World Academy of Science, Engineering and Technology
International Journal of Mechanical, Aerospace, Industrial, Mechatronic and Manufacturing Engineering Vol:8, No:5, 2014
Obliqque Wiing: Future Generrationn Transsonic Aircra
A aft
M
Mushfiqul
Allam, Kashyaapa Narenathhreyas
International Science Index, Aerospace and Mechanical Engineering Vol:8, No:5, 2014 waset.org/Publication/9998186
Abstract—Thhe demand for efficient transoonic transport has
h been
grrowing every day and mayy turn out to be the most pressed
innnovation in coming
c
years. Oblique winng configuration was
prroposed as an alternative to conventional wing
w
configuraation for
su
upersonic and transonic
t
passeenger aircraft due
d to its aerod
dynamic
addvantages. Thiss paper re-demoonstrates the aeerodynamic advvantages
off oblique wingg configuration using open source CFD coode. The
aeerodynamic dataa were generateed using Panel Method. Resullts show
that Oblique Wiing concept wiith elliptical wing
w
planform offers a
siggnificant reducction in drag at transonic and supersonic speeeds and
appproximately tw
wice the lift diistribution com
mpared to convventional
opperating aircraft
fts. The paper also
a presents a preliminary
p
connceptual
airrcraft sizing whhich can be usedd for further exxperimental anallysis.
Keywords—Aerodynamics,
A
, asymmetric sweep, oblique wing,
sw
wing wing.
NOMEENCLATURE
A,, B
I
Ixxx, Izz, Izx
i
K
L
m
N
p
r
s
Uo
u
v
x
Y
δaa
Sysstem matrices
Ideentity matrices
Mooments of inertiia, kgm2
√(--1)
Feeedback gain
Latteral moment (aat x-axis), Nm
Maass of aircraft, kkg
Dirrectional momeent (at z-axis), Nm
N
Roll rate, rad/sec
Yaaw rate, rad/sec
Complex frequenccy
Freee stream velocity, m/s
Inpput vector
Latteral velocity (aat y axis), m/s
Staate vector
Latteral force (at y axis), N
Bannk angle, rad
Ailleron input
disstribution. For an equivaleent span, sweep and volum
me; the
ellliptical wing distributes llift about tw
wice over thee span
compared to conventionall design [3
3]. Howeverr, the
preedominant isssue of stabilitty and control remained foor high
obblique sweep angles
a
(>40˚) [6], [9].
After groundding the Conccorde, there has
h been a reenewed
ressearch intereest in Obliqque wing duue to its su
uperior
aerrodynamic addvantages. Over the yearrs, there havee been
maany attempts to improve thhe stability off the aircraft at
a high
sw
weep angles such as slewed wing, twin-fuuselage
configuration an
nd formation flying ideas etc, but none of the
nce in the conncept’s
ideeas have yet provided enoough confiden
staability [4], [7], [8].
In this papper, the firsst section re-demonstratees the
aerrodynamic addvantage of thhe conceptuallyy designed elliptical
wiing swept to different sw
weep angles. The sizing of the
airrcraft has beenn done to com
mpare with Em
mbraer 145 bu
usiness
jett. The wing sppan of 24m annd root chord of 5.2m produuce the
asppect ratio of 8.8.
8 The aeroddynamic analy
ysis was donee using
Paanel Method program Tornnado which is a Vortex Lattice
L
Meethod for lineear aerodynam
mic wing dessign applicatiions in
conceptual airccraft design ddeveloped by
y Royal Instittute of
Bristol, Linköp
ping Universiity and
Teechnology, Unniversity of B
Reedhammer coonsulting Ltdd. The code is implemennted in
MA
ATLAB and provides widde range of design
d
opportuunities.
Thhe second secction shows thhe stability an
nd controllabiility of
thee system for different
d
sweepp angles at Maach 0.9.
The wing waas swept from
m 0˚ to 50˚ for
f the aerodyynamic
annalysis as show
wn in Fig. 1.
Subscripts
p,rr,v
o
D
Deerivatives
Inittial condition
I. INTRODUCTION
URING thhe developmeent of the Concorde in 1950s the
Oblique Wing
W
was prooposed as an alternative too deltaw
wing
configuraation by R. T. Jones at NA
ASA Ames Research
Centre [1], [10]]. In 1958 the Oblique wingg design was rejected
r
t same timee, R. T.
duue to flight coontrol compleexity [2]. At the
Joones discovereed that the w
wave drag andd induced wavve drag
reeduced by a variable
v
sweepp oblique winng with an ellliptical
M. Alam is a do
octoral student att the Departmentt of Measurementt, Faculty
off Electrical Enginneering, Czech Teechnical Universiity, Lab 051, Tecchnicka 2,
C
Republic (e-mail: mushfalaa@ fel.cvut.cz).
Deejvicka, Prague, Czech
K. Narenathreyaas is a former stuudent at Faculty of Electrical Enggineering,
Czzech Technical University
U
(e-mail: [email protected]).
International Scholarly and Scientific Research & Innovation 8(5) 2014
Fig. 1 Variablee Oblique sweepp about a pivot point from 0˚ too 50˚
II. AERODYN
NAMIC RESUL
LTS
As mentionedd earlier, the aerodynamicc analysis waas done
usiing Tornado solver. The wing analyssis was carried out
sepparately for backward swept semisspan and forward
fo
sem
mispan, and combined
c
them
m later. The lift
l distributioon over
thee wing span for
f Mach = 0.9 is shown in
n Fig. 2, wheere it is
seeen that lift diistribution is better in the forward swept part
888
scholar.waset.org/1999.8/9998186
World Academy of Science, Engineering and Technology
International Journal of Mechanical, Aerospace, Industrial, Mechatronic and Manufacturing Engineering Vol:8, No:5, 2014
compared to backward swept part, even though the magnitude
of lift is lower, the induced drag is reduced due to elliptical lift
distribution. From Fig. 2, it can also be seen that asymmetric
lift distribution will produce unwanted moments forcing the
aircraft to be very unstable. These moments include, the
negative rolling moment which also induces negative yawing
moment which is highly undesirable.
considerable loss of lift in forward swept wing at high sweep
angles.
Therefore, from the above analysis it was clear that
sweeping wing to oblique angles reduces drag significantly
even though lift is also compensated. The drag analysis was
done to visualize the difference in drag for different
configurations of wing planforms as shown in Fig. 4.
CL distribution for Oblique Sweep
0.35
0.3
L
C
0.2
0.15
0 deg sweep
30 deg sweep
50 deg sweep
0.1
0.05
-10
-5
0
wing span (m)
5
10
Fig. 2 CL distribution over span for Mach 0.9 with different sweep
angles
This means that, to maintain symmetric lift distribution, the
ailerons must be kept deflected throughout the flight which
might not be practical in terms of drag, aeroelasticity and
flutter etc.
One of the major problems for aircrafts is when
approaching Mach 1, after entering the transonic region (Mach
= 0.8 to 1) the drag rises rapidly due to shock waves formation
on the surface. Therefore the Lift-to-Drag ratio drops to very
low value in conventional aircrafts. But it can be seen that
Lift-to-Drag ratio could be maintained above certain value by
increasing the oblique sweep angle as shown in Fig. 3.
0o Oblique
14
o
30
13
Oblique
30o Sweptback
50o Oblique
12
L/D
International Science Index, Aerospace and Mechanical Engineering Vol:8, No:5, 2014 waset.org/Publication/9998186
0.25
11
10
9
8
7
0.5
0.6
0.7
0.8
Mach Number
0.9
Fig. 4 Drag coefficient at Mach 0.9 for different wing-body
combinations
As seen in Fig. 4, the wave drag has been reduced in all the
swept wing planforms but the oblique swept wing with 30˚
sweep has 8.95% lower total drag compared to sweptback
wing of 30˚ sweep and 40.63% lower total drag compared to
0˚ sweep. The oblique wing with 50˚ sweep has 34.8% lower
total drag compared to sweptback wing of 30˚ sweep, 10.17%
lower compared to Delta wing of 65˚ sweep and 57.49% lower
compared to 0˚ sweep.
III. LATERAL STABILITY
The lateral motion of the oblique wing configuration is
unstable primarily due to the asymmetric lift produced in the
front swept wing and back swept wing. The instability
becomes stronger with the increase in Mach number and
sweep angle.
Linearized lateral equations of motion were considered for
the analysis purpose and two situations were considered at
Mach 0.9 with Sweep 30o and 50o. For the initial lateral
stability analysis only the aileron input was considered. The
aircraft model can be presented as a linearized state-space
model [5].
1
(1)
Fig. 3 Lift-to-Drag ratio curve against Mach number
(2)
The Lift-to-Drag ratio has increased to 12 at Mach 0.9 for
oblique sweep of 50˚ and 11.33 for oblique sweep of 30˚
compared to 7.7 for 0˚ sweep. But the increase in Lift-to-Drag
ratio is not considerable when compared to 30˚ sweptback
configuration which yields 11.12. The reason is the
International Scholarly and Scientific Research & Innovation 8(5) 2014
889
scholar.waset.org/1999.8/9998186
World Academy of Science, Engineering and Technology
International Journal of Mechanical, Aerospace, Industrial, Mechatronic and Manufacturing Engineering Vol:8, No:5, 2014
IV. CONTROLLABILITY
cos
0
The controllability matrix of the plane is given by
(3)
,
0
0
1
tan
0
0
0
0
0
.
0
(4)
0
⁄
⁄
5.94
4
9.48
4
2.1
5
0
49.6
279
9.44
0.115
0
126
6.57
1
279
4.82
0.115
0
9.812
0
0
0
(6)
21.66
55.60
5.68 12
0
1.58 15
5.36 13
6.53 11
55.6
1.84 15
1.31 16
1.45 14
5.36 13
4.44 17
3.19 18
3.53 16
1.31 16
25.46
22.70
1.37 13
0
3.82 15
6.60 13
1.58 12
22.70
3.71 15
8.32 15
4.34 14
6.60 13
2.91 17
1.05 18
5.47 16
8.32 15
It can be seen that rank of C has the same rank as A.
4
9.812
0
0
0
Therefore matrix C is full rank and the system is fully
controllable. Hence simple state-feedback law can be used to
stabilize the system by arbitrary assignment of desired closed
loop eigenvalues.
21.66
55.6
5.68 12
0
V. STATE-FEEDBACK LAW
25.46
22.7
1.37 13
0
The linear, time-invariant, state feedback is defined by
(7)
The pole zero plot in Fig. 5 of the state equations shows that
the plant is marginally stable.
and the state-space model in (1) become
(8)
Pole-Zero Map
0.03
Hence the desired characteristic equation can be equated
with det (sI-(A-BK)) to find the feedback control gains of the
states.
o
Sweep 30
0.02
Imaginary Axis
International Science Index, Aerospace and Mechanical Engineering Vol:8, No:5, 2014 waset.org/Publication/9998186
Substituting the aerodynamic data at Mach 0.9 for sweep
30o and 90o into the plant matrix A and input matrix B, the
corresponding state equations were calculated.
39
244
2.7
1
…
where n is the rank of plant matrix A. In our case the rank of
matrix A in both the cases is 4.
(5)
⁄
0.000375
0.00184
2.17
4
0
,
0
Sweep 50o
0.01
VI. CONCLUSION
0
-0.01
-0.02
-0.03
-250
-200
-150
-100
-50
0
50
Real Axis
Fig. 5 Eigenvalues for 30˚ and 50˚ sweep at Mach 0.9
TABLE I
EIGEN VALUES AT MACH 0.9
Eigen Values
Sweep 30o
Sweep 50o
244
125.7477
0.02
0.3020
0
0.0647
0
International Scholarly and Scientific Research & Innovation 8(5) 2014
Oblique sweep configuration produces lower drag at higher
speed compared to symmetrically swept aircraft. This
configuration has superior aerodynamic advantages which
puts it in a unique position for the next generation supersonic
aircraft. The lateral motion of the proposed conceptual aircraft
is controllable. The new conceptually designed aircraft is
stabilizable with respect to lateral motion. Advanced
controller such using state-feedback or LQ (Linear Quadratic)
Controller can be used.
Future Investigation will be carried out considering the nonlinearized lateral motion with aileron and rudder inputs.
Higher Mach will also be considered in the future works.
ACKNOWLEDGMENT
The authors would like to thank Department of
Measurement, Faculty of Electrical Engineering, Czech
890
scholar.waset.org/1999.8/9998186
World Academy of Science, Engineering and Technology
International Journal of Mechanical, Aerospace, Industrial, Mechatronic and Manufacturing Engineering Vol:8, No:5, 2014
Technical University, grant No. SGS13/144/OHK3/2T/13.
Sincere thanks goes to all the reviewers of the paper.
REFERENCES
International Science Index, Aerospace and Mechanical Engineering Vol:8, No:5, 2014 waset.org/Publication/9998186
[1]
R. T. Jones, "New Design Goals And a New Shape for the SST,"
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[3] R. T. Jones, "The Oblique Wing- Aircraft Design for Transonic and Low
Supersonic Speeds," ActaAstronautica, vol. 4, no. 1, pp. 99-109, 1977.
[4] A. J. Van der Velden and E. Torenbeek, "Design of a Small Supersonic
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California, 1986.
[7] A. J. M. Van Der Velden and I. Kroo, "The Aerodynamic Design of the
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Center, California, 1990.
[8] J. M. A. Van der Velden and E. Kroo, "Conceptual Final Paper on the
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[9] J. W. Pahle, "Output Model-Following Control Synthesis for an
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[10] R. T. Jones and J. W. Nisbet, "Transonic Transport Wings-Oblique or
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