Development of a semi-empirical method for hydro-aerodynamic performance evaluation of an AAMV, in...

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]


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


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


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


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.


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


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


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


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)


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


with Froude number


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


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


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


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


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



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.

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