Project 6 Aircraft static stability and control

Transcription

1 Project 6 Aircrft sttic stbility nd control The min objective of the project No. 6 is to compute the chrcteristics of the ircrft sttic stbility nd control chrcteristics in the pitch nd roll chnnel. The necessry computtions hve to be done using digitl model of n ircrft, which ws creted within the Project No. 4 of "Aircrft Design I". The model ws creted using progrm AVL or PANUKL nd the sme softwre will be used for stbility nd control nlysis (student must use the sme progrm which ws selected in project No. 4). Due to the different cpbilities of the softwre, some steps of clcultion cn be different nd the procedure depends on selected progrm. Next chpters present the computtion procedures for both softwre listed bove. To recll the terms relted to rottions, Figure 1 presents definitions nd the sign convention of moment coefficients nd ngulr velocities. Student should modify the numericl model nd dd ilerons nd elevtor. Detil description of control surfces definition is described in next chpter. ontrol surfces definition: Figure 1 Moment nd ngulr velocity components AVL ontrol surfces cn be defined for prt or for the whole spn of the wing/horizontl til, red crefully documenttion. Aileron nd elevtor definition, with listed vribles, is shown below. Hlf of wing with defined control surfce is defined in Figure 2. ONTROL Aileron ONTROL Elevtor nme - nme of control vrible gin - used only for mixing deflection of multiple defined controls on one surfce, students should set it s 1.0 Jcek Mieloszyk, Agnieszk Kwiek, Tomsz Grbowski Project guide: ircrft sttic stbility nd control v.1.1 1

2 Xhinge - x/c loction of hinge, see Figure 2 XYZhvec - vector giving hinge xis bout which surfce rottes SgnDup - sign of deflection for duplicted surfce, n ileron would hve SgnDup = -1, n elevtor would hve SgnDup = 1 Figure 2 Wing with control surfce After loding geometry file with control surfce defined, student must set ngle of deflection of the ilerons/elevtor (defult is 0 - no deflection). In the OPER mode, under vribles list, lso nmes of the defined control surfces pper. Angle of deflection, defined in degrees, must be ppropritely chnged to fit roll requirements. Mke erodynmic nlysis nd red stbility derivtives needed for the roll requirements. PANUKL Figure 3 Aileron definition in PANUKL Jcek Mieloszyk, Agnieszk Kwiek, Tomsz Grbowski Project guide: ircrft sttic stbility nd control v.1.1 2

3 In PANUKL cse, the definition of wing hs to be completed by ileron definition (Figure 7). The irfoils of the prt of the wing with control surfces hve to be chnged. Airfoils with control surfces deflection cn be prepred in Xfoil in geometry mode GDES using commnd Flp. Asymmetricl mesh with wke for the right nd the left prt of the wing hs to be prepred seprtely nd then the two hlves of mesh connected. Two computtionl cses must be done: 1. cse with ileron deflected, ngle of ttck nd other stte prmeters equl to zero, 2. cse with not deflected ileron, defined roll rte (e.g. 1 rd/s), other stte prmeters equl to zero. The dimensionless derivtives cn be computed s follows: l l l l (1) where: l p l l (2) pb pb 2V 2 l rolling moment coefficient (tken from [.out] file), p roll rte [rd/s], b wingspn [m], V = 1 Procedure of elevtor creting is similr to ileron but ircrft with elevtor deflection is symmetricl object nd it is not necessry generting two hlves of the ircrft seprtely. Longitudinl sttic stbility The first tsk is clcultion of neutrl point position for the lift coefficient rnge corresponding with the flight envelope. Next step is estimtion of sttic (stbility) mrgin for the extreme positions of the ircrft s center of grvity (the most front nd the most ft position of the center of grvity for irplne configurtion during flight). Bsing on these clcultions Student should prepre digrm of the neutrl point trvel versus the lift coefficient, which rnge hs to correspond with the flight envelope (see exmple Figure 4). Figure 4 Digrm of neutrl point trvel Jcek Mieloszyk, Agnieszk Kwiek, Tomsz Grbowski Project guide: ircrft sttic stbility nd control v.1.1 3

4 If the ircrft is unstble, the sufficient modifiction of geometry or of grvity center position should be done. Figure 5 presents digrm illustrting vrious conditions of longitudinl sttic stbility. Figure 5 Longitudinl ircrft stbility AVL The neutrl point position should be clculted by AVL softwre for the lift coefficient rnge corresponding with the flight envelope. Position of neutrl point cn be obtined by ST commnd in oper mode. Next step is reclcultion the position of neutrl point from meters to percent of the men erodynmic chord. ATTENTION: heck the position of the reference coordinte system in numericl model. The sttic mrgin cn be clculted: h n X N X. G h n sttic mrgin [%] X N neutrl point position [MA%] X.G. center of grvity position [MA %] (3) If ircrft ws unstble nd geometry ws modified, the erodynmic nlyses hve to be repeted for the new configurtions. PANUKL To obtin neutrl point of stbility, clcultions should be mde for two different ngles of ttck equidistnt from the point (ngle of ttck) under considertion. Then the position of neutrl point cn be obtined from formul: Jcek Mieloszyk, Agnieszk Kwiek, Tomsz Grbowski Project guide: ircrft sttic stbility nd control v.1.1 4

5 m m dm 1 1 X N 100% 100% (4) d L L 1 L 1 where: X N neutrl point position [MA%] m pitching moment coefficient of the whole ircrft L lift coefficient of the whole ircrft In presented formul, these two equidistnt points re -1 nd +1. ATTENTION: The coordinte system used in PANUKL, differs from system presented on Figure 1. The X xis is directed bckwrd nd the origin is defined by user during defining of the ircrft geometry. The moment coefficients re computed with respect to point defined by user or computed utomticlly by progrm usully ¼ of MA. The coordintes of this point re sved in results file [.out]. X N is computed with respect to the sme point s moment coefficients. The sttic mrgin, like in AVL cse, cn be computed using Eq. (3). If ircrft ws unstble nd geometry ws modified, the erodynmic nlyses hve to be repeted for the new configurtions. Informtion bout ircrft s component moment coefficient contribution cn be obtined by unchecking the horizontl stbilizers ctive flg during the mesh genertion. Angle of horizontl til setting: In this prt of the project student should define n ngle of horizontl til setting. Using numericl softwre student should find configurtion of til which fulfils the following condition: Aircrft with no elevtor deflection should be in equilibrium stte for cursing flight condition. Trim nlysis: In this prt of project student should modify geometry of the numericl model nd dd the elevtor. Next student should mke numericl erodynmic clcultion for model with elevtor deflected. Result of this prt of project should be the digrm of ruder deflection versus to flight velocity which is necessry to obtin trim condition (M=0) see exmple Figure 6 Jcek Mieloszyk, Agnieszk Kwiek, Tomsz Grbowski Project guide: ircrft sttic stbility nd control v.1.1 5

6 Directionl sttic stbility Figure 6 Digrm of δ R (V) Next tsk is directionl stbility clcultion. This clcultion should be prepred for symmetricl model (heck symmetricl settings; for AVL model check iysym prmeters; for PANUKL ll symmetry flgs). Result of this prt should be digrm of yw moment coefficient referred to side slip ngle β. The clcultion should be computed for ngle of ttck equl 0. The clcultion should be computed for two points: β=0 nd β 0, in both cses the ngle of ttck hs to equl 0. Directionl chrcteristics should be compred with roll rte response criteri nd roll controllbility criteri described in the next chpter. Figure 7 Sttic directionl stbility Roll control chrcteristics In this prt of project student must dd control surfces to the min wing, which will Jcek Mieloszyk, Agnieszk Kwiek, Tomsz Grbowski Project guide: ircrft sttic stbility nd control v.1.1 6

7 work s n ileron to obtin derivtive nd define roll rte to obtin lp derivtive. l Simplified Roll Rte criterion Two fctors re used to rte flying qulities in roll: time constnt T R of inertil module, which describes roll chrcteristics using the first order trnsfer function: p( s) kr GR( s) (5) ( s) T s 1 where: p(t) roll rte, (t) ileron deflection. roll time T to perform roll ngle fter ileron deflection. R Bsic terms for derivtives clcultion Anlysis bses on the liner differentil eqution: L 1 Lp Lp t ( t) e, (6) where dimensionl stbility derivtives re defined s follows: derivtive of rolling moment with respect to ileron deflection: q S bl L I (7) XX derivtive of rolling moment with respect to roll rte 2 q S b l p Lp (8) 2 I V Dimensionless derivtives re defined s follows: l l l XX l (9) p b V l p 2 AVL: Both derivtives lp nd PANUKL: Both derivtives l lp nd could be directly computed by AVL pckge. l could be estimted bsing on results from PANUKL. Jcek Mieloszyk, Agnieszk Kwiek, Tomsz Grbowski Project guide: ircrft sttic stbility nd control v.1.1 7

8 Roll chrcteristics Roll chrcteristics re defined s follows (bsing on the model defined by Eq. 6): 1 o Time constnt of roll mode Tr. it is time necessry to perform roll rte: Lp e (10) where: ss ss ss is stedy vlue of roll rte o Roll controllbility: l p b b T(, ) 2 V (11) 2V l where T(, ) - time necessry to roll from ngle 0 o to ngle equl to fter ileron is deflected on. Acceptnce levels The cceptnce levels re defined by different regultion in different wys. The MIL-F8587 cn be used if there re not cler criterions in irworthiness regultion. Necessry highlights re below: Flight Aircrft phse clss Time constnt of roll mode Acceptnce level Time constnt T R [s] cnnot be greter thn A I, IV A II, III B ll I, IV II, III Jcek Mieloszyk, Agnieszk Kwiek, Tomsz Grbowski Project guide: ircrft sttic stbility nd control v.1.1 8

9 Ares: 1. recommended 2. cceptble 3. uncceptble Lines: ) mx roll rte 120/s b) mx roll rte 60/s c) time to perform roll ngle s d) time to perform roll ngle s Figure 8 Simplified Roll-Rte response criterion for trnsport ircrft Roll controllbility Aircrft clss Flight phse Acceptnce level (-T) roll ngle [ ] performed in time T [s] A 60 in 1.3 s 60 in 1.7 s 60 in 2.6 s I B 60 in 1.7 s 60 in 2.5 s 60 in 3.4 s 30 in 1.3 s 30 in 1.8 s 30 in 2.6 s A 45 in 1.4 s 45 in 1.9 s 45 in 2.8 s II B 45 in 1.9 s 45 in 2.8 s 45 in 3.0 s 30 in 2.5 s 30 in 3.5 s 30 in 5.0 s A 30 in 1.5 s 30 in 2.0 s 30 in 3.0 s III B 30 in 2.0 s 30 in 3.0 s 30 in 4.0 s 30 in 3.0 s 30 w 4.0 s 30 in 6.0 s A 90 in 1.3 s 90 in 1.7 s 90 in 2.6 s IV B 60 in 1.7 s 60 in 2.5 s 60 in 3.4 s 30 in 1.0 s 30 in 1.3 s 30 in 2.0 s Remrks: 1. In cse of ircrft of IV-th clss, for 1st level, stick nd pedls should be free during test. 2. Otherwise rudder my be used to reduce sideslip, however only if it cuses decresing of the roll ngle; ny use of rudder, which increses roll ngle is forbidden. Jcek Mieloszyk, Agnieszk Kwiek, Tomsz Grbowski Project guide: ircrft sttic stbility nd control v.1.1 9

10 Project requirements: Project s report should include: ll student s ssumptions (reference vlues should be lso included); result of sttic stbility mrgin clcultion (digrm nd tble with vlues), ngle of horizontl til setting, digrm of δ R (V) for trim condition; digrm of n(β) for α=0; plot of pressure distribution for model with ileron deflected (exmple Figure 9); results of roll chrcteristic clcultion which present tht requirements for roll for ll phses of flight re fulfilled; plot of lift distribution versus wing spn with ilerons deflected exmple Figure 10 (AVL T Trefftz Plne plot commnd, PANUKL from spnwise distribution file [.czy]); drw scheme with dimension of wing with ilerons nd til with elevtor; Figure 9 Exmple of the pressure distribution for model with ileron deflected (on the right) results of AVL exmple clcultion Figure 10 Exmple of the lift distribution versus wing spn results of AVL exmple clcultion. Jcek Mieloszyk, Agnieszk Kwiek, Tomsz Grbowski Project guide: ircrft sttic stbility nd control v

11 Bibliogrphy [1] R.. Nelson: Flight Stbility nd Automtic ontrol (second edition), McGrw-Hill, 1998 [2] Ajoy Kumr Kundu: Aircrft Design, mbridge University Press, 2010 [3] B.H. ook: Flight Dynmics Principles, Butterworth Heinemnn, rnfield 1997 [4] AVL user Guide ( [5] PANUKL user Guide ( [1],[2],[3] re vilble in Min or Fculty Librry or in E-books on WUT Min Librry e-resources Jcek Mieloszyk, Agnieszk Kwiek, Tomsz Grbowski Project guide: ircrft sttic stbility nd control v