Document
N A S A TECHNICAL NOTE ASA-TN---D-3910
o* M I n ;L I- r/, z I I ; WAG*) (CODE) I d (NASA CR OR TMX OR AD NUMBER) I
A SIMULATOR AND FLIGHT STUDY OF
YAW COUPLING IN TURNING MANEUVERS
OF LARGE TRANSPORT AIRCRAFT
and Robert C. Innis
by Walter E. McNeill
Ames Research Center
Moffett Field, Gal$
- . b
SPACE ADMINIST NASA TN 0-3910*-' /' A SIMULATOR AND FLIGHT STUDY O F YAW COUPLING IN TURNING ./ MANEUVERS OF LARGE TRANSPORT AIRCRAFT BY Walter E. McNeill and Robert C. Innis
1 A m e s Research Center
Moffett Field, Calif. - N A T I O N A L AERONAUT ICs AND SPACE ADMINISTRATION For sale by the Clearinghouse for Federal Scientific and Technical Information Springfield, Virginia 22151 - CFSTl price $3.00 A SIMULATOR AND FLIGHT S T U D Y O F YAW COUPLING I N TURNING M A N E U V E R S OF M G E TRANSPORT AIRCRAFT By Walter E. McNeill and Robert C . Innis Ames Research Center A p i l o t e d simulator study w a s made of the e f f e c t s of the aerodynamic yaw- coupling parameters (with Dutch-roll period and damping as secondary vari- a b l e s ) on t h e l a t e r a l - d i r e c t i o n a l handling q u a l i t i e s of a supersonic transport configuration a t landing approach airspeed. Based on p i l o t opinions and measured s i d e s l i p excursions i n sidestep maneuvers, t h e desirable combinations of the yaw-coupling derivatives tend t o ' b e more p o s i t i v e than i s t y p i c a l of current a i r c r a f t . Results of f l i g h t tests i n a l a r g e v a r i a b l e - s t a b i l i t y j e t transport show trends similar to those of t h e simulator data. Some areas of minor disagreement between t h e simulator and f l i g h t r e s u l t s were traced to differences i n p i l o t location with respect t o the center of gravity and i n d i - cated t h a t p i l o t consciousness of side acceleration forces can be an important f a c t o r i n t h e handling q u a l i t i e s of large a i r c r a f t . The r e s u l t s of t h e p r e s - ent simulator study tend to support t h e use of t h e frequency r a t i o q / w d as an indicator of desirable yaw-coupling behavior.
INTRODUCTION The problem of assuring s a t i s f a c t o r y l a t e r a l - d i r e c t i o n a l handling q u a l i t i e s i n t h e design of a new c l a s s of airplane i s a recurring one. For a transport airplane, t h i s problem must be considered not only from t h e stand- point of operational safety b u t a l s o from the standpoint of passenger and crew comfort. Recent studies of t h e l a t e r a l - d i r e c t i o n a l c h a r a c t e r i s t i c s of large a i r c r a f t , such as t h e supersonic transport, have pointed out some of t h e f a c t o r s t h a t a f f e c t the handling of a large airplane i n the lateral- d i r e c t i o n a l mode during such precision f l i g h t tasks as an instrument landing are g i v e n - i n references 1 and 2.
approach. Some examples of t h i s work In addition t o providing s a t i s f a c t o r y lateral o s c i l l a t o r y (Dutch r o l l ) c h a r a c t e r i s t i c s , roll control response, and s p i r a l c h a r a c t e r i s t i c s , it is desirable t h a t a m i n i m u m of s i d e s l i p be developed i n r o l l i n g maneuvers, such as t u r n e n t r i e s and reversals, i n order t h a t t h e rudder coordination required of the p i l o t be minimized. I n other words, s e l f -coordinating ( "two control") q u a l i t i e s should be b u i l t i n t o the airplane.
A s airplanes increase i n s i z e , t h e provision of two-control capability a t approach speeds tends to be more d i f f i c u l t because t h e moments of i n e r t i a increase much more rapidly with s i z e than do the aerodynamic moments involved.
The problem i s even g r e a t e r f o r supersonic-cruise a i r c r a f t because of t h e proportionately l a r g e yawing moment of i n e r t i a associated with the long I n short, any delay of the a i r p l a n e ' s yawing i n t o a t u r n slender design.
causes adverse s i d e s l i p , which, i n addition t o generating uncomfortable s i d e - can considerably impair the r o l l i n g performance if the dihedral e f f e c t forces, is large, and can e x c i t e the Dutch-roll mode if the damping is low.
To i n v e s t i g a t e the problem of y a w coupling i n a systematic manner, a piloted simulator study (including motion and a v i s u a l runway presentation) A SCAT 16 was made which involved repeated simulated ILS approaches.
supersonic-transport configuration was used f o r the study. The p r i n c i p a l and yaw due t o l a t e r a l variables i n the study were yaw due t o r o l l i n g , control, N s , which have long been known t o d i r e c l y a f f e c t the yaw character- *Y r?, i s t i c s of airplanes. Supplementary f l i g h t data were obtained i n a four- engined j e t transport adapted f o r v a r i a b l e - s t a b i l i t y testing. The experi- mental r e s u l t s of the simulator and f l i g h t studies have been summarized i n reference 3. The purpose of the present report i s t o elaborate on the anal- y s i s of the r e s u l t s , t o discuss the e f f e c t s of Np, Naa, and secondary vari- ables, such as Dutch-roll period and damping, on yaw coupling i n roll maneuvers, and t o present some observations on how optimum behavior may be obtained.
SYMBOLS
s i d e acceleration sensed at cockpit, ay + xp$ + Z h - g s i n ( P J
P f t / s e c2 f i r s t and second peak Ay, ft/sec2 l a t e r a l acceleration at center of gravity, ft/sec2 normal acceleration at center of gravity, ft/sec2 wing span, swept position, f t r o l l i n g moment s i d e force CY %Sb q0S
-
C wing mean aerodynamic chord, swept position, f t acceleration due t o gravity, ft/sec2 h a l t i t u d e , f t r o l l i n g moment of i n e r t i a , I X slug-f t2 pitching moment of i n e r t i a , =Y pitching moment t2 slug-f QSZ yawing moment of i n e r t i a , IZ slug-f t2 product of i n e r t i a , Ixz
k(rz - 1X)tan 2c, slug-ft'
yawing moment LP soSb SbC
, l/sec2
Lsa
I X '8r m airplane mass, slugs
- b qosbcnP , l/see
N P 2v I z N r NP '6a ' 8 , P Dutch-roll o s c i l l a t i o n period, sec r o l l i n g angular velocity, rad/sec P pitching angular velocity, rad/sec q dynamic pressure, pV2, l b / f t 2 q0 c r yawing angular velocity, rad/sec S wing reference area, swept position, f t 2 T t h r u s t , l b t time, sec t r u e airspeed, f t / s e c
v
weight of airplane, l b W cockpit distance forward of center of gravity, f t y P cockpit distance above center of gravity, f t zP a angle of attack, deg or rad s i d e s l i p angle, deg or rad P first peak s i d e s l i p angle, deg P 1 second peak s i d e s l i p angle, deg I 3 2 inclination of f l i g h t path with respect t o horizontal, positive f o r Y climb, rad o r rad a i l e r o n deflection, positive right-hand t r a i l i n g edge down, deg elevator deflection, positive t r a i l i n g edge down, deg o r rad rudder deflection, positive t r a i l i n g edge l e f t , deg o r rad E angular displacement of longitudinal principal axis below body reference a x i s a t nose, deg Dutch-roll damping r a t i o p i t c h angle, deg o r rad ground t r a c k angle with respect t o runway center-line extension, rad A wing leading-edge sweep angle, deg ALE a i r density, slugs/ft3 P 7 single degree -of -freedom roll time constant, R - bank angle, deg or rad cp f i r s t peak bank angle, deg second peak bank angle, deg r a t i o of bank-angle amplitude t o s i d e s l i p amplitude i n t h e Dutch- roll mode yaw angle, deg or rad undamped n a t u r a l frequency of t h e Dutch-roll mode, rad/sec undamped n a t u r a l frequency appearing i n the numerator quadratic of the 2 t r a n s f e r function, rad/sec 6a
a (
d t EQUIPMENT Motion Simulator The Ames five-degree-of-freedom motion simulator was used i n t h e present 1). The simulator w a s used e s s e n t i a l l y as described i n reference study ( f i g .
4, t h a t is, with t h e cockpit facing outward and with t h e lateral acceleration w a s subjected t o p i t c h and cues provided by centrifuge arm motion. The p i l o t yaw angular motions which approximated those of t h e simulated airplane. (Roll motions were attenuated t o 25 percent of the computed values t o avoid unreal- i s t i c side forces on t h e p i l o t caused by t h e cab t i l t i n g . ) To avoid exceeding t h e motion c a p a b i l i t i e s of the simulator cab and a l s o t o avoid spurious longitudinal acceleration cues due t o large angular velocity of t h e centrifuge arm around the track, washouts w e r e applied t o a l l cab angular rates and d i s - placements and t o the arm acceleration and rate. The v e r t i c a l motion capability of t h e simulator w a s not used.
Cockp it The cockpit controls and panel instruments e s s e n t i a l t o the simulation were s i m i l a r t o those i n conventional transport a i r c r a f t , except that a t h r e e - a x i s a t t i t u d e indicator replaced the f l i g h t director. Figure 2 shows t h e arrangement of t h e cockpit. The controls consisted of a yoke and wheel, rudder pedals, and two t h r o t t l e s (each controlling the two engines on one s i d e of t h e airplane). The panel display included the following indicators: angle of attack, s i d e s l i p , airspeed, airplane a t t i t u d e (three -axis b a l l which a l s o presented I L S deviation information), heading, a l t i t u d e , v e r t i c a l speed, a clock.
engine percent rpm, control deflections, and A televised image of a runway model w i t h motions reproduced as described i n reference 5 w a s used i n t h e v i s u a l portions of the test runs. In t h e the image w a s present study, because of limited space i n the simulator cab, shown on an 8-inch t e l e v i s i o n tube above t h e instrument panel.
Analog Simulation Simulator motion and instrument drive signals were obtained from a s i x - degree-of-freedom analog simulation. The airplane equations of motion (employing moments i n body axes and forces i n wind axes) and t h e necessary angle conversion formulas are presented i n t h e appendix.
Variable -Stability Airplane For the f l i g h t portion of t h e present study t h e 367-80 four-engined jet transport 707 prototype w a s made available by t h e Boeing Company under Contract No. NAS 2-2132. The airplane ( f i g . 3) was adapted f o r variable- s t a b i l i t y t e s t work by t h e i n s t a l l a t i o n of an i r r e v e r s i b l e rudder servo system with +loo of variable - s t a b i l i t y authority. The yawing -moment param- e t e r s t h a t were varied during the f l i g h t program were s t a t i c d i r e c t i o n a l s t a b i l i t y , NP, s i d e s l i p - r a t e damping, N;, yaw due to roll control input, Nga, and yaw due to r o l l i n g , Np .
TESTS Examp l e Airplane The example airplane used i n the simulator study was one of t h e f i n a l versions of t h e N A S A SCAT 16, a variable -sweep supersonic transport design, i n t h e landing configuration (with wing swept 30°). The basic airplane c h a r a c t e r i s t i c s , based on available wind-tunnel data and supplemented by t h e o r e t i c a l estimates, are given i n t a b l e I. The values shown i n the t a b l e f o r C i p and set approximately 60 percent g r e a t e r than t h e basic were values f o r t h e SCAT 16 to ensure a short roll t h e constant (0.3 s e e ) .
Simulator T e s t Maneuvers For simulator evaluation of t h e l a t e r a l - d i r e c t i o n a l c h a r a c t e r i s t i c s of the airplane, tasks were chosen t o represent t h e most c r i t i c a l low-speed operating conditions. The instrument landing approach w a s selected as t h e condition upon which to base t h e study. This condition requires close con- centration by t h e p i l o t on instrument f l y i n g technique and i s one of the s i t u a t i o n s i n which good handling q u a l i t i e s are desirable f o r safe operation.
Figure 4 i l l u s t r a t e s t h e approach geometry reproduced i n the simulator.
The i n i t i a l a l t i t u d e on a 3 ' g l i d e slope w a s 600 f e e t , which placed t h e simulated airplane approximately 2 m i l e s from the runway threshold. The approaches were performed under instrument conditions (using deviation information derived from a simulated instrument landing system) u n t i l v i s u a l contact with the runway w a s obtained a t an a l t i t u d e of 200 feet. From t h a t point, the p i l o t completed the approach v i s u a l l y t o a landing.
During some of t h e approaches, o f f s e t s corresponding t o a lateral deviation of 1 - 7 0 f e e t were introduced abruptly i n t h e l o c a l i z e r needle s h o r t l y after the airplane These o f f s e t s were simulated ( i n s t a r t e d down t h e g l i d e slope ( f i g . 4 ) .
e f f e c t ) by moving t h e l o c a l i z e r transmitter 170 feet to t h e r i g h t or l e f t of t h e runway center l i n e .
The p i l o t ' s task w a s t o correct, on instruments, the o f f s e t by executing a sidestep maneuver. A f t e r correcting t h e i n i t i a l o f f s e t properly, the p i l o t (upon breaking out at 200 f t ) found himself o f f s e t from t h e runway center l i n e ; thus, before he could land, it w a s necessary f o r him t o perform a second sidestep maneuver visually. A t t h e nominal approach speed of 130 knots, the time required for each simulator run w a s about 50 seconds.
The evaluation i n the simulator of each combination of airplane variables w a s based on t h e following three tasks: F i r s t , the p i l o t famil- i a r i z e d himself i n a general way with the airplane dynamics a t t h e approach speed of 130 knots by performing t u r n e n t r i e s and recoveries, roll reversals, steady s i d e s l i p s , and Dutch-roll o s c i l l a t i o n s . Second, he made s t r a i g h t - i n instrument approaches. Third, he made instrument approaches, but with the l a t e r a l o f f s e t s described previously. H e corrected the o f f s e t s by performing sidesteps with roll control alone and a l s o with coordinating rudder.
The sidestep maneuver was selected as a primary evaluation maneuver because it could be performed r e a l i s t i c a l l y i n the simulator, because it placed an appreciable demand on t h e p i l o t f o r proper phasing of rudder control when coordination w a s desired, and because the time required t o perform it was close t o the Dutch-roll o s c i l l a t i o n period predicted f o r the supersonic transport c l a s s of airplane at landing approach speeds. Hence, the p o s s i b i l i t y of coupling with and unduly exciting the Dutch-roll mode was introduced as a s i g n i f i c a n t f a c t o r . Detailed analyses of the sidestep maneuver a r e given i n references 6 through 8. Some f l i g h t work reported i n reference 9 indicated t h a t t h e minimum time t o perform a sidestep maneuver was about 10 seconds, which w a s without exceeding reasonable bank angles approximately the Dutch-roll period ( a t 130 knots) of t h e SCAT 16 used herein as t h e basic airplane. To uncover any e f f e c t s of resonant coupling between t h e sidestep and the Dutch-roll mode, nominal o s c i l l a t i o n periods of IO, 7, and 5 seconds were investigated.
The l a t e r a l o f f s e t of 170 f e e t referred t o w a s t h a t value which would r e s u l t from an idealized sidestep maneuver performed a t 130 knots with a sinusoidally varying bank angle having a period of 10 seconds and an amplitude of 20°.
Time h i s t o r i e s of t y p i c a l sidestep maneuvers performed with roll control alone a t nominal periods of 10 and 5 seconds a r e presented i n figure 5.
Test Variables The aerodynamic derivatives chosen as t h e primary variables i n t h e present study were yaw due t o r o l l i n g , Np, and yaw due t o the p i l o t ' s roll control input, N 8 a , the l a t t e r expressed i n terms of roll control e f f e c t i v e - ness as N E ~ / L ~ ~ . These derivatives were varied over t h e ranges indicated i n t a b l e 11. The ranges chosen were approximately those encountered i n several N A S A SCAT supersonic transport design studies. The values of Dutch- roll period were s e t a t 10, 7, and 5 seconds, and the damping r a t i o [d was s e t a t approximately 0.15 by adjusting t h e yaw damping, N r , (both a t Np = -0.118). The variations of period and damping r a t i o with Np over the range studied a r e shown in t a b l e 11.
Some runs were made with the damping r a t i o increased t o approximately 0.25 and 0.40 (P M 10 see) and a l s o with roll damping reduced t o $ approximately one - t h i r d t h e base value ( r e s u l t i n g i n a single -degree -of - freedom roll time constant of about 1 s e e ) .
These c h a r a c t e r i s t i c s a r e summarized i n t a b l e 111.
After completing the evaluation tasks described e a r l i e r , t h e p i l o t assigned a numerical r a t i n g t o each combination of variables according t o the scale presented i n t a b l e IV. (See a l s o r e f . 10.) Ratings and p i l o t ' s comments were obtained separately f o r maneuvers performed first without, then -with coordinating rudder. Two NASA research p i l o t s participated i n the study; however, both p i l o t s did not evaluate a l l configurations.
F l i g h t Tests The f l i g h t maneuvers performed i n the Boeing 367-80 v a r i a b l e - s t a b i l i t y jet transport were as follows: ( A ) Dutch-roll o s c i l l a t i o n s , a i l e r o n s t e p inputs, 5 O and 30° heading changes, and simulated sidestep maneuvers (S-turns) ; and (b) landing approaches using v i s u a l reference, then repeated using instrument reference. I n the instrument approaches guidance informa- t i o n w a s supplied by e i t h e r a deviation indicator or a flight d i r e c t o r .
Lateral o f f s e t s were corrected v i s u a l l y p r i o r t o landing. The p i l o t s rated each task according t o t a b l e I V and assigned an o v e r a l l r a t i n g t o each con- figuration. They used the rudder a t t h e i r d i s c r e t i o n and, i n assigning t h e i r ratings, considered how much turn coordination was required.
RESULTS AND DISCUSSION Simulator Study Effects of primary variables.- The r e s u l t s of the s i m l a t o r study a r e presented i n f i g u r e 6 as p i l o t opinion boundaries on the Np, N 6 a / b a plane for each of the nominal Dutch-roll periods of LO, 7, and 5 seconds. The individual t e s t points a r e shown w i t h the associated p i l o t ratings. The boundaries separate areas of s a t i s f a c t o r y and unsatisfactory c h a r a c t e r i s t i c s f o r normal operation (PR = 3.5), and areas of acceptable and unacceptable c h a r a c t e r i s t i c s f o r emergency, or dampers-out, operation (PR = 6.5). The numerical r a t i n g s f o r obtaining these boundaries were e i t h e r given by one of the two NASA research p i l o t s involved i n the simulator study (see t a b l e 11), or were the average of both p i l o t s ' evaluation of the same combination. Furthermore, the r a t i n g s were those given when coordinating rudder w a s used, except when coordination was i n e f f e c t i v e or detrimental.
Figure 6 indicates, f o r each Dutch-roll period, an area of s a t i s f a c t o r y These s a t i s f a c t o r y areas a r e oriented cordbinations of Np and N 6 /L a 6,' diagonally and indicate a "trade o f f " between the two yaw-coupling param- e t e r s ; f o r exanrple, as becomes more positive (tending t o yaw i n t o the Np must become l e s s positive i f the yaw-coupling c h a r a c t e r i s t i c s
t u r n ) , Nsa/LSa
These r e s u l t s indicate t h a t a p o s i t i v e value a r e t o r e m i n satisfactory.
(within l i m i t s ) of e i t h e r or both of these parameters i s desirable.
P i l o t comments indicated t h a t behavior i n sidestep mneuvers w a s s a t i s f a c t o r y when s i d e s l i p excursions were near minimum without the use of coordinating rudder. These comments a r e substantiated i n figure 6 by the diagonal long-dashed l i n e s t h a t pass through the s a t i s f a c t o r y areas. These Pl/cp,, the r a t i o of the f i r s t pea% s i d e s l i p l i n e s a r e l o c i of zero values of Y to the first peak bank angle as measured from records of the sidestep maneuvers performed without coordinating rudder. The short-dashed lines are loci of ( J + / u d = 1.0. The ratio q p / c q was evolved in reference 11 as an - indicator of incipient closed-loop lateral-directional instability for r o l l control with ailerons only for a pilot-airplane combination; that is, with values of much greater than 1 . 0 , such instability should be expected,
q / w
especially at low levels of Dutch-roll damping. The ranges of q / w in the
present study will be discussed in a later section.
In each part of figure 6 the two dashed lines agree well and, further-
more, intersect the vertical axis (NE~/LG, = 0) at Np = g/V, a condition
that, for most airplanes, results in self-coordinating, or two-control, behavior (see, e . g . , ref. 12).
The basic value of predicted for the SCAT 1 6 example was - 0 . 1 1 8 .
Np
In view of the requirements of figure 6 for at least as much positive
Np (with negative or small positive'values of NB~/LS,) suitable stability augmentation might be desirable if the positive increment cannot be Np obtained by design modification.
The widening of the satisfactory area at the intermediate Dutch-roll period of 7 seconds (fig. 6 ( b ) ) indicates a wider latitude or tolerance of variations of Np or Nsa. At first glance, this apparent tolerance might tend to confirm the existence of a resonant coupling effect between the sidestep maneuver and the Dutch-roll mode at the periods of 10 and 5 seconds.
The pilot's coments indicated, however, that resonant coupling was virtually undetectable.
To investigate the possibility of resonant coupling, two sets of available quantitative data were examined: (1) measurements of Pl/cpl in rudder-fixed sidesteps performed by the pilots during simulator runs, and (2) values of Pl/cpl in sidesteps programmed on the analog computer, wherein the simulated airplane was forced to follow closely a sinusoidal bank-angle c o m n d having a 10-second period and 1 0 ' mximum arrrplitude. Each set was obtained for several Np, Nsa combinations over the test ranges with nearly constant at 0 . 1 5 .
The two sets of data showed very similar trends. The sideslip excur- sions decreased progressively with decreasing Dutch-roll period (increasing These measure- N p ) and there were no peaks or dips in the plotted curves.
ments substantiate the pilot's comment that coupling between the sidestep mneuver and the Dutch-roll mode was insignificant.
The boundaries of figure 6 have a similarity to those from the piloted simulator study of a V/STOL aircraft in cruising flight (ref. 12) Effects of yaw and roll damping.- As mentioned earlier, a few config- urations were evaluated in the simulator with increased yaw damping, -NT, The evaluation of these additional- config- or decreased roll damping, -$.
urations by pilot B is summarized in table 111. The basic configurations LO * from t a b l e 11, i d e n t i f i e d as points A, B, and C i n f i g u r e 6, are included.
Incremental changes i n p i l o t r a t i n g from those f o r the b a s i c configurations a r e a l s o shown.
It was expected t h a t increasing the Dutch-roll damping r a t i o [d above 0.15 would improve handling c h a r a c t e r i s t i c s i n general and t h a t decreasing roll damping (e.g., t o about l / 3 the base value) would r e s u l t i n l e s s d e s i r - r e l a t i v e able coupling e f f e c t s due t o an increase i n the magnitude of Npp t o and i n the phase difference between roll r a t e and roll control N8,6a input It is evident from t a b l e I11 t h a t , i n one case, the use of yaw-rate damping t o improve the damping r a t i o resulted i n only a minor improvement i n p i l o t opinion and, i n the other case, a small d e t e r i o r a t i o n i n rating.
A s - N r w a s increased, those configurations based on point A ( N = -0.20, %a/L8a = 0.005) benefited somewhat from a decrease i n Pl/(pl, wgile those configurations based on point B (Np = 0, N8a/L8a = 0.034) suffered an increase i n Pl/(pl. The apparent anomaly concerning the e f f e c t on Pl/(pl of increas- ing the yaw damping i s explained by the f a c t t h a t although the yaw r a t e (a
contributor t o 8 ) decreased with increasing - N r during sidestep maneuvers
i n both cases, the increase i n -N, f o r the configurations based on point B caused a r e v e r s a l i n the phase r e l a t i o n s h i p of the y a w r a t e t o the roll r a t e , s i d e s l i p , and bank angle ( t h e remaining s i g n i f i c a n t contributors t o 8 ) and an increase i n P1/(p1. I n both cases, the s l i g h t change i n numerical p i l o t r a t i n g w a s about the amount expected from the change i n t h a t was Pl/cpl measured.
Other studies (e.g., r e f . 13) have point out the advantages 9f using
s i d e s l i p - r a t e daarping (additional yawing moment proportional t o P ) , and it
i s believed t h a t applying such a scheme t o increase the damping would improve handling q u a l i t i e s as o r i g i n a l l y expected.
The t h i r d group of configurations l i s t e d i n t a b l e I11 (P 7 sec) indicates the e f f e c t s of decreasing roll damping and, also, of decreasing t o zero the distance from the center of gravity t o the cockpit.
It i s seen t h a t decreasing roll damping t o about one-third the base increased from 0.29 t o 0.96 sec) did worsen the p i l o t rating. value ( T ~ The r a t i o q / w d decreased from 0.96 t o 0.85, suggesting an increase i n adverse s i d e s l i p . (Measured /3&~ increased f r b m 0.16 t o 0.20.) P i l o t B TR = 0.96 sec, xp = LOO f t , NP = -0.118, s t a t e d t h a t the combination of and maximum a i l e r o n yaw ( N B ~ / L ~ , = 0.034) w a s very d i f f i c u l t t o control with a i l e r o n alone i n t h a t the Dutch-roll mode w a s e a s i l y excited. Attempts t o coordinate with the rudder were of l i t t l e help.
\ The f i n a l configuration l i s t e d i n t a b l e I11 w a s i d e n t i c a l t o the decreased roll-damping condition j u s t discussed, except t h a t xp w a s assumed t o be zero. Consequently, somewhat l e s s side-acceleration force a t the cock- p i t should have been evident since s i d e s l i p would have been the only contrib- uting factor. P i l o t B commented t h a t the accelerations were much milder and that the contribution due to sideslip seemed very small. Overcontrolling tendencies were lessened. The pilot ratings tend to support this by indicat- ing a slightly smaller deterioration in rating, for TR = 0.96, from the basic - point C .
Flight Evaluation To obtain pilot-opinion data in a flight environment for comparison with the simulator results discussed in the previous section, certain combinations of Np and Na /% were evaluated by NASA pilots A and B in the Boeing 367-80 a a airplane described earlier. These conhinations were selected to represent ranges of variables studied in the simulator and were not intended to provide a point-by-point verification of the simulator results.
Comparison with simulator boundaries.- A comparison of the flight results with the simulator results is presented in figure 7 . The bounded areas indi- cated as satisfactory, unsatisfactory, and unacceptable are from the simulator (repeated from fig. 6) and the plotted points are the flight results.
For the period of 10 seconds (fig. 7 ( a ) ) , agreement between the flight and simulator ratings was good near the lower unacceptable boundary (PR = 6.5).
For the intermediate period of 7 seconds (fig. 7(b)), agreement between simu- lator and flight data was good only near the lower satisfactory-unsatisfactory
boundary (PR = 3.5). For the short period of 5 seconds (fig. 7( c) ) , the
limited flight data show considerable leniency with regard to adverse Np.
Overall, the flight points in figure 7 show less change in pilot rating than the simulator boundaries indicate.
with variations of Np and N E , / % , Furthermore, at positive Np, the flight ratings continued to improve as Naa/ka was made more positive, even to the limit of the range tested.
The differences between the simulator and flight results in figure 7 indicate that care must be taken in interpreting the results. A possible a interpretation is that, with current variable-stability techniques, conventional jet transport cannot adequately simulate the responses of a con- figuration such as a supersonic transport. Two fundamental items can influ- ence the quality of the simulation: (1) the differences in geometry between simulator airplane and simulated airplane, and (2) the accuracy with which the stability and control derivatives of the basic simulator airplane are known.
The following discussion will attempt to answer the question partially. Some new pmameters, which are shown to influence pilot opinion, are introduced.
Some attention also is directed toward the effects of airplane geometry.
Variation of pilot rating with P1/cpL.- In figure 8, pilot ratings are measured in pedals -f ixed sidesteps performed presented as functions of Pl/cpl The simulator data are indicated by the open in the simulator and in flight.
symbols and the flight points are shown as filled symbols. A l l pilot rating data fit approximately into two bands which suggest linear variations with Pl/cpl, the rate of increase of pilot For greater positive values of Pl/cpl.
rating probably would tend to decrease, since it would be expected that quite high values of P l / c p l could be tolerated without the airplane actually becoming uncontrollable.
The steep rise of numerical pilot rating for negative values of ~ l / c p l obtained from the simulator data reflects the objectionable characteristics (a tendency toward lateral instability with the pilot in the loop, an impres- sion of greatly decreased roll damping, and a tendency toward spiral diver- gence) associated with excessive yaw into the turn or with values of b + / W d greater than unity. When Pl/cpl was negative, coordination with the rudder was undesirable because of the cross-control technique required. Generally, is positive and less than 0 . 2 , rudder coordination is considered when Pl/cpl unnecessary .
The similarity in trends of the two sets of data in figure 7 is repeated in the corresponding data of figure 8 . Also, the lower sensitivity of pilot rating to changes in Np and Nsa/L5, in flight (fig. 7) is reflected by a lower sensitivity of pilot rating to changes in in flight (fig. 8 ) .
P l / c p l Effect of side accelerations.- The pilots felt that reduced sensitivity could be attributed to the absence of significant of pilot rating to P l / c p l side acceleration forces at the cockpit in flight. In the simulator, these forces included a substantial contribution from yawing angular acceleration acting through the assumed 100-foot cockpit arm and were noticeable, even
becoming objectionable for the short period of 5 seconds. Although in estab-
lishing their ratings the pilots paid particular attention to the magnitude the side of the sideslip-angle disturbances in turn entries and reversals, acceleration forces experienced in the simulator undoubtedly had a strong adverse effect on their opinions. The above impressions were confirmed by measurements of cockpit side acceleration computed by the analog computer dur- ing the simulation and by accelerometer records obtained during the S-turn maneuvers performed in the flight tests.
The results of the above measurements are shown as functions of Dutch- The roll period in figure 9 for the values of Np and Ns /Lga indicated.
a results are examined in terms of first-to-second peak sideslip and side- acceleration increments. Although somewhat higher sideslip/bank ratios are noted in flight, the trends with period are similar. The decrease in incre- mental sideslip for a given bank angle as the period is decreased is expected because of increased static stability. The increase in perceived side accel- eration in the simulator with the decrease in period is attributed to the yawing-acceleration component xp$ because of the assumed pilot ' s location far ahead of the center of gravity. The relatively constant side acceleration measured in flight resulted from the much shorter cockpit arm, which allowed the aerodynamic component YpP to be the major contributor.
From these results, it appears that the decreased tolerance of variations in Np and Ns /Ls at the period of 5 seconds in the simulator was a function a a of the increased side forces felt by the pilots.
Np and In the flight data, the lack of definition of optimum regions of could have been the result of insufficient coverage of these variables.
Nsa This, in turn, was probably due to uncertainties in the values and interrela- tionships of the stability and control derivatives of the unaltered 3 6 7 -80 airplane.
q,/w. - Plots of Pl/(p1, measured in sidesteps per-
Correlation with formed without rudder, as a function of are presented in figure 1 0
q/q
for the cases investigatd in the simulator and for the flight-test configu- rations. The b+/@ values were calculated using a digital computer program (not from approximate formulas) with the aerodynamic derivatives and physical characteristics of the airplanes as inputs.
The simulator data show gooa correlation between tQe two ratios in that near unity (actually, about the sideslip excursions were minim1 at
q/%
1.02) and that a clear relationship can be seen between large positive
(adverse) values of P l / r p l and Low Values of q/w. The relationship
appears to hold for a11 three values of Dutch-roll period investigated, with very little scatter.
The flight data show a similar relationship; however, somewhat more scatter is evident and zero sideslip excitation appears to correspond to a slightly greater value of Sufficient data were not available to show a clear trend for the >-second period conditions, but the p ~ / ( p l values measured were consistently less than those for the 10- or 7-second period condition.
in figure 1 1 .
The pilot-rating data are presented as functions of
w/q
It is seen that, in the simulator, the ratings were best near b + / q = 1 . 0 departed from 1 . 0 in either direc- and deteriorated progressively as w;p/w tion. This variation would be expected from the discussions of figures 6, 8, and 1 0 and also agrees quite well with the overall trends shown in figure 1.3 of reference 1 4 .
The flight data in figure 11 indicate generally the same deterioration of ratings for decreasing below 1 . 0 , but, as mentioned previously, * / w d
show more scatter. The flight data for ?/w above 1 . 0 indicate a con-
There seems tinued improvement in pilot rating rather than a deterioration.
to be no ready explanation for this continued improvement other than the possibility mentioned earlier of uncertainties in the basic aerodynamic derivatives of the 3 6 7 -80 airplane. ("Effective" values of the variable
derivatives were estimated and used in calculating 9 and Wd.)
In general, it appears that either pl/rp1 or q/w, within the ranges of
roll damping and Dutch-roll period and damping investigated herein, can serve as a reasonable criterion for assessing the behavior of large transport air- craft in sidesteps and possibly in other types of turning maneuvers. Each parameter has its particular advantages: has a theoretical basis, but 9/q can be measured easily (and therefore demonstrated) in flight in any P ~ / ( p l airplane equipped with sideslip and roll-sensing devices. Some effects of a similar parameter, LIP/&, on pilot opinion during turn entries are presented i n reference 15. A review of the data from reference 15 and t h e present study indicates similar variations of p i l o t r a t i n g with some simple measure 'of peak s i d e s l i p per u n i t maximum bank angle. Uncertainties remain as t o the e f f e c t s of several variables (such as dihedral effect, roll damping, Dutch- roll-damping r a t i o , and airspeed) on t h e u t i l i t y of J3l/cp, o r AP/hp as turn- coordination parameters. Additional research i n t h i s a r e a i s desirable.
Summary of P i l o t Comments P i l o t opinion seemed t o be influenced most strongly by the magnitude of the s i d e s l i p excursions generated i n abrupt, rudder-fixed turn e n t r i e s and t u r n reversals. When these excursions were adverse, the improvement realized by use of coordinating rudder w a s roughly proportional t o the amount of side- s l i p with roll control alone. I n the simulator, when s i d e s l i p was favorable ( P I / ( P ~ negative), t'ne p i l o t s considered the reversed rudder coordination required i n t u r n e n t r i e s t o be unnatural: and impractical.
When t h e s i d e s l i p excursions were l a r g e and adverse, there was a ten- dency t o e x c i t e an o s c i l l a t i o n i n heading when a small heading change was being made with a i l e r o n s alone. This problem appeared t o be independent of period and occurred when bank angle w a s used t o control heading. When t h e desired heading was not achieved, the p i l o t increased t h e bank angle. The desired heading change w a s achieved only with considerable s i d e s l i p . A s the s i d e s l i p returned t o zero, the p i l o t would see t h a t he had overshot and would correct back. I n extreme cases during IFR f l i g h t , t h i s o s c i l l a t i o n w a s could become divergent. The solution t o t h i s problem t o apply rudder vigorously. Although t h i s use of rudder control was effective, t h e r e s u l - t a n t increase i n the p i l o t ' s work load degraded h i s opinion of the configuration.
I n general, the p i l o t s found it d i f f i c u l t t o determine which parameter (Np, Nsa, o r other) was the primary cause of the s i d e s l i p excursions.
They did observe, however, t h a t the extreme p o s i t i v e values of seemed t o Np reduce the s p i r a l s t a b i l i t y of the vehicle. (These statements apply both t o t h e simulator and f l i g h t evaluations.)
CONCLUSIONS A p i l o t e d five-degree-of-freedom simulator and a l a r g e variable- s t a b i l i t y airplane have been used t o study the e f f e c t s of the aerodynamic yaw-coupling parameters on t h e l a t e r a l - d i r e c t i o n a l handling q u a l i t i e s of a supersonic transport at landing-approach speed. From t h i s study, the following conclusions are drawn: Cornbinations of Np (yaw due t o r o l l i n g ) and Nsa (yaw due t o roll 1 .
control application) corresponding approximately t o t h e frequency r a t i o q,,/wd = 1 resulted i n the most favorable p i l o t opinions because they required In some cases, m i n i m rudder coordination in turn entries and reversals.
these cordbinations included positive values of both parameters.
2. For the supersonic transport configuration represented in the simulator, the values of M required for optimum yaw coupling generally were positive ( i . e . , less Jverse than usual for Np at lift coefficients attained in the landing approach).
The amount of departure from o p t i m values of the yaw-coupling 3.
derivatives (especially Np) that could be tolerated in the positive direction was less than that in the negative (adverse) direction because of incipient closed-loop lateral-directional instability (pilot controlling) and the airplane's tendency to diverge spirally.
4 . The magnitude of sideslip excursions in sidesteps, for a given
cordbination of Np and Ns /Lg was related mainly to the static directional a a ' stability NP, and there was apparently no magnification, or resonance effect, due to coupling with the Dutch-roll mode at the nominal periods of LO and 5 seconds.
5 . In the simulator, q/q correlated well with the sideslip-to-bank
ratio Pl/cpl measured in pedals-fixed sidestep maneuvers. In flight, the correlation was somewhat less consistent.
6 . In the simulator, both and Pl/cp1 correlated well with
numerical pilot rating. The ratio /31/cp1 is easily measured in flight and may have application as a criterion for satisfactory or acceptable yaw- coupling characteristics in turning maneuvers. Values of P l / c p l between 0 and 0 . 2 were considered sufficiently small to require no coordination with rudder.
Anes Research Center National Aeronautics and Space Administration Moffett Field, Calif., 94035, Sept. 2, 1966 720 -04 -00 -01-00 -21 ) 5 ______..-- 1 " APPENDIX AIRPIAI!E EQUATIONS OF MOTION AND ANGULAR CONVERSIONS The following equations of motion were mechanized by means of a general- The moment equations were w r i t t e n i n purpose electronic analog computer.
t h e body system of axes and t h e force equations were referred t o wind axes.
were assumed t o be negligible.
The e f f e c t s of t h e product of i n e r t i a I= BASIC MOTION EQUATIONS Linear Accelerations Angular Accelerations RELATIVE WIND 8 = y + CL + p s i n rp FLIGHT PATH 1 8 1.
McNeill, Walter E . ; and Innis, Robert C . : A Simulator Study of t h e Lateral-Directional Handling Qualities of Two SCAT Configurations i n t h e Landing Approach.
N A S A "M X-905, 1963.
2 . Stapleford, Robert L.; Johnson, Donald E . ; Teper, Gary L.; and Weir, David H . : Development of Satisfactory Lateral-Directional Handliag Q u a l i t i e s i n t h e Landing Approach.
N A S A CR 239, July 1965 (Prepared under Contract NAS2-864 by Systems Technology, Inc., Hawthorne, C a l i f . ) .
McNeill, Walter E . ; and Innis, Robert C.: The Effect of Yaw Coupling i n 3.
Turning Maneuvers of Large Transport A i r c r a f t .
N A S A S P -83, 1965.
4. White, Maurice D . ; Vomaske, Richard F.; McNeill, Walter E . ; and Cooper, George E . : A Preliminary Study of Handling Qualities Requirements of Supersonic Transports i n High-speed Cruising Flight Using Piloted Simulators. N A S A TN D-1888, 1963.
McNeill, Walter E , : A Piloted Simulator Study of t h e Loss of Altitude 5.
by a Jet Transport i n a Go-Around From an Instrument Landing Approach.
N A S A TN D -2060, 1963.
6 . Etkin, B.: An Analytical Study of t h e A b i l i t y of a Slender Delta-Wing Aeroplane t o Perform a Sidestep Manoeuvre a t Low Speed. R.A.E. TN Aero. 2623, 1959.
Pinsker, W . J . G . : Further Consideration of the Control Requirements 7.
f o r a Slender Delta A i r c r a f t t o Perform Sidestep Manoeuvres a t Approach Speeds. R.A.E. TN Aero. 2735, 1961.
8 .
Tomlinson, B. N . : An Extensive Theoretical Study of t h e A b i l i t y of Slender-Wing A i r c r a f t t o Perform Sidestep Manoeuvres a t Approach Speeds. R . A . E . TN Aero. 2837, 1962.
Perry, D. H.; Port, W. G . A.; and Morrall, J. C . : A Flight Study of t h e 9.
Sidestep Manoeuvre During Landing. R.A.E. Rep. Aero. 2654, 1961.
10. Cooper, George E . : Understanding and Interpreting P i l o t Opinion. Aeron.
Eng, Rev., vol. 16, no. 3, Mar. 1957, pp. 47-51, 56.
11. Ashkenas, Irving L.; and McRuer, Duane T . : The Determination of Lateral Handling Quality Requirements from A i r f r a m e - Human P i l o t System Studies. WADC Tech. Rep. 59-13?, June 1959.
12. Dolbin, Benjamin H . , Jr.; and Eckhart, Franklin F.: Investigation of Lateral-Directional Handling Qualities of V/STOL Airplanes i n Cruising F l i g h t . Cornell Aero. Lab. Rep. TB-1794-F-3 (Contract No. P . O .
7 8 8 3 9 - ~ ~ ~ ) , Dec. 15, 1963.
13. Quigley, Hervey C. ; and Lawson, Herbert F. , Jr. : Simulator Study of t h e
Lateral-Directional Handling Qualities of a Large Four-Propellered STOL Transport Airplane. NASA TN D-1773, 1963.
14. Ashkenas, Irving L . : A Study of Conventional Airplane Handling Qualities Requirements; P a r t 11.- Lateral-Directional Oscillatory Handling Q u a l i t i e s . A F F D L - T R - ~ ~ - ~ ~ ~ , Nov. 1965.
15. Quigley, Hervey C.; Vomaske, Richard F.; and Innis, Robert C . : Lateral- Directional Augmentation C r i t e r i a for J e t Swept-Wing Transport Airplanes Operating a t STOL Airspeeds. NASA SP-116, 1966.
TABU I. - AERODYNAMIC AND PHYSICAL CHARClCTmISTICS OF THE BASIC
SIMULATED AIRPLAPE [ A l l aerodynamic coefficients a r e based on wing geometry a t 7 5 O sweep angle] Value Parameter Value is 63.26 0.2030 \LE( landing -0 9 5525 configuration) 30° -0 6284 0 . 0 0 2 3 7 8 -0 005 9 5 2 5 2 , 4 0 0 -0.0811 -0.1806 0.5~ -2.713 0-255 0 . 9 7 4 6 -0.1176 -0.1940 -0 1 3 3 7 0.0158 -0 0 0 7 5 -0.478 -0.102 -0 2 6 4 -1.357 -1.382 -3 * 443
-0.710
1.238 3-52 -1.457 0 . 6 6 0.119 1.083 -13 * 9 9 2.24~10~ 11.54~10~ Control 13 -37~1.0~ l i m i t 9.9~10~ 2 2 5 ' 4 . 0 ' f r 1 5 '
-200, loo
74 * 30 'Both a i l e r o n s deflected; referred t o t o t a l a i l e r o n angle.
'Single a i l e r o n .
T A B U 11. - P R I N C I P A L COMBINATIONS OF AERODYNAMIC DERIVATIVES
CONSIDERED AND PILOT RATINGS OBTAINED I N THE PRESENT STUDY P i l o t r a t i n g P i l o t A P i l o t B NP (a) Nominal period, 10 sec
I .005 0.15 0 . 8 1
0.69
9 . 9 m 7
.017
9.9 - 15 * 8 3
-69 e 8 6 .034
9.9 - 15 * 69 7
.005 10.3 .84 7 -112 * 15 * 72 -.034 11.1 .14 .81 8 -77 .005 11.1 .14 6
- 77 * 91
11.1 .03k .14 -77 -98 3 3 .034 11.9 .82 1.05 4 -112 e 1 3 13 .o .88 -BO34 .12 4 -112 - .017 13 .o * 12 .88 1.00 3 -112 3 -112 .88 13.0 .12 1.07 4 * 0 5 .034 13 .o .12 .88 1.15 6 6
-
( b ) Nominal period, 7 sec
-
-.20
.005 6-1/e
6 . 9 -54 * 90
-.20 .034 6 -112 6-9 -54 5 -93 - . 1 l C .034 7.1 .55 . 9 6 5 -112
-. 034 6
7-3 -56 * 92 e 0 0 5 7.3 -56 -96 3 -112 .017 4
7.3 - 5 6 . 9 7 3 -112
.668 -. 152 .034
-56
7.3 - 99 3 -114
.10 - .017 4 -112 7.5 * 5 7 * 9 7 .10 .005 7 . 5 * 5 7 3 3 -99 .10 . 0 1 7 1.00
2 -112
7.5 - 5 7
.10 .034 1.02 3 7.5 * 5 7 3
.20 -. 034 4
3 -112 7.8 5 9 * 99 * 20 - .017 1.00 7.8 -59 .20 .005 1.03 3 7.8 -59 3 .20 .034 1.06 4 -112 7.8 5 9
- -
( c ) Nominal period, 5 sec 4 . 9 -15 -005 -45 e 9 5 4 . 9 .i5 . 4 5 . 9 6 -034 5 - 0 .i5 . 4 5 . 9 6 .005
.14 .46 . 9 6 -. 034
5.1 .14 .46 .98 . 0 0 5 5.1 5 *1 -14 -46 -99 2 --- .034 5.2 .13 . 4 6 1.01 .034 .47 1.00 5.3 .13 -.034 - -017 5.3 .13 .47 1.00 .005 .47 1.01 5 . 3 .13 4 4
.034 4-114- I 4-114
5.3 .13 .47 1.03 4 I I I h
+q-i+y I 4 4
8 0
u
w
I I I I I m I I cu H
I 3 I3r-i
u I rl I . .
!2
Fr 0 ; 0 0 I I 1 I w I I H H H GA r n r n rn a , @
w w $i
0 0 0 R R R I G . d P d a , m a , k pc I rl Y c c z
/ 1
c x 0 - - - m
I
I I
I '
I
I \
\ '
- 1 0 pc -c-
- .
6- (\I Q 4 - u) 10- G 0 ’ Qi
- -
-10 20 I- r Right 30- - - Left 30- I I I I I I I 0 2 4 6 8 1012 1 4 0 2 4 6 8 I O 1214 1 6 Time, sec ( 0 ) PmlOsec ( b ) Pm5sec Figure 5.- Time h i s t o r i e s of sidesteps performed i n t h e simulator with = -0.20, N ~ ~ / L ~ ~ = 0.005.
a i l e r o n alone;
--
.3
-------
.2 . I - I" $ 0 & z -.I Q) E Q) - . 2 >
4 -*3
-.04 - . 0 3 -.O2 - . O I 0 .o I .02 .03 . O 4 -Adverse N&l - Lg (I (b) P = 7 sec Figure 6.- Simulator data points and pilot-opinion boundaries.
T
4 1/8 4 3/4
I I 1 I I I I I
4 -.03 -.02 -.o I 0 .o I .02 .03 . O 4 Figure 6 .- Concluded.
.3 .2 . I I a , u) & z - . I -.2 - . 3 -.03 -.02 - . O I 0 .O I .02 -03 .04 .05 .06 . 0 7 a N8 L 8 a (a 1 P =IO sec Flight .3 d 5 = .40 .2 .I
-
I a ,
w o
0.
z - . I
- .2
-.3
-
0 N8 La 0
( b ) P = 7 sec
Figure 7.- Comparison of p i l o t r a t i n g s obtained i n f l i g h t with opinion boundaries obtained from simulator data.
-- v -5 \IC 3 118 -.\ ; z * : * : . ..:'.:'. .....
:>.. ..
.............. ................. :..
..
....... :.,> .... 2 . ' .
pI .............. '.:'.. ...
........
........................
..... <. .....................
................ ............. : . . . : : : : : : : : : ;.
.......
: . : : G : : : . : : . & & .05
Si mu la tor data Flight data
Period , sec
Nominal period, sec .- z 5 t
E
t .-
E 4
I I I I I I I I
I
-
- > -. I 0 . I .2 .3 .4 .5 . 6
Figure 8.- Variation of p i l o t r a t i n g with the f i r s t peak sideslip/bank r a t i o f o r simulator and f l i g h t data.
-
1.6
-
0 ' 1.2 - &-E?
.8 I I Qi
*-
4 - I I 01 I I I I I (a) Sideslip/bank ratio
--- Flight, Np = -.20; - N8a a.0075
-
1 . 0 Lga - . 8 c u Q) \ a t u y . .
- . 6
$9."
- < F Q - . 4 - .2
- -------
-----
a 9 1 0 I I
5 6 7 8 Dutch roll period, sec (b) Acceleration /sideslip ratio Figure 9.- Variation of sideslip and side-acceleration parameters with period. Rudder pedals fixed; 5 , = 0 . 1 5 .
I I I d I I 8 I I I I I I I I I I . .
i
I i d" Simulator I I 0 I I I 1 I 1 Nominal period, see 0 I O 0 7 .6 I I I B B .4 I I I I I " I 80
@
I I I I I I I I
I I i
I I I Flight I I I I I I I I -. 2 . 6 .7 .8 .9 I .o 1 . 1 I .2
-
Wd
Figure 10. - Variation of t h e first peak sideslip/bank r a t i o with
for simulator and f l i g h t data.
w(p/wd 8- 7 - I 0 0 0 d 6 - d u , g 5 - e c - 3 - 2 - Simulator I I I I I I t I I Nominal period, sec 0 I O C l (dz.26 0 7 6 Cd".39 0 5 8 - 7 - 6 - I u , c -
'= 5
e t
.z 4 -
3 - I I 2 - Flight I I I I I 1 * .9 I 1 . 1 I .2 .7 . 8 Figure 11.- Variation of p i l o t r a t i n g with -/wd f o r simulator and f l i g h t data.
NASA-Langley, 1967 - 2 A-2264