AE Stability and Control of Aerospace Vehicles

Transcription

1 AE Sabiliy and Conrol of Aerospace Vehicles Longiudinal Saic Sabiliy Tailplanes Typically a ing alone ill have ve C M0 (C m a zero lif) (posiive camber airfoil) I may have a if CG is af of AC By posiioning a ailplane behind he ing and inclining i o give ve lif I improves he sabiliy of he ing-ail combinaion -ve lif reduces overall lif of aircraf, so ings mus carry more lif Resuls in increase of induced drag, plus drag of ailplane Trim Drag Usually symmerical airfoil are used for he ail because mus produce boh upard and donard airloads 1

2 Wing-Horizonal Tail Geomery l Wing/body zero lif line V b V z L b - ε M ac, Tail zero lif line i ε Wing flo field inerferes ih horizonal ail donash deflecs V donard V local relaive ind is reduced in magniude; ail sees loer dynamic pressure Fuselage blanks ou par of he ail D Donash ε The value of he donash a he ail is affeced by fuselage geomery, flap angle ing plaform, and ail posiion. I is bes deermined by measuremen in a ind unnel, bu lacking ha, lifing surface compuer programs do an accepable job. For advanced design purposes i is ofen possible o approximae he donash a he ail by he donash far behind an ellipically-loaded ing: 2CL 2 ε CL ε So, π AR π AR 2

3 Tail Conribuion Af Tail FRL ε l z cg Wing-ip vorex Wing-ip vorices are formed hen high-pressure air spills up over he ing ips ino he lo-pressure space above he ing. 3

4 Pressures mus become equal a he ing ips since pressure is a coninuous funcion (figure a). The free sream flo combines ih ip flo, resuling in an inard flo of air on he upper ing surface and an ouard flo of air on he loer ing surface (figure b). Complee-ing vorex sysem. Flo field around an airplane creaed by he ing 4

5 Tail Conribuion Af Tail = i ε + i L = L + L 1 2 ρv 2 S S L = L L = L + η L ρv S 2 S C C C C C ρv Q η = = Tail efficiency raio of dynamic pressure ρv Q Angle of aach a he ail Toal lif ing-ail configuraion Tail Conribuion Af Tail FRL ε l z cg ( ε ) sin ( ε ) cos( ε ) sin ( ε ) M = l L cos FRL + D FRL + z D L + M cg FRL FRL ac 1 2 = = ρ L = L M l L l V S C l Q S C 2 5

6 Tail Conribuion Af Tail 1 2 cg = = ρ L = L M l L l V S C l Q S C 2 M V S S C l C l C V C V 1 2 cg ρ 2 m = = cg L = η L = Hη L ρv Sc ρv Sc Sc 2 2 S H = l Horizonal ail volume raio Sc ( ) C = C = C i ε + i L L L Donash dε ε = ε0 + d Donash a zero angle of aach ε 2C L ( rad) = Finie ing heory π AR dε 2CL = d π AR ε 2ε 6

7 Tail Conribuion Af Tail dε C = V C ( + i i ) V C d V m 0 1 cg Hη L ε Hη L H = l S Sc C = V ηc mcg H L ( ) C = V ηc i ε + i mcg H L C = C + C mcg m0 m To have C m 0 e can adjus he ail incidence angle 0 > i Cm 0 e can selec properly and o sabilize he aircraf < V H CL can be increased for example, by increasing he aspec raio of he ail) (C L Example # 3 Consider he ing-body model in Example # 2 (previous class). Assume ha a horizonal ail ih no elevaor is added o his model. The ing area and chord are 1.5 m 2 and 0.45 m, respecively. The disance from he airplane's cener of graviy o he ail's aerodynamic cener is 1.0 m. The area of he ail is 0.4 m 2, and he ail-seing angle is The lif slope of he ail is 0.12 per degree. From experimenal measuremen, ε 0 = 0 and dε/d = If he absolue angle of aack of he model is 5 and he lif a his angle of aack is 4134 N, calculae he momen abou he cener of graviy. 2 q = 6125 N / m ; Cm = 0.003; i = 0 x cg c ac, xac, = 0.02; η = 1 (assumed) c 7

8 ( ε i ) H L, 0 ( ) C C V L L, H = L q S = 6125*1.5 = dcl 0.45 = = = 0.09 d 5 l S 1.0*0.4 = = = cs 0.45*1.5 xcg xac, b CL, dε Cmcg = Cmac, b + CL, b b VH 1 c c C L, b d + V C C mcg * = ( ) M = q ScC = 6125*1.5*0.4* = 240 N / m cg 0.12 = *5( 0.02) ( ) 0.09 mcg Example # 4 Consider he ing-body-ail model of Example # 3. Does his model have longiudinal saic sabiliy and balance? Cm cg xcg xac, b CL, ε = CL, b VH 1 b c c C L, b 0.12 = ( ) = ( ε ) C = C + V C i m, 0 mac, b H L, 0 = * 0.12*(2.0) = C m, cg = 3.56 e = = 0 0 e 8

9 Canard Alernaively pu he ail ahead of he ing knon as foreplanes or canards Canard needs o generae +ve lif o creae +ve piching momen abou CG This means ha canard conribues o overall lif of aircraf Canard can creae fas increase in lif, making aircraf very responsive Canard inerferes ih airflo over main ing causes resulan force vecor of ing o il backard increasing drag Fuselage Conribuion Sreamlined fuselage has pressure disribuion similar o body of revoluion No ne lif developed by pressure disribuion Nose-up piching momen developed by up-gus Piching momen is desabilizing because no counered by ne lif vecor Fuselage is desabilizing componen 9

10 Fuselage Conribuion ( ) dm = fn Vol, Q = 12 ρv 2 d k k lf 2 Cm0 = 2 1 f 0 + i f dx f 36.5Sc 0 Cm0 = f Cm = Sc Cm = Sc f f x =l f k2 k1 36.5Sc lf 0 x =0 ( ) ( ) 2f 0 + i f x 2f ε u dx ( deg ) 2f ε u x ( deg ) x =l f x = See exbook (pp ) for deails Fuselage Conribuion 10

11 Fuselage Conribuion Fuselage conribuion Gilruh (NACA TR711) developed an empirically-based mehod for esimaing he effec of he fuselage: C 2 m K fuse f f Lf C = S cc L L here: C L is he ing lif curve slope per radian L f is he fuselage lengh f is he maximum idh of he fuselage K f is an empirical facor discussed in NACA TR711 and developed from an exensive es of ing-fuselage combinaions in NACA TR540. K f is found o depend srongly on he posiion of he quarer chord of he ing roo on he fuselage. In his form of he equaion, he ing lif curve slope is expressed in rad -1 and K f is given in he able. (Noe ha his is no he same as he mehod described in Perkins and Hage.) The daa shon in able ere aken from TR540 and Aerodynamics of he Airplane by Schliching and Truckenbrod: 11

12 Poer Effecs Propeller Je Engine Boh ill produce a conribuion o Cm Propulsive Sysem Conribuion The incremenal piching momen abou he airplane cener of graviy due o he propulsion sysem is: here T is he hrus and N p is he propeller or inle normal force due o urning of he air. Anoher influence comes from he increase in flo velociy induced by he propeller or he je slipsream upon he ail, ing and af fuselage. 12

13 Propulsive Sysem conribuion In erms of momen coefficien, Since he hrus is direced along he propeller axis and roaes ih he airplane, is conribuion o he momen abou he cener of graviy is independen of. Then e have ( 1 ) N = N qs C ε p prop p N p here he propeller normal force coefficien C Np / and he donash (or upash) ε are usually deermined empirically Propulsive Sysem conribuion N prop is he number of propellers and S prop is he propeller disk area (πd 2 /4) and D is he diameer of he propeller. Noe ha a propeller mouned af of he c.g. is sabilizing. This is one of he advanages of he pusherpropeller configuraion. Noe ha n in is he propeller angular speed in rps. 13

14 Propulsive Sysem conribuion Propeller normal force coefficien Engine Nacelles Direcion of airflo hrough propeller or engine no changed if engine axis aligned ih fligh pah Direcion of airflo changed as necessary o flo in direcion of engine axis Side force desabilizing if resuling force causes nose-up piching momen Sabilizing if resuling force causes nose-don piching momen Propellers/ je engine inake behind CG are sabilizing 14

15 Sick Fixed Neural Poin C = C + C m m m cg 0 here, for a ing-ail-fuselage configuraion (see also previous examples): C = C + C + C m m m m f f 0 ( ε ) = C + C + V ηc + i i m m H L xcg xac dε Cm = C L Cm VH CL 1 + η f c c d Sick Fixed Neural Poin C m = 0 xnp x C ac m f C L dε = + VHη 1 c c C C d L L 15

16 Trim and Neural Poin Trim dcm Cm Cm = C cg m + C C 0 CL = 0 L L = dc Cm = 0; C L cg L = rim dc dc Neural Poin For once he NP is kno, he sabiliy a any oher c.g. posiion may be obained ih good accuracy from he folloing relaion: dc x m cg x = dc c c L NP m x NP x cg Sick fixed c c saic margin L Example # 5 For he configuraion of Examples # 3/4, calculae he neural poin and saic margin x cg = 0.26 x x C NP ac, b L ε = + VH 1 c c C L xcg xac, b as = 0.02; c c xac, b xcg = 0.02 = = 0.24 c c xnp 0.12 = ( ) = 0.70 c 0.09 x x NP cg saic margin = - = = 0.44 c c 16

17 Some Conclusions For saic sabiliy he cenre of graviy mus be in fron of he sick fixed neural poin When he cenre of graviy reaches he sick fixed neural poin he aircraf is neurally sable If he cenre of graviy moves behind (closer o he ail) he sick fixed neural poin he aircraf becomes saically unsable CG Movemen During fligh he CG can move subsanially As CG moves forard he aircraf becomes more sable The forard limi o CG posiion is limied by he momen ha he ailplane can produce This is a funcion of ailplane lif and he ailplane volume (ailplane momen arm imes is area) While sabiliy improves ih forard CG movemen Drag increases, his increase is knon as Trim Drag Aircraf maneuverabiliy can suffer, larger conrol movemens are required, and response becomes sluggish When CG moves backards Aircraf evenually becomes unsable Trim drag reduces CG posiion hen aircraf is on poin of becoming unsable is knon as he Neural Poin i.e. For longiudinal sabiliy he CG mus alays be in fron of he neural poin 17

18 CG Limis The disance beeen he neural poin and cenre of graviy is knon as he CG Saic Margin. For longiudinal sabiliy he CG margin mus be +ve The absolue limi for forard CG posiion is deermined by aircraf handling being oo sluggish o conrol effecively The absolue limi for rear CG posiion is he onse of insabiliy, and aircraf handling being oo sensiive o conrol Aircraf Designers and Regulaory Auhoriies impose a more resriced CG range in pracice Care mus be aken by aircraf operaors during loading o make sure ha he CG posiion says ihin he safe range Unsable Aircraf The adven of fly-by-ire compuer conrol sysems makes unsable aircraf feasible in pracice Compuer mus make coninuous iny adjusmens o keep he airplane conrollable Advanages are: Configure ailplane/canard o produce +ve lif Loer rim drag ih CG a/behind neural poin, improving L/D Quicker response o conrol inpus Disadvanage, if he compuer conrol sysem fails he aircraf is unflyable Mus have redundan sysems as safey precauion 18

19 Saic Sabiliy Parameers Tailplane or canard design Aircraf Cenre of Graviy posiion Main ing piching momen characerisics Tail size- bigger ail means more lif/donforce Tail momen arm furher aay from CG generaes greaer momen Tail angle of aack relaive o main ing angle of aack knon as he longiudinal dihedral Handling qualiies are imporan Aircraf ha are oo sable are difficul o conrol Aircraf ha end oards insabiliy can be difficul o conrol oo Conrol Sysems 19

20 Influences on he Longiudinal Sabiliy: Influence of Wing Flaps Changes in he ing flaps affec boh rim and sabiliy. The main aerodynamic effecs due o flap deflecions are: Loering he flaps has he same effec on C mo;b as an increase in ing camber. Tha is producing a negaive incremen in C mo;b. The angle of ing-body zero-lif is changed o be more negaive. Since he ail incidence i is measured relaive o he ing-body zero lif line, his in effec places a posiive incremen in he ail incidence angle i. Change in he spanise lif disribuion a he ing leads o an increase in donash a he ail, i.e. ε o and dε/ d may increase. Effec of Airplane Flexibiliy Flexibiliy of an airframe under aerodynamic loads is eviden in any fligh vehicle. The phenomenon ha couples aerodynamics ih srucural deformaions is sudied under he subjec of aeroelasiciy. There are o ypes of analysis: Saic behavior: Here he seady-sae deformaions of he vehicle srucure are invesigaed. Phenomena such as aileron reversal, ing divergence and reducion in saic longiudinal sabiliy fall under his caegory. Dynamic behavior: The major problem of ineres is associaed ih he phenomena of dynamic loading, buffeing and fluer. 20