Investigation of aerodynamics and longitudinal stability of unmanned aerial vehicle with elevator deflection

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 thereUAV  was0 and no o o o o vortexUAV 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 VUAV 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)UAV14UAV(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 the0o , 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 ofofe ( pressure0e (, 010, 10, – coefficients ,5 –) 5. In◦). Inthe◦ the case on case ◦ a of half ofe =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 samee (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) one =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 Buie 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) 0.52VS W 0.52 VS W 0.5V SW 0.5V 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) 0.5VS H 0.5VS H de =0.50 V(Fig. SH 7(a)) and0.5de =V10SH (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