Vietnam Journal of Mechanics, VAST, Vol.41, No. 1 (2019), pp. 89 – 103
DOI: https://doi.org/10.15625/0866-7136/13018
INVESTIGATION OF AERODYNAMICS
AND LONGITUDINAL STABILITY OF UNMANNED AERIAL
VEHICLE WITH ELEVATOR DEFLECTION
Hoang Thi Bich Ngoc∗, Bui Vinh Binh
Hanoi University of Science and Technology, Vietnam
∗E-mail: ngoc.hoangthibich@hust.edu.vn
Received: 28 August 2018 / Published online: 28 February 2018
Abstract. The elevator is usually hinged to the horizontal tail, whi

15 trang |

Chia sẻ: Tài Huệ | Ngày: 17/02/2024 | Lượt xem: 179 | Lượt tải: 0
Tóm tắt tài liệu **Investigation of aerodynamics and longitudinal stability of unmanned aerial vehicle with elevator deflection**, để xem tài liệu hoàn chỉnh bạn click vào nút DOWNLOAD ở trên

ich acts as a balance
and controls the altitude, establishes a steady motion for the aircraft at all lift coefﬁcients.
During elevator rotating, the aircraft needs to be stable to establish a new altitude. The
horizontal tail has a major role in the value of the airplane’s pitching moment (due to the
long arm from the aerodynamic center of the tail to the center of gravity) for the equilib-
rium and stability of the aircraft. The horizontal tail should be considered as an aerody-
namic component behind the main wing, inﬂuenced by the wing downwash wing rather
than just a minor wing. Therefore, the aim of this study is to examine the ﬂow through
unmanned aerial vehicles (UAV) including the main wing, tail and body and to calculate
the aerodynamic force on the horizontal tail when rotating the elevator using the Fluent
software for the viscous ﬂows. Small disturbance theory was used to calculate the longi-
tudinal stability of the UAV when controlling the elevator. Flying qualities are assessed
to show that changes in the aerodynamic characteristics of the wing, tail, fuselage and
conﬁguration of the UAV may be required.
Keywords: UAV aerodynamics; horizontal tail and elavator; equilibrium; longlitudinal sta-
bility.
1. INTRODUCTION
When ﬂying, the aircraft should be balanced and stable with environmental impact
using necessary controls. The horizontal tail with the elevator ensures the balance of the
aircraft with all variations in lift coefﬁcient. In calculating aerodynamic forces, viewing
the horizontal tail like a miniature main wing will eventually lead to large errors. The
horizontal tail should be placed in the main wing wake and be inﬂuenced by the down-
wash effect of the wing [1,2]. That is, the incidence velocity to the horizontal tail is not
the velocity at inﬁnity as for the main wing. Therefore, the aim of this study is to exam-
ine the ﬂow through the aircraft including the main wing, tail and body and to calculate
the aerodynamic force on the horizontal tail when rotating the elevator using the Fluent
c 2019 Vietnam Academy of Science and Technology
90 Hoang Thi Bich Ngoc, Bui Vinh Binh
software for the viscous ﬂows. When the elevator angle is zero, the aircraft is in equi-
librium ﬂight. When the elevator is deﬂected, it changes the lift on the horizontal tail
and the aircraft nose moves up or down. Until the aircraft reaches a certain altitude, the
elevator angle returns to zero and the aircraft registers equilibrium. Such changes in lift
and pitching moment require consideration of the longitudinal dynamic stability of the
aircraft.
By experimental method, Thomas and Wonhart [3] determined the lift coefﬁcient,
drag coefﬁcient and moment coefﬁcient of a model airplane to determine the static sta-
bility of the airplane. The numerical study has used the size and conﬁguration of the
experimental model airplane in [3] to calculate and to perform comparisons of numerical
results with experimental results, this allows applying calculations for UAV. Our com-
puter program for longitudinal stability calculations is validated when calculating the
stability of the model of Navion aircraft given in [4,5]. Flight quality assessment may lead
to requirements for changes in aerodynamic design and conﬁguration of aircraft [6,7].
2. AERODYNAMIC COEFFICIENTS AND PITCHING MOMENT COEFFICIENTS
2.1. Aerodynamic model of UAV
Fig.1 is the conﬁguration and size of the UAV considered in this study. Dimensions
of the fuselage are given in Tab.1. Dimensions of the main wing and horizontal tail are
shown in Tab.2. The vertical tail is arranged at the two tips of the horizontal and its
proﬁle is Naca 0010. The UAV velocity is 44.4 m/s.
Fig. 1. Configuration and size of UAV
Fig. 1. Conﬁguration and size of UAV
Table 1. The fuselage coordinates (mm)
For the boundaryx y, lower of meshing y, upper (Fig. 2),z the inletx andy, lower outlet surfacesy, upper werez respectively,
20c¯w and 50c¯w0 far away-158 from- the158 UAV0 (c ¯w is1660 the mean-318 chord of318 the wing);335 the top and
130 -268 21 150 3320 -318 318 335
bottom surfaces were 20c¯w far away from the UAV; the side surface was 0.5bw (bw is the
280 -300 104 210 3720 -234 285 286
wingspan) far520 away - from318 the197 UAV; For270 boundary 4000 conditions,84 the84 symmetry0 condition
was at the symmetry surface; the velocity at inﬁnity (V¥) was at the inlet surface and the
Table 2. Geometry and dimensions of the main wing and horizontal tail
Parameter Symble Main wing H. tail
Profile Naca 4412 0010
Span (m) b 15.4 3.3
Root chord (m) cr 1.0 0.57
Tip chord (m) ct 0.7 0.57
Mean chord (m) c 0.859 0.57
Aspect ratio AR 17.6 5.0
Setting angle (degree) i 4 0
Sweep angle of leading edge
0.57 0
(degree) LE
Sweep angle of trailing edge
1.72 0
(degree) TE
Area (m2) S 12.94 1.80
For the boundary of meshing (Fig. 2), the inlet and outlet surfaces were respectively 20 cW and
50 cW far away from the UAV ( cW is the mean chord of the wing); the top and bottom surfaces were 20
cW far away from the UAV; the side surface was 0.5bw (bw is the wingspan) far away from the UAV;
For boundary conditions, the symmetry condition was at the symmetry surface; the velocity at infinity
(V) was at the inlet surface and the pressure at infinity (p) was at the outlet surface; the symmetry
condition was at the side, top and bottom surfaces; the no-slip boundary condition ( v=0 ) was
enforced at wall (of the UAV) by default [8]. The grid size was fine enough in boundary layers, wing
tip zone, intersection domains of UAV components [9], 10]. Model of turbulence (k-ε) was used for all
simulation problems using Fluent 6.3 software in this work. Operations and meshing techniques with
Fluent were verified by the comparison of numerical results and experimental results on a model
aircraft [3] which were presented in Section 2.3.
2
Investigation of aerodynamics and longitudinal stability of unmanned aerial vehicle with elevator deﬂection 91
Table 1. The fuselage coordinates (mm)
x y, lower y, upper z x y, lower y, upper z
−158 −158 0 1660 −318 318 335
130 −268 21 150 3320 −318 318 335
280 −300 104 210 3720 −234 285 286
520 −318 197 270 4000 84 84 0
Table 2. Geometry and dimensions of the main wing and horizontal tail
Parameter Symbol Main wing Horizontal tail
Proﬁle Naca 4412 0010
Span (m) b 15.4 3.3
Root chord (m) cr 1.0 0.57
Tip chord (m) ct 0.7 0.57
Mean chord (m) c¯ 0.859 0.57
Aspect ratio AR 17.6 5.0
Setting angle (degree) i 4 0
Sweep angle of leading edge (degree) LLE 0.57 0
Sweep angle of trailing edge (degree) LTE 1.72 0
Area (m2) S 12.94 1.80
Fig. 2.Fig. Boundary 2. Boundary of meshingof meshing and and gridgrid on on the the symmetry symmetry surface surface of UAV of UAV
o
Fig. 3 presents streamlines through wing and fuselage with angles of attack UAV 0 and
o o
UAV 14 . In case of UAV 0 , streamlines were smooth, which showed that there was no separation
on the wing upper surface and at the trailing edge there was no vortex (except the vortex at the wing
o
tip caused by circular flows from the lower to the upper surfaces of the wing). In case of UAV 14 ,
streamlines were no smooth on the wing and fuselage. This meant that separations took place on the
wing upper surface and form vortices at the wing rear.
(a) (b)
o o
Fig. 3. Streamlines. (a) UAV 0 ; (b) UAV 14
Fig. 4 shows the lift and drag coefficients with respect to the angle of attack UAV for the
o
UAV, main wing, horizontal tail and fuselage when the elevator deflection angle was zero (e=0 ). It
was observed that the lift and drag coefficients of the UAV were mainly due to the main wing. The lift
coefficient of the fuselage was small, but its drag coefficient was equivalent to that of the horizontal
tail. Lift and drag of the vertical tail were not significant (not shown in Fig. 4). The lift of the
horizontal tail was very small compared to that of the main wing, but had a great influence on the
balance and longitudinal stability of the UAV. This was because the large distance (arm) from the
aerodynamic center of the horizontal tail to the gravity center of the UAV, thus creating a great
pitching moment. Lift coefficients of horizontal tail were negative with angles of attack less than 2
o o
degrees ( UAV 2 ). At angle of attack UAV 0 , lift coefficient of the horizontal tail CLH() 0. 015
3
92 Hoang Thi Bich Ngoc, Bui Vinh Binh
pressure at inﬁnity (p¥) was at the outlet surface; the symmetry condition was at the side,
top and bottom surfaces; the no-slip boundary condition (~v = 0) was enforced at wall (of
the UAV) by default [8]. The grid size was ﬁne enough in boundary layers, wing tip zone,
intersection domains of UAV components [9, 10]. Model of turbulence (k-#) was used for
all simulation problems using Fluent 6.3 software in this work. Operations and meshing
techniques with Fluent are veriﬁed in Section 2.2 by the comparison of numerical results
with experimental results on a model aircraft [3].
Fig.3 presentsFig. 2.F ig.Boundary streamlines 2. Boundary of meshing through of meshing and winggrid and ongrid and the on symmetry fuselagethe symmetry surface with surface of angles UAV of UAV of attack aUAV =
0◦ and a = 14◦. In case of a = 0◦, streamlines were smooth, which showed that
UAV UAV o
o
Fig. 3 presents streamlines through wing and fuselage with angles of attack UAV 0 and
there was noFig. separation 3 presents on streamlines the wing through upper wing surface and fuselage and at with the angles trailing of edge attack thereUAV was0 and no
o o o o
vortexUAV 14 (except. In14 case. theIn ofcase vortex UAofV 0 at, strea the0 , mlinesstrea wingmlines were tip causedweresmooth, smooth, which by circularwhich showed showed ﬂowsthat therethat from there was thenowas separation lowerno separation to the
UAV UAV ◦
upperon theon wing surfaces the wingupper ofupper surface the surface wing).and at and the In at trailing casethe trailing ofedgeaUAV edgethere= therewas14 nowas, streamlinesvortex no vortex (except (except werethe vortex the no vortex smoothat the at wingthe on wing the
wingtip caused and by fuselage. circular flows This from meant the lower that to separations the upper surfaces took of place the wing). on the In case wing of upper 14 surfaceo , o
tip caused by circular flows from the lower to the upper surfaces of the wing). In case ofUA VUAV 14 ,
andstreamlines formstreamlinesvertices were wereno smooth at no the smooth wingon the on rear.wing the wingand fuselage. and fuselage. This Thismeant meant that separationsthat separations took tookplace place on the on the
wing upperwing upper surface surface and form and formvortices vortices at the at wing the wingrear. rear.
(a) (b)
◦ o o o o ◦
(a) aUAVF=ig.0 3.F ig.Streamlines. 3. Streamlines. (a) (a)UAV 0UAV; (b)0 ; (b)UAV14UAV(b)14aUAV = 14
Fig. 4Fig. shows 4 shows the lift the and lift drag and dragcoefficients coefficients with with respect respect to the to angle the angle of attack of attack UAV forUAV thefor the
o o
UAV,UAV, main mainwing, wing, horizontal horizontalFig. tail 3 .and tail Streamlines fuselage and fuselage when through whenthe elevator the wing elevator anddeflection fuselagedeflection angle angle was zerowas zero (e=0 ().e=0 It ). It
was observedwas observed that the that lift the and lift drag and coefficientsdrag coefficients of the of UAV the UAV were weremainly mainly due todue the to main the main wing. wing. The liftThe lift
coefficientFig.coefficient4 showsof the of fuselage the fuselage lift was and small, was drag small, but coefﬁcients its but drag its dragcoefficient with coefficient respect was equivalentwas to equivalent the to angle that to ofthat of the attack of horizontal the horizontalaUAV for
thetail. UAV, Lifttail. and mainLift drag and wing, dragof the horizontal of vertical the vertical tail tail were tail and were not fuselage significant not significant when (not (not shown the elevatorshown in Fig. in Fig.deﬂection 4). The 4). The lift angle of lift the of was the
zerohorizontal (horizontald = tail0◦ ).was tail It wasverywas small observedvery small compared compared that to the that to lift ofthat and the of main drag the mainwing, coefﬁcients wing, but hadbut ahad of great the a great influence UAV influence were on the mainlyon the
balancee and longitudinal stability of the UAV. This was because the large distance (arm) from the
duebalance to the and main longitudinal wing. stability The lift of coefﬁcient the UAV. Thisof the was fuselage because was the large small, distance but its (arm) drag from coefﬁcient the
aerodynamicaerodynamic center center of the of horizontal the horizontal tail to tail the to gravity the gravity center center of the of UAV, the UAV, thus thus creating creating a great a great
waspitching equivalentpitching moment. moment. Liftto that coefficients Lift of coefficients the of horizontal horizontal of horizontal tail tail. were tail Lift werenegative and negative drag with with ofangles the angles of vertical attack of attack less tail lessthan were than2 not 2
signiﬁcantdegrees (not ( o shown 2o ). At in angle Fig.4 of). Theattack lift ofo the0o , horizontallift coefficient tail of wasthe horizontal very small tail comparedC 0. 015 to
degrees ( UAV 2UAV). At angle of attack UAV 0UAV, lift coefficient of the horizontal tail CL(H) L(H0). 015
that of the main wing, but had a great inﬂuence on the balance and longitudinal stability
of the UAV. This was because the large distance (arm) from the aerodynamic center of the
horizontal tail to the gravity center of the UAV, thus creating a great pitching moment.3 3
Lift coefﬁcients of horizontal tail were negative with angles of attack less than 2 degrees
◦ ◦
(aUAV < 2 ). At angle of attack aUAV = 0 , lift coefﬁcient of the horizontal tail CL(H) =
−0.015 that was due to downwash effect of the main wing (because the horizontal tail
had a zero setting angle and symmetry proﬁle).
Extracting from Fig.4 graphs of lift and drag coefﬁcients of the horizontal tail (as a
◦
component of the UAV) that are shown in Fig.5 (with de = 0 ). Fig.5 also shows graphs
thatthat was was due due to downwash to downwash effect effect of theof the main main wing wing (because (because the the horizontal horizontal tail tail had had a zeroa zero setting setting angle angle
andand symmetry symmetry profile). profile).
thatthat was was due dueto downwash Investigationto downwash of effect aerodynamics effect of the andof the longitudinalmain main wing stabilitywing (because of(because unmanned the aerialthe horizontal horizontal vehicle with tail elevator tail had deﬂectionhad a zeroa zero setting setting 93 angle angle
and symmetryand symmetry profile). profile).
Fig.F4ig.. Aerodynamic4. Aerodynamic coefficients coefficients of theof the UAV, UAV, main main wing, wing, horizontal horizontal
tailtail and and fuselage fuselage. (a). (a)LiftLift coefficient coefficient; (b); (b) Drag Drag coefficient coefficient
(a) Lift coefﬁcient (b) Drag coefﬁcient
Fig.F4ig.. Aerodynamic4. Aerodynamic coefficients coefficients of theof theUAV, UAV, main main wing, wing, horizontal horizontal
Extracting from Fig. 4 graphs of lift and drag coefficients of the horizontal tail (as a
Extracting tail from tailand Fig. andfuselage fuselage 4 graph. (a). sLift(a) ofLift coefficientlift coefficient and drag; (b); (b)D coefficientsrag Drag coefficient coefficient of the horizontal tail (as a
Fig. 4. Aerodynamic coefﬁcients of the UAV, main wing,o horizontalo tail and fuselage
componentcomponent of the of theUAV) UAV) that that are are show shown inn Fig.in Fig.5 (with5 (with e =e 0= ).0 Fig.). Fig. 5 also5 alsoshowsshows graphs graphs of oflift lift and and
dragdrag coefficients coefficientsExtractingExtracting of fromtheof the fromhorizontal Fig.horizontal Fig. 4 graph 4 tail graph tail (whichs of(whichs oflift islift andais component anda dragcomponent drag coefficients coefficientsof ofthe the UAV ofUAV of the) with the) horizontalwith horizontalelevator elevator taildeflection taildeflection (as (as a a
o o o o
component=of10 lift and ofo the drag UAV) =− coefﬁcients5 thato are of show the horizontaln in Fig. 5 tail (with (which e =o is 0 a). componentFig. 5 also ofshows the UAV) =graphs0 with oof lift and
anglescomponentangles e =e of10 theand andUAV) e ethat =−.5 areWith. Withshow three n threein values ◦Fig. values5 of(with of the the elevatore◦ = elevator 0 ). Fig. deflection deflection 5 also shows angle angle graphs ( (e =e of0, lift, and , ,
dragelevator coefficients deﬂection of the angleshorizontalde = tail10 (whichand dise =a component−5 . With of three the valuesUAV) with of the elevator elevator deflection
drag coefficients of the horizontal◦ tail (which◦ is a component◦ of the UAVo) owith elevator deflection
), deﬂectionlift), l coefficientsifto coefficientso angle (ofdeo = theofo0 thehorizontal, dhorizontale = 10 ,taild etail =at − angleat5 angle), liftof ofattack coefﬁcients attack = UAV=UAV of0 the0are horizontalare respectively respectively tailo o at − 0−. 0150. 015, ,
anglesangles = 10=e 10and and =−e5 =−. 5With◦. With three three values values of ofthe the elevator elevator deflection deflection angle angle ( = ( =e0 0, , , ,
0. 0620. 062, −0,angle e. 054−0. 054(as of attack (asshown showne a UAVin Tab.in= Tab.0 3).are 3). respectively −0.015, 0.062, −0.054 (as shown in Tab.e 3).
), lift coefficients of the horizontal tail at angle of attack =o 0o are respectively −0. 015,
), lift coefficients of the horizontal tail at angle of attack =UAVUAV0 are respectively −0. 015,
0. 0620., 062 −0,. 054−0. 054(as shown(as shown in Tab. in Tab. 3). 3).
(a) Lift coefﬁcient (b) Drag coefﬁcient
Fig.Fig.5. Aerodynamic5. Aerodynamic coefficients coefficients of theof the UAV’s UAV’s horizontal horizontal tail tail. .
Fig.Fig.5 5.. (a)Aerodynamic Aerodynamic (a)Lift Lift coefficient coefficient coefﬁcientscoefficients; (b); (b) D of rag ofD the ragthe coeffic UAV’s UAV’scoeffic horizontalient ihorizontalent tail tail.
Fig. 5. Aerodynamic coefficients of the UAV’s horizontal tail.
Fig. 6 is the 3D distribution(a) Lift ofcoefficient pressure; (b) coefficients Drag coeffic oni ent a half of the tail alone when the
Fig. 6 is the 3D distribution(a) Lift ofcoefficient pressure; (b) coefficients Drag coeffic oni ent a half of the tail alone when the
Fig.6 is the 3D distribution of pressureo o o coefﬁcientso o o on a half of the tailo o alone when
elevatorelevator deflection deflectionFig. 6 angle is angle the at 3Dthree at three distribution values values of ofofe ( pressure0e (, 010, 10, – coefficients ,5 –) 5. In◦). Inthe◦ the case on case ◦ a of half ofe =ofe 0= the ,0 pressure , tailpressure alone coefficient coefficient ◦ when thes s
the elevator deﬂection angle at three values of de (0 , 10 , −5 ). In the case of de = 0 ,
on theFig. upper 6 isand the lower 3D surfaces distribution of the of tail pressure were othe coefficients sameo o, so onlift acoefficient half of the of tailothe tail alonewas when zero the(CL(H)
on theelevator upperpressure anddeflection lower coefﬁcients anglesurfaces at on three of the the values upper tail were andof e lowerthe(0 , same10 surfaces, –, so5 ) .lift In of thecoefficient the case tail wereof ofe = thethe 0 , same, tailpressurewas so zero liftcoefficient (CL(H)s
o o o o o o o
elevator= 0). Lift deflection coefficients angle of atthe three tail values alone ofat threee (0 ,values 10 , – of5 ). eIno(0 the, o10 case, –o of5 )aree = 0shown, pressure in Tab. coefficient 3. s
= 0). Lifton the coefficientscoefﬁcient upper and of oflower thethe tail tailsurfaces was alone zero of at ( Cthe threeL(H tail) = values were0). Lift the of coefﬁcients samee (0,, so10 lift, of – coefficient the5 ) tailare aloneshown of atthe in three tailTab. valueswas 3. zero (CL(H)
on the upper and◦ lower◦ − surfaces◦) of the tail were the same, so lifto coefficiento o of the tail was zero (CL(H)
= 0).of Liftde (0coefficients, 10 , 5 ofarethe shown tail alone in Tab. at three3. values of eo(0 , o10 , –o 5 ) are shown in Tab. 3.
= 0). Lift coefficientsComparing of the the tail results alone in at Tab. three3 shows values that of thee (0 lift, 10 coefﬁcient, – 5 ) are of shown tail alone in Tab. differed 3.
signiﬁcantly from that of the UAV’s horizontal tail when the last suffered from interac-
tion with other components of the UAV, especially inﬂuenced by the main wing down-
wash [11]. Therefore, the calculation of the aerodynamic force on the horizontal tail alone
causes a large error.
Fig. 6. 3D distribution of pressure coefficients on a half of the tail
Fig. Fig.6. 3D 6 .distr 3D distributionibution of pre of ssurepreo ssure coefficients coefficientso on ona half a half ofo ofthe the tail tail
alone. (a) e =o 0 o; (b) e = 10o o; (c) e = o-5o
Fig. 6. 3Dalone. distralone.ibution(a) (a)e of= 0epre=; ssure0(b); (b) ecoefficients = e10= 10; (c); (c) one =a e half-=5 -5 of the tail
o o o
alone. (a) e = 0 ; (b) e = 10 ; (c) e = -5 4
44
4
that was due to downwash effect of the main wing (because the horizontal tail had a zero setting angle
and symmetry profile).
Fig. 4. Aerodynamic coefficients of the UAV, main wing, horizontal
tail and fuselage. (a) Lift coefficient; (b) Drag coefficient
Extracting from Fig. 4 graphs of lift and drag coefficients of the horizontal tail (as a
o
component of the UAV) that are shown in Fig. 5 (with e = 0 ). Fig. 5 also shows graphs of lift and
drag coefficients of the horizontal tail (which is a component of the UAV) with elevator deflection
o o o
angles =e 10 and e =−5 . With three values of the elevator deflection angle ( =e 0 , ,
o
), lift coefficients of the horizontal tail at angle of attack =UAV 0 are respectively −0. 015,
0. 062, −0. 054 (as shown in Tab. 3).
Fig. 5. Aerodynamic coefficients of the UAV’s horizontal tail.
(a) Lift coefficient; (b) Drag coefficient
Fig. 6 is the 3D distribution of pressure coefficients on a half of the tail alone when the
o o o o
elevator deflection angle at three values of e (0 , 10 , – 5 ). In the case of e = 0 , pressure coefficients
on the upper and lower surfaces of the tail were the same, so lift coefficient of the tail was zero (CL(H)
o o o
= 0). Lift94 coefficients of the tail alone at Hoang three Thi values Bich Ngoc, of Buie Vinh(0 Binh, 10 , – 5 ) are shown in Tab. 3.
Fig. 6. 3D3D distribution distribution of of pressure pressure coefﬁcients coefficients on aon half a half of the of tail the alone tail
Fig. 6. = ◦ = ◦ = − ◦
(a) de 0 ; (b)o de 10 ; (c)ode 5 o
alone. (a) e = 0 ; (b) e = 10 ; (c) e = -5
◦
Table 3. Lift coefﬁcient of Horizontal tail CL(H) with aUAV = 0
4
◦ ◦ ◦
Elevator angle de = 0 de = 10 de = −5
UAV’s tail −0.015 0.062 −0.054
Tail alone 0 0.15 −0.1
Note that the results of the aerodynamic coefﬁcients of the horizontal tail in Fig.4
and Tab.3 were determined when considering the horizontal tail as a component of the
aircraft (UAV). Therefore, they were referred to the main wing area of the aircraft (SW )
with the formulas of lift coefﬁcient CL(H) and drag coefﬁcient CD(H) as follows
L D
= H = H
CL(H) 2 , CD(H) 2 , (1)
0.5rV¥SW 0.5rV¥SW
where r is the air density, V¥ is the velocity at inﬁnity, LH and DH indicate the lift and
drag of the horizontal tail under the main wing downwash effect.
In case of considering the horizontal tail is a lift wing alone, the aerodynamic coefﬁ-
cients are referred to the horizontal tail area (SH) as the following
L D
= H = H
CL(H) 2 , CD(H) 2 . (2)
0.5rV¥SH 0.5rV¥SH
If comparing the aerodynamic coefﬁcients on the horizontal tail using 3D simulation
method and with those calculated by semi-analytical method based on 2D results, it is
necessary to use the formula (2). Because in the semi-analytical method, the horizontal
tail is considered a wing alone subjected to a uniform velocity ﬁeld V¥ and a downwash
angle # determined by semi-analytical method (according to the 3D simulation method,
the downwash angle # changes in all three directions (x, y, z)).
Comparing the results in Tab. 3 shows that the lift coefficient of tail alone differed
significantlyComparing from the that results of the inUAV’s Tab. horizontal 3 shows tail that when the liftthe last coefficient suffered offrom tail interaction alone differed with other
significantlycomponents from of that the of UAV, the UAV’s especially horizontal influenced tail when by the last main suffered wing downwashfrom interaction [11]. with Therefore, other the
componentscalculation of of the the UAV, aerodynamic especially force influenced on the horizontal by the main tail alone wing causes downwash a large [11]. error. Therefore, the
calculation of the aerodynamic force on the horizontal tail alone causes a large error.
o
Table 3. Lift coefficient of Horizontal tail CL(H) with UAVo 0
Table 3. Lift coefficient of Horizontal tail CL(H) with UAV 0
Elevator angle 0o 10o 5o
Elevator angle oe eo eo
e 0 e 10 e 5
UAV’s tail – 0.015 0.062 – 0.054
UAV’s tail – 0.015 0.062 – 0.054
Tail alone 0 0.15 – 0.1
Tail alone 0 0.15 – 0.1
Note that the results of the aerodynamic coefficients of the horizontal tail in Fig. 4 and Tab. 3
Note that the results of the aerodynamic coefficients of the horizontal tail in Fig. 4 and Tab. 3
were determined when considering the horizontal tail as a component of the aircraft (UAV).
were determined when considering the horizontal tail as a component of the aircraft (UAV).
Therefore, they were referred to the main wing area of the aircraft (SW) with the formulas of lift
Therefore, they were referred to the main wing area of the aircraft (SW) with the formulas of lift
coefficient CL(H) and drag coefficient CD(H) as follows:
coefficient CL(H) and drag coefficient CD(H) as follows:
L D
L H D H
CLH() H 2 ; CDH() H 2 (1)
CL(H ) ; CD(H ) (1)
0.52VS W 0.52 VS W
0.5V SW 0.5V SW
where Investigation is the air of density, aerodynamics V andis longitudinalthe velocity stability at infinity, of unmanned LH aerialand vehicle DH withindicate elevator the deﬂection lift and drag 95 of the
where is the air density, V is the velocity at infinity, LH and DH indicate the lift and drag of the
horizontalhorizontal tail undertail under the mainthe main wing wing downwash downwash effect. effect.
InThe caseIn lift case of coefﬁcient considering of considering of the the horizontalthe horizontal horizontal tail istail a liftis was a wing lift much wing alone, smalleralone, the aerodynamic the than aerodynamic that coefficients ofthe coefficients main are are
wing.referred However, to the horizontal the pitching tail area moment (SH) as the of thefollow horizontaling: tail was much larger than that of
referred to the horizontal tail area (SH) as the following:
the main wing and played an important role in the balance of the aircraft. Fig.7 shows
LH DH
pitchingL momentH coefﬁcientDH of the UAV and its components at elevator deﬂection angles
CLH() 2 ; CDH() 2 (2)
CL(H ) ◦ 2 ; CD(H ) 2 ◦ (2)
0.5VS H 0.5VS H
de =0.50 V(Fig. SH 7(a)) and0.5de =V10SH (Fig. 7(b)). It was observed that pitching moment co-
efﬁcientIf of comp thearing fuselage the aerodynamic was very small coefficients (near zero on the at thehorizontal angle oftail attack using being3D simulation zero). In method
caseIf of comparingd = 0◦ (Fig. the aerodynamic 7(a)), the UAV coefficients was balanced on the horizontal at the angle tail ofusing attack 3D asimulation= 0 ◦methodwith
and andwith with those ethose calculated calculated by semi-analyticalby semi-analytical method method based based on 2D on results,2D results, it is itnecessary isUAV necessary to use to theuse the
the pitching moment coefﬁcient of the UAV being zero, Cm(UAV) = 0 (the UAV was in
formulaformula (2). (2). Because Because in the in semi-analyticalthe semi-analytical◦ method, method, the horizontal the horizontal tail is tail considered is considered a wing a wing alone alone
equilibrium). In case of de = 10 (Fig. 7(b)), the pitching moment coefﬁcient of the UAV
subjectedsubjected to a to uniform a uniform velocity velocity field field V and V and a downwash a downwash angle angle determined determined by semi-analytical by semi-analytical
was non-zero, C 6= 0, and negative. The UAV was then out of balance and its nose
methodmethod (according (according to mthe (toUAV 3Dthe) simulation3D simulation method, method, the downwash the downwash angle angle changes changes the change the change in all in three all three
directionswasdirections down (x, y,(x, toz)). y, reduce z)). altitude.
◦ ◦
(a) de = 0 (b) de = 10
Fig.Fig. 7. P7.itching Pitching moment momen coefficientst coefficients of the of UAV, the UAV, wing wing and horizontaland horizontal tail. tail.
o o o o
Fig. 7. Pitching moment(a) coefﬁcients(a)e = 0e =; (b)0 of; (b)e the= 10 UAV,e = 10 wing and horizontal tail
The The lift liftcoefficient coefficient of the of horizontalthe horizontal tail wastail was much much smaller smaller than than that thatof the of main the main wing. wing.
However,However,The the longitudinal pitchingthe pitching moment moment stability of the of of horizontalthe the horizontal UAV tail when wastail changing wasmuch much larger

Các file đính kèm theo tài liệu này:

- investigation_of_aerodynamics_and_longitudinal_stability_of.pdf