Aircraft handling qualities data
Transcription
Aircraft handling qualities data
1. Report No. 2. NASA 4. Title and 3. No. Recipient's 5._Report l)ecemoer tIANI)LING K. Performing tleff!cy QUALITIES and Organization Systems Wayne Name Technology, ttawthmme, F. and Jewell Sponsoring Agency National Performing Organization Code 8. Performing Organization Report Name and Work Supplementary 16. Abstract 11. Contract for 10 for each information 14. representative by qualities, derivatives, (of functions parameters and have are the envelopes been systems Data presented inputs, computed the C-5A, aerodynamic are control power NT-a3A, inertia, augmentation airplanes. for including B-747, No. 4-1729 Type of Report and Period Covered Report Sponsoring Agency Code and F-104A, F-4C, functions, control this report} tabulated HL-10, for handling 10 The Distribution Statement Unclassified- stability 20. Unlimited Security Classif. (of this 21. page) by the National Technical Information No. of Pages 343 Unclassified sale airplanes Jetstar, systems Unclassified ' For different andXB-70A. 18. transfer given deriv- selected configuration. X-15, documented are dimensional several are derivatives, is sources and and approach Author(s)) airplanes, Classif. Flight conditions CV-880M, weight stability contemporary airplane. documented (Suggested on and transfer flight Security A(ln_inistration characteristics, qualities 19. Grant Notes ativcs, llandling or Contractor Space Available Words 1004-1 No. 20546 control Key Unit Address Address m_(t I).C. 15. Report 10. No. 90250 Aeronautics Washington, 1972 Technical Inc. Califon_ia Date 6. NAS 17. No. DATA 13. 12. Catalog CR-2144 Author(s) Robert 9. Accession Subtitle AII_CHAFT 7. Government Service, Springfield, Virginia 22151 22. Price* $6.00 TABIZ I. ii. III. IV. v. VI. VII. viii. D{. INTRODUCTION I • • • F- IO_A . . . F-4C • • • • . . 61 x-15 • • • • . . Io8 HL-IO • • • • • • 137 JETSTAR • . . 1 66 CONVAIR 880M . • • • 193 • . . 210 • . . 2_3 • • • 273 • . LOCKHEED C-_A .... XI. XB-70A • APPENDIX A. APPENDIX • NT-33A 747 APPENDIX COI_TERTS . BOEING x. OF B. C. • • • • • • • • 32 • • AXIS SYSTEMS, AND DERIVATIVE TRANSFORMATION DERIVATIVES TO EQUATIONS • SYMBOLS, COMPUTER MNEMONICS, DEFINITIONS .... OF STABILITY AXIS BODY AXIS ...... OF MOTION AND TRANSFER iii .... FUNCTIONS . . . A-I B-I • C-I SECTION I INTRODUCTION The gators purpose with craft. the aircraft's For following The insofar those data required are response to control augmentor aircraft the b. Mach/altitude 3- Control system 4. Stability 5- Tabulations derivatives 6- Dimensional, 7- Dimensional 8. Transfer 9" Selected_andling notation, An contemporary transfer analytical air- functions relating description of information was available, the presentation: computations (e.g., fuel are load_ made flaps, combinations description description and/or plots of non-dimensional for trimmed flight mass, and stability functions flight condition stability parameters derivatives for control qualities three and index inputs parameters has is presented been to make nomenclature, appendices. definitions of B gives derivatives. Appendix C includes used herein. this Appendix Appendix functions in Table report definitions, derivatives. transfer obtain investi- given. which augmentation cross symbols, in qualities sources intention as for Configtu_ations gear, etc.) arrangement number and handling representative to complete a. Data also contents General several inputs. is for which 2. described and on Flight conditions including: 10. is to provide data summarizes 7. document usable stability those page this readily Included aircraft's A of axis the completely etc. A covers nondimensional the I-1. system aircraft The axis and self-consistent system systems, dimensional transformations equations used is symbols stability for of motion the and the X I g o i i <_ o_ _ _ _ _ _o_ o_ _ _o _ _ _ aa _''_'" . _. . _ The and aircraft uses. were In considered each computed case_ for of interest. for up and of all trimmed Also, wind depending by stability Where motion Handling tion with are given. transfer A substantial mnemonics The small are be used in are used in of those shown, and the While qualities complete '_oest" data accessible for would to some the for also given are of this report printout over definitions the is of given HAS-on was picked flight Also, the axis body with in the the in the axis system " system or is 'body" of systems functions. on the functions body equations and handling quantities. axis. All position. acceleraThrust characteristics. form of computer MIL-F-8785. represent majority Although A are functions printout. A. report The in Appendix results, control in Appendix years. based clarification motion response are transfer pilot's along test effect axis plots are "rigid, of transfer transfer cruise) words in this the flight (Further defined given versions with engine are parameters present for the is presented significant stick-free cover the along parameters coefficients or speeds, configuration, Descriptions given 4) developed F.R.L. a any qualities past are by sizes, coefficients data_ given include this in conjunction handling given used fraction values portion handling always The plot. A.) has the (a z and do not case stability the are system parameters functions approach indicated Appendix systems are moment data with a bobweight) functions is to nominal and a body-fixed in this of qualities selected flexible aero aligned given handling coefficients. each for functions qualities transfer on control (as Transfer force a power range (generally aerodynamic This augmentation a longitudinal qualities The is were For data 3 estimated system used which a wide and configuration aerodynamic "stability" systems functions cases, "flight" span conditions. availability. a body-fixed and of of and indicated axis flight tunnel upon "flexible," for nominal in most a tabulation on rigid A away report conditions non-dimensional presented. with transfer flight regimes in this a presented only general to only SAS-off and yield here could SAS-on parameters. coverage be of desirable, author. aircraft, This and each the aircraft major is why also criterion only why, including 3 used isolated as those only people was the "latest" that and the data be flight conditions are more intimately familiar with each particular aircraft will recognize, the data presented may represent an early estimate in the design process and perhaps the "nominal configuration" is one which never left the drawing board. The data have been reviewed and, although not all those presented indicate unquestionable trends, those data known to be based on only early "guesstimates" or showing unreasonable trends have been deleted. In somecases data were estimated by the author. As to how well the data can be expected to match the flying aircraft, it is assumedthat those for whomthis document is intended knowwell the difficulties of obtaining derivatives from flight to insure reliable translation, from their source documents. test data. interpretation, The manufacturers of the aircraft Every attempt has been made and transcription of the data described herein can not be held account- able for the information presented, nor would they be bound to concur in any conclusions with respect to their aircraft which might be derived from its use. 4 -33A ACXSXOmm "The NT-33A variable stability airplane (Serial No. 51-4120) is an extensively modified T-33 jet trainer. The elevator, aileron and rudder controls in the front cockpit are disconnected from their respective control surfaces and have been connected to separate servomechanisms that make up an 'artificial feel' system. In addition, the elevator, aileron and rudder control surfaces have been connected to individual servos which can be driven by a number of different inputs. These servos receive their electrical inputs from the artificial commands, position or force), attitude and feel system (pilot's rate gyros, accelero- meters, dynamic pressure, _ vane and _ probe. through a response-feedback system, allows the derivatives to be augmented to the extent that This arrangement, normal T-33 the handling qualities of many existing airplanes, future airplanes or hypothetical research configurations, can be simulated. The original T-33 nose section has been replaced with the larger nose of an F-94 to provide the volume required for the electronic components of the response-feedback system and the recording equipment."* Transfer thrust trol functions although crossfeed and Aerodynamic longitudinal andMach the NT-33A feedback data, data number are for given also has only other the primary control surfaces surfaces and and engine a range of con- combinations. for the the high derivatives for most lift from part, was taken configuration NACA-RM-7116. 6 from was AFFDL-TR-70-71. obtained from LAL However, 1 27 0 .r-I 4_ .r-I 0 or-I 0 I1) m (1) 0 r-4 CD I::" 0 •_ 0 .r_ P-I 0 ,.-I •r_ _/_ t-.-.1 q_ bid .,rl ,-4 I I 0 0 0 0 0 0 q 0 Ca I o O .r_ 4_ E_ , _d o c) © 4_ I ¢- i f-! ! @ r/l .r-I -,-4 I:I O ,'d O 0 .,,-I .4,} d o Q 0 o (\J 4_ c_ i (_ 4_ q_ i O Ckl -P 0 ¢..} f2_ •,-I ,-I q_ b4] _lC4 _ _) cq b.O 4 4 cH I ,,--,i ,-,8_8oo _ _ t_ CO 0 _ _ 0.1 tk.l r"-t C} -P b[ [- 4 II tl p_ ._ 0 CL, 0 _£r -J II II \D ,--I _ _ 0 0 c_ _. _ kC_ C'_ 0 0 [_ C_d 0 0 _ O 0 0 0 Od II II II r4 0 % 42 II 0 bD _h '_d _ q_ r4 Ill 0 E_ ,rl # 4_ _ • Od _--7 4-_ c+d _: f ,,,4 .r-4 [:: O I-I _ H H Lr'_ > r-I _ _ @ II II htg N _ N N .JO __o 4._ d_ °" t_ qJ O ! I-'4 b I N II I! II .--i 8 NT-33A PITCH AXIS Variable Variable Feel Stability Input Input I FST(Ib) _..026 ROLL AXIS s z +.89s _]ST(in) ----] + 22.5 _.3 -I0 Variable Feel Input Be(rod) Variable Stability Input FLAT (ib) I sT YAW _._ OST _,n I0 _a(rad) AXIS Variable Variable Feel Input Stability Input I FpED(Ib)_ 78 Feel to system I_PED(in) = I _._ 2.34 parameter values the "Front Seat Engage" Figure 11-3. NT-33A 9 shown mode Control _. correspond (normal System NT-33) 8r(rad) TABLE Power_oach 11-I Non-Dimensional h = sea level VTo = 228 ft/sec oo = 2.2 ° Longitudinal Stability = Derivatives 139 kt Lateral-Directional ( Stability Axis ) cL = .813 cy0 = -.72/r cD = .139 Cn_ = CLm = 5.22/rad C_0 = --.127/rad CD_ = .94/rad C_p = -.O7/rad % = --.401/rad C_p = -.045/rad -mo/raa C_r = .20/rad Cnr = --.16/rad --.O09/rad Cmq : : .049/rad CL5e = .34/rad Cn5 a = Cm6e = -.89/rad C_5 a = .14/rad CYSr = .17/rad Cnsr = -.O73/rad C_5 r = -.OO2/rad 10 ' 14 w 12 B 10 n .... ------ SL 20,000 ft 40,O00ft Clo (deg) 8 D 6 D 4- \ Z- 0o 11 NT-33A 13700 Ib .263 Rigid 0 LO rrJ O oJ 0 0 I ,:_ _Q Od I -0 I I I 1.0 0 (%1 0 -O. _C) 0 o. , 0 F-r'- z_ (..) .4-W_- W.-- f..) 0_ x O0 O0 O0 I.LJ w. j.- _Jc_o o. 000J_ ! , :l II (.) I I I I I 0 o_ 0 -- LO o_ -0 0 12 - LO 0 0 m 6CL a (red NT-33A 13700 Ib ! I -I ) 4 4- Rigid ! ! ! SL ..... 20,O00ft -------- 40,000 ft 2- 0 0 I .4 I .2 I .6 I .8 .6 .8 Mach 1.2 CDa (rad "l) I I .8 l I I l % .4 0 0 .2 ,4 Mach 13 0 0 Mach .2 I .4 I (_ I .6 .8 I I / (rad -i) -.8 ..... --"-- -1.2 0 0 SL 20,O00ft 40,O00ft NT-33A 13700 Ib .263_ Rigid Mach • .2 .4 .6 _ .8 Cm& Cmd, -4 Cmq (rod") -8 -12 _Cmq -16 14 NT-33A 13700 Ib .263 F.," 1.0 CL Rigid M "21 0 | 2 _ _ 3 6 .4 Mach 8 4 i .6 -I.0 SL 20,O00ft 40,O00ft ..... ------.3CD M I 0 0 .2 .4 .6 .8 .6 .8 Mach Moch 0 .2 .4 0 Crn M -.2 -.4 15 .4 CL8 e (rod "l ) NT-33A .2 Rigid O0 I .2 I .4 I .6 I .8 .6 I .8 I Mach Moch 0o .2 I .4 I -.4 Cm_ e (rod -j ) -.8 -I.2' 1 _; Mach 0 0 .2 .4 .6 .8 I I I 1 Cy_ (rad-i) -.4 -- SL NT-33A ..... 20,O00ft 13700 ------- 40,O00ft Stability Rigid .2 Cn/_ (rad -i ) 0 I I .2 .4 I Mach f.®." / -.2 17 .6 I .8 Ib Axes Mach 0 0 .2 I .4 t ..... --- "-"- SL 20,O00ft 40,000 .6 l .8 -.2 -.4 c.tp (rod "I) m6 Boa ft NT-S3A 137001b Stability Rigid .O4 0 Cnp (rod "l) -.04 -,08 _4r _,f Axis • ------- SL 20,000 ft 40,O00ft NT-33A 13700 Ib Stability Axis Rigid .3- C._r_ Cn r .2 (rad "l) -- \',, \. %%% _ " """ C._r 0 I I I I .2 .4 .6 .8 Mach '.1 Cn t9 r .2O .16 C}s a (rad "l ) .12 0 0 ' SL ..... 20,000 ft 40,O00ft I .2 I .4 NT-33A 13700 Ib Stability Rigid I .6 I .8 .6 .8 Axis Mach .01 Mach .2 .4. 0 Cn8 o (rod -j ) -.01 -.02 ¢ So is sum of both right and left aileron deflections 2O Cy_ r (rod "l ) I .?_ O0 I .4 I .6 I 8 .6 I .8 I Mach Mach 0 .2 I 0 .4 I -.04 Cn8 r (rad"I) -.08 , ------ _m *== NT-33A 13700 Ib Stability Axis Rigid SL ?_O,O00ft 40,O00ft .04 C,_sr (rad "l ) .02 I _ 0 0 i .2 .4 Mach 21 I I .6 .8 _e <1 ,0 r,,l I'- o • o_ p • _ _ ¢'_ ¢_J +,PI i_ _ • _r+ ..4 _ -_ " _ _ I<'I 0j • .4 1%1 _"41" ,_ • <_ . • C._ 0 o 1%1 0 o P_I II Io 0 ell 3 _ . _ o eg _ I_ _+ o , r.- _ _; " 17 _o o _ ,-I __ ' _ _" _ + o _o t+_ o _%j o_ (_; _l" o 0_ _- _+ _ o _• _ • P". .• o + , _• ®• j o ; + t II I<"X I GO 22 0 _ o o o _ 0 o • • O • I 0 • 0 I" * O ,Ti _ I" o" I" " T • N l,O ; = I _, o• • I rJ_ H _. •4" ,,..4 I_. cO N I_. ,0 u_ 03 bl_ LIJ 0 N 0 4 _ o • 0 i o I" o 0 • I=I 0 0 _ o • I " _ I_ 0 o u I" 0 I" 0 _ _0 I" • _ _.i _ _ ",I" IJ" o 0 I " C) o ooo .i.) 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O u_ I_ 0 _r_ • o _ O 0 _ P_ I I um * o r_ * O ..t• O _0 0_ I I c_ • _ O + _ _ • 0_ _O O O O O _ _ _ • co _ o • • 4 (]Q _O O _1 _ _ ® a0 _ • _ r_ 0 o p 0_ e_I _ _ _ _1 • _ O _l ! v _0 r_ I-I + <_ 0 _ E_ u_ o r'_ .0 _. _ -,t" _ O O - I_ • • I "_ * 0_ I -.1" ,_ t_- O O" O * _ O - _ o _ o o _ t'-- ...0 o _ • ,-,I _0 • O _ _ • H * + @ ! ÷ A I I .-_ J 0 L+r', • I ,_ L_ I • c_ ,.,.,+ _ • 0 ('%1 P'-- ,'_ u", + • 0 _ .-4 _,+ I%J I t'%l ,_ _ l_ • + LU _- _ _ _ -- 3O <++._ _, <'%1 ,-,+ , r,,.,l Or, "_ I _j ._ NT-33A Hall, DATA SOURCES G. Warren, and Ronald W. Huber, System Description Performance Data for the USAF/CAL Variable Stability Airplane, Air Force Flight' D_nsmics Laboratory Rept. AFFDL Tests TR-70-71, Aug. 1970 of a I/5 Scale Wind Lockheed Aerodynamics Cleary, of Joseph a Model Results, Statler, W., and Pursuit C., et Tunnel Model of the TP-80C Trainer, Laboratory Rept. No. LAL 127, Jan. Lyle J. Airplane NACA-RM-7116, Irving and T-33 No. al, Gray, High Speed and Correlation .Jan. 21, The 23, 1948 Wind-Tunnel Tests with Flight-Test 1948 Development and Evaluation of the CAL/Air Force Dyuamic Wind Tunnel Testing System_ Part l-Description and Dynamic Tests Of an F-80 Model, A_'_'DL-TR-66-153, Feb. Flight 1967 Manual_ USAF Series T-33A Aircraft, 31 T. O. IT-33A-I. SECTION F-IO4A 32 III F- 104A The fighter a full F-IO4A is a powered by span boundary and are without fully The is edge flap. system. while A bobweight is used source with be at the of data the shown yaw LR have by superiority here. wing has a blowing-type and yaw Pitch is a longitudinal The conventional roll_ control in the pilot's was flaps Pitch_ is not air afterburner. is provided stabilizer. irreversible supersonic edge Control effect to engine Trailing their assumed primary lightweight_ turbojet all-movable however boost. position from an place_ single control and incorporated_ trols a leading layer rudder single BACKGROD'AID ailerons dampers and roll cable-actuated feel system. are conrudder Its location. 10794. Drag information was obtained LR-12873. The based loading on nominal actual at flight configuration weight manual and used balance approach here is the data. speeds. 33 The combat PA loading configuration for the F-]O4A is a typical o .H o c) ,-t \,- .,-4 OJ p_ o o •r-I o ._ o 0 ,r--I % ry_ o 4_ !o rl I I I 8 o 8 o o d q 41 q _1 i/] o o r_) I o °r--I ,--t o I f---4 H H u/ -e-I (1) -rq b_ .r-I ,-t o .,-I -r-t O o -,-I ii _3 .H ii1 -r-t .rt o ._I 4_ ._I .r-I 0 ,rl Od 4_ c) _-_ l_q 4_ 0 111 0 o "d O b.0 _ r-I ¢ :d c_ 4.> ¢+_ I ", o _ oJ oJ -p 4-> r_ rH i i b.O b_ _ ,--I _h cO II I1 ,-I o o _ _ o _, ksD _ _o _-_ 0 P, I'--I U II II rl o o _ 4._ r--I O H II r.D 34 03 f_ Cb 4_ _ II _ _ 0 I-4 H II H II 0 ID wu _0 r-i c_ © Z m o I & ! H _o ._ I !q- >° II rJ)._ iu C-_ 35 F-104A PITCH AXIS 8SsAs(rad) G 57.3 FST(Ib) 8s(rad) i -20 3.2 32.2 -I0 8s(deg) 0 I0 Oz B F B az assumed to be at pilot location /in) AXIS ROLL 8aSAs(rad) F LAT --I ST (Ib) --i I I 2.7 _! i 2,,4 5"_ _ 8a (rod) YAW AXIS SpED(in) 7.35 57.3 FpED(Ib) KDIR_ _ 8r(rad) 2.0 K°["/'Ib/in_ 1.0 o, 0 I I .4 .8 Figure 111-3. Mac h F-IO4A 36 I I I 1.2 1.6 2.0 Control System Power Approach Non-Dimensional Stability h = sea level VTo = 287 ft/sec _o = 2"3° _s = --7.1° Longitudinal = Derivatives 170 kt Lateral-Directional (Stability CL = .735 Cyp % = .263 CL= = 3.44/tad CDa = .45/rad Cm_ = -.6_/ra_ Cma = Axis ) --I.6/rad Cmq = ->.8/ra_ = -1.17/rad cn6 = .5o/r_ C2p = --.175/tad C_p = --.285/tad Cnp = --.14/rad C_r = .26_/rad Cn r = --.7_/rad Cg_s = .68/tad Cnsa = Cm_s = --1.4g/rad C£5a = 37 .O0_2/rad .039/rad Cy_r = .2OS/ra_ C_Sr : .045/rad C_ r = --.16/rad CY_d = • 0325/rad CnSd = --.025/tad Cg5 d = -.O044/rad I I I I I I 1 0 0 00_ G) 88 m_ o. jO _LLO _0 O0 I LL_D I 0 -- I I _ I OJ --0 Q I _ q I 0_1 0 0 0 0 000 Oooo _000 _J O0 Od 0 0 c_ O_ .l( _o. _J O0 _D / _o. q ! to ! _GO ! --LD I 0 ! I 0 0 I 0 I I 0 0 u f.j Q o L 40 0 0 IE q C_J .D 0q. ooo_ I N I 0 0 I JE o 0 J:: o co O0 E) q,.. q-- q_-" "-00 ooo8 ooo 0 'Ill I 'ili, 0 I 0 0 0 o. o. 0 0 0J I ! _1" I I i I=ll E E "o L_ L. 41 E r.j "0 O ,,.. 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I I I" F.i_ .,l"(.J w0 r,_ ,,_ ,0 r'• 00_0 • t{% 0 • • • I I _i I I o o_ ,0,0" I .,._- ,l) ,-_ e,l • ,-a_ ! ! g w O_ I.) _N_ w Z 58 _ ,0 _N ZZ ,,-a I I P" 0 oom _0___ • o ._, _ • • _ o ,_ , _- 0, - - e ,o m o_ r- o o0 . .t ._ , o _, • _, _, I ,4 0 o o, • o _- O" _ • N _. n,l • ,-_ • O, 0 • ,O o ,,.4- O" 0 • t_ m _ u_ o ,O • ,o U'_ ,4" -,1" 0 ,0 • u'_ 0'_ ,0 • I_ 0] ,0 _ 0 o _ _ _ 0 e_ o _. _- O _ _ 0 o 0 _q I',- 0 I _ o _1 ,-_ _ ,_- o ,.- o, _ .o 0, _ O I_- ,,I- N .-_ " _ 0" ..'_ o 3H H CH O D3 O3 _- _ o . _. 0 Pq I_ I'_ _ r- _ _ O .,- _ O_ o 0 _ _ _ _ _ _.. o o i_ ,,,I_ I_, O O I _ _ I n,i NoD r'- r_- _I _ • . • h. I _o fM I ILl UJ U') rf _ v % 0_. j O. 59 _ _ I O F- 104A Stabi? [ty and Control and No. LR 10794, 12 Dec. DATA SOURCES Handling 1955 Qualities_ Andrews, William H., and Herman A. bility and Control Derivatives Low Aspect-Ratio A!or. '1959 Performance t F-IO4D, Flight Manualt F-IO4A 15 Dec. 1961 Unswept Lockheed and Wing Technica ! Manual t Flight Controls Aircraft, T. O. 1F-104A-2-8, and a Tee-Tail, No. USAF LR-12873, Series t USAF Series 15 Mar. 1960 6O Lockheed Rediess, Flight-Determined of a Supersonic Airplane Rept. F-IO4B F-IO4A, NASA Aircraft, F-IO4A Stawith a Memo I May Rept. 2-2-59H, 1958 T. and O. IF-IO4A-I, F-I04C SECTION F-4C 61 IV F-_C BAC_DROUND The F-4C all-weather is an Air air-to-air ailerons in provides longitudinal is Landing speed edge (BLC). flaps deflection in layer and whose Lateral spoilers through by fighter combat. stability reduced Boundary on control a swept control. span conjunction control is is achieved by A swept edge is automatically and inboard plain layer control boundary induced and combination. flaps blowing-type stabilator stability fin-rudder leading with wing. mission Directional a conventional full primary when full flap occurs. Features F-4B, with accomplished is tactical missile combination control trailing Force distinguishing the USAF F-4C from its with flaps Navy counterpart, the are: Data • Lack of drooped higher landing • Dual flight controls resulting control system inertia. • Wing bumps to house larger in a slight drag increase. included Special here emphasis its relative been addqd ailerons speeds. was obtained is placed complexity to help on the when illustrate in main this system. resulting MAC control other Report No. system because aircraft. Also, in increased wheels from longitudinal to resulting slightly gear primarily compared down care Figure has 9842. IV-4 been taken of has to 0 retain e.g., s_m% qB The roll SAS functions and of the PBF (see Stability system Fig. is it is not nomenclaure used by the manufacturer, IV-5). Augmentation described since control block included faded out diagrams in lateral with the position. 62 are shown directional lateral control in Fig. SAS stick IV-7. on The transfer out of neutral _p :d q-i O O ,--I @ O (9 O m o o o .,q tl o .p ,m (9 oO i-.-] [.., <.9 -i (i;, rs] q_ rH qd O .rd 4g .r_ O C} d_ ® I I b4) r--I 0 0 o I 0 Od > H (b .r4 68 E ,-I r_ H .,-I 0 4-- q.- r-- _1" o .o II II II .Q IU 64 F-4C PITCH AXIS _SsAs (rad) Feel System I _ 18sT(in)_ .0569qePsF FST(Ib__ _-_.0369s + .OI57qBPBF 2 +.208s -* Gearing ,:_1 _-- / Actuator 8s(rad) _ I _'-_I- _ -I°_'+'1 See Fig and for feel system details Bobweight az ts---__) ROLL of JtB= 39.3 ft AXIS 8OsAs (rad) Feel Spring Gearing / _;T,,_ -I 2"961 =1_ i-_ Sa(rad) Spoiler -__ AR! CLEAN C38r {-.46 = _-.69 8sp( ra d ) Gain O ,/ PA SAS OFF SAS ARI __r ON I___-- <_rAm(rod) _-:1_ YAW AXIS 8rARl(rad) Feel Spring .._j_'_ Gearing 3rsAs (rad) \ \ / Rudder Flexure / SPED(i n) .___.J__ _"_°_'_- I _ I _I _ I- _ - l""txl _-- K mR G air V<235KIAS 36.61b/in -11.5deg/in V>220KIAS 8.51b/in -6.5deg/in Figure IV-3. F-hC 65 Control System 8r(rad) See Fig ID C O °_ C t_ .J_ C E o O S_ t_ .c _o __ ..Q ¢) _ "t_ C O'_ O Er0 c) _O 0,; v t_ C O °_ ,.i,.,. O D_ "- LL "_ {I) ,,i,.-. ._ c ,-4 © .Q O O .I rn C_ •-_ O °-- _L 'NI-- w I-4 ID •-_ O .t- I-- o "X- 66 .,.-4 .6 qB -4C q / I 4 O0 _---- 35,00Oft 389:)4 .... 55,00Oft .289 I 8 I 12 I 1.6 1 2.0 L 1.2 1 1.6 I 2.0 Ib Mach J.I m 1.0PBF (ft z) 8 I 0 I .4 I .8 Mach 60k 40k Viscous h "l//f/[_ (ft) Viscous 20k SLo" Domper b=_ I .4 Damper Off 3.03 Ib/in/sec I On Stop I .8 I 1.2 I 1.6 I 2.0 Mach Figure IV-5. F-4C Feel System 6? }arameters Stop N I I I ! , _o. i - I 00 rH o 0 I_ : © N //,,,/ ..c 0 //7 :E i ° _0. / I 000 H oOOq LO -r-I ['!ll= =111 l o I _ I _ I _. I O4 X I,I. 68 0 0 F-4C PITCH SAS E} (rad/sec) _1 .15s _SsAs(rad) - ROLL I s+l SAS PG(rad/sec) _I P6 = P (Roll rate -.265 gyro I assumed _--- 8asAs(rad) aligned with FRL) Note." Roll GAS faded out with lateral control out of neutral YAW SAS _I ,s rG (radlsec) _1 ay' _rsAs (rad) S+'5 (ftlsecz) I .0168 rG = r cos(-I.5 I-- °) +p sin (-I.5 °) I ay = ay + 9.9 _"-.391b Yaw rate lateral Figure gyro inclined accelerometer IV- 7. F-4C 1.5° below at ES. 198.0and Stability 69 FRL and W.L.23.0 Augmentation TABLE IV- I F-_C Power A_roach Non-Dimensional 8tability h = sea level VTo = 230 ft/sec % = 11.7° _s = -9 .1° Longitudinal = 136 = .915 CD = .242 CL_ : CD_ = Cm_ - Cm& - Cmq = CL5 s = kt Lateral-Directional (Stability CL Derivatives Axis ) Cy6 : --.655/rad Cnl3 : .199/rad 2.8/rad C26 = -.156/rad .555/rad C£p = --.272/rad .098/rad Cnp = -.013/rad .95/rad C_r = .20_/rad -2.0/rad Cnr = -.320/rad .24/rad CYSa = --.0359/rad] C-mss = --.322/tad CD5 s = --.14/rad Cnsa = --.O041/rad I = .o 7/r aj CYSr = .124/rad Cnsr = --.072/rad C_5 r = --.O009/rad 70 Spoiler Effects Included / cM _J I .Q 0 _1" IU _J / I d mm r¢_ t%l GO -M" 0000 0000 0000 # I i % ! i I li!l! 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I o I_, P- o" r '¢, • IE,_ • ! c_ ,D • o °o _, 0 ..0 t_- , ,-i ° °eq n'_ °_0 ,-4 • n_ • i° r.J _ I'_ I'M _2 ,r '_ i° ID I 0 o CD .r _o T _,1- cj v, u_ r--t',.,.-i • ° • ,.-t cu > H .-i _ .r q3 ,.¢_Tj • .--ip.- ¢,m .o cJ • ._,i I * ,o • _.J ..-_ I .o p.- _ o Pn"1 • o° _ , ¢M,-I .,-_ _0_0_ ,i ,o, 103 2 f_ ,_1" t'_ r,J C2 (_J _ c0 O _C c_ Cr OC) CO • b-Oq "N I _r_ ,$ • ! i o-" ,t, -,I"0" 0"D" O_ (:0 _ • i ,4" o , OLf" • Lr • O ..-4 ,r_ eO_e v Q. o (o ,_- • 0 _r, "'_ O' 0 C._ _ oo e_ ,.-IQ _,-i I I" I o _ U'. _ O,O N C0 'F- I',-r,, O0 • OU'_ *..* OO_.a I" co _r_ • • I v, _0 0 u'_o _ 0_ w_ _O_ C) . Itr_ OO_ ,0" _O _ • I i° ! ro v, 0 Lr_ o _O 0-,11 _O e'_,O u o_ O0 . O_O_O o_ I • I ÷ 0_ I -/ o -,1F v' U_U "-_ O" O_UOe _0_0 H _00_ 0_ ! I ÷ 8 .j I (..) .-.4 00_ 0_ v '0 ec_N • I ÷ rO --I" I _0 _¢_0 _ 0_ • o | _ _ I ,0 ,-_ 0 I ,.0 -,1" oo°_._ 0 "_ "_ I 104 _0_ • ° o • b, • • _C ° I ° I I ° .,,I" • i A ° I . ° ,-4 O_ I I • v v if] I'_ _G*u ¸, ¸ U" ,-.4 • , _r_¢'_ o.1 * 0 • i_'h urn )<DC O_ _', • • cwO c-] • I I i I • l_ t c,4 °LI'_ c,J • ° I I* c.j 0 t_ ,_0 g" grog" _0_ c,a • • • . I C'.I 0 , 0 _ •-4 0 t] 0 L.'_ e,} • • • .-, I tl I b0 0 • u_ cW • ._" • _{__ I I ,,--, .-,1" I I _q 0 _- 0 ,0 r_ r_ _ _'J ,_ • ,0 • I c_l o4 I I ' a]_OOC_ _0_ "r¢_ -k'Ca I I I "U] • I .OOm_O_L_ 0 _ _'I I _.ta. .< 105 I" ' ' ,-._ ¢'xl ¢,el >- >- >- • el. C_J u. 0 ..t •-_ r.r q 0 I v u% c,,_ cx. .,-j _. o c v' o IC, • ,,b O I_ o 0 ,,I o o o- _ o o = _., ,L) ,_D ,0 • @, _ _ _, _ . o o._,_ ! • _ N N v 0 Lr_ N i o o_ U_ r,- ,4" (") (7" _o co oJ 0 N rxi O" v i=i • i_, • I/% • u_ 0_ G_ _ _ N I I I 0 ' , .-i ,.I p_ o . ,_ ÷ ! ro --I- 0 _0 _r_ _D_ t_ _ _ _ _• _ O_ 4- I p., _.4 0 I _• _,_ i__ '-_ _ _ (_ i0 _- _ • _0• G G MJ B_ N m _. . .. _ g 106 = = I_- z F-4C Bonine, MAC W. J., Report B. C., SOURCES et al, Model F/RF-4B-C 9542, I0 Feb. 1964 Crawford, W. N., and G. Characteristics for Bridges, DATA Nadler, the F-4 Calculated Aerodynamic Derivatives, Static and Dynamic Control Aircraft, MAC Rept. F21_, Longitudinal Stability and System 16 Dec. Performance Characteristics of the F-hB/C/D/J' and RF-hB/C Aircraft plus AN/ASA-32H Automatic Flight Control System, MAC Rept F934, 19 Apr. 1963 Bridges, B. C., Calculated Lateral-Directional mance Characteristics of the F-4B/C/D/J the AN/ASA-32H Automatic Flight Control 3 May 1968 NATOPS Flight Manual_ I Nov. 1966 Navy Model F-4B 107 Stability and RF-4B/C System, MAC Aircraft, NAVAIR 1966 and the Perfor- Aircraft plus Rept. F935, 01-245 FDB-I, SECTION X-15 108 V X- 15 BACKGROUND The at X-]_ is hypersonic under the 45_000 speeds right ft and a powered for a single-place, wing a Mach in of number 300_000 in two configuration with pitch by and and feel. rudder provided the for stick_ Only the each given not loop_ SAS for have The and loop level however_ are this been flight the X-J5 the and recovered flown to and all aloft about prior the three performs to vectoring is capable from of the ventral and of conventional and is a stick roll the an of altitude off. X-J5 The axes. basic assume by the In addition known as to the gain settings maximum this is definitely show on actuated bungee roll both for control_ stick environments been made their consists The for to have pilot. considered is are by and for a side-located stick report flights. This missions this actual flight. surfaces pitch however_ center tail is provided for surfaces_ with first is at the flights. here. feedback set horizontal in high-acceleration the in aerodynamic control is used X-15 shown the force control; used three for through Control yaw shown manually here basic with aerodynamic for r -_5 conditions made the pilots all realistic intent launch_ airplane of center system airplane trimmed of the control control an the Most the about is an altitude technique, be flight carried glide been systems. used stick there is a deceleration yaw All pilot. although loops at After for of pitch augmentation feedback used are the center have is provided conventional control of side SAS A can airplane for here. hydraulic pedals option The considered control. irreversible pilot altitudes surfaces roll operational designed feet. control vertical 0.80. by configurations: is Aerodynamic about 6 and The is launched followed of airplane altitudes. and of this to high airplanes a B-52 number With attaining extreme mission_ a landing. Flights of a Mach flight excess and rocket-powered general effects. 109 the YAR speed and normal each are all for altitude rate p -_$a The transfer for unrealistic angular loop. SAS-on airplane of roll gains for functions loop. This for straight this may airplane_ variation ® \ \ do 0 _0 I 0 rl 0 0 rQb 0 a \ ® q_ qJ | ,--I \ o ® r_ E4 0 \ -- Od I 4o _J c_ 0 -p _rj I I I l 0 0 0 0 0 0 0 0 q o o (5 _ o d q o cO _0 _v _ cU r o 0 _ [._ 0 (I,) 4_ _ _ (J bD I-_ i hD [1.) ,_ r--I r_ bO 0 r,j O_ qi_ L,r_ "D _ II © II H II % II " F-H 110 0 _J (D I (_ LD ,, 0 _J I Iu _'u_O _u5 tC bO (,.9 . :_-4. L_ 0 (_J LL_ V & OJ _J b 4-- 0 - OJ 04 (_ -- II II II o d III X -15 PITCH AXIS 8SSAS (rad) 8ST(in.) I FST(Ib) _.. 2.8 _" 8s(rad) 8s(deg) -20 I (TEU) ROLL -I0 0 I I0 I 20 I (TED) AXIS 8aSAs(rad) ST (Ib) YAW BLAT'in_ ST { I FLAT r I 1.55 8a(rad) 2.4 --I 57.5 AXIS 8VsAs (red) BPED(inLI FpEo(Ib) 2.3 By(rod) 12.2 Figure V-3. X-15 Control 112 System X-15 PITCH SAS _(rad/sec) ROLL-YAW-YAR .75 SssAs(rad) SAS Roll Gain p (rad/sec) BasAs(rad) Yar Gain Yaw Gain .3O r (rad/sec) BVSAs(rad) Note: Gains variable in 10% maximum values which (e.g. roll gains .2_0, .25, .30, Figure V-4. increments are shown of the above. selectable are .05,.I0,.15, .35, .40, .45, and .50) X-15 Stability 1 13 Augmentation I e_ ! ! X I C_J oo o I-° I-_.u_) _ oo _qq 88°° [_ / !IIi /' .t I /" I / j,/ll I ¢_J I _ 114 ,_-° 1 _ o 0 uC,_l D _o. o Z x __ rood Q t I __ I I 0 a I I 0,.I 0 0 0 (J o 0 ooo 0oo o o oo _Io O'_OJ oo0 _0c0 I1! ill _o. ¢0 m 1 0 _ I I t13 Od .J 115 I -': 0 I if) 0 I o. _'X,I _o Q _o. ! I .Q ! 000 8008 eoooq __o O0 ×_ / (%1 --.6 / / / / / // ¢%1 to :E 0 / / / ./ / / / / / l # / OJ .,,.; -- (D I I IF) I I I -- I o I OJ 0 I:I0 0 0 116 I 117 D ,) I I I OJ _I o 0 I 1,0 I I 04 ..-= 2 l:3 ¢.) 118 0 0 I I I I I" I" 0 s: C.) q _o. 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I I I 0 O" -.t --JO ,0 aO ,0 _._ *cx; ,000" • o_ . i° I •-, tx¢ ),- >= .Ira Z _21C_ Ua _ tl_ _0 _L -._ v 132 :-_- _.L :.= 0 r_ _ O0 ,_ -.t" t'./ C c,_¢ ¢'_ r,-. Cr O_P r_1 L_ ..-I . C • ,.? l I C _D Card 0 _r pr, o5 _ _L.::., ° oc 0 C_ee, • _ • .co • I% • I_0 • ,.-i •,I • r<l / I I I ! .-4 O0 •_r_ °_S_ ' 0 _ / I • I 0 eJ c_ GO ¢r_ I'M I I I I" i 0 •0 .r._ _0 o° _ ..., C_L_ _D <l'_a 0 _ I I I I _0 0 Or',: •.C I_ _ ,,,T G_ I I 0 I..i • • C_ u'_ ba C) _ ,D _ o rl t I t _° _ _g •4" -4" b_ .--.l _ c,,j p_ . ,.-.j co ...-i • I "4" I I I I r.- _0 _T O0 ,,-I _ ,--I Pa _0_ r_ ._ oOCO 0 r_ -.,1- .r-J • 0 * • u_ cM .,.._ I I I u_ I I'M I/', co (,_ • IP_ r.-- _0_ r-• I l • 0_ i_i I I t / / -.I O0 ,_" ,0 _'_ O- N. P.-. e¢'l -4" {.D I"_ G:; _o_ .-i . * _0 I• _ • r_ It ? • _o I'M . "_ _1 I i u.J °_ Iu >- F _Z 133 _ >- o o o ° •--4 CO _0 I I • ,llm II I I ¢M 0 0, e_..D q-0a_ o,_ i%1o • .0,_, ,f,r_ I ..--I IN,--* I I I I II o ea oo ._ oo_ o_u% • e-,l I oo" • • 0 ,0 cO0 ,00 • ,f_ I • I I I I I I ! 0 _o -0 I'M 0 _t r,"l • o° ,-_ 0 ,-d o aO .--_ • • _o _o III i_- 00_ cO I'.-_ _ • 00 ,#, , I I I ,U _. I F_ r_ ! o(_ • I_. • I u_ o, I I1! _0 0 I o_ I ! I ,.LmlN (::)0 ,¢,'i .i-_I ._ 0 O_O00 .-, .=13 I I .rim I ÷ 0 IZl I I gg_ oo_ I ::> I _o _. r_ ¢ ¢0 0_1 o g¢._. I oo, I 0 • LP, 0 ._ I I Izl 0" oo_ og rj_ H ,-_ ,-..I i%1 r_ 0 ,-'xl t_,, l'xl L_ _ mm O0 .r _ '--40 • O0 rNl .-_ I I I og _t ,-_ • I I I I I I I o_ .oc0 *000_ °¢M I ,oco ,"el I I I I o, "_ • cO_ • ,i_cxl I I I,¢ I t I I I i ! I I I ÷ 0 _o _I0 3- ,o "M 0_ 0-4-o u'-. ,u%_ 1 I ! >.::¥ _ c') :_ GJ 'J.J 7 134 I I I .--4 Q _) O t_* h" ¢N 0 ao o ,o ..4 co N _ _J O I II II II II 0" O ,-d • I'_ ¢M * co r.., o% • 4) • U_ * _ * {%1 ,4" • v' o" o II • _0 * i_ O" _ •0 .,I" t.-- • 0_ • _ 0 0_ • ..4 . O t_ ,41--' o 0 0" _. o _ _ -_ _ N ,-4 . eM * _ a_ ,0 o O o, rtl 0_ r_ .-4 O [--I O u'_ O -,t ,,t" O _t" I I * _ t_a I I 0" ,'_ • • 0_ _ _ 0, .-4 • • ! i ! i I I I I ,4" • O • -O El Pq r3 v cO _ cO _ • .-. ,..4 ¢._ {_ o,_ 0 I'.- O" ,o ,0 0 o _ ,_t ¢'_ r_ 0 .,T n._ o N i:1 N -J u') ° o co • o _ _ ...4 ..4 _ _ ¢o * co N 4- 0 aO ,-4 0 o @ co ¢M ,o 07 0 • I IJu 3 1- LU _,0 _e o _ LU '-4 •-,i - _ ,'_ 135 O,. 0,. p_. _ _ I C_ 0 {3 _. (J _ a{3 _-- I-- I'- d.J "I- _'7 G. Ci. ¢. _ '_- :i[ "t" X-I 5 DATA SOURCES Revised Basic Aerodynamic Characteristics of X-15 American Aviation, Inc. Report No. NA-59-12033 Osborne, Robert S., Stability and Control Research August Characteristics of Model of the Final Version of the North American X-15 (Configuration 3) at Transonic Speeds, NASA TMX-758, Franklin, Arthur E. Characteristics tion 3) at Mach November 1959. Penland, and Final April Jim A. Lateral and Robert M. Lust, of a O.067-Scale Numbers of 2.29_ and David Stability Configuration 1960. of North a O.0667-Scale Research Airplane April 1963. the Aerodynamic of the X-15 Airplane _ConfigurAand 4.65, NASA TM X-38, E. Fetterman, Jr., Static Longitudinal t Directional, and Control Data at a Mach Number of 6.83 of the of the Tunnell, Phillips J. and Stabilit_ Derivatives Numbers from 1.55 to Investigation Model 2.98_ Airplane, 19_9. X-15 Research Airplane, NASA TMX-236, Eldon A. Latham, The Static and D_mamic-Rotar_ of a Model of the X-15 Research Airplane at Macb 3-50, NASA Memo 12-23-58A, January 19_9. Hopkins_ Edward J., David E. Fetterman, Jr. and Edwin J. Saltzman, Comparison of Full-Scale Lift and Drag Characteristics of the X-I} Airplane With Wind-Tunnel Results and Theory, NASA TM X-71 33 March 1962. Walker, Harold J. and Chester H. Wolowicz, Theoretical Stability Derivatives for the X-15 Research Airplane at Supersonic and H_personic Speeds Includin_ a Comparison With Wind-Tunnel Results, NASA TMX-287, August 1960. Yancey, Roxanah B., Flight Measurements of Stability and Control Derivatives of the X-I_ Research Airplane to a Mach Number of 6.02 and an Angle of Attack of 25 °, NASA TN D-2532, November 1964. Saltzman, Drag Edwin J. and Darwin Characteristics Taylor, Lawrence Augmentation W._ Jr. System, of J. Garringer, the X-15 Summary Airplane, and George B. Merrick, NASA TN D-1157, March Tremant, Robert A., Operational Flight Control System, NASA Experiences TN D-1402, 136 NASA X-_5 1962. of Full-Scale TN D-3343, Air_lane and Characteristics December 1962. Lift March and 1966. Stability of the X-15 SECTION HL-IO 137 VI EL- I 0 BACKGROUND The HL-IO airplane one of a number typically launched In numerous glide powered of and 1.8 is is Mach Following and 90,000 leading edge of Mod II configuration. lifting from a B-52 flights the body at research 0.8Mach HL-IO has vehicles. and been 4_,000 flown in The feet. excess feet. problems the of involving the tip The fins the loss of was modified. roll-control This information contained is by here effectiveness, became known is for as the Mod control by the II HL-IO. Pitch and conventional using combinations The The are stability all control rudder. combinations about roll three flight A of obtained subsonic speed specified or a transonic brakes_ in Fig. augmentation elevons elevon and yaw configuration flaps, and tip is fin a selected flaps. These VI-I. system consists of angular rate feedback axes. conditions shown correspond 138 to actual flight test points. loops _ o. q4 .&. 0 % _ E-I v £-_ • _) 0 ._I o ZJ ,-I (D m ,-I ID (.) _ _ .,-I 0 [-_ _-® .,-I ,-I 0 .,-I ff'x _ © r_ 0 N_ I I I I 8 0 0 0 0 0 0 o. o o o d o. o _I) _ e4 0 .,-I hO .el o 0 _1 (n _ o% i i- 0 • ,-I _ 4-_ 0 eO .,-I •,-4 0 .,.4 ._, .r-t _ 0 ° 0 t_ •,-I.,-I 00 _ OJ 4_ Od OJ 4_ ! C_J ! eo,...t .o v o .,-I 0 0 _ _ _ _ e8 _ al ,'el II .la _ II II II II i; bO _q _q M _q 139 O_ 0 0 0 -- ...I O_ - _i /I Ix 4,n © 11 --\ _,,. /I 0 0 i H -r4 -o C-_-'3 C2- -._ C:--_ o _. t'__ __. -il II C_.-_"I _lI U 0 ._i 140 HL-IO PITCH AXIS (_eSAS(rad) Gearing Feel Spring _ST (in.) I FST (Ib) G -_)_ (_e (rad) 57.3 6.5 ! -2O -I0 1 I _e (deg) 0 I0 I -- -2 G(deg/in) -6 ROLL AXIS (_aSAS(rad) Feel Spring SST I ST FLAT (Ib) YAW I (in.) Gearing 2.7 _,_ _ _o(rad) AXIS 8UsAs(rad) FpED(Ib) (Sr (rod) 22.2 Figure Vl-3. HL-IO Control 141 System HL-I0 PITCH SAS (rad/sec) _eSA S ROLL SAS p(rad/sec) YAW 8aSAs SAS r (rad/sec) Figure = VI-4. HL-IO J s 7"._,3 .4s Stability t42 I Augmentation _ arsAs 0 n o U_ TI.D , / / / / .-. / OI // •41" ,I-- ,¢-- /" / ,¢-- 0000 0000 oooo jO000 ,ll l / _. J" ='_ / I ! I, ® II li i .,p to o / ( x '% L,,,p ,,2 ,,_ I n I I --GO i I I I I 0 0 (xl (_] (x] -- -- o 143 0 °-- O_l -- 0 C- ® ¢0 U ® -- Od o_ ' 1 _P 0 _J_ _ 'r_ I I I I I tl_ N --: 1.0 t'M ." J o o. q 0 q 0 © Od 0000 0000 0000 -JGGGd o_cx],_- _O 00 II I! li Jj J__" i Q ® r- I I I I I q .-I (_) 144 1 o 0 0 Q OJ ! / # # .a / ' _0 / l LI.. / / _l.. t@-- _I" 0000 0000 qqoo .J cO oodd / } 0 _o --CO ® --C_I i i ro OJ i 0 i 0 ! .J -?_ 0 145 0 O 0,1 (D 0 IO N .c o -- 4 o o '1J (D - I' ill. ,I$-- _e.. _lj.. 000 ooo ooqo .ndooo_ 0 I I I O 0 O I" _. _r I" ! _T ÷ °_ o E v C.) 146 "_ o. 0 0000 0000 .Q o_ , J_ '-!-_ oooo \ / / jO000 \ _ / \ N m ,F 0 0 (, ,,% I I I S p CO-- --CO 0 0 0 0 I 0 0 147 I 1,0• ! m -I I O4• E o "- ! \ B i \ x •.= ,,_ _o _ =,,, , _ID"o J _1" 0 "r" _4DgD a_ 00 ! ! / I ® I / 0J N o._ ! ! ! m m o. o._ ! I t U o o CO- -- 01) I II 0000 0000 oooo ._10000 , I! 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I *O'.'Xl ,--40 0 I I , _ • m O" I w O [-4 _ o_'_ O ,d b+,, C_ rr. o_ p+. (0_o • * e+j e,_ r-- P,j o- • <_ t'I l a_, I I" I v o a_ co -_ <_ O0 u'x co_, ct_ • I'4 I "-I c_ ",r,.r... .-i co o CXll_ O" _ . • i_ *,+o ,o co o {_-1 + l'xt P'J I_ e_J 0 • I • {o txl + r_l c,+ ++.T "40 _0 o_o_ ao t-- • ++-+_ ! . t+,,l _0 eO U-x _rl .--t .0 ,,00 ' a0o._ o_¢_o,_ +.-+ • I I ,'-_ C) I ' I o | I q I o l'-P'- • O" _ ,0 0 +..+ r.. • i ,esl ,_ .o _n 0o e,l.t t_ 0o ¢'J 01_ t_ _00 I 0 _ N ,_ • o_ 1_ <<_ p.. * o O,,t_ • _.t oO coo,o _D 0 <",J +.--+i._ • +..+ 00 P.J Pc+ ..t • 0 ? _ +..+ L_ OOIII _ z 155 N o+ I I coo +-I en CO Z , i_ r... T-.T _ • 0 • G( • • r_ • ,,4 • ¢0 I_ • ,-4 0 ,o ,_• I_ ,._ ie C: | 0 I I 0 N l" ! h- um O" • ,I) ,.4 • I 0 _ • • v I ,, o _* $ o 0 LU _,• l I_ • LL • • m I _ e¢1 ,_ ell ,0 un o _) • o _ -,I" _ rq _ 0 O, ,-_ -,t I • I v v _J _ _D -r u. 156 LU o 0 , -.," ? T _ , ,,t" • , ; , ,.,t O o I I _ O 0 • • I 0 _ I I I I + I • _ o _ • _ ._ .+ 0 . J l_- ® .; I _ o a_ I I I I • o ,_ I I _- 0_ o o I • I .4" ,._ C I .-+ I_ t._. _ ! O, 0 u_ _ cO o_ 0 ,-,• o• _ _ I I u', ¢ _ _ _ 4" m m ,.1 o _• .'-'• 0 o I' I I l I • I t I I I I I • I I I I I I I I" 0 _ l_ 0 I I_ ..... C I ! I ,; • , I I 1 -- _ 0 .,P, I _ o_ I 0 _ I _ ,0 ao (.3 I I 157 I_ • 0 • I O' 0 -- o f_400 um um O_ 4" _.00 f'- 0 O, _o_ q .4 0 a[ 0 oO _ G" _o _go o_ @ I v o o _ 00 ..d r-- u'_ • _0 _ • _0 ._t I P- o um_-, _-0o_mo 0_0_ ',.q_ P"-O - c0oo 0_ I I w v A_ o a00 LF_ ._7,_ oo _ _ o_ _,_- u-_ ur_ _0 0 " _o_o 0_ O'4"O _'b o I • I ÷ v 0 o o" _0 oum 0_ ocx_O • _0 00_ o_ 0_ 4" •-_ o f'.,i • 0 0_ 0_ _ I _-_ > rY_ _>_ I ÷ o_ r_ 0 co I_. _0_ ,ooi%1 _0_ "_0 o I I oA ÷ 0, _o o:g,O ,0 _0_ 0_ ,--_ ooo r.-, t_ • ._t I w I 0 7 * _ -4" o , I _A °_oo0 ¢¢1 I • , mm• • I ° I v o_ g_Z _ o_ rq 0 _t ,0 • • ,0 I t 158 ,i,_ o • ,t,_ OC o • , I (_ o_ r-- I-• o • • -,_ ,:_ co u% _ 0- .n e% • co • I , ZJJ I I _o 0, 0r-_¢u ,.-4 o.-_c • t_ 0 I I I I I I ..o._ II ! I v • • o_,h • C, o • • . ° .0 ,rr) I I " o _oo _o o_o 0o_ 0 _0_ ' o o_ I I I o _0 8 o • .u,% o • o b-O-O u'% _ ._4 _0_ I I ! o_ °o.._ II 4- :m v 8 o [-4 o_ ---- O_N oo_ _o _ 0_ _o_ I cO rj_ , • I I II I I II + CH o_° U_ 4" e_J o'_ ,C _0_ I ao . o o o_ ._o_ _o oo_o ! 0 ÷ o ,_c _0_ ! I ! I o co o_• u- .-_ ,c_P- .u', oo .o_ . ..4' I O[" O_ I o_ _ II _v _N_ _N_ _znzz 7 159 ÷ 0 p- o _J aD ¢_ • 0 .00 C5 o r.-- • *_xJ ;.-T_ I' I .p. x' 0 4" O" (7_0_ • o ,_-¢ t. o o I ÷ w P- _ _o_Z o, I I aDO _0_ O0 + ,','_, _'x_ _oN*e I a v ° 0_ _o_ ..NN_ 0_, I I ,_ oe,,J o_0_o0 _0_* r-- 0 I _0_0 _0_ 00_@ I' I I I o I* o •-_ o c_ CO *_ I 77 160 7 _00_ r'm r-- ..T I_Oooe p- oc • • t l'_ cr _¸ ,4 • I • I • g ON_ o*_ _NOl _, ...._ 0 c0 • ,t ,-e ,ID ,.-0_._ d • • ,O ,._ _r_ N O ,42 ,..._ _0 N 0• O.-0 • eP.• • t%l _a'l ,..4 J ,'d .rl o0_ee_ _Oe_ • _ee O r...) ¢ 0'x _0 _0_0_ :> • rx;.4" • I • I eP'-Q ° ° _e. I 161 2 o o e_ 0 ,_ h0 "_" • t_- _ rq _ 0 O0_m ,CO C; • ,.--lrl_ • I ,N _t O" ¢0 0 • I I 4. _ _m _o00 I v o O" ,ON 0" h- • 0oo_ O0_eO I%10 ,e • cr_ M'_ ! 4- 0 o • 0_ • • I ÷ 0 0i'%1 "0 • • r_ _000 _0 • 0_ 0_00_ • • tX.; ÷ 0 O_ _OOe c00 00_ 0 ,_ _° _g. -.t,O _ o_o _ • • • ¢M .w' ,,1" o ON r_,O O_ "_ "0_," I 0 0 ONO_ _0_0 _0, o _0_0 ._,m I I o 0 N _7 162 7 I_",I_ • • _o _ooo _ite I r..- 0 _- o Ot_,O 0CO I • I I _'_0 1 • I O0 • o_ 0_ i'%_ erq o oo_o I I • _I" 0 erl I *0 I I • I I • 0 I • • I eO_1" • .-_ N _0 t _,i ,,,_ "d _o_ .,-4 o r...) 0 N • I o I H ,.1-0 ir_l ,_ ,_D 0_ .-_ erXl • ,.t ,0 I • _ I ww 0 _0000_ _0_ ! I • Ot_ _, I I e._,--I I 163 o o _ o _ o ,_ I'_ _ . ..--4 "_ MI" 0 _" _ _ _ _ _ _ _ _ _ ,4- r_ _ 4" I_ t_ P'% * .0 -'% ,0 .4" ,.., .-, ,, t'n aO O ,4" * (_ ,,o i_ o• 0" _1_ ¢0 • ,..., • • ,-4 • (%1 ¢'q • _• :'4 I'_* * @4 ,vl• ,-4 t_i * .,I" ,-_ ..4 #n * • 0 • _r • * d" I I . I I I 0" " _ I I I I I i I I I I I I 4- t_ O ,o r'.- E * ,=4 _ • • 4" .., 0 4- t_ • _* ,0• • ,-4 * i _ .-, c_ • I ÷ 0 . .,11" .0 _ 0 I-- .-_ .-i I'M ("-4 r_. £ _, co • .-_ ,'. 0 0 "T _ -- % 164 . . . .0 HL- I0 DATA I • , _° SOVRCES Ladson, Charles L., and Acquilla S. Hill, Aerodynamics of the HL-10 Flight Test Vehicle at Mach 0.35 to TN D-6018, Feb. 1971 Pyle, of a Model 1.80, NASA Jon S., Lift and Drag Characteristics of the ML-IO Body during Subsonic Gliding Flight, NASA TN D-6263, Ware, Lifting Mar. 1971 George M., Full Scale dynamic Characteristics Wind Tunnel Investigation of the Aeroof the HL-IO Manned Lifting Entry Vehicle, Oct. NASA TMX-1160, 165 1965- 166 JETSTAR The Jetstar is a conventional ailerons_ mechanically actuated activated The but assisted primary aerodynamics source were test data engine elevators_ with and hydraulic of aerodynamic the servo using control latter transport. rudder. boost. a The from utility by estimated _TC-TDR-62-24C-140. flight four BACKGROUND Controls Ailerons The rudder and consist elevators of are is mechanically tab. data CR-544 system and NASA flight description reference. 167 was CR-544. test was data based Power approach from solely on _, rn o r-_ _p Ca :> 0 -M 0 .rl 0 C; % ,--t _ % o L I o I I "_o , 0 o 0 "-" "- 0 oJ 4._ .i-I o 4._ ® ,-q v "7 I-i I-4 oJ oJ z _o _ O'x OJ OJ c_ OJ r_ o,J oJ 0_J 4-_ 0 I_0 _I r-I _,o _ _ _ I--I ._I .-=1 __Oo E-_ _ •r-I 0 CO _ o'_ 0 o o__ _g_o o oJ oJ Ox 0 b_ lf_ _ _ _o_ 0 , _ o.I _ _ II N 168 . _0__ ,-I .,q ¢) 0 11 _ II .._ LO_ II 0 0 _'_ II) H a3 4_ 0d c; I ..A t--4 .r4 N II II II 169 JETSTAR PITCH AXIS I' I FST(Ib) Note: -_ 52 Angle h/nge ROLL 8e (rad) + 2.95CI of attack moment effects are on elevator neglected AXIS LAT F ST (Ib) YAW = .75_q I 8a(rad) AXIS -_ 8r (rad) FpEo(Ib) Figure VII-3. Jetstar 170 Control System TABLE VII- ] JETSTAR Power Approach Non-Dimenslonal h = sea level VTo = 224 ft/sec % = 6._ o Longitudinal Stability = 132._ Derivatives kt Lateral-Directional (Bod Ax±s) CL = .737 CD = .O9_ Cn_ = .137/rad C_ = --.IO3/rad C_p = -.37/rad Cnp = -.14/rad = .O/rad CD a = .7D/tad Cm_ = -.80/rad Cm_ = --3.0/rad C_ r = .]I/rad Cmq = _8.0/rad Cn r = --.T6/rad CLSe = .4/rad Cn_a = --.O07_/rad CruSe = C_Sa = .054/rad CySr = .17_/rad Cn5r = --.O63/rad C_Sr = .O29/rad --.81/rad 171 SL 20,000 ft 40,O00ft JETSTAR 38204 Ib 12I0-_0 (deg) 8642- 0 o .2 I .4 I .6 Mach 172 I .8 -- OD ru -- 0_ 0 w_ o q q q a C.) 00 00 _00 o o S --00 _ II ! J 11 rc_) --0_ I 0 1, tO _ I I OJ -_ 0 ..J 173 6CLa 5 (rad-i) 4 JETSTAR 38204 Ib 5 2 0 0 1 .2 I .4 Mach I .6 I .8 I .6 I .8 1.2 .8 .4 %%%, 0 0 I .2 t .4 Moch 174 Mach 0o .2 .4 .6 .8 I I I I -.4Cma (rad "i ) ..... ---- ----- JETSTAR 38204 Ib .255 SL 20,O00ft 40,O00ft Mach 0 0 .2 .4 .6 .8 I ! I I -.4 Cm&, Cmq (rad-I) -.8 _'*'_:_) Cmq -1.2 175 CDM .08 t (rod "l ) .04 - 0 0 .2 .4 .6 .8 Mach Moch 0o _o I .2 .4 . .8 B -'.2t CM M -.3 - (rod "l ) -.4 - I "o 5 -6 - SL .... - JETSTAR 38204 Ib .25_ 20,O00ft 40,O00ft 176 CL8 e 4 - .2 m CL8 e , Cm8 e (rod'=) 0 ) .2 I .4 I .6 I .8 Moch .2 JETSTAR -.4 -.6 n -.8 -I.0 177 Mach 0 0 .2 I A I .6 J .8 I -.4 Cy_ (rad -t) 2 5 3 8 4 6 9 " _,,_ -,8 ----- - SL 20 O00ft JETSTAR 382041b 40,O00ft Body Axis .2 _-" -"_(_- -_ Cn B .I Cn_, Mach Cj_ (rod't) 0 •2 .4 .6 .8 I I I I c_ :2 178 Mach 00 .2I .4I .6I .8I -.2 C,_p (rad "I) -.4 JETSTAR 38204. Ib Body Axis SL -.6 ..... --- ---- 20,O00ft 40,O00ft Mach 0 .2 I 0 -.04 .4 i .6 I - Cnp (rod "i) -.08 -.12 -- - 179 .8 I • ---'---- SL 20,O00ft 40,O00ft JETSTAR 38204 Ib Body Axis .2 C_r C,t r , Cnr (rod "i ) 0 I I .2 .4 ! I .6 .8 Moch -.I Cn r -2 180 SL JETSTAR 20,O00ft 58204 Ib Body Axis 40,000 ill ft .08 CYaa (rod -I ) .04 O0 I .Z I .4 I .6 I .8 ; 8, Mach Mach 0o ,2 4, Cns a -.01 -(rod -l ) -.02 8a is deflection of aileron on one slide only 181 Cy8 r 2 5 3 846 ""_,o ._ (rod -I ) I .2 O0 I .4 I .6 1 .8 Moch Mach 0 o -.04 .2 .4 .6 .8 I I I I - Cn8 r (rad "i ) -.08 - ' ..... SL 20,O00ft JETSTAR 382041b 40,O00ft Body .04 C_8 r (rod "l ) .02 0 0 I .2 I .4 I .6 Mach 182 I .8 Axis N C3 C_ • t_ h Lr -.t _ ¢_ t_ t_ ,-< _ _ N _ • • • o r,J _- C C: c f_ _ O r_ C I I O c_ o c_ r,j I* o I in g I_- l"- ,_ t_ I%1 O0 u'h _ 0 o O _0 o i° 0_ co N c> H El H ¢_ I"-+ 0 03 N r,i 0 0 o o N I O _ 0 • i_ 0 0_ ,_) cO I" P- "-+ o _ _ lib ° ° i° I H • g _ • _ :: .; - i_ i_- .-.+ . _._ rq • co • h O t} t_ N + u-_ t,3 u_ O u_ _+._ c_ _-x 0" ,0 0o ,0 r_ I I I _r_ f_ _'_ O C> _ * • O • O O e,i c_ o • • _x_ o o I'M 0 0 _1 ?1 ! r_ [e O * • _ c) bx 183 o "_ o u_ ,.t o o N ,,0 I,_ I'M _ ,,0 ".0 I° , oc_ u", 4) _" c '¸ c_ ': • I %t _, _4- (_. • o C2 0 • G | "4 _ O 0 I_ • C_ t'- O _ 42 C_ c.D C_ O • "4" C'. 0 C._ O 0 . 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I _ • I I I -0 ,-* , I I I* _---J I • 0 0 0 ,_ _• D'- . 0 I _ _ I ,0 ,-4 _ I _ "4" | I 0 I ,. _ • O_ 0 -4" ,0 ,,0 o t_, I _" cD _0 0 o 0 e,_ 0_ o I_ ,_ I _ ° 0 0 • I -,1" wO I i o ...r. x >- -- -, z _ 188 z J z >. _ z >- "_ z o oo° _o_o. 0 O _O_ O ,_ I'_0 +_o++ • cMO O 0001 cO q- # . • * 0 • IPM .,-+ I • _ ,0 0 ....i I I I" _g _ aO _D _o O I'-+. 0,0_0 '_ If_ p-- _, N euo_ o 10 _O ,..+i "_ I I I I I 0 OC, o u_ o _°_ 0 o,o_, +, .0.-4 ! I I I "L °o _ o NG h cO t_ O "0 O,-'+ I_- N O sO _0 cO ue_ _ p<i O • +OO ' co • <_ 0 , IN I I I I p_ p(D._ -I- C_ .0 _0_ _O co co • O P• • O +.-,i O "-4 I I I_- <1" ¢_ I ! H _O _D I G_ cO 0 o_ I_- • ,-+ , I G'J ._ _0 0 ,_ o o. q _o_o O_O ,.-i (w_ _0_ _0 ,,--I "N ,-i I I CQ (2s _ p-+ ,--.I t_ 0 .4" _" N N c'3 0 ,--_ + _ oO ,-I .1i-_ • ll'l i O _ ,.O ,_ I b- _, N q_ _N-O G' ",O O" _.3_ <+_,l O _. ,-i (:u • ,--I • • <+_ , .-,I N J E-I O cO 0" •0 _ t_ •++'._ ."M co <:3 • ,-i ,-i ,-.+ + .,_ +-J O o +.-i _ t_'+ ,_ ¢"+.1 ,-+ O_ r¢_ +....+ -+,t tl_ t_ • . ! l,l_ _, O,-4(',I • .--.i ,.P+ I _ <,'.+: U_ 0.0 *_-_ 0 c,,I , I +-.I _j tr_ I N I , I "4 0 • + ._ . .-_ O" c,l I'M ,.,...+ • . eO ,O .-i I I I ,,-.4 O. Z 189 _N "--+ Z , o o o _°_ oo _-o_ , r--o II I * I I am _o_ 0 .o _j (,r_ ,0 • • °_ • I t I I! I 4_ o oo° o_o _ _-0 * 0 O ,"_ r,_ r_ o_ °o ° • I I _o ' I li I ÷ o_ rcl ¢,_ 0 '0 *4" O0 ,o-* • 4"0 o h.. _ * ,0 I 0 ,_ q" • o 0 ' ¢XI Lf_ ,-4 ,-_ o . 4D _ rJ_0 4"0_0 • '-40 • ._4 I ! • _ • I I _o_ 0 oo_ _0 • I _> ._ I I I I 01 + _o_ _0_ O0 0.0 _0_¢ eel 4" 0 o oP- e4 o o ,_ 0 0_ _7 _ oo vw co :w m- e,% ,0 * I v v ! o_ a0 oD e_l o oo O0 _ • o • • ,_ _ I ! I I _0_ _o_ _o_ " _ 0 * I w_ ÷ _ r_- _ , , I T ¢ , I • I w I! + o f_ ,-, I O_ oO .:I- o_ I I I I' e_l , , I vv _v ,..-i A _K e'3 _. O7y 190 " • o • , _L o _ q- _j ,...4 ,-.4 (_ ,...4 ! I_ o 0_ 0_ _ o 0 G'I _ 0 i_- _ 0 ,-I • I_ _7' 0" _ _ N 0 ,-_ 0" 0 0" (_J ,_ ,'_ N _ -0 ,._ _ _ _(%1 _ ! "J" 1- _ r_ r_ i-4 E-I 0 0 _" .rq _-u E-I M h- I 0 © 0 0 fW G" A r_ i 0 N _.1 L_"I r,J G" u_ 0 (_ ,0 u _ r _• 0 _ .-4 u2 o_ "_ a. 191 ,JJ :I[ J_S_4J_ DATA Myers, Russell Air Force H., Jr., and Carl Flight Test Center Clark, Daniel Conceptual C., and Design Flight Manual_ USAF T. O. 1C-140A-1 Jetstar Handbook Models C-140A S. Cross, Jetstar Flight Evaluation, Rept No. FTC-TDR-62-24C-140, Feb. 1963 John Kroll, General Report, NASA CR-544, Series C-140A_ of Operating and SO_CES VC-140B and C-140B_ and Maintenance Aircraft, 192 Purpose Airborne Aug. 1966 T. VC-140B Aircraft, Instructions O. IC-140A-2 Simulator-- for USAF SECTION VIII CONVAIR _OM 193 CONVAIR The tudinal and Convair and Lateral actuated Elevator, respective the used control in is directional rudder. hydraulic 880M a medium-size control control 880M BACKGROUND four engine jet transport. servo tab deflected consists consists of of servo deflected elevators ailerons plus spoilers. aileron, and rudder transfer functions primary surface deflections with system diagram shows in computing tab Longi- transfer a lag functions. 194 tab the 16sses spoiler are in terms included. actuator, of Although none was 0 •_ +_ 0 0 0 ,-I ID 0 .r-I 0 O -O o3 O .,-t +_ .r-t _d -,-I ,--I I I 0 0 0 0 0 0 _ "- I 0 0 , 0 O" 0 _D © .H I i- cO cO °H O rD H H (1) O .,-t -O .r-t O -r-t C_ _ O •,-I _-, / rD 4.0 q-t 4o _ 4o q-I , _ , _ _ 0d I -o O (2) 4-, O,1 -o I I O O O O O _io_o ff_ 03 O (2) 0 (D 0 O O LZh Oh 0 0 0 o o 0 0 0 0 0 0 M ®° O O _ _o m i1) _ 4._ II H ii Ii II _ _ ii d_ d_ N 1---I _ H N H 195 II II r-_ m O "7, O i < O 5 a0 co O o rj i H H H > -H ! o o _-.¢ 0 odm I_1 II tl _0 -Q Io 196 CV-880M PITCH AXIS ) _-- -Ch8te Oh8 ROLL 8te (rad) Be(rod) e AXIS I +.Is t -I.425 8Sp (rod) 8to(rad) 8tac _--- Ba(rad) YAW AXIS (Sir ,.._+ t< _ -Sr)c b St, (rad) L 8r(rad) i':':kg',kre '/! i_ -3. CV-880M 197 Control System TABLE VIII-I CV-880M Longitudinal Flight Condition Configuration Speed I 2 L PA 134 Altitude Non-Dimensional KTAS 165 Stability 3 KTAS 4 .6M .86M Derivatives 5 6 .7M .SM 7 .86M SL SL 23K 23K 35K 35K 35K 5.2 4.3 5.3 2.8 8.3 4.7 4.0 CL I .03 0.68 0.36 0 .I75 0.454 0.347 0.301 CD 0.154 0.080 0.022 0.019 0.025 0.024 0.023 _o (Deg) CL_ (I/rad) 4.66 4.52 4.28 4.41 4.62 4.8 4.9 CD_ (I/rad) 0.43 0.27 0.14 0.07 0.18 0.15 0.13 Cm_ (I/rad) -0.381 -0.903 -0.522 -0.572 -0.568 -0.65 -0.74 2.7 2.7 2.44 2.5 2.75 2.75 2.9 Ci_ (I/rad) 7.92 7.72 6.76 6.37 7.51 7.5 7.62 CLq (I/rad) -4 .I7 -4 .I3 -4 .I6 Cmc_ (I/rad) -I 2.2 Cmq -I 2 .I -I I .5 -4.66 -I I .8 -4.4 -I 2. -4.5 -I 2. -4.6 -I 2. (I/rad) CL5 e (I/rad) 0.22 0.213 0.193 0.141 0.203 0.190 0.180 Cm5 e (I/rad) -0.657 -0.637 -0.586 -0.438 -0.618 --0.57 -0.532 Ch5 e ( I/rad) -0.326 -0.328 -0.336 -0.278 -0.342 -0.31 -0.285 CLSte ( I/rad) (I/rad) 0.055 --0.164 0.0532 -0.159 0.0482 -0.146 0.0352 -0.11 0.0508 -0.155 O. 047 -0.14 0.0450 -0.134 CmSte ( I/rad) -0.287 -0.285 -0.297 -0.343 -0.31 2 -0. 335 -0.352 chste 198 TABLE Vlll-2 OV-880M Lateral-Directlonal Non-Dimensional (Stability Flight Condition Configuration 2 L PA 13 _ KTAS Speed Altitude C_B I SL 1 65 KTAS SL Axis Derivatives System) 3 4 .6M .86M 23K 23K 5 .7M 35K .SM •S<,Iv 35K 3!_X -I .01 5 -0.877 -0.788 -O .81 5 -0.807 -0 .UI25 -0.239 -O.196 -0.163 -0.145 -0.181 -0. _77 0.145 0.139 0.128 0.122 O.129 -0.395 -0.381 -0.329 -0.243 -0.341 -o.31 -0.087 -0.049 -0.0173 -0.0031 -0.023 -0.011 (I/rad) c% (1/_d) C% (1/_d) Cnp (1/_ad) C_r (l/tad) Cnr (I/tad) Cysa 0.129 2 O. 198 0 .I46 0.088 0 .I8O 0.153 -0.21 8 -0 .I85 -0 .I63 -0 .I89 -0 .I66 -0 .I65 0 0 0.309 0 .O01 9 0 .O745 0 .O044 o .00775 o .133 -0.294 -0.oo_ o.146 -0.165 0.00979 (I/rad) -0.0487 -0.0384 -0.0466 -0.0452 -0.0479 -0 .o_97 -0.0479 C_5 a (I/rad) 0.01862 0.0172 0.00746 0.01061 0.007 o .oo8o3 O .O0975 Cn5 a (I/tad) -0.607 -0.481 -0.236 -0.258 -0.2233 -0.2005 -0.258 O 0 0 0 0 0 0 -0.0072 -0.0056 -0.0068 -0.0071 -0.0075 -0.0071 0 0 0 0 0 0 -0.249 -0.227 -o .21 5 -0.21 25 -0.226 -0.235 -0.213 -0 _078 -0.031 5 -0.0189 -0.0175 -O.0189 -0.01 89 -0.01 75 0 .o805 0.0405 0.029 0.0281 0.0324 o .0329 0 .o339 0 .o258 0.01 29 0.011 46 0 .oi 09 0.00975 o .01004 o .oo917 0.223 0.21 55 0 .I904 0 .I394 0 .I99 o .I84 o.I 685 0 .O207 0.0226 0.01 76 O .0183 0 .O1 65 0.01 87 0.01 93 -0.O9_)5 -0.0958 -0.0845 -0.0534 -0.0848 -0.0756 -0.0644 -O.2140 -O.2125 -O.1626 -0.1844 -0.1345 -0.1491 -0.1924 0.0493 0.0467 0.0374 0.021 5 0.0404 0.0355 0.0316 0.0021 0.0027 0.001 6 0.001 8 0.001 4 O. O01 9 0.0020 --C, .020 -O .019 -0.01 5 -0.0077 -0.01 6 -o.o13_ -0.01 --0.25P, -< .N_;5 -0.267 -0.254 -0.27 -o.267 -0 ._C,5 Ch5 a (I/rad) (llraa) (I/rad) C_a Cn6ta (I/rad) Ch6ta (I/rad) Cyss C_ (1/rad) s (l/tad) Cn5 s I/rad) Cy_z ' I/rad) C_6 r I/rad) Cn6 r I/tad) Ch_ r 7/raa) CY6t r (llrad) C£Str (I/tad) CnBtr (1/rad) C" (1/rad; nst r -0.0068 0 199 1 O_ • O 0 P'÷ W 0 h= ,,,F* _ I'dILl U'_ c_ 0_ _ 0 0 0 o o o o 0 0 0 o 0 I ÷ o _ 0 • j _ _ ÷ ÷ o o -, _ ,- 0 _ ,'-4 0 ___ ._i 3 o r_q o • 0 _r_ ,'-'4 g • _ • I o o ! ÷ H H pq 4- ÷ ÷ = • o H _ ,-4 ,-d N ,-I • _ _• + I _J 200 I_• i_" 0 _ ",I" tO, • I 0 o 0 o 0 o r_l 0 ..-i _ _1 ',,t 0' o _ _ _ .o _ .t _ -_ _ o c_. -1- cO 0 0 0 0 0 ,D 0 0 0 0 0 0 _ * .-_ t_ • 0 • {_ l v r-- ¢v_ I" * • ." I' _' _f_ I_ c¢_ El o 0 t'• I' 04 _ o_ _ t _" 0 O • I _ 0 O ' I {_ _ 0 0 O • oJ _._ _ O_ 0 • _r_ • I N H U_ H H H ,,,7- _ uo o_ O O • I O • I O O O • O 0 • I O" I _r_ 0._ ,0 tZ_ _• o _.. 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I' I _E _w ZZ Z 206 v Z P-- _ o lJm_ i_0o ,-4 _o_ _0_ o_o o co0 oo ° ,._ ° _ ° °,,, I I" _o_ I I" ..s o~_ o 0_ _0 . o ej • I t_m r,j I_0 i._ f,el r_ _ Z _."_. _o co l_J I °,+, I I _°° II _o 0_ • I I I I , l_j mm + I I II P_ , I'_ u'_ 0o um II + H r.- °_ • o • I I I H H t:" _ q_ tl ._ F7_ F_ _,_ I-+ c" _0 O) oo • <N p_ ,_ • o I • I I_ eu l I I _o_ ..A'_ _ .-_,0 0_0 ,,IDrex ,-_ • ,,-I .4 + ,-i eq I ,0_ I I I II I o e_ _ "o _o_ o o _ e_R_o _0 • ,-'4 .-4 I,_,0 I ZOOWW v Z 207 Z 0 0 _ _ _ _ _ _ _ , I_ I'- p I_I | . -- 0 _ _ _ 0 _ _ _g_lg.._O_O_._ v + I_ I_ 0 + f_ CO . aO . f J O + 0 4_ ,--4 _ _• I_ I o u_ _ r- ,+ _ p_ l + <%j q _ • p_ ch _p o p_ ir Q U' w _ _p • _ +rt I 4 I '4" _ N _1 ¢O f_ • • 0 fJ" r,_ _ • " I I CO + _0 -- 00 • 0 • P P" O • P',I 0 +1 _ .,1+ oI_ _ .-w U 0 .+ v P r_l (P, ,..,I ..,i" w_ _ I " ! wD _ ..1" N I O, ,-_ I co _ I I ,,41" _ wO 0 P,,,. _ c'% P"- _, ",+" , _ • I"I .P' 0_ C) 0 _ 10, • h- ! •-+ _1 I_ f_ o lU 0 N • _ o l I • _J u x • P_ • N ,-4 • ,4" NO' _ f_l ,-.4 urs ,--4 _ 0_ ,_ _ e ¢_1 0 -1" I iii <_ r r, UJ _ w LU n. LU I_ -. _ _ +.J .J '_ nf ¢'_ ,,.,4 _ 208 ..4 1',,4 O. 1_ I_. _ _ )¢+ LIJ U.J g+.l 0 _ _ IJ <_ C) _ +-+ _ es I 03, I _1 _ I-- ID I- rJ I- I_ _. "_: I_ I_ _,. ,'_ CV-880M DATA SOURCES McNeill, Walter E., Calculated Factors of Three Subsonic and Flight Measured Jet Transports , NASA Brooks, Airliners, Peter W., The World's 209 London, Handling-Qualities TN D-4832, Nov. Putnam, 1962. 1968. _ECTION IX BOEING 747 210 BOEI__G The Boeing designed to 747 operate necessary low flaps Krueger the and inboard flaps through four and only each spoiler are The five as speedbrakes Directional (Boeing and this flaps. an spoiler aircraft has and inboard aileron panels Krueger slotted D6-30643). 211 while which with obtained is The operates each the wing most from solely outboard the between two obtained lateral the also con- inboard flaps down operate inboard rudder of inboard with from the trailing flaps control aileron is obtained was To obtain stabilizer. on transport triple-slotted Longitudinal conjunction control airports. The a movable outboard in intercontinental wing cambered panels_ wing. for edge segments spoiler the unslotted. an Information four-fanjet international variable and panel. description leading flaps_ symmetrically large existing standard five BACKGROUND characteristics type elevator outboard on speed are employs a very from nacelle Krueger trol is 747 sixth segments. a 747 simulator 2; (1) o X (1) o .i.Ii 4a ii1 co o o ® gh 0 o h i1) I I I 0 0 0 0 o cf o o "_ o ,d _ i+ 0 _J or) _ o o O _ • c_ o cu • 4D .r-I _J O ea 4_ b8 .H _H P_ bbI i .H # _J O b9 .H o O -i-4 O OJ -ID r_ I ,1-1 .,-I O O I"4 o o r_ o I-i 4D .-a .H O lag kD 0 _1 o Od +_ _H , Od 4D CH I rq r-I _0 0 X X _, ly_ Ckl u_ bD kO 0 ,-- kO 0 Io 0 0 GJ -ID r._ X L"- L¢_ ,-- h_ II II X _ • _ Lr_ OJ CO 0 4D cO II 212 fl II CO a_ _,D ._j "_I-- ° pr_ a_ f_ ,-I a_ 0 lqr)_ ! .J G _ o_ || II I| 0 b 213 B-747 PITCH AXI_. _eSAS I Fcc(Ib) K -2 4° k P" 8e(rad) 57.3 _cc(deg)[ 50 e,"s / 20 J" x ,°t 43 o 0 .2 .4 Mach I I I .6 .8 1.0 [fj ,-t 0 4_ 0 ROLL AXIS _t P I I Fwfib) r; I .161 Sw(deg) I 57.3 .5 H (1) b._ YAW AXIS FpED(Ib) 8rsAs(rad) ___ 43.5I }SPeD(in) I 214 7.15 57.3 B-747 YAW SAS rG (rad/sec) I 5.05_ I(s,.368)(s 3.68) Flaps Down -.688s s+.368)(s+3.68) _iNs(rad) -34.5s (s+lO) 2 r =r *INS: (Gyro and IP dt INS Aligned Figure IX-4. with B-747 215 FRL) SAS TABLEIX-I Landing Configuration h VTo Non-Dimensional Derivatives : sea level = 131 KTAS mo = 8.5 ° 5s = -6.3 ° Longitudinal 5a CL = I .76 CD = CL_ Lateral-Directional Cy6 = --1.081rad .263 C_6 = --.281/rad = 5.67/rad Cn_ = .184/rad CD_ = 1.13/rad C_p = --.502/rad Cm_ = --I.45/rad Cnp = --.222/rad CL& = -6.7/rad C_ r = .195/rad Cm& = --3.3/rad Cnr = --.36/rad CLq = 5.65/rad C_Sa = .0530/rad Cmq = --21.4/rad CnSa = .O083/rad eLM = --I.I CYSr = .179/rad Cm M = .36 C_5 r = 0 CI6e = .396/rad CnSr = --.ll2/rad Cm5 e = --I.40/rad = total deflection inboard aileron included of right inboard aileron plus left with the effect of outboard ailerons 216 TABLE Power Approach Non-Dimensional IX- 2 Configuration Derivative s h = sea level VTo = 165 KTAS co = 5.7 ° 5s = --2.1 O Lateral-Directional Longitudinal CL = 1.11 CyB = --.96/rad CD = .102 C_ = --.221/rad CI_ = 5.70/rad Cn_ = .150/rad CD_ = .66/rad C_p = --.45/rad Cm_ = --1.26/rad Cnp = -.121/rad CL& = --6.7/rad C_r = .101/rad Cnr - .30/rad Cm_ : -3.2/rad CLq = 5.4/rad C_5 a = .0461/rad Cmq = --20.8/rad Cn5 a = .O064/rad c_ = -.81 Cysr = .175/rad CmM = .27 C_5 r = .O07/rad CLte = .338/rad Cn5 r - .109/rad crime = -1.34/rad 5a = total deflection of right inboard aileron plus left _nboard aileron with the effect of outboard ailerons included 217 SL i _m mmm B-747 20,000 40,000 _m em mmme ft ft 636600 .25 _" Flexible Ib k i k k k 12 I0 m GO (deg) 8 m 6 42- o I I 0 4I .2 .6 " .8 1.0 Mach 2 ,_i_, ° " _0 I .2 (deg) I" .4..""_ .6 .8 Mach -2 -4 218 ._ I I 1.0 _o. u o I I I I o. o. m 0 0 _0 b- _D i P0 m_p O0 O0 o. qQ _00 u) od ,_'- 11 li _5 I I I I o. o _ c_ Od _1 o 219 CL SL B-747 20,000 ff 40,O00ft 636600 Flexible Ib a (rad-') 4l 2- 0o I .2 I .4 I .6 I .8 I 1.0 .8 I 1.0 Mach I CD a (rad-') .8 l l m , \ .4- 0o I .2 .4 .6 Mach 220 Mach 0 2_ .4 .8 .6 1.0 7------V--- 0 ,--------T-------T-------_ B - 74T 636600 Ib .25E Flexiable -.4 :8 Cm a (rod -j ) -I.2 -I.6 Mach .Z I .4 r .6 I .8 I 1.0 _ I -8 Cm&, Cn_q (rod "t ) SL 20,O00ft 40,O00ft .... .-.. -..- -12 Crnq --------®. ] J 221 I m CL M 0 I .2 .4 Mach .6 .8 (_ 1.0 ! SL B-747 20,000 ft 40,O00ft 636600 .25 Flexible .3- I / CD M # .I // m 0o l .2 1 .4 j .6 ®_/ , .8 1.0 .4 .2 Cm M I "(_._ 0 -,2 -4 222 t II I Ib B-747 " SL 20,000 ft --------- 40,O00ft .4 .3 CL8 e (rod -=) I .2 O0 I .4 I .6 I .8 I 1.0 .6 I .8 I 1.0 I Mach .2 00 .4 I -.4/ I -.8 -- I / I Cm8 e (red-I ) y -I.2 - -I.6 - / ' ." 7/ 223 Mach 00 .2 I .4 I .6 I .8 I 1.0 I -.4 Cy,o (rad "I) -.8 B-747 SL -I,2 20,000 ft 636600 40,O00ft Ib Flexible Stability Axis .2Cn_ ( rad-I ) O0 I .2 I .4 I .6 I .8 I 1.0 .4 .6 .8 1.0 1 I I Mach 0 0 .2 (rad "=) \j -3- 224 / SL B-747 636600 20,O00ft 40,O00ft Stobility Flexible Ib Axis Mach 0 0 .2 I .4 I .6 I .8 I 1.0 I -.2 Cyp (rad "l) -.4 .O4 I I 0 Cnp .2 1.0 (rad "i) -.04 -.08 225 SL B-747 20,000 ft 40,O00ft 636600 Ib StabilityAxis Flexible .3C_ r \ l (rad-') I .2 O0 I .4 I .6 I .8 I 1.0 .6 i .8 I 1.0 I Mach 00 .2 I .4 I -.I-- -2-Cn r (rad"l) -'.3-- --.4 -- 226 .... ----- B-747 636600 Flexible SL 20,000 ft 40,O00ft Ib .016 .012 .008 ! t t t DO4 0 0 i .2 I .4 I .6 I .8 I 1.0 Mach Note: • Because spoilers operate around a dead band their effect is neglected here • 8a is the total differential deflection of right and left inboard ailerons .004 Cn8 a .! (rad) 0 .2 .4 . Mach -.004 227 1.0 \ SL B-747 6366001b Flexible .... 20,O00ft "-------- 40 O00ft I CY8 r (rod "l ) I .2 O0 I .4 I .6 I .8 I 1.0 .6 I .8 I 1.0 I Moch 0o -.04 - -08 - .2 I .4 I Cnar / (rod") -.12 - .02 O0 - .2 .4. .6 Mach 228 .8 1.0 co I¢ ¢o tc, t_ c_ . eo rt <o D- .-_ r_ _ ,,t C I_ r - r-I• _: "_ t_, I_ _ __ _. 0 I'M O 0 _-_ 0 _ 03 C ,-_ I r,J ¢,j 0 r_ _, 0 0 if. 0 _, C r-J Pw 0 0 0 _ o 0 0 __ _ 0 C / • _ 0 ILl l.L I_ ,0 It" _., • • 0 (3 ,.0 c, _ t / v _0 + UA OJ H E'_ M N _- 0_ eq O, N + _a 4. 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I 4% l--orqoO ,0 , I I ,_q ,.-_ • ,.-_ 0 II I _d (D _d 0 r.5 v ; II I II CU 7 _q I II ,o O_ oo co ;-- oo _o I o o 0 i _v C __00 I _.__ 240 _O * GO • • • • CO # ...-4 • • .,f I I_ 0 0 0" _ O _n _0 _._ O O o 0 4" •_" O3 h_ 4J • r- I _ • _-* _'_ _ _ • • N • wD .--_ 0 _ • N _o ,-_ -- ,o _ • • • • I J 0_ .,-4 _ _ o _ _ $ _ _ _, _ l o _ _ _ _ _ _ _ _ _ -o . O I _ _ o _ • o _ N I I _'_ l "4 0 ..a wD 0 " I G 0 5 v X II. _ uJ ,- 0 0 rxl _. w o_. 24_ -- -- 1 tJ B-747 DATA SOURCES I-_.nke_ C. Rodney and Donald R. Nordwall 3 The Simulation of a Large Jet Transport Aircraft, Boeing Rept. No. D6-306433 Vols. I and II, Sept. 1970. 242 SECTION X C-SA 243 C-_A RACm_ROU_D The C-5 A is a very large turbofan engines. sections with ailerons and spoilers, surfaces are irreversible. A bobweight The of the Longitudinal an bobweight all-movable SAS is and is used position C-5 A military not control stabilizer yaw in the is assumed employs stability included logistics control consists for be at the augmentation here. 244 trim, of feel powered elevators roll a conventional longitudinal to transport in control four four employs rudder. system. by All The control effective pilot. about all axes. A description 0 .rt b_ °,-I CH 0 Q.) °H 0 ,--I rO m 0 •_ 4a _ .rt 4_ ,) ) 4u or-I r_ cl I r-I I 0 0 _1 0 0 o d ,'-t 0 "d c,l 0 o o I i I 4_ .H 0 ® X_ b9 ,.-I LFX I "7 (1) ,rl .M 0 4_ OJ OJ 0,1 OJ LF_ _0 OJ r'-I o _ _ i _o_o%_o _ o '._ _ II 4a X _ X -I_ X ,_ _, 4_ X _c_ _- _ C-- Io 0 _ ___ I -I"a _ I 4-_ r_ I CXJ 4a c+_ I _n _a m ,'M 0 0 0 ×x×_ _ _ '_0 0 0 X _ II II II II _._ 245 _ II II II II It 4-) r--I aJ I & i X ¢J D b N .J 246 C-5A PITCH AXIS 8esAs (deg) I Fcc('b)---_;)_" K I 8cc(in)_l _-'(_)_''se(r°d)-I -2'92 57..3 t 32.2 8.3 a zB at _. _B 30 i II ?" 20_ / KIlbl .._/,/ I0 o,ooo,, 40,O00ft I .2 O0 ROLL I .4 Moch I .6 1 .8 1 1.0 AXIS 8asAs(deg) I Fw(Ib) 8w(deg) 8a(rad) KLAT Config. K LAT 8sp(rod) YAW Cleon .121b/deg PA .155 Ib/deg AXIS 8rsAs(rad) _ 63.5 F'i_re X-3. -I 57.3 C-_DA Control System 247 TABLE Power A_&ch X-I Non-Dimensional h = sea level VTo = 247 ft/sec = 2.7 ° c:qO Longitudinal Derivatives = Lateral-D 146 kt irect ional (Stability Axis ) CL = I. 29 CylB = -.77/rad CD = .145 Cn# = .075/rad CI_ = 6.08/rad C_IB = --.123/rad CD_ = .622/rad C_p = --.458/rad Cm_ = Cnp = -.098/rad Cm&= - .3/rad C_r = .290/rad Cmq Cnr = --.293/rad Cysa = --.O044/rad Cnsa = .0091/rad C_sa = .089/rad CYSr = .211/rad Cnsr = -.106/rad C_Sr = .0209/rad CLUe --.827/rad = --23 . 2/rad = .385/rad = --1.6/r d 248 Spoiler Effects Included C -5A 654562 14 m 12 m IO m 8 1 Ib Flexible SL .... _- _ 20,000 40,000 ft ft (deg) 6 1 4_ 2_ I 0 0 .2 I .4 .8 Mach 249 1.0 0 rU I I I I OJ O0 O0 o O tl i0 iI U 0 L,. j _- .lj o .a 0J i LO (-) _0 OJ I I I Q _ J 0 250 I _ _o C-5A 654:562 Flexible SL - 20,000 40,000 Ib ft ft _ 5-4-5-2-I -0 0 I I .2 .4 I I .6 .8 I 1.0 Moch 1.2 -- ,8 -- .4 -- CD a f_ (rad -I) o 0 I I .2 .4 .6 Moch 251 .8 1.0 Mach 0 .2 .4 .6 .8 i I I I 1.0 I C -5A 654362 -.4 -- Ib .30 E Flexible , SL --- --- -----. - -- 20,000 40,000 ft ft Croci =-.% (rad -i ) .\ -1.2 -t Mach 0o _..,,-._ .2 .4 .6 .8 1.0 I I I I I -4-Cm_ , Cmh Cmq (rad -I ) -12 -- -16 -- -20 Cmq -- -24 -- -28 -252 Moch 0 0 .2 .4 -__-- I_ .6__-'L-_._.8 '_'_" I 1.0 C-5A CL M -I.0 -- -I.5 -- -2.0 -- -2.5 - -3.0 -- 654362 Flexible SL D CD M .12 -- .10 -- .08 -- .06 -- .04 -- .02 -- D--,,. 20,000 ft 40,000 ft I 0 0 .2 .8 n o6 n I .4 .6 .8 1.0 Mach o4 Cm M .2 0 m I I .2 1.0 -,2 253 Ib C -5A 654362 Flexible Ib -----.,-------- SL 20,000 40 000 1 CLSe (rad "t ) ,J 0 0 t I .2 .4 I I I .6 .8 1.0 Mach 0 -,4 -- _=8 J .2 .4 .6 .8 1.0 I i I t 1 CruSe -¢ (rad -I) -I.2 -- 254 ft ft Mach 0 0 .2 1 .4 .6 .8 I I I 1.0 I C-5A -.4 c_ -.8 (rod -I ) -I.2 SL -- -- -- 20,000 --- - -- .I ____--_:_: _o=. _,, c._ I 0 .2 I .4 .8 Mach (rad "l) 40,000 I ,_ .8/ t I 1.0 C_ -.I -.2 255 654362 Ib Stability Flexible Axis Moch 0 0 •2 1 .4 .6 I I .8 1.0 1 I C -5A -.2 C_p 654562 Ib Stability Flexible Axis -.4 (rod -I ) .----.(_... _ I,_'_ -.6 SL ------- 20,000 ft ---------- 40,000 ft Mach 0 .2 I .4 1 - .04 Cnp // - .08 (rad-') - .12 -.16 256 .6 .8 1.0 I I I C -5A 654562 .50 Ib E Stability Axis Flexible .4-- ,SL \ •----.---- 20,000 ft --------- 40,000 ft \, C_ r, Cn r °2 (rad -I) C_ r 0 .2 t I .4 .6 I .8 l 1.0 Mach -t2 -- _,__,___j_,,L_" 257 Cnr .04 .... _----" SL 20,000 40,000 I .2 I .4 C -5A 654326 ft ft Ib - C_.$o -I (red) .02_.-- 0 I 0 I .6 I .8 Mach .02 .01 Cn_ o -I (red) 0 -.01 -.02 / ]i -.03 258 I _ / tf I 1.0 Mach 0 .2 1 0 -.002 - -.004 - -.O06 - .6 I .4 I 2 5 5 6 1.0 I .8 I 4 87 9 C-5A 6545621b .O8 %%% .O4 0 0 I .2 ........ 1 .4 I .6 ,.,, 1 .8 1.0 Mach SL 20,000 40,O00ft .O2 C n 8sp (tad-l) .01 o [ 0 .2 I I .4 .6 Mach 259 I .8 I 1.0 ft .2Cy8 r (rod -j ) .l -- 0 0 I .2 I .4 ] .6 I .8 I 1.0 .6 .8 1.0 Mach Moch 00 .2 .4. I I I I i -.04. Cn8 r (rad "t } -.08 SL 20,000 40,000 C-5A ft ft 654..362 Stability Rigid Ib Axis C,ts r O0 .... I!0 Mach 260 _t" _ ,,1 C_ ,0 ,,t er, f'_ .--4 ,_, ,,1" ..-4 tr, • ! I c3 .--, 0 C) 0 0 0 _7 _3 * O0 I r_" _ • f_ 0 0 0 0 2 .. o o __ 0 {3 0 • _0 0 "4 0 * * O' O" I 0 "4. UJ ÷ ill 4" UJ 4111 • * 0 d ,0 0 0 • 0 U'_ • ,,0 .-4 • • • • I I O_ (_ 0 4UJ 4W + W ÷ W ,--4 . _ 0 O0 CO _ ,0 O_ 0_ . 0 er_ 0 _- 0 ,,II • II vll ,,0 _ _ 07 4- _ _D 0 • e • O_ _" " 0 o.} ÷ W ,....4 ,40 ,,,,1" * ' ' _ I _ CO 4LU _ 4W P" "_" IJJ r -_ O" * 0 0 u7 0 0 0 I I • .'-* t.,"x t-- 0 0 I • {3" ,_'_ fq _ O" -4r •0 r_ CO 4- 03 4- eO 4, I_+ I_- ,--i ,0 ,_ . . _ | o 261 • I t'_ _ • 0 I_- 0 0 0 0 _ co ! _ e,_ ,4 _" C. I_ I _" c _I_ 0 _ I_- -,1" _£ u', ° I° I" " _ _ _ "_ r_ 0 N C, _ 0 _ 0 ; c 0 I _', 0 I_ _ "..I ; l I" |" ";i.O. 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N r_ _0 c@ • I _ f_ _r_ O 0_ O O • .-'6 I _n o o o • co _n - o, m ,-.4 _ • N ¢ • r _ .-4 Ie o = -4 o o _ 00 N o m _ - m o o o "0 I¢ • f1_ i • _ .-4 • _ rg 0• N ',.I _1" eq O rq ,-4 i_ ÷ o •.,1" j _r_ ,4 _ I N u_ _ _t r_ .-_ e_ .j tn f,_ 0_ I O .4 N 0_ O ur_ I A I .e N J O O u'_ • 0_ ,0 I ,0 r_ 0_ 0_ O I r_ rn O _ ,,1" _ O 0• 0_ u'_ 0 _ ur_ N _0 • I I C_ •..4 ,..J e I rx) I IJLI 3 " G u., 1- uJ _ w _. _ _ _ 271 _ I C-SA DAT_ SOURCES C-5 Flight Control Report (Aerospace Vehicle) Stability and Control, Lockheed-Georgia Rept. No. LGIUS_2-1-1, 8 Feb. 1966 272 SECTION XB-70A 273 XI XB-70A The XB-70A supersonic craft was cruise to two SST-related XB-7OA's had zero The first airplane Pitch control geometric in takeoff is used. Yaw 45 flight identical dihedral while is considered Roll control is obtained is provided aircraft except that systems built with became long range research air- the second by the Lad the first 5 deg airplane geometric (XB-7OA-I) dihedral. here. elevon canard rotation is through of the and locked canard and a differential vertical surfaces fixed except canard action stabilizers of flap the about elevons. a line. shown test two interconnected where airplane Data were employs as a weapons problems. landing hinge The The and control deg designed capabilities. explore The originally BACKGROUND is here data equipped is where with stability a composite of many possible. 274 augmentation sources. The in all object axes. was to use o .,-i 4_ o r.D bO .,-i r_ 0 b- i H 275 0 o \ \ 4-) o E ,--t J 0 0 & ! I,--I X °,-t N ;! OD '+- o I.D -- II II 1'_ II 276 XB-70A PITCH AXIS (_eSAS (red) I .025s i - z +.35s+K See Fig. PA o/t Clean Config -- a z at 1B 50 _ SL _ 20,O00ft 40,O00ft / 60,O00ft / _/ l FS i I0 Ib/g__852/2 14 tb/g 1479.2 Clean PA 8c(rad) Effective Bobweight B _....... - // f "/'- --e I0 0 0 ROLL I 1 I I 4 .8 1.2 1.6 AXIS I I I 2.0 2.4 2.8 1 :5.2 8uSAS(rad) I FLAT/ CC ,in/Ib) Much =-- 8cc Meg) .41 = 57.:5 _ I 1+.075 I I .-_ 8a(rad] I YAW AXIS 8rsAs(rad) FpE D(lb) KDIR I I _PED(in) Config. Gear Gear Figure K DIR UP 281b/in DN 3lib/in XI-5. XB-70A 277 8r(rad) GDIR 57.:3 G D.R .96deg/in 4.0deg/in Control System B j-2169ft I0 96ft XB-70A PIT.___CH SAS 8 (rad/sec) -_ az' 34.8ft at -_x' = 1 36.4ft Normal 8¢¢(in)-_-4'65 ROLL at F.S. 1174 } SAS p(rcd/sec) | - j YAW Accelerometer Clean PA _ 8OsAs(rad) SAS r (rod/sea) _rsA s (rad) Figure XI-4. 278 XB-70A SAS TABLE Power Approach XI- I Nondlmensional h : sea level VTo : 347 ft/sec ao = 7.5 deg Stability : 209 Derivatives kt Lateral-Directional Longitudinal CL = -333 Cy_ = --.183/rad CD = .055 Cn_ = .132/rad CL_ : 2.6/rad C_ : --.072/rad CD_ = .56/rad C_p = --.18/rad Cm_ : -.23/rad Cnp = --.26/tad Cm& = +.09/rad C_r = --.03/rad %q : -1.9/ra_ Cnr = -.25/tad CL_e = .46/ra_ CY$a : -.063/rad %_e c_ a : .042/rad Cn5 a = --.O052/rad CYSr = .12/rad C_5 r = -.O018/rad Cn_r = -.103/rad : -.19/raa 279 GJ ® / CO N / Oea ¢'*" 1'7. 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' I • I • I .=.. • _" 0 I • eel .0,."4 i 0 • • I 0 0_ I I .,-I 4_ 0 0 O_ • i _ ._-j II "7 N om_ • o. • I I I I o , 7 I I I • ! ! _aaa _-_- 314 _ o.-.o o• N .-, _0 • .-.I .,_ o ® _ e_ eel ,41" 41 _ ,o _ .-, j • ,.-,I _ I_ • • -4 r'J • ._ g ÷ ,,f ÷ ÷ 0 • I_ OJ 0 0 '_ Od I_ Od _ _ 0,8 ,,I" 0 • t_ r%l _1 0,1 • • t",,I _ o • • ÷ ÷ 0', •. _ ,_ 0, _ I _ t o ,,, o _, ,,, _0 o I i- _< it,. 315 ILl XB-70A DATA SOURCES Estimated Aerodynamic Derivatives., No. 'NA-61-707, 29 June 1962 Aerodynamic Coefficients North American Rept. XB-70 , North American Rept. Obtained from Flight Test Data_ No. TFD-67-277, ]4 Apr. ]967 XB-70, Wolowicz, Chester H., et al, Preliminary Flight Evaluation ._f the Stability and Control Derivatives and Dynamic Characteristics of the Unaugmented X_B-70-1 Airplane Znciuding Comparis_i_s k_th Predictions, Estimated North XB-70 NASA TND-4578, Performance Report American Rept. No. Flight Control System Rept. No. NA-_6-360, 30 May ]968 for the XB-70A Air NA-6h-660, 26 Oct. Summary Test Sept. 19'66 316 Report, Vehicle 190_ North _o. I, American APPENDIX A AXIS SYSTEMS, SYMBOLS, MNEMONICS, AND DERIVATIVE I. AXIS COMPUTER DEFINITIONS SYSTEMS .XB,U,P _-_ _ YB ,Ys ,V,q _ / _-_ Inertial Ref. Za ,W, r g XB, YB, ZB -- The Body-Axis System consists of right-handed, orthogonal axes whose origin is fixed at the nominal aircraft center of gravity. It's orientation remains fixed with respect to the aircraft, the XB and ZB axes being in the plane of symmetry. The exact alignment of XB axis is arbitrary, herein it is taken along the body centerline reference. XS, YS, ZS - The Stability-Axis System is that particular body-axis system for which the Xs_axis is coincident with the projection of the total steady-state velocity vector (VTo) on the aircraft's plane of symmetry. It's orientation remains fixed with respect to the aircraft. A-I 2. SYMBOLS a S_peed of ay Lateral at the sound in ft/sec air acceleration along the y-body axis center of gravity (positive out right ft/sec 2 wing) Lateral acceleration axis a distance at parallel _x and to the _z from y-body the c.g., ft/sec 2 a_ = ay + _x_- _z_ T Normal a Z axis acceleration at a distance az = az axis _x from the z-body c.g., ft/sec 2 acceleration at parallel a distance b Reference wing B Bobweight gain B.L. Buttock _B from to the the z-body c.g. ft span ib/g line Reference ft chord C Longitudinal C. ,g. Center D Aerodynamic force (drag) velocity vector (positive FRL to the _xq r Normal parallel of Fuselage feel system ib/in./sec damping gravity reference line along aft) the (parallel total ib to x-body axis) Fuselage F°S. FST T Fped station Longitudinal control Longitudinal stick Lateral Rudder stick pedal g Acceleration G Pilot control force force force due to column to force (+ aft) (+ aft) ib ib (+ right) ib (+ right ) ib gravity surface A-2 gearing ft/sec 2 deg/in, deg/deg or h Altitude I Longitudinal Ix_ ly_ I z ][XZ ft feel system Moments (unless of inertia otherwise referred specified) to Product (unless of inertia otherwise referred specified) to The imaginary portion able s = J ±jc_ _B Effective (positive distance forward) Distance along c.g. (positive _X Sth Perpendicular line (positive due to thrust) Longitudinal KTAS Knots true KCAS Knots calibrated K Feel system pressure torques M Pitching slug- ft 2 complex varirad/sec the x-body forward) from axis c.g. from the ft the z-body down) system axis from the ft spring constant ib/in. unit (ib/in. airspeed constant about per the x-axis (positive right Aerodynamic force the total velocity plane of symmetry Mach axis ft spring moment M body due dynamic to wing aero- down) !lift) perpendicular to vector in the aircraft's (positive up) ft-lb ib s_igs number aerodynamic 2 airspeed dynamic Mass axis slug-ft of bobweight feel Rolling m the body 2 ft K T of ib/in./sec distance from c.g. to thrust for nose-up pitching moment Distance along c.g. (positive _Z inertia moment about torques MAC Mean aerodynamic MGC Mean geometric the y-axis rpositive chord chord A-3 due nose to up) ft-lb ft ft )/psf N Aerodynamic axis, normal but force positive along the Ib Yawing moment about z-axis due torques _positive nose right) P Roll rate, angular velocity (positive right wing down) Pitch rate, angular (positive nose up) q r rRG Dynamic pressure, Yaw rate, (positive Yaw rate I/2 y-axis lb/ft 2 about z-axis rad/sec rad/sec TED Trailing edge down TEU Trailing edge up TL Thrust U Linear perturbed velocity (positive forward) operator, wing rad/sec a + j_ ft 2 area line Linear steady-state x-axis (positive Stall speed Total linear along the x-axis ft/sec velocity along the forward) Linear perturbed velocity (positive out right wing) forwaz_ about signal Reference VT o x-axis 2 o VTo S V s ft-lb rad/sec Laplace V aerodynsmic rad/sec velocity S Uo to about angular velocity nose right) gyro z-body up steady-state ft/sec along the y-axis ft/sec velocity Cpositive ) W Linear perturbed (positive down) W°L. Water W We ight Wo Linear steady-state z-axis (positive kt velocity along the x-axis line in. lb velocity down) A-4 along the ft/sec X Aerodynamic force along the x-axis forward ) Y Aerodynamic force along y-axis out right wing) Z (positive (positive lb Aerodynamic force along z-axis (positive down) lb (L Perturbed rad _o Steady-state relative to angle Sideslip _O _a _e of attack (trim) the FRL path angle deg deflection (includes (positive for posirad Elevator surface deflection from (positive for nose-down pitching for aft surface) elevator trim control (positive Lateral stick tive right) column deflection aft) deg deflection from Spoiler _V Vertical tive for trim in. deflection from trim (posiin. Lateral wheel deflection tive about x-axis) $sp rad deg Rudder pedal deflection from tive right pedal forward) Stabilizer (positive trim moment deflection Longitudinal stick (positive aft) _r deg Aileron control surface spoiler effects, etc.) tive rolling moment) from _S attack rad flight Longitudinal _w of angle Steady-state Trim Sped angle surface for TED) surface yawing moment trim (posideg deflection from trim rad tail deflection nose-left yawing de_ection (posiin. from deflection Rudder trim (positive from trim moment) [positive (negative A-5 N)] for up) rad (posirad nose-le_ rad A g Denominator of airframe transfer Angle between principle (positive about y-axis) Damping ratio particularized inertia Inclination tive gives Mass axis of linear second-order by the subscript of The real portion s = a ±j_ mode and level rad of thrust line with FRL negative (--) z force] density and FRL deg Pitch angle, fq dt for straight flight, positive nose up iTH function [posi- slugs/ft3 air of the complex variable rad/sec Roll angle, (cos eof p dtstraight and level flight wing down) sin eofr dt) in (positive right Undamped natural frequency of a second-order mode, particularized by subscript Special Subscript a Aileron cc Control d Dutch e Elevator G Gyro INS Inertial P Phugoid r Rudder R Roll S Spiral SAS Stability sp Short ST Stick column roll navigation deg system subsidence augmentation system period A-6 rad rad/sec Special Superscript DIR Directional LAT Lateral S_mbols Unique to control control S_eclflc system (e.g., Aircraft Aileron-rudder interconnect BLC Boundary control KDIR FLEX Rudder flexure PBF Bellows force qB Bellows pressure 5d Yaw damper surface deflection (positive for nose-left yawing layer Aileron $tac Commanded 5t e Elevator (_te -- _e)c 5tr (Str -- 5r)c tab coefficient parameter tab tab F-4) (F-4) (F-4) ft 2 (F-4) deflection aileron (F-4) (F-I04, tab deflection lb/ft 2 deflection (F-I04) moment) (CV-880M) deflection Commanded rudder-rudder servo tab combination (input linkage)(CV-880M) A-7 (CV-880M) servo tab (CV-880M) (CV-880M) rad rad (CV-880M) Commanded elevator-elevator combination (input linkage) Rudder pedal) system ARI St a rudder tad rad tad rad tad 3- COMPUTER PRINTOUT MNEMONICS a. COMPUTER DIMENSIONAL, MASS,ANDFLIGHTCONDITION PARAMETERS rRINT OUT STANDARD NOTATION_ DEFINITION S S, wing reference B b, wing span C E, mean geometric F/C# Flight H(_) h, SL Sea M(--) M, VTO(FPS) VTo , true airspeed, VTO (KTAS ) VTo , true airspeed W, altitude, number feet Level Mach number weight, c.g., IX IY IZ IXZ knots airspeed, knots pounds Ix I e, knots center of gravity relative mean geometric chord Body Iy Iz Ixz _SI_N(DEG) chord Condition VTo , calibrated w( s) area inclination respect to axis (FILL) moments inertia, slugs-ft 2 of principle FRL, degrees axis Q(PSF) q, dynamic pressure, psf QC(PSF) qc, impact pressure, psf ALPHA(DEG) So, FRL _(DEG) 7o, flight LXP(FT) up(n) £x, x distance to pilot, ft _z' z distance to pilot, ft ITH(DEG) ith , thrust incidence to FRL, degrees XI(DEG) _o' /th, LTH(FT) A-8 ith angle of path + %' attack, angle, degrees degrees with respect degrees perpendicular thrust line distance from c.g., to ft to of with b. COMPUTER PRINT LONGITUDINAL PARAMETERS OUT STANDARD NOTATION_ XU* Xu ]/sec zu* z_ 1/see MU* M_I I/sec-ft XW Xw 1/sec ZW Zw 1/see MW Mw I/sec-ft ZWD Z_ I/sec 2 ZQ Zq I/sec MWD M@ l/sec-ft MQ Mq I/sec tXDDD X8 ft/sec2-rad ZDDD Z5 ft/sec2-rad MDDD M5 1/sec 2 DTH 5th Thrust FST Fst Stick U u fps W w fps THE e rad HD _ fps AZP a_ 1"t/sec 2 at _DDD DDD signifies = DA a control surface, e.g., A-9 for DEFINITION force elevator X = DDD Ax = DE; for aileron C° LATERAL-DIRECTIONAL PARAMETERS COMPUTER P:_INT OUT STANDARD NOTATION YV Yv I/sec YB Y_ ft/sec 2 LB' 1% I/sec 2 NB' N% I/sec 2 LP' I_ 1/see _, _' _' _ L_ N_ 1/see 1/seo 1/sec ty*DDD Y_* 1/see L'DDD I_ l/sec 2 N'DDD N_ I/sec 2 B _ rad P p rad/sec R r rad/sec PHI _ t DEFINITION rad t AYP tDDD DDD ag signifies = DA. a control surface, e.g., A-IO ft/sec 2 at for elevator _x, DDD _z = DE; for aileron d. TRANSFER FUNCTION PARAMETERS The following shorthand notation is used to print polynomials for all transfer functions*: (s + ]/Tx) i (_2 + 2_%s + %2)j where COMI_ER PRINT k + 2_ : ]/Txi , i : ] to k : _j;_nj , j : I to = n, OUT the order of the STANDARD NOTATION DET Roots of the N(X/Y) Numerator N_ A(X) Gain 'i/T(X)I ,z(x)J tw(x)j For the 2 DEFINITION denominator transfer function x/y _j Cenj, rad/sec example: to: OE NCM INATOR I/T(OET }I I/_IOET}2 .0318 2.2C Z{DET} W[DET] I 1 .06C9 1.13 NU M ERATOR N| 8 /OR A{B I/T|B I/T (B I/T (8 S } A. transfer } .o_(s(s + function x/y N_y x/y = .0295 -.0494 2.05 42.3 _I }2 }3 : 6r _Any roots specified, of polynomial I/Txi , rad/sec Translates *The the factored a .0318)(s is written .0609 X 1.13s as: Ax( sm + (S n + .o494)(s + 2.o_l(s + _2.3/ + 2.20)(s 2 + 2 X sm-1 Sn-1 + + enclosed in parentheses imply the e.g., Z(DET)I = (O.OO132)_I/T(DET)I A-II ... ... so ) S O) opposite order = 0.00132 of what is + 1.132s 2) e. COMIKITER PRINT OU LONGITUDINAL STANDARD HANDLING NOTATION QUALITY PARAMETERS EQUATION I DEFINITION --r W^ l. cs DCO)fO(U) (D_I_) _/_u, 68 de_rees/knot L (I. U o _O 9)(97.3) Uo O u Wo w •-uo _(s) Nz_ ¢ DEIo (_1_) Control ' for phugoid to Fs_/n (,.-/l=) time period 1/10 Stick seconds inverse ---_, per Stick The or force in 10 1.689 knot, per g, pounds g parameter is not has defined no meaning at this flight condition notation implies constant speed (u = eo _Ph < <' -_sp 0 2_ cycles amplitude force for ll_ _I for = 0). A-12 O -- _sp (s -I per 0 2 l_unds/knot _S_/G(uVG) = to amplitude, Short s rad/sec2/g in l/c(_/_o) =0 anticipation parameter, double (2) ! a(s) The hat s _(S)' , degrees/g 5e/g CAP(mD I_clsEC IG) *The for , g/rad for s = O < I 1 / J , for s=O f. LATERAL-DIRECTIO?_AL COMPUTERPRIf[UOUT STANDARD DR PERIOD(SEC) Dutch roll iic(i12) Dutch roll to SPIRAL (2) (SEC) I/2 _DTATIONj _ANDLING QUALITY PARI_4ETERS DEFINITION EQUATION period, seconds 2_/ahd inverse cycles in 2 Ts in _ -- _d2 for _d _ 0 amplitude Spiral time amplitude, Roll rate step input to double 2, for I/Ts £ 0 seconds at peak I for a unit of 5 a Pl + P3 - $2 P l + P3 P(OSC)IP(AV) Ratio the DEL-B-_gbX of the dutch roll roll frequency to frequency 2_.m : Maximum sideslip excurslon at the c.g., occurring within two seconds or one halfperiod of the dutch roll, whichever is greater for a step aileron-control command PHI to BETA, PHI TO BETA PHI TO VE *v e : (8)(VEAS) + 2P2 for _d _ for _d 0.2 ' A measure of the oscillatory to the average roll rate PHASE _/_ at s = (_; C0n)d, degrees I /BI at s = (_ O_)d, radlrad "_/Vel , VEAS at s = (_; o.h)d, : _p2_ 0 A-IS deg/fps Pl -- P2 Pl + P2 > 0.2 2. NGNDIMENSIONAL a) DERIVATIVE Longitudinal Body CN = N _-_ CX = X - _-_ c_ DEFINITIONS Axis , positive , positive up aft = _--_/_ CM 2Vmo_c_/_ V- M _ Sc = c_ = _cW_ c_ : -- _CN/_, c_ = _cWM Cxa = _Cx/_ CMq - et% 2Vmo -'-T- _cW_ 2v_° _c_/_q c CxM = _Cx/_M Cx_ : ID) Longitudinal _cx/_ Stability Axis CL - L _ S CD - D _ S ' positive ' positive up aft : c_ _Cn/_ - 2Vmo c Pitching c_ = ac_aM derivatives identical c_ = acD/_ those A-14 moment are to for body axis c) Lateral Body and Stability Though physically Axis and numerically different,* samesymbols are used for body axis and stability see Appendix B, the axis lateral rolling and yawing momentderivatives. The sideforce derivatives (Cy, etc.) physically and numerically the same in both axis systems. Whenthe al rolling or yawing momentderivatives are given in this report the axis system is specified. Whenusing the following all quantities should be for the sameaxis system. Cy Y L Cy_ = BCylB_ = _Cy/_ *The exception is C1 - qSb Cl_ = Clp N Cn - _Sb _CI/8 _ Cn_ = _C_8_ - 2VTo 8cml_ b Cnp - ev_° b 8CNI_ Clr - 2v_° _ci/8r b Cnr - 2VTo 8c_/8r b c_ = _/_ c_ = _cJ_ the zero trim A-15 angle of attack condition. 5. DIMENSIONAL STABILZTY DEF_I_ATrWE DEFINITIONS The same symbols derivatives. quantities a) are used for body- Care should be exercised so that a consistent _u = Body set of Axis I/see Xu+ Tu cos_o __ 0_o(_ m - We) - 2 CxM - Cx + _ OSUo 2m cxcz = [- CX_ - Wo (cx M %) 2 _o +_ -_ I/sec Zu - oS_o (_ Zw - ooo[wo . - _ CNM - CN + 2m _) CN(_ -CN(_ - 2 _oo (CN + _ CNM pSc 11sec sec2rad Zu - Tu sin_ o m ] ft CXse Z*u = z_ = I/sec ! osv_o x8e dimensional are used. I_ngitudinal Xw and stability-axis I/sec I/sec Uo - 4m Vmo cN& PS_T o ZSe - 2m M_ = _th Mu +-_--_I ft CNSe sec2rad sec-ft A-16 I sec-ft MII = oScUo Cm_ + pSc2 Uo I sec-ft (Cm + I sec-ft Cm_ = l_-y VTo I/sec 2 I/sec I/SeC pSC2VTo pScVT2o MSe - 2Iy- = CruSe _/SeC % b) = L_ter_-% Body Axis I/sec Yv = (pSVTo/2m) CY_ ft/sec 2 Y_ = VToYv ft/sec 2 Ysa = (pSV2To/2m)CYSa ft/sec2 YSr = (pSV_o/Zm)CYSr I/sec YSr = (pSVTo/2m) CySr _/_ = (_SV_ob/_I_)c _ 1/sec I/sec Lr = (pSVTob2/_Ix) Clr A-17 2 I/sec 2 L5 a = (DSVTJ/2Ix)C15 L_r = (PS_TJ/2Ix)C15 YS_ : (_SV_o/2m)Cy_a I/sec : ( SV ob/21,.)c I/sec 2 : (psv_J/41z)C_ p I/sec Nr : (pSVTob2/4Iz) Cnr I/sec Nsa = (oS_TJ/2Iz)Cnsa N5 r : (PS_T2/2Iz)Cn5 = (L8 + IxzN_/Ix)G I/sec 2 = (Lp + IxzNp/Ix)G I/sec = (Lr + IxzNr/Ix)G I/sec I/sec 2 r I/sec 2 I/sec 2 r : (_6r+ IxzNSr/IX) G NSr = (%_ + IxzNS_/Ix)O I/sec 2 = I/sec 2 (N_ + IxzL_/Iz)G : (_p+ I_zLplIz)G I/sec = (N r + IxzLr/Iz)G I/sec = (NSr + IxzLSr/Iz)G I/sec 2 = (Nsa + IxzI6a/Iz)G I/sec 2 I G I Ixlz A-18 ,,,'t "r4 _ _ r_ c_ r,_ U i i 0 -t- + o 0 ¢..) U I-¢ 0 k 'o 0 0 /.-, ' ' 0 ÷ 'o& 0 _ I 0 ¢0 H r,_ o t_ o eJ 0 m I II ¢O II II H II n tl H 11 0 r.,3 A _q ¢0 0 r_ H m r.3 4,r ! cr_ H _1 r_ c.) r_ F-I rj_ o o n tl C_, H CO II ! d B-I II II II II II II U il II b. TRANSFORMATION OF DIMENSIONAL FROM STABILITY AXIS TO BODY DERIVATIVES AA_IS Longitudinal (Xu) b = Xu cos2 (X )b = Z@ sin 2 ao (Xw)b = Xw cos2 (x,) b = X@ cos 2 ao -- Z@ (Xq;5) b = Xq; 5 cos (Zu)b = Zu (Z_) b = --Z@ sin (Zw) b = Zw cos 2 ao (Z-_-) b = Z@ cos 2 c_0 + X@ = Zq;8 (MU)b = Mw (M )b = -¢4@ sin = M w cos c_o + M u (_)b = M, _o (Mq;5) b = Mq; 8 (Zq;5)b _o - _o cos2 cos + + Zu) (Xu-- Zw) sin a o -- Zq;5 _o ao cos + c% cos _o sin c_o cos ao -- Z u sin 2 a o sin + Zw sin2 _ _o _o sin _o cos oo --Xw sin 2 _o sin ao cos c_ + Xu sin 2 _o cos ao c_o (Zu + Xw) sin + Xq;8 ao --Mu sin c_o cos _o -- (Zw--Xu) cos cos (Xw oo sin sin ao sin _o ao (ly)b B-2 c% Lateral-Directlonal (Yv; )b = Yv;5 (Y÷)b = Y@ (YP)b = Yp cos co -- Yr sin co (Y )b = Yr cos co sin cO + Yp T ! = L_; 5 cos c_ -- Nv; 5 = L_ cos = _ cos 2 _o- = L_ cos 2 _o -- (Nr -- _) = N_; 5 cos = N_ cos (N )b = N_ cos 2 Go -- (N_ -- _) (Nr)b : N$ cos 2 ao + (IX)b = Ix cos2 (Iz) b (IXZ)b c_o -- sin (L_ sin c_ co + N_) sin c_ cos _o + N_ sin 2 oo sin ao cos Go -- N_ sin 2 _o sin Go cos ao -- L_ sin 2 co + N_) sin ao cos Co sin 2 Go + 2Ixz sin a o cos co + Iz sin 2 ao = I z cos 2 Go -- 2Ixz sin co co + Ix sin 2 c_o = (I z -- Ix) f (Lr) b T ! (N$) b C_o + L_;5 ! sin co ! c% Go + L_ sin sin _o (L_ ao cos B-3 ao cos + Ixz(COS + _ 2 _o -- sin2 Go) APPENDIX C EQUATIONS OFMOTION,TRANSFER FDT_CTIONS, ANDCOUPLING hq]_RATORS I • Longitudinal a. Eouations (I-xa)s-x; -X_ s - X w (I-z_)s-zw -z_s - z[ --_s-N q. = .SO fi = --w cos Oo + u = sw -- Uoq _z, = a z -- ixS2O h' : h +_x oos _o Transfer _e 5e A A Denominator, A + (g = (1--Z_) = -(Mq = sin w 8 s2 --MqS O 0 + W o sin = ZSe M{5e 0o)8 00)8 Terms As 4 + Bs 3 + Cs 2 + Ds + XU)(J - Xw_ NOTE: sin 8 o I" X$e- Functions e I) (--Zq--Uo)s+g sin O 0 + (U o cos az b. cos -(M,_+ Mw) u 8o -] (-Xq+Wo)s+g including -- Z_) -- Z w- + Wo[M_ Xd, + E M_ + M_(] Zfl, Mfl_ X@ C-I - Z_)] + g_ are neglected sin 80 in polynomial expressions. [Se] D ---x_(Mqz_-._) -MuX _ +Mqx_z_ +g[%z_+M_(_-z_ oo_eo+Wo(M_z_ -._z_) + g(Mw-%X_)sin eo E = g(%Z* - MuZw)oOS eo+ g(MuXw - _,X_),i,, eo 2) Numerators N_ = Ass2 + Bes + C8 = %_ + %(, - %) B0 = xs[_z_+ ._(, -%)]÷%(_- %x_)-%[m.+×*!_ -%)] ce ="xs(%,,z _ -M_z_)+zs(M_x _. %,x*)+%(ZwX _ - x,z*) I_E = IA u = X5(I Au S3 + Bus2 +Cus +D u - Z.) W Bu = -_[Mq(, - z_)+ z_+ _] + %x_ - Wo[%% + _o('- %)] + Wo(Zw%-MJ_) + gX8% sineo D u = g(ZwM 5 - MwZs)cos N_ Aw= = eo + g(XsM w - MSXw)Sin 80 Aw s3 + Bw s2 + CwS + Dw Z5 B_= -%(Mq+ xu)+ UoM 5 + xs_ Cw = X_(ZsMq- UoM_) + Wo(ZsM u - _Z_) D w = g(Zs_ u - %Z_)cos H-747 eo + gMsX _ sin C-2 - gM 5 sin eO+ @o- XSM_g sin X5(M_U o - Z_Mq) eO N_ : A_s3 + B_s2 + Cis + Di A£ = - cos eoAw+ B_ = - cos eoBw + sin eoB u + (U O cos e O + W O sin eo)A e O_ = - cos @oCw + sin @oCu + (U O cos @o + Wo sin eo)B @ D_ = - cos @oDw + sin @oDu + (U O cos @o + sin @o)C@ sin OoAu Wo N_Z--Aa_s 4 + Ba[_3 +C_[s _+ D_ls + Ea z' A_ = A_ - ixAe Ba_ = Bw - ixB e - UoA @ Ca_ = Cw - ixC 8 - UoB 8 + Da_ " = D w Ea_ To 2. obtain = + az, - UoC @ + g sin let g sin g sin 8oB @ + g cos eo @oA9 @oC@ ix = O. Lateral a. Equations Wos Uos--g sin t eo- s-Y v Y5 a Y5 r VToS VT o ! P V -b s(s-_) --Lr s ! ! L5 a L5 r ! t Ia] r ! r s--N r v = VToO = _p_ +---r s s sv + Uor ay + lXlat N5 a N5 r -- WoP-- g(cos ! ] cos tan 8o ay = r eo s C-3 sr -- izS p 8o) _ b. Transfer Functions r N_Sr m 5a a = Denc_Linator, etc. m 5r Alat 4 I) _. Alat + bs 3 + Lhlat = as cs 2 +ds+e I b - -CY + + Nr) Uo C - WoL_ N_ + _(Yv + N_) - NSL_+ YvN_ VT o d VT o U° VT o L_N_) (N_- L_oNr)---_- + Yv(N_L_- (_ cos sin 80] e o + N_ VT o W o v% = _ VT o 2) [(_N_-- 5 (5 a N_L_) or 5r) = % = C0 = -Y_[_ + N_] Y_ (_N_ Wo + _ VTo D_ = _VT° (N_L_ (N_ = - L_) A_s 3 + B_s 2 + C_s , Uo Wo --N 5+--L VT o VT o "'_'_ -- _pLr/ _ __----g + L_ VTo cos , , , , (NsL r -- LSNr) - e O- Numerators N66 % cos L_N_) cos , 5 eo + , g + N5 _ T o (N_- sin e 0 +_9_gVT ° (N_L_ C-4 + D6 L_N_) U° --VT ° 8o -- N_) sin 80 sin e o) N_5 = Aps3 + Bps2 + Cps + Dp ! Ap = L5 = LS(Nr + Yv) + NSLr VT o Dp = -- g VT (L_ -- N_) sin eo O N_ = Ar s3 + Br s2 + Crs + Dr f Ar = N8 . _, f ! f Br = Y_N_+ n_Np-Ns(Y _ + $) Wo Cr = Y_(I%N_- N_%)- L_YvN _ + N_Yv% +VT o Dr -----g (L_N%-NgL%)ooseo VTo N_ A¢ = Ap + A r tan 8o Be = Bp + tan 8o C¢ = Cp + C r tan eo Br = Acs 2 + C-5 Bcs + C (LgN%--NgL%) _a' AT +_4 ___ ay ! H-747 _4s4+_2 +CayS2 +_ VToA_ + lxlatAr- lzAp ay = VToB _ + UoA r - WoA p + iXlatBr c_ = VToC _ + UoB r- WoB p- g D_ = VTD + UoC r- WoC p- g cos E_ = UoD r- To obtain __ _ ay, _ let WoD p- lxlat g cos eoC ¢ = i z = 0. C-6 cos - 8oA¢ lzB p + lxlatC r - eoB ¢ + iXlatD r - izC p izD p k L- [=. =_ -- _-_. .... :7 ..... _ _ _ __ " ..... . • - _ . p - Z -- -Lg'. 3 .... _ .-
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