Date Author Address
July 2008 J.L.F. van Kessel
Delft University of Technology Ship Hydromechanics Laboratory Mekelweg 2, 26282 CD Deift
Tuning the Air-Pressure of Aircushion
Supported
Structures at Model Scale
by
11F. van Kessel
Report No. 157 1-P
2008
Published in: Proceedings of the 18th International Offshore and Polar Engineering Conference, Vancouver, Canada, ISBN: 978-1-880653-70-8
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Tuning the Air Pressure of Aircushion Supported Structures at Model Scale
J.L.F. van KesselOffshore Engineering Department, Delft University of Technology,
Delft, The Netherlands
ABSTRACT
To allow transportation of bottom-founded offshore structures from a shallow building dock to deeper water, the draft of some structures is
temporarily decreased by pumping compressed air underneath the
construction. At the final location, the air is released and the structure is installed on the seabed. Motion behaviour and stability change when air escapes from the cushion underneath the structure.
This paper describes the change in motion behaviour of an aircushion supported structure at different drafts. Calculations are performed based on linear three-dimensional potential theory using a linear adiabatic law
to describe the air pressures inside the cushions. The water surface within the aircushion and the mean wetted surface are modelled by
means of panel distributions representing oscillating sources.
Results of model tests of an aircushion supported structure at a constant
draft are included and serve as a validation of the computational method. The description of the motion behaviour also includes a discussion of the heave added mass, damping, cushion pressure
variations and structural loads.
KEY WORDS: Aircushion support; motion behaviour; air pressure; structural loads; wave bending moments.
INTRODUCTION
The use of aircushions to support very large floating structures,
although only used in few applications, has been known for a long time in the offshore industry. In most of these cases the draft of a bottom-founded structure was temporarily decreased by pumping compressed air underneath the construction to allow transportation from a shallow building dock to deeper water.
The Khazzan Dubai oil storage tanks installed in Arabian Gulf in 1969
were probably the first large floating offshore structures passively
supported by air. Chamberlin (1970) and Curtis et. al. (1970) described the design, construction and installation of Khazzan Dubai oil storage tank No. 1. Eventually this structure was joined by two sister structures
129
in the early seventies, in order to float these open-bottom structures and towing them from the construction yard to the final location 60 miles offshore, air was pumped underneath the roof of each structure and pressurized until it supported the weight of the unit.
Once on location, the structure was submerged by venting the air under
the roof. The sudden release of air reduced the pressure and the unbalanced weight of the structure caused a dynamic descent. The
process continued with an increasing draft and angle of tilt up to 22 degrees until the structure was supported by its centre bottle. Each unit
contained an internal bottle shaped tank as an integral part of the
structure which was employed to maintain stability during
submergence. Submergence continued by pumping water into the bottle as described by Burns et. al. (1972).
Another example is the installation of the Maureen Gravity platform in
1983 as described by Berthin et. al. (1985). During this operation
compressed air was pumped underneath the bottom to float the 42,600 tonnes structure. The platform was finally towed out of the dry dock on its aircushion with a draft of 9. I metres.
Aircushions were also used to lift the 218,000 tonnes bottom section of
the Gullfaks C Condeep structure to a buoyant condition from the
construction dock in 1987. About 96% of the buoyancy was provided
by aircushions during this operation. The tise of air to improve the floatability of the structure was also used on the first Condeep's in
1974. To some extent aircushions were used in all subsequent Condeep projects as described by Kure and Lindaas (1988).
The behaviour of large aircushion supported structures in waves was studied by Pinkster et. al. (1997 2001) and Van Kessel et. aI. (2007) at Delft University of Technology. Model tests carried out by Tabeta
(1998) in the towing tank of the Ship Hydrodynamics Laboratory
served to validate the results of the computations. Pinkster (2001) and Meevers Schulte (1999) also performed model experiments of a large aircushion supported Mobile Offshore Base (MOB) in 1999. During
these model tests, air escaped underneath the structure at high sea
states, which was due to the fact that wave troughs were deeper than the
draft of the structure. As a result the volume of the aircushion
process of air leakage continued until the draft of the vertical walls
around the aircushion was deeper than the deepestwave trough.
Lee and Newman (2000) performed computations which gave a good description of acoustic disturbances in the aircushion. Thiagarajanet.
al. (2006) investigated the wave-induced motions of air-supported
offshore structures in shallow water by means of an analytical approach and model tests. Ikoma et. al. investigated the behaviour of aircushions
on floating structures at the College of Science and Technology at
Nihon University, this research was mainly aimed at investigating the
effects of air-chambers on the
hydroelastic response of floatingstructures (2002 - 2007). Tsubogo et. al. (2002) used a different
numerical approach to calculate the behaviour of an elastic aircushion supported structure.
The present contribution describes the behaviour of an aircushion
supported structure at different drafts, in which the displacement
remains
unchanged. A change
in the aircushion volume and subsequently the aircushion pressure results in a different motionbehaviour which can be of particular interest when aircushionsare used
for the installation of offshore structures as discussed before.
Firstly a review of the numerical approach will be given in this
contribution. Next the set-up is described of the model tests of an
aircushion supported structure at constant draft. Finally the behaviour
of an aircushion supported
structure at different drafts will bediscussed.
NUMERICAL APPROACH
The structure is assumed to be rigid and passively supported by one or more aircushions that may or may not be interconnected. No fans are
needed to maintain the air pressure in the cushions. Furthermore, the
aircushions are hounded by the rigid part of the construction which
extends sufficiently
far below the mean water level
within anaircushion in order to ensure that no air leakage will occur. lt is
assumed that no air from the cushions will be dissolved by the water.
The volume change in the aircushion is reversible and describes a
adiabatic process of the form:
PVK = constant
(I) When considering a conventional rigid body, the motions of the
structure are determined by solving a 6 d.o.f. equation of motion taking into account the wave forces, added mass, damping and restoringterms.
lt is customary to determine the wave forces on a captive structure
based on the undisturbed wave potential Ø and the solution of the
diffraction potential Ød . Added mass and damping coefficients are based on the motion potentials Ø obtained by oscillating the structure
in the six modes of motion in still water.
A different approach should be followed for a construction partially
supported by one or more aircushions in order to determine the
motions, pressure in the cushions, added mass and damping coefficients and other relative quantities such as structural loads and drift forces.
In this approach of aircushion supported structures, the rigid part is modeled in the usual way by means of panels representing pulsating sources distributed over the mean wetted surface of the construction. The free water surface underneath the structure is modeled by panels
representing oscillating source distributions laying in the mean free surface of each cushion. The mean surface level of individual cushions may be substantially different from other cushions and the mean water
level outside the structure.
All panels of the free surface within an aircushion are assumed to
represent a body without material mass, but having added mass,
damping, hydrostatic restoring and aerostatic restoring characteristics. Each free surface panel has one degree of freedom being the vertical
motion of panel n within cushion c. The total number of degrees of
freedom (D.O,F.) therefore amounts to:
D.O.F.=6+N,.
(2)in which:
N
= number of panels in cushion c = number of aircushionsThe number 6 represents the six degrees of freedom of the rigid part of
the structure.
The wave force
X,,, theadded mass and damping coupling
coefficients a,5 and b,5
are determined in the same way as is
customary for a multi-body system. The mean underwater part of the structure is discretised into a number of panels representing pulsating sources as is the case with each free surface panel within an aircushion.
The contribution of the total potential due to the discrete pulsating source distributions over the structure and the free surface of the
aircushions can be expressed as:
(3)
total number of panels used to describe the
structure and free surfaces of all cushions X1,X2,X3= a field point
A4, A2 , A3=location of a source
Green's function of a source in A relative to a
field point
surface element of the body or the mean free
surfaces in the aircush ions
strength of a source on surface element s due to motion mode j
potential in point due to j -mode of motion
The unknown source strengths o are determined based on boundary conditions placed on the normal velocity of the fluid at the centers of
the panels:
m=l,2....¡ç
(4)The right hand side of the above equation depends on the case to be
solved. If the source strengths for determination of the diffraction
potential are required the normal velocity vector becomes:
n t) -
_ød__ø()
(5) n,,, - n,,, in which: N, = X = A =G(X,A)
= AS, o.,j = =øi()
=lt should be remembered that in this case the wave loads due to the incoming waves and diffraction effects are defined as being the loads on the structure and the individual free surface panels in the cushions, all being fixed. The initial added mass and damping coupling
coefficients are found by applying normal velocity requirements. For the six rigid body motions (j = 1,6) of the structure:
j = 1,6 (6)
in which the panel index ni covers only the panels on the structure. 0mj are the general directional cosines for the panels on the structure given by: = cos(n,,,x1 ) = cos(n,,,,x2) n,,,3 = cos (n,, , (7) = X,,,2 n,,,4 - X,,,3 fl,,,2 n,,,5 = Xn,3 fln,i - X,, 11m3 = X,,,1 n,,,2 - x,,,2 11mi where:
Xmi = co-ordinates of the centre of a panel relative to the body
axes.
When the six rigid body motions are considered, the normal velocity
components on all cushion panels are equal to zero. For the
determination of the added mass and damping coupling arising from the
normal motions of individual cushion panels, the normal velocity
boundary condition is zero except for one cushion panel at a time for which the following value holds:
=1
aa,,,
where the value - I follows from the fact that the free surface normal is pointing in the negative X3-direction.
From the solutions of the source strengths for all these cases the wave force vector X,,, added mass a,, and damping coupling coefficients
b,,.2 can be obtained. The wave force follows from:
X,, = - p w2 (ø0 + ød.k ) .SThk (9)
k..I
(8)
in which:
ød,& = diffraction potential at k -panel obtained from Eq. (3)
X,, = wave force in the n -mode, n = 1,6 for the structure
N,, = number of panels involved in the force in the n -mode.
For the force on a cushion panelN,, = I. For the force on the structure N,, = N,
= generalised directional cosine of k panel related to n
-mode
¿ S,,,. area of k -panel related to the force in the n -mode
131
The added mass and damping coefficients follow from:
k..l
b,1 =-
1rn[PwØik
,,,k n,kin which:
motion potential value on k -panel obtained from Eq. (3) The restoring coefficients consist of two contributions, i.e. an aerostatic spring term and a hydrostatic spring term. The hydrostatic restoring term is equal to the product of the waterline area, specific mass water
and acceleration of gravity. The aerostatic restoring terms are related to
the change in air pressure in an aircushion due to, for instance, unit
vertical displacement of a free surface panel. The vertical displacement
of a cushion element is the result of the corresponding forces on all
panels belonging to the same cushion and the forces on the rigid
structure. Displacing the structure in any of the three vertical modes
heave, roll or pitch will change the volume of an aircushion thus
inducing pressure changes and consequently forces on all free surface
panels and the structure itself.
In the next equations, motions and force modes of the rigid part of the structure are considered when n = 1,6 and j = 1,6. When n > 6 and
j > 6, the coupling between the panels of the free surfaces in the
aircushions is described. The case of n > 6 and j = 1,6 represents the coupling between the rigid part of the construction and the vertical forces of the free surface panels in the cushions. When n = 1,6 and
j > 6 represents the coupling between vertical motions of the free surface panels in the aircushions and the six force modes on the rigid
part of the structure.
The motions of the cushion panels of a captive structure are determined
by solving the equation of motion for these panels using the above
mentioned wave forces, added mass, damping and restoring
coefficients:
00F.
{û1a,1, iwb,,, +c,1,}X, =X,,, n=7,D.O.F.
(10) in which: a,, b,1, CH) X.
X
= added mass coupling coefficient
= damping coupling coefficient
= spring coupling coefficient
= mode of motion
= wave force in the n -mode
In this equation, the added mass and damping coefficients and the wave
forces are the same as derived in Eq. (10). From the solution of the
equations of motions of the cushion panels the total wave forces on the
captive structure can be determined as well as the pressure variations
within the cushions.
The next step is to determine the added mass and damping of the structure including the effect of the free surfaces in the aircushions. This time, the equations of motion of the cushion panels can again be
solved based on added mass, damping coupling coefficients, aero- and a,,1 = - Re Øj.k n.k
hydrostatic restoring coefficients and the total forces on the cushion panels due to oscillations of the rigid structure, which are calculated by:
x,
={-ciìa-iú.b,,+c,}x,,
j=l,6 A
n=7...00F. (12)Substitution of Eq. (12) in Eq. (11) gives the cushion panel motions of an oscillating aircushion supported structure in any of the six degrees of freedom. The coefficients and wave forces in this equation are again in accordance with Eq. (9) and (10). Since the oscitlations of the structure change the pressure in the cushions, the added mass coefficients, damping terms and aerostatic forces of the cushions are added to the added mass and damping terms of the structure. Thus yielding the
added mass and damping including cushion effects.
Based on the obtained added mass, damping and wave forces, the wave
frequency motions of the structure can be solved from the normal six degree of freedom equations of motion:
{_(M,
+j-iw1
+c,}x
=X,
n=1,6, (13)in which:
M,L, = mass coupling coefficient for the force in the n
-mode due to an acceleration in the j --mode. In this equation the added mass, damping and spring coefficients as
well as the wave forces apply to the structure only and include the
effects of aircushions. Next, the wave elevations inside the cushions
due to the rigid body motions of the structure in the six degrees of
freedom are solved:
o_oJ.
{-a1a, -iwb, +c}x,
= (14)n =7,D.0.F.
in which x with j = 1,6 was calculated by Eq. (13) and X, follows
from Eq. (9). Next the air pressure variations inside the cushion can be
calculated based on the motions of the stnicture and the wave
elevations of in the cushion
VALIDATION OF NUMERICAL APPROACH
This section describes the model tests and the numerical model, which are not extrapolated to any full scale concept. Extrapolation to full scale
entails discussion with respect to the influence of the model and
stiffness of the aircushion at full scale as described by Kaplan (1989) and Moulijn (1998).
MODEL TESTS
Model tests were carried out by Pinkster et. al. (1998) in towing tank
No.1 of the Ship Hydrodynamics Laboratory at Delft University of Technology. This facility measures 140 m x 4.25 m x 2.5 m and is equipped with a hydraulically operated, flap-type wave maker, by
means of which regular or irregular waves can be generated.
A simple rectangular barge model measuring 2.50 m x 0.78 rn was constructed out of wood. The model consisted of a horizontal deck surrounded by vertical side walls. The rigid deck which closed the aircushion at the top was situated 0. IS m above the still waterline. The draft of the barge measured from the still waterline to the tower edge of
the side walls was 0.15 m.
The thickness of these vertical walls surrounding the aircushion was chosen to obtain sufficient transverse and longitudinal stability during free-floating model tests. The thickness of the walls at the front and aft of the structure was equal to 0.02 m, the side walls had a thickness of
0.06In.
The structure was supported by one large aircushion, which provided 62% of the buoyancy. The remaining 38% was provided by the vertical
walls surrounding the cushion.
Prior to all tests, the static (air) pressure in the cushion was increased relatively to the anibient pressure to bring the mean water level inside the aircushion 0.05 m below the mean waterline of the structure. The air cushion height between the free-surface in the aircushion and the
horizontal deck amounted to 0.18 m.
The main particulars of the model are presented in table I. This table contains the dimensions of the aircushion supported structure and a corresponding conventional barge. The barge is included in the table because it will serve as a reference in the discussion of the motion behavior of the aircushion supported structure in the remainder of this contribution.
Table I: Main particulars of the aircushion supported structure
(ACSS) and conventional barge.
The structure was only subjected to regular head waves during the model tests. I-leave motions, pitch motions and air pressures inside the cushion were measured during these tests and will be described in this
paper.
NUMERICAL MODEL
Only model test data is available of an aircushion supported structure (ACSS) with a draft of 0.15 m. These results will serve as a validation of the numerical model 'ACSS 4' as presented in Table 2. In addition, Table 2 shows the change in stability and natural frequency due to a change in the height of the cushion, i.e. the case when the draft of the
structure changes.
In practice, the height of the aircushion will change when air escapes underneath the structure, this can be caused by a wave trough which is
Quantity I ACSS Barge
Length ni 2.50 2.50 Breadth ni 0.78 0.78 Draught (structure) m 0.15 0.07 Draught (cushion) in 0.05
-Area of Water Line ni2 1.95 1.95
Displacement m3 0.13 0.13 KG nì 0.30 0.30
K,
ni ni 0.22 0.75 0.22 0.75 K1, w 0.73 073deeper than the draft of the vertical wall around the aircushion. This effect was observed in model tests of an aircushion supported MOB at high sea states as presented by Pinkster and Meevers Scholte (1999,
2001).
When the 'aircushion supported' structure is not supported by air,
which is
the case
for 'ACSS 1', the transverse GM-value isapproximately twelve times the
value of 'ACSS 5',
this lattercontiguration is for 75% supported by air.
Figure 1 and Figure 2 show the panel models of the 'ACSS I' and ACSS 5' respectively. Table 3 shows the number of panels used to
describe the conventional barge and the aircushion supported structure at different drafts.
Table 3: Number of panels on the aircushion supported structures (ACSS Y
Figure 1: Panel model of a structure (ACSS 1) with a draft of 0.32 m, which is not supported by air.
Table 2: Draft, stability characteristics and natural frequencies of the conventional barge and the aircushion supported structure (ACSS).
133
-Figure 2: Panel model of an aircushion supported structure (ACSS 4) with a draft of 0.15 m, which is for 62% supported by air.
DISCUSSION OF RESULTS
Table 2 shows that a change in the aircushion height results in a change of the natural heave and roll frequencies. The natural pitch frequency does not change since the cushion is supported by only one aircushion and the thickness of the vertical front and aft wall are relatively small compared to the cushion length. Since the side walls are thicker and
contribute more significantly to the restoring moment around the
longitudinal axis of the structure, the natural roll frequency increases
when the structure is less supported by air. On the other hand the
natural heave frequency decreases after air is vented from the
aircushion.
Figure 3 clearly shows the effect of an elevation change of the free-surface in the aircushions on the heave natural frequency. The heave
motion at the natural frequency can be decreased by pumping air
underneath the structure. When all air escapes underneath the structure, the heave motions increase by a factor 2.2 compared to the situation in which the free-surface inside the cushion is 6 cm below the waterline of the structure. The latter situation shows that heave motions in beam seas of a conventional barge are approximately the same as those of an ACSS which is for 75% supported by air.
In general it can be seen that heave motions in beam seas can be significantly decreased by increasing the aircushion pressure and
therefore decreasing the draft of the structure.
The effect of the aircushion pressure on the heave motions in head seas is less clear as can be seen in Figure 4. Though heave motions of the ACSS I' are higher at wave lengths up to LIA = 1.00, the difference with other drafts is small. The figure also shows that the experimental values correspond well with the computational results. The local peaks
in
the range between 2.00< LIA <2.50 are due to
irregularfrequencies in the numerical approach.
The transverse stability
of the
aircushion supported structure is small and nearly zero when the air
pressure is increased and 75% of the structure is supported by air.
As a result the computations give extremely high roll motions, while
in practice the structure would
capsize. Nevertheless, Figure 5 is included to show the difference of the aircushion volume on the natural roll frequency of the structure. Panels on Panels on structure cushions Total panels Barge 1496 n/a 1496 ACSS I 1784 n/a 1784 ACSS 2 1064 480 1544 ACSS 3 928 480 1408 ACSS4 636 480 1116 ACSS 5 480 480 960
l)iatt Buoyancy Stability Char. Natural Frequencies
T, [iii] T, [ni] Air l-i Skirt [-] GM1 rn] GM1 lin] Heave rad/si Roll ladis] Pitch lrad/s] Barge - 0.07 - - 0.49 7.51 5.61 5.81 5.7S ACSS 1 0.00 0.32 0% 100% 0.61 7.31 4.37 4.51 4.70 ACSS 2 0.03 0.25 37% 63% 0.17 1.38 4.39 3.04 4.27 ACSS 3 0.04 0.20 50% 50% 0.14 1.34 4.64 2.91 4.30 ACSS4 0.05 0.15 62% 38% 0.10 1.31 4.92 2.74 4.28 ACSS 0.06 0.10 75% 25% 0.05 1.26 5.25 2.35 4.27 Exp. ACSS 4 0.05 0.15 62% 38% 0.11 1.32 SUo 2.96 4.33
The aircushion supported structure is stable in head seas, independent of the aircushion volume. Figure 6 shows that computational results agree well with experiments values. However, computations tend to underestimate the pitch motions around LI 2 = 1.00.
In addition, the figure clearly shows that
pitch motions of the
aircushion supported structure can be significantly decreased when air is vented from the cushion. Pitch responses of aircushion supported structures are larger than those of a conventional barge due to a lack of
damping. On the
other hand,pitch motions of the
'aircushionsupported' structure are approximately the same as
those of a
conventional barge when all air is vented from the cushion.Heave added mass and damping coefficients of the conventional barge and aircushion supported structure at different drafts are presented in
Figure 7 and Figure 8 respectively. Heave added mass of the
aircushions is larger than that of the conventional barge due to a deeper draft of the surrounding vertical walls. Added mass of the aircushion decreases when the draft of the structure decreases.
Contrary,
heave damping of the
aircushion supported stnlcturedecreases when its draft decreases due to an increase of the cushion
volume. In general it can be seen that the heave damping of the
conventional barge is larger than that of the aircushion supported
structure, independent of draft.
Figure 9 shows the cushion pressure variations at different drafts in beam seas. Cushion pressure variations increase with an increase of
cushion volume as could be expected. In addition, Figure 9 shows that the maximum air pressure occurs at the natural heave frequencies as
presented in table 2 and shown in Figure 3. Since heave natural
frequencies change with the draft of the structure, maximum values of
the air pressure variations therefore also occur at different wave
lengths.
Figure 10 shows that experimental values and computational results
agree well with each other (in case the free-water surface inside the
cushion is 5 cm below the outside waterline). i.e. air pressure variations can be well predicted by the computational method. Pressure variations are nearly zero when the cushion length is a multiple of the wave length as can be seen in the same figure.
In addition, Figure lO shows that cushion pressure variations increase with an increase of cushion volume. However, this is only the case at
relatively long wave lengths (LIA < 1.00). On the other hand when
LIA >1.00, maximum pressure variations increase when the cushion volume decreases.
Figure 11
shows the midship vertical wave shear forces of a
conventional barge and the aircushion supported structure at different drafts. Maximum shear forces of the aircushion supported structure are significantly smaller than those of a conventional barge. These forces can be further decreased by decreasing the cushion volume. However, vertical shear forces are relatively large when all air is vented from the cushion and the structure is fully floating on its own buoyancy. Vertical wave shear forces of a conventional barge are largest when
LIA = 1.00. At this wave length, the cushion pressure variations are nearly zero and do not contribute to the wave shear forces. As a result these forces are relatively small for the aircushion supported structure
at this specific wave length. The maximum wave shear force of the
aircushion supported structure occurs at the natural pitch frequency, which is independent of the draft.
The midship wave bending moments are presented in Figure 12. This figure clearly shows that wave bending moments can be significantly
reduced by an aircushion. These moments are smallest when the free water surface inside the cushion is 4 cm below the outside waterline,
i.e.
when 50% of the buoyancy
is provided by the aircushion.Furthermore, wave bending moments increase with an increase of the cushion volume.
CONCLUSIONS
The motion behavior of an aircushion supported structure changes when air escapes. Air can be vented in a controlled way from the
cushion, but it can also escape when a wave trough is deeper than the
draft of the structure.
Results of computations show that cushion pressure variations in beam
seas are most affected by a change of the air pressure. As a
consequence, heave motions change and increase with decreasing
cushion pressure. Pitch motions in head seas are sensitive to a change
of the cushion volume as well. In contrast to heave motions, pitch
motions increase when more buoyancy is provided by the aircushion. Heave added mass and damping coefficients show a different behavior.
Heave added mass decreases when more buoyancy is provided by the aircushion, while at the same time the damping increases.
In addition, midship wave bending moments can be significantly
reduced by the aircushion and are smallest when 50% of the buoyancy
is provided by air.
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Heave Motions ¡n Beam Seas
CaIc. BayOs --CaIc. Ic = 0cm -Cdc. Ic =3cm - Caic.Ic=4cm - 'Calc.Tc-Scm -Caic. Ic 8cm
Figure 3: Heave motions in beam seas of an aircushion supported structure at different drafts and a conventional barge of
equal displacement.
Heave Motions in Head Seas
Caic. Barge --CaIc. Io = 0cm Cxlv. Te 3 mii CaIc.Tc-4cm - Calo Tc-Scni -Calo, Tc = 6cm o Exp. Tc=Scm
Figure 4: Heave motions in head seas of an aircushion supported structure at different drafts and a conventional barge of
equal displacement.
Roll Motions in Beam Seas
Calo. Baige -CaIc, To = 0cm - Calo. To = 3cm Calc,Tc=4cm - CaIc.Tc=5cm -Cale. Tc =6cm
Figure 5: Roll motions in beam seas of an aircushion supported structure at different drafts and a conventional barge of
equal displacement.
Pitch Motions ¡n Head Seas
Calc.Barge --Calc. Tc 0cm -'-Caic Tc=3cm CaIc.Tc=4c,n - CaIc.Tc=5cm CaIc. To = 6cm O Eap.Tc=acm 1.00 0.80 0.40 0.60 BIA 0.00 0.20 1.50 200 2.50 3,00 0.00 0.50 1.00 L/A o 000 0.20 0.40 060 8/A 080 1.00 2.00 2.50 3.00 1.50 L/A
Figure 6: Pitch motions in head seas of an aircushion supported structure at different drafts and a conventional barge of
equal displacement.
350 3.00 250-E » 2.00 z I 50 -.00 .5500 Figure 8: 0.00 -0.00 0.50 I 00 1.50 2.00 2.50 3.05 L/A
Figure 7: Heave added mass of an aircushion supported structure at
different drafts and a conventional barge
of equal
displacement. 1.2 1.0 0.8 0.6 0.4 G) 0.2 o»
Heave Added Mass
-Heave Damping
Calc.Barge -.-CaIc.Tc=Ocrn
--Catc.Tc3cm - - Calc.Tc4cm - CaIc.Tc..Scm -Calc.Tc=ecm
Cale, Barge --CaIc. Tc 00m
Cale, Te = 3 err - - Cale Te = 4cm
- Calc.Tc=Serrr -CaJc.Tcecm
LIA
0.00 0.20 0.40 0.60 0.80
B/A
Figure 9: Aircushion pressure variations in beam seas for an aircushion supported structure at different drafts.
Cushion Pressure Variations in Head Seas
Heave damping of an aircushion supported structure at
diflèrent drafts and a conventional barge
of equal
displacement.
Cushion Pressure Variations in Beam Seas
1.00 1.40 Z 1.20 1.00 0.80 0.60 0.40 C 0.20 000 0.00
Midship Vertical Wave Shear Forces
Calc.Barge -.-Cajc.TcOcm
--Calc.Tc=3mn - - Catc.Tc-4cm - -Cale. Tc=Scan -Cala. Tc-Ocm
LIA
Figure 12:
Midship longitudinal wave bending moments of an
aircushion supported structure at different drafts and a
conventional barge of equal displacement.
Midship Wave Bending Moments
CaIc. Barge --CaIe. Te 0cm
-Cale Te = 3 era - - Cale. Te = 4 cnr
- -Calc.Tc=Scnr -Calc.Tc=6cm 3.00 2.50 - 2.00 z s 1.50 .00 o u5 0.50 0.00 000 0.50 1.00 1.50 2.00 2.50 300 L/A
Figure II: Midship vertical
wave shear forces of an aircushion
supported structure at different drafts and a conventional barge of equal displacement.
0.00 0.50 1.00 1.50 2.00 2.50 3.00
LIA
Figure 10: Aircushion pressure variations in head seas for an aircushion supported structure at different drafts.
0.50 1.00 1.50 2.00 2.50 3.00 2.50 .50 2,00 3.00 1.00 0.50 1.60 1.40 1.20 1.00 0.80 0.80 V 0,40 020
