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250694
-OTC Paper 5208
DYNAMIC POSITIONING OF LARGE
TANKERS AT SEA
By:
J.A. Pinkster
U. Nienhuis
OTC 5208
DYNAMIC POSITIONING OF LARGE TANKERS AT SEA
By J.A. Pinkster and U. Nienhuis, MARIN
Copyright 1986 Offshore Technology Conference
This paper was presented at the 18th Annual OTC in Houston. Texas, May 5-8.1986. The material is sublect to correction by the author, Permission to copy is restricted to an abstract ot not more than 300 words.
ABSTRACT
In this paper, an unconventional dynamic
posi-tioning (DP) system is introduced which is
relative-ly simple from the point of view of the thruster layout and, by virtue of the same thrutter layout,
automatically positions the vessel in 0 favourable
heading relative to the environment.
This system, Which in principle is based on
thrusters installed
only
at the forward (or aft) endof the vessel, possesses automatic weathervaping
properties i.e. the DP system itself does not
con-trol the heading as this is governed by the
environ-mental conditions. The stable equilibrium heading of
the vessel is consistent with the minimum power
heading.
The basic principles of the system are
ex-plained and results of an extensive series of model
tests giving insight in the capabilities of this
type of DP system applied to a 200,000 DWT tanker
are presented and discussed. The model tests cover a
range of realistic sea conditione likely to be
regarded as limiting conditions for offshore loading
operations.
Such conditions include irregular waves, wind and current. For one test irregular cross-sea
condi-tions combined with wind and current were generated.
A number of tests were devoted to investigating
stand-by sea conditions and the effects of fast
Changes in wind direction. The latter tests give
insight in the reactions of the DP system to sudden
variations in the environmental conditions as can
occur, for instance, in cyclone prone areas.
The results of the model tests confirm that it is possible to DP a large tanker in operational con-ditions using a simple thruster layout and a
rela-tively small amount of installed power.
References and illustrations at end Of paper.
1. INTRODUCTION
Dynamic positioning or dynamic stationing is a Method whereby the position of a surface vessel is maintained In Close proximity to a required position in the horizontal plane through the controlled ap-plication of forces and moments generated by pur-posely installed thrusters. The required position generally applies to the co-ordinates of a point
(the reference point) of the Vessel in the
horizon-tal plane while for most Applications a specified
beading of the vessel is also a requirement.
The offshore industry has been making
increas-ing use of dynamic positionincreas-ing systems to station
vessels in a Wave, wind and current environment
since it Was first introduced in the sixties. Ini-tially DP systems were applied to relatively small
vessels such as survey ships and to larger
vessels-such as drill. ships. Today vetsels with displace-ments in the region of 130,000 DWT are being sta-tioned if not wholly then at least partly with the
aid of dynamic positioning systems, tee Ref. [I]. As
the vessel size increases., however, the power
re-quired by the DP system, the number of thrusters and
the complexity of the power generation system and of the thruster layout form considerable obstacles to a
wider application of what is generally considered to
be a versatile and useful way of station keeping.
In order to further the applicability of such
systems these are the areas in which improvements
should be sought for. In this paper a DP system is
introduced which, it appears, could result in a
sig-nificant reduction in the requited DP power and the number of thrusters installed in the vessel.
The price to be paid for these improvements
lies in a reduction of the number of degrees of
freedom .of the vessel which can be controlled from
three to two i.e. the. DP system does not control the
heading of the vessel. This is governed by the am-bient environmental condition and the weathetvaning property inherent to this DP system.
con-trol both the position of the vessel in the horizon-tal plane and the heading. In many cases it is clear
that heading control is essential,. for example, In
order- to be able to either minimize roll motions in the case of drill ship operations or to control the
swept path of the vessel in case it is working close
to other vessels or fixed objects. Early in the de-velopment of DP systems it was found that, under
more severe environmental conditions, It was not
al-ways possible, to .maintain the required heading of a
vessel due to overloading of thrusters as a result
of. high external loads. In such cases the heading
requirement. is .relaxed and at the cost of, for
in-stance, increased roll motions, a More favourable
heading with regard to the thruster 'loading Is
sought for. Nowadays DP control systems incorporate
such control algorithms as arenecessary to find
acceptable headings from the point of view of
thruster 'loading when such is required. From the aforegoing it can be inferred that conventional DP Systems are, under normal operating conditions, not
minimum power systems since relaxing the heading re-quirements generally leads to lower required thrust.
The thrust required to dynamically position a vessel is in many cases generated by a combination of transversely mounted tunnel thrusters installed. fore and aft which supply the transverse forces and yawing moment and main propellers which generate the
longitudinal forces. Nowadays increasing use is
being made of azimuthing thrusters which, by virtue of their azimuthing capability, can generate forces in all directions. In a few cases cycloidal
propel-lers have been used.
The distribution of thrusters both fore and aft
is a consequence of the positioning requirements. Since one usually requires heading control, it is
necessary to generate yaw moments on the vessel
beside the transverse forces and longitudinal
forces. Yaw moments are generated most efficiently by applying opposing transverse forces at each end
of the vessel thus requiring thrusters both fore and aft. Locating thrusters in the aft end of the vessel
may present considerable design problems due to the
fact that these may be in way of the engine room and
due to the hydrodynamic interaction of main
propel-lers and aft thrustera.
From the aforegoing it may be concluded that the requirement of heading control is of consider-able significance with respect to the design of a DP
system. If the heading requirement could be
ne-glected altogether, it would not be necessary to
install thrusters at both ends of the vessel since
there would be no requirement for generating yaw
mo-ments. This could result in significant
simplifica-tion of the thruster layout.
Obviously, this concept of a DP system raises.
many questions such as:
If heading is not controlled, which heading will
the vessel assume?
What will be the required thrust?
How should the thrusters be distributed over the
vessel?
In this paper, these aspects of a simplified DP sys-tem without heading control are investigated.
The investigations are based on theoretical
research carried out
in
the past and on an extensiveseries of model tests carried out recently with a
fully dynamically positioned model of a large tanker in realistic wave, wind and current environments.
The subject vessel for this investigation was a
fully loaded 200,000 DWT tanker. This vessel was considered a likely candidate for a DP system with-out heading requirement since on- and off-loading operations of tankers in the open sea generally do not place stringent requirements on such aspects as
roll motions of the vessel. There are numerous other cases where the same remarks apply however.
In the following, a brief discussion covering the selection of the thruster layout and the effect of the choice of the point on the vessel which has
to be positioned i.e. the reference point, will
first be given. After this discussion the model test
program will be covered. This includes details of the Model, the thruster layout, the DP control
sys-tem, environmental conditions etc. The results of
the model tests including a discussion of these
results will be given.
2. THRUSTER LAYOUT FOR A D.P. SYSTEM WITHOUT HEADING CONTROL
As stated in the introduction, a DP system
which does not control the heading of a vessel does
not require transverse thrust to be generated at
both ends of the vessel. The question is then where
should the transverse thrusters be situated? This
can be answered based on the requirement of
equilib-rium of the mean forces and moments acting on the vessel. The environmental forces acting on the ves-sel which are of relevance for the DP system, i.e.
the forces which have to be counteracted by
con-trolled thrust are:
Wind forces: constant forces and wind gusts. Current forces: generally relatively constant.
.Wave forces: mean and slowly varying second order
wave drift forces.
At this stage we will consider the equilibrium of the mean forces and moments acting on the vessel. The mean thruster forces may be represented as a
longitudinal and a transverse force component Fx
and F respectively and one may assume that, by
ap-proximation, the longitudinal position of the
trans-verse force Fy coincides with the position of the
thruster. The mean external forces and moments about the centre of gravity due to wavea, wind and current
are denoted as
FXE
(*)
'
FYE (*) And N (*)respective-ly. As indicated, the mean environmental forces and
moment and hence the mean thruster forces are a
function of the mean heading angle (40 of the vessel
which' at this point, still has an unknown value.
The various forces are denoted schematically in Fig.
1. The value xt denotes the position of the trans-verse thrust component in relation to the centre of
gravity of the vessel.
Equilibrium of mean forces and moments result
in the following requirements.
DYNAMIC POSITIONING OF LARGE TANKERS AT SEA OTC 5208
YT - TYE07)
Tr
YYT xt 3E(47)
In principle, given sufficient installed power, it
is possible to satisfy the first two requirements at
any given heading angle of the vessel relative to the environment. However, in general the third
re-quirement will not be Met for arbitrary heading
angles. The requirement for equilibrium of the mean
yaw moments acting on the vessel is equivalent to the requirement that the mean environmental yaw mo-ment about
a
vertical axis through the location of the thruster be equal to zero. This can easily bederived from equations (2) and (3).
Taking equation (2) into account gives:
RE(71;)
x
t
FYE(*)
Equation (5) shows that in the equilibrium position
the centre of effort of the mean lateral
environmen-tal force must coincide with the longitudinal
posi-tion of. the thruster.
This requirement will only be met for specific
heading angles of the vessel, see Ref. [2]. The
problem described here is fully equivalent to the
case of the same vessel being moored by means of a bow hawser which is connected to the vessel at the point coinciding with the position of the thruster. The equilibrium heading will therefore also be the
same. In principle, for a given sea condition more
than one equilibrium heading is possible. Usually
however, only one equilibrium heading is a stable
heading. In the case of the transverse thrust being
applied in the forward part of the vessel, the
stable equilibrium heading will be such
that the
vessel lies bow-on to the environment. The stable
equilibrium heading of a DP vessel without heading
control can be calculated based on information
regarding the mean environmental forces and yaw
moment. As an example, in Fig. 2 the mean surge
force (47), sway force
F(7i)
and yaw momentXE
3E(IT) about the centre or gravity are given for a
fully loaded 200,000 DWT tanker in the following sea
condition:
Irregular long crested wave:
Significant wave height 4.5 m
Peak period 10.4 s
Pierson-Moskowitz wave spectrum
Steady wind 36 kn. parallel to waves.
Steady current 1.5 kn. at a right angle to waves and wind.
The results of these calculations were found as
fol-lows:
Wind and current forces Were obtained from wind tunnel tests and model tests carried out in the
Wave and Current Basin of MARIN, see Ref. [3].
Mean second order wave drift forces were obtained based on 3-0 diffraction calculations, see Ref.
[4].
it follows that:
(4)
In Fig. 3 the stable equilibrium heading of this
vessel is given as a function of the point of
appli-cation of the transverse thrust component of the DP
system. In this simple analysis we have, assumed that
this point coincides with the longitudinal position
of the thruster, or group of thrusters, which supply the transverse force component.
Also shown in Fig. 3 Is the total mean
environ-mental force to be counteracted by the thruster. As can be seen from this figure, the mean, environmental
force Is at a minimum when the transverse thrust
component is applied at the forward end of the ves-sel.
The aforegoing example illustrates that if the
thruster system is located at the bow of the vessel,
an equilibrium heading corresponding to a minimum mean power heading will be assumed. It should be
noted that in order to deduce the stable equilibrium
heading, no information regarding the point being
positioned was required. This means that the stable
heading of the vessel in a given sea condition only depends on the thruster layout and not on the point
of the vessel which is being positioned. This
gener-al property of the present DP system will be
veri-fied by model tests described in this paper.
In the following section attention will be paid
to the influence of the position of the point of the
vessel to be kept on station i.e. the reference
point.
3: POINTS ON THE VESSEL TO BE POSITIONED: THE
REFERENCE POINT
In the previous section it was shown that the
stable equilibrium heading of the Vessel and hence the mean environmental forces are fully determined by the position of the point of application of the transverse thrust component and are not determined by the choice of the reference point on the vessel. This, however, does not mean that we may choose as reference point any point on the vessel, see Ref.
[2]. It can be shown, based on a stability analysis,
that assuming that the transverse thrust component is applied near the bow of the vessel, it is
possi-ble to position almost any point which is forward of
the midship region of the vessel. This includes
ref-erence points outside the physical limits of the
vessel, i.e. reference points forward or to either
side of the vessel. Such reference points are Of
relevance when positioning a vessel near, for
in-stance, a single point mooring or when using dynamic
positioning to maintain position relative to another
vessel while moving slowly.
In general it is found that the DP control
stability decreases as the reference point on the vessel is moved aft. The effect of the choice of the reference point on the DP behaviour of the vessel can be illustrated by first assuming that the
refer-ence point coincides with the position of the
thruster near the bow. The DP control algorithm
could be such that transverse thruster forces are
dictated by the transverse position error of the
reference point and longitudinal thruster forces are
dictated by the longitudinal position error. Keeping
the thruster position at the bow and moving the
ref-erence point aft we may still retain the same thrust
OTC 5208 PINKSTER AND NIENHUIS
3
From equation (3) RE(IT)
xt
control algorithm i.e. transverse thrust Is con-trolled by transverse errors in position of the ref-erence point. The thrust direction will be such that the position error is reduced.
When transverse thrust is Applied to the vessel at the bow, it will respond by moving in the trans-verse direction with a simultaneous yawing motion. These motions combine in such a way that somewhere
in the region of the midship there will be an
.effec-tive turning point where no transverse motions are induced by transverse thruster forces applied near
the .bow. In practice this means that if the
effec-tive point of rotation is chosen as reference point,
it will not be possible to correct transverse
posi-tion errors by means of transverse thrust applied at
the bow and as a result the system will tend to
be-come unstable.
In the aforegoing the effect of mooring the
reference point aft of the thruster was discussed.
It can be shown that moving the reference point
for-ward of the position of the thruster will not pre-sent any special problems since the transverse mo-tion response to transverse thruster forces will
always retain the same sense i.e. thrust to port
will result in motions to port. In the model tests
described in Section 5 the aforegoing effect will be illustrated clearly.
Before discussing the results of the model
tests a brief description will be given of the mo-del, the thruster arrangement and the measuring and
control system. 4. MODEL TESTS 4.1. The test
set-up-For the model tests use was made of a fully
loaded 200,000 DWI. tanker. The water depth amounted
to 82.5 m full scale with the model scale equal to
82.5. The main particulars and stability data are
summarized in Table 1. The body plan is shown in
Fig. 4.
To simplify the test set-up and control algo-rithm only one thruster was built in at frame 18.5
(125.5 m forward of the longitudinal centre of
grav-ity), Fig. 5. This thruster delivered both
longitu-dinal and. transverse thrust components as a function
of the position errors Of the reference point. The
particulars of the thruster have.been added in Table
1. The nozzle used was of the MARIN 19A type. The rpm, torque (power) and total thrust were
continu-ously measured during the tests. At the maximum
num-ber of revolutions,
so
rpm, this thruster is capableof delivering 440 t thrust. From a practical point
of view these would appear unrealistically large
values. This thruster was, however, chosen so that the required thrust could be met at all times. This allowed determination of required thrust even for
high sea conditions which would normally be excluded
for DP operations thus enabling determination of
limiting sea conditions based on different assump-tions with regard to actually installed power. In
reality the thrust would be generated by 2 to 4
thrusters located in the vicinity of the model
thruster.
During the tests the number of revolutions of
the thruster was variable from 0 to 80 rpm fu/1 scale. The thruster angle a was variable from -450' to +450% A limit was imposed on the rate of change
of both variables in order to obtain realistic
control characteristics. For the azimuthing angle a
maximum velocity of 19.8 deg/s was applied while the
maximum rate of change of the thruster rpm amounted
to 7.2 rpm/s.
The position of the tanker was measured with an
optical tracking system giving the position of a ship-fixed light source in space-fixed co-ordinates.
The ugh source was located at the bow (x = 148.38,
y = 0, z = 20.42 with reference to the centre of
gravity). Along with the measured yaw, roll and
pitch this completely determined the position of the ship.
The point of the ship which was to be posi-tioned (the reference point) could differ from the point where the light source was located. In. such
cases. the measured position reference signals were
combined to give the .position of the reference
point. This point was given the same vertical posi-tion as the centre of gravity and could have a
dif-ferent longitudinal co-ordinate for every test.
The composition of the 6 position signals was
carried out
in
real time in a shore-based computerand was performed every 0.1 seconds on model scale
(0.91 s full scale). The resulting position of the
reference point contained both low frequency motions (associated with the second order wave drift forces) as well as wave frequency motions.
The latter motions cannot be counteracted by active thruster employment. Therefore these motion components were eliminated from the total reference point motion by applying low pass filters. To avoid phase shifts associated with normal analog filters
and as two-sided filters cannot be used in real time
problems (unless large phase shifts are accepted), one-sided filters have been developed with minimal
phase shifts.
These so-called causal filters were obtained by comparing a -motion record containing both high and low frequency motions with the corresponding
per-fectly (low pass) filtered signal by means of system identification, Ref. [5].
Similarly one-sided differentiation filters
were developed with which the low frequency
veloci-ties
of
the reference point were obtained. Becauseof differences in motion transfer functions for
surge, sway and yaw in principle 6 filters were nec-essary for adequate position filtering.
After filtering the resulting position of the
reference point and its Velocity contained almost
only low frequency components. The difference be-tween the actual and required values of the refer-ence point position and velocity' were transformed
into ship-fixed co-ordinates. By applying a PID
controller extended with an average term one arrives at the required thrust of the propellers':
. .
= cx Ax + bx x + ix
f
Ax dt + Xaver (6)Xreq
In which C is a constant derived from still water thrust-rpm measurements. The average terms, in the above formulae equal the estimated mean
environmen-tal forces and serve the same purpose as the
inte-grators, i.e. to prevent the Ship from having an
average position error. The use of an average term
is favoured as integral terms tend
to destabilize
the control mechanism. However, in full scale
opera-tions the average forces are usually unknown.
The spring and damping coefficients used, were
determined by the environmental conditions, the
allowable offset and the mass (including added mass)
and hull damping of the vessel. In Ref. [6] rela.,
tions have been derived for optimal control
coeffi-cients also showing that the hull damping may
signi-ficantly influence these optimal coefficients. For
the tests an allowable position deviation of
approx-imately 4.0 m was assumed leading to spring coeffi-cients having values between 10 t/m and 30 t/m, and damping coefficients between 20 ts/M and 100 ts/m..
For most tests use was made of the average. terms
Xavery Waver* In one test integrators were used.
With the above test set-up a large number of tests have been executed in which the environmental conditions were changed as well as the position of the reference point and the control coefficients.
In the tests waves, wind and current were gen,-crated in the Wave and Current Laboratory of MABIN. This basin measures 60 m
x 40
m with a maximum waterdepth, of I m. Irregular waves can be generated
inde-pendently from two sides thus allowing cross-seas to
be investigated. Current is generated over the
length of the basin by large capacity axial pumps
situated in Current ducts external to the basin.
Wind is generated by means of batteries of portable
fans. Fig. 6 shows the test set-up in the basin
along with the position of the fans and the initial
position of the Vessel. This figure also includes the co-ordinate system and sign conventions which
have been used. 4.2. Test conditions
Five different wave spectra have been
consid-ered in the model tests. The spectra of these sea
states are shown in Fig. 7. One of these represented
cross-seas conditions with a resultant significant
wave height
H113 = 5.36
m (with current).The other four wave conditions represent uni-directional seas ranging from what is considered as
a limiting operational condition (H111 = 4.29 m, To = 10.1 s) to a more severe surviva/-aike condition
with significant wave height H1/I = 7.19.m and peak period To = 14.5 s. In some of ale tests 1 kn. cur-tent was present. In most cases the current is di-rected perpendicular to the waves leading to a more unfavourable condition where the ship will have an average heading not Coinciding with the wave
direc-tion. In such cases the wave forces in sway and yaw
direction may be considerable leading to possibly
larger position offsets and power levels.
The adjusted wind velocities correspond to the wave heights: Vw = 36 kn. for the lower sea states
(Beaufort
8)
and Vw = 50 kn. for the most severecondition (Beaufort 10). In two tests the wind
di-rection was changed to see if this sudden alteration
of environmental conditions would lead to
instabili-ties of the system. These tests simulate the event
that the wind direction changes suddenly.
The old
sea state will endure in that case as there has been
no time yet for formation of waves coming from the new wind direction.
As stated in the previous sections the choice of the reference point may strongly
influence the
position capabilities. Therefore the position of
this point has been varied for one environmental
condition. The longitudinal co-ordinate was changed
with intervals of 0.125 Lpp starting at the bow
working aft. In order to show that the vessel
can
also be positioned near a SPM the point of reference
was also located at
200.0
m forward of midship(ap-proximately 50 m forward of the bow).
Table 2 summarizes the test conditions for
which results are presented in this paper.
4.3.
Test_2rocedureFor each test the model was initially held
in
astationary position at an angle of 45° in the basin,
see Fig.
6.
In this position the reference pointcorresponded with the required position In the
hori-zontal Plane. All measured signals refer to this
initial position. After starting the current pumps,
the wind fans and the wave generators, the model was
released and it then rotated in yaw to assume the mean heading commensurate with the sea condition
while keeping the reference point in the same posi-tion. The thruster control algorithm included
aver-age longitudinal and transverse force terms, see
equations
(6)
and (7). These were set to a givenvalue prior to the tests in order to reduce the mean
offset of the reference point. For one test
integra-tors were used to this end. The test duration of all tests corresponded to 1.5 hours full scale.
All Channels were digitized and recorded by a POP-11 mini-computer. Directly after each test all
channels were subjected to a 'limited statistical
analysis. Final analysis including combination of
signals and filtering took place on a CDCCYBER. The
Yreq = Cy Ay + by vy +. 1y
f
Ay dtWaver . . (7)
in which: T1
Xreq = required longitudinal thruster force
component
yreq = required transverse thrust force
component
Ax, Ay x. longitudinal and transverse errors of
reference point position v , v
T1
X waver
x y
aver = required average thruster forces = rate of change of position error time interval of integration term
C, b, = control coefficient
From these quantities the thruster angle and the
re-quired number of revolutions are derived:
a =
req arctap (Yreq/Xreq)
(8)
nreq = C
\i/Xreq2 + Yreq2 . . .
. ...
(9)OTC 5208 PINKSTER AND NIENHUIS
time recor4s of the thruster rpm, the thrust and
torque, the longitudinal and transverse thruster
forces Fy and F,1. and the thruster angle a were
digi-tally filtered to remove components with frequencies
higher than m 1.27 rad/s full scale. This means
that these quantities retain fully any wave
frequen-cy components present in the measured signal. The
power signal which was obtained from the product of
torque and rpm was filtered to remove frequencies
higher than w 0.46 rid/s.
5. DISCUSSION OF TEST RESULTS
The main results of the tests it stationary conditions are given in the form of tables
contain-ing the results of the statistical analysis of the measured signals, sample time plots of the measured data and contour plots of the vessels' position in
the horizontal plane at time intervals corresponding
to 3 minutes full scale. The contour plots cover the
complete test duration of 1.5 hours full scale.
For the tests carried out with fast changing
wind conditions contour plots are given at 19 s
in-tervals. The transient behaviour of the measured
data during the heading changes are also given. No statistical analyses are given since the phenomena involved were transient. For the thruster angle a,
no results of the statistical analysis are given.
This is due to the fact that the thruster angle
varied from 450° to +450°. This resulted in the
situation that in some cases the thruster angle
could vary about 360 degrees while at other times it
varied about 0°. See for instance the results of
Test No. 6316 in Fig. 12. Statistical analyses of
such signals give an incorrect impression of the
thruster behaviour. The effect of the thruster angle
is correctly included In the results of the
longitudinal and transverse thrust components Fx and
Y.
5.1. General behaviour
A first impression of the behaviour of the
vessel in the horizontal plane is given in Fig. 8 to Fig. 10. The contour plot of the vessel
consists of
the outline of the vessel and on the centre line a line drawn from the bow to the reference point on
the vessel. On the contour plots it is seen that the
reference. point was varied from midship to ahead of
the vessel. In all cedes the reference point was on
the centre line.
Except for the tests with wind changes, (Test
No. 6304 and Test No. 6329) the vessels behaviour in
stationary conditions can be described In terms of a
mean position of the reference point, a mean heading and superimposed, slow position and heading changes. A striking feature of the motion shown on the con-tour plots is that the vessel yaws about the refer-ence point while, as indicated in Section 2, the
mean heading of the vessel is in accordance with the mean weathervane heading commensurate with a verti-cal axis through the location of the thruster which
was always located 125.5 m forward of the Centre of gravity.
The results of the measured thruster rpm and
thruster azimuthing angle records given in Fig. 11,
12 and 13 show that in general these records contain
very little wave frequency components. This reflects
the efficiency of the low pass filtering which was
applied to the measured position errors. In the
thruster forces FX and Fo on the othery hand signi ficant wave frequency oscillations are seen for some
test conditions. These wave frequency components in the forces are clearly not due to variations in rpm but rather due to fluctuating thruster inflow
velo-cities resulting from wave frequency relative
Mo-tions between the water particles and the thruster.
As such, these high frequency thrust and also torque
and power variations are unavoidable.
5.2. Effect of position of the reference point The characteristic behaviour with respect to
the mean heading is clearly demonstrated when com-paring the contour plots of Tests No. 6306, 6308, 6310 and 6312 in Fig. 8, in which the position of the reference point was varied from 148.4 to 0 in forward of the centre of gravity while all tests were carried out in the same sea conditions.
The sea condition consisted of irregular waves
with a significant wave height of 4.3 m, a 36 kn. wind parallel to waves and a 1 kn. current at a tight angle to wind and waves.
The mean heading is practically the same for these tests which is in agreement with the analysis
given in Section 2. The motions about the mean
posi-tion are very clearly around the reference point
selected for each of these tests.
It was indicated in Section 3 that control
stability would reduce as the reference point was moved aft. This is clearly demonstrated in the
con-tour plots of these tests as it can be seen that the
yaw motion amplitudes become increasingly larger as
the reference point is moved aft. The corresponding
sample time plots of the motions, thruster power,
the longitudinal and transverse thrust components, the thruster azimuthing angle and the thruster rpm are shown in Fig. 11. The time plots all cover the same section of the tests with respect to the wave elevation record and may be compared directly to
show the effect of moving the reference point aft.
From the results it can be seen that for Tests
No. 6306, 6308 and 6310 minor differences are pres-ent. For Test No. 6312 however, in which the refer.
ence point was situated at the centre of gravity, the reference point motions KR and YR and the yaw motion * increase considerably. A significant in-crease in required power and thruster force
fluctua-tions are shown. Whereas in Tests No. 6306, 6308 and
6310, the maximum thruster power did tot exceed
ap-proximately 7700 kW, in Test No. 6312 the peak power
amounted to 29,600 kW. The above data are given in Table 3 and Table 4. From Table 3 it can also be seen that the difference between the maximum posi-tive and maximum negaposi-tive values of the reference point motions KR and YR indrease somewhat as the
reference point is moved aft. When the reference
point was chosen at the centre of gravity the motion
showed a sharp rise thus reflecting the fact that the system is near to becoming unstable.
It Should be mentioned that the abovementioned tests were carried out with the same values of the
6
OTC 5208 PINKSTER AND NIENNUIS
7
control coefficients (see equations (6) and (7)). This was done purposely to demonstrate the trend
more clearly. The motions for the aft-most reference
points could be reduced if the control coefficients were optimized. The above tests show that for loca-tions of the reference point ranging from
approxi-mately 77.5 to 148.4 m forward of the centre of gravity (see Test No. 6306 and Test No. 6308), the
motions of the- reference point remained within a
circle with radius of about 4.2 m relative to the mean position. For the water depth of 82.5 m this
represents a positioning accuracy of about 5% of the water depth.
5.3. Effect of a small increase in the wave height
In order to investigate the effect of a slight
increase in the significant wave height, Test
No.
6313, with significant wave height 111/3 ,.. 4.74 m Was
carried out. The wind speed again-amounted to 36 kn.
parallel to waves and the current to 1 kn.
perpendi-cular to waves and wind. The reference point was
77.5 m forward of the centre of gravity. The results
of this test are directly comparable to the results
of Test No. 6308. The time plots in Fig. 12 again cover the same part of the test run. The comparison
of the time traces generally shows that the motions,
forces and thruster power increase with the wave
height.
The maximum thruster power amounted to 10,800
kW with a mean of 2,841 kW (7,436 kW and 2,065 kW respectively for Test No. 6308). The motions of the
reference point remained within a circle with radius
of about 4.5 m centered around the mean position
which is less than 6% of the water depth.
5.4. Choosing a reference point 50 m.fOrward of the bow
---In the same sea conditions as Test No. 6313, the reference point was moved to a point 200 m for-ward of the centre of gravity and Test No. 6316 was
carried out. This reference point corresponds to a point some 50 m in front of the bow, on the centre line of the vessel. Such reference points could be
relevant when dynamically positioning a tanker close
to a single point mooring.
In this condition the peak thruster power amounted to 11,000 kW with a mean power of about 2,900 kW. The motions of the
reference point remained within
a
circle with radiusof 7.2 in of the mean position,
see Table 3. The
contour plot of this test is shown in Fig. 9. It is again clearly seen that the mean heading is the same as found for Test No. 6313. The horizontal motions about the mean heading again are centered About the
reference point ahead of the Vessel.
5.5. Effect of adding integral terms in the control
algorithm
Test No. 6327 was carried out in the same sea
conditions as Test No. 6313 and for the same
refer-ence point position. The control coefficients cx, c
bx and b (see equations (6) and (7)) were also the same. In Test No. 6327, however, use was made of
in-tegral terms in the control algorithm. The effect of
the integral terms is to reduce the mean offset of the reference point to small values. The effect is clearly seen when comparing the results for XR and
YR in Fig. 12 and in Table 3.
5.6. Performance in an irreglillr cross-sea
Test No. 6317 was carried out for the same sea
condition, reference point potation and controller
settings as Test No. 6313. However, an irregular swell-like cross-sea spectrum was added which had a
significant wave height of 2.5 in and a peak period of 12.5 s. These waves were generated parallel
to
current (see Fig. 10). The resultant significant
wave height due to the Simultaneous presence of both
-irregular wave trains amounted to 5,3 in with a peak
period of 10.1 s. The ma-Latent spectrum of the wave
elevation record is Shown in Fig. 7.
Comparing the contour plots of Test. No. 6313
given in 'Fig. 9 to those of Test No. 6317 given in
Fig. 10 it is seen that adding the cross-sea results in 'a change of the mean heading so that the vessel
lies more beam-on to wind. At the same time the
total wave excitation is increased which shows in the larger motion amplitudes Seen in Test No. 6317. In this test a peak power value of 14,500 kW was reached. The mean power amounted to 4,160 kW. The
reference point remained within a circle with radius
7.5 in centered around the mean position. 5.7. Behaviour in extreme .conditions
Two tests were carried out in sea conditions
which could be considered as extreme. In such
condi-tions loading or discharging operations would not
normally take place. The vessel could, however, be
required to stand by, waiting for improvement in the
weather. For these tests the reference point was
Chosen at the bow (x 148.4 m). Test No. 6303 was
RP
carried out in irregular waves with a 7.19 m
sig-nificant wave height and 14.5 s peak period and with
a 50 kn. steady wind parallel to waves.
In this condition the vessel lies almost head-on to the waves (see Fig. 10). The motion of the vessel is dominated by large amplitude low frequency
surge motions as shown In Fig. 13. The thruster
force is almost entirely directed along the
longitu-dinal axis of the vessel. Roll, sway and yaw motions
are small. In order to reduce the thruster forces and power, the control coefficients were lower than
for all previous tests. The reference point remained
within a circle with radius of 12.5 m of the mean
position. The maximum thruster power amounted to
14,564 kW with a mean value of 4,548 kW.
Test No. 6302 was carried out in waves with a significant height of 6.99 m and a peak period of 14.5 s. A 50 kn. wind and a 1 kn. current were
gen-erated in a direction perpendicular to the waves,
see Fig. 10. This situation is not realistic for
steady conditions. It was tested specifically to
in-vestigate the behaviour of the system when the ves-sel is forced to take high bow-quartering waves.
As can be seen from Fig. 10 the yaw motions are
relatively large and the ability to station the
ref-erence point has deteriorated. Due to the large
angle between the waves and the longitudinal axis of
the vessel, roll motions were considerable with
a
significant value of 13.4 degrees. From Fig. 13-it
is seen that large transverse thruster force
varia-tions are needed to keep station. The reference
point remained within a circle with a radius of 24 in
amounted to 10,238 kW with a peak value of 29,090
kW.
5.8. Effect of sudden chart/es in wind direction
Two tests were carried out to investigate the
effect of fast changes in wind direction on the
behaviour of the vessel. In both cases the test was conducted under steady conditions with wind parallel to waves. After 0.5 hours full scale under steady conditions the wind speed was abruptly reduced to zero and simultaneously the same wind speed was gen-erated in a direction perpendicular to the waves. As a result the Vessel was forced to undergo a heading change and assume a new mean heading commensurate with the changed conditions. The wave direction and height remained unchanged. This sequence of events simulates to some degree sudden changes of wind as can occur in cyclone prone areas. The test condi-tions of both tests are indicated on the contour plots in Fig. 9 (Test No. 6329) and in Fig. 10 (Test
No. 6304) respectively. In both figures the wind
direction change is denoted by the dashed line
arrow. The contour plots in these figures made at
time intervals of 19 s full scale cover the transi-tion. The time plots of the measured data covering the period in which the vessel changes heading are shown in Fig. 12 and in Fig. 13. The measured data indicate that in both cases the vessel assumed the new mean heading smoothly and within a time interval
of about 500 seconds full scale.
6. CONCLUSIONS
The results shown in Section 5 confirm the
theoretical predictions that a dynamic positioning system based on the use of one azimuthing thruster
at the bow of the vessel constitutes a stable
weathervaning system which takes up a stable mean heading dictated by the position of the thruster and the ambient environmental conditions. Furthermore,
as was also predicted by theory, the reference point on the vessel need not coincide with the position of the thruster but may assume a More or less arbitrary position, forward of the midship. It was also con-firmed that the DP system tends to become unstable when the reference point is situated near the
mid-ship.
The conclusion that this DP system constitutes
a minimum power system is. primarily based on results
of computations of the mean forces in the stable equilibrium position. An example of results of such calculations has been given in Section 2. The model tests presented in this report Confirm that for the
vessel concerned, the power .requirements
of
thissystem are considerably lower than the power
re-quirements of conventional DP systems since these
are generally designed to operate at non-optimal headings.
The model tests described in this paper were carried out using one azimuthifig thruster situated at the bow of the veSsel which supplied both longi-tudinal and transverse forces. In reality, due to /imitations in the size of available thrusters, use
would have to be made of two or more thrusters
depending on the required performance. It should be noted, however, that for the longitudinal force use can also be made of the main propulsion system of
the vessel provided the longitudinal thrust is
con-trollable.
One of the parameters which has not been
in-vestigated here is the loading condition of the ves-sel. All tests were carried out for the fully loaded
condition. In designing a system for a particular
tanker it is recommendable that other loading
condi-tions also be investigated. Due to the large draft changes which are possible, large changes in the
relative magnitude of the wind, wave and current
forces will occur. This will also have its effect on the DP behaviour.
In this paper emphasis has been placed on the results of model tests. Prior to these tests
numer-ous time domain simulation calculations were carried Out in order to gain insight in the DP system behav-iour. Due to time limitations, mo data have been
in-cluded on the comparison between results of simula-tions and model tests. This comparison will be the
subject of a future paper.
7. NOMENCLATURE
thrust coefficient -(equation (9))
measured longitudinal and trans-verse thruster force: components. Derived from instantaneous measured thrust value and azimuthing angle of the thruster
estimated average longitudinal and transverse thrust. components (equa-tions (6) and (7))
longitudinal and transverse thrust components required by the control-ler (see equations (6) and (7)) Mean longitudinal force, transverse force and .yaw moment about the centre of gravity due to the envi-ronmental conditions_and dependent on the mean heading ti)
total average environmental force for the stable equilibrium heading
.significant wave. height 4/;(7)
wave spectral density thruster power spectral peak period
motions of the reference point in an earth-fixed system of axes (see Fig. 6). These motions include wave frequency and low frequency compo-nents
coefficients for the thrust control algorithm (equations (6) and (7)) variance of the wave elevation record.
measured rpm of the thruster required thruster rpm (equation (9))
low pass filtered rate of change of
ax, ay
respectivelylongitudinal distance of thruster forward of the centre of gravity of the vessel
longitudinal position of reference point forward of the centre of gravity F F X' Y Xaver' Yaver Xreq, req Fl H1/3 S(w) -P 0 XR, YR c- c b x' y. xb. y
x'y
mo rpm nreq vx,Vy xt xRpFY (T)
%Elif
IPAx-Re1/31. *a1/3' 2x1/3 *reqzero to maximum peak Value zero to maximum trough value significant zero to peak value significant zero to trough value significant peak to trough value required thruster azimpthing angle (equation (8))
wave, wind and current direction
with respect to longitudinal ship
axis
= yaw or heading angle of the vessel relative to the initial heading
angle- at the start of the test (see
Fig. 6)
* mean heading of
the
vessel relativeto the environment' pitch angle
roll angle
16w pass filtered longitudinal and
transverse co=ordinates of the
re-Oited position of the feference
point
in a
ship-fixed system ofaxes
wave. frequency
root-mean-square value (standard deviation)
* integration time of the integral
terta in the control algorithm
(equations
(6)
and (7))* wave elevation 8. REFERENCES
Wheim, H.
Gregersen, S. and Jenssen, N.A.:"Dynamic Positioning-.in Single Point Moorings",
Paper No.-4606, Offshore Technology
Conference, 1983, Houston.
Pinkster, J,A.: "Dynamic Positioning of Vessels
at Sea", Paper No. 105, Courses and Lectures
at
the Department Of EZpetimental Methods
in
Me-chanics, CISM, Udine, October 1971, MARIN
Publication No. 419.
"Prediction of Wind and Current Loads on
VLCC'S", Published
by:
Oil CompaniesInterna-tional Marine Forum, 1977, London.
Pinkster, J.A. : "Low Frequency Second
Order
Wave Exciting Forces on-FlOating Structures",
MARIN Publication No. 650, 1980.
Willemstein, A.P.: "Causaal Filteren", MARIN
Report No. HSO369-CA, WageningeO, 1983 (in
Dutch).
Niehhuit, U "Situlationt, of Low Frequency
Mo-tions of Dynamically Positioned Offshore
Struc-tures", Spring Meeting Royal Institute of :Naval Architects, London, 1986,
OTC 5208 PINKSTER AND NIENHUIS
OTC 5208
-10-Pinkster/Nienhuis
List of captions
Table 1
Main particulars of tanker / Main particulars of thruster
Table 2-
Summary of model test conditions
Table 3
Motions
Table 4
-Thruster ihfo
Fig. I :
Definition of environmental forces and thruster forces
Fig.
Mean environmental loads on a 200,000 DWT tanker
Fig. 3 :
Mean environmental force on a 200,000 DWT tanker in the
stable equilibrium heading
Fig. 4 :
Body plan of a 200,000 DWT tanker
Fig. 5
Azimuthing thruster arrangement
Fig. 6 :
Test set-up and co-ordinate system
Fig.
Fig. Fig. Fig. Fig. Fig. Fig. 7 8 9 10 11 12 13:
Spectra of irregular waves
:
Contour plots
:Contour plots
:Contour plots
:Time plots of
Time plots of
Time plots of
of model tests
Of model tests
of model tests
signals recorded
signals recorded
signals recorded
during DP model tests
during DP tOdel tests
during DP model tests
OTC 5208
-Ii-Table 1
MAIN PARTICULARS OF TANKER
Length between perpendiculars
Lpp m309.98
Breadth
B rn47.17
Depth. H
m
29.60
Draft
T
m
18,90
Displacement
at
240,897
Centre. of buoyancy fOrward of
FIT
m
6.81
Section 10
Centre of gravity above keel
TG
13.32
Metacentric height
71.in
5.78
(
Longitudinal radius of
kgyration
:YY
.
77,47
Transverse radius of gyration
k inxx
17,00.MAIN PARTICULARS OF THRUSTER
Designation
SymbolUnit
Magnitude
Diameter
Dm
8.25
Expanded blade
AE/Ao
0.487
Hub area ratio
d/D -0.288
Number of blades
z - 4Nozzle type
-19A
Table 2
SUMMARY OF MODEL TEST CONDITIONS
IRREGULAR WAVESWIND
CURRENT
Position
reference
point
No.
Test
Direction'180°
Direction 900
Speed
Direc-forward of
Remarks
centre of
tion
Speed
Direc-
tiongravity
H1/3
To
H1/3
Toin m
in sin m
.in0s
in kn, in deg,
in k . in deg.in m
6302
6.99
14.5 50 9090
148.4
6303
7.19 14.5 50 180148:4
6306
4.29
10.1 -36 180 1 90148.4
6308
4.29
10.1 -36 180 1 9077.5
6310
4.29
10.1 -36 180 1 9038.8
6312
4.29 10.1 36 180 1 900.0
6313
4.74
10.1 -36 180 190
77.5
6316
4.74
10.1 -36 180 190
200:0
6317
4.74
10.1 2.5 12.5 36 180 1 9077.5
Cross-sea
6327
4.74 10.1 -36 180 1 9077.5
Integrators
Table 3
MOTIONSTest
No. XR (m) YR (m) YAW (deg) ROLL (deg) PITCH (deg) _ _ _ 2 X aXi
+ X1-/
max+ max-If a Y1Y1/3- Ymax+
Ymax-* a
*1/3+
*1/3-*max41/3 *max+
*max- °max-01/3 °max+ 63024.48 7.19
14.575.23 25.37 10.05
0.37 3.84
6.28
5.10 12.06 10.331 -6.79
5.710.08 -14.82
6.80 -25.92 13.36 10.45 -10.61
3.31 3.02-3.17
6303-3.54 3.83
0.64
8.22
8.20 12.21
4.14 0.89
5.41 +3.067.66 +2.28'41.93
1.66 43.64 +39.93 44.39 +36.55
1.59 1.25 1.41 2.28 1.88 1.87 63061.25 0.83
2.44 +0.23
4.05
0.861.54 0.53
2.38 +0.794.13 +0.15 18.33
1.13 19.73 +17.06 21.28 +15.04
1.20 1.27 1.30 0.680.68
0.74 63080.00 0.96
1.33 1.20 3.232.33
2.52 0.52
3.32 +1.784.21 +0.93 19.40
1.70 21.36 +17.30 23.33 +15.34
1.00
0.95
0.88
0.63
0.64
0.58
63100.31 1.09
1.73 1.03 4.27 3.081.84 0.70
2.82 +0.89 4.180.26 19.43
2.35 22.06 +16.53 24.82 +14.08
1.03 1.000.98
0.640.64
0.65
6312-0.03 2.12
2.77
2.21 7.19 5.632.45 2.23
5.26 0.21 9.465.25 22.17
4.56 26.63 +16.16 37.87 +10.85
0.92
0.85
090 0.62
0.510.56
63130.40 1.09
1.870.93
4.43
1.852.05 0.72
3.10
+1.115.42 +0.04 19.24
1.84 21.21 +17.1223.70 +13.301
1.21 1.09 1.140.78
0.73
0.74
6316' 1.93 1.33
3.81 +0.33
5.62
3.242.75 1.09 4.38+1.40 7.71
1.73 19.43
1.06 20.66 +18.03 21.86 +16.67
1.19 1.101.06 034 0.75
0.75
63170.55 1.36
2.49
1.24 5.73 2.911.70 1.57
3.810.52
6.68
3.358.52
3.24 12.19
+4.68 15.29
2.95 2.72 2.38 2.68' 1.57 1.19 1.29 6327-0.81.1.01
0.56 2.09
2.66
4.03
0.18 0.66
1.210.72
2.60
1.51 21.23
1.76 23.46 +19.22 25.90 +16.70
1.26
1.30 1.190.70
0.64
0.73
Table 4
THRUSTER INFO
I'
(:kW)rpm (rev/min)
Ijlt (ti)
FY (tf)
Test
_ NoaP+P+
1/3
max nn1/3+ nmax+
F af +f-F+ Fm
ax_
1/3
ua
max
max-F '1. 3
F+F
1
3-max.max-6302
10238
5630 18706 29090
49
963,
74
163
63
270,
+81
369
+23
-14
87
95
207
146
340
i6303
4548
2640
8587 14564
- 38
8 '51
60
103
44
185
+37
292:+3
-14
14-1
39
1075
,6306
2255
1071
3901
7318
30 435
42
56
1985
+30
124
+11
10
21
48'26
84
84
6308
2065
991
3564
7436
.29
434
46
60
20.92
+32
139
3 5,22
45.'31
81
83
6310
2544
1087
4411
7722
32
4
38
46
65
22
'99
+33
148
53,16:
26
61 17"96
76
6312
5911
3944 13295 29575
.37
747
77
58
55
134
. 6207
248
572
116
110
383
261
6313
2841
1518
5489 10802
32 538
48
64
23
100,+32
.157
+18
27
54
36
77120
6316
2880
2023
6302 11000
31 436
44
48
.34
89
+5
134
144
H5
34
63
58
151
163
,6317
4160
2471
8790 14500
356
42
50
64
31112
+22
176
129
16
43
86
56
133
160
'6327.
3291
1456.
5852
9215
32 538
4745
23'
81
+11
129
37' 1 1625
26
53
78
OTC 5208
F-yT FYEWind, waves
current direction
\Initial
heading
4-) 500 -500-' 0 YE
Wave
:Sign. height .
4.5 m
Peak period
12.5 sDirection
180 deg.Wind
:Speed
36 kn.Direction
= 180
deg. Current,: Speed Direction. X:EFig. 24 Mean environmental loads, on a
200,D00 DWT
tanker
1.5 kn. 90 'deg_
1E5 -1E5 360 3.0180
270p in deg.
200
100
-100
Heading
in m
Fig. I: /lean environmental force on a 200,000 DWT tanker in the stable equilibrium heading.
100..
500 4-1250
M' 00
1-3 LriA.P.
6
7-10
Fig.
:
Body plan of a 200,000 DWT tanker
1.6
15-10
Frame t83
Fig. 5: Azimuthing thruster arrangement
Xeeq
(NJ
a
req,
Waves
-1800.re\IF
RP45°
XRFig. 6: Test set-up and co-ordinate system
OTC 5208
-20-Current
9.09 Waves90'
YR2.5 10.0 0.0 5.0 2.5 0.0
OTC 5208
Fig. :
Spectra of irregular waves
1-11/3. 4.3 m A
TO 10 $
DIR. 1190° CUF/RENT :1151..90° Hilw 70 m To .1455 DIR. 180 CURREN1:15/1..90° H113. 5dm TO 10.1 5 DIR. 18e/ 90° CURRENT:1kri.,90° 5.0 0.0 0.5 1.0 I/RYC FRCIXOCY IN RF10/5SPECTRUM OF CROSS SEAS : SPECTRUM 8 F
1.5 2.5 0.0 10.0 5:0 2.0 1.0 0.0 Fiu3. 4.7m To .10.1 5 DIR. .1130° CURRENT:155,9o° _ _ 111/3. 7.2 m To .14.55' DIR..180° CURRENT:01111
-21-14113 2.5 m To 12.5s DIR. 90° CURRENT:1 kft.se .01 /z
r 5.0 _.111 lc 5.0 0.0 0.5 10 1.5 -WAVE FRECRENCY IN F10/5 0.5 1.0 1.5 WE FREQUENCY IN RR13/5 0.0 0.5 1.0 1.5 NAVE FREOUDCY IN RPC/5 0.0 0.5 1.5WAVE rACDUENCY IN RA0/5
0.0 0.5 1.0 1.5
TEST No 6306
YR
TEST No. 6308
Fig. 8: Contour plots of model tests
1.kn. XR 35 kn.
43m
10.1 s TEST No. 6312 36ikn.4.3m
10.1 s 1 kn.TEST No. 6316
1kn.
36 kn. 4.7 m
10.1 s
Fig. 9: Contour plots of model tests
f\J
TEST No.6329el36km
I 36 kn. I 4.7 m 10. sSUDDEN CHANGE IN WIND DIRECTION
WITH EFFECT INTEGRAL TERMS IN CONTROL
TEST No. 6302
l\J
7 0 m
14 5 s TEST No. 6304
(1
kn.
SUDDEN CHANGE IN WIND DIRECTION
Fig.
10: Contour plots of model tests
50 kn.
XR
TEST No. 6303
01121 MS ry Tr .. RPNIVER1 Rev/oIN 111,101 DEC' 'TEST No. 6306 5.00 0 1.1 1 4 VI I IV-10.00 0 10.00-25.00 240 0 2.50 1 1DXIOT k 250.00. 0 250.00. 10.00 25. (3131 2.50 2.50 0 0000.00 250.01 250.01 0 I . -ZW.DQI 0 'I letke64 '1.41:60....M=MCOO... 0
6.4 :ma am.o an.o so. o Ta.a ro.o MO MO I
=CMOS TEST No. 6310 5.00 -1 A 1 y iv 10.00
0.0 MA ita4 mi..a sk.o =A ma ma tab sma
=Km
TEST No. 6308 5.00 0 10.03 25. 2.50 0 2.50 0 10000 250.on, 50.00 0 0 0 250./m
0 2.50 0 0Fig.
11: Time plots of signals recorded during DP model
testsII V V WO MO MO MO MO MA MO MO MO MO MO 01 sozoms 11:5T hOL 6312 5.00 0 10.00 0 10.00 V 60 01.0 MA MO LO 8L0 MA . :LO MA aLo =A MO 60
=MS
50.00 0100 ;;;;;FX 0OTC 5208
25
SR TR 11 ROLL 12ES PTTF.H. DEGYR ROVN-ItM REV/MIN RP1.41 REVimIN
OTC 5208
TEST No.. 6313 5.00 v Iiiievolesetw4w11.14144, I Aleqrtri01-
v V 31144",a0g6"..1%..._^...164.00"IINP.NPA*06-.-250. 250.°L_
50.00 50.50 -aILO SILO IRLI:1 MIL zo.a To.a ao-o 402.0 60.0 man sso.
=DOS TEST No 6316 1 0
---10.50.. TPW 25. 33 .1 DES 0 I 2.50 ...d.)24,0"egyv1.4640...,%..4.,pAtWAyo.w15...__...4.. 2.50 10100=L
,
250. 0°aL
===.7..
250. OCL 0 250. cal J so:do 0 0.0 .o, IMO M40 61.0 60.0. 271.k 60.0 d0.0 SM0 MU 16 SMINDS 25. ca 5.60 0 2:5D 0 TEST No. 6327 5.00 10.00 io.ca =CO 0 2.50 0 2.50Fig. 12: Time plots of signals recorded during DP
model tests
it t 1.01X0 0 0 MO. 03131 250.00.
ma amat 16.0 SILO asn.a co.o ma alio ea
ECM
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