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Maritime Technology and Engineering 3 – Guedes Soares & Santos (Eds)
© 2016 Taylor & Francis Group, London, ISBN 978-1-138-03000-8
Effect of wing geometrical parameters on the aerodynamic performance of
wing in ground marine craft
M. Mohamed
Department of Naval Architecture and Marine Engineering, Faculty of Engineering, Alexandria University,
Alexandria, Egypt
I. Amin
Department of Naval Architecture and Marine Engineering (NAME), Faculty of Engineering, Port Said University,
Port Said, Egypt
ABSTRACT: The aerodynamic performance of a 3-D NACA 6409 wing in ground effect was examined numer-
ically with different wing configurations. The influence of changing twist angles, anhedral angles, taper ratios,
and sweep angles on the aerodynamic performance was examined and compared with based model. Structured
mesh domains were built, and RANS turbulence model Spalart-Allmaras was solved with a commercial solver.
Base model numerical results show good agreement with available experimental data. The results show that
wash-in twist has a positive effect on wing aerodynamic performance near ground proximity, as well as anhedral
angles. Although swept wings have a negative effect on aerodynamic efficiencies compared with non-swept
wings, an optimum swept twisted wing configuration was proposed to achieve higher aerodynamic efficiency,
while applying wing sweep. Tapered wings produced a slight increase in aerodynamic efficiency in a narrow
range of taper ratios. Speed variation has no drastic or abrupt effect on results.
1 INTRODUCTION
Wing in ground effect vehicles are flying units that uti-
lize the effect of ground proximity interaction with the
unit’s wing to increase aerodynamic efficiency, besides
many more benefits. The pioneers of ground effect
vehicles; Alexeyev and Lippisch, worked on proposing
best solutions for a ground effect vehicle design, not to
mention wing shape optimization. Wing geometrical
parameters are critical for achieving optimum wing
aerodynamic performance for a defined flying mis-
sion. Wing geometrical washout twist has been proved
that it decreases induced drag in case of elliptical plan-
form by Phillips (2004). He also found that the total
angle of twist required to minimize the induced drag
on a wing of any planform shape is directly propor-
tional to the lift coefficient developed by the wing.
Ferris (1977) confirmed that the combination of wing
twist and camber increases lift coefficient. “The solu-
tion of the 1D simplified engineering model of the
wing indicated that a constant taper wing, with straight
leading edge and having a tip ratio of 0.4, gives the best
aerodynamic performance” that was the statement of
(Akwaboa et al. 2009) after his trials to optimize wing
weight while preserving aerodynamic performance
through applying wing taper. Kachel (2013) used taper
ratioin distributingwing weightand confirmed its pos-
itive effect.Adler (1947) compared the effect of sweep
on wings of constant aspect ratio at Mach 0.925, he
found a significant drop in drag with increasing sweep
angle, while the optimum lift he obtained was at 30◦
of sweep. (Yen et al. 2011) assured that swept wings
increase generated lift at a specific sweep angle, com-
pared to non-swept wings. (Yang et al. 2010) compared
forward and backward swept delta wings in ground
effect, backward swept delta wing achieved higher lift
to drag ratio than a rectangular wing and a forward
swept delta wing, also he described the how the lat-
ter wing moves both aerodynamic centre of pitch and
centre of height forward. In aspects of WIG craft unit
design sweep would be more helpful in providing a
wide range of flexibility in terms of enhancing the
craft’s stability, and its wing structural rigidity while
keeping or improving the aerodynamic performance of
the wing. The analysis of Kachel (2013) reveals that
the variation of the backward sweep angle of the wing
within a range from 0◦to 45◦improved wing’s rigid-
ity distribution, whilst the subsequent increase of the
backward sweep angle is associated with a diminished
effect of the torsional rigidity. Also, wing sweep can
be helpful to adjust pitch control in the design phase,
as pitch control is one of the main important topics
in designing a WIG craft to ensure smooth and effec-
tive response of the unit, as flying near the ground
or the ocean is dangerous and requires huge safety
margins of control. Wright (2011) was able to demon-
strate how forward and backward sweep are effective
in pitch control. Nuhait (1988), stated that dihedral
347
Table 1. Domain boundary conditions.
Face Condition
Inlet Velocity inlet
Outlet Pressure outlet
Top Symmetry
Left Symmetry
Right Symmetry
Ground Wall boundary
Wing surface Wall boundary
angles decrease the benefits of the ground proximity
in terms of lift and drag enhancement. Dihedral angles
tend to help in rolling an aircraft back to its position
whenever they are banked, that they can be used to con-
trol rolling moment, as the resulting rolling moment
is approximately proportional to the dihedral angle
as stated by Raymer (2012). In ground effect where
the wing is placed near the ground, induced drag is
reduced due to span dominated ground effect, mean-
while, an increase in lift takes place as a result of chord
dominated ground effect as stated by Rozhdestven-
sky (2000). Through WIG vehicle design phase, wing
geometrical parameters have important contribution
in the vehicle performance integrity. Due to the lack
of experimental data that reflect different geometri-
cal wing configurations performance in ground effect,
it’s hard to predict and select wings for a proposed
WIG craft. Therefore, an accurate calculation of wing
aerodynamic performance is needed to achieve an
energy efficient design of a WIG marine unit. This
current work provides numerical results of the aerody-
namic performance of different wings’ configurations
in ground effect, and help in building a better under-
standing of how wing’s geometrical parameters affect
the aerodynamic performance in ground effect. The
obtained results will be used as a wing design reference
of a future WIG craft.
2 NUMERICAL MODEL
2.1 Computation domain
A single ground clearance was used in all the simula-
tions which is h/c =0.3, while changing the wing geo-
metrical parameter throughout a range of Reynolds’s
number from 2 ×10E +5to4.8×10E +5. NACA
6409 section wing was used of an aspect ratio AR=2,
that was under turbulence intensity ratio I =5 and
have a surface roughness height to chord length
ratio =2.5 ×10E-3. Boundary conditions were cho-
sen as shown in table 1, and illustrated in Figure 1.
A structured H mesh was used all over the domain,
except for the free tip surface, where an unstructured
mesh was implemented as shownin Figure 2. The mesh
achieved a minimum orthogonal quality of 0.3981 in
few cells on a scale of 0 to 1. Y-plus (Y+) values
were kept into the logarithmic law region; (Y+)>30.
Spalart-Allmaras turbulence model was selected to be
Figure 1. Computation domain dimensions.
Figure 2. Domain grid topology.
used, as it was proved to have the best agreement with
experimental results if compared to other turbulence
models as shown in Figure 3, according to (Jung et al.
2008) and (Djavareshkian et al. 2011).
Table 2 with the aid of Figure 4, show the wing
geometrical configurations and their parameters that
were investigated in the current work. Also, an inves-
tigation was made to compare wing performance in
ground effect at ground clearance h/c =0.1, and wing
performance out of ground effect.
ICEM CFD was used to construct all the meshes,
and Ansys FLUENT solved the incompressible steady
flow Reynolds-averaged Navier-Stokes equation, to
obtain the results of these simulations. Flow is consid-
ered incompressible as the maximum Mach number
used is equal to 0.105 at ICAO standard atmosphere.
2.2 Verification and validation of the computational
method
Aerodynamic characteristics of NACA 6409 wing
with AR =2 were simulated at AOA =8, h/c =0.1
348
Figure 3. The coefficient of lift of NACA 6409 section wing
in ground effect at various ground clearances with different
turbulence models. (Djavareshkian et al. 2011).
Figure 4. Wing geometrical parameters; sweep, twist, taper,
and anhedral.
and Reynolds number =3.4 ×10E +5, these charac-
teristics were compared with experimental data and
previous simulation using the same turbulence model
Spallart Allmaras.The results showed good agreement
with experimental data and perfect agreement with
(Djavareshkian et al. 2011) similar simulation.
In order to preserve mesh independency an inves-
tigation of elements number effect on the results was
carried out as shown in Figure 5, which represents
a variation within 0.3% to 0.7% between Numerical
and experimental coefficient of lift and 15% to 17%
Table 2. Wing configuration parameters.
Wing configuration Parameter Step size
Wash in twist 0◦to 8◦2◦
Backward sweep 5◦to 35◦5◦
Twisted swept wing 6◦of twist & 5◦
5◦to 35◦sweep
Wing taper 0.25 to 1.00 0.25
Wing anhedral 0◦to 6◦2◦
Figure 5. Experimental and numerical coefficient of drag
and coefficient of lift at ground clearance h/c =0.1 in
different grid sizes.
Table 3. Number of element in each grid size and its results.
No. of elements Coarse Medium Fine
CL 0.837534 0.841093 0.846353
Exp CL. 0.84 0.84 0.84
CD 0.082161 0.080814 0.080658
Exp. CD 0.07 0.07 0.07
between Numerical and experimental coefficient of
drag for a range of coarse, medium, and fine grid
respectively. Also, numerical results vary in a range
of 0.4% to 1% between coarse, medium and fine grid.
Table 3 displays the number of elements of each grid.
For these 3-D simulations, domains were modeled as
shown in Figure 1 with the recommended dimensions
given by (Djavareshkian et al. 2011) after all their tri-
als to attain an independent mesh, at which results will
not be affected by domain dimensions.
2.3 Solving parameters
Semi implicit method for pressure linked equations
(SIMPLE) was used to discretize the pressure equa-
tion, while the second order upwind scheme was
chosen to discretize momentum equation. For accept-
able convergence of solutions, the tolerance value for
lift and drag results was set to be equals to 10E-4.
Approximately, 1.46 million elements were used in the
domains of these simulations.
349
Figure 6. Drag coefficient, lift coefficient, and aerody-
namic efficiency at different twist angles.
Figure 7. Percentage of aerodynamic efficiency change for
investigated configurations; twist, sweep, twist- sweep, and
anhedral.
3 RESULTS AND DISCUSSION
The coefficient of lift of wash-in twisted wing in
ground effect linearly increases by increasing the twist
angle for the same angle of attack, as shown in Figure
6. This is reasoned by the increase in angle of attack
of the wing tip, in addition to the decrease in ground
clearance at the tip if compared to the wing root. The
coefficient of drag increased also as the wash-in twist
angle increased. It has been noticed that the coeffi-
cient of drag is identical for all investigated speeds at
an angle of wash-in twist equal 6◦. It’s worth mention-
ing that the point of 6 angles of wash-in twist acted
as an inflection point of the speed curves, where at
twist angle equal 4◦, the wing had the least coeffi-
cient of drag at speed 2 ×10E +5. In contrary, the
highest coefficient of drag at angle of twist equal 8
was at the same speed 2×10E+5. Figure 6 shows that
at 6◦of wash-in twist, the maximum aerodynamic
efficiency occurs, which leads to the maximum per-
centage of increase in aerodynamic efficiency equals
17.27%, if compared to an untwisted wing under the
same conditions as shown in Figure 7.
Figure 8 shows that a swept wing at 5 degrees of
backward sweep is exposed to a slight increase in
drag. More degrees of sweep would have a remarkable
decrease in drag. The lift generated under a swept wing
in ground effect decreases as the angle of backward
Figure 8. Lift coefficient, drag coefficient, and aerody-
namic efficiency of various sweep angles.
sweep increase as demonstrated in Figure 8. It was
recorded that backward sweep has a negative effect on
the aerodynamic efficiency of wings in ground effect
through the specified speed range as shown in Figure
8. In comparison to a non-swept wing the percentage
of aerodynamic efficiency reduction due to wing back-
ward sweep angles can be detected through Figure 7,
it reaches 25% of reduction at 35 degrees. Figure 9
shows the coefficient of lift of the compound wing,
which has 6◦of twist and variable sweep angles tested
through different Reynolds numbers. The coefficient
of lift has a maximum value through the speed range at
6.5 angles of sweep.Angles 6◦and 6.5◦of sweep were
added to the investigation to verify results’curve and
detect optimum sweep angle among 6 tested angles of
twist in ground effect. The coefficient of drag has also
a maximum value at 6.5 degrees of backward sweep as
shown in Figure 9. However, the maximum coeff icient
of lift is at 6.5 degrees of sweep, the maximum aerody-
namic efficiency is at 5 degrees of sweep, which equals
to 10.24 at Re =2×10E +5. Through 3 tapered wings
investigated, it has been noticed that there were small
increases in lift coefficients at taper ratio equals 0.75.
Coefficients of lift faced slight reductions at 0.5 taper
ratio compared to those of 0.75 taper ratio. Wings of
taper ratio equals 0.25 generated significant decrease
in lift. Looking to speed curves in Figure 10, all investi-
gated speeds generated more lift at taper ratio equal 0.5
than non-tapered wings except at Re =4.8 ×10E +5.
Wing taper reduced drag coefficient by 5% at 0.25
taper ratio as shown in Figure 10.
The slope of drag curve is maximum between
0.5 & 0.25 taper ratio. 0.5 taper ratio recorded the
highest aerodynamic efficiency among the examined
tapered wings, which equals to 8.98 as shown in Fig-
ure 11. The optimum taper ratio was extrapolated
from the curves to be equals 0.54, but no numeri-
cal verification took place to verify this ratio. For the
pre-specified ground effect case, wings with 0.5 taper
ratio can increase aerodynamic efficiency by 3.0% at
Re =3.4 ×10E +5, which is can be interpreted from
Figure 12.
Anhedral angle did have a positive effect on the
coefficient of lift. Also, there are some variations in
350
Figure 9. Drag coefficient, lift coefficient, and aerody-
namic efficiency of 6 angles of wash-in twist at various sweep
angles.
Figure 10. Lift coefficient of airfoil section NACA 6409
wings with various taper ratios.
speed curves with anhedral angles. Referring to Fig-
ure 13 it’s detectable that coefficient of lift at anhedral
angle 4 is more than that of 2 degrees of anhedral
while this is not the case at Re =2×10E +5, at which
2 degrees of anhedral generates more lift on the wing
than 4 degrees. Despite these variations between 2 and
4 degrees of anhedral along speed curves, 6 degrees of
anhedral gives the maximum coefficient of lift through
all investigated speeds as shown in Figure 13. Coeffi-
cients of drag decreased as anhedral angle increased
through the 4 angles of anhedral tested as shown in
Figure 14. The most coefficient of drag reduction
occurred at 6 angles of anhedral at Re =2×10E +5.
Overall, the best aerodynamic efficiency achieved;
among investigated anhedral angles, is equals to 9.18
at Re =2×10E +5 and 6 degrees of anhedral.
Table 4. Displays the percentage of the maximum
change in aerodynamic efficiency for all investigated
wing configurations at Re =3.4 ×10E +5 compared
to a wing without any geometrical configuration in
ground effect.
4 CONCLUSION
In this paper, aerodynamic efficiencies of a NACA
6409 section wing of aspect ratio equals 2 were inves-
tigated in ground effect at ground clearance h/c =0.3
Figure 11. Drag coefficient, lift coefficient, and aerody-
namic efficiency of various taper ratios.
Figure 12. Percentage of change in aerodynamic efficiency
of different taper ratios compared to a non-tapered wing.
Figure 13. The coefficient of lift of different anhedral angles
in ground clearance h/c =0.3 within a speed range.
through many geometrical configurations; twist, taper,
sweep, and anhedral. Several simulations were car-
ried out using a commercial RANS solver to calculate
coefficients of lift and drag of each case. All config-
ured wings results were compared to non-configured
wings to extrapolate the percentage of aerodynamic
efficiency change. Ground effect increased aerody-
namic efficiency by 25% more than the same wing
in free stream. Wash-in twist angles increase aero-
dynamic efficiency, the maximum increase occurs at
6◦of twist. Sweep angles decrease the aerodynamic
efficiency of a wing in ground effect. The optimum
twisted swept wing has almost the same aerodynamic
351
Table 4. The percentage of the maximum change in aerodynamic efficiency for all investigated wing configurations.
Configuration Twist Sweep Twist & Sweep Taper Anhedral
-Parameter of max. 6◦wash-in 35◦backward 6◦wash-in & 0.5 6◦
Change 5◦backward
-% of change compared +16.9% −24.6% +16.52% +3.17% +4%
to IGE wing
Figure 14. Drag coefficient, lift coefficient and aerody-
namic efficiency of various anhedral angles.
efficiency of an optimum twisted wing without sweep.
Taper ratio increase aerodynamic efficiency by 3.0%
to 3.5% at taper ratio values 0.5 to 0.6. Dihedral angle
increase aerodynamic efficiency up to 4.5% at an angle
of dihedral =6◦. For the specified speed range, speed
doesn’t have drastic or abrupt effects on results.
The results presented in this paper can be further
used in designing wings for wing in ground effect units
with the same airfoil section or as a reference of com-
parison between wing configurations performance in
ground effect and out of ground effect.
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