Available information on weight and inertia, aerodynamic derivatives, control characteristics, and stability augmentation systems is documented

Size: px
Start display at page:

Download "Available information on weight and inertia, aerodynamic derivatives, control characteristics, and stability augmentation systems is documented"

Transcription

1

2 1. Reprt N. 2. Gvernment Accessin N. NASA CR Title and Subtitle ACHAFT tan)lng QUALTES DATA 3. Recipient's Catalg N. 5.Reprt Date l)ecemer Perfrming rganizatin Cde 7. Authr(s) Rbert K. tleffcy and Wayne F. Jewell 8. Perfrming rganizatin Reprt N. Technical Reprt Wrk Unit N. 9. Perfrming rganizatin Name and Address Systems Technlgy, nc. ttawthmme, Califnia Cntract r Grant N. NAS Type f Reprt and Perid Cvered 12. Spnsring Agency Name and Address Natinal Aernautics m(t Space A(lninistratin Washingtn, ).C Cntractr Reprt 14. Spnsring Agency Cde 15. Supplementary Ntes 16. Abstract Available infrmatin n weight and inertia, aerdynamic derivatives, cntrl characteristics, and stability augmentatin systems is dcumented fr 1 representative cntemprary airplanes. Data surces are given fr each airplane. Flight envelpes are presented and dimensinal derivativcs, transfer functins fr cntrl inputs, and several selected handling qualities parameters have been cmputed and are tabulated fr 1 different flight cnditins including the pwer apprach cnfiguratin. The airplanes dcumented are the NT-a3A, F-14A, F-4C, X-15, HL-1, Jetstar, CV-88M, B-747, C-5A, andxb-7a. 17. Key Wrds (Suggested by Authr(s)) 18. Distributin Statement llandling qualities, transfer functins, stability derivatives, airplanes, cntrl systems Unclassified- Unlimited 19. Security Classif. (f this reprt} 2. Security Classif. (f this page) 21. N. f Pages 22. Price* Unclassified Unclassified 343 $6. ' Fr sale by the Natinal Technical nfrmatin Service, Springfield, Virginia 22151

3 TABZ F CTERTS. NTRDUCTN. ii. NT-33A. F- A... V. F-4C v. x V. HL- 137 V. LCKHEED JETSTAR viii. CNVAR 88M D{. BENG 747 x. C-A X. XB-7A 273 APPENDX A. AXS SYSTEMS, SYMBLS, CMPUTER MNEMNCS, AND DERVATVE DEFNTNS.... A- APPENDX B. TRANSFRMATN F STABLTY AXS DERVATVES T BDY AXS B- APPENDX C. EQUATNS F MTN AND TRANSFER FUNCTNS... C- iii

4

5 SECTN NTRDUCTN The purpse f this dcument is t prvide handling qualities investigatrs with readily usable data n several representative cntemprary aircraft. ncluded are thse data required t btain transfer functins relating the aircraft's respnse t cntrl inputs. An analytical descriptin f the aircraft's stability augmentr is als given. Fr thse aircraft fr which cmplete infrmatin was available, the fllwing summarizes the cntents and presentatin: 7. Flight cnditins fr which cmputatins are made including: a. Cnfigtuatins (e.g., fuel lad flaps, gear, etc.) b. Mach/altitude cmbinatins 2. General arrangement 3- Cntrl system descriptin 4. Stability augmentatin descriptin 5- Tabulatins and/r plts f nn-dimensinal stability derivatives fr trimmed flight 6- Dimensinal, mass, and flight cnditin parameters 7- Dimensinal stability derivatives 8. Transfer functins fr cntrl inputs 9" Selectedandling qualities parameters 1. Data surces A page number crss index is presented in Table -1. The intentin has been t make this reprt cmpletely self-cnsistent insfar as symbls, nmenclature, definitins, etc. The system used is described in three appendices. Appendix A cvers axis systems, symbls and ntatin, and definitins f nndimensinal and dimensinal stability derivatives. Appendix B gives the axis system transfrmatins fr the derivatives. Appendix C includes the aircraft equatins f mtin and transfer functins used herein.

6 X g i i < aa '''"...

7 The aircraft cnsidered in this reprt span a wide range f sizes, speeds, and uses. n each case transfer functins and handling qualities parameters were cmputed fr flight cnditins which were selected t cver the flight regimes f interest. A nminal cnfiguratin (generally cruise) was picked fr all up and away flight cnditins. Fr this nminal cnfiguratin, plts f trimmed nn-dimensinal aerdynamic frce and mment cefficients are presented. Als, in mst cases, a pwer apprach case is presented alng with a tabulatin f aerdynamic cefficients. The cefficients are based n rigid wind tunnel data 3 estimated flexible data r flight test results, depending upn availability. This is indicated by the wrds "rigid, " "flexible," and "flight" n each aer data plt. Als, the axis system is indicated by "stability" fr a bdy-fixed stability axis system r 'bdy" fr a bdy-fixed system aligned with the F.R.L. (Further clarificatin f axis systems used is given in Appendix A.) Descriptins f cntrl systems and stability augmentatin systems are given alng with transfer functins. Where a lngitudinal cntrl system has a significant effect n the equatins f mtin (as with a bbweight) the stick-free transfer functins and handling qualities are given. Transfer functins are always given fr bdy axis mtin quantities. Handling qualities parameters are als given in the bdy axis. All acceleratin transfer functins (a z and 4) are fr the pilt's psitin. Thrust transfer functins d nt include any engine respnse characteristics. A substantial prtin f this reprt is in the frm f cmputer printut. The mnemnics used in this printut are defined in Appendix A. The handling qualities parameters given in this reprt represent nly a small fractin f thse develped ver the years. The majrity presented here are used in past and present versins f ML-F Althugh nly SAS-ff values are shwn, the definitins given in Appendix A are general and culd be used in cnjunctin with the HAS-n transfer functins t yield SAS-n handling qualities parameters. While cmplete cverage f each aircraft including nly the "latest" and 'est" data wuld be desirable, the majr criterin used was that the data be accessible t the authr. This is why nly islated flight cnditins are given fr sme aircraft, and als why, as thse peple mre intimately familiar 3

8 with each particular aircraft will recgnize, the data presented may represent an early estimate in the design prcess and perhaps the "nminal cnfiguratin" is ne which never left the drawing bard. The data have been reviewed and, althugh nt all thse presented indicate unquestinable trends, thse data knwn t be based n nly early "guesstimates" r shwing unreasnable trends have been deleted. n smecases data were estimated by the authr. As t hw well the data can be expected t match the flying aircraft, it is assumedthat thse fr whmthis dcument is intended knwwell the difficulties f btaining derivatives frm flight test data. Every attempt has been made t insure reliable translatin, interpretatin, and transcriptin f the data frm their surce dcuments. The manufacturers f the aircraft described herein can nt be held accuntable fr the infrmatin presented, nr wuld they be bund t cncur in any cnclusins with respect t their aircraft which might be derived frm its use. 4

9

10 -33A ACXSXmm "The NT-33A variable stability airplane (Serial N ) is an extensively mdified T-33 jet trainer. The elevatr, ailern and rudder cntrls in the frnt cckpit are discnnected frm their respective cntrl surfaces and have been cnnected t separate servmechanisms that make up an 'artificial feel' system. n additin, the elevatr, ailern and rudder cntrl surfaces have been cnnected t individual servs which can be driven by a number f different inputs. These servs receive their electrical inputs frm the artificial feel system (pilt's cmmands, psitin r frce), attitude and rate gyrs, accelermeters, dynamic pressure, vane and prbe. This arrangement, thrugh a respnse-feedback system, allws the nrmal T-33 derivatives t be augmented t the extent that the handling qualities f many existing airplanes, future airplanes r hypthetical research cnfiguratins, can be simulated. The riginal T-33 nse sectin has been replaced with the larger nse f an F-94 t prvide the vlume required fr the electrnic cmpnents f the respnse-feedback system and the recrding equipment."* Transfer functins are given fr nly the primary surfaces and engine thrust althugh the NT-33A als has ther cntrl surfaces and a range f cntrl crssfeed and feedback cmbinatins. Aerdynamic data, fr the mst part, was taken frm AFFDL-TR Hwever, lngitudinal data fr the high lift cnfiguratin was btained frm LAL 1 27 andmach number derivatives frm NACA-RM

11 .r- 4.r- r- 1) (1) m CD r-4 P-,.- ::".r r / t-.-.1 q bid.,rl,-4 q - Ca E,.r 4 d c) 4 i r/l.r- -,-4.r-4,'d : 4 # Q.,,-.4,} d,,,4..},rl d (\J ( c+d c q Ckl : f i i -P E,,--,i f2,-,88,- t C CL, C}.1 tk.l r -J r"-t -P 42 b[ [- 4 tl 'd \D [:: - H ll % q q cq r4,- b4] ) b. ch lc4 4 4,-- kc r4 p C'. c [. Cd d bd H > r- htg h N N N

12 .J 4. d " t qj -'4 N b.--i 8

13 NT-33A PTCH AXS Variable Feel nput Variable Stability nput FST(b)..26 s z +.89s ]ST(in) ----].3 -. Be(rd) RLL AXS Variable Variable Feel Stability nput nput FLAT (ib) ST,n a(rad) st YAW AXS Variable Feel nput Variable Stability nput FpED(b) 78 PED(in) = r(rad) Feel system parameter values shwn crrespnd t the "Frnt Seat Engage" mde (nrmal NT-33) Figure NT-33A Cntrl System 9

14 TABLE 11- Pwerach Nn-Dimensinal Stability Derivatives h = sea level VT = 228 ft/sec = 139 kt = 2.2 Lngitudinal Lateral-Directinal ( Stability Axis ) cl =.813 cd =.139 CLm = 5.22/rad CD =.94/rad % = --.41/rad Cmq : -m/raa : CL5e =.34/rad Cm6e = -.89/rad cy = -.72/r Cn =.49/rad C = /rad Cp = -.7/rad Cp = -.45/rad Cr =.2/rad Cnr = --.16/rad Cn5 a = --.9/rad C5 a =.14/rad CYSr =.17/rad Cnsr = -.73/rad C5 r = -.2/rad 1

15 ' SL NT-33A Cl w B... 2, ft 137 b ,ft.263 Rigid (deg) 1 n 8 D 6 4- D \ Z- 11

16 L r- rj J,: Q, F-r'- z (%1 -- C) d.. (..).4-- W- Jc J W.-- f..) x.lj w. j.-., :l (.) - L -- L -- 12

17 m 6- CL a (red - ) NT-33A 137 b Rigid SL... 2,ft , ft Mach 1.2 CDa (rad "l).8 l l %.4.2,4.6.8 Mach 13

18 Mach ( / (rad -i) SL... 2,ft --"-- 4,ft NT-33A 137 b.263 Rigid Mach Cm& Cmd, -4 Cmq (rd") Cmq

19 NT-33A CL M b.263 F.," Rigid " i.4 Mach.6 -. SL... 2,ft ,ft.3- CD M Mach.8 Mch Crn M

20 .4 CL8 e (rd "l ).2 NT-33A Rigid Mach Mch Cm e (rd -j ) ' 1 ;

21 Mach Cy (rad-i) SL... 2,ft ,ft NT-33A 137 b Stability Rigid Axes.2 Cn/ (rad -i ).2.4 Mach f.." / 17

22 Mach t l -.2 c.tp -.4 (rd ") m6 Ba - - SL... 2,ft --- "-"- 4, ft NT-S3A 1371b Stability Rigid Axis.4 Cnp (rd "l) -.4 4r,f -,8

23 SL NT-33A 2, ft 137 b ,ft Stability Axis Rigid.3- C.r Cn r (rad "l).2 -- \',, \. %%% " """ C.r Mach '.1 Cn r t9

24 .2 C}s a (rad "l ) ' SL... 2, ft 4,ft NT-33A 137 b Stability Rigid Axis Mach.1 Cn8 Mach (rd -j ) S is sum f bth right and left ailern deflectins 2

25 Cy r (rd "l ).? Mach Mach Cn8 r (rad") -.8.4, SL m *== ---?,ft ,ft NT-33A 137 b Stability Rigid Axis C,sr (rad "l ).2 i Mach 21

26 e <1, r,,l '- p i r+..4 j.4 1%1 <. C. - " - ' J +,P <' "41", 1%1 P 3 ell. eg ' + ; " " - + +,, r %j t+ P".. j,- (; l" t <"X G ; + 22

27 * " N l,,,ti " " T ; = " " rj H = 4" c u..,,..4. N 3 bl 4 i.i N " u " " " " ", LJ "," J" C).i.) t) -,-4 -- ff'l i " " " H A [/] -,- " lju i",4.u.t U L( 1 -- g... g) r w #q v ",,,1" - n, r'm uj..j -1" -.1- ur, N r'j,- "-,D * $ '. r l,-4,4) d u' 'd".,t ' h- -t c ( " "- " "-' N C ' r C " N c a l l " * 23

28 er, m,, e e,..,4 N fel.-, N f, C e..-, v. r. i 1" e( i N )N u <D rr,- ww. Pr'i eft/.n '.4" e - u f- ".r.-4 c J T. i ee.,--,i - N f phi. f,..-." '4" e rrl '$..-4c) " u u e, w njf,,.4p 1 fmf, ule U ",lr e- N..-,-4 f.r. r" e...4 r e ).--, lir u' "'.1" " i - D eje e - v Z 24

29 v Dur e.a f... v r- i-,4"., f" N " ', D.,t, C.N w. v (Du% ra- N,. 4- m-,.-*. UJ (N ",.T r.j 4 {. D. ' n.-:r 1.1% u,% uet.y L) U% H ---- E4 -P." v) r-- (,9 LrA H CH 9 r- r.9. erl kr%.-.-.i.,- r.2.e,j '.,4" (D i'- u,." re%,,t ur r--.(%1 uj -, u. c ".T -,T ' ",- ern UJ "4" p-p- r, D r r.,,-.4 ", eel c % ('4 (DT (D " ",.r> p%,.-n p. Z Z Z 2

30 v ur.-, P F.d (%1. t' m Q c N uj x p,,,,-4 m N * t i '-4 -J,m cn ' (% f. eel,- i* L * 1 26

31 r--,,1" c r-- r r L,-4 L Q " (..-4,..-4 (7' e c c '--,),," u' ) u - E H C ". "," "-",,," "- C c '-'4 -- el C'q -,, r H H,--1 C J cq # * r.* M t' c -4 + i.-1 N,--4 -" 27

32 e v n,',d ", C,,,-i r " " " ec} e'% '4, P" P.- er.% -.,D e4 N e,.. P.. c) r e.,4 P,- erl a, N 4,'-4 Nrr el1,- r, f, ' U ",,t t4 era4 u%, eq ',, ', 4" el%j D. u NU N P" er,,4",,,=4,,-.4,..,d",),, -*.-4, "'4,...4,,.,.., e-4 i,-j,,,.-4 ".J,-4,.4,.4 WD nwd,, Ml,e, (,q, r.- ;.i,-.4 /",('1,r,,,,.f,,,, ew p,- %1', U,U =ju u t,,"l CM h-,,..4 ee%;,,,--4 rl r-. e(,,...4 N.-e t H J " " ee. e,,-4. U f W 13 r " '4". Q,.,4 "" f%l,...4 ep,. e. N wwv v Z 5 28

33 4,, '4", e D P +..- N 4,-+ ) r-- e (,n (t "%U',n r " N,N, t.%tp...4 4" a) u,,,.-4 r C 4- ",, N ', L m'j,,,, i" T B + c,,.+- u%m-..-+( -% ( w- ", N.;i-f.,. 4"-4 i + 4.,,,-+ u'%,...+ 4" '. < H c,,t -,t c, u,% N C) + ic,.,-#,,, N tn j -1" -4" N.),4 u%. e4 N.-+ J ",4 ('4 ",, N@ g,,,, 2 ww z 7 Z

34 u, c - *, U' C u t e t - u **, u a -, " -J N t -- v" p.. - u r um * r *..t 41 P c -- (]Q 4 a c + r p e 1 1 l r - v + E t'-- r'.. -,t" - -.1" -, t-... u ",-, < H " * * + A.- J L+r',, c,.,.,+ P'--,' u",.-4 l L ('%1 +,+ %J t'%l + LU - <++. " --, <'%1,-,+, r,,.,l r, j,. 3

35 NT-33A DATA SURCES Hall, G. Warren, and Rnald W. Huber, System Descriptin and Perfrmance Data fr the USAF/CAL Variable Stability T-33 Airplane, Air Frce Flight' Dnsmics Labratry Rept. N. AFFDL TR-7-71, Aug. 197 Tests f a /5 Scale Wind Tunnel Mdel f the TP-8C Trainer, Lckheed Aerdynamics Labratry Rept. N. LAL 127, Jan. 23, 1948 Cleary, Jseph W., and Lyle J. Gray, High Speed Wind-Tunnel Tests f a Mdel Pursuit Airplane and Crrelatin with Flight-Test Results, NACA-RM-7116,.Jan. 21, 1948 Statler, rving C., et al, The Develpment and Evaluatin f the CAL/Air Frce Dyuamic Wind Tunnel Testing System Part l-- Descriptin and Dynamic Tests f an F-8 Mdel, A''DL-TR , Feb Flight Manual USAF Series T-33A Aircraft, T.. T-33A-. 31

36 SECTN F-4A 32

37 F- 14A BACKGRD'AD The F-4A is a single place lightweight supersnic air superirity fighter pwered by a single turbjet engine with afterburner. The wing has a full span leading edge flap. Trailing edge flaps have a blwing-type bundary layer cntrl system. Cntrl is prvided by cnventinal ailerns and rudder and an all-mvable stabilizer. Pitch rll and yaw dampers are incrprated hwever their effect is nt shwn here. Pitch and rll cntrls are fully irreversible while the yaw cntrl is a cable-actuated rudder withut bst. A bbweight is used in the lngitudinal feel system. ts psitin is assumed t be at the pilt's lcatin. The primary surce f data was LR Drag infrmatin was btained frm LR The nminal cnfiguratin used here is the cmbat lading fr the F-]4A based n actual weight and balance data. The PA cnfiguratin is a typical lading at flight manual apprach speeds. 33

38 \,-.H c),-t.,-4 J p r-.,r-- % ry q q d rl 1 i/] r) r--,--t f---4 H H u/ -e- -rq (1) -,- ii,rl. 4.,-t -r-t -r-t d 4 4 "d b..,- ii1.r- 111 c) J J - c -p 4-> lq 4.> + r i rh i r- ", b. b :d,--,-.h.rt 3 b.r-, ksd - h c P, 4. r-- 4 '-- U rl H 1 r.d 3 f Cb -4 H H 34

39 wu D Z m r-i c & H. q- rj). iu > C- 35

40 F-14A PTCH AXS 8SsAs(rad) FST(b) G s(rad) i F z B 8s(deg) -2 - B az assumed t be at pilt lcatin /in) RLL AXS 8aSAs(rad) F LAT -- ST (b) --i 2.7 i 2,,4 5" 8a (rd) YAW AXS FpED(b) KDR SpED(in) r(rad) 2. K ["/'b/in 1.,.4.8 Mac h Figure F-4A Cntrl System 36

41 Pwer Apprach Nn-Dimensinal Stability Derivatives h = sea level VT = 287 ft/sec = 17 kt = 2"3 s = Lngitudinal Lateral-Directinal (Stability Axis ) CL =.735 % =.263 CL= = 3.44/tad CDa =.45/rad Cm = -.6/ra Cma = --.6/rad Cmq = ->.8/ra Cyp = -1.17/rad cn6 =.5/r C2p = /tad Cp = /tad Cnp = --.14/rad Cr =.26/rad Cn r = --.7/rad Cgs =.68/tad Cms = --1.4g/rad Cnsa =.2/rad C 5a =.39/rad Cyr =.2S/ra CSr :.45/rad C r = --.16/rad CYd = 325/rad CnSd = --.25/tad Cg5 d = -.44/rad 37

42 1 G) 88

43 m. LL j- LLD J q Q J d c.l(

44 . D J. t- / q G --LD u f.j L Q 4

45 q CJ q..d E N J:: JE c E) q,.. q-- q-" "- 8 'll 'ili,. =ll E " L.. J 1" " E E L r.j,,.. i i,1 41

46 - N N. --cl " v) --,--: " 42

47 J q m r)i ii-) i cl) {D i J D (- cj E - D-- (.i{) -- m'- - u,t J -- J, i a L u) (w "T3 m i/1 i J.. L)

48 d B - j,, E. q m - -- i m i ' / - t, -, / t, i N i m., -.. m u u 8(. 1, N N q.. N T " '" L V 44

49 q N 3'( T,...- t,- u q-- r- U # / ',, " a').) Q.-- L- j lb. 45

50 q..l J# i i /,. CJ d -- u t- =E <.Q i,,re >,.-- ".'2 -:,, LL U') 'i g lb. w (..) lb. "-: m,. (3. i i 46

51 T Q c t- C t- t--.c,. 4-- FQ Q if)if) /)re)if) / t- CD D q-.q cd, ' gr / # --. : u e'- U x c m i t, C.). 47

52 m.. J J. r- (J =S --a J J -- l,,"..,.. -;- >" r,.- c " c < 48

53 d C, P,-,, r,.,c) e C, " q - - u X,d c l d.-., -??? lu q H H 'x,-. u', C, " " " r-,.,.-,,t, t- e ',-4 l,-a H C J ' :,-a " ",1 ", "??, -??? ut,, G G u,,,, fd LL.. "t" :> :> :: : 49

54 p..., uh C LF,,t '.- " c l l" - " " ' P "" 'i e l " " '-. 4".-4 TM " C) l " f" '-,",lj " J" AJ e, -.- e - cq "- " C i " ' ",t , ', t" -," gj " " " " T fll - 4) m C m m - N t. C ' " P'-,D " 7 ' 7 ' "' u ' " "

55 (D u",-4 -Z `, 4. e,, ` 4" f-, *".- c, 1 *, *f4. '4 f*-- 7,. t'4,,-,4 tkl 1 T 4) H ` * * c. i',- X) `,.-' * *u'.s * * r, j, * J *,.- et 7,.-4 * (;" " v" t.,...4 u,% ",,-.4 u,% c i-- *',?.T,- [-- r.),1" *4",, 4",-,,,u,%,4-,-4, C-- * b- ` u i'xl ` eel ` -.-*,,3 H -7, 4. *-4 `.4- ` r-- (xj.- u-%,4, ` r,- i ", H `.e4 t-- u% -4" 43 e4*., e,-4,..* i -<9 4. H q- pll m,,,--,* C -,t,'- * %J ` 1, 4. t-- i- P.,-,,. * *i m- t-- ` m-e4 q"..r c..4 fl,--- rn,-,-4 u3l r.- c - 4 '4" * ",,1",;.,' r'--.,--*4" 4. Un `.. e4 -,t U' rl r.-- cu,-i., ".,... xl u Aw,'-J A. W<WW Z 51

56 L," -. Cs -'4"? cr.4-,4- -." 4" - "- G CC CC e ad..4" e4w f'--, 1:,,.4.- ku<t CJ, '1 G ",F, :-4 e' v r 4 4 Ī 4".-e CC w,l-., LU an e4 ut% (7. ""i" N u% ",4" m 4" w u% 4,- '4"..,7 H u gg # tu t " r '% r'% u-,.-i 4-,,,C " u.t. R u u u u r,ll um u c2. c. r -. l..., a u', u% T,-4.- i'd " D.%1 b'. -3 (9 m-".u"..? t w - u'% N,4 t--,,. 4 u.j ",' - -r -r i.,t rl ',T "" Lu uj J \--f <'. ',,4 52

57 + br c,," mjr4 *.-,t" S hn.-.u"% l'4,1"4" '41"4 e,.- e,,ie,l,4,.-*(xj," *%J i rn, e4 'X* 4-."%,-', *., u'% ' t-.- (..) c.),4"a i,...e,,.--.i ad '.. ", i l ',4".-4,,.-' ' :xj n t-.. c L*'%,D. e H, ".4",4"-.1". ca -, t'- ",' w --, C) ( t--. (D ', *, u,% u',, t'.-.4 *..,.-4,,, r4 "" t-.i - --','4 H ; a.-. (x) c [*4 M rj J n.- e4, *u% -.tu * -4.) ;...-'--4.,-4 'N?.?,.C.- *Q'. t * u,. a r, :W t'- " e4 -e,-.,, a u'%, r,.-,a",.-s%,..4. 4" C'4m* C'4..-e"..-4 ' exl u-* *.Jt. U' 4".,- r,- e.4,,.. U-% (D. m.. a e " -- ", a 4" %1...e C3v #- u. :D,,% z :)' 7 Z 53

58 .e CZ um Cl::) "4",? u] (x' f'- "4-4" (% U% C, GC C, CJ*, -".-C.L.,,..-,N l. e,',,9 "- Q c2,.( ',.- c. -u' LL, 'M -, c('l4" b t" w,l - Um <'.,.td, r- i5 H,, LJ"- i (f,..-.,,'f,l -..4r 4" H L bfl [/3 H. CQ uu e*. L,---, gn f LU "11i',i l.u : 4 U "P g2;. i'--. ( i a.-i L] r,j T bj (.J nl l'- r,,l i ijj cu.r c." c? r..lu'.,.&,] i. l-.i.,. t " u pr, P. " " uj LP (:,, {Jc.-i..-4 w 'JJ 4".? cq..l,,t b- -u 4",.-',.-. r.t - i 54

59 Lr, r G r " i' rl ' Ct D.- rq N.-4 rq 1 H E- v -.t H uj g. %t ' T"- v N,,-. C,.--,--4 " C 4t,',.t- u' G.,L 55

60 ,"4 U -- h" N -- " 4 "--8 C ;-- C 3 " n 3 3. j n l," Q P- " N -, 3 h,-...- N N",-4, d u 56

61 + a.-e CY a - e.- --q.-, er * a ad * U',-4 ",-., D,... t.- i e ej i ', if- t " *.-4-4 * J C.'-4 e."4 1".4- r,. * c..4" tu, t-- u', '*,-' e *,.n a. e - " e,," * -e r. " - e C eee l ',,'l- a.,,,,t,,". u", ",t iu i t j, a ee j el%l.... N * *N,:r a, ZZ w Z Z 57

62 .F u' ().'n Q,..,, ',r.,- r,n,).-- 1', l. CP.-. wd, c l N N"@. " -:r.,f,4" 1 (xl N N,, e..,, u1..i.- "" ;..-.i,,.-4 N., ", (.-i i. ",h-.wd,, Lira er -4 (w i,g Ne. w,.- NWD(.-i " ( i le -,Ne; tn lu ".., e,,- erlc}.-,, N r-. r,, t l" r f, f, rl.. 3. ;-., rxl,d bk n,?,.- i" i'irm N (', P- P",.-4. i,,-a.,.- J r ell ii -a.(x;. ;',.',gr:, "i. " i F.-.,l"(.J w r,,,, r'- t{%,,",l),- e,l,-a, g w N.) N ZZ Z w 58

63 m., e -,, m r-..t.,, - -,,,,,4, ", -., N n,l,-,,,.4-, U',4" -,1" ", ] 1 t u u', N ",-,- m '.-..', e,.-,., " 3- H CH D3 H Pq - ',,- r- q n,i ND h...,- ',- r'- r-.. fm i,,,, Ll UJ. U') v rf % j. 59

64 F- 14A DATA SURCES Stabi? [ty and Cntrl and Handling Qualities F-4A, Lckheed Rept. N. LR 1794, 12 Dec Andrews, William H., and Herman A. Rediess, Flight-Determined Stability and Cntrl Derivatives f a Supersnic Airplane with a Lw Aspect-Rati Unswept Wing and a Tee-Tail, NASA Mem H, Ar. '1959 Perfrmance t F-4D, Lckheed Rept. N. LR-12873, May 1958 Flight Manualt F-4A and F-4B USAF Series Aircraft, T.. F-4A-, 15 Dec Technica Manual t Flight Cntrls t USAF Series F-4A and F-4C Aircraft, T.. 1F-14A-2-8, 15 Mar

65 SECTN V F-4C 61

66 F-C BACDRUND The F-4C is an Air Frce tactical fighter whse primary missin is all-weather air-t-air missile cmbat. Lateral cntrl is achieved by ailerns in cmbinatin with spilers n a swept wing. A swept stabilatr prvides lngitudinal stability and cntrl. Directinal stability and cntrl is accmplished thrugh a cnventinal fin-rudder cmbinatin. Landing speed is reduced by full span leading edge flaps and inbard plain trailing edge flaps in cnjunctin with blwing-type bundary layer cntrl (BLC). Bundary layer cntrl is autmatically induced when full flap deflectin ccurs. Features distinguishing the USAF F-4C frm its Navy cunterpart, the F-4B, are: Lack f drped ailerns with flaps dwn resulting in higher landing speeds. Dual flight cntrls resulting in slightly increased cntrl system inertia. Wing bumps t huse larger main gear wheels resulting in a slight drag increase. Data included here was btained primarily frm MAC Reprt N Special emphasis is placed n the lngitudinal cntrl system because f its relative cmplexity when cmpared t ther aircraft. Figure V-4 has been addqd t help illustrate this system. Als, care has been taken t retain sm% f the cntrl system nmenclaure used by the manufacturer, e.g., qb and PBF (see Fig. V-5). The Stability Augmentatin blck diagrams are shwn in Fig. V-7. The rll SAS described is nt included in lateral directinal SAS n transfer functins since it is faded ut with the lateral cntrl stick ut f neutral psitin. 62

67 @ p :d q-i,-- (9 <.9 (9 m.p.,q,m tl i-.-] [.., -i (i;, q rh qd rs].rd 4g.r C} d d b4) r-- > H (b.r4 68

68 E,- r H.,- 4-- q.- r-- 1"..Q U 64

69 PTCH AXS FST(b -.369s s Feel System F-4C SsAs (rad) Gearing / Actuatr +.57qBPBF -*.569qePsF,:1 18sT(in) '-- - '+'1 8s(rad) -- See Fig and fr feel system details Bbweight az ts---- ) f JtB= 39.3 ft RLL AXS Feel Spring Gearing / 8sAs (rad) ;T,, - 2"961 =1 i- Spiler Sa(rad) AR Gain - 8sp( ra d ) C38r {-.46 SAS FF = -.69 SAS N CLEAN,/ PA AR r -- -:1 <ram(rd) YAW AXS 8rARl(rad) 3rsAs (rad) \ / Rudder Feel Spring Gearing \ / Flexure..j' SPED(i n)..j " '- - - l""txl - 8r(rad) K mr G air -- See Fig V<235KAS 36.61b/in -11.5deg/in V>22KAS 8.51b/in -6.5deg/in Figure V-3. F-hC Cntrl System 65

70 .c S..Q ) ' Er C t 66,; v C,.i,.,.,,i,.-..Q rn -- 'N-- w D C.J C E t "t C t "- LL " {). c. - D -.t- -- "Xc) D,-4 C L -4.,.-4

71 .6 qb q -4C / ,ft 389:)4 b... 55,ft Mach J. m PBF 1.- (ft z) 8 L Mach 6k h (ft) 4k 2k Viscus Dmper n Stp b= "l//f/[ Viscus Damper ff Stp 3.3 b/in/sec SL" Mach Figure V-5. F-4C Feel System }arameters 6?

72 i N. -, : //,,,/..c rh N :E. //7i / q L H -r- ['ll= =111 l. 4 X,. 68

73 F-4C PTCH SAS E}(rad/sec) 1.15s - s+l SsAs(rad) RLL SAS PG(rad/sec) asAs(rad) P6 = P (Rll rate gyr assumed aligned with FRL) Nte." Rll GAS faded ut with lateral cntrl ut f neutral YAW SAS rg (radlsec),s 1 S+'5 rsas (rad) ay ' (ftlsecz) rg = r cs(-.5 ) +p sin (-.5 ) ay = ay "-.391b Yaw rate gyr inclined 1.5 belw FRL and lateral accelermeter at ES. 198.and W.L.23. Figure V- 7. F-4C Stability Augmentatin 69

74 TABLE V- F-C Pwer Arach Nn-Dimensinal 8tability Derivatives h = sea level VT = 23 ft/sec = 136 kt % = 11.7 s = -9.1 Lngitudinal Lateral-Directinal (Stability Axis ) CL =.915 CD =.242 Cy6 : /rad Cnl3 :.199/rad CL : 2.8/rad C26 = -.156/rad CD =.555/rad C p = /rad Cm -.98/rad Cnp = -.13/rad Cm& -.95/rad Cr =.2/rad Cmq = -2./rad Cnr = -.32/rad CL5 s =.24/rad C-mss = /tad CD5 s = --.14/rad CYSa = /rad] Cnsa = --.41/rad =. 7/r aj Spiler Effects ncluded CYSr =.124/rad Cnsr = --.72/rad C5 r = --.9/rad 7

75 d.q 1" U mm r t%l / cm J J G -M" / # i i % lil " ii J ) / / / k / (D D -- J L [,J m m e,j J c 1 i g 71

76 ?2

77 - ed t, / - ('U a,. 1 tim 73

78 .) c.,-. T " E a " "U T E E "/4

79 . J -c,l N N l 1 i: e,l J. r J -- z J -- E -= N J J" ' 75

80 .Q UU 44--'4-- q ' 1' J " " J E U 7G

81 q.i m 1 x, m'-t. c-. (9 4-" 4.-- ' 1 v <..),.. 77

82 (M J. J G. -- l s" J r C,- c,., q q --- q q Q. Q, 1 (, i.. 78

83 K 1.. " i i " i,

84 d.. T " >' 2 U 1 q q q q / -- q -- q..-.. ' c 8

85 d J i /, - \..C % % -%. N. 5. '- 81

86 c rn Lr ' C " "1" 2,n, /, r- " ',, - u',,-" r, " n a i r,- " q r-,., " v, C' C.. " i 4 4- th H ". *, ',,,3 r, -,: c,.1" r. e,j f'--., n'l :,,:.,. rl --,. - C CJ P- t J D'- F-- c r cm c - - WD r r,j rq + r/l ff' " nj "-- (, 'M J l% (%1 i. u u > J 82

87 cu ur,., v C" C 43 xl,,t * ( 2 r t t it, t, " * " " ". t'- t- *- r-} -.1" r4 n e P- t " ' " " " -,, tl -., ' * * * " ' " " N,.t r-- i i , C "," "," ur - :),.-..-.,. F - C, rc H..- i. ", C ' ' ' " " e T it, H - -,-4 " * ' * " ' rj r - $, $ N c b- -1" N.n ' " " r--,. i " " ' 83

88 CD - b'% N '- C/, D r-4 C) C u C,, CC C "C N t? ND,, c,q ' C, (D (D e4 t fl,-4,. c, tx, T. )1" ", e,e 4" c ad - v,4",4" NN c N e D 7',e N,4" 4,'- ' - c N C e N'.N ' SN e 7" -- N " -4 -, H P,n c -) N e ".,,N,, N e C N, H n el'.- ee',n?' N 'm' "," ",- Z...NN., 4 " ' ee, e4,:,,t u.-, r,2,4" v -' NN N N N wuj Z w Z v Z 84

89 t./.-+ ip. f, +. + N,,1 c,- r,, C:, P--t C: " ', L" <1" C qc" ; + UJ T ffc) P "+T " LL + q,-, r i.. e. e,, it c,,# +-< "d u <'+ i?, ' ' W i- Pq T.L,-+ +-+, lj,--+ " C J c,,d.4,-4.--i lr (D ur t gr - xe? LJ <.-, "'7 4" M ". ;. r r2 Eq eg' A,l',d, T wad " +N UJ '+r+ E- N uj, ' N,(..+ * -,," t'+xt l C U m t 1-1.r- aa i,l,-i cl#,,",h 4 - -), rlg "" [ r..1,.-., < - < +. ( 'Xl e,1,c u i. ie u.l N,.,.i,-i, " n +am. p..4,,- 3us g " i ''", T i.. l " " N Q Z 85

90 ,j c G) u'x v,4 c f ''4-4 C),-. cj,.,.1 if. t,.; c9 r', r-,, r,'l,..,,, : r, < e,,t t er- v c. -,,t e. r..,n um, p-,-..i. t.,d.c rr'. *'.,, u", "d fxj *,e -.. t : -. q,,. l.m,,,/j ul,,lr l <r i *,,t" <r el p-, ' r f,cl N m g,1.,1", *,4" " A 86

91 D-,,JC - -./ -,,4r r; u,-4 - ) + ' ~? rc "," " f-4 f + -.t MD t - N.f,/... m c.,-.j ' + g, -.r Sg l M 8?

92 c.- u-, w p-t v b*, u',. 4 trs x'. era 1,.-t (%1 N.@ S. n, (%t 'Jp., 1", ; '. '% L,3,. u",,,,c', / C v u", * ~ e lel ' LU E', t fxl "-- f c a.. ",,,-a ".-n,. ' u. iu, r N d C.-4 t%l m J r -..4, -,T.4r.-.4-,...4t rm LU 'rc "," ('.,-a.- t'., *c. <,,.,,t -J,, / ",. t-- rq U' m c-..,,-q. ee i J u z. v Z 88

93 .4",4-.-t,rr C, "...,4.5.-,., ".. Cl,*r.,,-4- "4",,,..., 4" -,t " " N 11),--t " [... -,, * *11.. " N,e N,,1",4" -.c,a,j "'4" N ^NN N Z 89

94 c L N 4 C h-. C,,,? "e4lf',cq "... erl t,j,., i,-..-.u-%.r,4 '.....ng.. Q 2 r',,-, lf P--,- wd NNN "e,n, " -4) t,% r).r-- U% e,.'4".,.-4.n,.,-i.z,,, N e 8 [-4 ' N, c 3 C3.4".r (%1..lr (..) g t), N.,,-4 e "N (%J U e,,,-.4 een ; Q. l,,e U '.-,-, N L,a.J 9-, p. ". Z.. 8 N ' ' N U DmDDDD Z 9

95 -4,--4 C,,it',t"n C,"nC " " t4 " t.4 - {t, 5 * n 4 m-.-. ~.G, cl 4.- ",.-.-. %1,N --. 6"% 4-u% * ".-4,.-.-e4 l *,?.- N " 4" '".-4'.:" -.- t'4 *1 *,-4 ",4" -"("4 -e ".TU "--*N *', r.,...,..,, [D v uu e(..u r,% t'- u (. c- u u% u a.- (X) t 4 D > H 4,.-e.l *', *t (D 42 "-4 C (j. *.-4. e4 *,'x3 * SZ.. %. "4" ' l - "?ec'' ec. e *--txj *.-4,4.,. * 91

96 u'c,/ 4-4",4).-4 L". r'- ' ' " +4"'4",4,,t {W C; b'% *('.f'4+ --,1,,..4 J,,L,1%.e c,4- e:'.,. N u' (,..#.#.,-.' "". Z ' * elk, * 'W C'-.,,,+ *.4) "-",,t" *," J Lf,-,-4 C {''-.f, 4".-.*., (D.--,.. *U% *4 4.. i v w% t- rn" v -" 'xt, --,,t.-- N 4" * c -, e.4 c c " 4" H.,,-.4,u','N u r. U ul v "% w r=, -'% " 1 J.-- ",T er% T 4.,, C r:%u'%".,,t +4" " ' "..U "," r" ".,4" xt..+. u.l l%j D -r +-.4, "4" Z 92

97 ..rl d C -, x5 a c.-g' -,t T..: = = t.- 1 T C,,-4C,.4" r -4",,--d Pq,,-.4. *(%1 * ad i,.-i,.- * * T.J c,. t{' '- Q " * -.- ::,-- -.t,.. *e Z t,d D,'d == ** h i r-- J * AJ,-- c r Trf',- *,,,r f- 1 Y1 r "1 ".T a a ' g" /,4",,4" " ( 93

98 v. C u'c um " -1",..j. c c. *ii.,=.- pr e, r.d,.,n,g.,4.,,.c.j.c,'l i,-.. E u m, ::> < '.@,.,, ", u,.-..),..4..-,.s- g,,,tn e-4- i. r -- i...".4" r P'-,', at, 1" v c r 22 Z Z 94

99 c N,'C C " " " it,,xj#',u" l.-.', 'M -. 1',.-,--4. C -N.'M,.,.- : i' ul erl fx '- r ' 1... rd umr, 8 8 " uu -U" H e..-,, 11"(. U " ', 7,. J 'rl t'1 '-' r"- ' m', " -.T i,m " " Nl... ", Z 95

100 fn N N ll.,--" #'b. is'. i 2'... -,-4, Ner,,1 N "N N, ' t H a 4a > Z M,- a,,, g.., - $. TM --,N-- eq 8 " r. e N % ", 4. g "" c ' i. ' 96

101 um i, " t Lr.. Q.,.-i -.,t -,:r u.j,7 P-- C, 2, G',,,rlcf,..,-.,i,-i-4, 2,gg" "'g r, ' u G '. C. c.,-, ' i,,-, c.n,,, LU - U cj r ,, (xl L,...t..i N,-.i,','-,? ru i.i.j- r, r' t' ,. -.t" e,l,- C2, 'J,,,1" -. r'-,'x (AT C,,--' r. 'Xl,imJ l'x (. -,.- - -,-i N c -. -.",,--, C--,, i v,, ",r,/ N " " t c,.-i..4 / c,l t r,) b" " "f', ",- F ' "1" Lu - c t'd N,-# " " 97

102 u" c t. " c". -.1",,.,,1" c.- c,n,,-4 a ".t " t"- t - * i f'.j x r-- e,j 1 i r,..,t. i,, v um, N (M,. t'l,- E-t rq ch r " =, ; i -- v v L t- ; ", " l- " r v t (,.,.,..J a') LL. < i :..,,. LL. L,,L. 98

103 C C; l r-- -.1,',z" " C.. -P, D. rr.". th i- C',-4,, CJ um /..,.... t,,.- " 7 T,..4 T " c ' t'-.r,,z ' N? H H q + v" ,.,,,.-, b:.. " S'....,-.,,.-,",,.,,,,-.,,5 ~.-..-,",q ' " ",-,4 t'- r..-,,.-,.,--,g.,,,,,.-, t d,g,,., D t r).i- i' r-- A M 1,,..,-.,-.,.,::,," Xl -.1" ". LL 99

104 C, f * "- 'M N C Z r ' "C "4 rj h ',.1 ('m (p. '*; " N G. 'q,-- J c" v =. ' i- -, u,, N *,.N, u"..-d 1 -,-# t h'- ' -- J" N.-4.i r*, - * * N r, r u- * h.- *,...i. N '.--, 'l. * (M + * l-. i-jc - * i N a i '.,T r,l * lj t *'" * t' 'M ( i.,.4 ME.- -.-w (% J g9 cj *,-.- '4 m N zz g z z 1

105 fx: rj cm r -J u u' C r* c e is ur,,t, rg t+,--., - + c,,,.r, q..9. " c, SL ct.(j. t T9 ' "+ ' i+, D p N,,-+ " <,,+,..-.,D ' C< E + -" + N. e,+..- u -r * 'N..-+ C. CH + C H : C u ic Pm.-+ 17,.-.t,t u Lql/ m m. + (3 C) rl.- a pq., (M c t d --+ cp, ur e pel,.,-+ U', " + ' NN c 4" f-+ rm 11"+1.i r-- en pr - r-- m -' P-.-..i,,.N,.-i u' c.-.+ i +..,i ' + l " c 7 11

106 y C' t". '.ig,t'l,- ",,.? cu',,,f-, l.c, rl,,,c.., CY' C..,. '- 1"- " r( C c(: S","- (. Ug X D,,t- Lcw, -'w C..-w (',. (" 'M c u'.4", " r.. (.d,...,.e,i CC.r'--.,-w r" u' ('h.-- l- - Pc, CJ r.. C1--,-2.( " r) t,". er. ",,t P", (F" wd ec,..t r 4 C.C. r-- f.- (2).,..,w.-,.-. 1,,'. " H -'-'- wd ", ---t r- C) f A D (,q M u', f. r. q C f,'i --T.c'q -4 1 ' -=1-.-s c, c,4. rss 'a,--.,--,-.t. c..,.v " ' " Z Z 12

107 ,p., P- " r ', E,,D, c.. t-,,-i eq n',-4 n i r.j ' 'M 2,r ' i D CD.r,1- cj v, u T > H r--t',.-,.-i,.-t cu.--ip.-,m.-i.r q3,. Tj..,i *, cj.j..-. p.- P- n"1, M,-.,-,i,, 13

108 r -",$, 2 f,1" t' r,j (: C2 (J c C c Cr i Lf" Lr..-4,r -,"" "D" C) b-q C "N,4",t, i ee v Q. r, (,- "' ' C. e,.-q,-i " U'. N C ',-r,, c r, 'F-.a *..* U' " r v, u' w C). tr," i v, Lr e', u -,11. -/ UU -,1F "- " Ue v' H 8 (..).j.-.4 v ' ecn r --" " ",,-,. -,1". 14

109 A b, C.,," i.,-4 v v G*u U" r ',.1,-.4, * ' i'h ', urn if] )<DC cw c-] i l t c,4 c,j L' * c.j t g", grg" c,a. C'., L.' e,} t] -4.-, tl b- cw." u {,,--,.-,1" q 'J - r,, r, cl 4 ' a]c -k'ca "r "U].m- L ' " ' ' CJ,-. 'xl,el.<.ta. >- >- >- el. u. 15

110 ..t - r.r v u% v' c,, cx..,-j. c,,b - =.,,.., N,L),D, N v Lr N i r,- U,4" (") (7" c J v N rxi '., " i, /% u,.-i i=i r G N,. p r --- p., 4- D t, i '- -.4 i- ( G G MJ B N m.... g = = z 16

111 F-4C DATA SURCES Bnine, W. J., et al, Mdel F/RF-4B-C Aerdynamic Derivatives, MAC Reprt 9542, Feb Crawfrd, W. N., and G. Nadler, Static and Dynamic Cntrl System Characteristics fr the F-4 Aircraft, MAC Rept. F21, 16 Dec Bridges, B. C., Calculated Lngitudinal Stability and Perfrmance Characteristics f the F-hB/C/D/J' and RF-hB/C Aircraft plus the AN/ASA-32H Autmatic Flight Cntrl System, MAC Rept F934, 19 Apr Bridges, B. C., Calculated Lateral-Directinal Stability and Perfrmance Characteristics f the F-4B/C/D/J and RF-4B/C Aircraft plus the AN/ASA-32H Autmatic Flight Cntrl System, MAC Rept. F935, 3 May 1968 NATPS Flight Manual Navy Mdel F-4B Aircraft, NAVAR FDB-, Nv

112 SECTN V X-15 18

113 X- 15 BACKGRUND The X-] is a single-place, rcket-pwered airplane designed fr flight at hypersnic speeds and extreme altitudes. The airplane is carried alft under the right wing f a B-52 and is launched at an altitude f abut 45 ft and a Mach number f abut.8. After launch the X-J5 perfrms a pwered flight missin fllwed by a deceleratin glide prir t vectring fr a landing. With this peratinal technique, the airplane is capable f attaining a Mach number f 6 and can be flwn t and recvered frm an altitude in excess f 3 feet. Flights t high altitudes have been made with all three f the X-J5 airplanes in tw cnfiguratins: the basic and the ventral ff. The basic cnfiguratin is cnsidered here. Aerdynamic cntrl is prvided thrugh cnventinal aerdynamic surfaces with vertical surfaces used fr yaw cntrl and the hrizntal tail fr bth pitch and rll cntrl. All f the aerdynamic cntrl surfaces are actuated by irreversible hydraulic systems. Cntrl frce is prvided by bungee fr pilt feel. A cnventinal center stick is used fr pitch and rll cntrl and rudder pedals are used fr yaw cntrl; hwever a side-lcated stick is prvided fr cntrl f pitch and rll in high-acceleratin envirnments at the ptin f the pilt. Mst f the X-15 missins have been made with the side stick althugh the pilts used the center stick n their first flights. nly the center stick cntrl is shwn here. The augmentatin system shwn in this reprt cnsists f angular rate feedback lps abut all three axes. n additin t the nrmal p -$a rll SAS lp there is an r -5 a feedback knwn as the YAR lp. The gains fr each SAS lp are manually set by the pilt. The SAS-n transfer functins given fr this airplane assume maximum gain settings fr each lp. This may nt have been realistic fr actual flights. The flight cnditins cnsidered fr this airplane are all fr straight and level trimmed flight. This is definitely unrealistic fr this airplane hwever the intent here is t shw general speed and altitude variatin effects. 19

114 d rl a,-- \ \ \ \ \ -- d r- Qb q qj r E4 4 J c -p rj l q q (5 d c v cu r J (D ( LD 4 (J - i hd bd % [1.), r-- r b qi L,r "D r,j [. H (,) " F-H 11

115 ,, J u '- u u5 tc b (,.9. :-4. V (J LL J J L & b J 4 ( -- d

116 X -15 PTCH AXS 8SSAS (rad) FST(b) 2.8 8ST(in.).. " 8s(rad) (TEU) -2-8s(deg) 2 (TED) RLL AXS 8aSAs(rad) FLAT ST (b) r 2.4 BLAT'in ST { a(rad) YAW AXS 8VsAs (red) FpE(b) 12.2 BPED(inL 2.3 By(rd) Figure V-3. X-15 Cntrl System 112

117 X-15 PTCH SAS (rad/sec).75 SssAs(rad) RLL-YAW-YAR SAS Rll Gain p (rad/sec) BasAs(rad) Yar Gain Yaw Gain r (rad/sec).3 BVSAs(rad) Nte: Gains variable in 1% increments f the maximum values which are shwn abve. (e.g. rll gains selectable are.5,.,.15,.2,.25,.3,.35,.4,.45, and.5) Figure V-4. X-15 Stability Augmentatin 1 13

118 X e CJ - -.u) 88 qq / [ i/' /.t /" j,/ll,- 1 J 114

119 uc,l. D x t a (J Q Z rd,. 'J c 1 ill. - m 'X, 1 t13 d -': if).j. Q 115

120 .Q. 88 eq l / /// (% %1 t- J.,,.; :E./ / / / / / / / / / / / / #/ -- (D F) -- J : 116

121 117

122 D,) J 1, 4..-= " " 2 l:3.) s: C.) 118

123 . (,D -ud q.q i u') x -,,6.J L),,-,,i- J J u.. (,D N m..,. -- G G-- % T N.-T m v 119

124 ' '" " T -: -' " i" " " " 12

125 D J c T X 11 a' 4,,- t,..,<i- c- J d- i\ ' 1111 / zili :,D -- " t t. i" " " re}, --,-- J. i c v. 121

126 , (Z) U') ( t m.q K / ' X \ /. if). C i N.. i N r..) r 122

127 (.D D.Q ur)d x q td D [3 - '4-- m 4).. -1 t L J rd- N..N. ".i- 4 c d. J ( 4 t" E) (D i J (13 J r" [3 J. d (.D 11 / ',lli i /) t (.3 tm (M i- j d q tm C - - G:) \,m.., uf) q q q q l c 1" - q q q ''- i- D 123

128 El iz') >, c. i "-, q d c.,. N -'. " re J -," q q q q e J " c " 124

129 Cs u' P c" q.,..-i c c 1,- r% cr' LF. " " ' :,.-, c c C C, C C5 c 4- <1 C (,m rl - U, C) cr] a} a C CJ q * D,- r r, q) a" - c { " V c H c; $ c, t C,. c c t c,- xl H i c r q" m crl ' D.- c c ' N J ' "- G 8 m 1 r *. C N 125

130 " " " ie t f g,. " D c'4 t-,l r,3,-4 * 'M,.-i " " i +++:" "-3",# ++ PM 1 " " ' " +"+ +"" +" +,.. : C. g TM P l" " l l" " " ' " "i" Pei h'.- rl, rm. %1 P'-.,+..,:, +--,?-.,-..l ',.., '4 u +).", P"-. +'el +,41 " ' "41 "T 126

131 ,-< cc -..t,, U,--re cj t'-.. ) ) C'' c -' c r, - ' C C7 Jc.+ 'JD prl CC rr 4, U'm " b-,. F- (" C'.a -.- C. C " " C,J> C. N,' L) t,. F-- +" [-- r t.+,--4 i',.. -.,---, c " e,j,- (-. u",, J" ) H [-i - E-t e,t L,+ p-+ p--,p.:1- )..1.,,.L) ". --,.-+ P '-.i L.m D -t (7. ) f,- r. lh rl --<.,: --- p:) (..)(p nr..,- L.),.--.+,, Cq-T.- r D pr c) L,,l P. el A.?- c gr.. f-j r f,... (x'.,,-,.l.. a:. r", (Y' r'. P",.,.,,a sd "T" N.-' v'... r.i g" gh :+.,,.--i,--+,,, C " : 127

132 v c E c C c, c) LC ",,--,u- c.,.-il--,,,' r i--. u', c c t c -,,-w - c,- C'- ~q?, e,j i? pr h' (D C.. C - cm,- G U',--wp F-, cq h"... t,, LF, t-.'i, C).#.. f CN h- WD r bm wt ( c,d u,tq.-,.r, N ', -J J, - () F'- '-- " C).t"- ('4 " c, {xjc. N " C c p ',-i r, *, c), 'N ),-i ,r H g. wd e,j, p.- u'-w -n.-e., -.wu,,{.u ---W- c v > Fzl ']. "J (D L) u ul r.- D.-- i" -,tm (Y' C.) * (D C (' -,t," v {D. J t, W&,, c.) Uh P-- u,,-w.. (. i'm a C t" r C.' C9,.,-w., 4.J L,c, (',1 P" ", t" C N., '-C re' w L,,T P" r' 41"- fe..- " *-4 D Z u u. w Z Z 128

133 c1 c- -,c u u LC, C (,q, (.q T,,...i 7 cn t-.-w t 1 eq c.--i c,, E-4 X.. -P -,, i- L, ch CH.L H U3 -M,J r.- g 1- (..) uh Lf 6q ---t D ; c C -4 N M i. f'-j '-,t -4 b 129

134 C.,.-4 c,a u * l l ", r- ' r C,, - -,.3 - L c..-i, J,-- -4,, c,-# i i. ll * R.-, --.,. -,. - tr,..t" i%1 i' c.,,i q.. C. - v, zl c'., * CD --,"4 1.# - 'T - -- i" -# c t, " ",.-4 [ ( 13

135 ,, Cb C. " " 12:) ',' C, C, t+ C.,,43 i.r, c, g,.?.,4g" t C, 'q "C, C ",- 1,1" p-.,- CD,.,..4 t + lm.@ " + 'q.,<,.7,..g C> " "4 C ' +tc elf,, c, t- C - v",. t -,,.1" l") 1:, i r ;,1..t,-,U' 4", t, 4 " -., "4. +S " ' *1. '.5-, i t,q. U" C C.3.- U c, e.j * t v,/ r '. b,.m' e T X m m 1 eq N Z. e,.,,, *N,,-i, u, i.4d '4" Z 13t

136 C gg,d g it,, - C e t C *r, t,j 1"- *C' *.,, - - -t -,t e,-, * C t- *. C,.--,i '.,, rl P- p...,re,,a cc C t t" J" c, tl ", r t ",:,..,c, r,..-,,..,dw.,-* tri ". v ',D,g D 4,N.. t,-- t,-.. i r'-- x i -2 m' " t.-., - *" > E-i U 1 C). t. t'j r'j P'- ", C-, "4" " '. g * C', r" rj,,- t,# P--,--.;gqg'.A e X * --J " -.t, a,.," *cx;. i -, tx.ra Z 21C Ua tl :-- ),- >=.L :.= L -. v 132

137 Card c C, -.t" t'./ c, Cee, r C ' r,-. Cr P r pr, 5..-.,.? L.::.,.c l r1 L %,.-i C D /.-4 r ' S, r<l / ej c G r " i 'M.r...., CL D <l'a G r',: t,,,t..i rl C ba u' C).C,D g.--.l c,,j p t b 4" -4" c...-i.,.-.j "4" r.- T,,-,-- C Pa r. r -.,1- * u cm.r-j.,.. u 'M /', c (, P r.-- r-- ii l t / /," -., ' - N. P.-. e 'l -4".-i {.D " G:; *. 'M. r t? 1 " i u.j >- >- u Z F 133

138 --4 C,, M,f,r..-- e..d q-a N,--*,llm i%1.,, ea. u% e-,l,f, " c, 'M t r,"l. - " g.. LP, zl,-d,- a.--, i-,#,,,u. c '.- ( (::),.LmlN.,,'i.i- r 1. gg 1 u,..-,.=13.rim ::> rj F Zl r H g,-,-.. i%1 r,-'xl t,, l'xl L mm.r rnl.- '--4 t,- g.c M,"el *,c " c,,icxl t i, 3-, "M u'-. -4-,u% 1 c') : GJ 'J.J >.:: 7 134

139 .--4 Q t h" J U ) * N ",-d * v' a ", c..4 N * r..- % 4) * *,4" ' M c, i {%1.," t.-- ". - N,-4. r "., ' t [-- u' em a * -,t *, ta ",',4",,t", rtl t" c c -, ,..4 El r3 i:1 Pq v n. N c i i.,t M, ", { '.-, N -J,-4 u') a * c N r,t c 7 Ju 3 LU, 1- e - p. C {3 LU '-4. (J a{ '- d.j "- "t" -,i,',.,. '- :i[ '7 G. Ci.. 135

140 X- 5 DATA SURCES Revised Basic Aerdynamic Characteristics f X-15 Research Airplane, Nrth American Aviatin, nc. Reprt N. NA August 199. sbrne, Rbert S., Stability and Cntrl Characteristics f a.667-scale Mdel f the Final Versin f the Nrth American X-15 Research Airplane (Cnfiguratin 3) at Transnic Speeds, NASA TMX-758, April Franklin, Arthur E. and Rbert M. Lust, nvestigatin f the Aerdynamic Characteristics f a.67-scale Mdel f the X-15 Airplane CnfigurAtin 3) at Mach Numbers f and 4.65, NASA TM X-38, Nvember Penland, Jim A. and David E. Fetterman, Jr., Static Lngitudinal t Directinal, and Lateral Stability and Cntrl Data at a Mach Number f 6.83 f the Final Cnfiguratin f the X-15 Research Airplane, NASA TMX-236, April 196. Tunnell, Phillips J. and Eldn A. Latham, The Static and Dmamic-Rtar Stabilit Derivatives f a Mdel f the X-15 Research Airplane at Macb Numbers frm 1.55 t 3-5, NASA Mem A, January 199. Hpkins Edward J., David E. Fetterman, Jr. and Edwin J. Saltzman, Cmparisn f Full-Scale Lift and Drag Characteristics f the X-} Airplane With Wind-Tunnel Results and Thery, NASA TM X March Walker, Harld J. and Chester H. Wlwicz, Theretical Stability Derivatives fr the X-15 Research Airplane at Supersnic and Hpersnic Speeds ncludin a Cmparisn With Wind-Tunnel Results, NASA TMX-287, August 196. Yancey, Rxanah B., Flight Measurements f Stability and Cntrl Derivatives f the X- Research Airplane t a Mach Number f 6.2 and an Angle f Attack f 25, NASA TN D-2532, Nvember Saltzman, Edwin J. and Darwin J. Garringer, Summary f Full-Scale Lift and Drag Characteristics f the X-15 Airplane, NASA TN D-3343, March Taylr, Lawrence W. Jr. and Gerge B. Merrick, X-5 Airlane Stability Augmentatin System, NASA TN D-1157, March Tremant, Rbert A., peratinal Experiences and Characteristics f the X-15 Flight Cntrl System, NASA TN D-142, December

141 SECTN V HL- 137

142 EL- BACKGRUND The HL- is ne f a number f lifting bdy research vehicles. The airplane is typically launched frm a B-52 at.8mach and 4, feet. n numerus glide and pwered flights the HL- has been flwn in excess f 1.8 Mach and 9, feet. Fllwing prblems invlving the lss f rll-cntrl effectiveness, the leading edge f the tip fins was mdified. This became knwn as the Md cnfiguratin. The infrmatin cntained here is fr the Md HL-. Pitch and rll cntrl is btained by elevns and yaw cntrl by a cnventinal rudder. A subsnic r a transnic cnfiguratin is selected using cmbinatins f speed brakes elevn flaps, and tip fin flaps. These cmbinatins are specified in Fig. V-. The stability augmentatin system cnsists f angular rate feedback lps abut all three axes. The flight cnditins shwn crrespnd t actual flight test pints. 138

143 . q4.&. v % E-,- D - m (.) - ).,- ZJ (D.,- [-.,-,- ff'x.,-.,- r 8. 1 (n d. ) e4 % N h.el i- i,- 4- e.,-.,.r-t.,.4,-4 t J d J,-.,- 4 4 CJ e,...t.,- v.la e8 al,'el b q q M q i;. 139

144 -- - i... x / 4,n 11 --\,,. / i H -r4 - C--'3. t'-. -- il l C2- -. C:-- C.--" U.i 14

145 HL- PTCH AXS (esas(rad) Feel Spring Gearing FST (b) 6.5 ST (in.) G ) (e(rad) -2-1 e (deg) G(deg/in) -6 RLL AXS (asas(rad) Feel Spring ST FLAT (b) 2.7 SST (in.) Gearing, (rad) YAW AXS 8UsAs(rad) FpED(b) 22.2 (Sr (rd) Figure Vl-3. HL- Cntrl System 141

146 HL- PTCH SAS (rad/sec) esa S RLL SAS p(rad/sec) 8aSAs YAW SAS r (rad/sec) = s 7".,3 arsas J.4s Figure V-4. HL- Stability Augmentatin t42

147 U T.D n / /.-. /,/ / 41",--, --, -- /. i j J" ='.,p n,ll l / ( /, x '% li L,,,- p,,2 / // /",, i --G t- (xl (] (x]

148 -- l -- C- U -- d 1 ' P tl N --: 1. t'm J. q 'r q -JGGGd cx],- li." J Jj J" i d Q r-.- () q 1 144

149 / / Q J.a ' ## / l.j c L.. l.. t@-- " qq dd / / / } --C --C i r J i i i.j -? 145

150 ,1 (D N -- 4.c '1J (D - ' ill.,$-- e.. lj.. q.nd " v. r T " E C.) " 146

151 .Q, J '-- / / /. \ \ \ j m N,F (,,,% --C C-- S p 4 1, m - E "- 147

152 B \ x.=,, =,,,, D" J 1" "r" 4DgD \ / i / a N J m m U. t.. C- -- 1).1,, " q, m q 1 N "m ' " " m llb 148

153 U3 m G ' n x "1 -A C ( Q. m t- (3 t3 e- U G-- GD QD -- L L'-- l i ---: ) i - L -- i Q,, < "1 C) c3 r t3 lh. D 1,. t e. -( lb. 149

154 ( \\. 'W # # 7- q q i q q 1 " a a q q q q q m,, n13 C,- v a7,- m V L 15

155 ' -J G t m. q c- G,1 1 "-:.... L -- >, "3 b C.D t,. m k- " e- v 151

156 C C: -/ 4- " +D 1"- i< ' r.- r, T 7'.? N T t'- u C t / T-- -) c) +.? %? :% 2?.. eq t'- t N, T + T 7 2

157 ix p C * * : " l' c., ".4 c.d - i v cj l / m," ' l" ' " --.1 H n H. ' '.,.- u 4" l -- F' 1"- R " el - G3 C". -4 ' " "f v' " r.,4",d, C t1,-- D uj uj u u. 153

158 i.. P-- * c d" =,. b, -,t... C + 1 C2 + 'n, ".'-+ C?+ "- * fm Mr i., +CCC. w r...i i,-- M- e..4 i c,, t+.- t 4,. Cp.-. ( F,.+ x: e fl, ih..,,13 et' %1 {M *+--t--,, v E- t+ eell rj +.. r'j.+ N %1 C. - += Ln +', 1]) -p,.,.-4.*" e ' *e'j " (M g f-.. ef, fi+-2 + > -' E+,.-+,,1" C.) +P-. eet. D +,- p-- cxl rl,..+ N e * cx, "1", U.,, ' N,+ Can N.cq s 4J P+- * Pr'i x,+" v -,. :. e L,' ',, - J. et'.- -",. +m+;; w ww Z 154

159 + i L, +.+ c+ (P + txj t; c+ h r,j + -++,. r,+-,.t..+ C. l',j c+...,+.,-< z+ G.C+ u,.-< c.? it ac. +,.+ c + t+-.j t+ r ' * P.+ pr pr (jl+. + (j cd t- c. y: cj + rx,.. b cxl.-+. pe t. rr, t'+ c.-+ j T m /+ <,++ P.J * G.D a.,< <> c" t'j ca,< <:D P i1 * +", u- c t, v X; c E4,d3 c i: rj u',c txl - +-t <t w tj. N,-4 g+. *'.'Xl, m,--4 " [-4 ',d b+,, C rr. p+. P,j - < a, ( * e+j e, r-- l t'- " v < u'x c, ct '4 a c - c ",r,.r..- a..-i t-- + l'xt P'J ej,'- C) ++-+ ' "- "4 c " CXll. *,+ i, c {-1 { txl + rl c,+ ++.T, +.-+ a.. t+,,l e U-x rl.--t.,, ' q l'-- P'- ",,. 'J 1 t C +..+ r.. i,esl n t e,l.t + N, * +- en D 1 Pc+..t << p.. c <",J +.--+i P.J,,t.t c,? +..+, i r... T-.T L z N Z 155

160 G(,. ie C: r l" h- um,),,4,.4 N ",-4 v,,, * $,, l LU LL m e 1, ell, ) -," rq un -,t,,- v v J D LU -r u. 156

161 ,? T,, ;, -.,",,t",.,t + l-..+. J.; a, -.4",. C.-+ t.., u c u', 4" m m,.1.'-',-, ' l t " l ,P, -- C,;,, a (.3 ' 1 157

162 .4 f4 um um 4" -. f'- g v, q a[ u'..d r--.t um-, P- -- m c ',.q P"- - w v a '4" LF 'b A.7, u- ur ",- v ry - > > r um " cx 4" - f'.,i c.,i%1 A " * 7, :g,-,,-- t -4" r.-,.t A w, 1, v mm,i, t gz rq t,, 158

163 v,.-4,t,, -.-c C -,,,: ( r-- --, c u% -.n e% c t ZJJ r- u...,h C,,rr).. " ' 8 4-.u,% u'%.4 b--.. :m 8 [ c rj +, CH v N U 4" ',C ej a..,c c.u', - u-.-,cp..4'.. [" v N N znzz 7 159

164 .p. t. x' p-. *xj " 4" C5 J ad r.-- ' (7-,- ;.-T w P-, Z ad +,',', 'x N*e v a,..nn, e,,j * r-- r'm ' * - c C *

165 p- c l' cr,4 e t N * Nl, g...,-e,d,.-. d, c,. r N,42,... N -,t.- ep.- t%l a'l,..4 J,'d.rl r...) ee ee e 'x :> ep'-q rx;.4" e. 161

166 4. 4- e v " h- 2,,N,N h- "" t- rq m,c C;,.--lrl e,e " t m " %1 cr M' i'%1 " r tx.; c e, -.t, g. M.w' N,,1" r, " ",", N.,m ", N

167 r..- - ite t, C i'% ' erq 1 " erl e1" *.- N "d.,-4 r...) t,i N,,, H irl erxl,.1-,,d.-,.t, ww t, e.,-- 163

168 , '.,4- r 4"..--4 * t P'% * " " r. -'%,.4" * d".,..,.-,,, t'n M" " " i a,4" * ( 4-, r'.-,, i " 1 t E *,..., 'q,=4,-4 (%1 4".., 4- t *, i.-, :'4 ' *,vl *,-4 *.,-4 ti *.,11". -- c.-,'..,",-. "T.-.-i 'M ("-4 r....4 #n, -- %.. 164

169 HL- DATA SVRCES Ladsn, Charles L., and Acquilla S. Hill, Aerdynamics f a Mdel f the HL-1 Flight Test Vehicle at Mach.35 t 1.8, NASA TN D-618, Feb. 1971, Pyle, Jn S., Lift and Drag Characteristics f the ML- Lifting Bdy during Subsnic Gliding Flight, NASA TN D-6263, Mar Ware, Gerge M., Full Scale Wind Tunnel nvestigatin f the Aerdynamic Characteristics f the HL- Manned Lifting Entry Vehicle, NASA TMX-116, ct

170 166

171 JETSTAR BACKGRUND The Jetstar is a fur engine utility transprt. Cntrls cnsist f cnventinal ailerns elevatrs and rudder. Ailerns and elevatrs are mechanically actuated with hydraulic bst. The rudder is mechanically activated but assisted by a serv tab. The primary surce f aerdynamic data was NASA CR-544. Pwer apprach aerdynamics were estimated using CR-544 and flight test data frm TC-TDR-62-24C-14. The cntrl system descriptin was based slely n flight test data frm the latter reference. 167

172 , r- Ca rn p :> -M.rl C; %,--t % L " "-" "- J v, 4..i- 4.,-q "7 -i -4 J 'x J J J r J z c,j J J 4- r- --., E- C.-=1 lf ' x g J J... L r- b, N.,-.,q )

173 ' ) H a3 4 d..a c; t--4.r4 N 169

174 JETSTAR PTCH AXS FST(b) ' C 8e (rad) Nte: Angle f attack effects n elevatr h/nge mment are neglected RLL AXS LAT F ST (b).75q = 8a(rad) YAW AXS FpE(b) - 8r (rad) Figure V-3. Jetstar Cntrl System 17

175 TABLE V- ] JETSTAR Pwer Apprach Nn-Dimenslnal Stability Derivatives h = sea level VT = 224 ft/sec = 132. kt % = 6. Lngitudinal Lateral-Directinal (Bd Ax±s) CL =.737 CD =.9 =./rad CD a =.7D/tad Cm = -.8/rad Cm = --3./rad Cmq = 8./rad CLSe =.4/rad CruSe = --.81/rad Cn =.137/rad C = --.3/rad Cp = -.37/rad Cnp = -.14/rad C r =.]/rad Cn r = --.T6/rad Cna = --.7/rad CSa =.54/rad CySr =.17/rad Cn5r = --.63/rad CSr =.29/rad 171

176 SL JETSTAR 2, ft 3824 b 4,ft 12- (deg) Mach 172

177 -- D -- r- u w q q q a C.) S -- J 11 r- c) -- 1, t J -..J 173

178 6- CLa 5 (rad-i) 4 5 JETSTAR 3824 b Mach %%%, t Mch 174

179 Mach Cma (rad "i ) SL... 2,ft ,ft JETSTAR 3824 b.255 Mach Cm&, -.4 Cmq (rad-) -.8 '*':) Cmq

180 CDM.8 t (rd "l ) Mach Mch B -'.2- t CM M (rd "l ) " SL... 2,ft - 4,ft JETSTAR 3824 b

181 CL8 e 4 - CL8 e, Cm8 e.2 m (rd'=) ) Mch.2 JETSTAR n

182 Mach.2 A.6.8 J -.4 Cy (rad -t) -, ",, SL ft ,ft JETSTAR 38241b Bdy Axis.2. Cn, Cj (rd't) -" -"(- - Cn B Mach c :2 178

183 Mach C,p (rad ") SL... 2,ft ,ft JETSTAR b Bdy Axis Mach i Cnp (rd "i)

184 S L JETSTAR 2,ft 3824 b ---'---- 4,ft Bdy Axis.2 C,t r, Cr Cnr (rd "i ) Mch -. Cn r -2 18

185 ill SL JETSTAR 2,ft 5824 b 4, ft Bdy Axis.8 CYaa (rd - ).4.Z Mach Mach,2 4, ; 8, Cns a (rd -l ) -.2-8a is deflectin f ailern n ne slide nly 181

186 Cy8 r (rd - ) "", Mch Mach Cn8 r (rad "i ) ' SL... 2,ft 4,ft JETSTAR 38241b Bdy Axis.4 C8 r (rd "l ) Mach 182

187 C3 C t t t,-< N C: h Lr -.t f c N C c r c r,j r,j C - * in g - l"-, t %1 u'h i H El H c> "-+ 3 c N r,i N,) c i " P- "-+ lib i H ::.; -. i i g t} rq c h t r N C> t,3 u- u u +. c -x, r f ' * + e,i c ", x r [e * c) b x " u,.t 'M N,,, 'M,, ". 1?1 183

188 , %t c u", 4) $'j, 4- (. " c ' c ': " c ie C C t'- 42 " C2 C c.d "4" C'. C c G G e, i C "4 C. "% C., C. CJ N C, Ca. " C) " ' " ' T l" T P " " le T u " ", ; ;.,," t" i ' ' - ' " ' e e -,.. i e tl,'.4, e " W " " " ' ' D " r? ' U% " " " u " "=,= r " l, 184

189 c c rl <1Lt * e (J r- Cr r i, txj,l,r t/ -1" t..# "?~. (. c *,, e C- r, r.,--4 tr, re, e r--- 'b.t <1-,- U-. t,- t zj r--,e., 7 '..+, v u- N c,.e,c ' "..,, H. " r,.- t r-d " P-' r w w frl,-,..i lm,r,),...t..t t u.-u,.1" q, nr..-d,.4 ",- C l,.,g -<,ff r-- ecl'-- r rq ff,e v.,e e. eel z 185

Aircraft Performance - Drag

Aircraft Performance - Drag Aircraft Perfrmance - Drag Classificatin f Drag Ntes: Drag Frce and Drag Cefficient Drag is the enemy f flight and its cst. One f the primary functins f aerdynamicists and aircraft designers is t reduce

More information

Introductory Thoughts

Introductory Thoughts Flw Similarity By using the Buckingham pi therem, we have reduced the number f independent variables frm five t tw If we wish t run a series f wind-tunnel tests fr a given bdy at a given angle f attack,

More information

~,. :'lr. H ~ j. l' ", ...,~l. 0 '" ~ bl '!; 1'1. :<! f'~.., I,," r: t,... r':l G. t r,. 1'1 [<, ."" f'" 1n. t.1 ~- n I'>' 1:1 , I. <1 ~'..

~,. :'lr. H ~ j. l' , ...,~l. 0 ' ~ bl '!; 1'1. :<! f'~.., I,, r: t,... r':l G. t r,. 1'1 [<, . f' 1n. t.1 ~- n I'>' 1:1 , I. <1 ~'.. ,, 'l t (.) :;,/.I I n ri' ' r l ' rt ( n :' (I : d! n t, :?rj I),.. fl.),. f!..,,., til, ID f-i... j I. 't' r' t II!:t () (l r El,, (fl lj J4 ([) f., () :. -,,.,.I :i l:'!, :I J.A.. t,.. p, - ' I I I

More information

A L A BA M A L A W R E V IE W

A L A BA M A L A W R E V IE W A L A BA M A L A W R E V IE W Volume 52 Fall 2000 Number 1 B E F O R E D I S A B I L I T Y C I V I L R I G HT S : C I V I L W A R P E N S I O N S A N D TH E P O L I T I C S O F D I S A B I L I T Y I N

More information

176 5 t h Fl oo r. 337 P o ly me r Ma te ri al s

176 5 t h Fl oo r. 337 P o ly me r Ma te ri al s A g la di ou s F. L. 462 E l ec tr on ic D ev el op me nt A i ng er A.W.S. 371 C. A. M. A l ex an de r 236 A d mi ni st ra ti on R. H. (M rs ) A n dr ew s P. V. 326 O p ti ca l Tr an sm is si on A p ps

More information

P a g e 5 1 of R e p o r t P B 4 / 0 9

P a g e 5 1 of R e p o r t P B 4 / 0 9 P a g e 5 1 of R e p o r t P B 4 / 0 9 J A R T a l s o c o n c l u d e d t h a t a l t h o u g h t h e i n t e n t o f N e l s o n s r e h a b i l i t a t i o n p l a n i s t o e n h a n c e c o n n e

More information

T h e C S E T I P r o j e c t

T h e C S E T I P r o j e c t T h e P r o j e c t T H E P R O J E C T T A B L E O F C O N T E N T S A r t i c l e P a g e C o m p r e h e n s i v e A s s es s m e n t o f t h e U F O / E T I P h e n o m e n o n M a y 1 9 9 1 1 E T

More information

Parts Manual. EPIC II Critical Care Bed REF 2031

Parts Manual. EPIC II Critical Care Bed REF 2031 EPIC II Critical Care Bed REF 2031 Parts Manual For parts or technical assistance call: USA: 1-800-327-0770 2013/05 B.0 2031-109-006 REV B www.stryker.com Table of Contents English Product Labels... 4

More information

Fundamental Concepts in Structural Plasticity

Fundamental Concepts in Structural Plasticity Lecture Fundamental Cncepts in Structural Plasticit Prblem -: Stress ield cnditin Cnsider the plane stress ield cnditin in the principal crdinate sstem, a) Calculate the maximum difference between the

More information

Section 6-2: Simplex Method: Maximization with Problem Constraints of the Form ~

Section 6-2: Simplex Method: Maximization with Problem Constraints of the Form ~ Sectin 6-2: Simplex Methd: Maximizatin with Prblem Cnstraints f the Frm ~ Nte: This methd was develped by Gerge B. Dantzig in 1947 while n assignment t the U.S. Department f the Air Frce. Definitin: Standard

More information

Equilibrium of Stress

Equilibrium of Stress Equilibrium f Stress Cnsider tw perpendicular planes passing thrugh a pint p. The stress cmpnents acting n these planes are as shwn in ig. 3.4.1a. These stresses are usuall shwn tgether acting n a small

More information

Phys101 Final Code: 1 Term: 132 Wednesday, May 21, 2014 Page: 1

Phys101 Final Code: 1 Term: 132 Wednesday, May 21, 2014 Page: 1 Phys101 Final Cde: 1 Term: 1 Wednesday, May 1, 014 Page: 1 Q1. A car accelerates at.0 m/s alng a straight rad. It passes tw marks that are 0 m apart at times t = 4.0 s and t = 5.0 s. Find the car s velcity

More information

Physics 2010 Motion with Constant Acceleration Experiment 1

Physics 2010 Motion with Constant Acceleration Experiment 1 . Physics 00 Mtin with Cnstant Acceleratin Experiment In this lab, we will study the mtin f a glider as it accelerates dwnhill n a tilted air track. The glider is supprted ver the air track by a cushin

More information

Building to Transformations on Coordinate Axis Grade 5: Geometry Graph points on the coordinate plane to solve real-world and mathematical problems.

Building to Transformations on Coordinate Axis Grade 5: Geometry Graph points on the coordinate plane to solve real-world and mathematical problems. Building t Transfrmatins n Crdinate Axis Grade 5: Gemetry Graph pints n the crdinate plane t slve real-wrld and mathematical prblems. 5.G.1. Use a pair f perpendicular number lines, called axes, t define

More information

q-..1 c.. 6' .-t i.] ]J rl trn (dl q-..1 Orr --l o(n ._t lr< +J(n tj o CB OQ ._t --l (-) lre "_1 otr o Ctq c,) ..1 .lj '--1 .IJ C] O.u tr_..

q-..1 c.. 6' .-t i.] ]J rl trn (dl q-..1 Orr --l o(n ._t lr< +J(n tj o CB OQ ._t --l (-) lre _1 otr o Ctq c,) ..1 .lj '--1 .IJ C] O.u tr_.. l_-- 5. r.{ q-{.r{ ul 1 rl l P -r ' v -r1-1.r ( q-r ( @- ql N -.r.p.p 0.) (^5] @ Z l l i Z r,l -; ^ CJ (\, -l ọ..,] q r 1] ( -. r._1 p q-r ) (\. _l (._1 \C ' q-l.. q) i.] r - 0r) >.4.-.rr J p r q-r r 0

More information

I M P O R T A N T S A F E T Y I N S T R U C T I O N S W h e n u s i n g t h i s e l e c t r o n i c d e v i c e, b a s i c p r e c a u t i o n s s h o

I M P O R T A N T S A F E T Y I N S T R U C T I O N S W h e n u s i n g t h i s e l e c t r o n i c d e v i c e, b a s i c p r e c a u t i o n s s h o I M P O R T A N T S A F E T Y I N S T R U C T I O N S W h e n u s i n g t h i s e l e c t r o n i c d e v i c e, b a s i c p r e c a u t i o n s s h o u l d a l w a y s b e t a k e n, i n c l u d f o l

More information

CS 477/677 Analysis of Algorithms Fall 2007 Dr. George Bebis Course Project Due Date: 11/29/2007

CS 477/677 Analysis of Algorithms Fall 2007 Dr. George Bebis Course Project Due Date: 11/29/2007 CS 477/677 Analysis f Algrithms Fall 2007 Dr. Gerge Bebis Curse Prject Due Date: 11/29/2007 Part1: Cmparisn f Srting Algrithms (70% f the prject grade) The bjective f the first part f the assignment is

More information

ENGI 4430 Parametric Vector Functions Page 2-01

ENGI 4430 Parametric Vector Functions Page 2-01 ENGI 4430 Parametric Vectr Functins Page -01. Parametric Vectr Functins (cntinued) Any nn-zer vectr r can be decmpsed int its magnitude r and its directin: r rrˆ, where r r 0 Tangent Vectr: dx dy dz dr

More information

MODULE 1. e x + c. [You can t separate a demominator, but you can divide a single denominator into each numerator term] a + b a(a + b)+1 = a + b

MODULE 1. e x + c. [You can t separate a demominator, but you can divide a single denominator into each numerator term] a + b a(a + b)+1 = a + b . REVIEW OF SOME BASIC ALGEBRA MODULE () Slving Equatins Yu shuld be able t slve fr x: a + b = c a d + e x + c and get x = e(ba +) b(c a) d(ba +) c Cmmn mistakes and strategies:. a b + c a b + a c, but

More information

Review of the Roll-Damping, Measurements in the T-38 Wind Tunnel

Review of the Roll-Damping, Measurements in the T-38 Wind Tunnel Internatinal Jurnal f Scientific and Research Publicatins, Vlume 3, Issue 12, December 2013 1 Review f the Rll-Damping, Measurements in the T-38 Wind Tunnel Dušan Regdić *, Marija Samardžić **, Gjk Grubr

More information

ENSC Discrete Time Systems. Project Outline. Semester

ENSC Discrete Time Systems. Project Outline. Semester ENSC 49 - iscrete Time Systems Prject Outline Semester 006-1. Objectives The gal f the prject is t design a channel fading simulatr. Upn successful cmpletin f the prject, yu will reinfrce yur understanding

More information

35H MPa Hydraulic Cylinder 3.5 MPa Hydraulic Cylinder 35H-3

35H MPa Hydraulic Cylinder 3.5 MPa Hydraulic Cylinder 35H-3 - - - - ff ff - - - - - - B B BB f f f f f f f 6 96 f f f f f f f 6 f LF LZ f 6 MM f 9 P D RR DD M6 M6 M6 M. M. M. M. M. SL. E 6 6 9 ZB Z EE RC/ RC/ RC/ RC/ RC/ ZM 6 F FP 6 K KK M. M. M. M. M M M M f f

More information

, which yields. where z1. and z2

, which yields. where z1. and z2 The Gaussian r Nrmal PDF, Page 1 The Gaussian r Nrmal Prbability Density Functin Authr: Jhn M Cimbala, Penn State University Latest revisin: 11 September 13 The Gaussian r Nrmal Prbability Density Functin

More information

Subject description processes

Subject description processes Subject representatin 6.1.2. Subject descriptin prcesses Overview Fur majr prcesses r areas f practice fr representing subjects are classificatin, subject catalging, indexing, and abstracting. The prcesses

More information

GENERAL FORMULAS FOR FLAT-TOPPED WAVEFORMS. J.e. Sprott. Plasma Studies. University of Wisconsin

GENERAL FORMULAS FOR FLAT-TOPPED WAVEFORMS. J.e. Sprott. Plasma Studies. University of Wisconsin GENERAL FORMULAS FOR FLAT-TOPPED WAVEFORMS J.e. Sprtt PLP 924 September 1984 Plasma Studies University f Wiscnsin These PLP Reprts are infrmal and preliminary and as such may cntain errrs nt yet eliminated.

More information

ES201 - Examination 2 Winter Adams and Richards NAME BOX NUMBER

ES201 - Examination 2 Winter Adams and Richards NAME BOX NUMBER ES201 - Examinatin 2 Winter 2003-2004 Adams and Richards NAME BOX NUMBER Please Circle One : Richards (Perid 4) ES201-01 Adams (Perid 4) ES201-02 Adams (Perid 6) ES201-03 Prblem 1 ( 12 ) Prblem 2 ( 24

More information

P a g e 3 6 of R e p o r t P B 4 / 0 9

P a g e 3 6 of R e p o r t P B 4 / 0 9 P a g e 3 6 of R e p o r t P B 4 / 0 9 p r o t e c t h um a n h e a l t h a n d p r o p e r t y fr om t h e d a n g e rs i n h e r e n t i n m i n i n g o p e r a t i o n s s u c h a s a q u a r r y. J

More information

I-1. rei. o & A ;l{ o v(l) o t. e 6rf, \o. afl. 6rt {'il l'i. S o S S. l"l. \o a S lrh S \ S s l'l {a ra \o r' tn $ ra S \ S SG{ $ao. \ S l"l. \ (?

I-1. rei. o & A ;l{ o v(l) o t. e 6rf, \o. afl. 6rt {'il l'i. S o S S. ll. \o a S lrh S \ S s l'l {a ra \o r' tn $ ra S \ S SG{ $ao. \ S ll. \ (? >. 1! = * l >'r : ^, : - fr). ;1,!/!i ;(?= f: r*. fl J :!= J; J- >. Vf i - ) CJ ) ṯ,- ( r k : ( l i ( l 9 ) ( ;l fr i) rf,? l i =r, [l CB i.l.!.) -i l.l l.!. * (.1 (..i -.1.! r ).!,l l.r l ( i b i i '9,

More information

Sections 15.1 to 15.12, 16.1 and 16.2 of the textbook (Robbins-Miller) cover the materials required for this topic.

Sections 15.1 to 15.12, 16.1 and 16.2 of the textbook (Robbins-Miller) cover the materials required for this topic. Tpic : AC Fundamentals, Sinusidal Wavefrm, and Phasrs Sectins 5. t 5., 6. and 6. f the textbk (Rbbins-Miller) cver the materials required fr this tpic.. Wavefrms in electrical systems are current r vltage

More information

Exhibit 2-9/30/15 Invoice Filing Page 1841 of Page 3660 Docket No

Exhibit 2-9/30/15 Invoice Filing Page 1841 of Page 3660 Docket No xhibit 2-9/3/15 Invie Filing Pge 1841 f Pge 366 Dket. 44498 F u v 7? u ' 1 L ffi s xs L. s 91 S'.e q ; t w W yn S. s t = p '1 F? 5! 4 ` p V -', {} f6 3 j v > ; gl. li -. " F LL tfi = g us J 3 y 4 @" V)

More information

NUMBERS, MATHEMATICS AND EQUATIONS

NUMBERS, MATHEMATICS AND EQUATIONS AUSTRALIAN CURRICULUM PHYSICS GETTING STARTED WITH PHYSICS NUMBERS, MATHEMATICS AND EQUATIONS An integral part t the understanding f ur physical wrld is the use f mathematical mdels which can be used t

More information

Future Self-Guides. E,.?, :0-..-.,0 Q., 5...q ',D5', 4,] 1-}., d-'.4.., _. ZoltAn Dbrnyei Introduction. u u rt 5,4) ,-,4, a. a aci,, u 4.

Future Self-Guides. E,.?, :0-..-.,0 Q., 5...q ',D5', 4,] 1-}., d-'.4.., _. ZoltAn Dbrnyei Introduction. u u rt 5,4) ,-,4, a. a aci,, u 4. te SelfGi ZltAn Dbnyei Intdtin ; ) Q) 4 t? ) t _ 4 73 y S _ E _ p p 4 t t 4) 1_ ::_ J 1 `i () L VI O I4 " " 1 D 4 L e Q) 1 k) QJ 7 j ZS _Le t 1 ej!2 i1 L 77 7 G (4) 4 6 t (1 ;7 bb F) t f; n (i M Q) 7S

More information

necessita d'interrogare il cielo

necessita d'interrogare il cielo gigi nei necessia d'inegae i cie cic pe sax span s inuie a dispiegaa fma dea uce < affeandi ves i cen dea uce isnane " sienzi dei padi sie veic dei' anima 5 J i f H 5 f AL J) i ) L '3 J J "' U J J ö'

More information

Computational modeling techniques

Computational modeling techniques Cmputatinal mdeling techniques Lecture 4: Mdel checing fr ODE mdels In Petre Department f IT, Åb Aademi http://www.users.ab.fi/ipetre/cmpmd/ Cntent Stichimetric matrix Calculating the mass cnservatin relatins

More information

I N A C O M P L E X W O R L D

I N A C O M P L E X W O R L D IS L A M I C E C O N O M I C S I N A C O M P L E X W O R L D E x p l o r a t i o n s i n A g-b eanste d S i m u l a t i o n S a m i A l-s u w a i l e m 1 4 2 9 H 2 0 0 8 I s l a m i c D e v e l o p m e

More information

A Simple Set of Test Matrices for Eigenvalue Programs*

A Simple Set of Test Matrices for Eigenvalue Programs* Simple Set f Test Matrices fr Eigenvalue Prgrams* By C. W. Gear** bstract. Sets f simple matrices f rder N are given, tgether with all f their eigenvalues and right eigenvectrs, and simple rules fr generating

More information

Activity Guide Loops and Random Numbers

Activity Guide Loops and Random Numbers Unit 3 Lessn 7 Name(s) Perid Date Activity Guide Lps and Randm Numbers CS Cntent Lps are a relatively straightfrward idea in prgramming - yu want a certain chunk f cde t run repeatedly - but it takes a

More information

Executive Committee and Officers ( )

Executive Committee and Officers ( ) Gifted and Talented International V o l u m e 2 4, N u m b e r 2, D e c e m b e r, 2 0 0 9. G i f t e d a n d T a l e n t e d I n t e r n a t i o n a2 l 4 ( 2), D e c e m b e r, 2 0 0 9. 1 T h e W o r

More information

EFFECT OF THE DIAMETER OF THE LONG-PULSE TUBE ON THE PULSATOR CURVE. M.A. v.d. Brandt and W. Rossing

EFFECT OF THE DIAMETER OF THE LONG-PULSE TUBE ON THE PULSATOR CURVE. M.A. v.d. Brandt and W. Rossing EFFECT F TE DIAMETER F TE LNG-PULSE TUBE N TE PULSATR CURVE M.A. v.d. Brandt and W. Rssing INTRDUCTIN Different makes f milking machines use lng-pulse tubes with varius inside diameters. At the request

More information

Differentiation Applications 1: Related Rates

Differentiation Applications 1: Related Rates Differentiatin Applicatins 1: Related Rates 151 Differentiatin Applicatins 1: Related Rates Mdel 1: Sliding Ladder 10 ladder y 10 ladder 10 ladder A 10 ft ladder is leaning against a wall when the bttm

More information

Chemistry 20 Lesson 11 Electronegativity, Polarity and Shapes

Chemistry 20 Lesson 11 Electronegativity, Polarity and Shapes Chemistry 20 Lessn 11 Electrnegativity, Plarity and Shapes In ur previus wrk we learned why atms frm cvalent bnds and hw t draw the resulting rganizatin f atms. In this lessn we will learn (a) hw the cmbinatin

More information

H NT Z N RT L 0 4 n f lt r h v d lt n r n, h p l," "Fl d nd fl d " ( n l d n l tr l t nt r t t n t nt t nt n fr n nl, th t l n r tr t nt. r d n f d rd n t th nd r nt r d t n th t th n r lth h v b n f

More information

Yeu-Sheng Paul Shiue, Ph.D 薛宇盛 Professor and Chair Mechanical Engineering Department Christian Brothers University 650 East Parkway South Memphis, TN

Yeu-Sheng Paul Shiue, Ph.D 薛宇盛 Professor and Chair Mechanical Engineering Department Christian Brothers University 650 East Parkway South Memphis, TN Yeu-Sheng Paul Shiue, Ph.D 薛宇盛 Prfessr and Chair Mechanical Engineering Department Christian Brthers University 650 East Parkway Suth Memphis, TN 38104 Office: (901) 321-3424 Rm: N-110 Fax : (901) 321-3402

More information

o C *$ go ! b», S AT? g (i * ^ fc fa fa U - S 8 += C fl o.2h 2 fl 'fl O ' 0> fl l-h cvo *, &! 5 a o3 a; O g 02 QJ 01 fls g! r«'-fl O fl s- ccco

o C *$ go ! b», S AT? g (i * ^ fc fa fa U - S 8 += C fl o.2h 2 fl 'fl O ' 0> fl l-h cvo *, &! 5 a o3 a; O g 02 QJ 01 fls g! r«'-fl O fl s- ccco > p >>>> ft^. 2 Tble f Generl rdnes. t^-t - +«0 -P k*ph? -- i t t i S i-h l -H i-h -d. *- e Stf H2 t s - ^ d - 'Ct? "fi p= + V t r & ^ C d Si d n. M. s - W ^ m» H ft ^.2. S'Sll-pl e Cl h /~v S s, -P s'l

More information

CHM112 Lab Graphing with Excel Grading Rubric

CHM112 Lab Graphing with Excel Grading Rubric Name CHM112 Lab Graphing with Excel Grading Rubric Criteria Pints pssible Pints earned Graphs crrectly pltted and adhere t all guidelines (including descriptive title, prperly frmatted axes, trendline

More information

Department of Electrical Engineering, University of Waterloo. Introduction

Department of Electrical Engineering, University of Waterloo. Introduction Sectin 4: Sequential Circuits Majr Tpics Types f sequential circuits Flip-flps Analysis f clcked sequential circuits Mre and Mealy machines Design f clcked sequential circuits State transitin design methd

More information

Trade Patterns, Production networks, and Trade and employment in the Asia-US region

Trade Patterns, Production networks, and Trade and employment in the Asia-US region Trade Patterns, Production networks, and Trade and employment in the Asia-U region atoshi Inomata Institute of Developing Economies ETRO Development of cross-national production linkages, 1985-2005 1985

More information

Kinetics of Particles. Chapter 3

Kinetics of Particles. Chapter 3 Kinetics f Particles Chapter 3 1 Kinetics f Particles It is the study f the relatins existing between the frces acting n bdy, the mass f the bdy, and the mtin f the bdy. It is the study f the relatin between

More information

Phys102 Second Major-102 Zero Version Coordinator: Al-Shukri Thursday, May 05, 2011 Page: 1

Phys102 Second Major-102 Zero Version Coordinator: Al-Shukri Thursday, May 05, 2011 Page: 1 Crdinatr: Al-Shukri Thursday, May 05, 2011 Page: 1 1. Particles A and B are electrically neutral and are separated by 5.0 μm. If 5.0 x 10 6 electrns are transferred frm particle A t particle B, the magnitude

More information

making triangle (ie same reference angle) ). This is a standard form that will allow us all to have the X= y=

making triangle (ie same reference angle) ). This is a standard form that will allow us all to have the X= y= Intrductin t Vectrs I 21 Intrductin t Vectrs I 22 I. Determine the hrizntal and vertical cmpnents f the resultant vectr by cunting n the grid. X= y= J. Draw a mangle with hrizntal and vertical cmpnents

More information

Chapter 3 Kinematics in Two Dimensions; Vectors

Chapter 3 Kinematics in Two Dimensions; Vectors Chapter 3 Kinematics in Tw Dimensins; Vectrs Vectrs and Scalars Additin f Vectrs Graphical Methds (One and Tw- Dimensin) Multiplicatin f a Vectr b a Scalar Subtractin f Vectrs Graphical Methds Adding Vectrs

More information

CHAPTER 24: INFERENCE IN REGRESSION. Chapter 24: Make inferences about the population from which the sample data came.

CHAPTER 24: INFERENCE IN REGRESSION. Chapter 24: Make inferences about the population from which the sample data came. MATH 1342 Ch. 24 April 25 and 27, 2013 Page 1 f 5 CHAPTER 24: INFERENCE IN REGRESSION Chapters 4 and 5: Relatinships between tw quantitative variables. Be able t Make a graph (scatterplt) Summarize the

More information

Flipping Physics Lecture Notes: Simple Harmonic Motion Introduction via a Horizontal Mass-Spring System

Flipping Physics Lecture Notes: Simple Harmonic Motion Introduction via a Horizontal Mass-Spring System Flipping Physics Lecture Ntes: Simple Harmnic Mtin Intrductin via a Hrizntal Mass-Spring System A Hrizntal Mass-Spring System is where a mass is attached t a spring, riented hrizntally, and then placed

More information

rhtre PAID U.S. POSTAGE Can't attend? Pass this on to a friend. Cleveland, Ohio Permit No. 799 First Class

rhtre PAID U.S. POSTAGE Can't attend? Pass this on to a friend. Cleveland, Ohio Permit No. 799 First Class rhtr irt Cl.S. POSTAG PAD Cllnd, Ohi Prmit. 799 Cn't ttnd? P thi n t frind. \ ; n l *di: >.8 >,5 G *' >(n n c. if9$9$.jj V G. r.t 0 H: u ) ' r x * H > x > i M

More information

.Sua. 8f fc"g. II f 8. *1 w. a -a M +» * <N H Q. o * H CO. * o M < a «* n 55 ti 55 «55 «55 Pi. u < < M C C * Ztf fc tf fctf tf tf ISO.

.Sua. 8f fcg. II f 8. *1 w. a -a M +» * <N H Q. o * H CO. * o M < a «* n 55 ti 55 «55 «55 Pi. u < < M C C * Ztf fc tf fctf tf tf ISO. 04 ti tf ti -0 T T5 T) " rt..9..9 *>!. +» 1 +* cc +> 0" +» c >. 0> v > U rt +» P p. e rt i < I' T rt >

More information

Example 1. A robot has a mass of 60 kg. How much does that robot weigh sitting on the earth at sea level? Given: m. Find: Relationships: W

Example 1. A robot has a mass of 60 kg. How much does that robot weigh sitting on the earth at sea level? Given: m. Find: Relationships: W Eample 1 rbt has a mass f 60 kg. Hw much des that rbt weigh sitting n the earth at sea level? Given: m Rbt = 60 kg ind: Rbt Relatinships: Slutin: Rbt =589 N = mg, g = 9.81 m/s Rbt = mrbt g = 60 9. 81 =

More information

Please pick up your Exam1 Answer Sheets at front

Please pick up your Exam1 Answer Sheets at front Pleae pick up yur Exam1 Anwer Sheet at frnt PHY205 Lecture 17 Ch. 8.4, 8.6 (kip 8.5) Rtatinal Equilibrium, Rtatinal rmulatin f ewtn Law Linear v Rtatinal Variable Linear Variable Tranfrmatin Table Rtatinal

More information

Dead-beat controller design

Dead-beat controller design J. Hetthéssy, A. Barta, R. Bars: Dead beat cntrller design Nvember, 4 Dead-beat cntrller design In sampled data cntrl systems the cntrller is realised by an intelligent device, typically by a PLC (Prgrammable

More information

AP Physics Kinematic Wrap Up

AP Physics Kinematic Wrap Up AP Physics Kinematic Wrap Up S what d yu need t knw abut this mtin in tw-dimensin stuff t get a gd scre n the ld AP Physics Test? First ff, here are the equatins that yu ll have t wrk with: v v at x x

More information

BASIC DIRECT-CURRENT MEASUREMENTS

BASIC DIRECT-CURRENT MEASUREMENTS Brwn University Physics 0040 Intrductin BASIC DIRECT-CURRENT MEASUREMENTS The measurements described here illustrate the peratin f resistrs and capacitrs in electric circuits, and the use f sme standard

More information

Q1. A string of length L is fixed at both ends. Which one of the following is NOT a possible wavelength for standing waves on this string?

Q1. A string of length L is fixed at both ends. Which one of the following is NOT a possible wavelength for standing waves on this string? Term: 111 Thursday, January 05, 2012 Page: 1 Q1. A string f length L is fixed at bth ends. Which ne f the fllwing is NOT a pssible wavelength fr standing waves n this string? Q2. λ n = 2L n = A) 4L B)

More information

February 28, 2013 COMMENTS ON DIFFUSION, DIFFUSIVITY AND DERIVATION OF HYPERBOLIC EQUATIONS DESCRIBING THE DIFFUSION PHENOMENA

February 28, 2013 COMMENTS ON DIFFUSION, DIFFUSIVITY AND DERIVATION OF HYPERBOLIC EQUATIONS DESCRIBING THE DIFFUSION PHENOMENA February 28, 2013 COMMENTS ON DIFFUSION, DIFFUSIVITY AND DERIVATION OF HYPERBOLIC EQUATIONS DESCRIBING THE DIFFUSION PHENOMENA Mental Experiment regarding 1D randm walk Cnsider a cntainer f gas in thermal

More information

Lead/Lag Compensator Frequency Domain Properties and Design Methods

Lead/Lag Compensator Frequency Domain Properties and Design Methods Lectures 6 and 7 Lead/Lag Cmpensatr Frequency Dmain Prperties and Design Methds Definitin Cnsider the cmpensatr (ie cntrller Fr, it is called a lag cmpensatr s K Fr s, it is called a lead cmpensatr Ntatin

More information

o ri fr \ jr~ ^: *^ vlj o^ f?: ** s;: 2 * i i H-: 2 ~ " ^ o ^ * n 9 C"r * ^, ' 1 ^5' , > ^ t g- S T ^ r. L o n * * S* * w 3 ** ~ 4O O.

o ri fr \ jr~ ^: *^ vlj o^ f?: ** s;: 2 * i i H-: 2 ~  ^ o ^ * n 9 Cr * ^, ' 1 ^5' , > ^ t g- S T ^ r. L o n * * S* * w 3 ** ~ 4O O. THE PENALTY FR MAKING A FALSE STATEMENT IN THIS REPRT AND/R CERTIFICATE IS S5. R SIX MNTHS IMPRISNMENT R BTH "D "? y. " cr TJ Xl^ " Q. rt 5' "g s r ^.. C i :? S :.. y ' : s s ^ST (X. I ^^ ^ ^ S : t ^ :

More information

Drought damaged area

Drought damaged area ESTIMATE OF THE AMOUNT OF GRAVEL CO~TENT IN THE SOIL BY A I R B O'RN EMS S D A T A Y. GOMI, H. YAMAMOTO, AND S. SATO ASIA AIR SURVEY CO., l d. KANAGAWA,JAPAN S.ISHIGURO HOKKAIDO TOKACHI UBPREFECTRAl OffICE

More information

NAME TEMPERATURE AND HUMIDITY. I. Introduction

NAME TEMPERATURE AND HUMIDITY. I. Introduction NAME TEMPERATURE AND HUMIDITY I. Intrductin Temperature is the single mst imprtant factr in determining atmspheric cnditins because it greatly influences: 1. The amunt f water vapr in the air 2. The pssibility

More information

Math Foundations 20 Work Plan

Math Foundations 20 Work Plan Math Fundatins 20 Wrk Plan Units / Tpics 20.8 Demnstrate understanding f systems f linear inequalities in tw variables. Time Frame December 1-3 weeks 6-10 Majr Learning Indicatrs Identify situatins relevant

More information

Experiment #3. Graphing with Excel

Experiment #3. Graphing with Excel Experiment #3. Graphing with Excel Study the "Graphing with Excel" instructins that have been prvided. Additinal help with learning t use Excel can be fund n several web sites, including http://www.ncsu.edu/labwrite/res/gt/gt-

More information

WRITING THE REPORT. Organizing the report. Title Page. Table of Contents

WRITING THE REPORT. Organizing the report. Title Page. Table of Contents WRITING THE REPORT Organizing the reprt Mst reprts shuld be rganized in the fllwing manner. Smetime there is a valid reasn t include extra chapters in within the bdy f the reprt. 1. Title page 2. Executive

More information

Ice Accretion Prediction Code

Ice Accretion Prediction Code Ice Accretin Predictin Cde Vladimír Hrák University f Defence Institute f Hydrdynamics, Academy f Sciences Czech Republic 1 Dedicated t the memry f Dr. Bhumír Hření 2 Mtivatin The in-flight icing may affect

More information

COASTAL ENGINEERING Chapter 2

COASTAL ENGINEERING Chapter 2 CASTAL ENGINEERING Chapter 2 GENERALIZED WAVE DIFFRACTIN DIAGRAMS J. W. Jhnsn Assciate Prfessr f Mechanical Engineering University f Califrnia Berkeley, Califrnia INTRDUCTIN Wave diffractin is the phenmenn

More information

205MPa and a modulus of elasticity E 207 GPa. The critical load 75kN. Gravity is vertically downward and the weight of link 3 is W3

205MPa and a modulus of elasticity E 207 GPa. The critical load 75kN. Gravity is vertically downward and the weight of link 3 is W3 ME 5 - Machine Design I Fall Semester 06 Name f Student: Lab Sectin Number: Final Exam. Open bk clsed ntes. Friday, December 6th, 06 ur name lab sectin number must be included in the spaces prvided at

More information

SPH3U1 Lesson 06 Kinematics

SPH3U1 Lesson 06 Kinematics PROJECTILE MOTION LEARNING GOALS Students will: Describe the mtin f an bject thrwn at arbitrary angles thrugh the air. Describe the hrizntal and vertical mtins f a prjectile. Slve prjectile mtin prblems.

More information

Synchronous Motor V-Curves

Synchronous Motor V-Curves Synchrnus Mtr V-Curves 1 Synchrnus Mtr V-Curves Intrductin Synchrnus mtrs are used in applicatins such as textile mills where cnstant speed peratin is critical. Mst small synchrnus mtrs cntain squirrel

More information

A Comparison of Methods for Computing the Eigenvalues and Eigenvectors of a Real Symmetric Matrix. By Paul A. White and Robert R.

A Comparison of Methods for Computing the Eigenvalues and Eigenvectors of a Real Symmetric Matrix. By Paul A. White and Robert R. A Cmparisn f Methds fr Cmputing the Eigenvalues and Eigenvectrs f a Real Symmetric Matrix By Paul A. White and Rbert R. Brwn Part I. The Eigenvalues I. Purpse. T cmpare thse methds fr cmputing the eigenvalues

More information

NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS

NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS r NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS TECHNICAL NOTE 1930 AN ANALYSIS OF THE EFFECT OF LIFT-DRAG RATIO AND STALLING SPEED ON LANDING-FLARE CHARACTERISTICS By J. Calvin Lvell and Stanley Lipsn v

More information

Space Shuttle Ascent Mass vs. Time

Space Shuttle Ascent Mass vs. Time Space Shuttle Ascent Mass vs. Time Backgrund This prblem is part f a series that applies algebraic principles in NASA s human spaceflight. The Space Shuttle Missin Cntrl Center (MCC) and the Internatinal

More information

MODULE FOUR. This module addresses functions. SC Academic Elementary Algebra Standards:

MODULE FOUR. This module addresses functions. SC Academic Elementary Algebra Standards: MODULE FOUR This mdule addresses functins SC Academic Standards: EA-3.1 Classify a relatinship as being either a functin r nt a functin when given data as a table, set f rdered pairs, r graph. EA-3.2 Use

More information

Precalculus A. Semester Exam Review

Precalculus A. Semester Exam Review Precalculus A 015-016 MCPS 015 016 1 The semester A eaminatin fr Precalculus cnsists f tw parts. Part 1 is selected respnse n which a calculatr will NOT be allwed. Part is shrt answer n which a calculatr

More information

Land Information New Zealand Topographic Strategy DRAFT (for discussion)

Land Information New Zealand Topographic Strategy DRAFT (for discussion) Land Infrmatin New Zealand Tpgraphic Strategy DRAFT (fr discussin) Natinal Tpgraphic Office Intrductin The Land Infrmatin New Zealand Tpgraphic Strategy will prvide directin fr the cllectin and maintenance

More information

the results to larger systems due to prop'erties of the projection algorithm. First, the number of hidden nodes must

the results to larger systems due to prop'erties of the projection algorithm. First, the number of hidden nodes must M.E. Aggune, M.J. Dambrg, M.A. El-Sharkawi, R.J. Marks II and L.E. Atlas, "Dynamic and static security assessment f pwer systems using artificial neural netwrks", Prceedings f the NSF Wrkshp n Applicatins

More information

46 D b r 4, 20 : p t n f r n b P l h tr p, pl t z r f r n. nd n th t n t d f t n th tr ht r t b f l n t, nd th ff r n b ttl t th r p rf l pp n nt n th

46 D b r 4, 20 : p t n f r n b P l h tr p, pl t z r f r n. nd n th t n t d f t n th tr ht r t b f l n t, nd th ff r n b ttl t th r p rf l pp n nt n th n r t d n 20 0 : T P bl D n, l d t z d http:.h th tr t. r pd l 46 D b r 4, 20 : p t n f r n b P l h tr p, pl t z r f r n. nd n th t n t d f t n th tr ht r t b f l n t, nd th ff r n b ttl t th r p rf l

More information

ADORO TE DEVOTE (Godhead Here in Hiding) te, stus bat mas, la te. in so non mor Je nunc. la in. tis. ne, su a. tum. tas: tur: tas: or: ni, ne, o:

ADORO TE DEVOTE (Godhead Here in Hiding) te, stus bat mas, la te. in so non mor Je nunc. la in. tis. ne, su a. tum. tas: tur: tas: or: ni, ne, o: R TE EVTE (dhd H Hdg) L / Mld Kbrd gú s v l m sl c m qu gs v nns V n P P rs l mul m d lud 7 súb Fí cón ví f f dó, cru gs,, j l f c r s m l qum t pr qud ct, us: ns,,,, cs, cut r l sns m / m fí hó sn sí

More information

OH BOY! Story. N a r r a t iv e a n d o bj e c t s th ea t e r Fo r a l l a g e s, fr o m th e a ge of 9

OH BOY! Story. N a r r a t iv e a n d o bj e c t s th ea t e r Fo r a l l a g e s, fr o m th e a ge of 9 OH BOY! O h Boy!, was or igin a lly cr eat ed in F r en ch an d was a m a jor s u cc ess on t h e Fr en ch st a ge f or young au di enc es. It h a s b een s een by ap pr ox i ma t ely 175,000 sp ect at

More information

< < or a. * or c w u. "* \, w * r? ««m * * Z * < -4 * if # * « * W * <r? # *» */>* - 2r 2 * j j. # w O <» x <» V X * M <2 * * * *

< < or a. * or c w u. * \, w * r? ««m * * Z * < -4 * if # * « * W * <r? # *» */>* - 2r 2 * j j. # w O <» x <» V X * M <2 * * * * - W # a a 2T. mj 5 a a s " V l UJ a > M tf U > n &. at M- ~ a f ^ 3 T N - H f Ml fn -> M - M. a w ma a Z a ~ - «2-5 - J «a -J -J Uk. D tm -5. U U # f # -J «vfl \ \ Q f\ \ y; - z «w W ^ z ~ ~ / 5 - - ^

More information

0 t b r 6, 20 t l nf r nt f th l t th t v t f th th lv, ntr t n t th l l l nd d p rt nt th t f ttr t n th p nt t th r f l nd d tr b t n. R v n n th r

0 t b r 6, 20 t l nf r nt f th l t th t v t f th th lv, ntr t n t th l l l nd d p rt nt th t f ttr t n th p nt t th r f l nd d tr b t n. R v n n th r n r t d n 20 22 0: T P bl D n, l d t z d http:.h th tr t. r pd l 0 t b r 6, 20 t l nf r nt f th l t th t v t f th th lv, ntr t n t th l l l nd d p rt nt th t f ttr t n th p nt t th r f l nd d tr b t n.

More information

Pressure And Entropy Variations Across The Weak Shock Wave Due To Viscosity Effects

Pressure And Entropy Variations Across The Weak Shock Wave Due To Viscosity Effects Pressure And Entrpy Variatins Acrss The Weak Shck Wave Due T Viscsity Effects OSTAFA A. A. AHOUD Department f athematics Faculty f Science Benha University 13518 Benha EGYPT Abstract:-The nnlinear differential

More information

A Matrix Representation of Panel Data

A Matrix Representation of Panel Data web Extensin 6 Appendix 6.A A Matrix Representatin f Panel Data Panel data mdels cme in tw brad varieties, distinct intercept DGPs and errr cmpnent DGPs. his appendix presents matrix algebra representatins

More information

L a) Calculate the maximum allowable midspan deflection (w o ) critical under which the beam will slide off its support.

L a) Calculate the maximum allowable midspan deflection (w o ) critical under which the beam will slide off its support. ecture 6 Mderately arge Deflectin Thery f Beams Prblem 6-1: Part A: The department f Highways and Public Wrks f the state f Califrnia is in the prcess f imprving the design f bridge verpasses t meet earthquake

More information

Fabrication Thermal Test. Methodology for a Safe Cask Thermal Performance

Fabrication Thermal Test. Methodology for a Safe Cask Thermal Performance ENSA (Grup SEPI) Fabricatin Thermal Test. Methdlgy fr a Safe Cask Thermal Perfrmance IAEA Internatinal Cnference n the Management f Spent Fuel frm Nuclear Pwer Reactrs An Integrated Apprach t the Back-End

More information

Q x = cos 1 30 = 53.1 South

Q x = cos 1 30 = 53.1 South Crdinatr: Dr. G. Khattak Thursday, August 0, 01 Page 1 Q1. A particle mves in ne dimensin such that its psitin x(t) as a functin f time t is given by x(t) =.0 + 7 t t, where t is in secnds and x(t) is

More information

Medium Scale Integrated (MSI) devices [Sections 2.9 and 2.10]

Medium Scale Integrated (MSI) devices [Sections 2.9 and 2.10] EECS 270, Winter 2017, Lecture 3 Page 1 f 6 Medium Scale Integrated (MSI) devices [Sectins 2.9 and 2.10] As we ve seen, it s smetimes nt reasnable t d all the design wrk at the gate-level smetimes we just

More information

n r t d n :4 T P bl D n, l d t z d th tr t. r pd l

n r t d n :4 T P bl D n, l d t z d   th tr t. r pd l n r t d n 20 20 :4 T P bl D n, l d t z d http:.h th tr t. r pd l 2 0 x pt n f t v t, f f d, b th n nd th P r n h h, th r h v n t b n p d f r nt r. Th t v v d pr n, h v r, p n th pl v t r, d b p t r b R

More information

Sub: Submission of the copy of Investor presentation under regulation 30 of SEBI (Listing Obligations & Disclosure Reguirements) Regulations

Sub: Submission of the copy of Investor presentation under regulation 30 of SEBI (Listing Obligations & Disclosure Reguirements) Regulations matrimny.cm vember 1, 218 tinal Stck xchange f India Ltd xchan laza, 5th Flr Plt : C/1, Sand Krla Cmplex, Sa Mmbai - 4 51 Crpte Relatinship Department SS Ltd., Phirze Jeejheebhy Twers Dalal Street, Mmbai

More information

Study Group Report: Plate-fin Heat Exchangers: AEA Technology

Study Group Report: Plate-fin Heat Exchangers: AEA Technology Study Grup Reprt: Plate-fin Heat Exchangers: AEA Technlgy The prblem under study cncerned the apparent discrepancy between a series f experiments using a plate fin heat exchanger and the classical thery

More information

> DC < D CO LU > Z> CJ LU

> DC < D CO LU > Z> CJ LU C C FNS TCNCAL NFRMATN CNTR [itpfttiiknirike?fi-'.;t C'JM.V TC hs determined n \ _\}. L\\ tht this Technicl cment hs the istribtin Sttement checked belw. The crnt distribtin fr this dcment cn be telind

More information

& Ö IN 4> * o»'s S <«

& Ö IN 4> * o»'s S <« & Ö IN 4 0 8 i I *»'S S s H WD 'u H 0 0D fi S «a 922 6020866 Aessin Number: 690 Publiatin Date: Mar 28, 1991 Title: Briefing T mbassy Representatives n The Refused Strategi Defense Initiative Persnal Authr:

More information