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TECHNICAL PAPER
Development of a semi-empirical method for hydro-aerodynamicperformance evaluation of an AAMV, in take-off phase
Mojtaba Maali Amiri • Mohammad Tavakoli Dakhrabadi •
Mohammad Saeed Seif
Received: 17 January 2014 / Accepted: 3 July 2014
� The Brazilian Society of Mechanical Sciences and Engineering 2014
Abstract An assessment of the relative speeds and pay-
load capacities of airborne and waterborne vehicles
accentuates a gap that can be usefully filled by a new
vehicle concept, making use of both hydrodynamic and
aerodynamic forces. A high speed marine vehicle equipped
with aerodynamic surfaces (called an AAMV, ‘aerody-
namically alleviated marine vehicle’) is one such concept.
There are three major modes of motion in the operation of
an AAMV including take-off, cruising and landing. How-
ever, during take-off, hydrodynamic and aerodynamic
problems of an AAMV interact with each other in a cou-
pled manner, which make the evaluation of this phase
much more difficult. In this article, at first aerodynamic
characteristics such as lift and drag coefficients, were cal-
culated, using theoretical relations in extreme ground
effect, and then a relationship was made between total
aerodynamic lift force and effective weight force in the
hydrodynamic performance. Then, taking into account the
aerodynamic, hydrostatic and hydrodynamic forces acting
on the AAMV, equations of equilibrium were derived and
solved. The developed method was well-validated against
experimental data, and finally, influence of different
hydrodynamic and aerodynamic parameters on the perfor-
mance of the AAMV was investigated. Time- and cost-
saving in the preliminary design stage of an AAMV are
some of the superiorities of the developed method over the
numerical and experimental approaches.
Keywords AAMV � Ground effect � Hydrodynamic
performance � Take-off phase
List of symbols
a Pitch moment arm of Rf (m)
B Hull breadth (m)
C Pitch moment arm of N (m)
c Chord length (m)
e Ostwald coefficient
f Pitch moment arm of T (m)
g = 9.81 Gravity (m/s2)
h Height above the surface (m)
L Aerodynamic lift (N)
N Hydrodynamic lift (N)
R Total resistance (N)
S Area of the aerodynamic surface (m2)
T Thrust (N)
W Weight (N)
V Speed of the AAMV (m/s2)
Ah The frontal area of the planing hull
AT Area of the cross section in transom (m2)
Ax Maximum of cross section area (m2)
BP Mean wetted breadth (m)
CL Lift coefficient
Cf Viscous friction coefficient
D1 Drag of the main wing (N)
D2 Drag of the tail wing (N)
ie The angle of the entrance hull (degree)
L1 Lift of the main wing (N)
L2 Lift of the tail wing (N)
M1 Aerodynamic moment of the main wing
(Nm)
M2 Aerodynamic moment of the tail wing (Nm)
Rf Hydrodynamic frictional resistance (N)
CF0 Frictional drag coefficient
Technical Editor: Celso Kazuyuki Morooka.
M. M. Amiri � M. T. Dakhrabadi � M. S. Seif (&)
Mechanical Engineering Department, Center of Excellence in
Hydrodynamics, Sharif University of Technology,
P.O. Box 11365-9567, Tehran, Iran
e-mail: [email protected]; [email protected]
123
J Braz. Soc. Mech. Sci. Eng.
DOI 10.1007/s40430-014-0217-0
CD,f Friction drag coefficient
CD,i Induced drag coefficient
CD,p Pressure drag coefficient
Dah Aerodynamic drag of AAMV’s hull (N)
dD1 Pitch moment arm of D1 (m)
dD2 Pitch moment arm of D2 (m)
dL1 Pitch moment arm of L1 (m)
dL2 Pitch moment arm of L2 (m)
Dws Whisker spray resistance (N)
CDah = 0.7 Aerodynamic drag coefficient of the hull
Swet Wetted area of the hull (m2)
qair Air density (kg/m3)
qwater Water density (kg/m3)
r Displaced volume of water (m3)
s Trim angle (degree)
DTO Take-off weight (N)
D Hydrodynamic weight (N)
e � 0 Angle between the direction of T and the
keel (degree)
b ðbetaÞ Dead-rise angle (degree)
k Mean wetted length
Fnr Displacement Froude number
V= g ðrÞ1=3� �1=2
Abbreviations
AR Aspect ratio of the wing
CG Center of gravity
ACV Air cushion vehicle
LCG Longitudinal center of gravity (m)
LWL Length of water line (m)
MAC Mean aerodynamic chord (m)
VLM Vortex lattice method
WIG Wing in ground vehicle
AAMV Aerodynamically alleviated marine
vehicle
HSMV High speed marine vehicle
ITTC International towing tank
conference
NVLM Nonlinear vortex lattice method
1 Introduction
During the last five decades, interest in high speed marine
vehicles (HSMVs) has been intensified, leading to new
configurations and further development of already existing
configurations [1]. Basically, to sustain the weight of an
HSMV, four are the forces that can be used: hydrostatic lift
(buoyancy), powered aerostatic, hydrodynamic and aero-
dynamic lift.
‘Buoyancy’ is the lift force most commonly used by
conventional vessels, and historically is the oldest. For
HSMVs it is not feasible to use only buoyancy, due to the
fact that the buoyancy force is proportional to the displaced
water volume, and at high speed it is better to minimize this
parameter, since as more vehicle volume is immersed in
the water the higher the hydrodynamic drag will be. The air
cushion vehicles class, such as the Hovercraft, uses a
cushion of air at a pressure higher than atmospheric, called
‘powered aerostatic lift’, to minimize contact with the
water, thus minimizing hydrodynamic drag. In addition, at
high speeds a marine vehicle experiences ‘hydrodynamic
lift’, due to the fact that the vehicle is planing over the
water surface. The fourth lift force that can be exploited to
sustain the weight of the vehicle, leading to reduced
buoyancy and therefore to a decreased hydrodynamic drag,
and in extreme cases even to elimination of hydrodynamic
drag, is ‘aerodynamic lift’. This thought has inclined the
researchers towards the construction of the aerodynami-
cally alleviated marine vehicles (AAMVs). AAMV is a
HSMV designed to exploit, in its cruise phase, the aero-
dynamic lift force, using one or more aerodynamic sur-
faces. AAMV’s drag is very low once the craft’s take-off
occurs, and therefore, this feature enables the AAMV to
achieve a much higher cruise speed than the other types of
marine vehicles. Additionally, due to the complete dis-
connection of the AAMVs from the water surface in their
cruise phase, these crafts are able to move with smaller
speed loss and reduced-motions during operation over the
waves, as compared to other fast marine crafts. Moreover,
an AAMV, due to using ground effect, possesses a higher
aerodynamic efficiency than an equivalent airplane and,
therefore, demanding a lower power to move in the same
conditions. Ground effect is the enhanced aerodynamic lift
force acting on a wing that is traveling in close proximity
to the ground or water surface, commonly less than one
wing chord height.
There are three major modes of motion in the operation
of an AAMV including take-off, cruising and landing.
Although an AAMV only transits through all the modes
except for cruising, take-off phase is of great importance.
This is due mainly to the AAMV’s maximum resistance
force, which occurs during take-off mode, and represents
the most crucial performance limitations imposed on
AAMV crafts. From the 1960s research activities has been
seriously started to evaluate the combination of ground
effect phenomenon with marine vehicles. The most popular
AAMVs are wing in ground (WIG) vehicles and sea
planes. Since 1940, NASA (NACA), in the United States
has published numerous technical reports on the hydrody-
namic and aerodynamic characteristics of sea planes. The
obtained results from these reports were based on the
experiments conducted in towing tank and wind tunnel. For
instance, Olson and Allison [2] examined the effect of
different hydrodynamic and aerodynamic parameters on
take-off phase of a flying boat. Also, Parkinson and Bell [3]
J Braz. Soc. Mech. Sci. Eng.
123
conducted the same experiments to evaluate the take-off
phase of a flying boat. Aside from the US, other active
countries in this field have been Russia, China, Germany
and recently Australia that were mentioned by Yun et al.
[4]. Most of the researches that have been conducted in this
area are related to the cruise mode of a WIG craft in ground
effect, and less attention has been paid to the examination
and analysis of the behavior of AAMVs in take-off phase.
Rozhdestvensky [5] investigated the airflow around a wing
flying in ground effect and extreme ground effect, using
potential flow theory. Kornev and Matveev [6] assessed the
stability of a WIG vehicle flying in ground effect,
employing non-leaner vortex lattice method (VLM). Yong
Seng [7], after construction of a WIG radio controlled
model, examined the stability of the vehicle, and drew an
interesting conclusion that, vehicle flying on the ground
surface is capable of taking advantage of ground effect at a
higher altitude than the one flying on the water surface.
Matveev [8] and Matveev and Soderlund [9] experimen-
tally examined the static characteristics (such as pressure
distribution under the main wing) of a WIG, which was
equipped with PAR moving system and flap, in extreme
ground effect. Yun et al. [4] provided a rather compre-
hensive historical review of WIG crafts, as well as a design
procedure for these vehicles. However, the main focus of
this study has been concentrated on the cruise phase and
the aerodynamic aspects of the WIG vehicles. Yinggu et al.
[10] developed a hydro-aerodynamic model for a WIG in
calm water. In this study, the hydrodynamic forces acting
on the WIG were calculated, using the semi-empirical
formula proposed by Savitsky et al. [11] and the aerody-
namic forces were estimated, using the conventional
aerodynamic methods, and finally the obtained results were
validated against experimental data. Collu et al. [12]
examined the longitudinal static stability of an AAMV
through developing a mathematical model in surge, heave,
and pitch directions. Priyanto et al. [13] estimated a WIG
power in take-off, using semi-empirical formula of Savit-
sky et al. [11] and VLM. Matveev and Chaney [14]
examined the heave motion of a WIG vehicle equipped
with PAR moving system in an extreme ground effect,
utilizing the linear potential flow theory.
Typically, an AAMV, in take-off phase, experiences the
aerodynamic and hydrodynamic force of the same order of
magnitude; therefore neither the HSMVs nor the airplane
models of dynamics can be adopted. The main purpose of
this work is to bridge this gap by developing a new model
of dynamics, which takes into account the equal signifi-
cance of aerodynamic and hydrodynamic forces. Conse-
quently, in this paper an attempt was made to examine the
hydro-aerodynamic performance of the AAMVs in take-off
through developing the existing semi-empirical formula.
First, aerodynamic characteristics such as lift and drag
coefficients were calculated in ground effect, employing
analytical methods. In take-off, hydrodynamic and aero-
dynamic behavior of the AAMV are coupled together
which was brought in the total aerodynamic lift force and
effective weight relation in the hydrodynamic performance.
Then, the angle of trim was determined through solving the
pitch moment equation of equilibrium with regard to the
hydrodynamic, aerodynamic, thrust and weight forces.
After conducting an experiment on an AAMV model of
1/15.28 scale of the prototype, present method was well-
validated. Finally, influence of different hydrodynamic and
aerodynamic parameters on the performance of the AAMV
was examined.
2 Aerodynamic and hydrodynamic mathematical
models of the AAMV
Figure 1 shows the variations of hydrodynamic and aero-
dynamic resistance and trim angle with speed for a typical
AAMV in different phases of motion including displace-
ment, pre-planing, planing and take-off.
In displacement and pre-planing phases, hydrodynamic
resistance is dominant, and in the subsequent phases
(planing and take-off) both the hydrodynamic and aero-
dynamic resistances are of the same order of magnitude.
The maximum hydrodynamic resistance and trim angle are
usually associated with the same speed (so-called the hump
speed), which occurs within the pre-planing range and with
more increase in speed the hydrodynamic resistance and
trim angle will gradually decrease.
Relation between aerodynamic and hydrodynamic
mathematical model of the AAMV was made as follows:
D ¼ DTO � L: ð1Þ
L denotes the total aerodynamic lift, DTO take-off weight
and D hydrodynamic weight of the AAMV before take-off.
It can be inferred from Eq. (1) that when take-off occurs,
the hydrodynamic weight becomes zero.
2.1 Aerodynamic resistance
Airflow governing equations around the WIG effect are
Reynolds averaged Navier–Stokes (RANS) and the conti-
nuity equations, which can be written as follows:
oðqujÞoxj
¼ 0 ð2Þ
o quiuj
� �oxj
¼ � oP
oxi
þ o
oxj
loui
oxj
þ ouj
oxi
� �� þ qgi ð3Þ
where, i, j = 1, 2 and 3 denote x, y, and z directions,
respectively. For a typical AAMV the maximum cruising
J Braz. Soc. Mech. Sci. Eng.
123
speed is 300 km/h (Mach number is 0.24), and therefore,
fluid flow can be assumed incompressible. In order to
develop the aerodynamic mathematical model, the fol-
lowing simplifying assumptions were made for the airflow
around the wings:
• Irrotational flow
• Incompressible flow
• Without energy loss
• No flow separation
Neglecting viscosity along with the above assumptions
turn the RANS equations into the Bernoulli equation. The
Bernoulli equation can be used in the whole domain of the
flow except in the boundary layer.
Grundy [15] and Barber [16] examined the effect of the
free surface deformations on the aerodynamic coefficients
of a wing flying in close proximity to the water surface,
using numerical methods. They have drawn the same
conclusion that the effect of water surface deformations on
the aerodynamic coefficients of a wing can be neglected.
Geometry and coordinate system demonstrated in Fig. 2
were used to calculate the aerodynamic coefficient of a
symmetrical and asymmetrical airfoil.
In Fig. 2, f ðxÞ denotes the airfoil profile with respect to
xoy coordinate system. f ðxÞ can mark a symmetrical or
asymmetrical airfoil. Using the relation h xð Þ ¼ hþ xsina�jf ðxÞj=cosa, one is able to calculate the distance of each
point at the lower surface of the airfoil from ground surface.
Using the Bernoulli equation between two points at the lower
surface of the airfoil (point 1 and 2 in Fig. 2), result in the
relative pressure between these two points as follows:
P xð Þ ¼ q2
V21 � V2
x
� �: ð4Þ
Using the continuity equation, one would have:
hV1 ¼ hþ hðxÞVxð Þ ð5Þ
Vx ¼h
hþ hðxÞV1 ð6Þ
Substituting the Eqs. (6) in (4), relative pressure
obtained as follows:
P xð Þ ¼ q2
V21 1� h2
hþ hðxÞð Þ2
" #: ð7Þ
Consequently, the F force was calculated by direct
pressure integration on the lower surface of the airfoil as
follows:
F ¼Z c
0
P xð Þdx ¼ q2
V21
Z c
0
1� h2
hþ hðxÞð Þ2
" #dx: ð8Þ
Fig. 1 Variations of
hydrodynamic and aerodynamic
resistance and trim angle of a
typical AAMV with speed
Fig. 2 Geometry and
coordinate system used for a
symmetrical and asymmetrical
airfoil
J Braz. Soc. Mech. Sci. Eng.
123
Numerical methods have been used to calculate the
force F due to complexity of the h(x). Then, the resultant
ground effect lift coefficient can be determined, using the
following equation:
L0 ¼ Fcosa! C
0
L ¼L0
q2
V21c
: ð9Þ
The total lift of the airfoil in ground effect is the sum-
mation of lift coefficient owing to ground effect, and airfoil
lift coefficient in the infinity, as below:
CLwig ¼ CL1 þ C0
L: ð10Þ
Anderson [17] has proposed Eq. (11) to convert the
slope of airfoil lift coefficient curve to the slope of finite
wing lift coefficient curve, as follows:
dCL
da
�
wing
¼dCL
da
�airfoilffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
1þ dCL
da
�airfoil
.p � AR
� �2s
þ dCL
da
�airfoil
.p � AR
ð11Þ
where dCL
da
�airfoil
and dCL
da
�wing
are the slope of airfoil lift
coefficient curve and the slope of finite wing lift coefficient
curve, respectively. Equation (11) indicates that the slope
of finite wing lift coefficient curve is less than the slope of
airfoil lift coefficient curve.
In addition, the total drag coefficient of a wing can be
written as follows:
CD ¼ CD;f þ CD;p þ CD;i ð12Þ
where CD;f denotes friction drag coefficient, CD;p pressure
drag coefficient, and CD;i induced drag coefficient. The first
two terms in the right hand side of Eq. (12) have to do with
airfoil (2D condition) and the third term is related to the
wing (3D condition). Friction and pressure drag coeffi-
cients in and out of ground effect are approximately the
same; however, ground effect results in a significant
reduction in induced drag. The lower induced drag in
ground effect in comparison to out of ground effect is due
to the fact that the induced lift vortices are restrained by the
presence of the solid surfaces close by. Accordingly, airfoil
drag coefficient (2D) in ground effect and out of ground
effect is the same. For exerting the height effect (ground
effect) on the induced drag coefficient, Eq. (12) is used as
follows:
CD;i ¼ rC2
L
epAR; r ¼ 1� exp �3:88
h=c
AR
� �0:66" #
: ð13Þ
e is Ostwald coefficient, CL denotes lift coefficient and
AR Aspect ratio of the wing. For elliptical wings, e is equal
to 1; the more similar to the elliptical wing, the closer to
one will be this coefficient. The present method was vali-
dated against experimental data of Fink and Lastinger [18]
experiments, in the case of the Glenn Martin 21 airfoil
section, and aspect ratio of 4 and chord to height ratio of
0.167. Figures 3 and 4 show lift and drag coefficients
calculated based on the present method and the experi-
ments of Fink and Lastinger. As shown in Figs. 3 and 4 the
present work results are in good agreement with experi-
mental data. However, there is a small deviation in lift
coefficient of the present work from the experimental data
in high angles of attack. The flow separation on the upper
surface of the airfoil can be a potential cause of this
deviation which was not taken into account in present
work. It is worthwhile to mention that flow separation
usually occurs at high angles of attack which are almost
impractical for AAMVs. Also, the drag coefficient of the
present work and the experimental data follow the same
trends except for some minor differences in a few angles of
attack. The average error for the present work, in com-
parison to the experimental data, is 3 and 7.5 % for lift and
drag coefficients, respectively.
0
0.4
0.8
1.2
1.6
2
0 1 2 3 4 5 6 7 8 9 10 11
Experiment
Present Work
CL
Angle of Attack (deg)
Fig. 3 Lift coefficient comparison between experimental results of
Fink and Lastinger [18] and present work for AR = 4 and h/
c = 0.167
0
0.03
0.06
0.09
0.12
0.15
0 1 2 3 4 5 6 7 8 9 10
Experiment
Present Work
CD
Angle of Attack (deg)
Fig. 4 Drag coefficient comparison between experimental results of
Fink and Lastinger [18] and present work for AR = 4 and h/
c = 0.167
J Braz. Soc. Mech. Sci. Eng.
123
2.2 Hydrodynamic resistance
Hydrodynamic resistance was evaluated in displacement,
pre-planing, planing and take-off phases. These phases of
motion of an AAMV are specified according to the dis-
placement Froude number which is defined as below:
Fnr ¼ V=ðgðrÞ1=3Þ1=2 ð14Þ
where, V denotes the speed and r displacement of the
AAMV (the amount of water displaced by the vehicle), and
g ¼ 9:81 m/s2 gravity acceleration. Accordingly, for
Fnr\1 the AAMV is considered in the displacement
phase, and for 1\Fnr\2 the vehicle is considered in the
pre-planing phase, and finally for Fnr[ 2 the AAMV is in
the planing and take-off phases [11, 19, 20].
2.2.1 Resistance in the displacement phase
In this phase, the weight of the vessel is almost completely
supported by the hydrostatic force of buoyancy. Resistance
in the displacement phase was calculated on the basis of the
Holtrop and Mennen method [21] as follows:
Rf
�Dis¼ 0:5qwaterCF0
SwetV2 ð15Þ
where, qwater denotes the water density (1,025 kg/m3) Swet
wetted area of the hull and CF0 frictional drag coefficient
(as defined in 1957 by International Towing Tank Con-
ference [20]).
2.2.2 Resistance in the pre-planing phase
In this phase, both the hydrostatic and hydrodynamic forces
contribute significantly in balancing the vessel’s weight,
and also, in this phase, hydrodynamic resistance is much
higher than aerodynamic resistance. An empirical relation
through the regression technique based on the 118 exper-
iments of the mono-hull crafts has been developed by Sa-
vitsky and Ward Brown [22] as follows:
Rt=D ¼ A1 þ A2X þ A4U þ A5W þ A6XZ þ A7XU
þA8XW þ A9ZU þ A10ZW þ A15W2
þA18XW2 þ A19ZX2 þ A24UW2 þ A27WU2
ð16Þ
X ¼ LWL=r1=3 Z ¼ D=qgB3
U ¼ffiffiffiffiffiffi2ie
pW ¼ AT=Ax
:
LWL denotes length of water line,r displaced volume of
water by the vessel, B hull breadth, AT the cross section
area in transom, Ax maximum of cross section area, D is
equal to the weight of the vessel and defined as D ¼ r� g,
and ie the angle of the entrance hull.
Ai constants was calculated by Savitsky and Ward
Brown [22] shown in Table 1.
2.2.3 Resistance in the planing and take-off phases
In order to evaluate the hydrodynamic resistance in
planing and take-off phases, the calculation of the trim
angle (s) and the average of wetted length to breadth
ratio (k) of the AAMV are required. In Fig. 5 the free
body diagram of the AAMV is demonstrated. To
describe the motion of the AAMV a body-fixed coordi-
nate system X0OZ 0 was used. The origin O was taken to
be coincident with the center of gravity (CG) position of
the AAMV. The aerodynamic force acting on an aero-
dynamic surface is usually represented by two forces
plus a moment. Lift, defined as perpendicular to the
velocity, drag, defined as parallel to the velocity, and
pitch moment, positive for a bow up movement. To
evaluate their values, the classical approach developed
for airplanes was adopted. Di, Mi and Li (i = 1, 2)
denote the aerodynamic drags, moments and lifts, (dL1,
dD1) and (dL2, dD2) denote the aerodynamic centers of
main and tail wings of the AAMV with reference to the
body-fixed coordinate system X0OZ 0, respectively. In
addition, the hull experiences an aerodynamic drag
force, which to evaluate its contribution Savitsky et al.
[11] proposed the following expression:
Dah ¼ ð1=2ÞqairV2AhCDah ð17Þ
where Ah is the frontal area of the planing hull, and CDahis
the aerodynamic drag coefficient of the hull (approximated
as 0.70). Since it is not known where the hull aerodynamic
drag acts, Dah is supposed to be acting on CG. Therefore,
no moment is generated by this force.
The vehicle, in the longitudinal plane, has three-degree
of freedom, and a system of three equations of equilibrium
is needed.
Surge equation: sum of the horizontal forces = 0.
�T cosðsþ eÞ þ Rf cos sþ ðD1 þ D2 þ Dah þ DWSÞþ N sin s¼ 0 ð18Þ
Heave equation: sum of the vertical forces = 0.
�W þ L1ð þ L2Þ þ N cos s þ T sinðs þ eÞ� Rf sin s ¼ 0 ð19Þ
Pitch equation: sum of the pitch moments = 0.
� Nc � Rfa � Tf � ðL2dL2 cos s þ L2dD2 sin sÞþ D2dD2 cos s � D2dL2 sin s
þ ðD1dD1 cos s þ D1dL1 sin sÞþ L1dL1 cos s � L1dD1 sin s � M1 � M2 ¼ 0 ð20Þ
In particular, since the aerodynamic drag of the hull Dah
and the whisker spray Dws are supposed to act through the
CG, thus their pitch moment is equal to zero.
J Braz. Soc. Mech. Sci. Eng.
123
Trim angle was calculated through satisfying Eq. (20).
Also, k was obtained using the semi-empirical method for
planing surfaces. The formula to calculate the total
hydrodynamic resistance in the planing and take-off
phases is shown in Eq. (21) which is fully explained by
Savitsky et al. [11]. In this equation W tan sdenotes
pressure resistance, Rf frictional resistance and Dws
whisker spray resistance.
RT ¼ W tan sþ Rf þ Dws ð21Þ
3 Results and discussion
In this section, the hydro-aerodynamic performance of an
AAMV with characteristics given in Table 2 was exam-
ined, using the method presented in Sect. 2. Figure 6 shows
the AAMV under consideration from two different views,
side and three dimensional views Figs. 7 and 8 show the
variations of the trim angle and resistance to weight ratio of
the AAMV with displacement Froude number.
Table 1 Ai constant coefficients in different displacement Froude numbers [22]
Fnr 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2
A1 0.06473 0.10776 0.09483 0.03475 0.03013 0.030163 0.03194 0.04343 0.05036 0.05612 0.05967
A2 -0.4868 -0.88787 -0.6372 0 0 0 0 0 0 0 0
A4 -0.0103 -0.01634 -0.0154 -0.00987 -0.00664 0 0 0 0 0 0
A5 -0.0649 -0.13444 -0.1358 -0.05097 -0.0554 -0.10543 -0.08599 -0.13289 -0.15597 -0.18661 -0.19758
A6 0 0 -0.16046 -0.2188 -0.19359 -0.2054 -0.19442 -0.18062 -0.17813 -0.18288 0.20152
A7 0.10628 0.18186 0.16803 0.10434 0.09612 0.06997 0.06191 0.05487 0.05099 0.04744 0.04645
A8 0.9731 0.8308 1.55972 0.4351 0.5182 0.5823 0.52049 0.78195 0.92859 1.18569 1.30026
A9 -0.0027 -0.00389 -0.00309 -0.00198 -0.00215 -0.00372 -0.0036 -0.00332 -0.00308 -0.00244 -0.00212
A10 0.01089 0.01467 0.03481 0.04113 0.03901 0.04794 0.04436 0.04187 0.04111 0.04124 0.04343
A15 0 0 0 0 0 0.08317 0.07366 0.12147 0.14928 0.1809 0.19769
A18 -1.4096 -2.46494 -2.15556 -0.92663 -0.95276 -0.70895 -0.7206 -0.95929 -1.1218 -1.38644 -1.5513
A19 0.29136 0.47305 1.02992 1.06392 0.97757 1.19737 1.18119 1.01562 0.93144 0.78414 0.78282
A24 0.02971 0.05877 0.05198 0.02209 0.02413 0 0 0 0 0 0
A27 -0.0015 -0.00356 -0.00303 -0.00105 -0.0014 0 0 0 0 0 0
Fig. 5 Forces and moments
acting on the AAMV
Table 2 AAMV characteristics
Hull characteristics Unit Value
Length m 11
Beam m 2.4
Weight Tons 6.6
LCG m 3.7
Dead-rise Degree 18
Main wing span m 12
Tail wing span m 6
Main wing chord m 3
Tail wing chord m 1.5
J Braz. Soc. Mech. Sci. Eng.
123
With regard to Figs. 7 and 8 it is observed that with
increase in the Froude number trim angle of the AAMV
after increasing in the hump point, decreases, which is
similar to high speed crafts. Also, increase in the Froude
number, will result in increase in the total aerodynamic lift
and therefore hydrodynamic resistance gradually decreases
due to the continuous reduction in AAMV’s wetted sur-
face. Additionally, it can be inferred that approximately at
Froude number equal to 8.7, take-off occurs. Because the
hydrodynamic resistance at this Froude number is
approximately zero which means that the AAMV’s wetted
surface has become zero. The total resistance to weight
ratio in this point is 0.121. However, increase in speed
results in an increase in Reynolds number either, which
subsequently will result in increase in aerodynamic resis-
tance. According to Figs. 7 and 8, it can be seen that the
maximum of the total resistance to weight ratio and trim
angle of the AAMV are 0.15 and 5.4�, respectively.
Prior to conducting a comprehensive investigation on
the influence of different parameters on the AAMV per-
formance in take-off phase, it seems necessary to validate
the developed method.
3.1 Validation
AAMV vehicles are a combination of high speed crafts and
airplanes. For the purpose of model test in the field of high
speed crafts the Froude number should be kept the same for
the model and the prototype. However, in airplane per-
formance evaluation, Reynolds number plays an important
role. Unfortunately, it is impossible to keep both, the
Froude number and Reynolds number the same for AAMV
model and prototype. Keeping the Reynolds number equal
means that the model test must be conducted in compara-
tively high speeds, which is almost impractical.
In this section, the present method was validated against
experimental data of a model of 1/15.28 scale of the pro-
totype. As mentioned earlier in this section, Reynolds
number is one of the most important non-dimension
parameters in examination of the AAMV performance.
Unlike the other high speed crafts Reynolds number is
effective not only on the hull resistance and wings but also
on lift forces of these components. It is sometimes
observed that the ratio of the lift to drag between prototype
and model is not the same, especially in the case of the
miniature models. Unfortunately, the scale effect is the
result of differences in full-scale and model Reynolds
numbers when prototype and model are run at equal Froude
numbers. In the past, it has been the practice, whenever
practicable, to use the models of equal size, thereby can-
celing scale effects. It is worth mentioning again that it is
impossible to model the Reynolds and Froude numbers at
the same time, due to air being 800 times less dense than
Fig. 6 Different views of the
AAMV under consideration
0
1
2
3
4
5
6
0 2 4 6 8 10
Tri
m(d
eg)
Fn
Fig. 7 Variations of the trim angle of the AAMV with displacement
Froude number
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0 2 4 6 8 10
Hydrodynamic ResistanceAerodynamic ResistanceTotal Resistance
Forc
e/W
eigh
t
Fn
Fig. 8 Variations of the resistance to weight ratio of the AAMV with
displacement Froude number
J Braz. Soc. Mech. Sci. Eng.
123
water. Therefore, all can be done is just taking some
remedial measures to minimize the difference in Reynolds
numbers of the model and the prototype. Consequently,
four remedies have been proposed which are listed as
follows:
1. Construction of a bigger model to minimize the
difference in model and prototype Reynolds numbers
[4].
2. Adjusting the angle of attack of the main wing of the
model for having the same lift coefficient as the actual
hull [23].
3. The model of the AAMV should be big enough to
obtain Reynolds number higher than 105[4].
4. Installation of flaps deflected 45�–90� on the main
wing of the AAMV model to obtain a higher lift
coefficient [23].
3.1.1 Experimental test
In this section, hydrodynamic performance of the AAMV
model, mentioned in the previous section, was examined in
the Towing Tank. Dynamical similarity between the model
and the full-scale was ensured by keeping Froude number
the same in model and the prototype which gives the main
dimensions of the AAMV model as Table 3. The length of
the model is 0.72 m, and therefore:
Model scale ¼ Lship
Lmodel¼ 11:0 m
0:72 m¼ 15:28:
An image of this AAMV model is shown in Fig. 9.
Tests were conducted as follows:
• In order to evaluate the hydrodynamic performance of
the AAMV in calm water, tests were carried out at
speed range from 0 up to 4 m/s with a step of 0.3 m/s,
and a total of 14 experiments were conducted.
• As mentioned in the previous section, Reynolds number
is the most important non-dimensional parameter for
AAMV performance prediction. One effective and
practicable procedure for enhancing the Reynolds
number of model, is installing a flap deflected 45�–
90� on the main wing of the AAMV [23]. Accordingly,
in order to minimize the difference in model and
prototype Reynolds numbers, the flaps deflected 45�were used on the main wing. The model after instal-
lation of flaps is shown in Fig. 10.
Tests for examination of hydrodynamic performance of
the AAMV were conducted in the Towing Tank of the
Marine Laboratory of Mechanical Engineering Department
of Sharif University of Technology, as shown in Fig. 11.
Table 4 shows the main properties of this Towing Tank.
Figure 12 shows the AAMV model in Towing Tank.
The experiment and developed semi-empirical method
results are compared in Figs. 13 and 14. Although the
general trends of both methods’ results are the same, there
is a slight difference between experiment and developed
semi-empirical method results which can be associated
with the following factors:
1. Despite taking a practicable remedial measure in order
to minimize the difference in model and prototype
Reynolds numbers, this number will not be the same
for the model and the prototype, which will certainly
result in a slight deviation of model test results from
full-scale results.
2. In the vicinity of hump and lower speeds, the
simplifying assumptions in resistance calculation of
the AAMV can be a possible cause of difference in
experiment and developed method results.
3. Water spray, particularly at high speeds, is of vital
importance in drag prediction of an AAMV, which is
introduced in the developed semi-empirical method
through a rather simple relation.
Table 3 Characteristics of the
AAMV modelModel
characteristics
Unit Value
Model length
(overall)
m 0.72
Model beam
(overall)
m 0.15
Model LCG m 0.242
Model bow
draft
cm 4.8
Model aft draft cm 5.3
Model max
speed
knots 8
Model main
wing span
m 0.80
Model tail wing
span
m 0.40Fig. 9 AAMV model
J Braz. Soc. Mech. Sci. Eng.
123
4. The constructed AAMV model certainly has some
differences in geometry with the AAMV under con-
sideration. For example, the exact position of the CG,
which has a significant impact on the trim angle.
3.2 Parametric study
The developed method is based on the analytical semi-
empirical relations and the effect of different parameters
can be investigated. By conducting a parametric analysis
an optimized configuration can be proposed, calculating the
best trade-off value of each parameter. In the following
section, the effect of different aerodynamic and hydrody-
namic parameters on the performance of the AAMV has
been evaluated.
Fig. 10 Model after installation
of flaps deflected 45� on the
main wing
Fig. 11 Towing tank of Sharif University of Technology
Table 4 Properties of the towing tank
Dimensions 25 m 9 2.5 m 9 1.2 m
Type of towing system Carriage ? electromotor (4 kw)
Maximum velocity 6 m/s
Maximum acceleration 2 m/s2
Fig. 12 The AAMV model in towing tank
0
0.04
0.08
0.12
0.16
0.2
0 1 2 3 4
Towing Tank Results
Semi-Empirical MethodResults
Fn
R/W
Fig. 13 Comparison between experiment and developed semi-empir-
ical method results (total resistance to weight ration)
J Braz. Soc. Mech. Sci. Eng.
123
3.2.1 Effect of the aerodynamic parameters
The profile of the wings of the AAMV is always kept the
same. With the aspect ratio fixed, a change of the chord
length leads to a change of the wing surface area, therefore
only one of these two parameters is varied: the chord
length.
3.2.1.1 Chord length [mean aerodynamic chord (MAC)]
MAC of the main wing of the AAMV is 3 m which was
varied from 1.5 to 4.5 m. Figures 15 and 16 show the
variations of total resistance to weight ratio and trim angle
with Froude number. Increase in MAC means increase in
the wing area, and thus will lead to an increase in aero-
dynamic lift and resistance forces. Increase in aerodynamic
lift, which sustains the weight of the vehicle, will result in a
reduction in get-away speed and therefore, the AAMV
leaves the water sooner and consequently will possess a
lower hydrodynamic resistance. However, increase in
MAC is accompanied with an increase in the aerodynamic
resistance, either. This is why the total resistance of the
AAMV of 4.5 m MAC is more than two other configura-
tions as shown in Fig. 15. Additionally, Fig. 16 shows that
the increase in MAC increases the trim angle of the AAMV
across the whole speed range, which can be associated with
the increase of the aerodynamic lift-up moment.
3.2.2 Effect of the hydrodynamic parameters
3.2.2.1 Dead-rise angle (beta) Dead-rise is the trans-
verse slope of the bottom of the boat, measured in degrees.
A boat with a flat bottom has 0� dead-rise angle. Figure 18
show that if the dead-rise angle is increased, the trim
equilibrium attitude at the same speed will be higher. This
is because if the dead-rise angle increases the hydrody-
namic lift generated will decrease, therefore to obtain the
same hydrodynamic lift it is necessary to have a bigger trim
equilibrium angle. From Fig. 17 it can be inferred that a
higher trim angle leads to a higher draft and resistance to
weight ratio (Fig. 17). Therefore, if the dead-rise angle
increases, the resistance to weight ratio will be higher
across the entire speed range.
3.2.3 Effect of inertia
The inertial parameters are the Longitudinal and Vertical
positions of the CG, respectively longitudinal center of
0
1
2
3
4
5
6
0 1 2 3 4
Towing Tank Results
Semi-Empirical Method Results
Trim
(deg
)
Fn
Fig. 14 Comparison between experiment and developed semi-empir-
ical method results (trim angle)
0
0.05
0.1
0.15
0.2
0.25
0 2 4 6 8
MAC=1.5 m
MAC=3 m
MAC=4.5 m
R/W
Fn
Fig. 15 Variations of total resistance to weight ratio of the AAMV
with Froude number
0
1
2
3
4
5
6
7
0 2 4 6 8
MAC= 1.5 m
MAC=3 m
MAC= 4.5 m
Tri
m(d
eg)
Fn
Fig. 16 Variations of trim angle of the AAMV with Froude number
00.020.040.060.080.1
0.120.140.160.180.2
0 2 4 6 8 10
Beta=10 deg
Beta=20 deg
Beta=30 degR
/W
Fn
Fig. 17 Variations of total resistance to weight ratio of the AAMV
with Froude number
J Braz. Soc. Mech. Sci. Eng.
123
gravity (LCG) and VCG, the total mass, and the pitch
moment of inertia, I55. Only LCG and mass have been
analyzed, since VCG is limited by the lateral hydrostatic
stability of the AAMV at rest and I55 does not have any
influence on the equilibrium attitude.
3.2.3.1 Weight In the conceptual design stage, the
examination of the weight effect on the AAMV perfor-
mance could be intriguing. Therefore, the AAMV’s weight
was altered from 4.5 to 7.5 tons. It should be noted that in
high speeds, with regard to Fig. 19, the least resistance to
weight ratio is related to the heaviest AAMV. Therefore,
with increase in the speed the best configuration in terms of
the resistance to weight ratio is related to the heaviest one.
This condition is very similar to the high speed crafts.
Additionally, it seems obvious that the heavier vehicle will
experience the bigger hydrodynamic resistance because of
the increase in the AAMV’s draft, and accordingly will
experience a higher trim angle (Fig. 20).
3.2.3.2 Longitudinal position of the center of gravity
(LCG) The LCG is a fundamental parameter of planing
craft design. It strongly influences the equilibrium attitude
and the static and dynamic stability of the vehicle. The
LCG of the AAMV is 3.7 m and it is changed from 3 to
4.7 m. It should be noted that CG cannot be transferred too
much backwards or forwards. Figures 21 and 22 show the
variations of total resistance to weight ratio and trim angle
versus Froude number for different CGs. As shown in
Figs. 21 and 22, increase in the LCG decreases the resis-
tance and trim, especially in the hump vicinity. As a result,
0
1
2
3
4
5
6
7
0 2 4 6 8 10
Beta=10 deg
Beta=20 deg
Beta=30 deg
Tri
m(d
eg)
Fn
Fig. 18 Variations of trim angle of the AAMV with Froude number
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0 2 4 6 8 10
Mass=4500 kg
Mass= 6600 kg
Mass=7500 kg
R/W
Fn
Fig. 19 Variations of total resistance to weight ratio of the AAMV
with Froude number
0
1
2
3
4
5
6
7
8
0 2 4 6 8 10
Mass=4500 kg
Mass= 6600 kg
Mass=7500 kg
Tri
m(d
eg)
Fn
Fig. 20 Variations of trim angle of the AAMV with Froude number
00.020.040.060.080.1
0.120.140.160.180.2
0 2 4 6 8 10
LCG = 3 m
LCG = 3.7 m
LCG = 4.7 m
R/W
Fn
Fig. 21 Variations of total resistance to weight ratio of the AAMV
with Froude number
0
1
2
3
4
5
6
7
8
0 2 4 6 8 10
LCG=3 mLCG=3.7 mLCG=4.7 m
Tri
m(d
eg)
Fn
Fig. 22 Variations of trim angle of the AAMV with Froude number
J Braz. Soc. Mech. Sci. Eng.
123
with regard to the Fig. 21 it can be inferred that CG had
better to be moved forward.
4 Conclusions
An efficient and low-cost method for analyzing the AAMV
performance in take-off phase was developed. Performance
assessment employing experimental and numerical
approaches, due to the urgent need of these methods to
precise laboratory equipment and computer with high
processing abilities, can be remarkably expensive and time
consuming. However, this method can properly estimate
the AAMV performance in the shortest possible period of
time, requiring only an ordinary computer. In this method,
total aerodynamic lift force in the interaction with effective
weight was placed in the hydrodynamic relations. Equi-
librium equation was expressed at the same time with
regard to hydrodynamic and aerodynamic forces, and
hydrodynamic characteristics were determined on the basis
of the equilibrium equation. After conducting a model test
in towing tank the developed method was well-validated
against experimental data. In addition, the effect of various
aerodynamic and hydrodynamic parameters such as chord
length, dead-rise angle, mass and LCG on the hydro-
aerodynamic performance of the AAMV was examined.
With the increase in the wing chord and keeping the aspect
ratio constant, the AAMV’s take-off happens in lower
speeds and the craft possesses totally a lower hydrody-
namic resistance; however, the AAMV will experience a
higher total resistance due to the increase in aerodynamic
resistance. Also, increase in the dead-rise angle will
increase the total resistance and trim angle of the vehicle in
the entire speed range. The variation of LCG has a sig-
nificant effect on the trim angle and the longitudinal sta-
bility of the AAMV. Increase in LCG decreases both the
trim angle and total resistance, especially in the hump
vicinity. It is worthy to mention that one of the distinct
advantages of the present method is that, for the purpose of
improving the performance of the AAMV, this method can
be employed in parallel to an optimization algorithm to
find each hydrodynamic and aerodynamic parameters
optimized value.
References
1. Meyer JR, Clark, DJ, Ellsworth WM (2004) The quest for speed
at sea. Technical digest, Card rock Division, NSWC
2. Olson RE, Allison MA (1960) The calculated effect of various
hydrodynamic and aerodynamic factors on the take-off of flying
boat. NACA Report No. 702
3. Parkinson J, Bell J (1934) The calculated effect of trailing edge
flaps on the take-off of flying boat. NASA Report No. 510
4. Yun L, Bliault A, Doo J (2010) WIG craft and ekranoplan. Book,
Springer, New York
5. Rozhdestvensky V (2000) Aerodynamics of a lifting system in
extreme ground effect. Springer, Berlin
6. Kornev N, Matveev K (2003) Complex numerical modeling of
dynamics and crashes of wing in ground vehicles. Am Inst
Aeronaut Astronaut 1–9
7. Yong Seng J (2005) Stability, performance and control for a wing
in ground vehicle. Thesis of Master of Science National Uni-
versity of Singapore, Singapore
8. Matveev K (2007) Static thrust recovery of PAR craft on solid
surface. J Fluids Struct 24:920–926
9. Matveev K, Soderlund R (2008) Static performance of power-
augmented ram vehicle model on water. Ocean Eng
35:1060–1065
10. Yinggu Z, Guoliang F, Jianqiang Y (2011) Modeling longitudinal
aerodynamic and hydrodynamic effect of a flying boat in calm
water. IEEE 2039–2044
11. Savitsky D, DeLorme MF, Datla R (2007) Inclusion of whisker
spray drag in performance prediction method for high-speed
planing hulls. Mar Tech 44(1):35–56
12. Collu M, Minoo H, Trarieux F (2012) The longitudinal static
stability of an aerodynamically alleviated marine vehicle, a
mathematical model. R Soc 1–21
13. Priyanto A, Maimun A, Noverdo S, Jamei S, Faizal A, Wa-
qiyuddin M (2012) A study on estimation of propulsive power for
wing in ground effect (WIG) craft to take-off. J Tech Sci Eng
59:43–51
14. Matveev K, Chaney C (2013) Heaving motions of a ram wing
translating above water. J Fluids Struct 38:164–173
15. Grundy IH (1986) Airfoils moving in air close to a dynamic water
surface. J Aust Math Soc 27:327–345
16. Barber T (2006) Aerodynamic ground effect: a case study of the
integration of CFD and experiments. Int J Veh Des
40(4):299–316
17. Anderson JD (1999) Aircraft performance and design. McGraw-
Hill, New York
18. Fink M, Lastinger J (1961) Aerodynamic characteristics of low-
aspect-ratio wings close proximity to the ground. NASA Report
No. TN D-926
19. Mercier JA, Savitsky D (1973) Resistance of transom shear crafts
in the preplaning range. Davidson Laboratory, Stevens Institute
of Technology, Report No. 1667
20. Faltinsen OM (2005) Hydrodynamics of high-speed vehicles.
Cambridge University Press, UK
21. Holtrop J, Mennen G (1978) A statistical power prediction
method. Int Shipbuild Prog 25(290):253–256
22. Savitsky D, Ward Brown D (1976) Procedure for hydrodynamic
evaluation of planing hulls in smooth and rough water. Mar Tech
13(4):381–400
23. Kapryan WJ (1960) Effects of gross load and various bow
modifications on the hydrodynamic characteristics of a high-
subsonic mine-laying seaplane. NASA Report No. TM X-71
J Braz. Soc. Mech. Sci. Eng.
123