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Int. J. Aerodynamics, Vol. 1, No. 1, 2010 97
Copyright © 2010 Inderscience Enterprises Ltd.
Effects of design parameters on longitudinal static
stability for WIG craft
Wei Yang, Zhigang Yang*
and Chengjiong Ying
Shanghai Automotive Wind Tunnel Centre,
Tongji University,
Caoan Road 4800, Jiading District,
Shanghai 201804, P.R. China
Fax: +86-21-69583785
E-mail: david_yangwei@yahoo.cn
E-mail: zhigangyang@tongji.edu.cn
E-mail: yingchengjiong@126.com
*Corresponding author
Abstract: The longitudinal stability characteristics of a wing-in-ground effect
(WIG) craft are quite different from that of conventional airplane due to the
existence of ground effect. The effects of design parameters including wing
section, stabiliser, wing planform and endplate on longitudinal static stability of
WIG craft were studied based on numerical results. Contributions of these
parameters on stabilising the WIG craft by shifting the aerodynamic centres in
pitch and height were discussed respectively. The present study resulted in deep
understanding of relationship between longitudinal static stability and WIG
craft configuration, provided references for designers and operators of WIG
craft theoretically.
Keywords: wing-in-ground effect; aerodynamics; longitudinal static stability;
computational fluid dynamics; CFD.
Reference to this paper should be made as follows: Yang, W., Yang, Z. and
Ying, C. (2010) ‘Effects of design parameters on longitudinal static stability for
WIG craft’, Int. J. Aerodynamics, Vol. 1, No. 1, pp.97–113.
Biographical notes: Wei Yang received his Master’s degree in Fluid
Mechanics from Nanjing University of Aeronautics and Astronautics, China, in
2006. Currently, he is a PhD student of Automotive Engineering in Tongji
University, China. His main research focuses on fields of aerodynamics of
crafts and vehicles, and ground effect.
Zhigang Yang is a Professor in College of Automotive Engineering, Tongji
University, China. He received his PhD degree from the Department of
Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY. His
main research interests are in the areas of flow instability and transition,
turbulence modelling, vehicle aerodynamics and airflow, flows and combustion
in aero-propulsion systems flows and wind tunnel corrections.
Chengjiong Ying is currently a postgraduate student at the College of
Automotive Engineering in Tongji University, China. His research interests
include topics such as automotive engineering and aerodynamics.
98 W. Yang et al.
1 Introduction
The wing-in-ground effect craft is considered to be a promising form of transport, due to
its high speed and low fuel consumption. Unlike conventional aircraft, the characteristics
of force and moment of a WIG craft vary due to pitch and height, when the craft
approaches the ground. Only appropriately designed, can WIG craft escape from the
potential danger of kissing the ground (or water surface). The most important issue for
the operation of WIG craft is the longitudinal static stability, for the longitudinal dynamic
stability can be usually fulfilled when the system parameters, which provide the static
stability, are within a certain range.
The issue of longitudinal stability of wing-in-ground effect craft has existed for
decades as a very critical design factor since the first experimental WIG craft has been
built. A series of studies were performed and focused on the longitudinal stability
analysis. Kumar (1968) derived equations of longitudinal motion of a WIG vehicle by
using quasi-steady aerodynamic derivatives. Irodov (1970) carried out his work on
longitudinal stability of ekranoplans and formulated the criterion of longitudinal static
stability as the requirement. Rozhdestvensky (1997) applied mathematics of extreme
ground effect (EGE) to study the cross-section of wing in ground effect. Taylor (1995)
has carried out an elegant experimental verification of the stability of a schematised
Lippisch configuration. The longitudinal stability analysis on a 20-passenger WIG was
conducted by Chun and Chang (2002) based on wind tunnel test data. At the same time,
WIG crafts with different configurations considering longitudinal stability have been
built (Halloran and O’Meara, 1999; Rozhdestvensky, 2006; Matveev and Soderlund,
2008; The WIG Page, http://www.se-technology.com/).
In regard to the longitudinal stability of WIG craft, the current study investigated the
relationship between longitudinal static stability and some design parameters in 2D and
3D. Based on numerical results of convenient CFD method, the aerodynamic centres in
pitch and height were calculated and the flows with different configurations were
presented. The shifting of aerodynamic centres in pitch and height was studied
respectively, and then are the contributions of design parameters to longitudinal static
stability of WIG craft. The present work reaches a clear understanding of relationship
between longitudinal static stability and design parameters of WIG craft, and provides
theoretical directions for designers and operators of WIG crafts.
2 Numerical approach
2.1 Computational arrangement
As mentioned, the CFD method is convenient and time saving. In the present study, flow
in ground effect region is simulated by solving the incompressible Reynolds-averaged
Navier-Stokes equations with the realisable kε
−
turbulence model (Shih et al., 1995) at
the Reynolds number of 2 × 107 (based on the chord length of main wing). The governing
equations are written as:
0
i
i
U
x
∂=
∂ (1)
Effects of design parameters on longitudinal static stability for WIG craft 99
2
''
()
1()
ij
ii
ij
jijjj
UU
UU
Pvuu
tx xxxx
∂
∂∂
∂∂
+=−++−
∂∂ ∂∂∂∂
ρ
(2)
where ''
()
ij
uu− is the Reynolds stress term. The transport equations of k and
ε
are written
as:
() ( ) ( )
t
j
kb Mk
jjkj
μk
kku
μ
GG Y S
tx x x
∂∂ ∂ ∂
⎡⎤
+=++++−−+
⎢⎥
∂∂ ∂ ∂
⎣⎦
ρρ ρε
σ
(3)
2
12
1
() ( ) ( )
t
j
jj j
b
μ
uμCS C
tx x x kv
CCGS
k
∂∂ ∂ ∂
⎡⎤
+=++−
⎢⎥
∂∂ ∂ ∂ +
⎣⎦
++
ε
ε3ε ε
εε
ρε ρε ρ ε ρ
σ
ε
ε
(4)
This turbulence model has been extensively validated and well behaved for a wide range
of flows, including rotating homogeneous shear flows, free flows including jets and
mixing layers, channel and boundary layer flows, and separated flows. The
incompressible Navier-Stokes equations, eq. (1) and eq. (2), are solved by the SIMPLE
algorithm with a second-order upwind scheme applied to the convection terms.
Figure 1 Lift, drag and pitch moment coefficients for NACA0012
0 2 4 6 8 10 12 14 16 18 20
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
α
C
L
Experim ent
Computati on
0246810 12
0
0.005
0.01
0.015
0.02
0.025
α
C
D
Experiment
Computation
(a) lift (b) drag
0246810 12 14 16 18
-0.25
-0.2
-0.15
-0.1
-0.05
0
α
C
m1/4
Experiment
Computati on
(c) pitch moment
100 W. Yang et al.
Before numerically investigating the aerodynamics of wing in ground effect, the present
computational method is firstly validated based on aerodynamic characteristics of
NACA0012 airfoil out of ground effect at a Reynolds number of 6 × 106. Lift, drag and
pitch moment are compared with experimental data (Abbott and von Doenhoff, 1959)
with free transition in Figure 1. Good agreement of lift is achieved while drag is not
predicted accurately. Pitch moment is predicted well before separation occurs and bad
after. A possible reason is that more viscous effect is introduced and viscous drag is
overestimated.
For the computational domain, the inflow was placed 6c upstream of the trailing edge
of airfoil, the outflow 15c downstream and 6c in height. The side boundary was placed 6c
away from wing tip in 3D cases. The computational grids in the current simulations are
made of structured blocks. Cells of ten layers were clustered towards the walls with a
stretching ration of 1.1. The y+ value at the wall is around 200, which is suitable for wall
function applied in numerical simulation. A velocity inlet boundary condition prescribed
a uniform velocity. At the outflow boundary, a pressure outlet boundary condition
specified a gauge pressure of zero. A slip boundary condition (symmetry) was specified
on the top and side far boundaries. A no-slip boundary condition was specified on the
wing and the ground. The ground was considered to be rigid and had the same velocity as
inlet.
2.2 Longitudinal static stability
Firstly, a WIG craft should be stable in pitch like an airplane. The WIG craft should
respond by a negative increment of the pitching moment to a positive increment of the
angle of attack, mathematically given as follows:
,0
m
C<
α
(5)
where m
Cis the moment coefficient with respect to the centre of gravity (c.g).
An additional stability condition should be considered for the variation of force and
moment of a WIG craft with height. Since the force and moment change with pitch angle
and relative height, the following derivatives can be conducted:
,,
,,
LL Lh
mm mh
CC C h
CC C h
=+
=+
α
α
δ
δα δ
δ
δα δ
(6)
,0
Lh
C< (7)
According to Staufenbiel (1978) and Staufenbiel and Schlichting (1988), the relative
condition for height stability is:
,
,,
,
0
mh
Lh L
m
C
CC
C
−⋅ <
αα
(8)
Taking requirements (5) and (7) into account, the height static stability criterion can be
written in the form proposed by Irodov (1970):
,,
,,
0
mmh
LLh
CC
CC
−<
α
α
Effects of design parameters on longitudinal static stability for WIG craft 101
or,
0
h
xx−>
α
(9)
where ,
x
α
corresponding to the aerodynamic centre in aircraft stability, is the
aerodynamic centre in pitch for WIG craft. h
x
is the aerodynamic centre in height. The
axis x is directed upstream for body axis system and the symbols are
non-dimensionalised. According to this criterion, we can see that the position of the
centre of gravity does not influence the height stability of WIG craft. It is worthwhile
keeping in mind that certain behaviour of craft can be achieved by locating the centre of
gravity. The location of centre of gravity in relation to the location of aerodynamic
centres is important. Favourable position of the centre of gravity can provide a properly
designed WIG craft with sufficient stability (Nikolai and Konstantin, 2003). As
experience shows, the centre of gravity should be located between the aerodynamic
centres in pitch and height and close to the centre in height. To make things a little bit
more challenging the positions of both centre in pitch and centre in height are dependent
on height and pitch angle.
3 Numerical results and longitudinal stability analysis
For ease of analysis,
x
α
and h
x
are calculated from the leading edge and x is positive in
downstream direction against body axis system. Accordingly, the requirement (9)
becomes:
0
h
xx−>
α
(10)
2D flow of wing in ground effect is firstly simulated considering tail unit and wing
section, and then are the wing planform and endplate in 3D study.
3.1 Airfoil section
Not many wing sections have been designed for operation in ground effect. The WIG
craft usually just utilised some commonly known wing sections. A very popular wing
section of Clark-y was assumed to be good in ground effect, because of its flat bottom.
Also, an s-shaped wing section allows WIG craft operates stably in ground effect.
Figure 2 shows 2D computational grids in ground effect for Clark-y and N 60 r.
Figure 2 2D computational grids
(a) Clark-y (b) N 60 r
102 W. Yang et al.
Figure 3 Aerodynamic centres of Clark-y
33.5 44.5 55.5 6
0.25
0.3
0.35
0.4
0.45
0.5
0.55
α
x/c
x
h
h/c=0. 05
x
α
h/c=0. 05
x
h
h/c=0. 08
x
α
h/c=0. 08
x
AC
OGE
0.3 0.32 0.34 0. 36 0.38 0.4 0.42 0.44 0.46 0.48 0.5
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
x
c.g
x/c
x
h
x
α
(a) at xc.g. = 0.35 (b) at
α
= 5 , h/c = 0.08
Figure 3(a) shows the shifting of the aerodynamic centres of Clark-y in ground effect
based on computational results. The centre in pitch
x
α
moves forward and the centre in
height h
x
moves backward with increase of angle of attack. Both
x
α
and h
x
shift
towards the leading edge when leaving the ground. This is why not designed properly
WIG craft shows a dangerous pitch up tendency when climbing out of ground effect, just
like a race boat flips over on the sea surface. Figure 3(b) describes the fact that a
statically unstable WIG craft can not become stable by shifting the centre of gravity. The
centre in height is independent of the location of centre of gravity. Meanwhile the centre
in pitch is slightly affected by shifting of the centre of gravity.
Figure 4 Aerodynamic centres of N60 r
33.5 44.5 55.5 6
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
α
x/c
x
h
h/c= 0.05
x
α
h/c= 0.05
x
h
h/c= 0.08
x
α
h/c= 0.08
In order to keep stable, requirement (10) is indispensable. Generally a common airfoil
will be unstable in ground effect. One popular solution to stabilise a WIG craft is to
utilise a favourable s-shaped wing section. The s-shaped airfoil contributes in shifting the
centre in height upstream. Thereby, a single wing of s-shaped airfoil can be stable in a
narrow region as shown in Figure 4. The centre in height is sensitive to angle of attack
that restricts the operation of the WIG craft.
Effects of design parameters on longitudinal static stability for WIG craft 103
Figure 5 Pressure coefficient at
α
= 4
00.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
-1.5
-1
-0.5
0
0.5
1
x/c
C
p
OGE Clark-y
IGE Clark-y
IGE N 60 r
For conventional airfoils out of ground effect (OGE), the aerodynamic centre is located
approximately 25% of the chord from the leading edge of the airfoil, and the location is
usually unchangeable. Static pitch stability of aircraft can be satisfied by positioning the
centre of gravity. This is impossible in ground effect with two unfixed aerodynamic
centres recognised in a WIG craft. Furthermore, the two aerodynamic centres are located
after 25% of the chord. Figure 5 represents the pressure coefficient distribution along the
chord for airfoil of N 60 r and Clark-y in and out of ground effect. For Clark-y in ground
effect, the lower surface exhibits high pressure from the leading edge to the trailing edge,
resulting in rearward moving of the aerodynamic centres. It also indicates that the
s-shaped airfoil achieves height stability through unloading the rear part of the lower
surface at the cost of lift. Thus, WIG craft with s-shaped airfoil section shows better
height stability and worse aerodynamic performance.
Figure 6 Computational grids with tail
3.2 Horizontal stabiliser
Although some wings can be stable in ground effect, a highly positioned horizontal tail is
always essential. The tail unit with wing section of NACA0012 was applied in 2D
simulation. Figure 6 shows the grids. The main wing section is Clark-y. Figure 7 depicts
the aerodynamic centres in pitch and height with tail. In theory, the aerodynamic
characteristics of horizontal tail are not affected by ground effect. Accordingly the tail
does not have any influence on the position of .
h
x
On the other hand, tail will give a
negative part to ,m
C
α
improving pitch stability.
104 W. Yang et al.
Figure 7 Aerodynamic centres with tail
33.5 44.5 55.5 6
0.38
0.4
0.42
0.44
0.46
0.48
0.5
0.52
0.54
0
.
56
α
x/c
x
h
h/c=0. 05
x
α
h/c=0. 05
x
h
h/c=0. 08
x
α
h/c=0. 08
Comparing Figure 7 with Figure 3, we can see that the tail unit makes WIG craft stable
by shifting the centre in pitch rearwards, and the centre in height is affected too. The shift
of h
x
cancels out the positive shift of
x
α
partially. Performance of horizontal tail will
suffer from the existence of the wing tip vortices in practice. These make the tail unit less
efficient than expected for height stability of a WIG craft.
Designers of WIG craft capable of OGE flight are often worried about the selection of
position for centre of gravity, for only one position can not insure simultaneously stable
for both IGE and OGE flights. Such worries often result in a design with horizontal
stabiliser approximately 30% or more of the area of the main wing. This compares to an
aircraft tailplane, which may typically be 15–25% of the area of main wing.
Figure 8 3D computational grids
(a) Rect wing (b) FS wing
(c) RFS wing
Effects of design parameters on longitudinal static stability for WIG craft 105
3.3 Wing planform
Upon extension of the longitudinal stability analysis to 3D wings in ground effect,
the configuration of a rectangular wing with a modified airfoil section coupled with
a big horizontal tail is very popular. Synchronously, a typical configuration of
Lippisch, reversed forward swept delta wing, was introduced by a German
aerodynamicist – Lippisch in 1963, and was extended to be Airfish series (Fischer and
Matjasic, 1998). In the present study, three planforms with the same area and aspect ratio
of three were calculated in ground effect, including rectangular wing (Rect wing),
forward swept delta wing (FS wing) and reversed forward swept delta wing (RFS wing).
The computational grids were shown in Figure 8.
The shifting of aerodynamic centres in Figure 9 shows the details of the effect of
main wing planform. It is found that both centres in pitch and height are near the leading
edge with forward sweeping, which makes the locating of centre of gravity more
reasonable and flexible as out of ground effect. The aerodynamic centres of reversed
wing locate downstream that of forward swept wing. This can be explained by the
aerodynamic characteristics of the wing.
Figure 9 Aerodynamic centres in 3D
0.03 0.04 0.05 0. 06 0.07 0.08 0.09 0. 1
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
h/c
x
h
Rect wing
FS wing
RFS wing
0.03 0.04 0.05 0. 06 0.07 0. 08 0.09 0.1
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
h/c
x
α
Rect wi ng
FS wing
RFS wing
(a) centre in height (b) centre in pitch
Forward sweeping of wing introduces a loss of lift and a decrease in drag, shown in
Figure 10. Total pressure distributions near the wing tip are presented in Figure 11. It is
predicted that ground effect is weak with forward swept wing than that of rectangular
wing. Also, the wing suffers less from wing tip vortices, leading to decrease of induced
drag. The reversed wing prevents the high pressure exiting through the wing tip instead
of the trailing edge and consequently contributes in augmenting the lift further. The drag
decreases by the same reason.
Figure 12 depicted the static pressure distributions on the lower surface. The ground
effect consists of two parts, they are chord dominated ground effect and span dominated
ground effect. The former exhibits high pressure under the wing when approaching to the
ground. The later is described by reduction of induced drag or high span efficiency. For
planforms in this paper, the reversed forward swept delta wing can not only keep higher
pressure under the wing strengthening the chord dominated ground effect, but also avoid
loss from wing tip vortices fully behaving span dominated ground effect.
106 W. Yang et al.
Figure 10 Aerodynamic coefficients in 3D
33.5 44.5 55. 5 6
0.45
0.5
0.55
0.6
0.65
0.7
0.75
0.8
0.85
0.9
0.95
α
C
L
Rect wi ng
FS wing
RFS wing
33.5 44.5 55.5 6
0.01
0.015
0.02
0.025
0.03
0.035
α
C
D
Rect win g
FS wing
RFS wing
(a) lift coefficient (b) drag coefficient
33.5 44.5 55.5 6
25
30
35
40
45
50
55
60
α
L/D
Rect wi ng
FS wing
RFS wing
(c) lift to drag ratio
Figure 11 Total pressure distribution near the wing (Pa),
α
= 4 and h/c = 0.05
2.00e+03
1.90e+03
1.80e+03
1.70e+03
1.60e+03
1.50e+03
1.40e+03
1.30e+03
1.20e+03
1.10e+03
1.00e+03
9.00e+02
8.00e+02
7.00e+02
6.00e+02
5.00e+02
4.00e+02
3.00e+02
2.00e+02
1.00e+02
0.00e+00
Z
Y
X
(a) Rect wing
Effects of design parameters on longitudinal static stability for WIG craft 107
Figure 11 Total pressure distribution near the wing (Pa),
α
= 4 and h/c = 0.05 (continued)
2.00e+03
1.90e+03
1.80e+03
1.70e+03
1.60e+03
1.50e+03
1.40e+03
1.30e+03
1.20e+03
1.10e+03
1.00e+03
9.00e+02
8.00e+02
7.00e+02
6.00e+02
5.00e+02
4.00e+02
3.00e+02
2.00e+02
1.00e+02
0.00e+00
Z
Y
X
(b) FS wing
2.00e+03
1.90e+03
1.80e+03
1.70e+03
1.60e+03
1.50e+03
1.40e+03
1.30e+03
1.20e+03
1.10e+03
1.00e+03
9.00e+02
8.00e+02
7.00e+02
6.00e+02
5.00e+02
4.00e+02
3.00e+02
2.00e+02
1.00e+02
0.00e+00
Z
Y
X
(c) RFS wing
108 W. Yang et al.
Figure 12 Static pressure distribution on the lower surface (Pa),
α
= 4 and h/c = 0.05
1.60e+03
1.32e+03
1.04e+03
7.60e+02
4.80e+02
2.00e+02
-8.0 0e+01
-3.6 0e+02
-6.4 0e+02
-9.2 0e+02
-1.2 0e+03
-1.4 8e+03
-1.7 6e+03
-2.0 4e+03
-2.3 2e+03
-2.6 0e+03
-2.8 8e+03
-3.1 6e+03
-3.4 4e+03
-3.7 2e+03
-4.0 0e+03
Z
YX
(a) Rect wing
1.60e+03
1.32e+03
1.04e+03
7.60e+02
4.80e+02
2.00e+02
-8.00e+01
-3.60e+02
-6.40e+02
-9.20e+02
-1.20e+03
-1.48e+03
-1.76e+03
-2.04e+03
-2.32e+03
-2.60e+03
-2.88e+03
-3.16e+03
-3.44e+03
-3.72e+03
-4.00e+03
Z
YX
(b) FS wing
Effects of design parameters on longitudinal static stability for WIG craft 109
Figure 12 Static pressure distribution on the lower surface (Pa),
α
= 4 and h/c = 0.05 (continued)
1.60e+03
1.32e+03
1.04e+03
7.60e+02
4.80e+02
2.00e+02
-8.0 0e+0 1
-3.6 0e+0 2
-6.4 0e+0 2
-9.2 0e+0 2
-1.2 0e+0 3
-1.4 8e+0 3
-1.7 6e+0 3
-2.0 4e+0 3
-2.3 2e+0 3
-2.6 0e+0 3
-2.8 8e+0 3
-3.1 6e+0 3
-3.4 4e+0 3
-3.7 2e+0 3
-4.0 0e+0 3
Z
YX
(c) RFS wing
3.4 Endplate
Endplate is a specific feature of all WIG craft as compared to conventional aircraft.
Endplate showed a substantial improvement in aerodynamic characteristics. Thin
endplates were attached to the rectangular wing in current work. The computational grid
with endplates was shown in Figure 13.
Figure 13 Computational grid with endplate
Based on the computational results, the static height stability, ,
h
x
x
−
α
was presented in
Figure 14. The static height stability was improved when diving into 3D from 2D.
Whereas, the endplate is not favourable for static height stability since the value of
h
x
x−
α
is approaching to that of 2D while the ground clearance is increased. The shifting
of aerodynamic centres was shown in Figure 15 respectively. With enhancement of
110 W. Yang et al.
ground effect, both centres move rearwards. Especially, the centre in pitch locates
backwards that in 2D. In general, the endplate deteriorates the static height stability while
giving burdens to locating the centre of gravity. This brings some differences from study
of Park (2008) that the endplate can improve static height stability.
Figure 14 Static height stability, 4α= D
0.035 0.04 0. 045 0.05 0.055 0.06 0.065
-0.1
-0.08
-0.06
-0.04
-0.02
0
0.02
h/c
x
α
-x
h
2D
3D
3D + endplate
Figure 15 Aerodynamic centres
0.03 0.04 0.05 0.06 0.07 0. 08
0.31
0.32
0.33
0.34
0.35
0.36
0.37
0.38
0.39
0.4
h/c
x
α
2D
3D
3D + endplate
0.03 0.04 0. 05 0. 06 0.07 0.0 8
0.32
0.34
0.36
0.38
0.4
0.42
0.44
0.46
0.48
h/c
x
h
2D
3D
3D + endplate
(a) centre in pitch (b) centre in height
Figure 16 Wing tip vortex
without endplate with end
p
late
Effects of design parameters on longitudinal static stability for WIG craft 111
Figure 17 Lift coefficient
33.5 44.5 5
0.7
0.8
0.9
1
1.1
1.2
1.3
α
C
L
2D
3D
3D + endplate
The similarity of locating of positions for centres in pitch and height between 3D wing
with endplates and 2D wing relies on the similar aerodynamic performance. Figure 16
depicted the wing tip vortex of 3D wing with and without endplate. The lift coefficient
was shown in Figure 17. Endplate forbids flow to escape from the wing tip to a certain
extent. And that wing tip vortex is formed outwards with endplate. Thus the wing suffers
less from the wing tip vortex, and the aerodynamics approaches to that of 2D.
Notwithstanding, endplate is widely used in design of WIG crafts for it can capture
the high pressure air under the wing and increase the lift and lift to drag ratio further. Gap
in longitudinal stability is usually filled by accommodating other design parameters.
4 Conclusions
Designers of WIG craft going to great lengths to balance the aerodynamics and
longitudinal stability often run into trouble. It is for this reason that the current work
carried out a study on relationship between longitudinal static stability and some design
parameters of WIG craft based on CFD methods.
Wing section is an important parameter in design. It is feasible to utilise an s-shaped
wing section in order to achieve sufficient stability or reduce tailplane. This costs a bit in
lift consequently. The Lippisch inverse delta wing has shown reliable levels of
longitudinal static stability over a sufficiently wide range of pitch angles and height. It is
adopted in some small or middle size WIG crafts. While most big WIG crafts employ
‘composite wing’ configuration, a complex of a central wing of small aspect ratio with
endplates and side wings of high aspect ratio, achieving high takeoff efficiency when
using power augmentation. A large and highly mounted horizontal stabiliser serves to
shift the centre in pitch rearwards, enables one to ensure static stability, and introduces
large empty weight as well as parasite drag. The endplate behaves in an opposite way.
In contrast to an airplane, the longitudinal stability of a WIG craft can not be provided
by an appropriate selection of the centre of gravity, but can be provided only through
appropriate design of the aerodynamic configuration. In the case of longitudinal static
stability, height stability is indispensable. The requirement (10) points out that any
positive value of h
x
x−
α
will give longitudinal static stability. The longitudinal stability
achieved by rearward shifting of the centre in pitch is not sufficient and promising, for it
112 W. Yang et al.
is practical only in extreme ground effect region. The one provided by forward shifting of
the centre in height is the essence for a WIG craft to operate stably in and out of ground
effect.
Acknowledgements
The authors would like to recognise the support of Shanghai Automotive Wind Tunnel
Centre. This work was supported by Programme for Changjiang Scholars and Innovative
Research Team in university in China.
References
Abbott, I.H. and von Doenhoff, A.E. (1959) Theory of Wing Sections, Dover Publications, Inc.
1959, pp.462–467.
Chun, H.H. and Chang, C.H. (2002) ‘Longitudinal stability and dynamical motions of a small
passenger WIG craft’, Ocean Engineering, Vol. 29, 2002, pp.1145–1162.
Fischer, H. and Matjasic, K. (1998) ‘From Airfisch to Hoverwing’, in Proceedings of the
International Workshop WISE Up to Ekranoplan GEMs, The University of New South Wales,
Sydney, Australia, 15–16 June 1998. pp.69–89.
Halloran, M. and O’Meara, S. (1999) ‘Wing in ground effect craft review’, DSTO-GD-0201, 1999,
Defense Science and Technology Organization, Canberra.
Irodov, R.D. (1970) ‘Criteria of longitudinal stability of ekranoplan’, Ucheniye Zapiski TSAGI,
Moscow, 1970, Vol. 1, No. 4, pp.63–74.
Kumar, P.E. (1968) ‘An experimental investigation into the aerodynamic characteristics of a wing
with and without endplates in ground effect’, College of Aeronautics Report, Aero 201, 1968.
Matveev, K.I. and Soderlund, R.K. (2008) ‘Static performance of power augmented ram vehicle
model on water’, Ocean Engineering, Vol. 35, No. 10, pp.1060–1065.
Nikolai, K. and Konstantin, M. (2003) ‘Complex numerical modeling of dynamics and crashes of
Wing-in-Ground vehicles’, 41st Aerospace Sciences Meeting and Exhibit, Reno, Nevada, 6–9
January 2003.
Park, K. et al. (2008) ‘Effect of endplate shape on performance and stability of wings-in ground
(WIG) craft’, Proceedings of Word Academy of Science, Engineering and Technology,
Vol. 30, July 2008.
Rozhdestvensky, K.V. (1997) ‘Stability of a simple lifting configuration in extreme ground effect’,
in Proceedings of the International Conference on Wing-in-ground-effect Craft (WIGs), 4–5
December 1997, Papers No. 16, The Royal Institution of Naval Architects, London.
Rozhdestvensky, K.V. (2006) ‘Wing-in-ground effect vehicles’, Progress in Aerospace Sciences,
Vol. 42, 2006, pp.211–283.
Shih, T-H., Liou, W.W., Shabbir, A., Yang, Z. and Zhu, J. (1995) ‘A new
−
κ
ε
eddy-viscosity
model for high Reynolds number turbulent flows – model development and validation’,
Computers Fluids, Vol. 24, No. 3, 1995, pp.227–238.
Staufenbiel, R. (1978) ‘Some nonlinear effects in stability and control of wing in ground effect
vehicles’, J. Aircraft, Vol. 15, No. 8, pp.541–544.
Staufenbiel, R. and Schlichting, U.J. (1988) ‘Stability of airplanes in ground effect’, J. Aircraft,
Vol. 25, No. 4, 1988.
Taylor, G.K. (1995) ‘Wise up to a WIG’, Marine Modelling Monthly, June 1995.
The WIG Page, http://www.se-technology.com/.
Effects of design parameters on longitudinal static stability for WIG craft 113
Nomenclature
c = mean chord length, m
D
C = drag coefficient
L
C = lift coefficient
Cm = pitch moment coefficient
1/ 4m
C = pitch moment coefficient with respect to location of 1/4 chord
p
C = pressure coefficient
h = flight height (ground clearance, calculated from trailing edge to ground), m
h/c = relative height
i
U = velocity in i direction, m/s
..cg
x
= center of gravity with respect to the leading-edge (LE)
x
α
= aerodynamic center in pitch with respect to LE
h
x
= aerodynamic center in height with respect to LE
A
C
x
= aerodynamic center in OGE with respect to LE
α
= angle of attack for the wing
ρ
= density, kg/m3
v = kinematic viscosity, m2/s
Subscripts
h = differentiation with respect to the dimensionless variable, h/c
α
= differentiation with respect to the angle of attack