NACA-RM-L57D18A · INFLUENCE OF AUTOMATIC CONTROL OF ROLL COUPLING AND PITCH-UP ON TAIL LOADS

I RESEARCH MEMORANDUM I

AND PITCH-UP ON TAIL LOADS

I I

I By Ralph W . Stone, Jr . I

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NATIONAL ADVISORY CQMMITTEE

FOR AERONAUTICS

WASHINGTON

NATIONAL ADVISORY C0MMI"EX F O R AERONAUTICS INF-CE OF AUTOMATIC CONTROL OF ROLL COUPLING AND PITCH-UP ON TAIL LOADS By RaJph W . Stone, Jr.

SUMMARY An a n a l y t i c a l study has been made of t h e e f f e c t s of automatic aug- mentation o r controlling systems on t h e t a i l loads experienced i n r o l l i n g maneuvers and i n pitch-up. The r e s u l t s were calculated on an analog com- puter and t h e equations of f i v e degrees of freedom were used f o r t h e r o l l i n g maneuvers and t h r e e degrees of freedom f o r pitch-up. The results of t h i s report are not intended t o be of general application, but rather t o point out some of the problems t h a t may be encountered on any s p e c i f i c design and t o indicate some probable trends.

The r e s u l t s indicate t h a t , f o r t h e r o l l i n g cases calculated, most automatic systems tend t o reduce not only t h e violence of t h e maneuver but a l s o the t a i l load encountered. The results show, however, that, if automatic systems are t o be used, they must be considered i n the i n i t i a l design t o obtain acceptable motions i n r o l l s and t o evaluate properly t h e t a i l loads.

For t h e pitch-up problem, the maximum t a i l loads are predominantly the r e s u l t of control deflection, and systems which e s s e n t i a l l y reduce the input o r pull-up deflections w i l l generally improve t h e acceleration overshoots and reduce t h e horizontal-tail loads. I n general, systems used f o r pitch-up m y be c m p a t i b l e w i t h problems of r o l l coupling. On the other hand, of the systems studied f o r r o l l coupling, only the p i t c h damper would be h e l p f u l f o r pitch-up.

INTRODUCTION i Trends i n performance and design of airplanes have brought about some very serious s t a b i l i t y deficiencies i n recent years. I n problems involving such deficiencies, aerodynamic changes, of course, should first be considered. There is a major trend, however, toward t h e use of auto- matic augmentation systems or controllers i n meeting these deficiencies.

This paper is concerned with t h e e f f e c t s of such systems on t h e aerodynamic loading conditions f o r two of t h e more c r i t i c a l deficiencies, these being divergencies i n r o l l s and pitch-up. The fundamentals of these problems have been discussed i n numerous publications ( r e f s . 1 t o 10 and 1 1 t o 20, respectively). This report, therefore, i s confined primarily t o t h e horizontal- and v e r t i c a l - t a i l loads encountered when autamatic systems are used. The r e s u l t s presented herein are indicative of only some of t h e problems and trends t h a t may be expected and are not necessarily of general application.

SYMBOLS l i f t coefficient CL CD drag coefficient CY side-force coefficient rolling-moment coefficient Cm pitching-moment coefficient Cn yawing-moment coefficient moments of i n e r t i a about the X, Y, and Z body axes, respec- t i v e l y , slug-ft2 product of i n e r t i a (positive when p r i n c i p a l a x i s is inclined below X body axis), slug-ft2 angular momentum of engine r o t a t i n g p a r t s , ft-lb-sec weight, l b m mass, w/g, slws acceleration of gravity, 32.2 f t / s e c w i n g area, sq ft w i n g span, ft

e . e . . e e . . m --

e e . e e e . . e .

e .

e . e .

e e . e e . e .

e . e . e .

NACA RM L57Dl8a e e e . e * e .

-

C mean aerodynamic chord, ft longitudinal distance from center of g r a v i t y t o c/4 of

x~~

horizontal t a i l , f t longitudinal distance from center of g r a v i t y t o E/4 of XVT v e r t i c a l t a i l , f t v e r t i c a l distance from center of g r a v i t y t o E/4 of v e r t i c a l

%

tail, f t air density, slugs/cu f % P velocity, f t / s e c

v

Mach number M pressure a l t i t u d e , f t

kp

a i l e r o n deflection, deg E a s t a b i l i z e r deflection, positive when t r a i l i n g edge i s down, iT deg rudder deflection, p o s i t i v e when t r a i l i n g edge is t o t h e left, 'r deg U angle of a t t a c k , deg angle of s i d e s l i p , deg B E downwash angle, deg r o l l i n g a n g u h r velocity, radians/sec P pitching angular velocity, radians/sec r yawing angular velocity, radians/sec t time, sec h o r i z o n t a l - t a i l load, lb LHT v e r t i c a l - t a i l load, l b

Lvr

normal acceleration, g u n i t s nZ 0 . 0.. 0 0.. . 0 . 0 . . . 0 ... 0 .

NACA m ~ 5 7 ~ 1 8 a

nY lateral acceleration, g units

5 damping r a t i o

- d ! l

rate of change of damping r a t i o with angle of a t t a c k da A increment C L = ac, * m

c% = aa

'cm

c - &Y

c, = -

YP - q r

qg

Subscripts: 0 i n i t i a l value maX IIBXimUm HT horizontal t a i l V T v e r t i c a l t a i l Dot over a symbol indicates a first derivative with respect t o t i m e , .. e . . ...............

. . . . . . . . . . . . . . . .

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. e . . . . .

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MElRODS The results discussed herein are based primarily on calculations Table I f o r hypothetical airplanes t y p i c a l of contemporary f i g h t e r s .

lists t h e c h a r a c t e r i s t i c s of t h e airplane used f o r t h e r o l l cases.

I n Table 1 1 lists those of t h e airplane used f o r t h e pitch-up cases.

t h e calculations, f i v e degrees of freedam w e r e used f o r t h e r o l l cases and three degrees of freedom f o r t h e pitch-up cases. The equations f o r f i v e degrees and three degrees of freedom appear i n many references, f o r example, references 1 1 and 21, respectively. I n t h e three-degree-of- freedom calculations, however, CL, CD, and were introduced as functions of angle of a t t a c k and Mach number, these functions being non- l i n e a r with angle of attack. For sane r o l l i n g maneuvers, calculations w e r e made of t h e loads from motions obtained i n a c t u a l f l i g h t s . The equations used f o r calculating t h e horizontal- and v e r t i c a l - t a i l loads are : and

pv*s

yB,vT (B - r + P) + cys,,4.]

L v T = 2

DISCUSSION Roll Coupling Divergences i n r o l l s are caused generally by r o l l i n g t o o rapidly that exists (ref . 1) .

f o r t h e d i r e c t i o n a l s t a b i l i t y Thus, r o l l i n g veloc- i t y and v e r t i c a l - t a i l s i z e are dminant factors i n r o l l i n g divergences.

The e f f e c t s of these f a c t o r s are shown i n figure 1.

Here, t h e maximum maneuvering h o r i z o n t a l - t a i l loads and the maximum v e r t i c a l - t a i l loads encountered i n r o l l s at d i f f e r e n t r o l l i n g v e l o c i t i e s are p l o t t e d against t h e average r o l l i n g velocity of each maneuver.

R e s u l t s are shown f o r an o r i g i n a l t a i l s i z e and f o r a t a i l s i z e optirmrm f o r r o l l coupling. Also shown i s t h e c r i t i c a l r o l l i n g velocity, ‘which, as defined by P h i l l i p s i n reference 1, is that r o l l i n g frequency which equals t h e lower of t h e pitching or yawing ( i n t h i s case t h e yawing) n a t u r a l f re quency .

a. . a * a . a * a a. a. a a a a * * .a a . a . a . a a m . * * a * * a a . * * a a * . a a a . a a a * . - - - NACA RM L57D18a The results show a very l a r g e increase i n t h e t a i l loads encountered as the r o l l i n g v e l o c i t y approaches c r i t i c a l and t h e n a drop-off i n t h e loads beyond t h i s value. Limiting t h e r o l l i n g v e l o c i t y t o some value l e s s than c r i t i c a l would c l e a r l y solve the problem. How fast an a i r p l a n e must roll, however, i s a controversial subject and i s not one f o r present discussion. It i s sufficient t o say h e r e i n only t h a t p i l o t s generally i n s i s t and (because of t h i s i n s i s t e n c e ) t h e services require t h a t air- planes roll a t v e l o c i t i e s l a r g e r t h a n c r i t i c a l f o r many current and planned configurations.

Changing t h e t a i l s i z e i s t h e second d i r e c t approach t o t h e problem.

There i s , however, an optimum t a i l size; smaller or l a r g e r tails l e a d t o more violent motions and l a r g e r loads.

For t h e case i n (See r e f . 3 . ) t h i s paper t h e optimum t a i l i s somewhat l a r g e r than t h e o r i g i n a l t a i l .

The optimumtail s i z e i s t h a t f o r which t h e pitching and yawing natural frequencies a r e about t h e same f o r the present case.

For t h i s s i t u a t i o n no roll divergence, as such, i s possible. A resonance condition exists, how- ever, when the r o l l i n g frequency i s about equal t o t h e n a t u r a l frequencies i n pitch and yaw, and t h e loads increase near this r o l l i n g v e l o c i t y w i t h the optimum tail; thus, r e l a t i v e l y l a r g e loads a l s o exist and the motions s t i l l may be r a t h e r violent.

Because of t h e wide v a r i e t y of f l i g h t conditions, speeds, and a l t i - tudes now possible, a solution such as an optimum t a i l s i z e may not be s u f f i c i e n t o r f e a s i b l e f o r any s p e c i f i c design. (This i s true f o r nor- m a l s t a b i l i t y as w e l l as f o r r o l l i n g divergencies.) Thus, t h e t r e n d towards t h e extensive use of automatic systems p r e v a i l s . For t h e problem of roll coupling, several systems are possible. This report t r e a t s b r i e f l y f i v e types of systems which are shown i n t a b l e 111.

The first system i s a perfect c o n t r o l l e r which maintains zero side- s l i p and zero changes i n angle of a t t a c k ( r e f . 1 0 ) . This i s a r a t h e r complex system requiring t h e sensing of a t t i t u d e angles. The next system i s a more p r a c t i c a l representation of t h i s system (ref. 10). The t h i r d system is called a coupling-moment canceler (ref. 5 ) . This canceler i n e f f e c t balances o r cancels t h e i n e r t i a coupling p a r t s of t h e p i t c h i n g and yawing moments, which, as indicated i n reference 5 , are t h e primary The last two systems are dampers, a p i t c h cause f o r r o l l i n g divergences.

damper and a yaw damper.

The choice of systems presented does not imply t h a t they are t h e most promising controlling or augmentation systems but is intended only t o show the influence of some t y p i c a l systems on t h e loads encountered.

For t h e calculations shoxi, t h e automatic systems are assumed t o have no l a g s and all proper gains. For any specific design t h e influence of these f a c t o r s must, of course, be obtained.

Some t y p i c a l r e s u l t s of two of these systems (the p i t c h damper and the p e r f e c t c o n t r o l l e r ) are shown. I n many investigations of r o l l cou- pling, t h e predominant influence of pitching v e l o c i t y has been evident (refs. 1, 3, 4, and 9, f o r example) and the p i t c h damper has been indi- cated as a simple and d i r e c t way t o influence t h e motions encountered.

Figure 2 shows the e f f e c t of a p i t c h damper on the t a i l loads. Here a r e p l o t t e d t h e maximum maneuvering h o r i z o n t a l - t a i l loads and the maximum v e r t i c a l - t a i l loads encountered as functions of average r o l l i n g v e l o c i t y with and without the p i t c h damper operating. The damping r a t i o of t h e a i r p l a n e with the damper operating was 0.5, and t h e maximum s t a b i l i z e r d e f l e c t i o n allowed f o r t h e damper (the control a u t h o r i t y ) was 1.8O.

These r e s u l t s were obtained from flight t e s t s of a contemporary fighter which except f o r a l a r g e r v e r t i c a l t a i l i s similar t o t h e hypothetical a i r p l a n e used i n t h e other r o l l i n g calculations. As noted before, t h e s e a r e not measured loads but they have been calculated from motions encoun- tered i n a c t u a l r o l l s and aerodynamic loading c o e f f i c i e n t s measured during other flights.

A considerable improvement i n t h e loads encountered w i t h t h e damper operating is shown. Rolling v e l o c i t i e s much i n excess of c r i t i c a l w e r e rates with the dam- not obtained, however, and t h e e f f e c t s of l a r g e r r o l l per operating have not been established i n flight. Some calculations of t h i s nature have been made, however, and a summazy of such r e s u l t s i n comparison with t h e r e s u l t s f o r other automatic systems are discussed i n t h i s section.

The p i t c h damper is more e f f e c t i v e i n reducing t h e v e r t i c a l - t a i l loads than the h o r i z o n t a l - t a i l loads; t h i s i n d i c a t e s t h e dominant i n f l u - ence of pitching v e l o c i t y through i n e r t i a coupling. The results shown here f o r t h e p i t c h damper are t y p i c a l of those obtained f o r most of t h e other systems except, of course, t h e magnitude of reductions varies f o r each system. These differences are discussed subsequently.

Some results f o r the most complex of t h e various systems i n t a b l e 111, t h e p e r f e c t c o n t r o l l e r , Ere show? i n Pigum 3 . For t h i s c o n t r o l l e r no v a r i a t i o n s i n normal acceleration o r l a t e r a l a c c e l e r a t i o n exist. P l o t t e d are t h e maximum maneuvering horizontal-tail load and t h e v e r t i c a l - t a i l load as functions of average r o l l i n g velocity. The controlled and uncon- t r o l l e d cases are compared and t h e r e s u l t s are shown f o r two i n i t i a l nor- m a l accelerations, 1 g and 2g f l i g h t s .

These r e s u l t s show that t h e controller not only eliminates t h e vio- lence of t h e maneuver but reduces t h e t a i l loads encountered, except at the controller tends t o cause t h e t h e l a r g e s t r o l l i n g v e l o c i t i e s when h o r i z o n t a l - t a i l loads t o be l a r g e r than are otherwise encountered. The uncontrolled loads occur primarily from angle of a t t a c k and s i d e s l i p , whereas t h e controlled loads occur primarily from c o n t r o l deflections.

These control deflections (ref. 10) are a d i r e c t function of t h e r o l l i n g velocity, its square, and i t s derivative; therefore, increasing r o l l i n g velocity requires l a r g e r deflections and, as a consequence, l a r g e r t a i l loads. For t h e uncontrolled case t h e loads drop off beyond t h e c r i t i c a l r o l l i n g velocity i n t h a t t h e motions eventually become s t a b l e again ( r e f . 1). Thus, loads with t h e controller tend t o become l a r g e r than those without a t r o l l i n g v e l o c i t i e s beyond c r i t i c a l .

Another pertinent point regarding t h e perfect c o n t r o l l e r i s shown i n figure 3 , t h a t is, t h e increase i n loads both with and without t h e con- t r o l l e r a t t h e higher i n i t i a l acceleration. The loads are, thus, a func- t i o n of t h e i n i t i a l angle of attack, and even l a r g e r i n i t i a l accelera- t i o n s w i l l lead t o l a r g e r loads.

Before t h e r e s u l t s of a l l t h e calculations a r e summarized, a point of significant i n t e r e s t which e x i s t s , p a r t i c u l a r l y with t h e perfect con- t r o l l e r , merits some a t t e n t i o n here. Because t h e automatic systems (par- t i c u l a r l y t h e perfect c o n t r o l l e r ) reduce t h e excursions i n angle of a t t a c k and s i d e s l i p , the airplane with the systems operating tends t o r o l l faster at any aileron deflection than without t h e system operating. I n f i g u r e 4 a r e shown the maximum maneuvering h o r i z o n t a l - t a i l loads p l o t t e d against average r o l l i n g velocity and a i l e r o n input f o r 2g f l i g h t with and without the perfect controller operating.

For l g f l i g h t (not shown here) the loads are smaller with the con- t r o l l e r operating than without a t any a i l e r o n deflection as w e l l as any r o l l i n g v e l o c i t y except f o r t h e l a r g e s t r o l l i n g v e l o c i t y as shown i n figure 3. For 2g f l i g h t , however, t h e loads, although smaller at a given rolling velocity with the controller, a r e always l a r g e r f o r any given p i l o t o r aileron input. Thus, t h e r e i s a tendency i n rolls from g r e a t e r t h a n l g f l i g h t f o r t h e h o r i z o n t a l - t a i l loads with t h i s type of c o n t r o l l e r t o be l a r g e r than without the controller f o r any amount of applied aileron.

I n figure 5 i s shown a summary of t h e maximum maneuvering horizontal- t a i l loads and t h e maximum v e r t i c a l - t a i l loads calculated i n 360' rolls at a l l average r o l l i n g v e l o c i t i e s up t o about 2.2 radians per second.

Each bar represents t h e magnitude of t h e maximum load f o r each of several conditions: The o r i g i n a l t a i l The optimum-sized t a i l The perfect controller ( A )

The coupling-moment canceler (c)

The p i t c h damper (0.7 c r i t i c a l l y damped) ( D ) The yaw damper (1.246 c r i t i c a l l y damped) (E).

The p r a c t i c a l controller i s omitted here because it resulted i n loads and motions quite similar t o those of t h e perfect controller.

0. 0.0 0 0 0 0 . 0 . 0 0.0 0 0 0 . 0 .

0 0 . 0 . 0 .

0 0 0 0 .

0 0 0 0 0 0 0 0 . 0 .

NACA RM ~ 5 7 ~ 1 8 a 0 . 0 0 0 0 0 0 0 .

For 1 g flight, these r e s u l t s show t h e l e a s t h o r i z o n t a l - t a i l load f o r t h e coupling-moment canceler; t h e p i t c h damper shows similar r e s u l t s .

The yaw damper showed l i t t l e improvement over t h e o r i g i n a l unaugmented case. For t h e v e r t i c a l tail, t h e p e r f e c t c o n t r o l l e r has t h e least load w i t h reductions shown f o r the coupling-moment canceler and t h e p i t c h dam- per, but again l i t t l e improvement is shown f o r t h e y a w damper.

The opti- mum t a i l shows the improvements previously discussed ( f i g . 1).

For 2g f l i g h t , t h e h o r i z o n t a l - t a i l l o a d f o r t h e p e r f e c t c o n t r o l l e r has t h e increase i n load t h a t w a s discussed previously ( f i g . 4). Sizable reductions i n t a i l load with t h e coupling-mament canceler and the p i t c h damper e x i s t , however.

For t h e v e r t i c a l - t a i l load, t h e l e a s t load i s encountered with t h e p e r f e c t c o n t r o l l e r as f o r t h e l g case, only f a i r reductions i n loads are obtained w i t h t h e coupling-moment canceler, and a somewhat l a r g e r reduc- t i o n w i t h the p i t c h damper. N o data are available f o r t h e optimum t a i l and t h e yaw damper f o r t h i s flight condition.

It is c l e a r , however, t h a t f o r a l l systems t h e loads increase mark- edly with t h e i n i t i a l normal acceleration of the f l i g h t .

The t a i l loads without an automatic system a r e , of course, caused primarily by t h e angles of a t t a c k and sideslip. With an automatic sys- tem, however, t h e loads a r e caused by t h e s t a b i l i z e r and rudder deflec- t i o n s as well. The amount of control deflection required by any system i s therefore of extreme significance.

Figure 6 shows t h e maximum control deflections required f o r each of t h e various systems. Each bar represents the magnitude of t h e maximum d e f l e c t i o n required i n r o l l s of various average r o l l i n g v e l o c i t i e s up t o about 2.2 radians per second. The b a s i c airplanes with t h e o r i g i n a l and optimum tails of course use no controls as noted by t h e zeros. N o data a r e a v a i l a b l e f o r the optimum t a i l or t h e y a w damper i n 2g f l i g h t . The deflections used i n 2g f l i g h t a r e appreciably l a r g e r than those used i n l g f l i g h t . The l a r g e s t s t a b i l i z e r deflection is used by t h e p e r f e c t con- t r o l l e r and t h e l e a s t , by t h e p i t c h w e r . The l a r g e s t rudder d e f l e c t i o n i s used by the coupling-moment canceler and t h e least, by t h e yaw damper.

S t a b i l i z e r deflections of t h e order of 1l0, used by the p e r f e c t con- t r o l l e r , may be a l a r g e r portion of t h e t o t a l a v a i l a b l e d e f l e c t i o n than it i s desirable t o use. The rudder deflections used by t h e p e r f e c t control- l e r and t h e coupling-moment canceler are extremely excessive and c e r t a i n l y could not be used. They a r e l a r g e r than the t o t a l a v a i l a b l e d e f l e c t i o n of 40'. For s p e c i f i c cases, therefore, t h e e f f e c t s of l i m i t i n g t h e amount of c o n t r o l d e f l e c t i o n used must c e r t a i n l y be investigated.

It is not s u f f i c i e n t t o evaluate an automatic system on the basis of t h e t a i l loads encountered o r t h e c o n t r o l deflections required alone because, except f o r t h e perfect c o n t r o l l e r , v a r i a t i o n s i n the n o m 1 and lateral accelerations a l s o e x i s t . With some automatic systems operating, these accelerations s t i l l may be i n t o l e r a b l e t o t h e p i l o t .

I n figure 7 are shown t h e maximum normal and l a t e r a l accelerations calculated i n 360° rolls a t a l l average r o l l i n g v e l o c i t i e s up t o about Each bar represents the magnitude of t h e maxi- 2.2 radians per second.

mum accelerations calculated f o r each of the various systems previously discussed. The accelerations shown occurred during r o l l i n g maneuvers which w e r e i n i t i a t e d from 1 g and 2g f l i g h t .

The r e s u l t s ( f o r both 1 g and 2g flight) show t h a t t h e v a r i a t i o n s i n normal acceleration below the i n i t i a l values o f l g or 2g are only s l i g h t l y improved by any of the systems except, of course, the p e r f e c t c o n t r o l l e r f o r which no changes occur. Negative accelerations are experienced f o r a l l other systems. The p o s i t i v e v a r i a t i o n s i n normal a c c e l e r a t i o n are, however, appreciably reduced by a l l systems but the y a w damper. For the l a t e r a l accelerations, improvement i s obtained by a l l systems, although

accelerations of 5 g f o r 1 g flight and l g f o r 2g flight s t i l l are

experienced.

There is a s i z a b l e increase i n t h e accelerations encountered i n rolls from 2g flight over those from 1 g f l i g h t .

It appears t h a t , i n coping w i t h t h e roll-coupling problem, a con- siderable compromise must be made between the motions o r accelerations t h a t t h e p i l o t must t o l e r a t e , the t a i l - l o a d s encountered, and the con- t r o l deflections required by a system.

Pitch-Up The other dominant s t a b i l i t y deficiency i s the problem of pitch-up.

Pitch-up occurs, of cowse, from n o n l i n e a r i t i e s i n the pitching-moment c h a r a c t e r i s t i c s of an airplane.

The pitching-moment c h a r a c t e r i s t i c s f o r t h e hypothetical airplane used f o r t h e calculations of t h i s paper are t y p i c a l of those of airplanes w i t h swept wings and high h o r i z o n t a l t a i l s having moderate n o n l i n e a r i t i e s w i t h angle of a t t a c k and are shown i n figure 8. The calculations were made from a Mach number of 1, and changes i n aerodynamic-center p o s i t i o n ( f i g . 8) with Mach number as w e l l as pitching-moment n o n l i n e a r i t i e s w i t h angle of a t t a c k influence the results.

It i s important t o r e a l i z e t h a t t h e dangers from pitch-up are not only those occurring i n t h e p i t c h plane, but a l s o those which may occur

-

NACA RM L 5 7 D l h i n t h e l a t e r a l modes of motion when t h e large angles of a t t a c k r e s u l t i n g from pitch-up may cause i n s t a b i l i t i e s i n sideslip, violent wing dropping, and spinning. Aerodynamic cures are most desirable, of course, but if not possible, automatic augmentation of some s o r t appears necessary. For t h e cases shown herein, t h e nonlinearities occur i n the range of angles of a t t a c k and normal acceleration f o r which it is desirable t o operate the airplane. Thus, automatic systems which abort a maneuver r a t h e r than allow it t o progress reasonably are not desirable.

For t h e r e s u l t s presented herein, only two automatic systems are These systems are shown i n the following table: t r e a t e d .

SENSING DESCRIPTION SYSTEM REQUIRED 5 =DAMPING RATIO 4 AND Q.

VARABLE- PITCH DAMPER OR nz

[ILL

U The first system i s a r a t h e r complex p i t c h damper, a variable p i t c h damper. It i s representative, however, of systems which do not abort maneuvers. The variable damping system i s one which becomes operative beyond some predetermined angle of a t t a c k so t h a t the motion is not slug- gish i n t h e normal operating range of angles of attack, but a l s o s o that t h e damping increases rapidly as t h e angle of a t t a c k of pitch-up is approached, as shown by t h e s m a l l sketch of t h e v a r i a t i o n i n damping r a t io.

The second system i s a s t i c k pusher which does abort the maneuver.

The pusher used, however, i s one which senses only angle of a t t a c k or normal acceleration and becomes operative o n l y after t h e desired normal acceleration i s reached. For the r e s u l t s considered herein t h e pusher returned t h e s t a b i l i z e r only t o the original trim position as shown by the small sketch.

I n figure 9 are shown the r e s u l t s f o r t h e variable p i t c h damper. The maximum normal acceleration, the maximum h o r i z o n t a l - t a i l load (which is negative and increases i n magnitude downward on t h e figure), and the maxi- mum s t a b i l i z e r deflection required are shown as functions of rate of damping r a t i o with angle of attack. For these cases, t h e aug- change of menter became a c t i v e when t h e angle of attack exceeded the i n i t i a l trim ............... .......

. . . . . . . . . . . . . . . .

. . . . . . .

NACA RM L57Dl8a 12 ..........

angle of a t t a c k f o r l g . Also shown are t h e values of t h e loads f o r t h e airplane with a l i n e a r pitching-moment curve. The results show an appre- ciable reduction i n t h e normal-acceleration overshoot (accelerations greater than 4g) with increasing rate of change of damping r a t i o , the large values leading t o less acceleration overshoot t h a n even t h e l i n e a r case, The t a i l loads are s i m i l a r l y reduced i n magnitude and again, a t t h e l a r g e r damping r a t i o s , smaller loads are obtained than for t h e l i n e a r case. Rather s i z a b l e s t a b i l i z e r deflections a r e required by t h i s system; however, values of as much as 5 ' are required and t h i s i s somewhat g r e a t e r This may be considered an than that used by a moderate a u t h o r i t y system.

excessive mount of control.

Some results for t h e s t i c k pusher are shown i n figure 10. Here are shown t h e maximum normal acceleration and t h e m a x i m u m h o r i z o n t a l - t a i l load as f'unctions of push rate, t h a t is, t h e rate of change of s t a b i l i z e r deflection with time. The results are shown f o r three d i f f e r e n t s t a b i l i z e r input rates, or rates of pull-up. The results show l i t t l e improvement f o r a s t i c k pusher of t h i s type. The normal a c c e l e r a t i o n overshoot i s reduced only s l i g h t l y and t h e t a i l loads are e s s e n t i a l l y unchanged. Both the loads and accelerations a r e appreciably l a r g e r than t h e values f o r t h e l i n e a r pitching-moment case.

It appears t h a t a pusher of t h i s type, which allows t h e maneuver t o reach i t s desired acceleration before operating, not only a b o r t s t h e maneuver but does l i t t l e good f o r t h e maximum loads encountered. A pusher which operates e a r l i e r would, of course, produce less loads but would a l s o stop t h e maneuver much sooner.

A pusher with a n t i c i p a t i o n based on pitching v e l o c i t y or acceleration i n conjunction with a p i t c h damper undoubtedly would prove u s e f u l on a l l counts.

Compatibility of Systems f o r Rolling Maneuvers and Pitch-Up Inasmuch as airplanes may be a f f l i c t e d by both pitch-up and r o l l i n g divergences, t h e compatibility of an automatic system f o r one deficiency with the needs of t h e other deficiency i s important. Because of t h e nature of pitch-up, a l l systems, used as a cure, require nose-down pitching moments. I n addition, a l l roll-coupling systems require nose- down pitching moments at t h e onset of t h e r o l l i n g motion, primarily because of t h e i n i t i a l p o s i t i v e pitching v e l o c i t y t h a t exists. A s a a l l systems but t h e p i t c h damper require only nose-down matter of f a c t , moments. Thus, systems f o r pitch-up would generally not have detrimental e f f e c t s i n rolls and may be helpful. Systems used f o r roll-coupling which require a sensing of r o l l i n g v e l o c i t y would not operate i n a pitching maneuver and thus would have no e f f e c t on pitch-up.

It m u s t be pointed out t h a t i n r o l l i n g maneuvers f o r which t h e p r i n - c i p a l a x i s i s below t h e f l i g h t path, i n f r o n t of t h e center of gravity, i n i t i a l negative pitching v e l o c i t i e s are developed r a t h e r than p o s i t i v e

- 0 0.. . . 0 0 . 0. 0.01 0 a 0 0 om

0 . 0 0 . 0 0 . 0 a 0 0 0 0 e .

NACA RM ~ 3 7 ~ 1 8 a values which occur f o r t h e cases discussed herein. Thus, f o r such cases nose-up r a t h e r than nose-down pitching moments would be required by an automatic system at t h e onset of a r o l l . An automatic system f o r pitch-up such as a pusher might t h u s be detrimental, whereas a pitch-damper would s t i l l be e f f e c t i v e f o r r o l l i n g maneuvers.

CONCLUDING RESIARKS I n summary, a cursory study has beenmade of t h e e f f e c t s of auto- matic augmentation and controlling systems on t h e t a i l loads and accel- e r a t i o n s i n r o l l s and pitch-up. The r e s u l t s of t h i s study are not neces- s a r i l y of general application but primarily show some of t h e problems and trends that may be expected.

Calculations similar t o those presented herein must, of course, be made f o r any specific design.

The results f o r r o l l s i n d i c a t e t h e existence of an o p t i m u m t a i l s i z e from the standpoint of t h e loads encountered, t h i s s i z e being most n a t u r a l l y t h a t which i s least l i k e l y t o cause divergences. Automatic systems ranging from a simple p i t c h damper t o a p e r f e c t c o n t r o l l e r show reductions i n t h e violence of t h e motions and, i n general, a reduction i n t h e t a i l loads. A t average r o l l i n g v e l o c i t i e s somewhat l a r g e r than c r i t i c a l , t h e h o r i z o n t a l - t a i l loads obtained w i t h c o n t r o l l e r s which sense r o l l i n g v e l o c i t y may be l a r g e r than are obtained w i t h no c o n t r o l l e r . In any event, i f automatic systems are t o be used, they must be considered i n t h e i n i t i a l design t o obtain acceptable motions i n r o l l s and t o evaluate properly t h e loads encountered.

E For the pitch-up problem t h e maximum t a i l loads a r e primarily t h e r e s u l t of c o n t r o l deflection and thus systems which e s s e n t i a l l y reduce the input o r pull-up deflections w i l l generally improve t h e acceleration overshoots and reduce t h e h o r i z o n t a l - t a i l loads encountered.

F i n a l l y , i n general, systems used f o r pitch-up may be c m p a t i b l e w i t h the problems of r o l l coupling and generally should not be detrimental.

On t h e other hand, of t h e systems studied f o r r o l l coupling, o n l y t h e p i t c h damper would be h e l p f u l f o r pitch-up.

Langley Aeronautical Laboratory, National Advisory Committee f o r Aeronautics, Langley Field, Va., March 3 , 1957.

1 4 NACA RM L57Dl8a REFERENCES 1. P h i l l i p s , W i l l i a m H.: Effect of Steady Rolling on Longitudinal and Directional S t a b i l i t y . NACA TN 1627, 1948.

2. White, R . J., Uddenberg, R . C . , Murray, D., and Graham, F. D.: The Dynamic S t a b i l i t y and Control Equations of a Pivoted-Wing Supersonic P i l o t l e s s A i r c r a f t , With Domwash, Wake and Interference E f f e c t s Included. Doc. No. D-8510, Boeing A i r c r a f t Co., Jan. 9, 1948.

3 . Weil, Joseph, and Day, Richard E.: An Analog Study of t h e Relative Importance of Various Factors Affecting Roll Coupling. NACA RM ~ 5 6 ~ 0 6 , 1956.

4. Gates, Ordway B., Jr., Weil, Joseph, and Woodling, C . H.: Effect of Automatic S t a b i l i z a t i o n on t h e S i d e s l i p and Angle-of-Attack D i s - turbances i n Rolling Maneuvers. NACA R M L55E25b, 1955.

5 . P h i l l i p s , W i l l i a m H.: Analysis of an Automatic Control To Prevent Rolling Divergence. NACA RM L56A04, 1936.

6. Gates, Ordway B., Jr., and Woodling, C . H.: A Theoretical Analysis of t h e Effect of Engine Angular Momentum on Longitudinal and Directional S t a b i l i t y i n Steady Rolling Maneuvers. NACA RM L55GO5, 7. Finch, Thomas W., Peele, James R., and Day, Richard E.: F l i g h t Inves- t i g a t i o n of t h e Effect of Vertical-Tail Size on t h e Rolling Behavior of a Swept-Wing Airplane Having Lateral-Longitudinal Coupling. NACA RM H55L28a, 1956.

F l i g h t Experience With a 8. Sisk, Thomas R., and Andrews, W i l l i a m H.: Delta-Wing Airplane Having Violent Lateral-Longitudinal Coupling i n Aileron Rolls. NACA R M H55H03, 1955.

Some Notes on t h e Violent Lateral-Longitudinal 9. Stone, Ralph W., Jr.: Coupling Motions of t h e Douglas X-3 Airplane i n Aileron Rolls. NACA RM ~ 5 6 ~ 1 5 , 1956.

Theoretical Investigation of t h e Effect of Rudder 10. Woodling, C . H.: and S t a b i l i z e r Deflections on t h e Angles of Attack and S i d e s l i p i n Rapid Rolls. NACA RM L57A30a, 1957.

Effect of Sweepback and 11. Shortal, Joseph A., and Maggin, Bernard: Aspect Ratio on Longitudinal S t a b i l i t y Characteristics of Wings a t NACA TN 1093, 1946.

Low Speeds.

NACA FQ4 L57D188.

12. Donlan, Charles J., and W e l l , Joseph: Characteristics of Swept Wings a t High Speeds. NACA RM L52Al5, 1952.

13. Weil, Joseph, and Gray, W. H.: Recent Design Studies Directed Toward Elimination of Pitch-Up. NACA RM L>3123c, 1933.

14. Toll, Thomas A.: Longitudinal Characteristics of Wings. NACA RM L5312lb, 1933.

15. Polhamus, Edward C., and Hallissy, Joseph M., Jr.: Effect of Airplane Configuration on S t a t i c S t a b i l i t y a t Subsonic and Transonic Speeds.

NACA RM L56AO93, 1936.

16. Curfman, Howard J., Jr.: Theoretical and Analog Studies of the Effects of Nonlinear S t a b i l i t y Derivatives on t h e Longitudinal Motions of an Aircraft i n Response t o Step Control Deflections and t o t h e Influence of Proportional Automatic Control. NACA Rep. 1241, 1955. (Supersedes NACA RM L5OU-l.)

17. Oswald, Telford W.: The Effect of Nonlinear Aerodynamic Character-

i s t i c s on t h e Dynamic Response t o a Sudden Change i n Angle of Attack.

Jour. Aero. Sci., vol. 19, no. 5, May 1952, pp. 302-316.

18. B i e l a t , Ralph P., and Campbell, George S.: A Transonic Wind-Tunnel Investigation of t h e Longitudinal S t a b i l i t y and Control Character- i s t i c s of a 0.09-Scale Model of the B e l l X-5 Research Airplane and Comparison With Flight. NACA RM L 5 3 ~ 1 8 , 1953.

19. Campbell, George S., and Weil, Joseph: The Interpretation of Non- l i n e a r Pitching Moments i n Relation t o the Pitch-Up Problem. NACA RM ~33102, 1953.

20. Sadoff, Melvin, Matteson, Frederick H., and Havill, C. Dewey: A Method f o r Evaluating t h e Loads and Controllability Aspects of t h e Pitch-Up Problem. NACA RM A55D06, 1955.

21. Bihrle, W i l l i a m , Jr., and Stone, RalphW., Jr.: Analytical Studies of the Response t o Longitudinal Control of Three A i r p l a n e Configu- r a t i o n s i n Landing Approaches. NACA RM L53B10, 1953.

-

NACA RM L57Dl8a.

1 6 TABLE I M A S S CHARACTERISTICS. STABILITY DERIVVATIVET. AND 0 - FACTORS USED I N TRE C A X I J I N I O N S O F ROLLING MANBJWS C A l l coefficients and d e r i v a t i v e s a r e based on w i n g area] I X ’ S l u g - f t 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 0 . 976 3. Slug.ft2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5 7 . 100 I Z ’ s l u g - f t 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 4 . 975 Ixz’slug-ft2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

q . lb/sq ft . . . 197 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

s. sq f t . . . . 376

b. ft . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56.6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.32 E . f t . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

W. . . . . . . . 2 3 . 900

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

m . slugs . . . . 742 v. f t f s e c . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

hp. ft . . . . . 3 2 . OOo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

p. S l u g S f C U f t . 0.000826

M . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0.7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

17. 554 IXe0e. ft-lb-sec . . . p e r r a d i a n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -0.0528 ‘a C 1 . p e r r a d i a n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

-0.255 P CZr. per radian . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0.042 CmiT. per r a d i a n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -1.0 Cmq. p e r r a d ian . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

-3.5 C . . p e r r a d i an . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -1.5 C . . p e r r a d i an . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

-0.36 C , p e r r a d i a n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

nga C . p e r r a d i a n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

-0.03 % Cnr. p e r r a d ian . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

-0 0g5 C . . p e r r a d ian . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

CUB. per radian (original t a i l ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

0.057 c . per radian (opt- t a i l ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0.114 “B Cyg. p e r r a d i an . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -0.50 CL,’ per radian . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3.85 Ch.HT. p e r radian . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

0 755 d.5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0.43 da per radian . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -0.23 Cy6r.vT. p e r radian . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0.074 C l g ( a ) . per radian (shown in following p l o t ) : 1 ... ._ .

-0.5 o / oo 6 ’ 12’ mo a ...

.

~ ....... ...............

. . . . . . . . . . . . . . . .

. . . - ..... .............. ::. ..

... e .

TABLE: I1 M A S S CHARACTERISTICS, STABIIJTY DERIVATIVES, AND OTHER FACTORS USED IN TEE CALcuLclTIONs O F PITCH-UP

5, slug-ft 2

. . . . . . . . . . . . . . . . . . . . . . . .

f t . . . . . . . . . . . . . . . . . . . . . .

1 , PV%, lb/sq . . . . . . . . . . . . . . . . . . . . . . . .

s, sq f t . .

-

. . . . . . . . . . . . . . . . . . . . . . . . 16

c, f t . . .

. . . . . . . . . . . . . . . . . . . . . . . .

W, l b . . . 34,450

. . . . . . . . . . . . . . . . . . . . . . . .

m, slugs . . 1,070

. . . . . . . . . . . . . . . . . . . . . . . .

V, f t / s e c . . 971

. . . . . . . . . . . . . . . . . . . . . . . .

kp, ft . .

35,000 . . . . . . . . . . . . . . . . . . . . . .

0.000737 p, slugs/cu f t .

. . . . . . . . . . . . . . . . . . . . . .

1.00 Mach number . . .

. . . . . . . . . . . . . . . . . . . . . .

CmiT, per radian -0 773 -2.27 . p e r r a d i a n . . . . . . . . . . . . . . . . . . . . . . .

Cmg

0.867 C . p e r r a d i a n . . . . . . . . . . . . . . . . . . . . . . .

ma

4.41 , p e r r a d i a n . . . . . . . . . . . . . . . . . . . . . . .

cLa

TABLF: I11 SOIIE TYPES O F R O L E C O U P L I N G CONTROLLfZElS AND AUGMENTERS

Sensing required I Controls used

System A Perfect controller

-

B Practical controller

-

C Coupling-Eoment canceler Pitch damper D Y a w darrrper E I 18 EFFECT OF ROLLING VELOCITY ON MAXIMUM TAIL LOADS 3600 LEFT ROLLS FROM I g FLIGHT -ORIGINAL VERTICAL TAIL --- OPTIMUM VERTICAL TAIL MAXIMUM MANEUVERING MAXIMUM VERTICAL- HORIZONTAL-TAIL LOAD TAIL L W IO X I 0 3 I:

F'"

CRITICAL 0 I 2 3 0 I 2 3 AVERAGE ROLLING VELOCITY, RADIANS/SEC Figure 1 EFFECT OF A PITCH DAMPER IN ROLLING MANEUVERS FROM FLIGHT TESTS 360" LEFT ROLLS FROM I g FLIGHT -NO AUGMENTATION 0.5; --- WITH AUGMENTATION (DAMPING RATIO, MAXIMUM CONTROL AUWORrY, 1.8") MPXMUM MANEUVERING MAXIMUM VERTICAL- TAIL LOAD HORIZONTAL-TLUL LOAD T O 3

[xd

I I CRITICAL /' ROLLING MLOCITY 0 I 2 3 0 I 2 3 AVERAGE ROLLING VELOCITY, RADIANS/SEC Figure 2 ....... ...............

0 . . 0 . 0 0 . . 0 . 0 .

..... .......

0 .

NACA RM L 5 7 D l k : ; :,, ...e ............ 0 .

EFFECT OF PERFECT CONTROLLER ( B = A Q = O ) 360' LEFT ROLLS - WITHOUT CONTROLLER

--- WITH CONTROLLER

I g FLIGHT MAXIMUM MANEUVERING MAXIMUM VERTICAL- HORIZONTAL-TAIL LOADS TAIL LOADS 29 FLIGHT

1 2 r X I 0 3 1211 x103

~ H T , MAX 1 A,,,,':' LVT, LB MAX' :b, ROLL C,RylCAL I NG VELOCITY

~ H T , MAX 1 A,,,,':' LVT, LB MAX' :b, ROLL C:ylCAL I NG VELOCITY

I I 4 4 I / I / / #/. / #/.

-*I -*I

- -__--- - -__---

0 I 0 I 2 3 0 I 7 1 2 3 0 I 2 3 AVERAGE ROLLING VELOCITY, R A D I A N S I S E C - ., AVERAGE ROLLING VELOCITY, RADIANSISEC Figure 3 MAXMUM MANEWERlNG HORIZONTAL-TAIL LOADS WITH PERFECT CONTROLLER 360° LEFT R O L L S FROM 2 9 FLIGHT

- WITHOUT CONTROLLER

--- WITH CONTROLLER

i

0 I 2 3 5 IO 1 5 20 25 30 35 AVERAGE ROLLING VELOCITY, TOTAL AILERON RAML\Ns/SEx: DEFLECTION, DEG

Figure 4

MAXIMUM TAIL LOADS IN 360° LEFT ROLLS TYPICAL FIGHTER; ~ a . 7 ; hp=32,000 FT; ROLL RATES UP TO 2.2 RADIANSISEC MANEUVERING VERTICAL- HORIZONTAL-TAIL LOAD TAIL LOAD 6 d o 3 6 p I O 3 LVT, MAXl4 AL HT, MAX9 L B 2 L B n 0

-

12 r ~ ~ 0 3 0 IO 8 8 LVT, MAXI 6 AL m, MAX- 6 L B 4 LB 4 ORIG.wT. A C D E 'OPTL . ,

-

- \ TAILS SYSTEMS TAILS SYSTEMS Figure 5 MAXIMUM CONTROL DEFLECTIONS REQUIRED IN 360" LEFT ROLLS TYPICAL FIGHTER; M.0.7; b=32,000 FT; ROLL RATES UP TO 2.2 RADIANS/SEC r STABILIZER DEFLECTION RUDDER DEFLECTION I g FLIGHT 6 0 ' T , MAX940 Sr, MAX* DEG 30 DEG 30 I O ' O t O , , , o , , , 0 WIG. A C D E A C D E OPT OPT.

-

L_r_ k c SYSTEMS TAILS TAILS SYSTEMS F i b m e 6 ....... ...............

. . . . . . . . . . . . . . . .

..................

. . . . . . . . . 0 . . 0 . 0 .

NACA RM L 5 7 D l k * * * ........

MAXIMUM ACCELERATIONS IN 360" LEFT ROLLS TYPICAL FIGHTER; m0.7; hp=32poO FT; ROLL RATES UP To 2.2 RADIANS/SEC NORMAL ACCELERATION LATERAL ACCELERATION I g N G H T "z; MAx*2 g UNITS 0 n Y , MAXs2 -2 9 m T S O 2 g RIGHT "z, MAX* g UNITS -0 -2 - -

m A C D E OWG A C D E

OPT. OPI:

J --

-' TAILS SYSTEMS TAILS SYSTEMS Figure 7 PITCHING-MOMENT CHARACTERlSTlCS FOR PITCH - UP CALCULATIONS 0 , -.IO Cm -20 -.30

t

I I I I I I 1 -40 I I I I 0 8 1 6 24 32 40 Q, DEG Figure 8 EFFECT OF MAGNITUDE OF VARIABLE PITCH DAMPING ON LOADS IN PITCH-UP M4.O; hp=S,OOO FT; PULL-UP TO 4 9; INPUT RATE, 2.5O/SEC MAXIMUM NORMAL ACCELERATION 71- MAXIMUM HORIZONTAL-TAIL LOAD MOMENT CURVE

'1 r W L U E WITH

LINEAR PITCHING- LHT, MAX, - 1 0 MOMENTCURVE LB MAXIMUM CONTROL REQUIRED -20 $ 1 0 : 1 I I 0 .05 . I O .15 .20 dS/da DEG 2 0 .05 .IO .I5 .20 db/da Figure 9 EFFECT OF STICK PUSHER ON LOADS IN PITCH-UP M.I.0; $=35QOO FT; PULL-UP TO 4 9; INPUT RATE, 2.So/SEC INPUT RATE, DEG/SEC 0 - - 2.5

0 --------

- 5.0

A ---

- 8.0

MAXIMUM NORMAL ACCELERATION MAXIMUM HORIZONTAL-TAL LQAD -30 L L ~ ~ 0 3 , I 0 IO 20 0 1 0 20 PUSH RATE, DEG/ SEC Figure 10 NACA - Langley Field, Va.

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CON FI DENTlAL