ' CALCULATED I UI I UI
DRAUGHT DRAUGHT DRAUGHT
Fn 0145 - DRAUGHT MEASURED DRAUGHT I n UI -DRAUGHT Fn '0.145 --.-- DRAUGHT 0.5 M. [2G]
05M REVISED VOSSERS MEASURED
DRAUGHT I -. /
,,
/ / / Fig. 20a.Response of low frequency pressure at
Fig. 20b. Response of low frequency pressure at
Fig. 20e. Response of slamming. station 18. station 18; comparison. 0.5 10 05 10 X 05 lo X L 05 10 1.5 2 D 3 2
Fig. 21a. Response of low frequency pressure at
station 17.
Fig. 2lb. Response of low frequency pressure at
station 17; comparison.
o
X
Fig. 22b. Response of low frequecy pressure at
station 16; comparison.
30 20 Io o
Fig. 21c.
Response of slanirning.
Fig. 23. Heave potential at station 18.
DRAUGHT m Fn r 0145
,/
%r___.. CALCULATED I ifi IDRAUGHT DRAUGHT DRAUGHT
Fr Ci45 - DRAUGHT MEASURED I G UI DRAUGHT En O145 DRAUGHT -.-*-.-- DRAUGHT CALCULATED I UI I Ill DRAUGHT MEASURED DRAUGHT DRAUGHT Fn 0145 -DRAUGHT I a Ut DRAUGHT DRAUGHT Fnr0145 ---.--. DRAUGHT
WITHOUT FREE SURFACE
SURFACE
/
/
/
-- WITH FREE/
z
z
/
/
/
/
05 IO ISFig. 22a. Response of low frequency pressu re at
station 16. OS Io X 05 10 15 o 05 to '5 05 10 15 05 10 3 0 20O lOo. 15 I.0 W 3jo 05 o
IS 10 5 o DRAUGHT I DATA MODEL GRRITSMA [22] HAVL0CK [23] Fn 0145 -- JOOSEN [24] MARUO [os] DRAUGHT III DATA [22] GERRITSMA MODEL HAVELOCK [23] Fn r 0145 -- JOOSEN [24] MARUO [25] 1; /7 N. '-'r
'/
I.-,
\_/ /
. NFig. 24a. Mean increase of resistance in waves for
Fig. 24b. Mean increase of resistance in waves for
ballast draught I.
ballast draught Ill.
o 05 10 15 05 10 15 5
E o 0.4 02 o o 0 G o So 25 o o o I D ID DRAUGHT -. -. -. DRAUGHT -DRAUGHT I II DI DRAUGHT DRAUGHT -DRAUGHT I li III DRAUGHT DRAUGHT V
r
r
--r
DRAUGHTr
.r--
.7---r
r
.-
--.9. --I U DIDRAUGHT DRAUGHT DRAUGHT
Fig. 25.
Significant heave versus significant wave height.
Fig. 26.
Significant pitch versus significant wave height.
wl/3
Il
'
151
Fig. 27.
Significant vertical acceleration at F.P. versus significant
Fig. 2R.
Significant low frequency pressure at station 19 versus
wave height.
significant wave height.
4 6 8 çwl/ 6 8 10 8 10 2 o
05 0 0.5 o E o I li III DRAUGHT - ---DRAUGHT DRAUGHT I D
DRAUGHT DRAUGHT DRAUGHT
0 2 4 6 8 I U UI DRAUGHT DRAUGHT - DRAUGHT I DRAUGHT -DRAUGHT Fig. 29.
Significant low frequency pressure at station 18 versus
Fig. 30.
Significant low frequency pressure at station 17 versus
significant wave height.
significant wave height.
8
r,T
Hg. 31.
Significant low frequency pressure at station 16 versus
Fig. 32. Sustained speed in irregular head seas.
significant wave height.
4 .. 5 10 tw113 111 4 6 8 10 15 o > 10
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