Research Memorandum

... ."

I RESEARCH MEMORANDUM

AN ANALYTICAL EVALUATION OF TEE EFFECTS OF AM AERODYNAMIC MODIFICATION AND OF STABILITY AUGMENTERS ON THE

". FOR._ AEROhlAUTlCS

0 3 c;' WASHINGTON April 21, 1958 L NclCA RM A57K07

4 <-

AN ANALYTICAL EVALUATION OF TEE EFFECTS OF AI? AWODYNAEQIC

MODIFICATION AND OF STABILITY AU- ON TEE PITCH-UP B3HAVIOR AND PR0BABI;E: PILOT OPINION OF TWO FIGETEZ Am

By Melvin Sadoff andJohn D. Stewart

The effectsof a wing modification andof stability augmentation on the computed longitudinal behavior in the pitch-up region and probable pilot opinionof the pitch-up characteristicsof two current fighter airplanes are presented.

The cornputations indicated that the additionof a wing leading-edge extension to oneof these airplanes would(1) reduce the peak and overshoot anglesof attack forall flight conditions hvestfgated, with the exception of those at take-off speeds, (2)and ahould lmprove probable pilot opinion of the pitch-up behavior from unacceptableto unsatisfactory - the category of the elevator-controlledF-84F and F-& airplanes. Added pitch damping provideda simple by pitch damper with constant gain did not materially reduce the response overshoots and would not be expectedto improve pilot opinionm this airplane. One beneficial effect attributable to the damper, pitch however, was a reduction in the peak positive maneuvering tail-load increments. For the ather fighter airplane, the computations indicated that added pitch damping provideda smleby pitch damper withnonlinear gaFn reduced thepeak: and overshoot valuesof angle of attack significantly for all flight conditions considered but the landing approach. !This should improve the probable pilot opinionof the pitch-up behavior for this airplane from unacceptable or unsatisfactory to unsatisfactory but acceptable - the rating category for YE"86D the and F-86F airplanes. The results for this airplane equippeda stick with pusher, which ais device intentiedto prevent pitch-up altogether, indicated that the pitch- up regionwas generally avoided with this deviceoperata, even far extremely rapid maneuvers. Canparisonof two versions of this device 2 NACA RM A57KO7

showed that care must be intaken the designof such systema to minimize reductions in the maneuvering capabilitiesof the airplane.

INTROlXTCTION

Desi@ considerations for supersonic fighter airplanesmay, in some cases, lead to configurations which would be expected a severeto have pitch-up problem at high anglesof attack. Three possible approachesto this problem are the use of aerodynamic modifications, stability augmenters, and devices for preventing entry into the pitch-up region. Gener- ally, the approach selected would be onbased carefa weighing of several important factors, such as possible performance lossesto extensive due aerodynamic modification, the comglexity of the stability augmenters or pitch-up preventers required, and the magnitudeof the basic pitch-up ". . problem.

In reference 1 aa analytical studyof the comparative pitch-up . . .. behavior of several airplanes is presented and the computed axe results .. . correlated with documented pilot opinion.By comparison of the cmputed pitch-up characteristicsof new airplane designs with the corresponding results from reference1, the probablerelative severity of pitch-up and the associated probable pilot ofopinion pitch-up may be determined prior to actual flight experience. Appliedin this manner, . .. the method is alsouseful for investigating the effectivenessof aerodynamic modifications orof automatic control devices in altering the severity of pitch-up on existingairplanes. This method for estimating - probable relative severityof pitch-up is basedon only the longitudinal dynamic behavior in the pitch-up region: The effectsof othecmodes of motion such as roll-off, airectional divergence, and spin not entry are considered. Although beyond the scopeof the presentstudy, some con- sideration should be given to the possible adverseon effectspilot -1 - opinion of these other modesof motion; this could be basedan inspec-on tion of wind-tunnelrolling- and yawing-moment datain the pitch-up region. 1

In the present report the three approaches.the to pitch-up problem . noted above, that is, theof useaerodynamic modifications, stabillty augmenters, and devices for preventing entry into the pitch-up region, are assessed in the lightof their specific applicationto two example supersonic airplanes - the F-1OlA and F-l&A airplanes. The methods of references 1 and 2 are usedto eyduate the effects on the pitch-up behavior and on probable pilotophion of pitch-up of a wing leading-edge modification and of added pitch damping F-1Ol.Aon the airplane and of' added pitch dampingon the F-l&A airplane. Also presented are the NACA RM A5Z07 3

3 results of an analog study of the effectivenessof a limiting device, c referred to as a stick pusher, for preventing pitch-up altogether on the F-104A airplane.

I- DESCRIPTION OF AIRPIAXES Basic Airplanes

The two example supersonicfighter airplanes consideredin the present studyare the McDonnell F-lU and the LockheedF,-l&A airplanes. Two-view drawings of these airplanes, hereinafter referred air-to as planes A and B, respectively, and their pertinent physical characteristics are presented in figure1 and tableI, respectively.

Wing Modification

In aadition tothe basic airplane A, a configm-ationwith the wing leading-edge extension modification shownin figwe 2 was also studied.

Stabflity Augutenters

Pitch dampers.-Two types of pitch dampers were ccmsideredin the present study. For airplaneA, a pitch damperwas considered which *.; increased thetotal pitch damping to five timesthat of the basic airplane. In this case, itwas assumed themer was operative atall times witha gain constantof 52t/V. (See AppencuX A for definition of symbols.) A block diagram of this lFnear pitch damper is presentedFn figure 3. For airplaneB, a pitch damper witha gain of 52t/V was again assumed. For this case, however, it was assumedthe danper becomes operative onlyin the pitch-up region.The set-up assumed for theanalog cornputations for this nonlinear dampershown is In block-diagram form in figure 4.

Stick pusher.- The stick pusheris a device designed by Lockheed Aircraft Corporationto limit the attainable airplaneangle of attack to values below those at which pitch-up occurs. The assumed operational envelope for the stick pusher, providedby Lockheed, is shown figurein 5. When the combinedsi-s from sensors sensitive to pitching velocityand I angle of attack reacha predetermined value establishedby this envelope, an action signal is transmitted to the solenoid valve actuator assembly. which in turn moves the stabilizer and cockpit stick into unisonthe trim position (i.e., the position forstick zero force .in steady level flight). If the pilot does not attempt to override the device, the stabilizer returns to trim at the of rateabout 20' per second. A block diagram, assumedto represent the stick pusherfor the analog cmputa- tions, is shown in figure 6.

The dynamic behavior of airplanes A and B in the pitch-up region was computed bymeans of the evaluationmeuver and the basic equations of motion presentedin referenc-e 1. A representative time historyof the evaluationmaneuver from reference 1 is reproduced in figure 7. For the present study-, since wfnd-tunneldata indicated a large decreasein control effectivenessin the pitch-up region for twothese airplanes, these equationsof motion were modifiedto include this effect.Also, the equations were rewritten in ofterms absolute rather than incremental (from n = lg) values of &(u) and Cm(u) since it was desired to record absolute values of a and n. The modif'ied equations are: - -mv(6 - dL) = + %S (a)2t 8.1 qS + w (1) and

Several flight conditions were selected for foranalysis each airplane. These are presented in the table beluw.

Center of gravity location,-

I I I C 1 1 A 0.25 Sea level Take-off 0.286 85 35,000 Cl!=€Ul ,286 1.20 35,000 Clean .2% B 23 Sea level Landing .20 approach .&I 353 OOo Clean 9 07 975 35,000 Clean - 07 *9

I. EACA RM A57K07 5 c - The basic aerodynamicdata for these flight conditions were obtained from wind-tunnel measurements provided by LockheedMcDomell and and are presented in figure 8 and in tableI.

This section is' dividedinto two main subsections. In the first, the computed pitch-up behavior of the two example airplanesall the for flight conditions consideredis discussed insane detail. Particular emphasis is placedon the effectiveness of thewing modification andof the linear pitchdAmper QU. alrp7e A and of thenonlinear pitch damper on airplane B in minimizing thepeak angles of attack and thewing and tail loadsin pitch-up maneuvers. Also, the effectivenessof a prellmi- nary version of the Lockheed stick forpusher preventing entry into the pitch-up region is assessed.In the second sectlon, the effectsof the wing modification and of the pitch damperson probable pilot opinionof the pitch-up behavior of airplanesA and I3 are presented and discussed.

With the exceptionof the take-offand landing-approach condLtions, all results are presented for initial stick-deflectionr-s corresponding to an average load-factor entry rateinto the pitch-up region of approximately 0.5g per second. For the low-speed flight conditions, the initial stick-deflectionramps were programnedto provide a gradual stall entry comparableto that used Amesby pilots in evaluating lg stall characteristics.

Computed Pitch-UpComputed Bhaxior \

The results of the computations are presentedin figures 9 through 17. Computed pitch-up time historiesfor the two example airplanes.for the various flight conditions cansidered shownare Fn figures 9 and 12. Fig- ures 10, U, 13, and 14 show the variations WLth recovery-control of rate the overshootsin airplane angle of attack and load factor and of the maneuvering tail-load incrementfor airplanes A and B. In figures 15 through 17, the effectof stickipusher operationon the maneuvering boundaries of airplane B is shown. Figures 15 and 16 also show the boundaries for the onset of buffetingand lateral unstead5nessprovided by Lockheed from flight-test results.

Ef'fect of wing modification.- The effectson pitch-up of thewing madification, as'applied to airplaneA, may be determinedby comparing ic' the basic and modified airplaneA results in figures 9, 10, .and El.. The 6 - NACA RM A57K07

results indicate some improvementin the behaviorof the airplane Machat numbers of 0.85 and.l.20. The peak angles of attackand overshoots are lowered about20 to 30 percent at thelmr recovery-control rates. This order of improvement may be sufficient-to reduce the possibility of inadvertent spin entries at moderate subsonicMach numbers. At a Mach number of 0.25 at sea level (fig. g(c>),no improvement is observed, since no recovery occurs either for the or basic the modified airplane, even at the maximum recovery-control rateof 30' per second, within the available data limits. An appreciable increase in stability just prfor to the unstable break (fig.8(c)) my, however, provide sufficient warning to prevent inadvertent pitch-ups low at speeds.

The resultsfor a pllach number of1.20 at 35,000 feet shm in figure 9(b) also indicate that criticalwing loads may be experiencedduring supersonic pftch-up maneuvers for both theand basicmodffied airplanes. Peak airplane load factors8 toof gg, corresponding to overshoots of 3 and kg, areshown for this flight condition (see g(b)figs. and U(a)).

The effects of thewing modification on the maneuveringtall-load increments are relativelysmall. Peak valuesof about 10yOOO pounds at a Mach numberof 0.85 and 22,000 pounds ata Mach numberof 1.20 are shown in figures10(b) and ll(b). It should be recognized that thesevalues rder only to the out-of-balance portionof the total. maneuveringtail load. They do not include thetail loads requiredfor balance. Addi- tional information is presented in AppendixB relative to maximum positive and negative total maneuvering tailin pitch-uploads maneuvers for two of the flight conditions considered for airplaneA in the present study.

Effects oflinear pitch damper.- The effectsof increased pitch damping on the pitch-up behavior of airplaneA were first investigated by arbitrarily increasing the pitch damping@ to five tlmes thenormal aping at low angles of attack. The actual decreasein control effectiveness was not taken into accountin thfs initial study, The results obtained (figs. 10 and 11) indicated a sufPicient orderof improvement in the pitch-up characteristicsto wantfurther investigation ofa pitch damper which realistically reflects the large indecrease control. effectiveness of the airplane at high angles &:attack (fig.8). The type of pitch damper assumedfor.%he.andog computations.is shown in block-diagram formin figure 3. The computed results with this damper operating (figs. 9y loy and U) show that relatively6malL reductions in the peakand overshoot angles of attack andlo& factors wererealized _. with this type danger.of

Beneficial effects attributable. .to"norind operationof the linear pitch damper area redgction In the severityof the recovery transients (lower negative peake) and an associated reductionin peak maneuvering ta21-load increments to about50 percent of the values for the basic airphne. - (See figs. lO(b)and - U(b). ) MCA RM A57KO7 7

FZfect of nonlinear pitch damper.- Initially,a pitch damper with L constant gainsimilar to the type assumed in the analysison airplane A was investigated on airplane B:' However, sinceno appreciable reduction in the overshootswas noted with this typeof mer, it was decided to try -thenonlinear type shownin block-diagram fom in figure 4. It msy be seen from the inset figures gainthat was the nonlinear, varying from 0 for a < a* to 52t/V fora > a*. The pitch damper thus becomes operative when two conditions are satisfigd, As, that a exceeiJs some critical vdue 'a* (in the present case a a? eth) ana e exceeas 6th. The damper remains in operationuntil either 8 attains 8 predetermined large negative value of the order of 5 radians per second squared aor decreases below the criticaldue u*. The effect8 of this meron the pitch-up behavior of airplane B are shownin figures 12, 13, and 14. These results show that the nonlinear pitch damper an effects appreciable improvement in the pitch-up behavior allfor flight conditions with the exceptionof' the landing approach. For example,a Machat numberof 0.80 at 35,000 feet, the peak anglesof attack were reduced from values sme*tin excess of28O to about24' at low recovery-control rates (fig.=(a) ) . The overshootsa& maneuvering tafl-load increments (Pig.13) are roughly only 50 percent of comparable dues for the basicailple. At a Mach number of 0.973, the eak e of attack and airplane load factor were reduced from about32 87 to 2 and from 7.2g to 6.6g, respectidy, at a recovery-control rateof 20° per second (fig. =(b) ) . The results in ffgures 13 and 14 indicate that the effectivenessof the pitch damper apparently increasesa6 the recovery-control rate rewdTu$ is Q@gw 20° per -- second. Also shown in figures 13 and 14 is the benefhial effect 'of the pitch damper Fn reducing the maneuveringtail-load increment tram about 12,000 to 6,000 pounds. It should be pointed out that the pitch damper system illustrated in figure 4 was designed to investigate only the principleof switching on the dRglper as a function of both a and e'. Questions of system relia- bility, servo authority, and methodsof mechanization werenot examined. Also, the indicatedkprovement in the pitch-up behavlorof amlane B due to the pitchmer would be realized onlyif the reductions In peak angles of attack were sufficientto prevent or minfmize the possibility of spin entryor other uncontrollable motions in androll yaw. This would have to be establishedby referrhg to wind-tunneldata on the rolling and yawing derivatives at high anglesof attack for this airplane.

=In the presznt study,it was convenient to selecta* as the value of a at which 8th was attained for an 6 of 0.5g per second. Ear- ever, other values fora* could be selected (e .g., values corresponding to a \ of zero at various Mach numbers).It is only necessary to select a* at 8 level sufficiently high that the damperdoes not become operative during abrupt maneuvers below the pitch-up region. 8 NACA RM A57K07

Effect of stick pusher.-As noted previously, the stick pushera is device designed tolimit the attainable airplane angleof attack below those at which pitch-up occurs. This device in block-dhgram form is shown in figure 6. In an attempt to simulate partial overridingof the device by the pilot,a recovery-control rate of 15O per second, in addition toa maximum recovery-control rateof' 23' per second, was assumed. Also, various values of control-system time constantT from 0 to 0.5 seconds were considered.In addition to thenormal maneuver rateof O.5g per second.,2 ratesof 1 and 3g per second were investigated to check the operationof the device in rapid maneuvers. With the exceptionof the case at0.80 Mach number and35,000 feet, for whicha peak angleof attack of 17' was attained (for assumed valuesof ri, T, and Earec of 3g per second, 0.2, and 15' per second, respectively),no significant effect msnoted with variationsof these qwtities within thelimits investigated. The foUow5ng discussion is, therefore, primarily concerned with the results obtained for valuesof 6, 7, and 6srec of 0.58 per second, 0, and 25O per second, respectively. Figure l2 presents canparative time histories-for airplaneB illus- trating the operation and effectof the stick pusher.It is apparent that the deviceperforms its function well; that is,meximum the values of a attained arewell below those where pitch-up is experienced. However, someloss in the maneuvering capabilities of airplaneB is indicated as shown by the resultsin figures 15 and 16. In these figurest the maximum values of a, CL, and n, attainable for the airplane with the stick-pusher system operating, are cered with values corresponding to a (2% of zero and the maximum values attained with the basicairplane in pitch-up maneuvers afor recovery-control rateof 20° per second. The permissible steady-state maneuvering accelerakion boundarya function as of Mach number, basedon the zero C& boundary furnished Loclrheed,by is shownin figure 17. Also shown in figure 17, are two boundaries which represent limitat$ons imposedin gradual maneuvers(6 * 0) by two versions of the stick-pusher. The lower curve represents resultsof the present study foran early versionof the stick pusher for whichan operational envelope furnished by the manufacturer(fig. 5) was assumed. Subsequent to the completion of the present investigation,an improved versionof the stick pusherwas developed by Lockheed which reduced the maneuverability loss to that Indicated by upperthe stick-pusher boundaryin figure 17. .. - This improvement WBS effected primarily by the incor rationof 8 eo-called washout circuit which reduces the magnitudeof the cantribution to the stick-pusher activationsignal in gradual maneuvers (see ref.3).

?For the landing-approach conditions(M = 0.23 at. sea level), the stabilizer entry ratewas programmed to providea gradual stall entry rate similar to that used Amesby research pilotsin evaluating low- speed or lg stall characteristics. L NACA RM A57KO7 9

R Probable PilotO-pFnion

U this sectiona qditative assessment is presented of' the effect of a wing modification andof pitch damperson probable over-all pilot opinion of the pitch-up behaviorof two example supersonic airplanes. The prediction is basedon a comparison of the computed angle-of-attack and load-factor overshootsfor these airplanes with the corresponding values from reference1 for six reference airplanesfor which pilot opinion was obtained. The flight conditions selected for the evaluation are 0.85 &ch number at 35, OOO feet for airplane A and 0.&I Mach number at 35,000 feet for airplane B, since theseflight conditions corresponded closely to those for which opinionpilot was provided for thesix reference airplanes(i.e., M = 0.w at 35,000 ft).

It should be pointed out the that procedure outlinedin reference 1 for estimating probable pilotopinion of pitch-up is based onlyon the longitudid dynamic behaviorin the pitch-upregion. The effectsof other modesof motion, such as roll-off, directional divergence,or spin entry, arenot considered. E these other modesof motion are suspected to be importantin a given case, comparisons, such as those presentedin the following sections, should servea preliminary as guide to theprob- able relative severity of pitch-up. Although beyond the of scopethe present study,a supplementary analysis of the fmsortanceof these other modes of motion shouldbe made based on wind-tunnel rollinn and yawlag- moment data at high angles of attack. Reference 4 presents such data for a model. similar 3n configuration to that of airplaneB.

Effect of wing modification.- Figure18 presents a cnmparison of the overshoots at0.65 Mach number andat 35,000 feet for several configurations of airplane A with valuestaken from reference1 for thesix reference airplanes. Theee results Fndicate that.the attitude overshootsfor the basic airplane (fig.18(a)) are as much as 50 percent greater than those for any of the reference airplanes and would probably resultan in over-all pilot opinionof pitch-up (basedon question V of table II) of . unacceptable, particuhrlyif the airplane were precipitatedinto an inadvertent high-speedstall or spin. A description of the pilot rating schedule usedis presented in table III. The effectof the wing leading- edge extension (fig.2) was to reduce the angle-&-attack overshoots to values comparableto those for theF-aF aweat low recovery-control rates and to values between for those the F-84F and F-lm airplanes at the higher recovery-controlrates. Shce there is same efidence presented in reference1 that the pilot formshis opinions on the basis ofan airplane's behavior lowat recovery-control rates, the pilot opinion for this configuration (airplaneA) should be comparable to forthat the elevator-controlled F-84F airplane, particularlyif a,n inadvertent spin entry or other UnsyrOmetrical maneuveris avoided. Although this indicated improvement in pilot opinion from unacceptableto unsatisfactory may not 10 NACA FH ~57~07

be considered si-icant on the example airplane whichhas a severe pitch-up problem, these results should rule not out the useof relatively shple aerodynamic modifications (such as that considered in here) other cases with basically less serious pitch-up problems. For example, flight-test results presentedin reference 5 kdicated that the additian of a wing leading-edge extension eliminated pftch-up entirely over most

of the speed range ofan airplane witha moderately severe pitch-up . .. ". problem.

The resultsin figure 18(b) also indicate that the load-factorover- shoots for both the basicand modified airplaneA are moderateand can- parable to values computedfor the F-100A airplane. This is due prhcipally to the higherwing loading and lowerlut-curve slope in the pitch-up region for ailplaneA.

Effect of linear pitch damper.- Figure18 presents a comparison of the angle-of-attack and Load-factor overshoots,and with without the linear -pitchdamper operating on airphne A, with corresponding values for the six airplanes investigatedfn reference 1. The effect of the linear pitch damperon the pitch-up behavioraf afmplane A was to.reduce the a overshoots about10 to 20 percent (fig. 18(a)). It is apparent that these relativelysmall reductions Fzl avershoot wouldnot be expected to materiallyimprave probable pilotopinion over that for the basic airplane. Despite thelack of effectiveness of the type of pitch damper assumed in the present calculations, it is felt further considerationof some formof pitch damperis warranted, particularlyin view of the more encouraging results obtained with nonlinear the type of pitch damper assumed for airplaneB.

It should be pointed out wWe thatthe linear pitch damperwag relatively ineffectiveon the example airplane whichhas a severe pitch- up problem,a similar approachon airplanes with milder pitch-up tendencies may prove somewhat more effectiveand should be considered as one possible approachto the problem. ETfect of nonlinear pftch damper.- Figure 19 presents a comparison of the angle-of-attackand load-factor overshoots, withand without the " nonlinear-pitch damper for airplane B, with corresponding values for the" six airplanes considered in reference1. In view of the large attitude overshoots and the associated extreme ofangles attack (w> 28.6O) indicated for the basic airplaneB at the lower recovery-control rates, probable pilot opinton shouldrange fram unsatisfactory to unacceptable (see tableIII).

Comparison of the overshootsfor the nonlinear pitch-damperconfigu- ration with those for the basic airplaneB in figure lg(a) indicates that the damper reduces thea overshoots to values comparable to those experienced by theYF-86D airplane. The probable pilot opinion corresponding to these overshootsshould be unsatisfactory but acceptable. It should be mentionedin connection with the interpretation of these results that the peak anglesof attack evgn with the pitch dAmper operating are stillof the orderof 24' to 26 at the lower recovery-control rates (fig. 12) because of the relatively highangles of attack associated with onsetof pitch-up. Poor controlLability in roll and yaw at these high angles of attads may affectopinion pilot adversely andcannot be accounted for by the of type comparison shownin figure 19. For airplanes with somewhat milder pitch-up tendencies than those considered in the present study, this approach should prove effectivein mizingthe pitch-up problemto an acceptable degree.

CONCLUSIONS

An analytical evaluationhas been made of the effectsof a wing 4 modification and of stability augnentationon the pitch-up behavior and 'probable pilot opinionof the pitch-up characteristicsof two fighter airplanes with severe pitch-up tendencies. Pitch-up behaviorwas computed for several flight conditions, while pilotwas opinion estimated for thesetwo airplanes fora Mach numberof about 0.9 at 35,000 feet. The resultsof this analyticalstudy indicated thefollowing:

1. The additionof the wlng leading-edge +ension to airplaneA reduced the peak and overshoot ofangles attack for thelower recovery- control rates about20 to 30 percent atMach nunibers of 0.85 and 1.20. This orderof improvement may be sufficient ta reduce the possibility of iaadverteqt spin entriesat the lower Mach nmiber. At the higherMach number, an increase in the maneuverhg capabflity before onsetof pitch- up of aboutlg with no penalty in increased load factorwas obtained due to a decrease in overshoot load factor.

2. Probable pilotopinion of the pitch-upbehador of -themodified airplane A at a. Mach number of 0.85 at 35,000 feet should be -roved from unacceptable to unsatisfactory - the categoryof the elevator- controlled F-84F and F-86A airplanes. 3. The effectof added pitchdamping, provided bya shple pitch damper wlth constantgain, did not materfally reduce theovershoots on ' airplane A and wdd not be expected to inrprove pilot opinion appreciably.

4. For airplaneB, added pitchdamping, provided bya pitch mer with nonlinear gain, reduced the peakand overshoot valuesof angle of attack significantlyfor all flight conditions considered except the landing approach. 1 5. Probable pilot opinion of the pitch-up behaviorof airplane B with added pitchdamping at a MEtch number of 0.80 at 35,000 feet should be improved from unacceptableor unsatisfactory to unsatisfactory but acceptable - the rating for YE-86Dthe and F-86F airplanes. 6. The effectof the stick .pusherwas to prevent the attainmentof angles of attack at which pitch-upoccurs for airplane B. Re6dtS for two versions of this system indicated that care must be taken to insure that the maneuvering capabilitiesof the &irplane are not compromised.

Ames Aeronautical Laboratory National Advisory Cormnitteefor Aeronautics MofYett Field,Calif., Nov. 7, 1957 NACA RM A57K07

airplane lift caeff icient,L CL -cis c, airplane pitching-moment coefficient about airplane centerof .

wing mean aerodynamic chord, ft

Q acceleration dueto gravity, 32.2 ft/sec2

=Y hP pressure altitude,ft K parameter denoting the ratioof airplaae daurphg to horizontal-tail damping

constants defining operational boundazy for Lockheed stick pusher

2t distance from airplane center of gravity to aerodynamic center of horizontal tail, ft L airplane lift, lb Lt horizontal-tail lift, lb I# maneuvering tail-108~3increment, FI m airplane mass, - slugs g’ pitchlng moment about airplane centerof gravity, ft-lb

airplane normal force, assumed equivalentto

IT n airplane normal load factor, w 14 rr NACA RM A57KO7

Mver increment in n from value at pitching-acceleration threshold to nmax n' airplane normal load factor due toa, assumed equivalentto CL (a)SS W Gver increment Fn n' from dueat pltching-acceleration threshold to & n load-factor rate at entry into pitch-up region, g/sec

V2 Q dynamic pressure,%, lb/sq ft

S differential operator

S wing area, sq ft

St horizontal-tail area, sq ft t time, sec - V airplane velocity, ft/sec W airplane weight, lb a airplane angleof attack, deg or radians increment in a from a* to amax

&n value of a at pitching-acceleration threshold,deg

Y flight-path angle, radians

6, stabilizer aagle, degor radians

&SP stabilizer angle due to pilot stick deflection,deg or radians stabilizer angle due to pitchdamper operation, degor 6SD . .. . . ". . . . mdim6 0 angle of pitch, radians

P mass density of air, slugs/fts NACA RM ~57~07 -

airplane longitudinal short-perioddaqfng ratio

control system time constant, sec

airplane longitudinal short-periodfrequency

curve defining variation of ahplane lift coefficient with a

curve defining Variation of air-plane pitching-mment coefficient with a curve defining varation of stabilizer effectiveness with a

pitch damping derivativedue to pitch damper,

a( - (*I dt

.. d2G e equivalent notation for -at2

Subscripts

th threshold valueat which pilot is first cognizant of pitch-up

rec recovery

over overshoot max maximum. value 16 NACA RM A57K07

APPENDIX B

HORIZONTAL" LaADs 7N PITCH-UP

In a previous sectionof this report the maneuvering tail-load increment ALy- was presented as a function of recov&ry-control rate for emax airplanes A and B. It was noted that this representsonly a portion of the total aerodynamic load on the tail; that is, theload balancing waa not included. In this sectiona more complete analysis whichindudes the balancing tail load is presented for A airplanefor Mach numbers of 0.85 and 1.20 at 35,000 feet.

Figure 20 shows the variation of the total aerodynamicand loadof the maneuveringand balancing componentswith recovery-control rate. Also shown in figure 20 are the valuesof angle of attack at whlch these loads occur. It will be noted that these are loads referred to as "first-peak'' andIf second-peak" loads. The first-peak total loada is negative (down) loadfor stable. %ail-off configurations and occursshortly after the onsetof pitch-up at the time peak the positive pitching acceleration is attained. The second-peak total load may be elther negative or positive and occurs at the time..thepeak negative pitching acceleration is reached during the recovery ofphase the pitch-up maneuver. The maneuvering componentof this load was previously presentedin figures 10 and U. The first-peak total loadsin figures go(&) and 20(c) were determined by addlng the.. maneuvering component,-Iy(O-) &, to thebalanchg component. Values of e- are presented in figure 21 as a function of recovery-control rate, and bahnclng the tall load was determined from the tail-off pitching-moment curvesin figure 22 at the values angleof of attack at which 0- occurred (fig. 20). Iia similar manner, the second-peak total loads in figures 20(b) 20(d) and were determined.

These results inaicate that the first-peak loads are Fn critical supersonic pitch-up maneuvers where the does pilot nut attempt to check the pitch-up; that is, zero recovery controlin ratefigure 20(c). At subsonic speeds, the second-peakloads are genera.lly criticalin a post- tive sense where the pilot attempts tothe pitch-upcheck by applying rapid recovery control (fig.20(b) ) . .. NACA RM A57K07' - CONFIDENTIAL

1. Sadoff, Melvin, Stewart, John D., and Cooper,George E.: Analytical Study of the Comparative Pitch-Up Behavior of Several Airplanes and Correlation With Pilot Opinion. EACA RM A57DO4, 1957. 2. Sadoff, Melvin, Matteson, Frederick H., and EEavill, C. Dewey: A Method for Evaluating the Loa& Aspects of the Pitch-Up Problem. NACA RM A55D06, 1955.

3. Holleman, Euclid C., and Boslaugh, David L. : A Simrl'lRtor Investiga- tion of Factors Affecting the Design and Utilization of a Stick Pusher for the Prevention of Airplane Pitch-Up. NACA RM H57J30, 1957

4 Tiding, Bruce E. : Subsonic AerOayaamic Characteristics Up To Extreme Angles of Attack of Airplane Model Having a Lou-Aspect- Ratio WFng and a High Horizontal Tail. XACA RMA57KO5, 19%. 5. Matteson, Frederick E., and Van Dyke, Rudolph D., Jr.: Flight Investigation of the EXfects of a Partial-Span Lea,ding-EdgeChord Extension on the Aerodynamic Characteristics of a 350 Swept-Wing Fighter Airplane. NclCA R14 A54B26, 19%. 18

'pABI;E 1.- AIRPLKNE CHARACTERISTICS USED IN ANALYSIS (a)Airplane A

Airplane weight, lb ...... Airplane mass , slugs ...... : . . . . : . . . . :. . Airplane pitching momentof inertia, slug-ft2 ...... Wing area, sq ft ...... Wing mean aerodynamic chord,ft ...... Center-of-gravity po6Ltion~percent F ...... -...... Horizontal-tail length, ft ...... Horizon". tail Deflection limits, deg ...... Maximum deflectfon rate, deg/sec ...... Mach number, 0.85 at 35,000 feet . . .. .- Dynamic pressure, lb/sq ft ...... True velocity, ft/sec ...... C% + cm;L (assumed invariant witha),'per radian per sec . . 1*25zt CG, per radian per 8ec .. . . . , ...... I . -v Mach number,1.20 at 35,000 ft Dynamic pressure; lb/sq ft ...... 502 True velocity, ft/sec ...... z,168 + (assumedinvariant with a), per radian per sec . . -0.09

Cq; per radian per sec ...... I . .. Mach number, 0.25 at sea level Dynamic preseure , lb/sq ft ...... 98 True velocity, ft/sec ...... 287 CG + Cm;, (assumed invariant with a), per radian per' sec . . -0.267 1 .25tt per %, per radian sec ...... v %.(a) I1 1 For design combat configuration: Airplane weight,W, lb ...... 15,200 Airplane mass, m, slugs ...... 472 Airplane pitching moment of inertia, Iy, slug-ft2 .. ; ... 56,655 Center-of-gravityposition, percent 'E ...... 7 Horizontal-tail length, Zt, ft ...... 20.4 Mach number, 0.80 at 35,000 ft Dynamic pressure, q, lb/sq ft ...... 222 True velocity, V, ft/sec ...... 778 + % (assumed invariant with a), per radian per sec . -0.081 1 .25zt w, per radian per sec...... V cms p Mach number,0.975 at 35,000 ft Dynamic pressure, 9, lb/sq ft ...... 330 True velocity, V, ft/sec ...... 949 % + % (assumed invariant witha), per radian per sec . . -0.093 1.252~ per radian per sec ...... - .... I w, V %&a) I Min5mum lamling weight configuration: Airplane weight,W, lb ...... l2,360 Airplane mass, m, slugs ...... 384 Mrplane pitching momentof inertia, Iy, slug-ft2 ...... 52,752 Center-of-gravity position, percent'E ...... 20 Horizontal-tail length,2t, ft ...... 19.16 %ch number, 0.23 at sea level Dyaamicpressure, g, lb/sq ft ...... 78 True velocity, TT,ft/sec ...... *. 256 % + '2%(assumed invariant with a), per radian per sec. -0.145 1.25~~ %, per radian per sec...... I v %js(a) I Horizontal tail Deflection limits, deg...... -l7.3,+5 pllaximum deflectionrate, deg/sec ...... 25 wing ma, s, sg ft ...... 196.1 Wing mean aerodynanlc chord,'E, ft ...... 9.9 20 - NACA RM A57K07

~~ 11.- QUESTIONPIAIREFOR PILOT PITCK-UP RATING

I Is pitch-upregion useful at allfor maneuvering? Yes or No. I1 Consider thefollowing situations:

A. If you are tracking a target airplane and enter the pitch-up region, what is your assigned rating of your ability to return to or remain on the correct flight path to continue the tracking?

B. If you have entered the pitch-up region during a gunnery run, what rating would you give the airplane as a gun p1atfoi-m fn the pitch-up region?

C. If rating for A and B is-poor, is reason other than insuffi- cient or inadequate controllability?

D. How would you rate this airplane with regard to the tendency for a pilot to apply rapid and perhaps excessive control during pitch-up recoveries?

I11 Ratethe pitch-up according to abruptness. (What is response quantity whichyou feel is related to the abruptness of pitch-up?)

N Ratethe pitch-up according to overshoot loadfactor. (What is your definition of overshoot load factor?) v What rating do you assign the airplanewith regard to how much pitch-up restricts or limits maneuverability of the airplane? NACA RM A57K07

0 Satisfactory - Satisfiesstability and control requirements. Marginally Satisfactory - Pitch-up barely perceptible. Does 1 appreciablynot r?imlnfsh usefulness of the 2 airplanein performing 8 desired task. Abruptness of airplane response and overshoot in attitude or load factor during pitch-up not much increased mer comparable satisfactoryairplane. Little tendency for the pilot to apply rapid and excessive corrective control. Unsatisfactory but Acceptable - Fit&-up is more apparent. More or less Mfficultyeerienced performing the desired task. Abruptness of airplane 5 motion and overshoot in attitude or load factor during pitch-up considerably increased over that for marginally satisfactory atr- plane. There may be some tendency for the pilot to apply rapld and perhaps excessive corrective control. Unsatisfactory - Pitch-up severe ranging from controllable 6 only ~5ththe greatest difficulty to practi- 7 callyuncontrollable. Abruptness of airplane 8 motions during pitch-up appm- degree where pilot feels he has little or no control over the overshoots in attitude or load factor, Which are relatively large. Increased tendency for the pilot to apply rapid and excessive corrective control.

Unacceptable - Pitch-up so severe that airplane is uncon- 9 trollable. me abruptness of theairplane 10 motions and the magnitude of the overshoots are so extreme, even at high altitude, that the pilot would not consider approaching the pitch-up boundary because of concern for the structural integrity of the airplane. Some possibillty of enterin@;into a spin or other unusual maneuver from which recovery may be difficult or impossible.

L 22

" NACA RM A57K07 23

P67-45' 1

(a) AirplEtne A.

0 0 (b) Airplane B . Figure 1.- Two-view drawings of the two example airplanes. 24 NACA RM A57K07

Basicairplane

Modifiedairplane . .

I t t 1

Main servo

0, = 5 cps 5 = 0.7 critical I

Figure 3.- Block aiagcam of linear pitch aamper. Relaynotation Q Airframe 9 NO - Normally open a* A - Arm 1 J - Normally closed + coil - radians + Coil - NC -5 "NO NO -- sec' --A A Gainschedule NC NC R elay Relay Relay Servo Leth a* 30]20 / 1 I lot 0- 0- .7 .8 .9 1.0 1.1 M

a>a at Assumedservo characteristics : Gain a'" = 5 cps = 0.7 critical C 0

Figure 4. - Block diagram of nonlinear pitch damper.

.a I ......

* I 1

Figure 5.- !Pyplcal.operatioJlal. envelope for etlck pusher.

...... - . . .. -

Relaynotation

NO - Normally open A Arm NC - Normallyclosed

(limits max. recoverycontrol 8,rec to 8, 1 trim + Coil - Recoverycontrol - NO NO L A A -- 1.00 - --NC NC c-

1 Relay . I-" Pilot input K,u + K,B = I where: K, = 0.0714; K2 = 1.79

(u givenin deg , in radians/sec 1

Figure 6.- Block diagram representing stick pusher for analog study.

..:I NACA RM A57K07 -30

-20 Incrementalelevator position, As,, deg -I 0

IO Incremental angle of attack, nu, deg IO

0 4 Incrementalairplane loadfactor, An, g 2

0 Incremental airplane loadfactor due to 2 angle of attack, An', g 0 I

.. 0 Pitching acceleration, 8, radians/sec2 -I

-2

4,000 Maneuvering tai I - load increment,load 0 (ALtB#Ib) -4,OOC Figure 7.- The history of- standard pitch-up evaluation maneuver. 30 - NACA RM A57KO'T 1.6

I. 2

.8 CL .4

-.4

radian

(a) Airplane A; 6, = -4'; M = 0.83; hp = 35,000 .feet.

Figure 8.- Aerodynamic characteristics of ehe-two fighter airplanes obtained from wind-tunnel measurements. 2.0

I .6

Qb,deg

(b) Airplane A; 6, = -4'; M = 1.20; hp = 35,000 feet.

Figure 8.- Continued. 32 r NACA RM A57KO7

I .6

1.2

CL .0

Figure 8.- Continued. L - I .6

1.2

c, .a

-. I Cm -. 2

-.3

-3

-2 Cm per SS radian -I

n -0 4 a 12 16 20 24 28 32 a, deg

(d) Airplane B; 6, = 0'; M = 0.80; hp = 35,000 feet.

Figure 8.- Continued. 34

2.0

1.6

1.2

CL .8

0 NACA RM A57K07 I .6

.4 .I

0 0 Cm -.I

”2

-3

-2

radian -I

0 0 4 8 12 16 20 24 28 32 a, deg

Airplane B; 6, = oo; M =-0.23; hp = 6- ievel. Figure- 8.- Concluded. - NACA RM A57K07

6, radians/ 'sec

AL+i I Ib

-I

Figure 9.- Typical t& htstories of 'computed pitch-upmaneuvers; airplane A. n

.. 8, radiar

A L+*

Figure 9.- Continued. .I 8, radian

Time, sec

.. (c) M = 0.25 at sea level-; init-1 6 sp programmed to provide gradual low-s@ed s-kll entry.

Figure 9.- Concluded...... I . a

4.0 7

3.6 0” Basicairplane Modified oirplane 3.2 Lyl Linear 5;+itch8B 1damper, CyDs 7Cm (a) 2.8 1

“over’

(a) %ver kver Figure 10,-Variation of several response quantities with recovery-control rate; airplane A; M = 0.85; hp = 35,000 feet. .QW ......

(iSp)rec deg/sec

Figure, 10.- Concluded.

.. .. - ...... " ...... "...... ,. , ...... r e ,

Figure ll.- Variation of several response quantities with recovery-control rate; airplane A; hi = 1.20; hp = 35,oOO feet. c P ...... - ...... - ...... - ...... NACA RM A57K07 - 43

5 Time, sec

(a) M = 0.80 at hp = 35,000 feet (fi LII 0.5).

Figure 12.- Ty-pical time histories of cmputed pitch-up maneuvers; airplane B. w ci," 44

Time, sec

(b) M = 0.975 at hp = 35,000 feet (6 * 0.5).

Figure 12.- Continued. 45

8, radians/s

Time, sec

Figure 12.- Concluded...... - . . .. - ......

12 2.4

IO 20

8 1.6

'over I deg 6

4 .8

2 .4

0 IO 20 IO 20 30

Figure 13.- Variation of several response quantities with recovery-control rates; airplane B; PI = 0.80; hp = 35,000 feet.

...... ". . . -1

I I L b

2.0 2 0,oo 0

I.6 16,000

1.2 12,000

I "over I i .8 8,000

.4 4,000 I

n IO 20 30 "0 IO 20

(Ssp) rec ' deg/sec

Figure 13.- Concluded. 5

.. 12 2.4

IO 2.0

8 I.6

1.2 "over 3 g

n- IO 20 30 0 IO 20 30

Figure 14.- Variation with recovery-control rate of several respmse quantities; airplane B; M = 0.975, 4 = 35,000 feet.

I I

...... ! ......

I I. A b

2.0 20,000

I .6 16,000

1.2 12,000

I AL Ib "over 1 g te , mox .8 8,000

.4 4,000

n IO 20 30 "C I IO 20 30

Figure 14.- Conclude&.

...... ". . .

I .8

I .6 I Peak, normal airplane I /I

1.4

1.2

I .o

CL .8

.2 .4 .6 .8 I .o M

Figure 15.- Maximum angles of attack and lift coefficients attajnable for unimpeded etick- pusher operatian and their relationship to pitch-up warning and pitch-up boundaries; hp = 35,000 feet.

I * "

I...... - . . - ...... -...... '' - I * I . . I

0 c-4

2 I

OL 4 " .7 .8 .9 1.0 1.1 .7 .8 .9 I.o M M

Figure 16.- bkxhm load factors and laaaeuverlng tail-laaad increments attainable for unimpeded stick-pusher operation and comparison with results for airplane with and without pitch hp = feet. damper; 35,000 UI P ...... - . . . . , ...... - ......

0 0 .2 .4 .6 .0 I .o 1.2 I .4 I.6 1.8 2.0 M

Figure 17.- Maneuvering capabilities of airplane B; hp = 35,000 feet, NACA RM A57K07 - 53

"0 IO 20 60 70

(8)%ver - Figure 18.- Comparison of the angle-of-attack and load-factor overshoots for airplane A with results for the six .reference airplanes. 54 n NACA RM A57K07

-0 IO 20 30 40 50 60 70 80

(&ip) rec J deg Figure- 18.- Concluded. mACA RM WE07 tv”-L 55

rn Q) u IO L L Q > 0 U 8

0 1 0 IO 20 30 40 50 60 70 80

Figure 19.- Ccrmparipon of the angle-of-attack and load-factor overshoots for airplane B with results for the six reference airplanes. 4 .O .

3.6 Unsatisfactory but

3.2

L Basicairplane 2.8 damper pitch7 Nonlinear

(b) nover

Figure 19. --Concluded. I

30,000 lncremen t

20,000 EI Balancingtail load

0 W 20 U

0 0 IO 20 30 40 30,000 increment I

1 W a :20 ti

0 0 IO 20 30 40

Figure 20.- Concluded.

...... 59

radians/sec2

L IO . 20 30 40 ( Wrec ' deg/sec

Figure 21.- Variation with recovery-control rate of the maximum positive and negative pftching accelerations;- airplane A, hp = 35,000 feet. 60 - NACA RM A57KO7 .2

cm -.I

-. 2

.cl (a) M = 0.85 .2

c, -.I

-2

-. 3

- .4 0 4 8 12 16 20 24 28 32 36 a, deg

(b) M = 1.20

Figure 22.- Wind-tunnel measurements of. the variation of pitching moment with asgle of at;acbj at-f-plane A;

NACA - Langley Fleld, Va E

i .