Simulation of three supersonic transport configurations with the Boeing 367-80 in-flight dynamic simulation airplane

NASA E_LTA

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The basic confi_tion flown in the program was a representative delta wiDg supersonic transport. The geometry a_d stability derivatives are given in Appendix 2. As with the NASA 20 the approach speed _ 135 kts indicated and the simulation _a_ flown at this speed. _here _ no stability augmentation system (SAS) on the be_Ic aircraft.

LO_ IT_D]_L_L _TION Figs. 61 and 62 indicate an accurate simulation of the static longitudinal stability. Both the column deflection and stick force versus velocity shov clost a_reement with predicted values. The maneuver characteristics are docu- mented in Figs. 63, 64 and 65 and show close agreement with calculated results.

Data for these curves were obtained from a _vLud-up turn. Due to the l_rse d_ cha_e with a_le of attack (CDo) of the delta the pilots had difficulty holdi_ speed in the rind-up turn which accounts for some of the scatter shown.

The elevator response sensitivity is shown in the pitch reversal data of Fig. 66.

0nly one data point is shown, as the pilots had trouble with this maneuver and most of the data had large errors.

Dynamic response of the aircraft to an elevator input is shown in Fi_s. 67 to 69.

The short period char_c_eris_ic_ a_, _.h_.,_._ _n I_A_s. 67 and 68 indicate close agreement with the predicted response for the first six seconds of the motion.

At this point the aircraft behaves as if the static stability were la_er than predicted, i.e. the aircraft pitches nose down and the an_le of attack returns toward equilibrium. This error was cause by the non-linear pitchi_ _o_ent of the -80 thrust reversers which are driven to change the drag equation terms.

The unaccounted for pitch moment of the thrust reverser _. caused the aircraft tO deviate from the predicted values of static _+._'bi!!ty. A_ the figures rD J_ I. II!!

&_'ffNO I NO D6-I0743 PAGE Q_ _ the motion is correct for a relatively lc_ tie period and the pilot will not be aware of the problem durt_ active control of the aircraft. The :atchl_ of initial response and peak values was excellent.

Good phugoid data was difficult to obtain since any slight error in trimatD_ the aircraft resulted in a velocity drift and gusts disturbed the motion.

Flg.69 shoes t_at the period is off by about 2.0 see and th_ da_ptx_ is essent- ially correct. The small error in period cannot be detected by the pilot as he is only mildly aware of the ph_oid during active aircraft control and does not see the period at all.

LA_RAL-DI_CTID_L DOC_IP_TID_ The static lateral-directlonal characteristics of the I_A z_ are s_ in Fig.

70 . The data were obtained froa steady sideslips _ show good agreement with the predicted values . The error in _ vs. _ indicates an error in C_ vhich is due to inaccuracy in knovi_ C_A of the basic -80. The roll rate, obtained as a function of wheel position is shown in Fig. 71 and the roll acceleration in Fig. 72 • Both of these curves indicate that the simnlati_ was close to the predicted NASA _ response in roll. _ simulation limits are dictated by the maximum capability of the -80. Examination of pilot wheel inputs In_lca_e_ _nat a _n_i_.A_ _f 15" Ar_ _ ,Aed azd the input rarely i exceeded iO ° . For this ra_e of wheel, the simulation is excellent.

The dynamic response of the slm_tor to vheel and rudder pulses is shown in Figs. 73 to 78. The adverse yaw characteristic of the stability axis is shown in the _ vs t plot. T_e flight test data falls very close to the pr_lict_ v-__!_,,es for _ first 9 seconds Indicati_ good agreemeat. The por- tio __ of t_e curve after I0 second_ indicates a positive spiral stability, TD I_ L-Ri PA_E _ _.YOeO while the calculated values are divergent. It is dificult to determine whether this is a dy_atc problems or a lateral mistrim. The spiral mode is very sensitive to trim, however the bulk of the flight test mterial iDdicates that the spiral _s slightly convergent. This should not detract from the | sim_ation duri_ the active control, approach and flare situation since the pilot is 'interested in initial response _o his control input.

The roll rate response for the vheel pulse looks good except for the same splr_l co_ver_e_nce after six meco_ds. _he sideslip response indicated the trends vlth close initial a__t and then a departure from the pre- dicted due to the spiral.

The d_c response to _dder in_ts shovs excellent a__t in sideslip (note the slight mAstrim), roll rate snd yav rate for the first five seconds.

Follo_ this period the trace e_kibltsthe sue spiral convergence noted in the vheel l_lses and a lover dutch roll da_pi_ than predicted. These two results izxllcate that the v_e of C_/_ is higher than predicted in the steady sideslip. _ C_p would result in lover Dutch roll dampi_ and hlgher spiral stability.

For both the lo_Itud_l and lateral dlrectio_ dynamics, the .response to control &ppeLrs to be excellent. There are sone errors in the free _Irplane dyes in both caseo, but since the alrcraf_ vas to be evaluated under active control, it is the controlled aircraft response that is important.

AD_ITIDILIL PROBLIMS Since the Delta operates at a lov static margin it is necessary to subtract out o_ _ae _sic -_0 s_a_Ic s_abiii%y. As a resui%, a A_ :_- _ ,-,- TD 1_14 L-It3 Q early Delta work that the mc_mmat of flight personnel longlt_y in the aircraft was sufficient to produce a very measurable change in the Delta pitch response. Care was taken to ma_uataln the c.g. position eund per_l movements controlled to main1_tn correct reslxxme.

The n_-linear pitchA_ ao_nt characteristics of the thrust reversers caused problems in early Delta york. A coyote r input to the SST throttle produce a nose down pitch for decreased thrust. Fllght work waa not consistent, with a pitch up for certain runs and a pitch down for other runs. Once this problem was understood, care was take_ to operate as much as possible in the linear area of the curve.

The Delta flAes at a hJ_h trim angle of attack in the _ approach con- dition. It is l_ossible for the -80 to fly the same pitch altitude so that in the slm_latlom the pilot is lower than he would be in the actual SST. This produces two probleas. First t his position relative to. the ground at fourth- down is Incorrect. There is little to be done to correct this problea and since the pilots felt that actual _ contact va_ an i_ortant evaluation point no attempt was made to flare at some point above the rummy.

Second, the pilot sees certain motions differently due to hls location and expressed in the folloeing equations:

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n__#o = - SIN o_c + Co5 o_c

where :

c_ = c_, - OC s °

TO IS4& L-It3 NO. D6-I0743 PAGE 88 sees this as _dverse yav for sharp roll inputs, since this adverse yaw Is a false cue due to pilot positio_ It vas partially re_ from the slna_tion by uslag a rudder input vith vheel (TCP). This technique does not cha_e the free alrplaae d_Nwles az_ only sli_htl_ changes the static reslxx_se. It serves to ra_ve the false cue at the point vhere it is obvious to the pilot; at a sharp vheel input. _als input also served to correct an apparent error in the Cn_ of the l_ic -80.

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TO 44,1 C-_4 NASA DELTA AUO_ The au_nented version of the Delta contained both io_i_ stability a_- m_tatio_ an_ l_teral-directional a_tion. The !o_Itudlx_Ll S_ consisted of pitch ra_e and aa_le of attack feedbacks and a colum_ to elevator gearing cha_e to maintain the stick force per "g" constant.

The elevator was driven accord_ to the followi_ expression:

+ i ._oc

gE = x4 6c ÷ /.4 d

BA $I," This system is desi6ned to increase the short period frequency while leavix_ the das_ix_ ratio app_tely constant, vn this case the r_tural frequency goes from 0.75 to 1.46 rad/sec while the damplx_ ratio goes from 0.867 to 0.793.

The lateral-directional au_ntation consisted of a roll damper which was imple- mented accordi_ to the followlm_ relation:

6 w - o. 5¢

P where _w is the pilot wheel input. The lateral-directiomal augmentation is P designed to _ecrease the rolli_ mode time constant from the basic value of 0.80 to the augmented value of 0.575.

IX)I_GI'_II_AL DO01_ATI_011 The static lo_itudinal characteristics of the NASA _ A ere ahmwrn in F_s. 79 to 80 . The s_reement with the predicted curves is excellent altho_ there is considerable scatter and there was insufficiemt data for speeds above trim.

Based upon the information showa in the col_ deflection vs. velocity curve -___d the _cc,_,_te fore v_-: _ef!_ct!on characteristics of the stick, it is safe to assume that the static calibration should be equally good at higher speeds.

TD _S4_ L II|

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PAGE 108 ,.,_0 F_s. 81, 82, and 83 indicate s reasonably good match of the Delta Augmented _aneuver characteristics. There is some error apparent, especially at the load factors. There is also an error aPl_re_t in the lift-cuA'ee slope (_w vs. load factor) si_Alatlon. Da_a reduction of the wind-up turn is diffi- cult a_ there is considerate error Inked by the iia_er in which the maneuver v_s performed. The aircraft was difficult to fly in the wlz_-up turn and the high _ resulted in high r_tee of s_ to maintain veloclty.

Pitch accelerati_ da_a ix_cates e_cellent si_Alati_ of the elevator c_trol and sensitivity. The doc_aw_tati_ shown here when used in co_uncti_ vlth the Basic NASA Delta d__tl_ l_icated that the loz_l_Lem_ char- acterlstics were slm_Yated correctly.

The lateral-directional d_tati_ _ limited since the only change w_ the inclusl_ of the roll da_er. Bath the i degree of freedom roll rates that the ch_e in roll _a_i_ was correctly si_ulate_.

Fig. 87 _hc_ a typical r_d_er pulse response to de_strate the Dutch roll chara_terlstles of the s_ed version of the Del_. As with the lo_i- t_diDal _tation, the d_t_ shown here i_ conjunction with the B_slc KASA Delt_ shows that correct si_l_tlon was achieved.

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static margin of the basic delta configuratio_ was 2.5%. In order to eval_te the effect of C. G. posltioD on the delta control response, a forva_ C. @. configuration vas selected at _ static _in.

This configuration l_s set up and docuaented and received a short pilot ew_l- uation. _e testi_ of this configuration was discontinued because the pilots reported that the loDgitudlnal control response a_lit_de va4 too s_ a_d that the forces were extremely high.

The data from the confi_tio_ documentation tests are shown in Figs. 88 to 93 The speed stability chaza_terlstlcs are shown in Figs. 88 sad _ The colu_ deflection required to cha_e airspeed is approxi_tely twice the cal- culated value for this conflgurati_. Calculations shov _t the s_tlc m_Lu of the _ht test conf_ration vu 35_. It appears that this con- figuration was not set up correctly on the sA_tion computer. Fi_s. 90 to 92 shoe the vlnd-up turn dat_. _ angle-of-attack to maneuver is si_ted correctly, _t the col_ deflection and stack force are higher than the predicted values, l_ta from the pitch reversals are shown in Fi_. 93. These a:.+=,i_i_ate that the iO_t_ control pover was higher than calculated, vhlch is contradictory to the low response in the speed stability tests.

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l i NASA A B _ne NASA Delta B is a variation on the basic Delta• This confi6_uration had an adverse yaw due to roll rate, N_ = -.I, and .05 Dutch roll damping ratio. The • was increased from -.00_9 to -.0352 and the value of Cn_ was value of Cn increased from 0 to -.138. Since the lon61tudlnal configuration was not changed, the documentation of the basic configuration holds.

The lateral-directional documentation is minimal consisti_ of the roll response data, and a Dutch roll response. Fig. _ _hows the roll acceler- ation, and indicates the CA_6w is sli6htly smaller than expected. However the peak roll rate shown in Fig. 95 indicates that the roll damping re,st be slightly lov so that for a given wheel a correct roll response is obtained.

Fig. 96 shows the Dutch roll response with the low damply6. The mea_Ared Dutch roll frequency and damping are .996 rad/sec and .055 which comI_res well with the theoretical values of .982 rad/sec and •05.

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T I F!_, q_; D6-I0743 N_A 72 The NASA 72 is a confi_n_ratioa representative of a variable sweep w_ng SST with the wings in the full aft position (72" leadia_ edge sweep). The stability derivatives of this configuration are presented in Appendix 2. Tae actual aircraft has an approach speed of 180 kts indicated but the si=_lator was flown at 150 kts because of the 367-80 structural speed placards. The appropriate corrections were made to the equations of motion to account for the difference in speed.

The lon6itud/nal characteristics of the NASA 72 configuration measured in flight did mot agree well with the theoretical characteristics. The column deflection, stick force, and angle of attack in the wind-up turn were high and the column deflection and stick force required for airspeed changes were also high, although there was a good match of the elevator pulse response I i !'

data.

These errors were caused by the mls-match between the flight speeda of the 367-80 and NASA 72. Also, since this configuration was evaluated only briefly, it was not checked-out a_ tailored as carefully as the others prior to pilot evaluation.

In order to corre_ _,e_ :r:____-, t_ flight test data was used to calculate the actual NASA 72 configuration flovn, using the equatioms and methods Of appendix 2. This configuration is listed in Appendix 2.

The static longitudinal characteristics of the NASA 72 are show_ in Fig. 97, 97A, and 973. There are goc4 matches of the column deflection, stick force, _n _ - -_n=_!e of attack vs. speed. The maneuvering characteristics, measured in the wind-up-turn are shown in Fig. 98, 98A, and 98B. There are good matches of the column deflection, stick force, and angle of attack vs...gi, up to i._ TO ll41 t.il3 _dFJAb'_ [ No D6-I0743 PAG_ !30

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load factor. The longitudinal control sensitivity, 1assured in the pitch reversal, is shown in Fig. 99. For the limited data available, there is good agreement with the theoretical characteristics.

The airplane response to an elevator pulse is shown ia Fig. I00 and i01. The amplitude of the flight response is slightly higher tham the theoretical characteristics, but there is good agreement in tke shape of the responses.

The phugoid trace of airspeed, shown in Fig. 102, has good agreement in periog (short by about 2 seconds) and lover damping than predicted. The actual value is difficult to determine due to a mistrim of the airplane and the sensitivity of the phugoid to gusts which disturb the motion).

The static lateral directiomal characteristics of the NASA 72are s_vn in Fig. 103. The agreement of all three parameters vs. sideslip is good although there is a lateral mlstrim ms indicated by the bank angle vs. sideslip plot.

Tke lateral control power as represented by roll acceleration vs. wheel posi- tion is shown in Fig. i0_. The mistrim is evident, however, the" slopes are the same indicating a good simulation of control power. The steady state roll plots indicate that the roll damping is correct since Figs. 105 and 106 are R nc__arison between control power and roll damping and the previous figure showed _ simulation of control power alone.

The dynamic response of the aircraft to a wheel pulse is shown in Figs. 107 to 109. The roll rate response show an error in the peak roll rate which is due to a -80 simulation limit. For NASA 72 wheel deflection above about 40 ° the rolling moment capability of the -80 drops off. Since most of the pilot inputs were limited to the area below this, the iimit sh_!_ no_ be a degra- dation of the simulation. The sideslip response is __c_ad_ for the first eig._ seconds. The Dutch roll frequency is off as sho_n in all three figures. _ne i'0 ,ill L.Ill No D6-I0743 _dTArJ,,%,'dD" PAGE 131 i,-ff)g4 • predicted dampe_ frequency Is 1.22 tad/set while the flight test shows 1.36 rad/sec. The error in peak roll rate shifts the yaw rate response towards zero resulting in the curve shown in Fig. I09. The basic _ode shape and magnitude are good.

The rudder inputs show the same basic trends as the wheel responses. Roll rate is slightly low at the peak (note that the high roll rate required is equivalent to e_cut a 45 ° of wheel and is achieved by -80 aileron motion).

The Dutch roll frequency is off as indicated above and the damping appears to oe low. (The gust response of the aircraft tends to make the Dutch roll damping less than predicted). The sideslip response is goo_ except for the miatrlm shown. For a linear simulation this curve can be shifted so that the agree- ment is good. Yew rate shows the same problems with a mistrim, and the low peek roll rate tending to separate tae predicted and flight test results.

The basic response data of the NASA72 shows good agreement with digital runs.

Simulation limits in lateral control power show up in the wheel and rudder pulses, however, if this effect is removed and the mistrim corrected the response is excellent.

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APPENDIX I 307-80 Char_cterlstlcs TO IS4& I.ll| AI'_JY,4V'_" 367-80 Confib'ar_tion Doc_unentation Flight tests were performed in August, 1904 (Boein_ Test No. 643-i to t/_3-4) to document the 36y-80 flight configurations used for SST simulation. Speed stability tests were run to document the lift-dra_ cha_cteristics and the effect of the spoilers. The thrust reversers were calibrated by holding constant speed and varying clamshell door angle. The lateral control static characteristics were measured by cross-control sideslips and the dynamic characteristics were documented by performing step wheel inputs. The airplane response to pulses of __ii the controls w_s documented for use in setting up the simulation computer.

Three configurations were documented in these tests: flaps 30 °, BPR I, flaps 30 ° , BImR 4 and flaps 20 ° , BPR i. The configuration with BLC w_s not used for slm_zlation, so only the data for the BPR 1 confi&n_r%tiuns are presented here..

The lift and dra_ characteristics at a number of speed brake deflections are shown in Figs. 11 3 to IiI, The elevator-static stability relationships meas- ured .in these tests are shown in Figs. 117 and 118. Figs. ll9 to 122 are cross-plots of the lift and dra_ curves which show the speed brake effective- ness. Fig. 123 is a cross-plot of th= ela;-_tor cu_v_ to show the spoiler pitching moment. Fig. 12_ 18 a correction of fig. 123 to show the spoiler pitching moment at constant airplane an_le-of-_ttack. Figs. 125 and 126 show the thin, st reverser calibration. The thrust curve has been normalized as the ratio of actual thrust to the thrust at 30" clamshell door angle. In the elevator curve, the 8_Lrpla_ewas initially trimmed at 0 Q clamshell with O ° elevator. The rudder and control wheel required in the c_-oss-contro!

TO 1£46 L.RJ

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PAGE l_O _"_ sideslips with speed br%kes up and down are shown in Figs. 127 to i_3_ The roll rate l-esponse to wheel step inputs is shown in Figs. 131 and l_ .

Following these tests, the 367-30 vas modified frown servo tab operated aileron and elevator controls to powered hydraulic controls. This modification Changed the effectiveness of the elevator and lateral controls. For small deflections (to 15Q), the elevator effectiveness was increased by a factor of 1.26 over the tab elevator. The modified lateral control char_cteristlcs are shown in Fig. 13} This is shown for a trim condition with the speed br%kes at C ° which w_s used for SST simulation.

Later flight testir<4 also sh_wed that the 3<;#-60 had a moderate ta_l buffet when the inboard speed brakes %Tere deflected above lO ° . In order to prevent this buffet from de_radin_ the simulation quality, the inboard speed brake deflection was limited at IO ° by the computer while the outboard speed brakes operated to !_ ° for m_xlmum lift modu!at_on. The effectiveness of the inboard s_d outboard speed brakes, measured by wind t_nunel testln_ and corrected by flight test data is s_l_._ in Fi_s. I34and 135.

TD I_ L-R9

I

PAGE 151 ,._coo 307-80 3tabilit_ Derlv_tives T_ne 367-80 stmbility derivatives a_d d_n_c stability characteristics used for slsaAlation of the NASA 20, NA_AZ_ , and NASA _[_ SST configurations are tabulated on pages 176 to 17_ • These derivativeB have beem updated from the initial theoretical values by flight testing with the simulation system.

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V ,i ,.. - SimJlatien Cm 6s8 _!ina! DYn_micCharac%eristics Short Period Undamped rmtural frequency 1.53 Damped natural frequency 1.09 Dampir_ Rstlo •702 r _ i L . i.! , , I : . .... , , 367-*_O Late_-Directiona] _ _'_ ..... _" ..... .b_ract eris _ c_ NASA-20 -' -'%0_.'_ ,a, NASA- 72 Flight Con_diticn Simulation S! mulati on L J Ve 135 KTS 15o Flap Angle 30 ° 20 © W_i_'_t r._. _ Ibs I_ .,OOO 150,000 C. G. Location 30 3o Speed Brake Trim anzle 6 ° 6" Side Force Deriva=ives cy_ .149_ .o86s /'r_..'_?c Cy_ .C_5 .o7<4 /r_.."s ec Cyg& .i?i2 .?177 Ir_d JY_A O O cy g sp - .039 -. oBq /r_ Cy SwH -.O128 -.O!__ /r_d Ro]:ILug _:om_at Deriva%ives CB_ 1 _D -#

.o_ 17 •03,90 ,C"Ud Is _c

• 0_02 /rmd C2#_ .0179 C _A P .0c09 c_.. .c468 •077 rind "_A _ gw@ * _ I a 2.57xlO6 2. _7xlO 6 SIu_- Ft givmla tlon S imu!a ti om Yawing Moment Derlv_tives

Onp /r_d •

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later_ITDirectionmlu_namic Characteristics Spiral [)iver%ence -188.8 _27. "s_c Time Constant (convergent) Rol! Convergence .665 .6_ sec Time Constant Dutch Roll Undamp_._ natural frequency .799 .8_& r_/sec •798 D_ped n_tural frequency Damping 7_tio .0_19

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APPenDIX 2 SST Test Configuratlons Tneoret Ic_l Calculations TD 1_14 L.II3 _f_ No D6 -107 4 3" PAGE 180 _T _ COmrII_URATIOES The theoretical SST stability derivatives and d_a_c characteristics used in these tests are _abu/ated on p_ges 182 to 185, _xe supple_ental ic_6itudlnal test configurations are su_zed on p_e 186and the lateral configurations on pete .1.87..

The _ and equations used to calculate the theoretical SST longitudinal characteristics and the calculated values are shown on pages l_to 197. The lateral-dlrectlonal calculations are shown on pages I_ to 20_.

TO 154_ L-'II|

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PAeE ) i_ 6-_ ,__ was^ 72 coa,_ .o_A_o,, (Corrected to Natc_ F_tSht Data) rad/8_ rad/sec I NO _-107_3 l , , L / / S $.7T LA'P:./-<A T, '_I _'_ ...... _'" " f :_-in-t ]ondi tion " ........

Ve 135 _ _ !% KVa T e m _e t _ht 2-._0, 9.© 2cO, " .'_ ,1"7f_,01_ 35 46 V:( L Side Force Derivatives C3p -. 573 -. 5272 -. _928 /r ud/a e c Cy_ •025 _, .04_7 .... 4_ Cy_ •Oct,, .i'46 .0692 /m'_,,"s e ¢ tYdc_ .1146 •ii 4_ .i!i_6 /'rua CYjWh 0. O. 0. /ru_ R_o]lin_ Noment _erivati,se._ _Jp .1547 ._°_= /r_ --.0249 C2_ --.2269 -.0_; C_ •07 __ .073 ,Ir_.,_/s e 0 Oo C • .... 1146 .0573 .(O86.

! X_ 2. _6xlO 6 2.222x106 .o. m -zo? 3.

PAGE ,_ i.+iL _,r7/ " Y_W%:,g !_:oment Deriv_ti+_es /r_d cn_ .2oo6 .i_ .I_4 cn_ -._7_. ..to2 -.o55_.

Cns,, . .0/_ .one9 .00z IZ8 20xlO 6 20xlO 6 i_xlO 6 S'l..ug.Pt 2 Slug.Fh 2 Jxz 8 O. O. O.

.I_teral.Directionsl Dynamic Charscteristics Splral Divergence z 9 74-9 -17.7 ee_aat (convergent) _c ]Roll convergence Time Constent .48 .802.+ 1.7 see Dutch Roll 1.2_ Undamped natural freq_emcy .628 .811 Damped natural frequency .618 •750 1.22 Damping Rtio .186 .381 .169 J Modified NASA 7'2 Configuration (Corrected to match flight data) _'s/g= 66 ibs d T/_ = .oon.8 / _/.ec _V S_ort Per iod = 1.232 rad/sec = .411 Phugoid = .1172 rad/sec = .232 TD )_ L|!

_o D6-1u/_,_, £V_IgAM_ _'AGE186A LATERAL TEST CO_FIGURATIORS Roll Con- Divergence vergence Spiral I I utch Roll

Conf_uratlo_ g

T" --- .sec Basic .48 ._28 .18_ ° _ASA 20A _5 .621 .282 _* Dsmper_ Pitch ra_e + .478 Alpha Aug.

201t Deteriorated Lateral 3_ ._92 .64a .051 N_ = -.i_ Pitch Rate + A_pha Aug.

Deteriorated Lateral 3P7 .692 .o51 Basic Longitudinal .... _ = , ',, _Z i_ _ NASA Basic .802 74.9 • Szl .38l Roll Damper lO9.2 .573 .829 • 379 Pitch Rate + Alpha Aug.

NASA_ Deterlorated Lateral 99.6 .3_5 ._2 .o5 _ = -.i Pitch Rate + pha Aug.

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t Basic 72 -17.6 l.y )54¢) t.R] I No. D6-1074S _- eAGE 187 _.,_ Nu, M_ER , _v (TR A _ORET!CAI, C ALCDW_ATIONS I, PEKD STABILITY NQUATION_ ELEVATOR/VELOC iTY C 0 LLE_/'__iO CITY 3TICK FO.._CE VELOCITY Tt_P " -_.IV_TION OF ECUATIONS: le ÷ CL 6E

C L = CLo +

_E e Differentiatin4 : __ -- _._._...f. CL ---__ - "..-L_ av 6E a v dv .:e_ _s • Rearranging _ _ d6E d C.

g_ - CL,_e a v _ d--G-- dv CL _ _o For Steady-!_tate Pitching _oment (where e and _ = 0): +C C_ = C% + C,n@_o( + C., v_v roSE _'E :q j- Dii'ferent iat ir4_ : _+ +C go( C/v d $ E d_ ;%ubstitut.ir_ Ec_lat_on 3 into Equation 5 for ------ • 4v • C_ C d 6E dgL 4- __ (9 C L_ L_-W-V--V ÷ d v a v @ILl d _a - C,, ,_ a--P- '.-e Now the lift er;!]Kt.ion is a L- v SoL q_, Different_atlng:..

o - a S C L_V Jr, NUMBER D6..I/7"/I_3 ._E BUEJN_ co.p_v REV LTR B I0.

Rearranging Terms:

_ICL 2 V C,. 2 cL

Jv V a - y

R_ and Bubstttutl_ F_luatlon 10 :l_to Y_uatton 7: • C_ Cm _ Therefore:

_v- - _v -x--_

Se

For conftgumatlons vtth lo_itudln_ augmentation, the walue of a-_-- does IK)t ¢ha_e. The pilot h_s an additional elevator 4nput to equal to g£ - a rJ_ The equlwalent pilot elevator input Is: Aot - °

_6E/._ _6e] -- Sa . 4O(

_ v - _ v J .,,....,,.i° ,_ .¢ ,_ v

SHEET 189 NUMBER REV LTR THe Bg_JNG =OM_ANV ii, W]_D-UP _URN CHARACTerISTICS I THEORETICAL CAIEULATIONS I ELEVA_)R PER NORMAL ACCELERATION: From Dynamics of Flight by Etkln (PaEe 301 - Equation 9.8, b), The Elevator AnEle in the Turn, Z_ _E, is Given As C n+l 6 Wind-up Turn III This was calculated by a digital computer 6CoL _ _ _col.

_ _ CoL gs N ,_ 0.. _ tt _ CoL I for configurations with longitudinal augmentation, the value of does not change. For these configurations, an equivalent value _' 6CoL _ of pilot elevator Input,-_--_-, was _A_l_t=d. +_ nbt_in -- and -- SHEET 19o AD 4872G _.7000 NUMBER REV LTR THEORETICAL C_TIONS

! 1

PULL-UP CHARACTBR_TICS i EL_ATOR P]_ _RNAL ACTION: i i • i

n_am=a ot FL_t by main (Page 56 - r_ation 3.x, ?)

The Elevator A_le per "g" :In _ Steady Pu].l-up is Given as:

ASE _6E C . o C ,., oc + -9- C.,,, d C= .c

I"1-1 ,_1'_

CL_;E C,4_ - CL C_ _r_

For aonflsuratlona vith lo_ttudtnal sl_bility _tatloB, _n equl_ent _ue of pilot elmmtor input ls used: _ . _ .

B /1 z_ _ J vw._u6MSN'rlO-- O ,_ n.

m CL o C(N£11_ _ STICK FOBCE PER EOl_Mi, ;,,_,______._aq'lOE: -- m, ,i ,,,, i ii _ tam Above ituattoa f_ _--_ , t_e Coin-- ua Bt', .ek Foroe per .g. _a a Btea6y Pul£-up tJ i Bttok-For_e

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SHEET 191 b-70OO N U._,'_BER D6-I0743 _ BOEI_VG co ...... REV LTR T_X)RE_rICAL CAECUI, ATIONS ACCEI,ERATIOII PER AIIGLE Or ATTACK

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The Normal Acceleration per Ansle of Attack, Usually Given as _z _ C L,( oC CLo WHERE C. Lo= CLTRIM H_e_er, this Fdluatton Neglects Lift Due to Elevator Deflection, Which can be _abetantlal at Times. To Compensate For the Elevator Lift, the C L_ Term in the Above Equation May be Replaced by an _fective C L o_ Which Varies with Elevator Deflection.

Using this Term for CL_ " tn the Top Equation Results in <SE TIz CL_,E ._ CL d, EFF CL_.. + T/Z CLo CLo Rearranging Terms:

!

TIz CL </CLo

AT CON STANT .SPEED i o( I- _ CL_.___._E 7)7_ CL o

I

NOTE: Z/_ Will Vary for e Steady Pull-up and a Wind-up Turn Since it Includes the _E/7] _r__,

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,-4 ÷ SHEET I_ AD 4_72G 6°7000 D(-__C, i3 BO,_=:/',4_"G .........

RE"-' LTR A ,_dO C", OJ -¢ ,.','-t,...D 0". (%1-i'- :TO _m OJ .":7., u_ -.¢- _.m O,,l C_ ,r,,, .,:_.._ :., "7..-._ . i e . .

<:i ,.-:4,4_ J ,.44 .Ag F _ 44 J, .'_.1-Q ::00dl ,..rx

_,_o

-_'-_" 04:0 0,1 ,..._ 0 "_, -.,,90 .'2-.-- _-,, .4 _4 _ j Ad o:, ,--t ,.---t ,--t,--4,-'-t,'-I _ _ o_ _., :_ _, 0 0 C'r, 0 _4",, o _4AGJ "_,4F4 VO r_ O H E_

* _,* *

o _,£

0 o • • • • " -; -i 4 _'_ !

I I I i I I I i I I I i t I I I I | I O O r_ '_ _ ._, 0 !

P _ o n_ i.i 0,1 ,'Y'I _o I ! I I I ILl _0 + o SHEEf 195 ,r_'_ _, "p _,-_ q 4441_ ¢::1 _.t. _, De_ ,..4"_ ..¢(M __ ._.._ b--. ._00 0 b-.

I-,I -4 t.I "._" 44_" t,o ,--,i :>I_IA ';___ .--4 '---_,.._ ",.£,A_ 4 I I ! I ! ! ! ,-,_ ,-t ('M ! ! ! I _4 ! ! ! !

.,DJ_'-_ :t .", _'__ ,-4 ,--4 N 4 _ v 0 0 0 t I.-I 1,-i ,,--I g , II I I t_ O q H + _-,J.

q q b- I-I

Q

8H

SHEET !96 m i xJ q u-x u_ _ 4_ V _o q ,-i t__,. _ 0.4

o. o.o. _

! ! 8 I I _ !

N

q -,4 C_" _ =_ _ 0 III

C_ _2

v ,,,d Q -I Q !

el m t _u 4o I TO 1&16 L.ILI N UMB E R D6-10?k3 REV LIR TKEOP_YICAL CALCULATIOI_S - b_TEADY SIDESLIP Derivation of E_uatioss: Four degrees of freedom are used for analysis - only static terms are considered Y Z Yawing moment _WH

N=O- Cn/3 +Cn p R Cn w H

Lift F z :O= LIFT-W CO5 @ o Side Force Fy --0 = Cy_ /3 + Cy,_R IR + _ StN (l) _e ,¢_m,_,,mR_,, 4,- _oiii_L_ --_:.

L =O = C2f _ _+C2_wH 6WH-,-C/$ a ga SHEE1 NUMBER D6-1o7_3 REV LTR Calculation of rudder and wheel required: From i and _, Cn_R _R +C_wHSWH =- Cn_/3 C16 R SR +CQ _V_,.l SWH = -Cj_/3

$R

- c_/s CJ.#w_ + c.trs Cn:_wH

/6

C_gR C._iwH-Cn_iwH C./',SR

SWH

- C-ns RC.tr_ _ C,n_ C# ,_ R

/3 C_ 5 R C.ISwH-C'n_wH C_ _ R Calculation of bank angle: From 3, _r.S LIT Cy_/3 ÷ CY(_R (_R'+CLI_, _ =0

' i-

¢)- CL!_ _ CY(_/'3 "t" CYgR _;

CALC : - c"_" _. CY/3 + C y S R

L

D6-IO743 SHEET Pa_e 199 _D 4_7." G T}Y_ORETICAL C_UIATIONS - ROLL RAI_ Bo]ling moment equation: _FSb For steady state roll rate, $ -- 0 "Ene theoretical value of $5S was calculated by an IBM program which computes the _irpiane response to a step wheel input in three-degrees-of-freedom.

On the NASA_and NASA y2 configurations, it was difficult to measure the steady-state roll r_te correctly because of the high inertia cross-product term. On these configurations, a one-degree-of freedom roll rate was used.

This was calculated from the roll _nd yaw equations, assuming that _and_ are O: J_z @ WH _sb = - C_wM C_:_ w_ i z 3_z = Iz .J_z CAL_ : C_, _ WH I z ,T*Z CALC I Z D6-I07_3 ": ..... l:_l_e 200 _OA_JNG .........

In reductin_ the data, was measured at a point where _ was zero s_nd the measured value of vas corrected for the measured sideslip: J_cz CI/S + I z C"n,_

. ,,,'3

TE_T

cs,/, .,..T _z

'z-_SEORETICAL CALCUlaTIONS - ROLL ACC_TION The roll reversal data w_s measured at a point where , q_ , /3 = O .

The roll and yaw equations become: I_ "" J_z - _-_ _ + ¥-5_ _A=- cjs_ . _.

Be J_z Iz _ =- C_w H_wH

_-gb

I z J_z

- Ix Iz J_z 2

(_sb)2- (_s_) _

J-x.z I_ J_z z

=_-c _rsb _r s_

If the maneuver was not performed correctly, the measured value of _" was corrected: t_)"FLIGHT "- (S)°MEA-.%

Iw- J_z z

TE ST t s :_.L_ D6-I07_3 Page 201 THEORETICAL I_L-DL-_TIONAL CHARACTERISTICS CONFIGURATION NASA 20 1.05_/sec _* 1.35

• _3 _.3o9

NASA 20A

o._/.ec

I NASA 2OB IP

o. 3_5/sec

_r

| I I i , ' _ I IHII r ! , I!L NASA Z_

.6o2 1.26/ae,= _

.837 i. 23/see.

i NASA Z_A .795/se_ [ !

i NASA _B l.h3 /sec i _r

_r

r] n - ' • i Lc L,- :i = NASA 72 0.619 -0.228 14.6b O. 343/see 2

o. _3o/sec

4_

* --corrected to ID value "I TO 1s46 L-Ill OOE'#AV_