How does tail configuration affect spinning characteristics?

Tail configuration affects spinning characteristics by influencing spin damping properties, yaw damping, and pitching moments during spin conditions.

What testing methods were used in the study?

The study employed static wind tunnel tests to evaluate the spin damping characteristics of an isolated tail section oriented to simulate equilibrium spin.

What factors were found to influence yaw damping?

The vertical position of the horizontal stabilizer was identified as a primary factor affecting yaw damping.

What conclusion was drawn about rudder size during spins?

It was concluded that a full-span rudder produces greater yawing moments than a partial-span rudder under steep spin conditions.

An experimental study of the effect of tail configuration on the spinning characteristics of general aviation aircraft

Q: What was the purpose of the study?

The purpose of the study was to determine the feasibility of using static wind tunnel tests to obtain information about spin damping characteristics of an isolated general aviation aircraft tail.

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TUE EfP£CT Of TAIL CONfIGUbA1IC~ OM ThE SPIHIIU~ CHARAC1ERISTICS Of ~&dEaAL A~IAIIOH Unci"':.> llHCBlfT ft.~. 1hcsis (f~nuhylvaDi4 ~tat~ 0919S IJniv.) 181 p ilC AIl~/"F AO 1 CS'..:L 01C G)/Od .. ~ ", ~~i~;:'·.~~~:-;l.~ . . ,~t~';;:' .. ~':'.~~,:"j'~'~" ~'<~_,,:,,!I, ::=t~ ~'t:-·,;~:.~, .. ~3:;, ,<~rr~~)'T~:~,'-"'< ,"~t: ":~', ' • ~'~." ",': .", '.V' , .," ......

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:~, - , - " ' _ e P e nns y lv a ni a St a t e Univ ers it y T h e G r ad u a t e S c h oo l Dep a r _ent o f Ae r ospace E ngin ee ring A n Ex pe r ime n t al Stu d y o f the Effect o f T ai l Co n f ig ura ti on on t he Sp i n n i n g Ch arac t e risti cs of Ge n eral A v i a ti o n Airc ra ft A The sis i n Ae r o s p ac e E n gin e er i ng b y • Ha rk G . B_l l tn i Submitt e d In P ar ti a l _Ifillme n t of the Requirements for the Degree of .R_st e r of Sc i e n ce Mnrch1982 I gran t The Pennsyl v ania State Universi t y the nonex c luslv e righ t to use t his work for the Universi t y's own purposes and to make sln£1e c opies of the work available tO the p u bli c on a no t -for-profl t basis if c opies are not otherwise available.

m Hark G. 5allin J We app rov e t h e th e sis of M a rk G . Ballln.

Da t e o £ S i gn at ure: S i gna t or i es: c B a rn e s W. M cC orm ic k, Prof es s o r a n d H e a d o f A e r os pa c e Engin ee ring T he s i s Advis e r Jo s e ph J. Eisenhuth, Asso c i a te Pr of e sso r o f Ae r osp ace Engl n eer iu g Hubert C. Smi t h,Assistant Pr o fessorof AerospaceEngineering • • .• .

iii !

ABSTRAC T Spi n ni ng ch a ra ct er i s ti cs of ge n eral a vi a ti o n a i rc r a ft a re close l y i re late d t o th e spl n- da m p in g prop e r ti e s of t h e ta il. Pr e vious ex p e rim e ntal st u di es ha v e c o nc e n trat e d on o bt_I n l n g aerody nami c c hara cte r is ti c s o f a co m p lete ai rp lan e , m a king d ynami c t esti ng n e cess ary to d upli ca t e th e e ff ec t s o f a rotational flow fi e ld. In s tu d ie s o f an isolated tail, stat i c testin g m a y b e possible. The p ur po se o f this investi g ation is to determine the f e asibility of usin g stati c wind t u n ne l tes t s to o b ta in in f orm at ion a bout spin d a m p in g c h a ra c teri s t ic s of ..... • a n isol a ted g e n e ral avi a tion a ir c r a ft t a il. A rep r e sentativ e t a ll s ec tion w a s o ri e nt ed t o th e tun n el fr ee s tr ea mline a t a ngles simul a ting.

a n equilibr i um sp i n. A full range of norm a lly en c ountered s pin c o nditions w a s employed. In addition, p a rametric s tudies were performed to d ete rmin e t h e effec t o f s p in dam p ing on s ev er a l t a il design parame t ers. _e resul t s show satisf ac tory a greement with NASA rotary balan c e tes t s. Wing and body interferen c e effe c ts a re present in the NASA studles at s t edpspin a ttitudes, but agreement im p roves with in c reasing pit c h angle a_d spin rate, suggesting that rotational flow• effe c ts are minimal. Verti c al position of the horizontal stabilizer is found to be a primary parameter affe c ting ya w d a mping, a nd horizontal tail c hordwise position indu c es a substantial effe c t on pit c hing moment.

A full-_pan rudde r produces greater yawing moments th a n a partlal-span rudder under steep spin conditions, while differen c es are small under flat spin conditions. Correlation of yawing moments to exposed verti c al tall area is fair for steep spin =onditlo n s. For a flat spin, a three- dimensional model of the separated r_<_ : .on above the horizontal tall is ne c essary for an improved correlat[_ , :_.

iv T_ BLE O F CO NT EN TS P a e.

A_ S TR ACT ............................ ill L I ST OF TABLE S ......................... v i LIS T O F F IG U R ES ........................ v ii L I ST O F S YM B OL S ........................ x iii ACKN OW LED G ------------------- _ I.'TS ." ....................... xv C HAP TE R I - INTR ODUC TION I Overv i e w o f Sp i n Dy n ami c s ................. i S c op e o f th e P re s e nt Testing ................ 5" R e c e nt Fr ee -Flight S p in Tu n n e l T e sts ........... 1 2 Rotary B ala n c e Te sts ................... ' S pin Orientations ..................... 1 8 Mod e l Configurations .......... ..... • •.. • 23 Effects o f S pin Rate o n A er o dynamic M o ment C oefficients . . 43 Effects of Control Deflection r .............. I00 CI I AP T ER V . DEVELOPMENT OF A PREDIC T IVE PARAMETER ....... 10b i i Adequacy of the Tail Damping Power Factor ......... II0 !

M o ment Co rrelation with a Modified Anti-Spin Pa r ameter . 112 I r • i i !

| v B-- I !

J i" P a._ _ e

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APPENDIX A. MODELAND APPARATU S DIMEN S IONS AND C O NFIGURATIONS . 12 2 i AP P ENDIX B. AERODYNAMIC M O MENT C OE F F IC IENTS A S FUN C TIONS O F SPIN RATE......................... 12 7 , AP P ENDIX C T ES TD A TA " 1 5 2 I . .

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l vi q L I S T OF TA. _ LES Table Pag e : 3-1 Angleof Atta c kas a Fu, : c_ion of Pit c hAng l ean d Spin ' Rat e f o r T e st O rient a ti o ns 22 % • • • • • • • • • • • • • • • • A-I C o nfigu r ation Dimension s .... 12 3 C -I C on f igur a tion A T es t Dat a ................ 15 3 C - 2 C on f igu r ation B T.-,r Dat a ................ 1 54 - on u r a on C T est a t a ................

C 3 C f ig ti D "'' 1 5 5 C-4 C on f iguration D Test Dat a ................. 1 5 6 C - 5 C onfig u ration E T e s t D at a ................. 15 7' .

C -6 C o n figuration F Test Dat a ................ 15 8 C - 7 C on f iguration G Test D ata ................ 1 5 9 C- 8 C onfigur a tion H Test Dat a ................ i60 C- 9 C onfiguration J T e st Data ................ 16 1 C-10 Config u rat i on K Test Dat a ................ 16 2 C-II Con gura i n L Test Data ................

C -1 2 Co nfiguration M Te s t Data . 164 • C-1 3 Co ntrol Defle c tion T est I Data, 8 = 40°, u = 2 0.71 ° • • . 16 5 v C-14 C ontrol Defle c tio v Test 2 Data, 8 = 80 ° , a = 30.08 Q . . . 166 v vii L IS T O F FIGURE S 2-I Computation o f the Tall Damping Power Factor ...... I0 .

2-2 Tail Damping Power Factor as a Func t ion of IYMP, - < 15 ......................... II 2- 3 General Aviation S pin C rit e rion Based on the TDPF (1947). 1 3 2-4 NASA Typical Single-Engine Genera_ Aviati o n Design • • • 14 3-2 Tall Orientation with Respect to Total Velocity Vector . 20 3-3 Configuration A ..................... 26 , 3-4 V ariation of h / bv .................... 2 7 3-6 Variation of ARv ............. • • • •-__ •. • • 29 .° 3-9 Model and Support in Test Section, C onfiguration A; e r 4-1 Tails Used in Comparison with NASA Rotary Balance Data . 45 4-2 Pitching Moment as a Function of O and _, viii 4- 3 Y awi n g M o ment as a Fu nc tio n o f 8 an d _, Confi g uration C ..................... 4 8 4 - 4 Pitc h ing Mo m ent as a Function of e and _, C o nfiguration B .................. . . . 49 4-5 Yawing Moment as a Function of O an d _, 4 -6 Pit ch ing M oment a s a F un c ti on of V erti c a l PoSiti o n o f 4-7 Pitching Momenta s a Function of Ve r ti c a l P o s i tion o f 4 -8 Pit ch ing M o ment as a Fun ct i on of V ertic al P o si tio n of Horizontal T ail,_ = . 5 ................. 5 4 4 - 9 Pitching M o ment as a F u nction of Verti c a l P os iti o n o f 4-10 Pitching Moment as a Fun c tion of Vertic a l Pos i tion o f Hor i zontal T ail, _ - .9 ................. 5 6 4 -11 Fl o w About Co n f igurations C and D at High Spin Rate . . 5 7 4-1 2 Yawing Moment as a Fun c t i on of Vert i cal Po si t i on of Hor i zontal T a il , _ - . 3 ................. 5 9 _- 4- 13 Yawing Moment as a Fun c tion of Vertica l Position of Horizontal T ail, _ = .5 ................. 6 0 . 4-14 Yawing Moment as a Function of Vertical Position of Horizontal Tai l, _ = .7 ................. 6 1 4-15 _awing Moment as a Fun c tion of Vertical Position of 4-16 Yawing Moment as a Function of Horigontal Tall 4-17 Yawing Moment as a Function of Horizontal Tail 4-18 K as a Function of Vertical Position of Horizontal i 4-19 Pitching Moment as a F u nction o f V ertic a l Tail A spec t ix .°

mgure

• ° 4 -20 Pitchin g Moment as a Function o f Ve r tlea l T all As pec t - 70 Ratio, _ = .5 ......................

4- 2 1 Pit c hing M o ment as a Functi o n of V er tl c al T all As pe ct - 71 Rati o , _ = .7 ......................

4 -2 2 Pit c hing Mom e ntas a Fun c tion of Vertical TallAspe c t R a tio _ = 9 7 2 , • eeeeo oo eee l eeee o e o eee o " 4- 23 Y a wing Moment a s a Fun c tion of Ve rti ca l T al l Asp ec t Ratio, _ = . 3 ....... ............... 7 3 . " 4- 2 4 Y a win g Mome n t a s a Fun c tion of V e rti ca l T ai l As pec t R a tio, _ = .5 ...................... 7 4 4- 2 5 Y a wing Moment a s a Fun c tio n of V e rti ca l T a ll Asp e c t Ra t io _ = 7 75 , • eee e eoeoe oQoQ oe _ eeeee o 4- 2 6 Yawing Moment as a Fun c tion of Vertl c al Tall Aspe c t 6 4- 2 7 Effect of 8 and _v on Unbl a nke t ed Vertical Tall Are a at t 4- 2 8 Definition of Sideslip Angle .............. 7 8 • 4- 2 9 Vertical TailNormalFor c eas a Function of Sideslip 4-30 ?it c hlng ' Moment as a Function of Horizontal Tall 4-31 Pitching Moment as a Fun c tion of Horizontal Tall Aspe c t Ratio, _ = .3 .................. 8 2 4-32 Pitching M o ment a s a Fun c tion of Horizontal T a ll 4-33 Pi t ching Moment a s a F u ncti o n of Hor--lzont a l Tail 4-34 Pitching Momentas a Functi o n of Horizont a l Tall Aspect Ratio, _ = .9 .................. 3 5 4-3 5 Y a wing Moment as a Function of Horizontal Tall Aspect x b

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P . _ m m

! 4 - 36 Y a wing Moment as a Fun c tiozt of Horizo n tal Tail As p e c t 5 87 - - Ra tio, - ......................

! 4- 37 Yawing Moment as a Function o f H o rizontal T ail Aspect 1 4- 38 Yawing M o m e nt as a Fun c tion o f H or izo n tal Tail Aspe c t ' R a tio _ = .9 ...................... 8 9 % _- 4-3 9 Pit ch i n g Mo m e n t as a Fu n c ti on of Ho riz ont a l P os itio n . - 4 - 40 Pitching Moment as a Fun c ti o n o f H ori z ontal P o sition I i o f Ho rizontal Tail, _ - . 3 ............... 9 2 4-41 Pit c hin g M o ment as a Function of Horizontal Position ° _ ' of Horizorta l Tail, _ - . 5 ....... " 9 3 • eeo ee o 4 - 4 2 • Pitching Moment as a Fun c tion of Horizonta l Position i 4 - 4 3 P itching Moment a s a Fun c tion o f H o rizontal Pos i tion i o f Hor izontal Ta il , _ - . 9 .............. 9 5 4 - 44 Yawing Moment a s a Functi o n o f Horizont al Po s ition of 4-45 Yawing Moment as a Function of Horizontal Position of Horiz o ntal T ai l , _ = . 5 . . 9 _ 4-46 Yawing Mo m ent as a Function of Horizonta l P osition of 4-47 Yawing Moment as a F u _n of Horizonta l Position of 4-48 PitL . ning ! _oment as a Fu nc ti o n of Elevator D e fle c tion i01 4-49 Yawing Momen t as a Function of Elevator Deflection 102 4-50 P i tching Moment as a Function of Rudder Deflection, 4-51 Yawing Moment as a Function of Rudder Deflection, 4 - 5 2 P i tch i ng Moment a s a F u nction of C o_ined C ontrol xi F_ ure Pa_e 4-5 3 Y awi ng Mo m e n t as a Function o f C e m Sin e d Co ntr o l : 5 -i Yawing Mo m ent a s a Function o f Tail Damping P o wer _ " Factor ......................... iii 5-2 Actual Flow Around a Stalled Airfoil C ompared with the 5 - 4 Yawing M o ment as a Fun c ti o n o f T a il Anti -S pln Parameter . 11 7 A-2 NASA IR- 2 1 Balance ................... 12 5 B - I Pitching M o ment as a Function of 8 and _, - B-2 Pitching M o ment as a Functi o n o f O and _, Co nfiguration B ..................... 129 " , B-3 Pitching M o men t as a Function of 8 and _, B-4 Pitching M o ment as a Fun c ti o n of 8 an d _, ° B-5 Pit c hing M o m ent a s a •Function o f @ and _, B-6 Pit c hing Moment as a Function of 0 and _, B-7 P_tching M o ment as a Function o f @ an d _, B-8 Pitching Moment as a Function of 9 and _, B-9 P itching M o ment as a Function of 8 and _, Config u ration J ..................... 136 •.

B-IO Pit c hing M o ment as a Function o f 0 and _, Configuration K ..................... 13 7 ; xfi B-!I Pit c hing Mo m entas a Fun c ti o n o f @ and _, Configuration L ...................... !38 B-12 Pitching M o ment a s a F u ncti o n o f @ and _, B-13 Yawing Moment as a F u n c t ion of 8 and _, C onfiguration A. 140 B-14 Yawing M o ment as a Fun c t ion of e and _, C onfiguration B . 141 B.-15 Yawing M o ment as a Function o f 8 and _, Configurati o n C . 142 B-16 Yawing M o ment as a Fun c t ion o f e and _, Configuration D . i_3 B-1 7 Yawing Moment as a Fun c ti o n o f 0 an d _, C onfiguration E 144 B-18 Yawing M o ment as a Fun c tion of 0 and _, C onflgura c l o n F . 145 " B-19 Yawlh_M o mentas a F u n c ti o n o f 8 _-d_, Co nfi g uration G . 146 B-20 YawingMomentas a Fun c tion o f O and _, C onfiguration H . 14 7 B-J1 Ya%!ng Mome.mtas a Function of @ and _, Configuration J . 148 i_ - 2 2 Yawing M o me nt as a Fun c t i o n o f @ an d _, Configuration K . 149 B-23 Y a wing Mo m en t as a Function of @ and _, Configuration L . 150 B'24 Yawln_ Moment as a F u nction of 8 and _ Configuration H . 1 5 1 .0 q : 1 xiii ! I | LIST O F S YMB OL S t _ A axial fo r ce : A R aspec t r a ti o b spa n o f w in _ o r t al l s u rf ace , : C L l lf t c o efficien t fo r a fi n i t e w ing o r ai rpl a n e, L / - 1 2 O V2 S i t# C L ll ft c urv e slo p e fo r a fini t e w ing o r ai rp lane, " " . '" a 1 _ L 1 1 2 ' _ V2 S _ CI sec t i on llf t c ur ve slo p e, I / O V 2 € _ . .. _ I V2 CF si d e force co e fg lc le nt , Fs / _ 0 S s • V 2 _m pit c hing m o m en t coe f f i cien t m / ½0 Sc C. n orm al f o rce coefficien t • N / 1 0 V 2 S i_ ..

C yaw in g m o._e nt c oeff lc i_nt , n / _ C V2 Sb I C p p r e ssur e c o efficien t , p / _ O V" c c h o rd lengt h m e an ae r odyn a m ic c ho r d F s i d e fo rce t_ g a c cele r a t i on of gra v it y h verti cal dist a n c e from th e hor iz o n t al s tabiliz er t o th e fu s el a ge re f e r e nce line $ h / b ratio of horizontal stab i lizer height to v e rt ic al tail span V I monent of inertia about the x-axis x I m o ment of i ne r t i a about the y-a xi s Y K pressure d._.str i butl on under the horizontal ta i l K1 constant used i n sp i n pred i cti v e pa r ameter xiv K2 c o n sta n t us e d in _ pln pred i ct iv e p a r a m ete r L llft 1 dis t a n ce from h o riz o n ta l t a il I / 4 -chord p o int t o e . g .

t m pitching m o m ent; a ir c raf t m=s n ....

S norm a l force n ya w in g moment R s pt n r a d ium ..

n S area o f wing o r ta_l s ur fa c e Vd des c en t velocity . '. "" VT t o t al vel oc it y x, y. = b o d y -fix e d coordin at e axes; x p osi t ive for wa rd, z p o s i t iv e do w n • . . • .

a a n g le a t w hi c h flo w app ro a ches th e t a il i n t he pl a ne par a lle l v t o t h e spin a xi s a nd t he b ody-fixed y- a xis ;v ' ta il , b o d y -fixed s idesli p a ngle - . " a pi t c h a ngl e :: d ensi ty c o effici e n t , m / ." Sb , " density ro ll a ngl e _ s p in r a t e. r ad i a ns p er se c on d nondi _ e n sion al sp in ra te. _ , ; h hori --on e s I t a i l - i!

v v e rt i cal ta t l ;.I :1 w ma in w t nq !!

I! , xv " ACKN Ot _ 'LE D G E. _I E h_ S I w ou l d l ik e t o ex p r e ss m y a ppr e ct atl o |_ t o Dr. Barnes W . M cCormick for his . _ utd a nce tn th e concep t ion and r ea l l z a t i on of t h is w ork. I a m alb o indeb t ed t o H r. Rex J a c o b s c _nd H r. Leon Fe tt ero l f for t he l r h e l p trr des i g n i n g a nd bui ldl nR t . h eex p erimen t_ tl ap pa r a t us.

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C lIAP T E R l I h_ RO D UCTIO N I n a s t e ad y s pin, t he ve l oc ity a t t he t al l o f an a ir p l ane r e s u lts from t he vec tor sum of t he v e rti ca l d e s cen t v e lo c ity an d tra n sv e rs e v e lo ci ty ca us e d by rot a t i o n of t he a irpl ane. The r e s u lt ing f low th e r efore a p p ro ache s the tal l from below an d to o n e s i d e , at an ang l e ?

w hich Is d e p en d en t o n p itch an d ro ll att i t ud e , s pin r at e . an d d esc e n t vel o ci ty . F r o m t he a i rc r aft r efe r ence fr a m e, t he f low i s r o t a t ional, m a ki ng con v e n t i o na l wi nd tun ne l st u di e s i nap propri a t e f or de t e rmi n i ng i ae rod y n a mi c f or ce s on a c om p l e t e a ir p l ane. Th e p urpos e o f t h is l n v e st [ g a tion is to determi ne whether or not f o rce s a t t h e t a il can be a c c urat e ly obta in e d with stati c win d t u nn el te_ t s by orienting a model ..

t a il to the f low a t a ng ! e s duplic a ting a n actu a l s p i n . In a d d ition , th e i eff e ctiv e ness o f s e ve r a l ta l l c o nf i gu r a tions to d a m p a s pln i s i nvestig a ted thro ug h pa r a m e tri c st u di e s o f hori z o n t a l an d Verti ca l s t a b il i z e r pl ac ement, p l anf orm s ha pe, and s iz e, u s ing a re p res e nt at i ve ' ' J g en e ra l av i a tion ai r c r af t , . al l . Th e effec t ivene ss o f s pin r ec o v ery I co n trols in p rovidi n g pitching an d y a wi ng mom en t c han g e s is al so e x a mi n ed, O ve r v i e w o f Spin Dy n ami c s The sp in iS define d a s th e motio n o f an ai rp l a ne, usu a l l y a t a n an g le of atta c k abov e sta l l b ut und e r g O°, d es ce ndln_ : tow a rd s the e arth 'a hile rot a tin g about a vert i cal axis (Nethouse e t al. 19bO). Th e motion involves rollln_,,pltchln R, and ya_ ' Inqas the airplane operates i n the • • . . . • , • . • . • • . . .

nonlln ea r a erody n amtcr eg lon.w e ll b e yond s tall. As shownIn flgur e . IT[, t he cen t e r of gra v ity of t he s pi nn i n g ai rc r a ft d esc rib e s a he l ix. T F_ . .

d ist ance from t he ce nt e r of gr av ity to th e v e rti ca l a xis is d e f ine d a s t he sp i n r a dius, Rs, a nd 0 is d e f ine d a s t he pit c h an gl e wit h r e sp ec t to - t he v e rti c al fli gh t p at h .

Sp l nn l ng is cause d b y a c ombi na t i on of a e ro dyna mi c a n d i ne r t i a l for c es o pe r a t i n g si mult ane ously , Y a wing moments a re c r e at e d by t he au t orot a tt v e effec t o f a s ta lled wi n g an d rotatio n o f t he ta ll a n d f usel a ge about t h e f lig h t p a t h. R olling an d y a wing mom en ts a re c re a ted by t h e n eg a ti v e l ift s lope o f a st a lled wing; i n a roll, the dow n 'goin g- wi n g e x perie nc e s r educ e d li ft , the re b y p er p e tu a t in g t h e roll . A Nose- dow n pit ch i n g mom e nt is c r e at e d by flat p la t e dr ag o f t he h orizo n t a l

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tail o perating at a h ig h a ngle of atta c k . Gyr o sc o pi c m o ments c reate d bY ......

cen tr if ugal f or c es on t he n ose, t a ll , a nd win g s tend to oppose tile pri nc ipal ae r ody na mi c _ o me n t s. A n e quilibrium spin i s a tt a ined w h e n t h e n ose_ d own aerodvn a mic moment equals t h e n ose-up inertial moment , a n d • . . • . . . , .

ae rody n ami c m o m en ts t endin g to rotate t h e air c ra f t a bout t h e spin axis a r e b ala n ce d by spin- d ampin g aer od yn a mi c an d inertial moments . Fi g ure 1-2 sh o ws typi c al c ur v es of eqL_ili b rium about earth- f lxe d y an d z -axes when pl o tte d as f uncti ons o f pitch a n gle a nd dpin rate . The i n terse c tion of the two c urves results i n an e q uil i brium spi n.

The c o mplex i ty of the spin phen o men o n has ma d e analytical stu d ies d i f ficult, s o spin resear c h has tra d iti o nally inv o lve d a lar g e am o unt of empirical analysis . Similarly , this rep o rt is c o ncerne d primarily with experime n tal studies of sp i n dynamics . For m o re i nformation on the analysis of spinni n g , the rea d er is re f erre d t o Blhrle a nd Bar n hart o r McCormick (1981 ). T estin g tech n htues i n volve the use of spin-tunnel Sp i n Axis

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. o Horizo n . _ 0 Figure i-l. Air c raft Fll R ht Path in a n Equilibrium Spi n

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r I J RO T ATI O N R A T E • Equili br ium A bo u t / i • , . ° " Pit c h E quilibrium PITC H INCIDENCE Figu r e i-2. Balance of F orc e s Nec e s s ary for Equilibrium Spin • . • . . .

m ode ls In both fr ee- fllght and rota r y balance studi e s; dynamically s cal ed m o del fl i ght test s , a n d full s c ale f i l ght tes ts. S u c h tes ts allow c o n trolled study of th e I nf luences of confi g uration and mass ' distribution on equilibrium s p in mode s and recovery c haracteristics, and analysis of spi n re c overy techniques. In mu c h of the testin g , s p e c ial .'

c onsideration must be g iven to time s ca ling of t h e dyna m i c tests and s c aled model mass distribution, as well a s re- c reatlon of the rotational f low field e x perlen c ed by the spinnin g air c r a ft. These factors .....

c omplicate the testin g pro c ess t b ut are important in simulati ng the a c tu a l s p i n dynami c s. '' .

S cope o f th e Pr esen t Tes ting Almost all p a st tall studies have invol v ed an entire spinni n g aircraft or model in order to duplicate a c tual spin conditions. Many of these tests have b e enqualltatlve in nature and were concerned only wi t h determining equilibrium spin modes and departure / reco v ery cha r acteristics. The tests have not attempted to isolate airplane components to examine their separate influences.

The present study investigates the feasibility of using st a ti c testing techniques in a conventional wind tunnel to study the isolated effects of an aircraft tall in spin. The testing c onsisted of stati c wind tunnel force measurements of several tall configurations. The tails were positioned in the tunnel at extreme angles of atta c k as determined by the spin rate, pitch angle, and verti c al des c ent velo c ity.

m Spin orientations co v ered a full range of equ i librium s p in conditions typical for general aviation air c raft. A representative general aviation alrcraft tail, designed to Incorporate average characteristi c s • 6 • of S e v erai air c raft c urrently p rodu ce d, w as us ed f o r t h e te s ti ng . T h e aft fu se l ag e sh ape wa s not a te s t p ar a m e ter and it s c ro ss -se c tion wa s therefore chosen to Influence ex perimental results a s little as possible. Configuration parameters consisted of vertical and horizontal pl a cement cf the h o r izontal stabillzer, vertical and horizontal tall aspe c t ratios, and deflection of elevator and rudder controls. Airfoil c ross- s ectlon, horizontal tall dihedral angle, angles-of- s weep, and taper ratios were c onsidered of secondary import a nce and were held constant for all tests.

• •

i -

CHAPT ER I I i P RE VI OUS R ESEA RC H

l

° E arly Stu d i e s I Th e first theoretical d e s c ription of spi n ning a nd r ec o v ery i t ec hniques was present e d in Gr e at Britain during W o rld War I. At this !

time the spin was a c tually used as a ta c ti c al maneuver to evade c ombat.

[- I •During the 1 9 2 0 " s, th e f irst r ot ary balan c e measur e m e nts w e r e performed D in conventional wind tunnels, while in the next de c ade, the first spin tunnels were developed and the importan c e of inertia and tall design be c ame apparent ( C hambers 1 980).

T he Inertia Yawing Moment Parameter (IYMP), defined by I - I IYMP = x y mb2 was foundto be an important factorin spinning cha r acteristics a1:d spin recovery. If the aircraft weight is distributed mainly along the wing (the case of a multl-englned airplane with wlng-mounted nacelles), the moment of iner t ia abou t the roll axis is greater than the moment in pitch' and IYMP will be positive. If the pitching moment of inertia is greater than "the rolling inertia, as is the case for most modern fighter aircraft, the loading is defined as negative. For most general aviation aircraft, I_IP is found to be close to zero. Spinning characteris_i<s and recovery procedures are quite different fo r the • . • . . . • .

.... . . . . + thre e ma j o r ma s s d is t r ibuti on s. Fo r the ze ro lo ad i n g c o n d iti on, t h e " m o st e ff ec ti ve recov e r y co nt ro l s are found t o b e pos i t i ve (do w n) " " e l eva t o r and a rudd e r de fl e cti on oppos i ng t he yaw ro t a ti o n.

E ar ly research concen t ra t e d o n t he im por t a nc e o f t he t a il i n da m p i ng t he sp in. T h i s le d t o t he Ta il Damp in g Po w er F a ct or ( T DP F ) , a / / d e sig n cr it erion which late r re sea rch prove d t o b e o f qu e sti on abl e value. The T DPF was an attem p t to define satisfa c tory re co very _=hara e te r istics of an ai r c r aft throu g h a meth o di c al des c ription of the ....

g eometry o f the tail. Un f ortunately, the early re s ear c h f ailed t o is o late tall effe c ts from th e rest of the airplane. This was t h e rest, lt' o f underestimating the importan c e of o ther fa c tors which can override t h e a n ti - spin pro p er ti e s o f th e tail. : _ As r e c e ntly as 19 7 1, th e three m o st Influ e ntial factors w e r e _st e d_ as relative distribution o f mass between wing and fuselage; density of the aircraft relative to th a t of air; and tail design (Bowman ) . More r ecent research 'has shown definite contributions from • such paramete r s as" wing leading edge shape, aft fuselage shape, strakes and ventral fins, outboard wing leading edge droop, and wing placement.

The T all DamplngPower Factor The T all damping Power Factor was derived from early spin res e arch conducted by the Briti s h Royal Aircraft Establishment in the late 1 920 " s and early 1930 ' s. It is actually the product of two terms, the Unshi_ided Rudder Volume Coefficient (URVC) and the Tall Damping Ratio ITDR). The two terms, although de v eloped independently, were thought to be of equal importance in determination of spinning qualities, and were therefore multiplled to f or m the TDPF.

The URVC, developed by the Roy a l Air c raft Establishment, is used to provide an indication e_ rudder recovery effectiveness. Referring to Figure 2-I, it is determined by the equation LI + L2 SR1 SR2 UR VC - S(b / 2) The TDR, defined by S r L2 TDR = S(b/2) 2 is determined for body and / o r vertical tail area beneath the horizontal tail. It was developed by NACA in 1939 from the previously used Body Damping Ratio in an effort to improve correlation with spin tunnel f i ndings. ' Be c ause the density c oeffi c ient, _, and the Inertia Yaw i ng Moment Parameter were known to be signifi c ant fa c tors affe c ting re c overy ch a racteristics, they were used as parameters in determining bounda r ies for satisfa c tory spin re c overies. Figure 2- 2 is typi c al of those developed in the late 1940 " s by NACA, based on spin tunnel re c overy studies of over I00 military and civil airplane designs.

In the studies, a spin tunnel model was considered to have satisfact o ry r ecovery characteristics if it stopped spinning within two turns of application of recovery c ontrols. In addition, re c overy tests were performed with a modified control c onfiguration, based on the assumption that it is unrealistic to expect a pilot to apply pe r fect recovery c ontrols. This relaxed recovery criterion was r eferred to as

L1 "]

.... SRI Ful"-Span 30 ° ' Rudder _ SR 2

I- L I

.= L 2

// ll6o ° >

/

Part ial-Span .5°

_&_ / _o o i / l l_ ° , _, , ___

Rudder - _ l / _F S F

v_ I

TDR < 0.019 T D R > 0 . 019 An g le of Relative Wi n d A ngle o f Relative Wind A ssumed to be 45 ° Assumed to be 30 _ TDPF = URVC x TDR L 1 + L 2 L 2 SR I SR 2 SF TDPF = x S(B / 2) S(b / 2)2 Q • . Figure 2-1. Computation of the Tail Damping Power Factor _ i .. . .

2000 _o o O xlO -6 o RECOVERY O Reversal of R u dder Al o ne o 0 Sa t isf a c tor y • R evers a l of R u dd er Alone D Unsat l sfaetory 1600 D Slmult an eo u s R eve r sal of Rud der m a n d E leva t or Sa t is f a ctory - . Sl m u ltaneous Reversal o f R udd er , " o an d El e v a tor U nsati s f ac t or y o o . (I] o o o 1200 o o O o GDO O o o o O O0 _ D M 0 0 _ 0

+0 - o oi++

R eg ion for S a tis- O S fa c tory Reco v ery by ° , _ °a o O o° _ A T_I_ o O D .

400 Rob . or Re o al A1o e __

0 _ 0 _ / . , ._"_n ^ 0 € _ • Reg i on for Satis fac , o r y Recover y = Ou m " 0 _ - O° _ o__ _%_ • by Simult a neous R ev e . sa ! o f Bo th

o _ _f_ ¢ _! d " , . .,o , / ,, , ,__ • _ o o • "

-' _ 2 0 -240 - 1 6 0 - 80 0 80 160 2 40 x I 0-_ I - I x_ / ____Z mb2 : e • _ i Figure 2 - 2 . T all Damping Pow er Fa c tor as - a F v ,, c tlono[ IYMP - , p . < 15 _ i | ...." 1 2 D the " cr it e ri on sp l n. " It w a s d ef i ned as th a t recovery effec t ed by the appli cat i on o f one-thlrd of f ull ail e ron d e f lect i on i n th e dir e ct i on oppos tn _ sp i n r e cov e ry (us u al l y s tl ck-l e ft in a r{gh t s pin) , t w o-th l rd s of full n eg a ti ve el e va t o r d eflec t ion, and one -t h l rd o f f ull pro-rec ov ery r u d d er def l ec ti o n . A mod e l w a s Ju d g ed s a t isfac t ory l_ i t r e co v er e d wit h i n 2.2 5 t urn s .

The res ul t s s ho w a s i gnifican t scatter a m ong s o ti s factory a nd un satisfact or y d e signs, ma k i n g t he d ete rm i n e d bo un d a r ie s q u esti ona b l e .

I t wa s concluded a t the t ime t hat " ...ot he r f a c t or s ( s u ch as wi n g d e sign) undoubted l y i n fl u e n ce re c ov ery c ha r a cte r i st i cs _ n d _ay a cc ount i n pa r t fo r some mi x tu r e of th e sat i sf a c t or y a nd u nsa t isfac t ory p o i n t s sh o wn" (Nelh o use et aI. 1946 ).

Th e T DP Fw a s app l ie d to l i g ht g e ne ral a v iati o n a ir cr a f t tn a 19 47 NACA s t ud y ( Ne t hou se). The cr it er i o n de vls ed ( Figure 2- 3) wa s d e v el o pe d fr om th e p r evtou_ t e sting , us in g on l y t ho s e c o nfig u ra t io n s r e s emb li n g . • g eneral a vi at i o n types . Ailero n c ontr o l effe c ts were n ot c o ns i d e r e d.

• 1 The crite r ion i s c on s er v a tive In t h at b ou nd arles a r e d etermine d s uch t g that n o u n sati s fa c tory r e co ve r i e s lie i n the s atis f a c t or y r e gi o n, alt ho u g h severa l s atls f ,lct o ry reco v er i es !i e in the un satisfact o ry r e gi o n . Rec o ve r y r equi r e_ent s w er e re l axe d, h o w e ve r, f o r g enera l aviatio n a i r craft . Reco v ery w a s co n s id e r e d satisfact or y i f the mo d els r ecove r ed wit hi n 2.2 g tu r ns afte r initi a tion o f f ull r ecove r y contr o ls .

Recent Free-Fllght S pin Tunnel T ests Si=ilar studies have been conducted =ore r2cently usln_ the "typical _ t nglc_enqine " _ • gcn _ ra l avi a tion d e_i_n" _hown in F ig u r e 2-4.

T_e cfferts O f cont r ol deflections _c r e a_a l n studie d as functions o f • . . . • . . .

• , . . . • . • Sa ti s f . _ c :ory Re c ov_ .r y b ' ! Rudde r A lo ne ' Satisf a ct o ry or R e c o v, - ry b y Rudder and Eleva t o r I ; ns a tl sfa, : t ory • . 600 . • . • ...

_ - 400 %

]o

I 1 I I I j - 20 - _0 -4f J 0 40 f_O 12 0 X I0-4 I x - I¥ Ine rti a Y awl n _, H o ._ n t P ara m e te r, =_ 2 • • . + F l _.ure 2 -3 . C*_ . n er a l A v i atio n Spi n ' f . r i' t er lo n Base ' d ' o n " t h eT DP F ( 1 94 7 ) - "_ ' J_ _ 10.4:) J

.3 i

. 24.4 _ ) _ 1=.95 ' _ i L _ Fig u r e 2 - 6. [IA SA T yp i cal " S i n gle-E n g i n e G eneral . Aviation D esi R n !

15 i\ .

I I t a il c o n fL gu ratlo n , e . g . positio n , a n d f u s e l age / wl n g modifi ca tio ns . T he r es ul ts sh ow e d tha t, al tho u gh tai l c o n f ig u ra t i o n i s an imp o r tan t p a ram e t e r , ot he r featu r e s s u ch as ro u nd e d fuse l a ge bottom , th e addi ti on o f vent r al f i ns, wi n g fil l e t s an d s t ra k es h ad a n apprecia bl e e f fec t o n th e e quilibrium sp i n mod e s and r ec o ve r y c h arac t e risti cs. C o nclus ion s m a d e a bout t ail c onfi g ur a tio n w e re mi n im a l, al tho u gh se v e r al possible t r en ds wer e n ot e d. T he t e sts a lso prov e d t ha t t he TDPF did n ot c orr e ctl y pr e di c t spin r ec ov e ri es , an d it w a s c on c lud e d th a t ". . .t he l ex i sti n g ta ll des ig n cr it e rion ob v iou s ly cann ot b e u s e d to p r ed l c t r ec ov e r y cha r ac t e risti c s" (Burk e t a l . I_ /7 ) .

R o tary B ala nce T es t s Spin tu nn el r ota r y ba l a nc e test s c o n d uc t e d b y NASA h av e pr o ven to be u s eful in analyti ca l studies o f fu l ly d e veloped s p ins. Rotary bala nc es ha ve.bee n in use f or se v e r a l y ea rs, but the abi l it y o f a " b a lan c e to o b ta i n a ccurate a nd repe a t a bl e d a t a h a s been a r ec ent deve lo pment . The rotary ba la n c e app a r a t us e na bl e s n et for c es and mome n ts due to ae r ed y n a ml c an d i ne rtia e f fe c ts to be measured as fu nc tio n s of s p in r a r e , orient a tion , an d sp i n radius. I t c onsists of a strain gage balan ce att ac hed to a rotat i ng rig as shown in Figure 2-5.

The present balance has a pitch angle range of 0 to 90 ° , a roll angle range of + 15.° , and a rotation rate of 0 to 90 rpm.

Is o lated aerody n amic for c es may be measured by e nc losing the model.

In a box structu r e, making aerodynami c for ce s neglig i bly small. The test is perfo r med fo r a given condition , and isolated inertial lurers are r e c orded. The test is then r e peated without the model •enclosure, "" and Ine r tial ; forces are subtracted from the net force measurements.

. • . . .

. . . . .

|

I

i ........

I

Fi gu re 2 -5 . , ' ]A . qA - L a RC Rot nr 3 ' B n l n nce A pp ; Ir ; itu . q 1 7 Data pr e s e nt e d by Bihrle e t al. ( 19 7 8) a re the r esults o f tests • run fo r Rs e qu a l to O , 0 r a ngin g from 3 0 to 90° , a n d a ro ll an gl e , € , J app roxlm are ly eq u a l to O . Th e p r esen t t es ting dupli ca t e s th e s e c o n ditions ,and a c o m p a rison of th e two t es t s is p r e s e nt e d In Cha pt e r IV.

|

i ClL_ TER III i J EXPE R I M ENTAL PROC E D U R E i I Spln Ori e ntations Th e m aj o r sp in o r i e nt at ion par am e ters we r e s imulat ed in the win d ! "" tu nn el by o r ienting a mo d el t all at p re-determlned angl e s t o th e tun ne l !

free streamline. Relevant angles are p resented i n Figure s 3- I and 3-2.

As seen In the first figure, the airc r aft Is assumed to be spinning about a verti c al axls passing =hrough its e.g., with _ equal to 0. The tall experien c es a net velo c ity c ontaining c omponents from the des c ent velocity, Vd, and the product of the spin rate and horizontal distan c e to the spin axis, _ltsiue. The angle In the v ertical plane at which the resultant velo c ity im p inges the verti c al tail, ev, Is a prima r y " controller of spin damping. Note t h at for these static wind tunnel tests, Vd is related to the test section velo c ity by V d=VT C° S v" Pitch angle• also has a la r ge Influence b y determining the shape of the separated region above the horizontal stabilizer. Pitch angle is related to ev by the equation = tan _ sln0 a v [Vd J = tan S F igu re 3- 1 . Veloc i t ie s A ff ec t ing Ta t 1 in a n I deali z ed £ pin " 20

t

%

V T VT cos a v " - V T co s a v cos O sin % Figu r e 3-2. Tail O r i e ntation wit h Re spe ct t o Total V e locity Ve ct o r i i !

I 2 1 I , !

i ; w_e re !

_ = ____ 2V d " The dime n si on le ss s pin r at e , _, i s an impor t a nt pa r am ete r in scal e3 s pi n s t u di es . E q uilibri u m va l ues o f _ f or act u a l sp in s v a ry d e p en di n g on th e d e gr e e o f spin . Ste e p s pin s a r e n o rmally c har acte ri ze d by l o w v al ues o f 6 and l o w s pi n ra tes , wi th a p i tc h angl e o f 4 0 ° an d a sp i n ra te o f O.3 b e i n g typi c al. Fl at sp in s no rm a lly possess high t h eta va l ues, u sua lly ab o v e 6 0 °, with _ t ypically having a v alu e o f 0 . 7 . Equilib r ium s pin s tat e s a re s t ron gly d e p en d en t on ma ss- i n e r tia p ro p e r ties a n d ae ro dy n amic characteristics of an aircraft, and therefore will vary from one configuration to another.

The present testing is concerned with a wide range of spin rates and pitch angles to obtain information about equilibrium conditions of a . .

va r iety o f ai r c r aft c on figuratio n s. Ov e r the r a n ge te s ted, v alue s o f a v were determined •using reference values of It and b, and are presented in table 3-I.

The assumption that Rs is equal to 0 should not affect results greatly. Spin r adius can be approximated as a function of pitch attitude by equat i ng gyroscopic and aerodynamic forces acting on the aircraft. For an aircraft in an equilibrium spin having a negligible roll a n gle, .

R = g (der i ved in Mc C o r mick 1981) s _2 tan0 F or a t ' lat s pin, Rs is the r efore small c o mpared to the w i ngspan. The • . . . . . , . • . .

Table 3 -1 Angle of Atta c k as a Function of , P it c h Angle and S pin Rat e for Test Orientations a v (Degrees)

8 " 40= 60° 80°

I 0 0 0 - .3 1 2.78 1 7.00 - ..

3O.O8 t . 5 2 0.71 2 7. 0 0 .7 2 7 .8 9 35. 5 0 3 9 .0 4 i " • .9 - 4 2 . 5 2 46. 2 0 assumptlon is l e s s v ali d for l o w theta val u es. Be c ause the air c raft is nosed inward toward the spin axis, the principal effect of neglecting Rs • . . • is an Unde r estlmation of yaw damping. The assumption is therefore conservative for steep spin conditions, it should be noted, however, t hat any analysis of spin departure should include the effects of spin radius.

The roll angle is also assumed to be zero. Full scale flight tests show this assumption to be valid for flat spins, while steep spins possess a slight roll angle, having the effect of increasing pitching moment and decreasing yawing moment tall contributions. Such effects are probably negilglble because of the small magnitudes of #. However, flight test results show that roll angle is o_cillatory in an actual spin (Stough and Patton 1979). Roll angle should therefore be an additional parameter for _ complete dynamic analysis.

1 !

"1 " Model Configurati o ns The tail sec t ion models were designed to be typical of general aviation aircraft tails, based on available information. The baseline m o del configuration (Configuration A) w as designed based on average tall volume coefficients and tail planforms of several light single-englne aircraft. Because of the wide differences in planform and configuration, however, some assumptions were necessary. The vertical tail angle-of-sweep, sometimes used to increase the moment arm and stalling angle of attack of the vertical tail, was found to vary . , c o nsiderably between manufacturers. Angle-of-sweep was set equal to zero a_ mld-chord to result in a vertical tail planform resembling that of the .NASAtests. Many aircraft use varlable-lncldence horizontal stabilizers (also known as all- m ovlng tails) which allow greater e.g.

range and better control. The fixed tail configuration is equally popular, and was used in the present testing. Most aircraft have cross- sections varying from root to tip, averaging appr o ximately 8% thickness..

Construction complexity and strength considerations necessitated a horizontal s t abilizer of constant thickness with respect to span, and slightly increased thickness for extra strength. A symmetrical NACA 0012 airfoil section was used for all surfaces.

Because of Its variable influence, _Ft fuselage cross-sectlonal shape should be the subject of a separate test program, and its influence was not determined in the present studies. A circular cross- section was used, preventLng a propelling yawing moment under all test orientations. Although points of flow separation are not well-defined on a fuselage shape of this type, they do not change position with cLv orientation. The primary influence of the aft fuselage is therefore a 2 4

I

fairly co nstant f o r c e i n the dlre c tI G n of V .

I A s c ale drawing o f th e baseline co nfiguration i s p r e s en ted in Figure 3 - 3 . Note that t h e horizontal tail is pla c ed at a mid-span position on r ._evertical tail. Horizontal and vertical tall tips are formed by rev o lving the airfoil , . e c tionaround the tail surfa c e tips.

Test parameters consist of Lhe vertical position of the h o rizontal ' t a il, cho rdwise p o siti o n o f the h o rizontal tail, ve r tical tail aspect

i

rati o , and h o rizontal tail aspe c t rati o . The effe c ts o f co ntr o l i deflections are also stud i ed, for buth full-span and partlal-span rudder • co nfigurations.

i The verti__alposition of the horizontal tail c an have an • appreciable effect on yaw damping c haracteristi c s. It is e x pressed in terms o f the height, h, o f the horizontal tall abo v e the fuselage / reference line, divided by the vertical tall span, bv. C onfigurations B, A, C, and D were used in variation of h / bv from 0 to 1.0, as indi c ated in Figure 3 -4. Five distin c t locations were used i n the earlier NASA spin tunnel studies. I n the present study, four lo c ations are used be c ause o f diffi c ulty in mating the horizontal tail to the c urved upper fuselage. Also, note that c onstruction of Configuratloa D, with h / bv equal to 0, ne c essitated c utting appro x imately 3 .4 square inches from the root of the horizontal tail.

The c hord_ r ise po3ition of the horizontal tall may have an effe c t on pit c h and yaw damping through mow_nt v ariation and verti c al tail - , blanketing. Three chordwise positions were employed: 20% of the chord forward of the neutr . _lposition; neutral; and 2 0% of the chord aft of neutral, represented by Configurations E, A, and F (see Figure 3-5).

The vertical tail aspe c t ratio, ARv, is defined as the vertical

fl 25 I

tail span sq u ared di v idedby the v ertlcal tail area, hv2 / Sv. " It is • i L I found to vary conslderably among sta n dard tall configurations, with a . . . ,.

value of 1.3 being an approximate average. Aspect ra c lo was varied from i a minimum v alue of I.! t o a maximum of 1. 7 in the testing, measured from the reference centerline of the fuselage. Ta!,erratio was h eld co nsta n t, res u lting in v a r ying l eading a nd trailing ed g e sweep angles.

i As in d i c ated in Fi g ure 3-6, Conflguratlons G, H, A, a n d J represent the variation of ARv and its effe c t on vertical tall planfcrm.

Finally, the horizontal tall aspe c t ratio, ARh, was varied while main t aining c onstant horizontal tall llft effe c tiveness at low angi_s of" atta c k. The three-dimenslona] lift c urve slope c an be obtained from a p p ro x imate lifting surfa c e theory by: i a AR + [2(AR + 4) / AR + 2] " CL _ CI_ AR Thus_ In order to malntain the same llft effectlveness,

AR h S h

ANh + [2(AR h + 4) / ARh + 2] = C This, of course, assvmr" a co n stant C 1 for all horizo n t a l taJl surfaces.

Four horizontal _tabilizers were constructed, varying _R h from a minimum of 3.48 to a maximum of 5.40, represented by Configuca,ions K, A, L, and M (see Figure 3-7).

2 6 I i

"I

Sca le 1:4 b h i 20 i n.

b v - 7. 5 in.

"_1 TM 1 0 0 in . " Sv " 3 7.5 in.- AR h " 4.0 , U_ , " 1.5 h / b v " O. 5 • . • • . . .

Ff t ;ure 3 -3. Confi_,uration A I 2 7 i ..

I : C o nfiRurati o n B h v !

C on f l g_ sra t i o n C Fi._ur, , _-._. V ,i r l : ltio n of h / b V

I

.I • .

F l qu r t_ 3 -5. Var i ati on o f T. ailplane Ch o rdw f se Po s i tio n i 2 9

'!

C onf ig ur a tion G / Fi g ure 3 - t b. "ari a tlo n o f A R V

I

3O Figure 3-7 . Var i at i on of AR h f I ! 31 ' i R u dde r tr a vel is e q u a l to _ 2 5 ° for both full-s pa n and par t ia l-s pa n controls. The pa rti a l-s pa n rudder e xt e nds from h / bv equal to 0. 2 to l .O. El e vator travel is e qu a l to _ 15° . Relevant d imensions a nd test par a m e t e rs f o r each co nflgu ra ti on a r e presen t ed i n Append i x A.

" B ec au se of th e limit ed ra ng e o f p aram e t e r s f e a sib l e in an exper im e nt o f th is s c o pe, s o m e pa r am e t ers w ere el imlnat ed. Ho rizo nt al tall tap e r ra t io , an gl e -of- s we ep, a n d dih e d ra l angle w er e he ld consta n t for a ll te s t c onfi g u ra t i on s . Verti ca l t al l t ape r r atlo a nd an g le-of- s wee p were a l s o h e ld fixe d. S u c h p a ramet ers m ay influ e n c e tall d am pi n g c h a ra c t e ri s t ics ap pre c i a bl y a nd s hould be in c lude d in futur e s tudie s . .

G ener_ l E xp e r im en tal De s ign The exp e rime n ta l set- up is shown i n F i g ure 3 -8. T h e t e sts wer e ."

p erformed in a four-foo t by flve-foo t a t mo sph eri c c lo s ed- r e t urn wlnd t unnel. All t a i l s were moun t ed on a s u pp or t ing s tru ct ure whi c h allowed ro t a ti on abou t t h e bod y -flx ed y -axls a nd t he t un n el-fixed x-axl s .

Orlen t a t lon s we r e roa intained t h r ou R h a pln-locklng s y st em as show_ in Figure A-L. An in te rnally-moun t ed st ra i n- g age b a l a n c e, bo r rowed from NASA-L a ngley R e s earch C e n t er, wa s used for all force and momen t m e asu re m e nt s.

A forward body which abuts, but does not touch, the af t fus e lag e was used In order to provide a continuous fuselage surface. In addition , u n de r st ee p spi n c o t . _itto n _, t : _te r f e reneeor flow Inte r uptton from a forward fu s elage may be sl gnifIcaut, making a n abutting fuselage necessary for accurate modelli n g of the actual flow field. Moreover, the forward fuselage eliminates flow ImpIn_In R directly on the e x pos e d part of the balance a n d It mtnLmLzes s trut Interference. The fuselage" . - i i P i t c h Axis Internal Bal a n c e Rol l Axis_ -.", , i; %

" _i_ j

Abutting !

Fusela g e T o Mi c rov o ltraeter ;.

Support Strut . .

50rle n tin g F i gu r e: 3 -_8. Schematic o f ,Model and ._leasu r t ' ment S\ ' ,,it e ra .." . .

. • . . .

• , . . • . . . .

• 33 _, I was attached t o the f o rward part o f the o rienting support, a ndtheref o re" : did no t dire c tly con trib u te to t h e for c es an d mome n ts w h i ch w e r e m ea sured on th e tail , A s ca l e dr a wing of the forw a rd fuselage is pres e nted in Figur e A- 2 . Not e th a t a door w a s c ut in ord e r to provlde access to th e pit c h a dj u stm en t w it h out dis a ss e mbly .

T he mod e l w a s ce nt e r e d l a t e r a lly i n t he wi n d tun ne l for a ll t e sts, an d ang l e s w e r e a djust e d during a ss e mbly from an a lig n m e nt position d e sign e d i n to t he or ie nti n g support , This z e ro po s itio n c orr e spond e d to ..... _ " a pJt ch : i n gle of 90° a nd an a v e qu a l to O, a s shown i n Figur e 3-11.

A 5 v olt b a l a n ce e x c it a tio n w a s provid e d by a d. c . pow e r sup p ly ..

w h i c h m a i n t a i ne d c onst an t v olt a g e to _ O . 0 2 Z . Out p ut v olt a ge w a s obtained from an integrating mi c rovoltmeter. The str a in gage balan c e f- w as provided with a n e x te n siv e set o f ca libr a tion equ a tions c o n t a i n ing ..

linear a nd nonlinear Intera c tlot_terms. A full ca libration of the balan c e was last performed by NASA-LaRC in 19 7 7. A rough c he c k of the ca libratlon showed'agreement to within a pproximately "1%.

Model Constru c tion Co n sid e r a tions All test model s wer e built by the a uthor fro_ Philippine m a hoga n y, lami:.cted to prevent warpage. Verti c al tail surfa c es were reinfor c ed with O.125-1nch T-3 aluminum bars, and horizontal tall surfa c es were reinforced with steel rods extending the entire span of ea c h horizontal tall. Verti c al tails were bolted to the aft fuselage, while horizontal tails were held in pla c e by tenslon, which c ould be adjusted by bolts in ea c h wlngtlp. Bending of the models due to wind for c es was too small to be measurable. Wood outer surfaces were finished in gloss polyurethane co a ting, hand •rubbed with rottenstone and glass polish. Outer wingtip

It

C , a ,_ t _, , : , , - i' A '-_ .

- B I. ACK AND WHIT E PH O TOGRAPh L

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Figu r e 3-9 . Mo d el- an d Su pp o r t in Test Section , Configuration A ; _e = 15 °' _r = 25 ° ORIGINAl: PAG E 35 B L ACKAND WHIT E PHOTO_ "I .:.

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-. Figure 3-10. Configuration B in Test Section ! •

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Figure 3-11. Configuration H; Alignment Position ..... _'f / " " ' t - ' ORIGi t _AL" PAGE .BLACKAND WHITE PHOTOGRAPH

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F orward Body Aft Fuselage , Fi_,ure 3-12. Fuselage and Vertical Tail Models Figure 3-13. Hori z ontal 'rail Models .. .

• • • . . , • • . . • I I i f airln g s we r e c ast fromwoo d molds u s ing a mixtur e of W h it e spo t pu tty and fib er glass re sin. A ll f i nal s ur fa c es were waxed bef o re testln s .

o Te stin g Cons_d e ratlons At the a ngle s of atta c k s imulating the empennage in a spin, s eparation i s weil-deflned at the leading and traillng edges of the tall s urfa c es. Reynold s number effe c ts should t h erefor e be small, as shown by spin tunnel t e sts run a t Reynolds numbers as low as 6% of fu l l- sc ale.

The tests demonstr a ted that longitudinal aerodynami c c har ac teri s ti cs are.

j n ot s ignifi c antly aff ect ed by RE f o r p i t ch a tt i t udes grea t er th _n 30° ( Bihrle et al. 19 7 8). Preliminary tests were run to determine the effe c t of RE In the present testing, and a small v a riation was n oted in the force measurements. This variation may ha, ' e been ca u sed by a change "" in tunnel turbulen c e level with tunnel velo c ity. The in c reased i turbulen c e may have affe c ted the separation noint on the a ft fuselage enough to c ause a variation in the data in so_ c ases. Orientation c hanges made the use of a bound a ry l a yer trip wire Impra c ti c al, and it was therefore derided to #erf0rm all tests at the relatively high tunnel speed of I00 f[s. The Reynolds number, b a sed on reference main wing MAC, was thus e qual to 4.5 9 x 105, whi c h was approxl_ately 2 1% ot full s c ale.

W a ll " ter fer en c e eff e cts we r e minimized by use of model wingspans - which werL le s s t han 50% of the tes t se ct ion height. Corre c tions were not feasible be c ause of t he lack of appl_ c ablii t y of current c orre c tive me t hods. Heyson (196 2 ; 19 7 1) has dev e loped a linearlzed boundary c orre c tion to account for the large wake defle c tions chara c terizing V / STOL testlng. Unfor t unately, large transverse velo c ities encountered in m o st t e st orie nt at i on s preven t ed i t s a pp l lcatt on . Sol i d bloc ka g e and w ake blo cka ge correc ti on s wP re es t im at ed, ba s ed o n m odel pro j ec t ed area , / .

u si ng th e appro xim a t ion pre s en t ed by Pope (1 9 5 4 ). The ir e ff ec t s w ere - found t o be n egl i 8 1 ble.

, Th e t es t i n g procedure wa s str ai ght f ot _ a rd, wi t h no un expected d i ff i cul ti e s occurring. Each confi g u ration w as a l i gned after ass e m b l y.

and b ala n ce al ig nment w a s che c ke d pe ri o di c a l l y. Th e ba la n ce w as ze ro ed b efore each test to co m pensate fo r mod el w eight, ex c it a t i o n v o lta g e fl uc tu a t i o ns , and t e m p e r at ure c h a n ges. T u nnel v eloc it y w as allo w ed t o s t a b ilize b ef or e readi ng s w e r e t a ken. V el o c it y w as de t e rmin ed b y m ea n s of a p l to t -s t a t ic t u b e connec t ed t o a w a t e r m a nom e t e r, and t e m pe rat u r e was me as u red w i th a t h e rmom e t e r m o un ted in t h e se ttl i ng sec t io t ,.

Sour ce s o f Ex pe r i m e nt_l Err o r The r e ar e sev eral p _s s lbl e s o ur ce s o f e rro r , " but their ef f ects on th e fi n a l r e sultsar e mi n imal . Er rors ca us ed b y volt a ge osci lla t ion s i n the r ea d i ngs _ e re r e du ce d b y the use o f a n inr e gr a tlng ml c rovoltm et er . - " -.

Thes e Flu c tu a t i ons w e r e cau s e d by wind tunnel turbulen c e previously m e ntioned , a nd by vorti ces sb e dd e d f rom the f or war d a nd af t f usel a g es .

_ " Mor e ov e r , a larg e a ir c om p r e ssor lo ca t e d i n c los_ proximity to th e wind tunnei c re a ted a noti ca ble lo_ f requen e y vib ra tion . La ter a l os c lltat l ons wer e redu c ed with the a ddltlon o f a su p po r ting br ac e, se e n In F igure 3- 9. .

The c o m pressor a lso contr i buted t o lln e f lu c tu a tions , whi c h v arie d pe r i o di c ally by app r o x imately + 5 _ V . E x cl t a t l on vo ltage a l s o drift e d, but the b a lance cal[bration check suggested it had a minimal e f fe c t on I .,, , .

. . , . , • .

read l n g s.

.... • • . . .

' A ll su p po r t a ngl e r n e , t sure m en ta and po sltlt_n rae a su r ement s w ere I t = l ie d b y t o ler en c e w ass oci a te d uith r =e t a t w o rk . l _ecau_e o f th e s upp o rt de s ign, a ss ail p i tch a ng l , _ error s c a n r es ul t [n a ng ula r e rror s at t he b al , _ n c # center . Th e s u p port w as a l i g ned an d p oa ttton e d In th e teat sect i on ma n u al ly , al so res ultin g h_ poss ibl e e rror s.

S m all 4 ourc es o f error a re als o In h eren t In the r_ o d e l design. Th e e ff ect o f ftov on the front sur fa ce o f t he af t f usel a g e t s u nkn s_ w n _ but - I t pr o b a bly h a s a n In s igni f ic a n t e ff e ct on ta il nor ra4 l a nd a ide f o r c e s . ' • &l tho u g h the fl o w t e a s tai nt _ l = ed ui th the u se of t he a b u ttin g body. a er i e te s t o rien tat i o n s _a y cre a t e a hig h er d yn arI lcpressure In s ide t he ..

f o rv a rd fu s el a ge, causi ng bleed fl o e b et w ee n th e t w o fus e l a ge s. C on t rol horns. _ l s ed to na tn tat n c o n t rol s u rface a n g ul a r posi t ion, r aay a l s o h a ve ' a sna i l e f f e c t on .fo r ce me as ure me n ts. They w ere pla ced on t he le e w ard side o[ a ll r ail s urf a ce s ( w l t h l n t h e st alle d a ir c a vi t y ) t o _ Intmi =e t heir influences.

_ od el di r nen si onn we r e acc ur a te t o ui t hin + 0 , 0 25 inch e s a nd a ll su rt _ c e a w e re _ r _o o th . | l ol es and g a ps b et _ en t a il surf a ces _ .'er e f illed wi th c l a y , ma king e rror s ori g in a t in g f r o _ m od e l con s t ruc tio n a nd con f i g u r a t i on ch a n ge s ne g li , q ihIy s _ a lI .

D a t . t R e d ttet i o n T hree f o rc e s and th ro t : moment ¢om pon ent.a sure recorde d f or each tea t r un. M or a en t s _ e re re=t_l ved a b o ut t h e b a l a nce c en t er, wh ic h was l oc a t e d 4.0 5 inc hes for ua r d of the l / 4-chord point of the ba s el i ne h o r ' , zo n t al ta il. , _ Ex pe r l , , e n t a ipr e cl. _ [ o n was s a t i s f a c to r y , Two b a s e, l in e re s ts , correct e d for dt fl ertng t _m= h , l vel _ ct tie a a nd pe r[or b ed o t_ di f feren t " -" "" ; _ " "L._ • _. . - ,.. . . , . , , . . " _ 2 _ . . .

W 4 2

I

day s , re su l te d i n an a ver a g _ n o r mal force error of -0. 7% , a n a xia l force erro r of 14. 0 _, an d a side force error of 1 .9 1% . The higher a x i al force . e rror I s so m e w h at =t sl e a dlng because e xt r eme ly sm_ , l l f o r c e s w e r e [ experi enced In the ax ia l direc t io n .

In order t o pre s en t t he d ata in a us a b l e f or=, t yp i c al re f erence va lue s o f I t , Su, cw, and bu we r e e m ployed tn converting t o r dt= en s tonle ss m o m ent coe f [tc t ents resolved about a n aircr aft center o f

i

g r av ity. Base d o n a ty _t ca l hor i zo ntal tail v o lum e coef fi cien t o f 0 . 5 9 6 . .- and an a ver age v a lue o f Sh / Sw o f 0 .1 69 , t he fo ll owing reference !

t qua n t i t ie s w e r e us ed. I

!

Sw=591.2 In. 2 . . C w -9.92 I n. . ;_ bw = 59 . 5 in. !_ lt = 35 . 0 I n .

A ll data w ere r ed u ce d u s in g t he a bov e re f e r e n ce valu es nnd t he des c ent ve lo ci ty , Yd .

e . . . , .

C I I AP T E R IV RES ULT S AND D IS CU SS I ON Th e followi n g di s c us sio n will c o n sid e r t h e p it ch i n g a n d y awi ng reori en ts ge ne rat e d b y th e t a ll ab o ut t he a i y' c raft cen t e r of g ravi ty . .

Tal l f orct , co eff i cien t s a n d ro l l in g mom en ts ._r en ot di s c us sed be c a u s e o f thei r compar a ti v ely s m a ll e ff ect o n air c raft s pin ch ara c te r ist ic s. Fo r c omplete n es s , ho_a_ver. they are p r es en ted in. A y p o n dtx C .

[ "

Ef f e c ts of S pi n R a te o n A er odyn a mi c . H ome n t Co e ffi c ie n ts a l I Measured raom e nts _tt' fu n c tio n s of s p i n r ate are presented t n A pp e ndix B fo r, s ll tail c o n figu r atio n s . A s in di ca t e d in F ig ures B-I " . . i 1 t hr oug h B - 12, h i gh er pitch a ngl e s re sult i n larg e r pit c hing moraents, ii c au s ed bv th e gr e ater pr ofll_ dra g as s ociat e d with larg e r an gl e A of _i i attack. Th e curve s a l s o displ a y "1 concave downw ard c h a racteri s ti c , with Cm i n cre a s i n g I n mag n itude with i n creasing splt_ r a te. Y a w ing mome n t B-,, * . l tlght, r s pi n rat e s e ff ec t s are prese n ted i n Fi g ures 8-1 3 through _ ' , r e s ult in greater y-direction velocity compo n ent s , creati ng g reater I m a gn itudes o f C n . I n terfe r e n ce f ro_a t he hori z o n tal tail I s ev ident t n the pl o ts , caused primarily by blank e ting e f fects o p.d horiz o nt a l tail pos i t lo s ing.

It in i n ter e sting to n ot¢, that i n s ever a l ) ' awi n g mome n t ph_ts , curves o f co n ,q t o ni d i n te r sect e ,l ¢ h other i n the regio n of ,-_ e q ual " " 0.3. Pitching raoment € ' urves suggest th a t e rrors caus e d b y inc,_rrect orie n tati o n a r e n egli g ible. Pos_', b le c a u s es for the ph e no me n o n will be dt:;cus s ed. .. . .

• . • .. • . . .

J • . - , • • • Co m p ar ison with Ro t a r y B ala nc e Da ta To d e term i n e the use f u l n ess o f a convent i on al win d tunn el in i so lat ed tall stu d i es , r epre _ en t at l v6 con f lRur a tton s ca n b e com p a r e d "I with sim i la r NASA t es t con fig u rati ons us e d in t he r o ta r y b a la nce studies o f Bihrl e e tal . ( 1 97 8 ). ¢ on f i gurat i o n B was f ou nd t o rese mble ta l l 5 o f th e NA S A te s t a, wit h t h e m a j or d iffer enc e he f n g t he l ove r h o r i zo n tal t a i l a sp e ct ra tto a nd hi gh er t a p e r ratio o f t h e NA S A t atI .

Conf i gu r a t i o n C la s i mi l a r to NA S A ta i l 3 e xc e pt f or th e a b o ve p la n f o rm dlff e r e n ce _ a nd a l ow e r h o ri z on tal ta i l v e r ti c a l pl a c e m ent, a s _h o w n in . . • F ig u re _ -1, " - .!

For p r op n r c om p a r i s o n , t e st d a t a w a s adjusted t o conf or m t o NASA test c o n d it io n s as c lo se l y as po ss ib le b y calcu l at i n g mom e n t s u sing r e f e renc e l e n gth s'a nd ar e aJ b a s e d on th e NASA t e s t air pl a n e . Sca l ing o _ " .

t h e s e v alu es was b a sed on t he ar e a_ o f t h e ve r tic a l tails, which ar e t € s i m il ar .in planfgrm. . _ t e e ff e c t of c hanging to t h e NASA r e fer e nc e qu a n ti ti e s i s s lg n i_ ic a n t, a s c an b e se e n by c omp a r is o n o f t e st data In Figur e B -3 with that of F ig u r e 4 - 2 . B ec aus e of t his , mome n t ' c oeff ici e nt s pre s e nte d in App e nd i x C ar e r e s o l ve d a bo ut th e b a l anc e ce n ter, Fig u r e _ - 2 i s a pi t ch i ng mom ent co_parl s o n o_ C o n f i g u ra t io n C w i th NA S A b o dy and tall d a ta BII3 V. R e su l ts f r o m th e two te s t s s h o w a high corr e latio n , especially at low theta a t lgles, At high e r angles of p itch, Configurat l on C di_pl^ys a pitchi n g moment of higher m a gn i tud e , bu t the cha ng e o f C with spin rate [ s s imi l ar for b o th t e st s. Th e d i s cr e pa ncy .

a t hig h th e ta a n gl os may possi b ly b e attributed to horiz o n t al tail area d i f f e r e nc e a . B e c a use s c a li ng o f r ef e ret _ c e v alues t s based ot _ ve r tical \ ' 1 ta i l a r e a , t hes c a l .d hor tz o ut a l t a i l a re a o f th e NASA res t s i s 4 5 F i gure 4-I. Tail s Used in Compari s o n with NASA Ro_ary Balan c e Data

!

4 6 J app ro x lm a te ly 7 0 Z o f th a t o f Co n fig u r a t i on C. T h is r esul t s in ne t Cm val u e s of l ow er m a gnit ude , no t ably a t l o w er spin r at e s and hi g he r p it ch ra t es wh ere norm a l fo r ce a t t h e tal l i s caused a lm os t e nti rel y fro m . f la t -pla t e d r a g e ff ects.

I Y a win g resul t s are a ff ec t ed by contri buti on s f ro m t he fus elage o f the a ir c r a ft , l_ n il e fus elage e ff ec t s a r e n ot acc o u n t e d for In the pr e s e nt tal l s tud i e s, all rot a r y ba l a n ce dat a c ontain bod y t a re an d i n t e rf e r ence e f fec t s. In ord er t o obt a in t he c o r r ela tion s ho _n i n i Figur e 4 - 3, body data w er e s ubtr ac t e d from the NASA body-t a ll d a t a . i A l though th i s a ssumption of sup e rpo s it i on doe s not acc ount for th e i n te r f e ren c e eff e c ts , i t do e s pa rti ally acc oun t for th e fu s el a g e c ontribution to the n e t mom e n t . The figure s ugg e sts that at hi gh e r sp l n ra t es , fu se l ag e I n t e rf e tsn ce is sig n ifi ca nt . T he l ar g e di ver g e n ce a t O equ a l to 8 0° i s prob a bly ca u s ed by diff e r ences in h / bv v a lu es for th e two t a i l s. As w i ll b e dis c u s s e d , t h er e is a dis crepa n cy b e twe e n NASA re s ult s a n d th e p re s en t res ults c o nc er n ing t he e ff ec t o f h / b v at h i gh " i pitch a ngl e s.

Ret a ry balan c e d a t a for th e T- t a ll c onfigu ra tion is a v a il a ble only II for a c omplete wlng-body-t a ll c ombin a tion. As in the previous ca se, wing a nd body C ontributions were subtra c ted from the c omplete airplane data using measurements from an isolated wing-body test in order to obtain isolated tall moments. Figures 4-4 and 4-5 show that interferen c e effe c ts, probably from the stalled main wing, a re conslderable, p a rtl c ularly under steep spin c onditions. The yawing moment co mparison shows a strong c orrelation at th e high pit c h angle, lending support to the premise that wing wake interference is signifi c ant at.lower pitch angles.

I 4 7

1 •

•" T. HEI " _ N AS A BH3 V --- o A0 ..qE _ E. S .

b 80 ,DEGREE S I TES T DA T A -- a 6 3 DEGR E _.

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-_ ] . / 5' _"_. . _ ... _ . . _ . _,_._ "_ - ,.,,. . _, "_ .

' _", , ""_ Cm t _% -. ,, - I. / 5.- " 0 . _ 0 ., 3. i 0._ O._ ,9 . 9 O.O :J . l 9.9 _].a Nomdlmoa_'Ior_ a i 901o ROt, c J ..

Figure4-2. Pl t chln_ Momen t as a Func t ion _ Z e and _, Conf iF , urat ion C _t

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NASA BH3V- B --- T.'_"I R TEST DA T A _ o 4BDEGREES u 60 DEGREES a 8Q g E ORE ES

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J / I / J , i -D .

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i J i - _ . " ,2 s q 3 .[ } : ].L 21.2 _ 9 . 3 D. 4 _.5 _ . 6 3 . 1 _ . S 3 . o ._o . "_lmene l ,3nr JI S pin . R u l e Figure 4-3. Yawing Homent as a Func t ion of 8 and _, '" Configura t ion C

I 49

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N A SA_N1H5V- BW1- o - "l"_ E !'.q r, 8 :3 DEG R EES I TE S T D A TA _ • 4_]D E _ S A 9_ D E GR EES

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- I] . 5 1 ] - 1 . J - _ - _ 1 ] , .; 5 -_ _ " -. .

Cr A _ '""' --. _,, . , • . . . • .

- i , .. : 3D_. x -_ . 2 S- i -i . _ . 0.

I - 15 • :] . 3 .'l.t _. 2 .3._ 1 3 ." _3._ D .{3 . g . l 0._ : 3 .Q Ho.".z ll m o n_ 'l . c no; _pin RoLo Figure.4-4. Pitching Moment as a Function o f _ and _, ..

' Configuration B " • . • • . , .

X - -o . 125 ...... ; r ........ _ ........ I 11 I TI _i , , _ ; { ; ; llt llill Itl .... i , = ; , , i I I = I I IT I I I , I ; ; I l' i" _. 3 0 . _ 0.2 _. 3 _._ . O.S O . O 3. / O.S .' 1 ._ Nonol; , n .o n cl _no l _pln RoLe Figure 4-5. Yawing Moment as a Function of O and _, Configuration B I n a d ditl o nt o th o s e a lr e ady n o t e d, t he re ar e s e veral d iff ere n ce s in the tw o studies whl c h make quantitativ e comparis on diffi c ult. The NASA tests used a des c ent velocity o f 25 feet p er se c ond, c o nsiderably Slower than that used in the present testing. However, studies .

performed with the rotary balan c e tests s ho wed Reynold3 number effe c ts to be small ( see Blhrle et al. ) . The NASA aft fusela ge dire c tly under the h o rizontal tall has a flat b ottom, which may c ause interference effe c t s which c ould not be a cc ounted for by subtra c ting body data from body-tall data. Finally, the NASA test s were perf o rmed at non-zer o roll angles. The r o ll angles _ere measured in fractions o_ a degree, h owever, and their effe c ts are pr o bably Inslgnlflcant.

o _ ......_ . _ Effects of Horizontal Tall Vertical Posltlon " " Figures 4 - 6 th r ough 4 - 10 show the effe c ts of h / bv oz,plt c hlng moment. At low sPln rates, they are minimal, with a larger effe c ts developing with in c reasing _. At moderate spin rates and higher pitch rates, a low horizontal tall appears most favorable, while at high spin rates, a mld-span horizontal tall pla c ement results in stronger pit c hing moments The first effe c t is a dire c t result of fuselage and verti c al tall blanketing of the leewlrd horizontal tall surfa c e at high values of h / bv. A se c ond effe c t may arise from a h6_Izontal tall-fuselage intera c tion as shown in Figure 4-11. Configuration C, with h / bv equal to 0.25, may produ c e a larger net downwash than Configuration D, even though the leeward surface is largely blanketed. A larger increase in h / bv destroys such a llft eff e ct because flow is more prone to deflect a r ound the leading and trailing edges of the vertical tail.

At 0 equal to 40° , a combination of interference effects c auses an THETA o "" DEGR~£S c 63 DEGREES -0.50 -0.'75 p----5---~~-----_~ :\ ......

/" .

"., -1.50 , .

'" ." \, '.

.. .... -.

-2.~n ..... -' .

.' .

~'i ::.~- :J.:J 0.2 0.4 O.G 0.9 1.3 h/b v .. "' .

. ;i:!"'" . -1,:: :., ;0;;_ 4':"6. Function of Vertical Pitching r:oment as a r ':c" Fi8ur~ t i'.,..: Tail, w -= 0 Position of Horizontal .:" ~ : ". :-.

l'" "- .' r "'~

I

THETA. .

o l~ DEGREES r:l62 DEGREES -3.'33 -13.75 I'

!

., -1.2~ i i J I ,

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-1.25

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"r-l"'T"T"T-r-l"'T"T"T-r- ...... T"T .............................. r-.-r ro, ... , 'T' ",-,""'" '" 'T,."..,... ... , .." ... ,..."r-~ r T---.-.-.-.-

a.s a.~

FiRure 4-7. Pitching Mo~ent as a Function of Vertical

Position of Horizontal Tail, W ~ .3

J., ~ '" .'(~;: II ' '.;.' - r -. 'ft • ~~;\;:~,~~;:<~ <;y~/ .J l,' , I':,.

, j' -.~ .

.......

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. --

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THETR 0.£:] DEGREES c 6a rn::~EES A 62 DEGREES

-aosaL ... · ----..---

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em

-1. /5·

i

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. - ..

-, .'oJJl· 'ri ... , ... , ... ,..,., ... ,-.·-.'....,...,'~i .-, .-, .... , ..-, ~, ... , ... , ... , .... -rj ... , ... ,-.,-.,-.,r-.r-, ....... , .-, T"I ..-, ..-, ....... , ... , ... , ... , ... , ..,., ~,-.,-.,-.,-.,r-, ...... , .... ...., .,...,... J i- \ J.9 D.G O.J I I \

i

l

Fi~;ure:4·-8. Pitc"i:1~ ~O~f\t <\s i1 Function of Vcrt1c.11

I

rusition of Horizont:ll Tail, w •. 5

f '- .

1 -

/':-

. _ .....

-" . , ... - ....

• _ ... -1 .. .... ~ ....

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. "

THETA

o 4" DEGREES

a 63 DEGREES A 63 DEGREES

-a. 1331

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", ... : I' -.

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", ....... ,-"-,,...,..,......- .... , ..... II .... , .... , ... , ... , ........ "Y""T..,., ............ ...,......- ................ ,...... .............................. ...,......-......- ............. T""'\" I •• i' •• , ; i 'i ., ., i • ii' i' i' I.J 0.3 n.G 0.- 3.3 ~ . .!

Fi~ure 4-9. Pitchinr, ~!or:'Cnt ::19 a Function of Vertical Position of Horirontal Tail. ~ - .7 ...

..." ...

~.- .. _. :~-

.. ~. ..... . ~ - ...... \.

'. -.

or ..

...... '_~~:":' . .;.,. _ --;'!'" __ .. "'-tr~·~-,. ~ ... " - ~ ..... --

-O . 1 5.

r" - 1 .7 5 - " 4

t

: 23 i _Jb, , """ Figure " -10 . Pitchtn_ ._ment as a F t,nct ! on _ of V ert i ca l . I P o ._ftlon o f H o ri=ontal Ta l l, _ ,, .9 t / x I a --_ ... --,- .

, "

----

---~-~--------

~ratlon D

I

f

I

i

\' T Conf1~ur3tion C F1,~ure 4-11. :'~low About ConfiRurations C nnd D at High Spin Rate • o I S- sha ped c u rve at l o w spl n r at e s . H ori z on tal tall b la n k et i n g eff e ct s ..

de s cr ib ed e a rl i er re su l t i n a p o s i ti ve s l o pe , a nd f o r wa rd f u s el a ge w ake " Int e ra ct{ on low ers th e o vera ll p it c h ing mom en t a t a n h / b v va lu e o f 0.25.

At hi gh er valu es of h / bv, t he hor i zonta l t a ll i s c l ea r o f t he f u sel a ge wa ke .

f j

Var iation o f h / b v h as a su b s t a nt ial ef f ec t on y awin g mom e nt, as I in d i ca t ed in F i g u res 4- 1 2 t h r ou g h 4 -1 5 . T h e T - t all p ro vid es by fa r the g rea t e st side f o rces in _l lca c es, whi l e a t mo d er a te sp i n rat es , th e a a c tuall y pr o v id es I au_o r otatlv e e ff ec t o f th e hor i z o ntal t a l l p r op e llin g ya win g mom e n t , B ec au se of d i ff e r e nc es in ho riz ontal tall .o t ! pl a nfo r m a nd ar e a, th i s e ff ect is not see n in the NASA t es t da t a for the s te ep sp in case ( F igu re 4-16 ). I n f a c t , var i a t i on o f h or i zo nt al t a l l h e igh t s h o w e d l lttle e ff ec t o n y a wing m o m e nt In NASA st ee p s pin d a t a .

It Is s uspe cted th a t l ow e r aft fu s elag e s hap e has a s u b stantial e ffe c t on th e aut o r otativ e fo r c e cr e a_ e d b y the ho r izonta l tall at l ow va lue s o f h / bv. Fu r th e r t est in g in this are a would be hel pf ul.

A flat s pin yawing moment comparison i s s hown in Figure 4-1 7 .

De s pite d iffering horizontal tail planform s , s pin v elo c itie s , an d fuselage effe c t s , s imilar trend s a r e indi c ated in both test s at lower pi t ch angle s . Again, the autorotative component of s ide force is pre s ent, notably a t a pit c h angle of 60° • At l o w h / bv and high values, however, the correlation break s down. This may be c ause d by differing horizontal ta l l planfo r ms; at high pit c h angle s , vertical t a ll blanket i ng is large fo r the l o w a s pe c t r atio NASA h or izontal tail. It i must also be not e d that fuselage effects were not subtracted out of the NASA data.

Analytica_ prediction of the effect of horizontal tail vertical 5 9 'i TI'IL_I. q o 40 DE_ ,', 6 {3 D E GR E E S 0 . _5 - B. 3 08- -O. _25 I -_. _5 0 .

Cn -O . 37 5 } = O . L 3O -_. 12 5 8 . : 0.2 O ._ 0.13 0.8 1. 3 h l ov Fi g ure 4-12. Yawi n g M oment as a Function o f Vertical Position of IIorlzontal Tail, _ - .3 .................... y - _, . q 6 0 •-_ . i _] - -13 . i2 . € - • ,.,,, ,,,, I,, ,,,,,,Vl,, ,,, 11 ,,i,1 ,,, ,, , , i , , , , , , T , , l 0 . 3 0 . 2 _ . " _.G _ . 9 1.3 h l b v F igure 4- 1 3. Yawing Hor e nt as a Function of Ver t ical " Position of Horizontal Tail, _ = .5 • , • • , .

• 4 8 D E _k'_3 A 8 '3 DEnS _" o 6_ D E CR_- ES 8 . _ 2 5-

!

l 8 . _B ...................................................................................

T -8._25, "' " " } - _ . i 2 5 _ .3 0 . 2 0 . ,_ 0 . 6 0 . 9 I. .3 h / b v Figure 4-16. Yawing Moment as a Function of Vertical Position of Hor i zontal Tail, _ TM .7

......... 62 _ 1

o .

TI-_ R i n 6_ 9EI _ EE8 " 8 0 9E _E E8 8 . _ ]25 - Figure 4-15 . Yawing Mo r dent as a Function o f Vertical Position of Horizontal Tail, _ = .9

]

6 3 THE TA • 30 DEGRE E S • 40 D E &RE E S • 45 DEGRE E S o= 60 DEGRE E S { _. 32 5- NASA N e t Mom e nt D ata: Soli d S y mbol s ; _ = 0 .2 5 T e st D ata: O p e n Sy m b ol s ; _ - 0. 3

D

1] -_._2s. i

D

C n ..

-B .3 7 5. " 8. 3 B.2 Q._ _ . 6 _.S i .3 _. h / b v _ '' i Figur e 4-16. Yawing _1oment as a Function of , HorizontalTail VerticalPosition ' i . - • , • , , . , . . ' , . : % • • . , • TH O R ......

• _ 4{ _ D E GR EES • _ 8_ O EG REE S I o 6 0 D E GR EES Tes t D at a: O pen Sy m b o ls ; G - 0. 7 U NASA Ne t Mo m entData: SolidSymbols; G - 0.6 i .....

0 . Z Z S - ..................................

]

- - 6 . _2 5,

T

- 0 . _5 0 _ Cn - 0 . _7 5.

° .

-0 . _ 25 , i w , , , i , w i i i , , i , J i i | _ } ._ {]. 2 0.4 6. 8 {} .8 1. 3 h / b v Figure 4 - 17. Yawing Moment as a Function o f Horiz o ntal "" Tall Verti._al Position for a Flat Spin g

Ii •

• I

' " " " pos lti on h as n ot p revio u sly met w i t h s u ccess be c au s e o f t h e need f o r i s ol a ted tall s l d e for c e da t a for c om p ari s on, M cC ormi c k (19 7 9) Investigated the simple relation presented below, which is further i examined using side for c e d a t a from the pres en t testing.

If the lo ca l differen c e in pressure c oeffi c ient along the verti ca l tall Is assumed to be a fun c tion of the distan c e doom from the horizontal tall relative to h, then side for c e c an be expressed as

i

I 1 V2 S h _ s v o P where z is d efine d as the vertical d istance from the gi v en v ertical tail i l o cati o n t o the fuselage re f erence line . T he a bov e equati o n may b e • simplifie d t O i V2 (_ 3 f C (x) d x .

" Fs = _ 0 S v P • V O .' .

Ignoring interference and vertical tall planform effects, let i f c (x) d x = K o P Since F s CF - s 1 / 2 0 V2 Sh S v h CFs = Sh bv K 6 6 : s '_ ' _ _ ! , / £P_ .

• , , . :,. - .

or 9 <

•4 " • ) " K - cF s h " , .

s v _-_ .

. . _._ A plot of K versus horizontal t a ll vert ic al position is s hown i n _ Figure 4-18 for _ equal to 0.5. Curves for other spin rates displayed .'._. 2 _ '€ ' _ o' " simil a r cha ra c teristi c s. T h e results s h ow t ha t K ca nnot b e c onsidered a = - ' f , ,; c onst a nt for any position of the horizontal t a il. In addition to _ . . _ - _.. _# interferen c e effectsf r omthe fuselage, the horizontal tallmay c re a tea -_ . - h igh dyn a mi c pressure on th e ve rti ca l t a ll are a I mmediately bel o w it. . _ , _.

_,. . :_ Thls highpressure regionm a y be independent of horizontal tallverti c a l - ._._ position, making K st rongly d ep e nden t o n b o t h h / bv and ver t i c al ta ll . I r°_f -.

It is evident from model and full-scale flight tes t ing tha t the _ highest va lueof h / b v possible i s fa v orable f o r spinsafety. In fa c t, e' i " : testtall5 (h / b v equalto 1.0)did not havea flatsplnmode. This " _: suggests that in c reasing yaw damping to prevent equilibrium is more , ,,' _ ' _ , ' •_ , , - - , _. _,, e f fective than in c reasing the'nose-down pitching moment, and that the , _._ .

pit c h i ng penalty paid for In c reasing h / by Is min o r c ompared to the ._,'_ : m , advantages of increased y aw damping. :iv + _ ' .. / , .; :-.

Z ' - ' ' Effects of Vertical Tall Aspe c t Ratio ,_ - _ _ _-r • .o The c hange•in C m w i th a change in vertical tail aspect ratio is small, as shown in Figures 4-19 t hrough 4-22. The differen c es seen In some curves are believed t o be the resul t of experimental scatter or _ m i n o r I nterference effects. 4 - Yawing moment effects are more noticeable. At _ equal to 0.3 ....

• . . . . .

., ' _.. :- . , .-" ...-_ / : - " , : " { THETA ' : * *40 DE G REES _;.:.: o613 DEGREES _.,_:' A80 DEGREES • .j.

, ..\ • ,' : 2. S- A • ....._. • ..... 1.5- _ A e ,_,-. 0 K A 1 .1_ - <> 13 0.5- ' 0.0- '''' ..... I' '' ...... I ......... i' ' '''' ' '' l ' ..... '''I' ' '' '' ' ' ' I '' '' ''' ' ' I ''' ' ' .... I' '' ' ''' ''I .... ' ' '' 'I . , 0.13 :a. I 0.2 0.3 0.4 0.S 13.6 0.7 0.8 0.9 I .0 h / b v Figure 4-18. K as a Function of Vertical Position of Horizontal T ail, _ = .5 O_ • • • . • ........ o o.

( F :_ ure 4 -2 3 ), li nes o f con s tant 9 are seen t o cross a t a val u e o f A R v equal to 1. 45 . Vert ic al tail area above the horizo n tal tail ap p are n tly ca u s e s lar g er ya w ing m om e nts a t th e lower t h et a valu e. On_ p oss ib le % exp l a n at ion i s th at unbl a nk et e d a r ea in t hi s r eg io n de c r eases _ it h i i n c r easing theta , rat h er t han i ncreasing, a s i t woul d at h igh s / in r ates _!

• wh e n tra n s ve r se f l o w b e c ome s l arge (see Fig u re 4- 27). T est re s ult s f ro _ t h e T -ta ll c onfiguration, wh ich does n ot sh ow _h e e ff ect, subs t ant'. at e _!

this c on c lu s ion. Th e ya w da m p ing eff ect iv en e ss of t h e ver t i ca l t all at low pi tc h a ngle s l s a no t her p o ss ible fa ct or. A t low v a lue s of O , t h e • a ngl e of att a c k as se en by t h e v e r t ical t all i s s m_ll. B eca u se th e t wo- _ dim e n s ional normal fo rce c urv e rea c _e s a lo ca l m ax imum Imm e dla t ely I b e fo re s tal l , s u ch low' ang l es of a tt ac k m a y pro du c e a lar g er n o r m al for c e on th e ex pos e d p ar t o f t h e v e r t i ca l ta il.

I To inv est ig a te t h_ p h e nomenon more c lo se l y , t h e bod y-fi xed s i des li p , a ngl e s e en b y t he ver t i ca l r a il , _v, _ ; a sdet e rmin e d for eac h orienta t ion ( see F i gure 4-2_). The verti ca l t a ll formal for c e _ s t h e n plotted a s a fu nc tion of _v for the bas e line c onfigura t ion as show n in Figure 4-29.

Be c ause of t he la c k of e xpe=Imen t al d a ta be _e_ _v values _f 0 a nd 1 7 °, i t is diffi c ult to determine t he influe t ,ceof the un s talled par t of t h e ! c urve. The f_gure doe s indi ca te, howev_ c , that ther_ i s a strong pit c h angle influen c e on y.... damping for c e, with lower pit c h angles providing •_ higher fo r ces. Th i s result sugges t s that ta!l geometry, and not s t alling an_le o f attd_k, is the more influential fa c tor. Note t ha, lines of c onst_f it _ are n early llne_r, i n c reasing i n s lope With _ i in c reasing _ . ag n ttude of spin rqte. It c an b_ see n that the c urve co r re_pondlng to _n _ of 0.3 has a slightly negativ_ slope, giving rise _ ' - to the Intersecting c urves of Figure 4-23.

• . • • . . , | 6 9 t + • . T , H E T_ _ : € 36 3 0g1 _ :£ 5

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,\ I._ - - a 1 5 f I - " 0 ( : ] .. _ j ....

Cm -2 :, L 2_ . . + ....... ; . . , _.i l.a "_.g I . / Figure : , - 19 . P ltchl n _ .tlo.._'nt a,J a Functter, of Vertica l . .

"a(.1 Aspect Rat i o . _ , " .3 1-

)

l

j . . .

¶ .+ Figure 4-20 . Pltchin_ ,Honent as a Function o f Vertical Tall Aspect R_itlo,_ ,, .5

\

7 1 -t. 1 5 - i ? i

_, t. a t s _. / il

qRv ' ?

Figur:c4-21. Pitching Ho ment as a Function of Vertical " ,

• I

. ."" ...... T ail Aspect Ratio, _a - . 1 '"" " (

t

• J

• • . - . - . .

I . • .- . • T ttETFI. • u 8_ DEG R EES" a 8_ DEG R EES

l I

t -B. / 5 -t

{

-1 . _ - I @ : -1. 2 S - " " o __ .... _ ._ ..

Crn ! .. _ • .

-1 . i S.

i

-2. : _ }- _, i i . i' 1 . 3 I . _ I . I _ !qRv _' t' F ig ure _ - _2 2 . P i tchin g . _Ioment as a Function of Vertical Tail Aspect Ratio, _ - .9 i

!

• ° .

°.

THETR • 48 D E _ EE':3 i C n -_. _l_ -0. _25 l . i" 1 .3 i . 5 l . i .q. _ v Fi g ure 4-23. Yawin g Mom e nt as a Functlon of Vertical Tail Aspect Ratio, _ - .3 7 4 °.

THETR o 4 B DEG R EES '_ 6_1DEC . R_EEB A 88 13ECR_EES B. g_ - -B. _5 - 4 i I I . '_ 1 . 3 I. _ I . l i .qR v F i gu r e " _' t _-_4. Yawin g Homent as a Function of Vert i cal . •' Tall Aspect Ratio, _ - . 5 . • . . . . . . . . .

, i • . .. . • .

-0._25 - I ." 1 .._ I . _ l . / _Rv Figure. 4- 2 5. Yawing ,tiomentas a Function of Vertical Tail Aspect Ratio, _ - .7 T_= T. q I ! Q 6 _ DEG R EES z _8B DEGREES

I

, • Figure 4 - 26. Yawing Mome_nt as a Function of Vertical • Tall Aspect Ratio, _ = .9 t

• _ - 0 .3

VT Di r e c tio n 8 = 40° Fig u re 4 - 27. Effect of 0 an d c_ v on Unblanketed Vertical Tail Area at Low Spin Rates • • . • .

r

7 8 • ° _ . .

Figure 4-28. Definition of Sideslip Angle THETA o48 DEGREES a68 DEGREES A80 D EGREES -. / _= 0.9 /

!

J // / 0.8- / / 0.6- / / _. _ _ = 0.7 CN 0.4- _ _ = 0.5 0.2 °

o. 0--1

" ' ..... "'' I'" ....... I ''" l ' ' .... I ...... ' ' 'I'" ....... I ....... '' I" ..... "''' I ......... I .... '''' 'I O 10 2 0 30 40 50 60 7 0 80 9 0 •_ CDQ g reQ=) V •Figure 4-2 9 .. Vertical Tail Normal F o rce as a F_ctio q of Sideslip _'gle, Configurat i on A t n !

| "

80 , , _ ., -_

T "4"

At lar g er v alues o f _, t h e low v erti c al t a il a spect r a tf o : .

sur p risingly r esults in gr e ater yawin g m o ments t h a n i n t e rmediate v alu e s _ of ARv, as shown in Fig u res 4 -2 4 t h ro ug h 4 -2 6. For e ac h verti ca l t a il, _ T the h o rizontal tall height ab o ve the fuselage ce n terline, h , was .

c o nstant. This was d o n e t o prevent h / bv effects fr o m d o minating the g ¢%" , results. The c on figurations were n early identical below the h o rizontal / ' _ \ . _ .tail level, The unexpected result must therefore again be related to interferen c e e f fe c ts of the verti ca l tall area above the horizontal

T / '

; tail, _._ q_ . . At high spi n rates_ t h e be n eficial effect o f a l o w aspect ratio

I "

disappears because the high aspect rati o v ertical tails are n o t t o tally -.¢ " blanketed by the stalled air cavity ab o ve the h o rizontal tai!. This _ '. _ phenomenon leaves the tail designer with the d ilemma of choosing between satisfactory steep spin o r flat s p in characteristics. Fortunately, increasing exposed area under the horizontal stabilizer can provide satisfact0ry characteristlcs f o r b o th spin m o des. _ .

Effects o f Horizontal Tail Aspect Rati o The horizontal tall aspect ratio plays a small part in the overall p itchlng moment contrib u tion of the tail. As seen in Flguces 4-30 through 4-34, Cm is greatest in magnitude at the lowest aspect ratio, AR h equal to 3.48, and it decreases with increasing ARh. Although all horlzontaltails tested were designed to possess identical llft effectiveness at small angles of attack, they obviously do not possess / simil a r llft characteristics in stall. The results show that it benefits the designer to employ a lower aspect ratio, lower efficiency horlzontal tall for spin safety. At h_Bh spin rates, however, fuselage • . . • . .

o " r r _-_ - 81 , i!. : . .. .

€" . . ' ] r o 4_ ] D E G_EE_ .

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_ ' _ [ o 15 ;] DEC4_EE8 • _, ' = . ' - ; .

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-i . = . ; _- '_" ! ° I ' -i . 1 5_ , - 2. 3 -_ - 1 . 4 3 .9 4. 2 4. 0 5 . _ E.$ £._h , .

Figure •4-30. Pitching Moment as a Function of Horizontal Tail Aspect Ratio, _ = 0

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, J

i

- _ . / 5 - _ _ - !

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cm ]

i I - ; . / 5 4

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* 3 . 4 _ . € 4. 2 4 . C 5 . _ _ . _ Figure 4 - 3[ . Pz2chin_ Moment as a Function qf t i o rfzontal T , ,11 A';pect Rat io , ' _, _ .3

g

a

i!£Tq (I .&3 :JiGl\EES c G:l DEGREES 0\ ~ DEGREES

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.. .:, ~;J-l , \ C:.J 4,~ 3,'& 3.:3 Fl-:Ilr., ... - , ... l'lt\'hln~ ~,'~'nt .\'; ,I Flln=t1<'1l ." .!i.'rl::"llt,ll 7.111 ASpl .. ,'t f\.\t 1,\, .... 1 •• ~ _. _ .- -- 11 . !

-a . J 5- F igure "-33. Pttchlng _k'r_, n t as , _ Fun c t i on of I t or i z on t+l!

T.111 Aspect R_itio, , o - .7 t - 3. / 5 k FIRure 4-34. Pi tching H ov_, , Atas a Functlo n of H o rizo n tal Tall Aspe c ,_ , _itlo. _ - .9 ..

l° m T H ET. q = 63 DEG _ ES i o A_ }BE t _ S E ES ;- _. ;_2 S -t i _ , - * - ---o * -°o ** .... . .... °.....° . ...° oooo.° ..... ...o .. . . o.... . . . . . ..... ...

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- 8 . :} 25 J

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'1 • . j -i }. :}S _ ' _ . • C n 3 .4 3 . _ 4. 2 4. 6 5.,} 5 . 4 _ R h F tgnre ,_-35. Y a wing ._loment a .q a FLmction of !tori : ontal T ai l Aspe_ ' t R a tio, _,_ - .3 • • , . . , , , . . .

1 i

• 87 • . • T! '_R " i .

• 4 _ DECRE ES _' 8_ DECW_F. E g. " 8._325 - -8._B - . • C n " 4

i

-_ . _75 _ -ft . _SB - ] -O. x25- 3 .4 , 3 . 3 4. 2 4. 0 5 . _ 5 .4 .q . _h Figur e 4-36. Yawing Homent as a Function of llorlzontal Tall Aspect Ratio, to- .5 m

T HE I R

. (, 4 _ DEGR E E,R ,_ 6 3 D EGREES B : _ DEGR E E 5 _ ] 3.32 5 _ 3 -- g - B . _2 5 i I • x. , • [ T T l _ ( , , ..... l i ft ' , , _ 1 [ 1 " " _ 1 _ T F I, • _ j • , _ • " _ " T I 3 . 3 . S 4 . 2 4 . G 5. 3 5 . 4 ? q.R_ " ' F L gure 4_-3 7 . Yawfng H om e nt a s a _Fu n ct i on o f H o r i zon t a l ..

Ta i l Aspect Ratf o , , o " .7 • 89

i

_H E _ R i " = 60 [:]EI: ; RE ES A _3_ DEGREE S

i o. _2s\

i

i " 8 . _ 0 8-_-........................................................................

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" !

+ !

cn _i .-=

-o._Ts _ 1

,I Figure 4-38. Yawing Moment as ; I Funct i o n of l!orfzo n tal Tail _qpcct Ratio , _ - .9 , • • .

• • , . , . . • . , .

• , , , , + .

!

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blanketing o f th e leeward tall can ca u se the higher aspect ra t[ o _ l o nger spa n ho _I z0 ntal t a ll to hav e a sl i ght adv a n ta ge ¢ a s seen i n Figure 4 - 34 ) . I n m os t t e st ca ses, t hi s int e r f e r ence e ff e c t i s o utweighed by t he g r e a t er fl a t-plate d rag of the lower a s p ect r ati o tail surf a c e .

T H o riz o ntal ta l l aspect rati o a lso ha s a re latively s m all ef fe ct o n " y a wing moment (Fig u res 4 -3 5 thr o ugh 4-38). C omplex effe c ts fr o m th e - a ltered ch o rd a nd s pa n o f the ho rizontal t a il surface m a ke e xp l_n a tion o f the re s ults difficul_. Nevertheless, defini=e t r ends can b e n o ticed: und e r flat sp in c onditio n s , the hig h er a s pe c t rati o t ails prov id e .. stronger yawing mo m ents; under steep spln conditions, a _ a lue of ARh • I equal to 4.62 appear s to be the optimum v a lue for the co n figuration T - tested.

As staged previously , under zero - load l n g condi=lons, p reventing ?r brea ki n g e quil i briu m i n y a w a p p e ar s t o b e th e do min a nt factor I n s p i n safety. T herefore, a moderately high aspec[ " atlo horizontal tail , p#obably h a s _ a _l i ght spin - d a mplng advantage. Relat i ve magnitudes o f the effects are small, however, and ARh should not be considered a primary design parameter to prev e nt spin.

Effects of the Horizontal Tail Cl_ordwise Position The horizontal position of the horizontal tall has a significant effect on the pitching moment of the a i rcraft, particularly at hlgh spIn rates. Figures 4-39 through 4-43 show that the aft posltion o f the horizontal tail i s most favorable for breaking pitch equilibrium. Note * that the resultant cu r ves a r e nearly l i near in the intermediate spin range, probably caused by the inc r eased moment arm associated with the aft position. The e onfigurat[on tested, with h / bv equal to 0'5, also _ r_q ,48 DEC._EES a 6 8 DE_EES • - 1 . 25. - Cm - I. 1 5 ° .

"" - 2. __!,,, M -T o_i Po e _ L: o n _n _ C ho: ' d [ * Fo - _ar. d ) Figure 4-39. Pitching Moment as a Functio n of Horizontal Position of Horizontal Tail, w - 0

U

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. ° y -1.58 -

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-1 . J S- T - 2 . Z__ " " -2_ - 1_ _ 1_ ] 2_ "- H-T a ',I Po_l_on "_ _ Cho,_ c l ( . F o. '.o : " . d} Figure.4 - 40 . Pitching Homent as a Functi o n of H o ri z ontal . ." ... Positionof H o L'izontal Tail, _ " .3

-i._ !

t

-2 . _'_, , ....... , ......... _ ......... , .........

H-T o ii Po _ , ! { , I on In _ Ch o ."-d ( + P o .,"w a .'-di Figure 4-41 . Pitching _loment as a Function of llorizontal Position of Horizontal Tail, _ = .5 ...

-rHETR

o .to DEGREES

c 6~ Dr'"JkEE5 b. S~ DEGREES

-e. "'1

~ __ ---y-- .. -----~-f1

-e.15j

i

-l.J __ ---------~

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-1.50

-Lls·1

-2 J~I i --r-r-r~""""l I .......-r-r-r""""""'-'-r-"lj i~'-'--'-'-r-r-' I ~, ...-.---.-..,...-,-,--,-, I -20 1~ H-To' I Po,,:l :.:-', '., t Chor-d ( + Fcrwo,...dl Figur~ 4-42. Pitching }!omen:: as a Function of Horizont;.;.l Position of ~orizontal Tail, ~ - .7 Flgure 4-43. Pitch i n_ .H o r_nt as a Function of l | o r l zontal Posit i o n of i!_ri z o nta l T ai l , _- . 9 • . • [ _ Tq • _ 8 _ G £ EES

g _

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i |', . , st.t<. ,, ' , tt , , ,t H , , rt :, ,t_t , l l T.z l l. , , , - . I 97 i l._-l.q : ] : " _ . _-i- ........................................................................

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Figur e , ,, ' - ' 5 , , . Y.,wt.ng ._!,,ment ,le_ a Functt_,n o f !{ o rl. zm_tal - " . t' , , siti,,n , , f i :, , ri. = . o nt._l Tall. , :, " <' • . • , . . . • . - . . . .

• . ". . • . .

Fl < ur_ ' ._.-_.b . Y J w i n c , ._' o r._,nt ._ , _ l - ' m_ c tio n , , l l h, ri :on r ;tl , I', , _iti, , _ o l l{o r i:_ n t . ll T , lil, . , - .7 Fi g ure 4-_7 . Y , lwin v , Hor_'nt as ,l Function o f Horizo n tal ; Po._Iti_n of l {ortzontal Tail , _ . _ - .9

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1 00 s ho w ed a n i nc re as e i n n o r m a l f o r c e with aft p o s i t ion i ng, s u gg e sti n g a f u s e l ag e bloc k ag e e ff e c t i n th e f o r wa r d po sitL on.

Yaw i n g r e s u lts a r e a ff e ct e d g re a t l y b y 3 . At lo w spi n rat e s ( Fi gur e 4 - 44 ), co nst a nt O curves in t erse c t b e t w e e n th e 0 a nd 2 0% -c h o r d d at a points. Th e pheno m e non c a u si ng gr e ater y awi ng m o m en ts at s t e ep spin v a lu es i s e v id ent l y a l so re la t ed t o c h e r d u ' i s e h orizonta l t a l l I i l oc at io n . Poss ibl y t h e gr e a ter e xp o s e d ve rti c al ta l l ar e a in t h e ho ri zo ntal tail - aft con [ .tg u r ati on t end s t o am p l i f y t he tr ends n oted pre v io usl y . A t inte rm e dia t e an d high spin ra te s (Fig u re s _ - 45 t h r ough : - 4-47 ) , a conc a v e do wnw a r d tr e n d is s een , r e sult i ng i n h i g h e r yaw in g • m o me n t s fo r b ot h for wa r d an d a f t horizon tal t a il p o a i t io _m . I n th e for w ard p osi t ion, mo re r u dd e r ar e a I s expo s ed , a nd i n L h e a ft po siti o n, more forward Ve rtic a l t a l l a re a i s e xp o s e d. - , .

# NA S A t e sting wa s l i mited to th e low ho r t =ontal t a i l con f tgur ati o n, r whe r e [o r _ardpositio ni ng of the horiz ont al ta i l (NASA t ail I ) r e sulte d

i

in a sl ig htly f lat t er s t eep spin which r equ t re d elevat o r d efXec tto n as l we l l as r u dd e r r ev e r sal f o r Cri te r i o n sp i n r e c ove r y. P os si bly r u dd e r blanket i n g w a s a f act o r in t h e tests , a n d th e small differ e nces in d ic a te that, d e spite la r g e rel a t iv e e ff ects on pi tching mome n t, c hor d wise i hori z o ntal tail loca t io n is n o t a p rim ar y para m e te r.

E ffec ts of Contr o l Defle c tions " All control eff e ctiv e ness tests w e re p er formedat an In t erm e diate !

spi n rate of _ e qual go 0.5. T ime cons i d er atio n s limited the t e s t s t o two theta angles, simulating a steep and a flat spin. All tests were per f ormed wi:th the baseline c onfigu r ation. Elevato r d eflect i on alone Indu c e d small changes to pitch and y aw_ as shown In Figu r es 4-48 and I . i 01 _ = .5 T_n .

= 0 o 4 B OEOREES r " 8_ O EGR E E _ I T J .....

-_. _5

Cm -1.25 " _ -I . _ . 8

l

-1. / 5 !

-2 . _ _. 5 l_ 15 .

Elovo_,_ Do t loc_ ' on {Oo_ r '_oe) F i gure 4-48 . P i tch l nR Mom e nt as a Function of Elevator Deflection 1 02 = . 5 THETR _ r = 0 _ 48 D E GR EE S " 8 _ I_ . G REE S -B . _ 5 .

-8 . i_ .

m . . .

- t3 . L 2 " " " 51 • " Eiov aL o r 5o l ' l o cL_on (O o gr oe e l F igure 4-49. Yawing !foment as a F unction of El*_vator Deflection 10 3 • TH E TA: 4@ DEGREES A 7 H ET A : 8_ UE OR EES o T H E TA : 4 _ OEGREE S PQR T IQL_N RUOOER R T HE T FI = 8_ DEGREE S PQ,RTI R L SPQN RlFOOER -8 . 58- / [ -8 . / 5.

-l. Z _.

l

I Cm_l . 2 fi .

-I . _B -I . I S t_ 'i ,_uddorOafl_l.lon (Oe_9,'-goel :_ ' F i gu r e 4-50. P i tching Homent as ,i F u nct i on of _! Rudder Deflection, w - .5 • • • . , .

I06 o ff k :'TR : 48 BE_EES THET.q : _:_ DEC4_EES o T." L r ' TR : 48 OF--C, ! REES I:_qRT!AL b 'F_flN RUDOER uTHETR : _ DECRR_E5 P.qRTIRL b- ' F_qN RUO n . , ER , ,, _. _25-

U

-0._ 75 -D. i_ -g. x_ .£udd_r Do{"i ocL 1 o n _Oogr o oe i • Fi gure4-51. Yawin&Momentas a [unction of RudderDe f lection, _ " .5 @ 1 0 5 * T H E T A : 4 @ D E GR EES oTHET R : 4 @DEGR EES P. qR T. t RL SPR NRU [ 73 E R _ T H E TA = _ DE G R EES _TH E T A : 8_ DEG R EES PARTIP L SPANRUD DE R -I._- o° , ° .

' -1.25 C m - 1.58 - -l.75 - - 2 . _;'1.

Con t r oiDeflec L tone_ o f Fuil) •Figure 4-52. Pitching l • _oment as a Function of ..

C ombined C o ntrol Deflections, _ = .5 " I m o "i ' H ET.B : 4 1_DE O REEB A I ' H ET A: 88 OF 'O RE E S o THETA : 4 _ OE_RFFS ._. RTIAL _P. q N RUDI3ER #THETA : 8_ DEGREE S t ]R T IAL SPAN R U DDER _ . Z25- ° " -B. _SB Cn -B . _75 -D . i 2 5 ConLroi O o f'locL ' .one (% o. r F u il) Figure •4-53. Yawin_ Moment as a Function of • . ' .. C o mb i ned Control Deflections, _ = .5 " . .

. • . • • U . . • 4-49. At a pit c h _ngle o f 40 ° , el e v ator d e fl ec ti o n r e sult e d in a 14% i n c r e m e nt to C m a t t h e m ax imum positive d e fl e ction of 15° . Yawing moment was also affe c ted at a low pit c h angle, probably by increased v ertical tall blanketing. Flat spln e l e vator d e fl ec ti o ns r e sulted i n minimal p i t c h and yaw effe c ts. The r esults Illustrate the danger In I re lying o n the e levator for spin r ecovery. In s o me ai r craft, however, high wing l o ad l ngs make rudder reversal ineffe c tive, leaving the elev a tor as the p rimary re c o v ery c ontrol. Tall designs which m a ximiz e i the nose - d o wn p i t c hing moment are ne c essary f o r su c h aircraft. - • • , . • _ T h e eff ec ts o f rudder d e fle e t fo _ " _np i t c h and yaw are sh o wn In , Fi g ures 4 - 50 and 4 - 51. E ff e c t s on pit c hing m o ment are s ma l l, b u t yaw i ng "• m o ment is strongly Influenced by rudder reversal. Steep spin results Indicate a 53% in c rement in yawing moment at the maximum rudder " defle c tion of 25°. Note that rudder effectiveness de c reases wlth increasing pitch. The high spin rates common at hlgher pitch angles would probably tend to minimize th i s loss of influence.

The partlal-span rudder is mu c h less effe c tive than the full-span • rudder under steep spin c onditions. At a pitch angle of 80°, the differences are small, with the suggestion of reversal of the above trend: yawlng moments produced by the part l al - span rudder are slightly greater than those produced by the full-span rudder. This result is in agreement with Y LSA tests, where L t was found that NASA tall 2, identical to tall 3 except for its partlal-span rudder, did not have a flat sp l n mode, while tall 3 exhibited an unreco v erable flat spin mode as well as a moderately flat steep spin mode. Such a control configuration apparently prevents a spin in two ways: by reduced rudder effectiveness While deflected in a pro-spln direction, and by increased 1 0 8 • , y a w d_m p l n g aft e r ru dde r r eve rsal. It is questi o nabl e wheth e r t hi s r i slight incr e ase In flat spin C n i_ w o rth the trade- o ff in l o wered steep spin damping. NASA testing indicates that it i_, 8 t least by preventing • _ high pro-spln yawing moments _h_n the rudder Ls deflected in a p ro - _pln direction.

n

S imultaneous deflection of the elevator and rudder p rovides _ery little additional p o sitive effe c t, a_ide fro m the fa c t that it s ums the effe c ts of ea c h c ontrol surfa c e. Overall co n trol effectiveness is v ery poor und e r flat spin condi t io n s. U nd e r st e ep spin condi=ions, rudd e rl effectiven e ss is actually lessened with the combined deflections becaus e of i n creased rudder blanketing caused by the deflected elevat o r. For this r e ason, standard re c ove r y procedure co n s ists o f rudder reversal followed by elevator defle c tion, applied before the spin be c omes fully developed.

i

I i • .

............................ T " I

I "

CF A PTER V i D EVE L OFHEh'r O F A PRE DI CTIVE PA R A .V _TE R ..

.I

A s pre v ious research has sh ow n , t h e Ta il D a: _I n g Po w e r Fact or a n d i its assoc i ated general av i a tio n aircra f t de sig n cr i ter i on I m ve proven t o be i ns u ff i cie nt for pred i ction o f sa ti s f ac t ory sp i n characteristics a n d re c o v ery. Thi s is due i n par t t o t h e con tributio n s of o th er _ Irplan e co m ponents. Nev e r t h e le s s , a trul F e ff ec ti v e de s ign cri t er i o n f or g ener _ l av l a tl on t ai ls w ould be use f ul t o th e desi g ner. I t m us t • • .

l in corpora t e a m easure u f control e ff ec t ivene s s w h i le a ccoun t in g f or effec t s of p oss i ble adverse a i l eron deflec t ion (Burk e t al. 1977). It = us t a l so be dependen t on t he n lrcraf t densi t y co e ffic i en t a nd p it ch a ngl e. !n ad di tion , because s p f n h a s b ee n show n t o be depen d en t o n me th od of contr ol reversal, the pa ra m e t er m us t a lso a ccoun t f or in correc t o r i ns uf fi ci e nt (cr it er i on) con t rol de f lec t io ns .

A des ig n cr lt er l on such a s described above w ould be l e ss t han prac ti c al because o f i t s co _ p l ex lt y. Ce rt ainly i t w o ul d involve ex te nsi v e spl n tu nn e l an d r ad i o c o n t r o lled m o d el t es t s. A =or e f e as i b l e _.it e r n a tlv e would b e e xt e n siv e wind tu nne l studl e s o f t a i l c on fi gur a tions, wit h t a bulation o f nondlm e nsion a [ for c e a nd mom e n t c o e ffi c i en ts f or v a ry i ng p i t c h, ro ll , and sid e slip an g le s . C o n trol d e riv a tiv e s c ou l d a lso b e tabu l at e d fo r spin c ondit i ons . Nith th e us e of o ne o f th e ranny no nl lnear num erica l simul a tion ro u ti ne s b ec oming availabl e , th e d e signe r _ould t h e n b e abl e t o st ud y t he s p i n cha r acte rt stl c s o f s e v e r al c onfigu r atl o ns and c hoose the o pt [ -.alon e f o r h is needs. Of cou rs e, full scal e flight testing w o uld still be nec e ssa r y, but by in c r e as i ng con f iden c e in p r edi c t i v e _eth o ds, :u c h I I0 !

t ef fo rt ¢ o u hl bL , x_ved i n o t her p r t+l i _I n a r v J t _|di e m, i _d e qo a c y of ti_ e T,+ll flapping P o _ r Fa ct t_r Ti le d exi_ n er w o ul d al._o f ind u sef ul ,s _ri_er i o n w h l c h _ro vt d e x a " [ r , mgh I Pa li _ ' a_ l , + n of t he \pi n chara c t e r istic\ o! the t a ll, So c h a cr l ter i L_ n w o uld be h e lpf ul d url ng p r el i mi nar y lavL_it a nd s izin g, Th e

l +

p r e_ en t t ail , l e_Ig n c r it e r i o n f or l i g h t g e n e r al avia t i on a ircr af t I x n o t a ¢ ¢ eptabl e ,. . _ .t, h ' a st i n i t s p r exent f o r_, P_- c aux e o f It_ conser va t i v e.

i+atu r e0 ,_ev er .il,tesl_ ns s h o wi n g acc e p t a b l e m p i n re co v er y ar e d e e m e d F tm , _c c ept .s b|e b \' t h e cr it e r l on _ s ee Ch . : pt e r 2), ..

t . lll . h , _Ign c ri t e ri,_ n _hl ch w o uld r . _ : t b e m i aleadi n g m u _t on ly t ' , , _ c ert; thi . +d,mp tn _ c l u sr n c t e rist icM ,a t th e t all , Tht t x. tt i + n ece s sary t o d e vel o p a f a ct ,+ r which app ro x i mat e ly pre di c t\ pi tc hi ng an d yawi ng ._= e n t_ a n d i n dt_'at e ,_ co n trt_l e f f e c t lve n e_ i n tercel. of i nc reased ., -_o r'_ , n ts . Flgt_re 5- 1 i s a pl o t of \ ' awi n. _ m o _s : t a s a \t ra c t i on ,_t t i_ , T . I|I l+ . _._pi n _ i',++¢,r F. + ¢ tor f , + r t , _C l l ¢ o n l+l_u r atl o n te s t e d. _ r t , t° t vpicai !

spl n c on dltl+_ ns a r t, +h,+w n . C orr el.lti on o f th e _+I ' F +ith v+_wl n ,_ m_+r a e n t i._ p,+,+r , p+| r t lcul, sr l y u nd e r t l , st spi n co _xllti o n_.

Th,-* r e a rt , +cver.;l re.+m on ._ t o e ti|e i n a, i equ ,s c v o f th e T t+ P F. _,¢atsse it i s ._ . _dt " up _t t l + p ro du _ ' t of t_ o o ther c r lt_ , r l a , the t'_ V C and th e T:+R, it ¢ , -ttttx_+t .'_€,. ' It_urt. s t, pa r ,_t.e c o t l ; r tbut io nm t_+ \ ' awin_ ,.'_+m e n t o t+ e+l_'h t , l_'t,+r ; tht , ru,hi , , r a c t \\+ s tir h+ ss tlm , ,ha . s t p ur e+me of c on t ri butl:_R t o t: tx : t , _ _t n ,i_,tlt,¢te,i p , _lth ' , n , and c o, tri t est t_t a i_ sl ttve vawi n }_ i n _ 'r e me| I t while _| e l l ec ted. l_ add_ . t lo :_, th e Ta l l D+_ ' _ p i n _ R ati_ wa, _ r blt r ,|ritv s e t tip t_ i:_ < lud_, _¢rc - a o n ly _i,+ r the , tx , _r t e o txt . _ _, _t,_bilL re r..

• , tht' h_+ r l+'_+;xt,_t ".at| sit+hit;' ,-.+t_ t_._., , .1 ,¢r,_ . -_, i ! _ " ,+t:t , ,'t ,m t+t,, T :+R .

I Q co .3

oTHETA = 40 DEGREES

cTHETA ft 60 DEGREES

(Ja .9

aTHETA c 80 DEGREES

. ~ 6 ..

o . 0001-:- ------ - - -------- -----~-.~.---~----------:--~-----------------.-------------------

~ (> g 6' v¢ . ~

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en -0. 075~ 6-

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II I I ., A 1 t:.

., A -O.IC0"j , i .., I1 2 ".

S p ln a n g l es use d in th e TDPF a re s e t u p a r bit r a r i ly, The a l rc r a ft is a fis um e _ t o 45 ° of if t t D s p l n a t a pitc h a ng l e uses a f u ll -s p a n rud der .

If a par tial -s p an r u dde r i s u sed, i t m ay sp i n at a n a tt i tu de of 30 ° or 45° , d ep e ndin g o n t he v a lu e o f t he TD R. F in all y , t he r e is n o e st i mati on of th e s hap e of th e b lankete d r e g io n o n th e v e r tic al t a ll.

u

Mom en t Co rr el aclo n wit h a H odl f led A n tt -S pl n Par a m e t er Pe rh a ps t he great e s t utility o f an y c r ite r i o ndeveloped is in . . pr ovi d ing so m e me asu r e of co r re lat i o n w it h t he man y f ac t ors i n flu encing t ail f orce s. Th e TD P F h a s pro v e n to b e un sa tis f ac t ory; a t rue d a mp in g . p ar a m e ter m us t c orr e l a t e w i th generat e d mom e n ts . Tb. ls d i s c u ssi on is con c e r ne d_i th s i mpl e i mpro v em e nts ba s e d o n tai l g e om e tr yand s h ap e of ' .

th e ai r c av i ty i n two dime n sion s , a n d it w il l t he r e for e b e a pp roximat e.

T estin g h a s sh o wn that F or a z er o - lo a d e d a i r c ra f t , yawing v e loci ty is the =a Jor c o n tr i but o r to i n e rt ia l mome n ts which perpetuate a sp i n .

The vert ica l t ail a n d rudder t h us pro vi d e t he l a rg e s t tai l c ont r ibut!on to sp in dam p i ng. Fo r thi s re a son , a tail anti -spi n p ar am e t e r (referre d t o as TASP b elow) shou ld b e b ased p r imar il y o n un bl ankete d vertical ta i l a re a. Rud d er c ont ri bution to yawi n g m o men t sh o u ld b e add e d as a separate f a c t o r , and on ly d ur i n g sep a rate c o =p a r l s ot _ of r u dd er e ff ect i ve n es s : U nblanketed Area " TASP - S ( b / 2) + K2 x Rudder V o lume Co effi c ient t he c o n s t ant K 1 is n e ede d to p re v e nt t he fi r st te rra f rom domi n a t i n g th e para= e t e r, a n d. must b e d e t e r ra i n e d throug h a st u d y of th e rela ti ve i mpor t an c e of e ac h t e rm .

; , , . . ...... . ......... 4 ~ . _ .. -, _ .....

" _ 113

n

Th e c a v i ty wh ic h bl an ket s p a rt of th e v ert ica l t al l is o f th e sh ap e s h o w n i n F ig ure 5- 2 . Mc Cormi c k, in an u n publ i sh e d s tudy, deri ve d a num e ri ca l m e thod for d e t e rmin i ng two-dim en slo na l ca v i ty sh a p e s of fl a t result s 8 h o w_ th a t p l a tes a t h ig h ang les of a tt ac k . Exsmf na tIo n o f t h e ca vity widt h in the p l a ne of the pl a te is rel a tively c o n st ant with

I

| respe c t to e.

I It is this r e se arc h w h i ch f o rms th e b a s i s f o r th e tail vo lume ca l c ulati on as shown in Fi g ure 5- 3 . The cavity h a s b e en simplified to which f orm a b l a nketing a re a determined in siz e by lines 11 a nd 1 2 , a r e separa t ed a distan c e o f 2.282 in the plane of the horiz o nt a l tail. Th e € J l in e s are parallel a n d at an angle o f 0 to th e horizont a l. Are a s a r e " defined below: - A I Are a o f the verti ca l tall n ot in the blanketed re g ion o r defined by other areas.

A2 T r i a n gular are a f orw ar d of the leadin g edg e of the hor i zontal tail; determined by a llne ext e nding f orward from the leading edge at an angle of 4 5 °.

A3 U pper forward tip o f the ve r tic a l t a il; bounded by the lin e 11• A 4 Triang u lar a re a aft o f the trailing edge of the h o ri z ontal - tail; determined by a line e x tending aft from the leading ed&e at an angle of 45 °.

A 5 High pressure r egion immediately below the horizontal tail and above the unblanketed lower area, A I.

1 14

I

U

I

t

'4 Figure 5-2. Actual Flow Around a Stalled Airfoil Compared with the McCormick Image Model

t

t A .

t • . "

i ]

• !

A 2 _" .... ..... A 5

A t

Figure 5-3. Approximation of Unblanketed Vertical T ail Area , . _. , . L ........ I ........... " 1 Th e ac tu a l dime n sio n s o f t h e h igh pr e ssur e r e gio n sh ould b e determined experiment a lly , For the a ppoxd-_tlon present e d, th e height of A 5 w a s a rbitr a rily set a t O.l_, a nd the width w a s set e qu a l to _.

. Th e r e sulting c o e ffi c ient b ec om e s AIL 1 + A 2L2 + A3L3 + A4L4 + K2A5L5 TASP = S(D / 2 ) T where L I through L5 represent the dist a n c es from the air c raft e .g. t o the c entrold of ea c h are a . The variable K 2 represents the value qA S / qA 1 ' a nd must be det e rmined e xp er imentally. A v alue of 1.2 was used in th e following analysis.

o- Results are presented in Figure 5-4. They show a fair c orrelation .

i under st ee p spi n c onditions, but the relationship breaks down at high spin rates and pit c h angles. The major ca use for poor c orrelation is the highly thre e -dime n slonal flow whi c h o cc urs at high s p ln rates, ' affe c ting the shape of the c avity. Results a lso indi c ate, even at low pit c h angles, that blar&eted area is being overestim a ted. Perhaps the - - roundeJ leading edge of the horizontal tall affe c ts the forward shape of the c avity, c reating a larger unblanketed verti c al tail area. In addition, autorotatlve effects witnessed in the testing were not a cc ounted for, and aft fuselage shape was not c onsidered.

: Better correlation may be obtained by applying some theory estimating the three-dimenslonal cavity shape formed by the horizontal tail. This would allow parameters AR h and Sh_tail as well as a v to be A taken into a c count.

i J CTHETA = 40 DEGREES _ = .S aTHETA = 60 DEGREES _ = .S ATHETA = 8B DEGREES _ = .9 . 0 O00-4, "

l

-0 025-_ -0 O50 i 1 3 Cn -0 07E_ A I

A A_

-0 10_- A

A ,, !_

- 0 125- ' , -0 1 50- "- _ -- r_ r _ - _ - T-r-r_ -i -_ - , - t - _ - _-_ - F- t _ .=_ :_ , ,_' _ - T - r_ r _ l_-r- r , , , , .

0.00 0 . 02 0.04 0 . 08 0 . 08 T o ll A n S I -S p l n P o r o moL_r ' Figure 5-4. Yawing Moment as a Fun c tion of Tail Antl-SplnParameter

]

i , / C P AP T E R V I CONCL U SION S _D RE CO MMENDA T ION S ' T h e pr es ent tests have s h o wn the p os sibility o f using c on ve n ti u a a l wind tunnel testing to obtain information about aerodynamic moments p r o du c ed by the t a il of a spinning airplane. T he te s ts enable tail p arametri c studie s t o he performed without influen ce from a main wing a nd b o dy, and they allow f o r inten s ive studie s of the c auses of aer o dynami c interf e ren c e from the aft fuselage and h o rizontal tail. T he major c o nc lusio n s o f the p r e sent study are summarized bel o w.

I I. The tests sh o w satisfactory a g r eement with NASA rotary balance data, with discrepancies at low pitch angles and spin rates attri b utable to - " wing and body interference e ff e cts not modelled in the present studies. _ The influence of a rotational flow field on tall forces is considered to be minimal.

2 . The primary parameter influencing spin damping is horizontal t a il vertical position. Ve r tical t a il aspect ratio can also have a large yawing effect for high values of ARv.

r

[ 3. Horizontal tail aspect ratio has a small effect on spi n dampi n g, ' with a moderately high ARh inducing larger yawing monents because of reduced vertical tail blanketing.

"j 4. Horizontal tail chordwlse position has an appreciable effect on pitching moment, but a small effect on yaw damping. This paramete r may be important to aircraft which must break pitch equilibrium for r ecover_.

i I

I

5 . Th e r u d d e r Is a m ore e ff ec tive s p in rec ov e r y co nt r ol t!: a nth e [ - e levator under e q uilibrium c o nd itions, in c rem e nting y awin g moment as m uch a s 5 0% i n some cases . Th e parti a l - span r u dder co nfiguration _ displays some advantage under flat spin conditions.

T 6. Som e low h o ri zo nt a l t ai l con figuratio n s can a c tually pr od u c e pr o - - sp l n m om e n t s un der s t eep spin con dit i ons.

I

7. T o be u s ef ul, an y p a r am e ter d eve l o p e d t o pre di c t t a il dam p ing c hara c _erlstics mu s t _ cco unt f o r all major int e rf e r ence e ff ec t s o f thai h o rizontal t a ll, and It will be stro n gly dependent on the spin rate. A s imple tail v o lume related fa c t o r will pr o bably no t b e usable.

Addi t: i0 n a _ t es ting o f tall parameters t o pr o vide data f o r . ' analyti c al studies and numeri ca l simulations is hfghl / r eco mme n ded.

Spe c ifi c ally, further study is needed to determine the effe c t of fuselage shape dire c tly below the horizontal tall on the pro-s p ln forces en c ountered at low values of h / b v . Control effe c tiveness should be determined for all co nfigurations, with special study o f the influence | o f h / b v and ch o rdwlse p os ition o f the h o rizontal tall o n rudder

I

effe c tiveness. The effe c t of a partlal-span rudder to in c rease yawing I forc e s at hlgh spin rates should also be thoroughly investigated.

For a satisfa c tory analytical model of tall forces to be developed, further testing would also be nece s sary. Tests should be performed which determi n e the pressure distribution o ver the v ertical tall, !

particularly in the region below the horlzontal tail. Flow measurement and visuallzat[on would also be helpful in the development of a tl_ree- dimensional ca v ity model, which is necessary to a cc urately predict the " effect of tall configuration on yawing moment under flat spla conditions.

|

" R E F E RENC ES ]- I. Ballln, Mark G . and Zilliac, Gregory G., "Report on the Condition of the Low-SpeedWind Tunnel." (In t erdepartmental report, Departmentof AerospaceEngineering,The PennsylvaniaState : Uni v ersity,198 0 .)

!

2. Beauraln,L., "GeneralStudy of Ligh t Plane Spin, Aft Fuselage Geometry,Part I," NASA TechnicalTransla t ionTTF-17,446.

- Washi ng t on, D .C.: Go v e rn m en t Prin t ingOffice, 1977.

3 . Bihrle, William,Jr., Hultberg,Randy S ., and Mulcay, William, "RotaryBalan c e Da=a for a Typical Single-Englne, Low Wing G eneral Aviation Design for an Angle-of-Attack R ange of 30° to 90o,''NASA U o n tractor R ep or t 2 9 7 2. Washingt o n, D.C.: G ov e rnment Pri n ting Offi c e, 1978.

.r 4. R!hrle, William, Jr., and Barnhart, William, "Spin Pred l c tlon _echnlques," AIAA Paper 80-1564. New York: Ameri c an Insti t ute of Aeronauti c s and Astronautics, 1980.

5. Bo%=an, James S., Jr., "Summary of Spin Te c hnology as related to Light General-Avlatlon Airplanes," NASA Techni c al Note D-6575.

Washington, D.C.: Government Printing Office, 1971.

b 6. Burk, Sanger M., Jr., Bowman, James S., Jr., and White, William L., "Spln-Tunnel Investiga t ion of the Spinn i ng Chara c teris t i c s of Typi c al Single-Engine G eneral Aviation Airplane Designs, I - Low- WingModel A: Effe c ts of Tall Configurat i ons," NASA Techni c al Paper • 1009. Washington, D.C.: Government Printing Offi c e, 19 77 .

7 . Burns, B.R.A., " G olng for a Spin - Fighter Style."

_ / L_ 9 _.t.l_11£_, Apr i l 8, 1978, pp. 985-989.

8. Chambers, Joseph R., "Overview of Stall / Sp l n Technology," AIAA Paper 80-1580. New York: Americsn Institute of Aeronautics and Astronautics, 1980.

9. Grunwald_ Kalman J., "Wall Effects and Scale Effects in V / STOL I Model Testing." AIA !%. Aerodynami_ Testln_ Conference, Mar_h 9-I0_ 1964. New York: American Institl,te of Aeronautics and Astronautics, 1964.

I0. Heyson, Harry H., "Linearized Theory of Wind Tunnel Jet Boundary . Corrections and Ground _ffect for VTOL-STOL Aircraft," NASA • Technical Report R-124. Washington, D.C.: Government Printing Office, 1962.

II. Heyson, Harry H., "Rapid Estlmatlon of Wind Tunnel Corrections with Application to Wind Tunnel Model Design," NASA Technical Note D-6416. Washln_ton, D.C.: Government Printing Office, 1971.

12. McCormick, Barnes W., Aerodvnamles of V /STOL Fli_ht. New Yorki Academlc Press, 1967.

• . ] 121 :

1-

1 3 . M cCo rmi c k, B a r nes I_.,Aer odynamics. Aeronautics. and FllRht ..

Mechanics. New York: J o hn Wiley and Sons, 1979.

• 14. McCo rmi c k, Ba rn es W., "Equilibrium S p l n nlng o f a Ty p i c al S i n gle- Engine Low-Wing Air c raft," AIAA Paper 81-4076. New Y o rk: American - _ Institute of Aerona u ti c s and Astronauti c s, 1981.

1 5 . Neihouse, Anshal I., "Tail Design Requirements for Satisfa c tory _ S pin R e covery f o r P e rs o nal Owne r Type Light Airplanes," N AC A Technical Note 13 2 9. Washington, D. C .: Government Printing Offi ce , 1947.

16. Neihouse, Anshal I., Licht=nsteln, Jacob H., and P e poon, Philip W., ....

"Tail Design Requirements f o r Satisfa c tory Spin Re c overy," NA C A Te c hnical N o te 1045. Washington, D. C .: Government Printing Office, 1946.

17. Nelhouse, Anshal I., Klinar, Walter J., and S c her, S tanley H., "Status of Spin Resear c h for Recent Airplane De s ign s ," NASA Technical Report R-57. Washington, D.C.: Government Printing Offi c e, 1960.

• i 18. Polhamus, Edward C., "Effect of Flow Incidence and Reynolds Number on Low - Speed Aerodynamic Characteris t i c s o f Se v eral Non-Circular / C ylinders with Application to Directional Stability and Spinning," ......... NASA Technical t_ o te 4176. Washington, D. C .: G overnment Printing 1 Office, 1958.

19. Pope, Al i n, W_d Tunnel Testing, 2nd ed. New Yor_: John Wiley and I Sons, 1954.

20. S c her, Stanley H., "An Analytical Investigation of Airplane Spin- Recovery Motion by Use of Rotary Balance Aerodynamic Data," NACA Technical Note 3188. Washington, D.C.: Government Printing Office, 1954.

21. Stough, H.P., III, and Patton, J.M., Jr., "The Effe c ts of Configuration Changes on Spin and Re c overy Chara c teristi c s of a Low - Wing General Aviation Resear c h Airplane," AIAA Paper 79-1786.

New York: Ameri c an Institute of Aeronautics and Astronautic s , 1979.

2 2 . Torenbeek, Egbert, Synthesis of Subsonic A%rp%_ne Design.

Rotterdam: Delft University Press, 1976.

i

l ,i A PPEN D IX A MODEL AN D APPARATUS DLMENSIONS AND CO NFIGURA T IOI_ S • IL I i s T able A - 1 _ Con f ig u ra tio nD i me n s i ons i v b h v S h llln_e Position r X_ Tallplane I ur a tio n (in) ( i n ) ( i n 2 ) ( I n 2) ARv A Pes (.) Rud d er Eleva t or Po sit io n A 7 . 5 20 3 7 . b 1 00 1 .5 4. 0 15 . O 6 0 6 0 0 . 5 Ne u t ral B 7 .5 20 3 7. 5 I O0 1. 5 4 .0 1 5 .O 60 6 0 l.O N e ut ra l C 7. 5 20 37.5 1OO 1. 5 4.0 1 5 .O 60 60 0.2 5 Ne u t ra l D 7 . 5 20 3 7 . 5 1 0 0 1. 5 4.0 1 5.O 60 60 O Ne u t ral : E 7 . 5 20 3 7 . 5 I 00 1. 5 4. 0 1 5 .0 6 0 6 0 0.5 : 2 0 X Forward F 7 . 5 20 37 .5 100 1. 5 4. 0 1 5. O 6 0 60 0.5 2 0Z A f _ G 5.5 20 27.5 i 00 i.I 4.0 2 0.0 60 60 0.5 Ne u t ra l II 6 . 5 2_ , 3 2.5 1 00 1 . 3 4. 0 17 . O 6 0 60 0.5 N e ut ral J 8.5 20 4 2 . 5 1 0 0 1. 7 4. 0 1 2 .5 60 6 0 0 .5 N eu t ral K 7. 5 19.3 3 7. 5 1 0 7 .1 1.5 3 . 4 8 15. 0 6 0 60 0.5 Ne u t ra l L 7 . 5 20 . 8 37 . 5 9 3. 7 5 1.5 4 . 6 2 1 5 . 0 6 0 60 0.5 Ne u tr a l H 7.5 21 . 1t 3 7 .5 88. 23 1.5 5. 4 0 15 .0 6 0 60 0.5 Ne u tr al A ll Con f igur a t ion s - _v = 0.5, _h =1"0 , t i c - . 1 2 .f ° r all sur f aces , , fi v(C / 2 )'. ,= O, / [ h = 0 " _ ' _ ] g_

J

!( i

. -.

\

.R7,)-20 nm • 3R Rt~JCI

-'. .-1,,-· - - - - _

,.... _._---'\..---

--~·t.-L· ~oc__.---=-----.J

!

""--Bal;,~cc Support

. i

. : , I , , !

· I ! : ~ :

..---1----'

• i · .

, ' I / 26.7')" (J AdjuHr:lCnt ·v

'" "

......... __ ... "

I

SO!:le dc::tails omitted I for clarity.'

j

fl

I

F1 v,lJrc A- L odc .. t ln~ S.t~pport and Stn,lt

I

._ .. J

i I I

S cal e 2:3 .i

• ' " -i .5 " _' , ; O.7 5 _ '- 2.0

®

4 t " _

+1 -- - ] t _

+ n Ho te 0 .8 7 5- 20 TX D i Attac h ed to Aft Fuselage Atta c hed to Support Figu r e A-2. NA S A I R - 2 1 Bala n ce Scale 2:3 j , ,

_ -

----.I, _

Fi gur e A - ] . F orw ard B o dy t _ O_ i . .

APPENDIX B AER O DYNAMIC MOMEN T C O EFFI C IENT S A S F U N C T IO N S OF S PIN RATE - .

° f

Y

1 2 8 " " T HET R . _ 4 _ _ EE _ , _ o 6_ O£ G , _ E E . _ A 8_ DEG R EES - 0, 1 5 _ N, J -1 . l S-J .. ?

- 2 .30 - _. O 0. _ _ . _ 13. j 0. 4 O._ _.0 ; J . / O . :. ' . 9 o .q Nondi ' _en^_om u i So ; ". _Jte F I Rurtl B- 1 . Pltchfn_ Homent as a Fu n c t ion of O and _ ' , '.,. C onfiguration A ' . • , , .

• . , , . , • • .. ,

!

1 2 9 ; o 4 _D E GRE E S _ 6S D£GR£ES , A 8_ DEGR_S 7" ; - ] i -8. 1 5 a-

__._J "-

-I . '25

•

r - m " " " ' ' t " . "t . .

t -i._

, -_ . ; 5- • .-2.23- 3 . _ 8 L 13 2 0.3 O _ _ . 5 _.O 3 1 _ 9 : _o -- Non d l_ o n e tonai $01_ RoL e Fi g ure B-2. Pitchin g Homent as a Function of 0 and _, . Confi g uration B

13 0

• { .

• o • j I _H ET R • 4_ DE_gE S m 6_ DE G RgE_ I A 80 D E GR EE. _ ,

{

-_. 5B - - O. 1 5 / -i. ,_._ Cm -I.qB.

- i. ; 5

I

. - 2 . _ O . _ 8 . _ 3 . 2 _ . 3 O. z 8 . _ 8. C _. t 8._ _. o _iRu r e B-3. Pitchin_ Momen t as a Function of 0 and _, Configura t ion C "

{

i TH ET R • 4 Z D E G R EES D 6Z DE GRE E S 8S D E GR EE s

-Z. 5 _

.1

-8. 1 5 - o ; C m -1 . 2 5 -I . _ . _,

-_ . 1 5-

- 2 . _ _. ,.3 ,3 . i. ,3 . 2 . ' 1. 3 0 . _ £ ] .=j £ ] .6 _ ./ 3 . 9 , 3 . 9 No n di_e n _, i a n o i S o ln , q u L e Figure Br4. Pitchin_ Moment as a Fun c tion of 0 and _, '" .. Configuration D • . , . , • . -. . . . .

° .

• 132 .

i I THET R " 4 B D EC R EES 8 _ DEG R EES = 6 _ D EG R EES i - _ . 5B- ; ; - 3 .7 5 - ....

[ " .

I o . • • [ Cm -1. 2 S , -_ . 1 5 , -2 . _ .

_ .3 0 . I _. 2 _. 3 0.4 _.5 _.8 _ ./ _._ _.9 Nondl_en_lonai S p i n R o LO Figure B - 5. Pitching Moment as a Funct i on of 0 and G, Configuration E . ,. .

1 33 •. TH ET .q • 48 DEG R E ES i m 6B D EGR EE S ! A 8 _ DE GR EE S

• !

' I

, i

Cm --l.=.O . . - " -I. 7 5 - -2. JO _ . .O B.i 0 . 2 0._ _ . _ 13._ _ . O 0. / O.B O.Q " Non d lm e n e ion u i S pln ._OLO Figur e B-6. Pitching M o ment as a Dunction of e and w, ..

• Confi_urat ion F 1 34

t

THETR a 6_ DEC, REE_) I o 41_ DF' O REE S A 8_ DECR E E S I -8" _B- U -B . 7 E " -l._- U ..

U - 1 . 2_. - Cm . . .

-1.5_ .1 I • -2.294 ..... , .... . ...... ,...... , ....... ,....... , ........ . ....... , .........

21.:] D.i g.2 .' ; " 1 .3 O .t - -q ._ _.6 :; "1 . I g.8 .'1 .9 Noncl i _eneianni St.,in R_i. ,e .. .

• .'," . . . • .

• . . . . • . .

Figure B- ? Pitchin p _ Moment as a Function of 0 and _, Configuration G

i 1 35

T HE T FI .

M BB DEC , REE._ i o 4 8 DEC , R g E S A S a DEC , REKB T -

i -_ ' _L

o I

i

'. - 3 .75 ......

.. ] : 4

1" "..i"

- I . 2,_.

C m - l. q Z I - I. 1 5 I I m °' , -23 Z 13.3 D.i : 3.2 D.3 _.d 13 . 5 G._ _ . ! 3. 9 : 3.q .Nondi'_en - tonoi _pln .Rote Function of and g, Figure B-8. Pitching Moment as a Confi£uration H

t

-0. ?5.

-I. I S- -2 . .I l ....... I ..... | ........ + ........ + ' ' + ........ i ...... + ....... +..... '' : + ,0.21 0._ . g.2 g._ g._ ._.5 ,_ .6 O. l I:]._ 13.9 Nondlmenelonoi _p f n £obe Figure B-9. Pitching Moment as a Function of 0 and _, ' Configuration J • • . • Fizure B-IO. Pitchln_ Yo,-,:ntas a Function of '_ and _, Configuration K "--,--,-~--'-,,.~~ _._-.-~ .. _--- , , q, , "'.2"(4 (

I

, ft1£~q

f

• 4,1 ~h~£E~ o fO Gf.l",l\£L'

j

6\ SJ ~t:.e.-:£E~~ ! \ -J.::J.

~- " '-.

..._-~----..- -

, -

_ t' " r1~lIrl' !I-It. l'lt"h:l'~~ ~1"~'l1t ;1'; ,I FWd·tl,'t1 "f :\ .'1!l,t .• ' (''!If (':\I';,\i ("11 l.

-_.:' .... ~ ......

/ ° 1 39 !

Pli.;tirt. I!-|. _. !'lt_-h t l_ _!,..-,1.11t ,l : i .i P_l_i_-ti o n o i ;i ilil d . , , 1" 0 11! 1_t4tll.i[ I[ 0 11 ,_1 • . . . , • , .

t-- j!1E'T~ .

\) 4;) Dt"~EE"~ c eJ GE,--",EES 0\ ~J aEGREES --- - -.- .

. i

-J .• ,~~ J

I

; 'J . . ~-i' I , .

. J. ,~~-4 ~- ................ ~ .......

., ~, .... ~ , ., .

Figllr~' 11-:13. Y.I\.:in~: ~1<'r.l1.·lIt .IS .1 FIII\<'[1"n ,'I II ;111<\ u'.

t\'1lIi~lIr.lt1ll~1 " l F igure B-I : +. Yawing .Hotr_., n t _ls a Function of 0 a nd t_, , .

• Con figur n t l o n B 14 2 I "f.q..P T q • a ft D FGRK£S • a _ : 3 DF._EE.q

"i

.. $. 9 25 t

•i t

3 . 3_ , -...........................

-ft. 32 s - i -- C.n 1 ?

,;3 . ff7.'5 _

I

g , !

THE'I,q " " o 4 8 DE_EE. _.

a _ 0 DEGREES.. " " o _ .3 DE O _EE. _ • .....

I _"_=__ ............

• ] . • . . .

_i.+ " .

,. t P i

i 1

-_. _._ _.. ..

_ c_

i i

t

!

t -_" "_ "!

I !

" -_ ,kFi + . + o- , ; + ..,. _+= . .. . ,& , - ....... i.+....... _++,..... .;-.,,,,,,+;+- ...... _ .... .

_ . _ _. L ,]. 2 _ . 3 O . * 3._ _ . C 0 ., " O ._ 3 ._ Figure B-I t _. Yawln R H orn, hi a,q a Fu n ctio n of O and _o.

Configuration D - 3 . l ; = F 3. 3 9 . ' _ 9 .-' O . ,z 3 .4 3. 5 O . C 3. / 3 . 9 3. q , . _ o _ J im o n PI3 n o i _ oi n _ ,J _ , O Figure B-I T . Yawing Motr_nt as a Functlonof 0 and _, '."

Configuration E F igu_e'B-18. Yawing Moment as a Function of 0 and _, ..... Configuration F " . , • , .

I Figure B-19. Yawing _oment as a Function of 0 and _, Configuration G 1 4 7 J Figure : B-20. Yawing Moment as a Function of 0 and _, ' " Configuration H '':''! .

... -~ .. - ...

i .

\

[

I

I I I l ,

[

!

T!iET~ o 4:l DE GREER c 6~ DEGREES f.

~ S~ DEGREES ~.:l~~ ••..•••... --- .. - -- .. --.- - -- ".' .• n _ .. _n ••

J

I

oj J25

J

- •• 1

I ,

-0. ~!3~ ~

en ~

i

l

-~. :]75 ~

j

-0. ·.~a-J

. ~

~. \

'. ~ . \

~ \

-D. 12;:; ~ .... , ...... .,.." .cr' .cr, ~'l"'" ...... .,.." '''''''''''''.1"'''' .,..,.. .. ,..,... ,.....,..'"", '''''.T'' ..,., .. ""', .~,,..,.. .. ,..,.. .. ~~"""""'.""'.""".,..,.., ..... , ~~.,...,..,..,..,...,..,.. .. "",:,. , ..... .,......,..,--:- ~. / D.I ~.2 D.3 D.'3 ~o~dlmon~i~nal ~pin ~aLo FigureB-21. Yawing Moment ~s a Function of e and W, Configuration J ....... .:-.~, .... - ... - .. ~.~..-,,,,.~~ ..... : ...... - •.• - _"~_'_~-.-- ... , .. ; .... ~ .... ,~.~~ ......... ( '7", .......... "'.""& ...... ..,. ............. : ... 1 .• ~:>E .• ·.·=..., ... ~. "\ .. · .... ·~O;:'· .. -_·_t ..... ",_ ... ~., .

... ·- ... ~_~Ly-....,.-_ -.,. .•• _- ...- ._~ -----. ... ;O--::--~;-- ............. -....'f~_.

THETR ~ 4::l DEGREES o 6n DEGREES A an DEGREES

U251

:3. ~m~ -; n un - n _. • n n .. n -_. - - ---

1·

I

... ~ ...

'--

.. ~. 050

en

'" , ~.

. "'1.

-0.075 i

~

-::1. i~G ~

\ '

J

, ... J 0_.

-O.iJ

.. '\' . f,- .ft,.fl.. f .1' .. f"" .. I,f .. ~f .. tf .iI . . t. . .. if "i. it .f

. - .. ~~ .;..

::J.2 O . .:J n.4 ::J.S (l.G n,l ::J.9 :J.:J lJ. L

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..... r' .;.': '-I Yawing Moment as a Function of e and w, Figure B-22.

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x_ T a b le C- I • _ Co ,' .f i gurat i o n A T e s t Data* I) , :n._ i t / .qor=a 1 Ax i al Pi tch ing R olli ng Y aw in g S i de .... ( _ l ug._ / V T V d F o r _:e Fo rc e H o_ -. en t M omen t M G= ent Force • 6 . 't v f.t3) • (f t / s t. c) (f t / sec) (lb) (lb). (i n -lb ) (ln - lb) (l n - l b) (Ib ) i , .'

' . 80 /, 6 . 20 0.00225 99. 1 4 68.62 8.967 1 . 082 52. 3 5 - 1 8.02 -14.79 - 3 .35 1 , - SO _9. , )a 0 . 0022 3 1 00.8 78.31 9.853 0.9789 55.7 8 -1 5. 0 7 - 13 . 0 0 -2.9 3 9 " BO 30 . 0_ 0.0 0 223 100.7 87 . 1 4 1 0.34 0.9767 59.30 - 1 1.7 1 -9.937 -2.246 60 42.52 0.00223 1 01 . 3 74.68 8.180 0.7844 46.42 - 1 4.60 -9.827 -2.38 7 ,, 6 0 35.50 0.00222 101.2 82. 4 3 8.758 0. 74 19 48.65 -12.2 8 -10.39 - 2 . 42 1 _: ) 27.00 0 . 00222 1 02 . 0 90 . 9 1 9 .288 1 .007 5 3 . 31 -9.444 -8.38 1 - 1 .95 1 60 17.f_O 0.00222 1 0 1 .8 97.40 9.774 0.7440 53. 1 3 -6. 3 09 -4.615 - 1 .0 1 4 60 0 0 . 0022 1 1 01 . 8 1 0 1. 8 9.677 0. 44 20 52.77 1 .807 - 1 .0 4 0 -0.25 1 7 40 27 . 89 0.00221 99.08 8 7.56 6.728 0.232 5 36.99 -7.327 -8.936 -2.006 40 20 . 71 0 . 00221 101.2 9 4 .62 7.222 O.3221 39.17 -3.631 -7.07 0 -1.5 1 3 40 12 . 7,_ 0 . 00220 1 02.5 99 . 95 7 ._6B 0 . 1 50 1 39 . 73 - 0 .8351 -5.842 - 1 . 1 47 4 0 0 0 . 00220 1 02.9 1 02.9 7.550 0.0 0 _5 4 0 . 0 9 4. 1 55 0 . 4 99 6 0 . 1 269 t. m , % 1 , , c_,.nts resolved aboutbalance center, t _ , ' ° [ • Table C-2 C on f igu r atio n B Te st D ata j D e ns i ty Normal A xl a l Pit c hi n g P o l l l n g Yawi n g Side (slugs / VT Vd Forc e Forc e Homent Hom e n t Hom e nt Forc e 0 ' U v f t 3) ( f t / s e c ) (ft / s e c ) ( lb ) (lb ) ( i n- l b) . ( i n- l b) (i n- l o) ( l b) 80 4 6. 20 0 .0022 1 99 .04 6 8.5 5 7.' 335 0 .9574 4 3 .4 3 -23 . 4 2 -2 1. 1 3 - 4.3 0 7 80 39.04 0.00220 97.9 3 76.00 8.009 0 .997 48.5 9 -19. 35 -19.54 -3. 8 75 80 3 0.08 0 . 00220 99.55 86.1 3 9. 6 59 1. 0 74 5 7. 3 7 - 16 . 25 -1 6 .7 9 - 3 .1 3 7 60 42.52 0.00219 98.54 72.6 5 5.946 0.7250 34.74 -25.54 -20.12 -4. 0 2 0 60 3 5.50 0.00218 100. 3 81.66 6 .666 0.7515 38.70 -23.25 -1 9 . 0 3 -3.68 2 60 27.00 0.0021 8 99.0 5 88 . 25 7 .29 5 0. 7 4 2 8 41.4 0 -1 5 .10 -14.46 - 2 .7 6 8 60 1 7 .00 0.00220 I01.I 96.6 9 8.63 7 0 . 87 80 48.68 - 9 .40 2 -I0 .64 7 -1. 928 60 0 0.00219 100.4 100 . 4 9 .4 71 0 .549 2 52.5 8 -0 .8055 - 0 . 32 1 3 -0.0067 40 27 . 89 0.00219 99.50 87.93 5 .471 0.18 3 7 3 0.4 3 -2 0 . 2 7 -1 6 .0 2 - 3 . 3 5 8 .U 20.71 0.00218 98.63 92.26 5.54 2 0.1776 30.7 9 -14.90 -1 2 .07 - 2.460 40 12.78 0.00218 10 2 .6 I00.I 6.769 0 .1550 36.3 2 -9.8 5 1 -8.07 5 -1.49 3 40 0 0.00220 100.4 100.4 7.064 0. 2 10 3 37.8 5 2.1 3 -1.738 -0.1400 . ° Table C - 3 Con f lgurP " o n C Test Data D ensity _ ; or_ml Axial P itchin g Ro ilin g Yawing S i d e (slu g s / VT V d F o r ce F o rce Moment Moment Moment For c e 0 av ft 3) (ft / sec) ( f t / sec) (I b ) (l b ) (ln-l b ) (]n - lb) (in-l b ) (l b ) 80 46.20 0.0022 3 100. 8 69. 7 6 9.5 8 6 1. 3 1 1 55.40 - 23.53 -1 4 . 7 1 -3.401 80 39 .0 4 0.00 22 3 1 0 1 .8 7 9 . 1 9 1 0.38 1.1 1 6 60.14 - 1 7.68 -9.276 -2.468 80 3 0.0 8 0.00 222 1 00.9 87. 32 10.63 1.083 6 1 .02 -10. 55 - 4 .937 -1.761 60 42 . 52 0.0 0221 1 0 2 . 4 7 5 . 5 0 9 . 5 34 0.8713 5 4.21 -1 5 .8 5 -2.730 -1.218 60 3 5 . 5 0 0.0 0221 1 0 2 .8 83.7 1 1 0. 2 0 0.7863 55 .43 - 1 2.38 - 2 .166 -1. 11 4 6 0 2 7 . 00 0.00 22 0 1 0 1 .6 9 0. 55 9.6 45 0.7070 5 2.77 -8.8 1 8 -2. 4 70 -1 . 104 6 0 1 7. 00 0.00 221 1 0 1 . 6 9 7 . 14 9 .888 0.76 4 1 5 3.16 -6.022 0.1714 -0.49 5 1 60 0 0. 00221 102 . 6 102 . 6 9.9 0 1 0 . 7 00 0 5 3 .08 1.841 - 3.526 -0 . 59 29 40 2 7 .89 0.00219 101 . 8 89.95 6 . 988 0. 1612 3 8 . 27 -9 . 6 3 4 - 5.0 61 -1 .4 95 40 20. 7 1 0.00218 101.2 94 . 68 6.'8 3 9 0 . 1230 3 6.60 -6 . 8 70 - 3.7 80 -1 . 028 40 12. 7 8 0.00218 101 .7 99 . 2 6 . 911 0 . 1418 3 6 . 5 0 - 2. 68 3 -3 . 87 8 -0 . 8 70 0 40 0 0 . 00 218 1 00 . 0 100 . 0 6 .707 -0 . 0 571 3 4.Q7 2.334 -0. 6667 0.0 01 4 Ta b le C-4 Con f i g u r at i on D Test Data D e nsity Normal A x i al Pitchin g R o lli n g Y awin g Sid e (slugs / VT V d F o rc e F or ce M oment Moment M o m e n t For c e i O .... _v ft 3) ( ft / sec ) ( ft / sec ) (lb ) ( lb) ( tn-lb ) ( In- l b ) (_n-lb ) ( lb) 80 4 6.20 0. 0 0 22 2 101.5 7 0.2 7 8 .2 8 8 0. 87 0 0 4 6.60 -20.6 7 -I3.1 5 -2.8 4 6 8 0 3 9.0 4 0.00221 1 0 1.9 7 9.22 9. 8 9 1 0.93 3 55.25 -20.55 -8. 4 36 -1.9 54 80 30.08 0.002 2 0 1 01.8 88.12 1 1.10 0.8 743 60.8 5 - 15.61 -0 . 9 7 0 7 - 0.5459 6 0 4 2. 5 2 0. 00 220 102. 5 7 5 .6 1 9.203 0. 5 290 5 0.02 - 1 7.67 - 4 .803 -1. 1 78 6 0 35 . 5 0 0. 0 0219 1 01 .0 82.23 1 0. 35 0. 5 0 8 0 55 . 51 - 1 6.02 1.1 63 -0 2 5 36 60 27. 0 0 0.002 1 9 1 03. 1 9 1 .86 10.68 0. 4 8 4 0 5 6. 55 - 1 1.28 3 . 7 66 0. 14 90 60 17 . 00 0.00 219 101 . 2 96 .8 2 9.9 2 4 0 . 50 80 5 1. 8 1 -7 . 26 0 3 . 5 64 0 . 2 7 3 1 60 O 0.002 1 8 10 2 . 5 1 0 2 .5 9.845 0.4 3 46 50. 73 1.05 9 -2 . 330 O .15 7 0 40 2 7. 8 9 0 . 0 0 218 10 1. 8 9 0.01 7.215 0.0825 3 7.59 -1 2 . 2 4 - 2 .838 -0 .9 2 10 40 20. 71 0.0 0 2 17 102. 8 96.2 4 7 . 501 -0.0099 38.3 5 -9. 7 08 -0.01 54 -0.2 7 26 40 1 2. 7_ 0.00 222 i01.i 98. 6 4 7 .444 0 . 0 1 28 37 . 7 5 -5. 8 6 2 1. 8 11 0.1 71 5 40 0 0 . 00220 102.6 102.6 7 .546 -0.1465 37 . 7 4 2 .711 0. 2 775 0.0025 Table C -5 Conf i gurat i on E Test Data Dens i ty Normal Ax i al Pltch l ng Roil i ng Yaw i ng S i de (slugs / VT Vd Force Force Moment Moment Moment For c e 0 av ft 3) (ft /sec) (ft/sec) (lb) (lb} (in-lb) (in-lb) (in-lb) (lb) 80 46 . 20 0 . 00222 99 . 82 69 . 09 8 . 250 0 . 6216 38 . 42 •'21 . 10 -16 . 56 -3.624 8 0 39.04 0 .0 022 2 10 2. 0 79. 2 7 9. 3 80 0.6 39 4 4 3 . 6 6 -1 5 .5 6 -1 3 .74 - 2 . 9 4 2 80 30 . 08 0.00221 i00.I 86.60 9.933 0 .7065 46. 0 5 -11.56 - 11.61 - 2.373 60 42.52 0.00220 i01.0 74.49 7.870 0.4904 36.03 -15.85 -10.80 -2.519 60 35.50 0.00220 100.4 81.72 8.285 0.5003 3 7 .49 -13.18 -11.28 -2.453 60 27.00 0.00220 102.2 91.10 9.11 3 0.5000 40.80 -10.80 -9.7 8 4 - 2 .01 3 60 17.00 0.00219 100.4 95.99 9.053 0.4 3 07 39.87 -7.271 -5.95 3 -I.010 60 0 0.00218 99. 3 2 99.32 9.19 3 0. 3 500 41. 38 0.66 3 1 -0.455 3 -0.3815 40 27.89 0.00219 102.0 90.12 6.774 0.0144 3 0.0 3 -10.54 -10.06 -2.140 40 20 . 71 0.00219 100.4 93.94 6.84"7 - 0 .0115 2 9.55 - 6.4 23 -7. 002 -1.4 2 4 40 17 . 78 0.00218 101.2 9_. 7 0 7.225 - 0.0197 31.09 -2.67 6 -5.118 -1. 0 15 40 0 0.00218 101.5 101.5 7 . 7 14 - 0.2290 32.33 2.23i - 0. 8 47 - 0.1833 • • Q .

Tabl e C- 6 Configuration F Test Data T Density _ Vd Normal Axial Pitching Rolling Yawing Side (slugs / T Force Force Moment Homent Moment Force 0 av ft3) (ft i see) (ft / sec) (Ib) (ib) (In-lb) (in-lb) (in-lb) (Ib) 80 46.20 0.00222 102.0 70.64 10.79 0.7426 69.43 -22.23 -17.23 -3.574 80 39.04 0.00221 10 ] . 3 7 8 .85 10.75 0.6369 69.77 -16. 8 0 -16.36 -3.201 80 30.08 0.00221 1 0 0.6 87.06 i1.08 0.7081 71.41 -ll.16 -12.84 -2.49 8 60 42.52 0.00221 101. 9 75.1 8.591 0.4486 55.41 , - 1 4.7 2 -12.65 - 2 .695 60 35.50 0.00220 99.4_ 80.96 8.493 0.4080 55.07 -I1.79 -i1.06 - 2 .341 60 27.00 0.00220 100.2 89.28 9.421 0.3947 59.65 -9.105 -8.081 -1.593 60 17.00 0.00220 I01.7 97.30 10.06 0.3769 63.30 -7.024 -5.626 -0.97 2 4 60 0 0.00219 100.5 100.5 9.696 0.1924 60.32 2.153 -2.22 2 -0. 2 758 40 27.89 0.00220 100.9 89.22 6.943 -0.0547 44.43 -9.076 -11.20 -2.613 40 20.71 0.00219 101.2 94.74 7.195 -0.1580 45.03 -7.045 -7.359 -1.614 40 12.78 0.00219 101.8 99.36 7.285 -0.17 2 7 45.03 -2.637 -5.768 -I.17 2 40 0 0.00219 101.2 101.2 7.633 -0.3056 45.96 2.4_3 -0.6820 -0.0151 tJ1 • . • :I T a bl e ¢ - 7 Co n f igu ra ti o n G Test Data Density Normal Ax ia l Pit c h i ng R o ll i ng Y a wing S ide • .- " ' " ( slugs / V Vd • O. a T For c e F o r ce M oment Moment Mom en t F or c e v 'ft3) (f t /sec ) (ft /sec ) (ib_ (ib) (In'Ib) (In-lb) (In-lb) (Ib) 80 46.20 0.00219 9 7.88 67 . 75 8. 3 77 0 .8 2 7 3 4 3 .11 - 1 5 .83 -14. 35 -3 .1 45 80 39.04 0.00219 196.10 74.68 8.826 0.8112 49.58 -13.77 -11.64 -3.529 80 30.08 0 . 00217 100.9 87.36 10.29 0.8861 57.95 -11.82 -1 2 .03 - 2 .367 60 42 . 52 0.00217 98.47 72.60 7.362 0.5836 41.30 -13.12 -12.14 - 2 .667 : 60 35.50 0.00216 101.0 82.20 8.442 0.5930 46.73 -12.41 -12.63 -2.668 60 27.00 0.00216 100.1 89.23 8.?98 0.6815 48.80 -9.136 -10.73 -2.174 60 17.00 0.00216 98.69 9 4.38 8 .786 0.5966 48.07 -6.863 -7.019 " -1.282 60 0 0.00215 97.39 97.39 8.705 0.3?02 47.18 0.6196 -1.905 -0.3098 40 27.89 0.00215 101.0 89.26 6.592 0.2802 36.89 -7.591 -9.975 -2.196 40 20.71 0.00215 98.38 92.03 6.546 6.1999 34.75 -3.938 -7.322 -1.632 40 12.78 0.00215 101.6 99.05 7.3088 0.2153 38.19 -1.564 -6.002 -1.179 40 0 0.00215 101.6 101.6 7.146 0.0428 37.47 2.903 -1.386 -0.1860 ° , Ta b l e C- 8 Configuration H T es t l ) a t a Normal Axial Pi t ching Rolling Yawing Side Density VT Vd Moment Momen t Force (slugs / Force Force Momen t 0 a v ft 3) (ft / s ec) ( ft / sec) (ib) (Ib) (in-lb) ( in-lb) (in-lb) ( Ib) 80 46.20 0.00221 102 . 5 70.93 5.277 6 . 8919 54.32 -18214 -15.15 -3 . 426 80 39.04 0.00220 100.8 78.35 9.645 0.9158 55.85 -15.11 -13.83 -3.052 80 30.08 0.00220 99.26 85.87 l O .Ol 0.9 7 80 5 7. 0 7 - 9 . 12 4 -1 0 .5 0 - 2 . 2 5 2 60 42.52 0.00220 98.82 72.86 7. 7 06 0.59 8 3 42.74 -13109 -12.05 -2.7 2 0 60 35.50 0.00218 102.4 83.34 9.401 0.8688 49.55 -12.06 -12.54 -2.540 60 27.00 0.00219 99.29 88.47 8.775 0.5747 48.03 -9.338 -I0.39 -2.058 60 17 . 00 0 . 00218 10 2 .4 98 . 0 9.4 7 0 0.5422 5 2 .1 3 -6.69 7 -6.5 78 -1. 2 2 3 60 0 0.00217 102.0 102.0 9.518 0.4223 51.77 2.116 - 1.530 -0.2918 40 27.89 0.00223 I01.3 89.55 7.153 0.3169 39.62 -5.269 -9.325 -1.939 40 20.71 0.00222 102.4 95.83 7 .609 0.3386 41.1 3 -3 . 51 7 - 7 .116 -1. 37 0 40 12.78 0.00222 102.1 99.58 7.365 0 .1661 40.01 -0.9997 -5.036 -0.9825 40 0 0 . 00221 102 .8 102.8 7.409 -0.1185 38.89 41.122 0.1996 0.1122 O' , • O • • • . .

, .

.dl T abl e C - 9 C on figuration J T e st D ata Density Nor m al Axial Pitchi n g Rolli n g Yawi n g Side (slugs / VT Vd Force Force Moment Moment Moment Force 0 _ v ft 3) (ft / sec ) ( ft / sec) ( Ib) ( lb) ( In-lb) ( in-lb ) ( In-lb ) (lb ) 80 46.20 0.00219 100.9 69.86 9;049 0.8401 52.65 -18.91 -16.46 -4.524 80 39.04 0.00219 99.98 77.70 9.656 0.83 7 6 55.54 -13.48 -14.63 -13.14 80 30.08 0.00218 98.68 85.37 9.987 0.8899 56.76 -9.153 -11.08 - 2.2 7 4 60 42.52 0.0021 7 102.2 7 5.35 8.502 0.5544 4 7 .40 -]4.06 -12.13 -2.785 60 35.50 0.0021 7 i01.i 82.28 8. 7 4 7 0. 5 906 4 7 . 7 3 -11.04 -11.82 -2. 7 80 60 27.00 0.00222 102.4 91.24 9.450 0.6101 52.54 -8.{52 -10.0 7 -1.926 60 1 7 .00 0.00222 101.7 97.23 9. 7 77 0.5460 52.88 -5.517 -5.553 -1.083 60 0 0.00220 101.9 101.9 9.669 0.3995 53.42 2.512 -36991 -0.7147 40 27.89 0.00219 I00 . 0 88.41 6.548 0 . 0481 36.32 -7.486 -10.67 -2.181 40 20.71 0.00219 101.2 94.68 6,816 0.1508 37.78 -3.700 -9.290 -1.930 40 12.78 0.00218 102.6 i00.I 7.518 0.0 7 15 39.29 -1.507 -8.108 -1. 5 85 40 0 0.00218 101.3 101.3 7.124 -0.1159 3 7 .58 3.2 7 4 -0.9248 -0.11 7 9 Table C-10 i Conf_gur_tlon K Test Data ...... Density VT Vd Nor_l A xial Pitching Rolling Yawing Side • @ _ •(slugs / Force Force Moment Moment Moment Force • v ' ft3) (ft / sec) (ft / sec) (Ib) (Ib) (In-lb) (in-lb) (in-lb) (Ib) 80 46.20 0.00224 101.6 2 0.36 9.362 0.8510 51.89 -19.24 -15.74 -3.445 80 39. 0 4 0 . 00 222 101.8 79.15 10.26 0.8238 56.43 - 16.42 - 13.98 - 3.048 80 30.08 0.00222 102.5 88.71 I. O 0.9397 61.57 -12.76 -0.879 -2.210 60 42.52 0.00221 101.4 74.75 8.746 0.6441 46.91 -17.29 -ii.ii -2.585 60 35.50 0.00221 i01.0 82.20 8.998 0.6776 48.23 -13.43 -11.20 -2.504 60 27.00 0.00220 102.5 91.37 9.822 0.6691 51.•92 -11.86 -9.370 -1.906 _0 17.00 0.00221 102.4 97.92 10.39 0.6763 53.99 -8.957 -5.253 -1.049 60 0 0.00220 i01.0 i01.0 I_.06 0.4040 52.67 1.6308 -2.069 -0.3340 40 27.89 0.00219 103.5 91.52 7.112 0.1223 37.24 -9.418 -9.564 -1.824 40 20.71 0.00219 102.1 95.54 7.169 0.1361 36.89 -5.920 -6.346 -1.202 40 12.78 0.00219 102.3 99.78 7,968 0.1556 39.34 -0.2904 -10.43 -2.092 40 0 0.00219 102.8 102.8 8.320 -0.0724 41.62 3.434 -0.9978 -0.0350 Table C-11 Configuration L Test Data Densl ty Normal Axial Pitching R o lling Yawing Side • (slugs / VT Vd Force Force Moment Moment Moment Force 0 a v ft 3) (ft /sec) (ft/sec ) (Ib) _ib) (in-lb) _In-ib) (in-lb) _Ib) 80 46.20 0.00223 100.3 69.46 8.658 0.9847 49.97 -22.66 -19.74 -3.736 80 39.04 0.00222 102.2 79.47 9..299 0.8981 53.24 -16.08 -16.00 -3.095 80 30.08 0.00222 101.4 87.75 10.02 0.9209 54.79 -12.51 -12.50 -2.290 60 42.52 0.00221 100.1 73.82 7.529 -1.717 42.01 -14.40 -i1. 8 3 -2.402 60 35.50 0.00221 102.1 83.14 8.236 0.6844 45.64 -13.70 -14.27 -3.071 60 27.00 0.00220 102.5 91.33 8.683 0.6752 4 7 .64 -10.90 -11.13 - 1.979 60 1 7 .00 0.00220 101.7 97.22 8.861 0.6516 48.22 -8.175 -7.071 -1.125 x_ 60 0 0.00219 i00.i i00.i 8.684 0.4754 47.61 0.7864 -3.372 -0.1832 40 27.89 0.00220 102.9 90.91 7 .05 2 0. 3 4 7 6 3 9 . 5 7 -9 .70 9 - 1 1 .8 3 -2 . 330 . 40 20.71 0.00220 I01.0 94.44 7 .015 0. 3 752 37.81 -2.1 3 0 -10.32 -1.91 1 '% 40 12.78 0.00218 102.4 99.87 7.127 0.2025 38.69 -1.1306 -8.054 -I..456 40 0 0.00218 100.9 100.9 6.858 0.0078 36.91 2.664 -1.877 -0.1218 ) _ , '. .- , . ......

_ ., _ 4_ • i " s J • • : " " _ _ ° . _ l \ . T a b le C - 1 2 ; _ Configuration M Test Data i; Density Normal Axial Pitching Roll i ng Yawing Side (slugs / V V d .. . , O a T " For c e For c e Mo m ent • M oment M oment For c e v . ft3 ) (ft / sec) (ft / see) (ib ) (ib ) ( i n - lb) (_n-lb ) (In - lb) _Ib ) x " ' 80 46.20 0.00216 98.66 68.28 7 ' 482 0 .8048 4 2 .85 -26.92 -18.5 2 -3. 7 90 80 39 04 0,00216 I00.I 77.77 8.691 0.6662 47.70 -18.81 -15.79 -3.089 -" 80 3 0 08 0 . 0 0217 98.52• 85.23 8.902 0.6197 47.76 -13.00 -11.37 -2.166 _ 60 42 52 0.0021 7 98.77 72.82 7.162 0.4261 38.6 7 -14.01 -9.718 -2.064 60 35 50 0.00217 99.60 81.08 7.960 0.1446 4 2 .62 -12.59 -10.69 -2.181 60 27 O0 0 .00218 100.6 89.68 8.129 0.4749 43.57 -10.43 -9.897 -1.907 60 17 O0 0.00217 100.7 96.30 8.233 0.3553 43.89 -7.234 - 5 .994 -1.068 60 0 0.00217 99.31 99.31 8.077 0.1944 43.41 1.081 -1.002 -0.1263 40 27.89 0.00218 99.94 88.32 5.895 -0.0161 33.00 •-8.631 -9.874 -2.128 40 20.71 0.00218 102.0 95.39 6.406 -0.0478 34.68 -5.777 -7.896 .-1.665 40 12.78 0.00219 102.7 100.2 6.642 -0.0830 35.46 -1.853 -6.521 -1.268 40 0 0.00220 102.6 _02.6 6.917 - 0 .23 7 0 35.54 2.458 0 .1934 0.1185 i T MJ l e C-1 3 C_nt_o l l)ef l L.ct J on T est 1 Data, 0 - 40 .0" , _ - 2 0.7 1 ° v - " 2 't _" _-_ . ' . L. Z --" -- Z - . LT. -. -q-- _ - _Z . -_ -_"_-- --- , L , ,. : : ; it > , t_orma l Axia l Pi tchin g R o l l in g Y awin g Si d e c r (s l ugs / V_ , V d " Fo rce Fo rc e Mome n t :lonL. n t H o = _ent F orc e . !_ ......... ( o ) ....... _it_3)..... j_ f t. /suc ) (ft /s ec) (lb) ( lb) (in-lh) (tn-l b) (tn-l b) (lb) • . . .

:) 0 0.0022 3 I 00 .I 9 3 .6 7 7 1 58 0.24 7 3 38 . 48 -4 . 048 -6.833 - 1 .435 Io 0 ..00222 101.1 94.58 7.874 0. 0 30 0 43.46 - 4.856 -6.489 -1.53 1 13 0 [ ) .0022 1 100.4 9 3 .97 8.205 -0.1807 44.4 3 -5.645 -6.1 7 4 -1. 3 18 t] _5.7 0 . 0 0220 10i. 0 94.54 7. 3 90 -0.0059 39 . 93 -6.796 - 10 . 8 6 -2. 1 97 0 25 6 . ( } t ) 220 1 01 .8 95. 1 9 7 .4 1 8 -0 .0 7 3 3 4 0 .81 - 7 .?2 2 -12.1 3 -2. 2 5 7 1 5 25 0. 00220 I 00.9 9_. 3 6 8.652 - 0 .4 00 7 "5.59 -7.05 0 - I1 .46 -2. 0 9 5 I0 16.7 0.00220 100.6 94.14 8.00 0 - 0 .2 470 43.06 -7. 7 6J - I 0.58 -2.06 1 0 16.7P* 0.00220 100.6 94. 1 4 7.163 0 .1940 38.98 -?. 07 g -9.200 -1.836 0 251 ' 0.00219 101.8 95.28 7 .216 0.1208 40.38 -7.595 -1 0 .26 -2.009 1 5 25P 0.002 1 9 , -3 u .2 93. 7 4 8.2 1 5 - 0 .2 170 44.8 3 -7.239 -8.988 - 1 . 81 8 I 0 16 . 71' 0 .00219 9 9 . Z, 9 9 3 . 0 7 7 . 7 50 - 0 .05 27 4 2 . 1 5 - 7 .406 -8 .5 14 - 1 . 741 * Partial-span rudd e r.

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Ta b l e C- 1 4 Cont r ol Def le ct i o n Test 2 D ata, 0 = 80 = , cA = 30.O 8 " • . V Dt . n: , i ty No r r_ a I Axial Pi t c h in g Ro l l ing Ya w i ng Si d e t _ V c r (._ lug : s / VT d F o rc e F o rc e Ho = ent Mome nt Mom e nt Force ( o ) t o ) f t 3) ( ft / sc . c ) (f ' . /st - c ) (lb) (l b ) __ (ln;lb) ( l n-lb) (ln-lb, 0 0 0.00224 I ¢) 2.2 8 3 .43 I h .86 1 .0_ , 0 61 . 55 - 10 .93 - 1 0. 6 7 -2.3 3 9 IO 0 0 . 00222 l h O 3 86 .7 7 1 0 . 68 0 . 49 9 6 58. 40 -10 . 97 -1 , 3 . 64 - 2 . 162 I _. 0 0 . t j0222 10 ¢ ) 1 86 . 65 10.59 0.202 3 _7.4 5 - 1 1 . 14 -i0.98 - 2 .17 3 € ) 16 . 7 0 . f )0221 lO t j 8 87.2 1 10 . 32 O . 8001 5d.OO -11.2 8 -12 . 17 - 2.5 43 O 25 O . O0220 I O1 3 8 7. 61 1 0 . 46 0. 707 9 5 8 . 59 - 11 .28 - 1 2.5 6 - 2. 6 3 1 " 1 5 25 0 . 002 2 0 1 0 1 6 8 7.9 4 10 .59 - 0 . 03 9 4 58. 04 - 11. 5 9 - 13 .2 5 - 2. 611 I0 I: ). 7 0 . 0q220 I 00 7 87. 1 3 1 0.5 1 0.3405 5 7 .9 6 -1 1 . 43 - 1 2 ,63 - 2 .546 : ) I ; ,. 7P * 0 . 0921 9 IGI 1 87.4 9 1 0 .61 ;1. 9 559 5 9 .04 -11.70 -12 .6 7 - 2 .641 , tj 25P 0 . h 02 1 8 9g 64 8 5 .34 9, _g2 0.9032 5 6.16 -11.04 -12.2 5 -2 .5 t , l 15 2 5P 0.002 ] h i I01 0 87 .37 1 0 . 71 0.3027 5 8 . 1 9 - 1 1.94 -13. 2 3 -2 . 66 7 ]O I , ;. 7 P O.0 : )2 " 2 0 I 0 1 O 87.37 1 0.77 0 . 6336 5 9.q , 7 -11 . 48 - : 2.76 - 2.628 : ..............................

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Overview

Key points