A compilation and analysis of helicopter handling qualities data. Volume 2: Data analysis

TABLE OF CONTENTS SECTION Page I INTRODUCTION .......................

II GENERAL PILOT-VEHICLE LOOP STRUCTURE ...........

B. Assumed Piloting Technique ..............

C. Aspects of Multiloop Manual Control Theory ......

D. Application of the Crossover Model ..........

E. Use of a Pure Gain Pilot Model ............

F. Use of Constrained Variables .............

G. Identification and Labeling of Response Modes .... 2o III INNER LOOP REGULATION ..................

A. Background ......................

I. Pitch Axis ....................

_8 2. Roll Axis ....................

3. Yaw Regulation ..................

C. Cross Coupling ....................

I. Pitch-Roll Cross Coupling ............

2. Turn Coordination ................

OUTER LOOP REGULATION ..................

IV 81 A. Background ......................

B. Primary Control Response ...............

2. Sway (Lateral) Control ..............

3. Heave Control ..................

TABLE OF CONTENTS (Concluded) 8ECT!ON P_ge V ATMOSPHERIC DISTURBANCES .................

A. Introduction .....................

B. Inner Loop Gust Response ...............

A. System Descriptions .................

I. UH-IH Stabilizer Bar ...............

2. AH-IG SCAS ....................

1 25 B. Effects on Handling .................

I . AH-IG ......................

2. UH-IH ......................

3. c_-93D .....................

VII CONCLUSIONS AND RECOMMENDATIONS .............

I_3

• _:ic Anall%ical Approach .............. 1 43 B. Primary Control Response in the Inner Loops ..... lhh C. Axis Cross Coupling .................

! f D. Primary Control Response in the Outer Loops ..... I _o E. Gust Response ....................

F. Effects of Vehicle Augmentation ........... 1 48 G. Application to More Complex Mathematical Models REFERENCES ............................

1 49 APPENDIX -- SUMMARY OF CLOSED LOOP HELICOPTER TRANSFER FUNCTIONS vi LIST OF TABLES Page II-1 Examples of Closed Loop Relationships 11-2 Mode Label Formulation ..................

111-I Survey of Approximate Pitch Axis Response Transfer Functions (Hover) .....................

3o

III-2 Essential Features of Pitch Attitude Control in Hovering Flight ......................

III-3 Correspondence of Pitch Response Modes to Dominant Stability Derivatives (Hover) ...............

Survey of Approximate Pitch Axis Response Transfer Functions (60 kt Forward Flight) .............

III-6 Survey of Approximate Roll Axis Response Transfer Functions (Hover) .....................

III-7 Survey of Approximate Roll Axis Response Transfer Functions (60 kt ) .....................

III-8 AH-IG Roll Response, 60 kt, SCAS Off ...........

III-9 Survey of Approximate Yaw Response Transfer 111-10 Desired Control Interaction ................

IV-1 Survey of Outer Loop Control Characteristics (at 60 kt) ........................

IV-2 Survey of Outer Loop Control Characteristics, Varying Airspeed, OH-6A ..................

V-I Survey of Attitude Response Due to Gusts for 0H-6A in Hover (Case 4) .....................

1oi V-2 ENS Gust Response .....................

1o2 vii LIST OF TABLES (Concluded)

page

v-3 Relative Effects of Individual Gust Components for

Random Gusts/Deterministic (Step) Gusts/and Stability Derivatives (OH-6A, hover) ................

VI-I 1 21 Stabilizer Bar Dynamics ..................

VI-2 Survey of Approximate Roll Axis Response Transfer 1 36 Functions for Augmented Vehicles (Hover) .........

A-I A-2 A-4 A-5 Outer Loop Gust Response .................

viii LIST OF FIGURES Page 11-I Assumed Pilot-Vehicle Loop Structure for Low Speed Flight ..........................

11-2 Closed-Loop Pilot-Vehicle System .............

II-3 Conventional Bode Plot Illustration of Crossover 11-4 Bode Root Locus Illustration of Crossover Model II-5 Conventional Root Locus of Crossover Model Examples 14 11-6 Examples of Closed-Loop Relationships (Block Diagrams) ........................

111-I Required Pitch Damping to Provide 30 deg Effective Phase

D5

Margin for a Given Control and Pilot Lag .........

111-2 Existing Pitch Damping Requirement ............

111-3 Pitch Damping as a Function of Rotor Hinge Offset and Lock No ..........................

D7 III-4 Sample Pitch Loop Bode Root Locus (High Pitch Damping), B0-I05_ Hover ...................... 4o III-5 Sample Pitch Loop Bode Root Locus (Low Pitch Da_ping)_ AH-IG_ Hover .......................

III-6 q III-7 Variation in Roll Damping with Airspeed ......... _o III-8 III-9 Root Locus of Lateral-Directional Modes for Varying 111-10 Closed-Loop Responses in Step _ (AH-IG, 60 Kt, SC_ Off) .......... ? .............

III-11 Root Loci for the Dutch Roll ...............

ix LIST OF FIGURES (Concluded) Page III-12 Sideslip Stiffness as a Function of Airspeed for Five Helicopters with Two Superimposed Levels of Equivalent Directional Stiffness Provided by Active 6o Yaw Regulation in Hovering Flight ............

III-]3 Block Diagrams Comparing Compensatory Loop Structures with and without Pursuit Crossfeed for Pitch and 111-14 q>c+0 Cross Coupling Effect ..............

III-15 71 6c+ _ Cross Coupling Effect ..............

iii-16 Sketch of How Key Rotor System Parameters Affect Inertial Cross Coupling .................

III-17 79 Survey of _c +_ Cross Coupling ............

!II- 18 Turn Coordination Characteristics ............ 8o IV- I IO4 V-1 Attitude Response to Step Gust Inputs ..........

v-2 Closed Loop Aspect of Spatially-Dependent Gusts .....

V-4 u VI-I Approximate Equivalent Feedback Loops for UH-I H Stabilizer Bar ......................

VI-2 128 SCAS Off Pitch Response (AH-IG in Hover) .........

Bode Root Locus for Roll .................

VI-5 vi-6 Bode Root Locus for Roll .................

Bode Root Locus for Roll .................

vI-7 v!-8 Bode Root Locus for Roll .................

Bode Root Locus for Roll ................. 14o VI-9 LIST OF ABBREVIATIONS Po_e or zero associated with stability or control augmentation system HD Pole or zero associated with dominant heave mode, heave dampin_ LD Pole or zero associated with dominant sway (lateral) response, sway dampin_ NOE Nap-of-the-earth P Pole or zero complex pair associated with longitudinal phugoid PD Pole or zero associated with pitch damping PL Pole or zero complex pair associated with lateral phu_oid Revolutions per minute rpm R Pole or zero associated with dominant roll mode, roll dampin_ S Laplace operator SAS Stability augmentation system (CH-_SD) SCAS Stability and control augmentation system (AH-_G) SD Pole or zero associated with dominant surge (fore and aft) mode, surge damping SP Pole or zero complex pair associated with longitudinal short period mode VTOL Vertical takeoff and landing aircraft YD Pole or zero associated with dominant yaw mode, yaw dampin_ xi

LIST OFSYMBOLS

Lateral cyclic swashplate deflection A1 s Ae High frequency gain in @/SB transfer function High frequency gain in _/'8A transfer function High frequency gain in $_/8p transfer function i_ Longitudinal cyclic swashplate deflection B1 s C Longitudinal tip path plane deflection of stabilizer bar (UH-]H) d Lateral tip path plane deflection of stabilizer bar (UH-]H) g Gravity constant h Altitude, --z Altitude rate, -_ Moment of inertia about x-axis I x Moment of inertia cross product Ixz Moment of inertia about y-axis Iy Moment of inertia about z-axis I z

joo Imaginery component of s

K General representation of a pure gain Pilot gain Kp L Rolling moment Dimensional rolling moment derivative, (]/Ix)[_L/_ ( )]

T,( )

[L( ) + (Ixz/Ix)N)]/[] -- (I_z/Ixlz) ] m Vehicle mass M Pitching moment Dimensional pitching moment derivative, (]/ly)[_tM/_()]

)

xii

LIST OFSYMBOLS (Continued)

N Yawing moment

Dimensional yawing moment derivative, (]/Iz)[_N/_( )]

N( )

[N( ) + (Ixz/Iz)L()]/[] -- (l_z/Ixlz)]

Ni)

Transfer function numerator for perturbation of motion quantity, a due to control or gust input, b Angular rate P Rotary gust about earth fixed x-axis Pg Rotary gust about earth fixed y-axis qg Rotary gust about earth fixed z-axis rg t Time High frequency time constant in predominant hover pitching mode Tsp Low frequency root in @/_B (associated with surge damping) 1/To 1 High frequency root in @/8 B numerator (associated with heave ]/To 2 damp i ng) u Perturbation velocity component in body fixed x-axis Translational gust along earth fixed x-axis Ug v Perturbation velocity component in body fixed y-axis Translational gust along earth fixed y-axis Vg V True airspeed W Perturbation velocity component in body fixed z-axis Translational gust along earth fixed z-axis Wg X Translation along earth fixed x-axis x-force X Dimensional x-force derivative (]/m)[_X/_()]

x( )

xiii LIST OF SYMBOLS (Continued) Translatior_ along earth fixed y-axis

Y

Y

y-force

Dimensional y-foroederivative, (I/m)[_Y/_()]

Y( )

Controlled element transfer function Yc Pilot element transfer function Yp Translation along earth fixed z-axis_ _n Z z-force Dimensional z-force derivative, (]/m)[_Z/%()]

z( )

Perturbation angle of stabilizer bar with respect to mast in

%

mast-fixed axis system Perturbation angle of mast with respect to inertial reference CL m frame in mast fixed axis system Angle of sideslip 7 Lock Number Lateral cyclic stick deflection Longitudinal cyclic stick deflection Collective stick deflection _c Rudder pedal deflection Rotor blade pitch-flap coupling Determinant of open-loop characteristic equation 2x' Determinant of closed-loop characteristic equation E Rotor hinge offset ratio Damping ratio Pitch Euler ar_gle p Air density Real component of s xiv

LIST OFSYMBOLS (Concluded)

Effective control lag T C Effective pilot delay 1:e Roll Euler angle q_ Phase margin Yaw Euler angle CO Natural frequency Crossover frequency LD C Rotor system angular velocity 4 Phase angle 8ubecrlpts C Controlled elementj also command Crossfeed CF d Dutch roll Gust g Rotor mast axis system m Pilot element, also phugoid P Roll r s Spiral Short period sp X x-axis regulation y-axis regulation Y Z z-axis regulation e Pitch axis regulation Roll axis regulation cp Yaw axis regulation XV This volume presents a collection of closed-loop pilot-vehicle analyses based on the compiled helicopter handling qualities data presented in Volume One. The main purpose of this volume, in fact, is to serve as a guide to one use of the compiled data.

The approach taken utilizes elements of multiloop manual control theory with examples of representative helicopter vehicle dynamics to address important handling qualities aspects. In order to focus our efforts on a relevant application we are addressing handling qualities in the context of low-level, low-speed Army helicopter missions, especially in the nap- of-the-earth (NOE) environment.

The emphasis is distinctly on the method of analysis rather than on the specific numerical results obtained. While the basic data were obtained from each respective airframe manufacturer and therefore are presumably the best data available, certain inherent modeling limitations, nevertheless, are recognized. For example, all the data are based on a six-degrees-of- freedom set of equations of motion with quasi-static representation of the rotor tip path plane. While revealing some important cross coupling features, this form neglects short term control lag effects connected with the rotor degrees of freedom*. Where possible, flight test data have been used to qualify certain analytical results obtained. The general analytical approach, however, is not tied to a given level of mathematical complexity and could be used with higher-order models.

Use of a closed-loop pilot-vehicle analysis technique has allowed us to go considerably beyond the behavior of the strictly open-loop system which is demonstrated by the conventional bare airframe response modes.

Short term control lag effects associated with the rotor degrees of freedom can be included, to some extent, in the effective time delay which will be introduced subsequently in connection with the crossover model.

Our has been to look at handling characteristics in terms of what the

pilot perceives whenmanually controlling the helicopter. In doing so, we

concludethat including the pilot-in-the-loop doesnot necessarily intro-

duce complication but in some ways its inclusion tends to simplify the

systemanalyses, especially wheremultiple loops are involved.

For the most part the analysis methods used are not new. They have

beenborrowedfrom various applications to other vehicles and operating

conditions. Also, most of the features of helicopter flight dynamics

identified here havebeenwell knownfor sometime. The material presented

is a systematic description of multiloop analysis applied to several

examplesof cross-coupled helicopter vehicle dynamics. As a result a

numberof conclusions can be drawnregarding handling qualities metrics

and simulator modeling.

Themethodsfor performing multiloop analysis and the format used to

describe vehicle dynamicsare described in detail in Ref. I. Manualcontrol

theory ideas which served as a guide are summarized in Ref. 2. The reader

maywish to consult these two sourcesfor a general background.

In preparing this volumeonly a small portion of the compileddata

in VolumeOnewas used. In most cases only hover and 60 kt nominal loading

flight conditions were analyzed. At the sametime, an effort wasmadeto

search for interesting and significant features. Some of the items found

include an analytically pathological roll responseterdency at high rates

of climb and a point of maximum sensitivity to horizontal wind shear in

the low-speedrange.

Thereport is organized in a manner which divides handling qualities

aspects into well-defined groups. Following a general discussion of pilot

loop structure topics (Section II), the handling qualities features are

addressedaccording to inner-loop (attitude regulation) features (Section

III), outer-loop (position/velocity regulation)features (Section IV), and

gust disturbance effects (Section V). Vehicle stability and control

augmentationeffects are discussed in Section VI. Thereport endswith a

summary of conclusions and recommendations (Section VII). An appendix is

provided which summarizes transfer functions appropriate for viewing

specific handling features.

SECTION II

GENERAL PILOT-VEK_CLE LOOP STRUCTURE In the following pages we shall discuss the features of the pilot- vehicle loop structure to be used in the subsequent handling qualities analyses. In formulati_ this structure, we shall utilize results from the investigation of multiloop manual control theory in order to choose a pilot model of minimal complexity but at the same time to reveal important closed-loop handling features.

We begin by defining certain piloting objectives which help us to formulate an assumed piloting technique. Then we discuss features of the pilot model itself and especially its numerical definition. Other concepts useful in subsequent sections are also discussed including the use of constrained variables as a device for simplifying the multiloop system and identification and labeling of response modes.

A. PILOTING OBJECTIV_ In this study the piloting objectives are expressed so as to be relevant to low-level flight while at the same time recognizing the limitations of the helicopter mathematical model involved. In particular, we address nap-of-the-earth (NOE) operation which is defined in Ref. 3 as "flight as close to the earth's surface as vegetation or obstacles will permit 3 and generally following the contours of the earth." According to Ref. 4, much of the time in a typical NOE mission is spent in very slow flight or hover with occasional accelerations to higher speeds when dashing across open areas. When flying in close proximity to the ground, the pilot must be constantly aware of rotor clearance to obstacles and must be able to judge whether to go around, between, or over obstacles. While operations can take place during night and day conditions, essentially all visual informa- tion available to the pilot is from outside reference. Aural or vibrational cues, such as rotor rpm, may be used, but head-down cockpit reference is not involved.

Working within the context described above, our pilot-vehicle analyses involve only those state variables corresponding to outside visual reference, that is, attitudes defined in terms of body Euler angle rotations and translational components in terms of an earth-fixed reference system. The effects of varying airspeed are addressed, in general, by considering flight conditions at hover and 60 kt.

Pilot-vehicle analyses are applied in the context of short- to medium- term maneuvering and regulating operations of the helicopter. We exclude the long-term trimming or configuration change effects. Also, because of model limitations, we must limit the pilot's actions to use of basic flight controls and assume that the pilot is taking appropriate measures to regu- late rotor rpm effectively (in the model, rotor rpm is constant). In this context, the function of the pilot's basic flight control loop structure is to (1) stabilize and regulate attitudes and (2) regulate position (or velocity).

The attitude loop structure consists of roll, pitch, and, where applicable, yaw regulation. Such regulation can range from being highly precise to the point of merely staying right-side-up. We make certain assumption_ regarding precision of the attitude re_]ation depending upon the piloting task and the degree of simplification required. The loop structure con- nected with regulation of yaw depends upon whether we are considering a hover or forward flight condition. In hover, yaw must be regulated actively; while in higher speed forward flight, yaw regulation is unnecessary if directional (sideslip) stability is adequate. The aspects of inner loop regulation will be fully discussed in Section III.

Regulation of position or velocity constitutes the outer loop structure and must be addressed subsequent to applying appropriate inner loop regu- lation. The distinction between position and velocity regulation is crucial in terms of the degree of pilot compensation required. Naturally, position regulation refers most directly to near-hover conditions while velocity regulation is more appropriate to forward flight conditions. Outer loop re_]ation will be the subject of Section IV.

B0 ASS_D PI_OT_G TECHNIQUE In general, a normal helicopter piloting technique will be assumed, Pitch attitude controlled by longitudinal cyclic stick Roll attitude controlled by lateral cyclic stick Yaw controlled by rudder pedals (at low speeds) Longitudinal position or velocity controlled by commanded pitch attitude Lateral position or velocity controlled by commanded roll attitude Altitude or flight path angle controlled by collective stick.

This structure is depicted in block diagram form in Fig. II-1. It will be shown by a_lysis that the determining feature in closed-loop pilot- vehicle dynamics is the implicit loop structure itself rather than the explicit pilot gains and compensation. In other words, under certain conditions it is sufficient to recognize only the fact of active pilot regulation rather than the numerical value of a gain representing that regulation. This is not to say that specific features of the overall pilot loop structure will be neglected. We will, in fact, look at pilot compensation requirements and note where manual control difficulties could be expected. For the most part, though, pilot model complexities will be minimized in order to concentrate on airframe-related characteristics.

C. ASI_ECTS OY MULTIIDOP MANUAL CONTROL THEORY Our objective in applying manual control theory to helicopter vehicle dynamics is to reveal handling quality features in as realistic a way as possible. A secondary objective is to focus on individual aspects of handling qualities so as to separate potential handling qualities problems.

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The crossover model, as described in Ref. 5, is a guide to setting numerical values for closed-loop control system compensation, where the pilot is assumed to be the essential element of that compensation. We shall review the details of the crossover model shortly.

The successful extension of the crossover model to multiloop control situations is described in Ref. 2. In fact, we utilize direct experimental results from pertinent multiloop manual control experiments in order to set numerical values for pilot-in-the-loop features in the analyses to follow. These experimental data consist of the investigations reported in Refs. 6 through 10.

D. APPLIGATION OF THE CROSSOVER MDDEL It will be useful to review briefly the application of the crossover model to the manual control situation. The crossover model is described in detail in Ref. 11, but we can summarize the main points as follows.

First, consider the pilot-vehicle combination expressed in vector block diagram form according to Fig. II-2. The controlled element, Yc' is specified in terms of the helicopter mathematical model. Our task is to establish an appropriate pilot strategy, Yp; to do so we can utilize the so-called primary rule of thumb from Ref. 5: "At frequencies just within and beyond the input band- width, seek or create (by equalization) a fair stretch of - 20 dB/decade slope for the amplitude ratio and adjust the loop gain so as to put the unity-amplitude crossover frequency near the higher edge of this region, while maintaining adequate stability margins."

* Control action depends only on perceived errors in states -- precognitive actions and pursuit tracking (e.g., control crossfeeding) are not involved.

The name "crossover" refers to the frequency range of validity where the model's open-loop amplitude ratio "crosses over" unity.

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_ _ o,_ 4-_ o _ _ _ O O O n | O ,--I q) ._ o OJ 4_ o +s, I H H (1) (1) _J r_._ r._ _:_ In applying the primary rule of thumb it is convenient to have an established value for the desired crossover frequency, co . As mentioned c previously we shall rely heavily on observed crossover frequencies from the experimentally derived data previously referred to. For inner loop control we shall regard a reasonable level of regulation as having a crossover frequency range between ] and 2 rad/sec. For outer loops (position, velocity) we shall consider 0.2 to 0.5 rad/sec as an appropriate crossover frequency range. Any more preciseness in specifying loop tightness, fortunately, will be unnecessary.

We should add that the choice of crossover frequency cannot be completely arbitrary. If _ is too low then the closed-loop response of the regulated c state variable is sluggish and the disturbance error suppression ineffective.

On the other hand, if _c is too high, precision suffers from pilot-induced noise or remnant and, in the limit, system instability results. Even if ren_nt is low, then the system stability is limited by effective delays in the pilot and controlled elements. Methods for rationally determining _c are available as exemplified in Ref. 12, but this degree of sophistica- tion is considered unnecessary for our purposes. Hence, we ma_e use of experimentally determined _ 's.

C In addition to requiring a choice of crossover frequency, the crossover model also calls for an effective time delay, re, which is normally on the order of 0.3 sec for a purely visual compensatory task not requiring low- frequency lead compensation.* Based on the following sketch from Ref. 2, we can see that r e increases with increasing pilot lead, i.e., an increase in slope of Yp versus _ at the crossover frequency.

o _ 4-- (forcing function bandwldth _ssume_ sm_ll) o I L -20 0 20 40riB/dec -I 0 41 +2 Leod Units o I-_ j _c * The forcing function bandwidth is assumed to be much less than I rad/sec.

In the interest of maximizing mathematical simplicity we shall selectively include the effects of _ only where it is significant. Use of a six- e degree-of-freedom quasi-static model, of course, automatically sets a limit on the validity of our analyses in the high frequency range because rotor system lags are neglected.

Let us conclude our review of the crossover model by considering an example. Suppose that roll response due to lateral control is given by: = ___ = 1.2 (rad/in) (II-l)

Yc _A (s - 0.OT)(s + 1.5)

Mode Mode In order to achieve _cq 0 = 2 rad/sec, Yp would require first-order lead compensation at I .5 rad/sec because of the presence of the roll mode so as to make: _ e -Tes

(Iz-2)

YpYc s This implies that y A K (s + 1.5) e -Tes (II-3) P P and A +10 (11-4)

d _n(_)J Q)

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I0 Thus from the abovesketch, Te _ o.4 sec (11-5) and I .67 in.

= 1.2 =

The open-loop Bode plot of YpYc is shown in Fig. II-3 and two varieties of root locus plots (Bode root locus and conventional root locus) are shown in Figs. II-4 and II-5_ respectively. We would expect this to be an example of a good loop closure since (i) a generous amount of phase margin (approxi- mately )4 5 deg) exists at the assumed crossover frequency_ and (ii) a large amplitude ratio is present at low frequencies (nearly 30 db). The most direct impact on pilot opinion would probably be associated with the anti- cipation involved in the lead compensation, although the lead in this situation would have only a slight adverse effect according to the results presented in the following sketch from Ref. 2 for pilot rating decrement versus order of lead equalization.

I0 I 0 J I -20 0 20 40 riB/dec -I 0 +I +2 LeGd Units dlYplj] d in u) i_ c _.. tlSS07 A PURZ GAIN PILOT MDD_L The form of pilot compensation is a fundamental aspect of the closed- loop pilot-vehicle analysis described in this report. It is desirable to introduce the pilot in a way that will minimize added system complexity.

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_t '.D r_ 0,1 O _ II II I1 1 U _P4 O Strict use of the crossover model, however, forces consideration of a variety of pilot compensation possibilities in each loop thereby increasing system order and adding new variables.

We can avoid this increased complexity, though, by making use of a corollary of the crossover model w_hich can be stated as follows. First, it has been experimentally determined that all human operator loop closures lead to crossover-model-like characteristics, i.e., Yp is adjusted to make IYpYcl like IK/sl . Second, the lowest pilot workload seems to be imposed when Yc = K/s .* These two ideas taken together imply that the pilot desires to function with only pure gain compensation. Further, if a pure gain pilot cbmpensation cannot produce suitable closed-loop dynamics then a handling problem is indicated.

Hence, we shall use a pure gain pilot to explore various handling qualities features. If good closures cannot be produced using pure gain compensation then we can assume the pilot would have to adjust his strategy with the penalty of correspondingly higher workload. Most importantly, vehicle features which would force a departure from a pure gain can there- fore be considered as significant handling qualities features.

F. US_ OF OO_ST2AIN_ VASIAB_ Our approach to analyzing handling qualities relies heavily on the use of ideally constrained (i.e., perfectly regulated) variables for a number of reasons. The main advantage is that it greatly simplifies the mathemati- cal relationships while at the same time it retains important aspects of the full six-degree-of-freedom quasi-static vehicle model used here. Further, it enables us to dwell on the airframe features rather than to introduce an unnecessary number of pilot-related parameters.

The process of artificially constraining variables is an idealization of the pilot's role in each of the loops. For example, by constraining pitch attitude we mean to represent the essential results of a pilot (or autopilot) regulating pitch attitude. Historically, this technique was A "rate command" controlled element.

applied in the analysis of aircraft dynamics at an early stage (Refs. 13 and I 4) and is equally useful in the application considered here.

Prior to using constrained variable relationships we need to consider their limitations. This can be done in a general way, but we will only illustrate the general approach using heuristic examples. These examples will be adequate to show the nature of any limitations involved but will not detract from the main objectives of Section III and IV- to analyze aspects of inner loop and outer loop regulation in helicopters.

Three kinds of constrained variable relationships which are of interest include: • Direct commanded response • 0ff-axis cross coupling • Direct control response with off-axis regulation.

These are exemplified by (i) e/e c with e _5 B , (ii) _/Qc with G _SB, and (iii) e/5 B with _SA, respectively. Figure 11-6 shows corresponding block diagrams, and Table II-I indicates how well each is characterized by numerator ratios. The key to showing conditions of validity for constrained variable relationships is assumption of cross-over-model-like behavior in the pilot-vehicle, e.g., for 9 _5 B regulation in the region of crossover: YoN_B _ce ] - " _C°c9e -'_es -" (II-7) & s ( _e s ) s 1 +--_-- The implications of Table II-I are significant. First, in cases where we desire a reasonable approximation to commanded attitude response we can express it in terms of crossover model parameters, i.e., crossover frequency and effective delay. For example, assume _cQ = 1.5 rad/sec and T = 0.3 sec.

* _ +5 B signifies pitch attitude, Q, controlled by longitudinal cyclic, 5B .

I VEHICLE I I I I I i _I L a. Direct Commanded Response p..

I I I I VEHICLE I 8c Y8 I I t J b. 0ff-Axis Cross-Coupling I I I bB I ;- I VEHI C LE I I I I I I I I I L .I c. Direct Control Response with Off-Axis Regulation Figure 11-6. Examples of Closed-Loop Relationships (Block Diagrams)

TABLE II-I

EXAMPLES OFCLOSED LOOP RELATIONSHIPS

(Simplified Expres sions)

I DIRECT CO_9._q,'PDE2 RESPOI_SE OFF-AXIS CROSS COU_LING O_7-AXIS REGULATION I DIRECT CONTP_L RESPONSE WITH CLOSED-LOOP _ _ with q '_th u ---_5 B _ with e _t B QLL_¢TITY 6 c e c b B _SA LV_A C T = Y6 N_B RE IATIONB HZP Oc A ÷ Y_ NBB 6B A + Y _A " m, --Y NSA + I y,d N_'B Y_. N_ B B A REARRANGED EXpKESSION Y'e N_B I{_, A - ' I + -- + I :. ,6 N[Bh6 A + s 1 ---

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VALUE IN PSGION T e r a I - -_s _%._s - N [,BN,5 A .

8F CROSSOVER IZ IZeG CROSSOVER + I - S + MtDEL STJBS T! TJT IC, N" + I --2Zs + I _'e 2 (_ _e) _Cp ----- + 1 1 + "_S LOW f'P£ qb-ENC Y VALUE N% N_A • b_gnitude and shape of • Overall character given by • Time delay T e nu_erator ratio except where %//0 C response given by ntumer ator ratio • Undamped natural nratttal cross coupling product frequency is sig_lifice/%t, i.e., • Delay a/_.d response sazLe as ESSENTIAL for e/9 C L_B-_ A F EATLTLES I • Crossover model parameters are @ Dampir_z ratio ! higher order effects = - -- w

-)

* According to the crossover model: "e d_e_ ' ] - -r-s Y,_ N_ B We _e__eS ._ s A T e Yt N_A Ze- . :*c. 1 - -_-s i- and = S-_--e -_e_ s A then, o - 1 - o.1> s (ZT-8) Oc 0.1 s 2 + 0.52 s + I i.e., m n = 3.2 tad/see, _ = 0.82. Next, for cross-coupling characteristics we can use a simple numerator ratio in combination with the direct commanded response, or _% - _B 0 (zz-9)

o

Oc N B e Finally, off-axis regulation can be included in a direct control response transfer function such as @/_B by simply using the appropriate coupling numerator ratio. Thus to include the effects of roll regulation in the basic pitch response, -- "- (If-to) Hence, the off-axis control numerator becomes the transfer function denominator.

G. IDENTIFICATION AND IABELING OF EESPO_E MDDES It is frequently convenient to assign labels to dominant modes. Nor- really, there is little difficulty in doing so if longitudinal equations of motion are decoupled from lateral-directional ones. In the case of six degrees of freedom (or more) we must consider a more rigorous procedure for determining dominant modes. The following approach serves our purposes.

The method we shall use to identify response modes is based on the assumption of a conventional transfer function form for a closely related state variable-cockpit control combination, e.g., 8, and 5B. As long as the longitudinal-lateral-directional coupling is not too extreme, we know that the numerator-denominator combination should have an effective minimal degree of freedom form although it involves a number of approximately cancelling dipole factors. As an example, consider the OH-6A in hover: e -.74(0.02)* [- .03;0.5] (0.24) (0.9) (D.O) (II-11) = [0;0.4](2.0) [-.03;0.5](0.23)(0.8)(4.9) E ffe ctive Appr0ximately minimal cancelling dipole degree of factors freedom form The effective minimal degree of freedom form can be 6asily related to normal dominant modes. In the case above, the second order roots are clearly the phugoid, and the first order is pitch damping. All other denominator (poles) roots are nearly cancelled by respective numerator roots (zeros).

These other roots must be idemtified by considering appropriate transfer functions. For example, to identify roll damping we would use the _/6 A transfer function.

The following shorthand will be used to express polynomial factors: (a) _ (s + a) and [_,(o] _h= Is 2 + 2_cos + co 2] (II-12) 2O Mode label formulation is summarized in Table 11-2. In addition to considering basic open-loop denominator modes we also assign labels to certain numerator roots which ultimately become response modes in a closed- loop sense, e.g., surge (or speed) damping does become a response mode when pitch attitude is regulated. Also, we take the liberty of applying conventional labels in other than purely open-loop transfer functions.

For example, phugoid and pitch damping labels are used for denominator factors in the 0/5 B transfer function where roll and yaw are constrained.

This is convenient for keeping track of important response modes as loops in other axes are variously closed.

A note of caution- this procedure cannot be considered as exact nor does it always apply. In many cases response modes cannot be identified such as when the response deviates too far from the norm, when two modes are very close in numerical value, or when augmentation significantly changes the complexion of the pole-zero form.

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•. 'T "_

?1 o II U i b _ II _ Cu._ o .5 o ,_ _ ' H 041 r_l E_ C _ _ 0,--4 _" Pd _,,-_ c;6 _ v ° _ 0 0 o_ _ _._ _ cu o & _, 0 09 Oc_ 0J ii 0 I I H II II II II Jl ul Ii l_ 4_ ._eJv_ r_ II iI II II II ._ ° C _ >

;I

SECTION Ill LOOP _GD_A_Z0N A. BACEGROUND In this section we discuss how helicopter handling qualities related to inner loop regulation (roll_ pitch_ and yaw regulation) can be put in the context of the overall pilot-vehicle. To do so we treat inner loop aspects in terms of (I) primary control response and (2) cross coupling effects.

We shall show that primary control response features for a coupled longitudinal-lateral-directional system are_ in fac% essentially similar to the more conventional two- and three-degree-of-freedom descriptions (e.g._ as variously described in Refs. I, 15_ 16_ I% and 18). Our main task will be to reduce the apparent complexity of high order transfer functions coupled with multi-axis manual loop closures. One point of interest will be the effect of off-axis relation on each primary response mod% for exampl% the effect of roll attitude regulation on pitch attitude response.

In dealing more directly with cross-coupling effects 3 we exercise the six-degrees-of-freedom helicopter model combined with the pilot-in-the- loop. One aspect demonstrated is the variety of potential cross-coupling effects, and we propose a method for defining each in terms of an overall closed-loop metric which is devoid of an explicit numerical pilot descrip- tion.

B. PRIMARY CONTROL RESPONSE Primary control response for the inner loops refers specifically to: • Roll due to lateral cyclic stick_ 5A • Pitch due to longitudinal cyclic stick, 5B • Yaw due to rotary rudder pedal, 8p.

Each of these responses is expressed in terms of an Euler angle* and respective cockpit controller deflection.

In viewing any particular primary control response it will be important to de'_l effectively with the other two axes. That is to say, the primary response in one axis should be considered in the context of realistic regulation of the other axes. There are two compelling reasons for this: (i) There may be off-axis dominant modes which are lightly damped or even unstable which would unnecessarily complicate analysis of the primary axis.

(ii) Regulation of off-axis variables may alter the transfer function of the axis in question m its gain, poles, and zeros.

Among the following examples which exemplify the effects of off-axis regulation on primary pitch control response, we shall assume perfect regulation of roll attitude and yaw. This assumption permits the use of coupling numerator ratios to represent limiting values of the transfer function in Eq. III-1, i.e. : e I Ns_ + q_SB5 A + _I_5B5 p + zq0_l_SBSA5 p (III-1)

I

P -*-Sp with regulation of roll attitude and yaw defined by transfer functions Y_ and Y$_ respectively. Note that pitch response is simply (III-2) 5 B A without regulation of roll attitude and yaw (_ = Y_ = 0).

*The standard aircraft Euler angle set as described in Volume One.

with perfect roll attitude regulation but without yaw regulation (YT = O) NS_ 8 I _- 5B6ASP (iii-_) Finally, with perfect roll attitude and yaw regulation where Y_ and Y_ are the pilot's compensatory control actions in regulating roll and yaw. Accord- ing to Table II-I, the assumption of perfect roll axis regulation is valid if I -- (NsBNsA/NSB_ _ Q __I_A) is small in the frequency range of interest (say, approximately I rad/sec). Similarly, perfect yaw regulation is valid if I -- (N_ N_ /N_ N_ ) is small. We can give an indication, by example, of -u_ p -_ p how good are the perfect regulation assumptions.

As an example of the above let us consider the pitch attitude response of the OH-6A in hover. For a six-degrees-of-freedom quasi-static model the completely open loop pitch attitude-to-longitudinal cyclic control transfer function is:

o

-.737(o.oi 64) I(o.249)(o.892)(4.96)[-.o34;0.554]} (III-5) [0.001 ;0.408] (2.01) I(O. 229)(0.821 )(4.93) [- .028;0.51 2]} 5B A P PD HD YD R PL Dominant Approximately Pitch Response Cancelling Dipoles The various response modes have been identified and are labeled according to the procedure outlined previously. Note that the lateral phugoid mode is unstable and would remain so even with pitch attitude perfectly reg_ated.

(The pair of zeros corresponding to the lateral phugoid is also in the right half plane.) This lateral instability would not exist, however, with normal manual regulation of roll. Therefore, it is important to provide some degree of roll attitude regulation when describing pitch response.

If _erfect roll attitude regulation be implemented, then pitch response to longitudinal cyclic becomes: e_ e I - NSBSA : -.747(0.0161) I(0.253)(0.892)(0.0216)I (ZZI-6) 6B _ N_ A [-.008;0.395] (I .87) I(o.232)(o.812)(o.o216)I P PD HD YD LD J Dominant Approximately Pitch Response Cancelling Dipoles The lateral phugoid complex dipole pair disappears and a low frequency sway damping dipole emerges. But, more important to the pitch loop, the longitudinal phugiod is destabilized by the roll loop!

If we also consider yaw regulation, the pitch response to longitudinal cyclic is further altered. This is shown in the limiting case of perfect roll attitude and yaw regulation, i.e., N e _ G -.746(0.0148) I(0.340) (0.0218)I _ 5B$A6p (!II-7 ) 5B %¢ [-.12_;0.471 ](I .85)I(0.3_8) (0.0216) P PD HD LD Dominant Approximately Pitch Cancelling Response Dipoles Two things occur, the yaw damping mode disappears and the phugoid becomes even more unstable.

For the same case as was used in the previous examples, if Y_ and Y_ are defined as a pure gain corresponding to I rad/sec crossover frequency for roll and yaw, then: e -.737(0.016) I(0.333)(0.478)(6.28)(17.3)[0.2o3;1.11]} (111-8) 6B [-.196;0.462] (1.82) {(0.368)(0.464)(6.28)(12.3)[0.202;1.12]I P PD HD / Dominant Approximately Pitch Cancelling Response Dipoles Compare the dominant pitch response in Eq. III-8 with that in Eq. 111-7.

The same closed-loop features appear in the dominant pitch response as when perfect roll attitude and yaw regulation are assumed. The phugoid damping is destabilized and the pitch damping is reduced slightly.

To summarize, we have used an example of the pitch attitude response of the OH-6A in hover to illustrate that: Primary (pitch attitude) control response does vary with off-axis regulation.

The nature of variation in primary control response due to normal off-axis regulation can be indicated by assuming perfect off-axis regulation.

Assumption of perfect off-axis regulation, in fact, simplifies the primary control response transfer function by reducing transfer function order (effec- tively, stabilizing lightly damped or unstable off- axis dominant modes).

These results are motivation for looking at primary inner loop control response in the context of realistic manual off-axis regulation. Further, in creating this context, we have demonstrated that there is considerable advantage to assuming perfect off-axis regulation. Hence, these ideas are central to the analysis of primary control response for each of the three inner loop functions: pitch and roll attitude and yaw regulation.

In the following pages we do not dwell on handling qualities aspects related to the dominant response features. This is done in a comprehen- sive way in Ref. 16 for VTOL aircraft in general_ and specifically for helicopters in Refs. I_ and 19. The latter source contains a detailed discussion of the long standing helicopter handling qualities military specification (MIL-H-8_OIA, Ref. 20) in the context of the closed-loop pilot-vehicle. We do point out, however, those features of the five helicopters included in Volume One which are important to primary control response.

I. Piteh Axls The predominant features of pitch axis control for an unaugmented helicopter can be summarized in terms of the general form of the transfer function given in Section II, i.e., for hover, Approximately cancelling dipole factors SD HD

e Ae( ) l( )

e-TCS

]( )1( ) } (nz-9)

P PD tID for forward flight, Approximately cancelling _dipole factors SD HD e-TcS e Ae( )( ){ , } (III-lO)

[ ][ ]t

P SP *A transport delay function has been added to the above expressions to indicate the existence of some effective lag associated with rotor system tip path plane dynamics and control system dynamics which are_ of course, absent in the six-degrees-of-freedom quasi-static form employed here. A similar effect is involved in the other control transfer functions. For simplicity, however_ we shall omit this effective lag notation and absorb it in the pilot's effective delay_ _e" The above form is meant primarily as a guide to arranging the transfer function factors which are cataloged in Volume One and, if possible, assign- ing labels to those factors which are especially relevant to the pitch axis response. Although a separate form is shown for hover and forward flight, there is really a continuity between the two fornm, because the pitch damping and heave damping modes, usually two first-order roots in hover, do couple to form a classical short period mode as forward velocity is increased. We shall consider the bridge between hover and forward flight more thoroughly in Section VII.

a. Hovering Flight A survey of pitch axis response in hover for various helicopter examples with varying degrees of off-axis regulation is shown in Table III-1. This survey, as well as those to follow regarding other features, is meant primarily as an illustration of how the basic handling qualities data pre- sented in Volume One can be viewed, and is some indication of how the handling qualities features are likely to vary among several vehicles. In this table dominant transfer function factors are labeled where possible.

In the cases of the AH-IG and UH-IH, the normal classification of the factors does not apply well because of low levels of pitch damping and substantial cross-coupling effects with other axes. In the case of the CH-53D there is an example of the inability to discriminate between two modes which are nearly equal in value, i.e., yaw damping and heave damping. We shall see that the ability to apply classical mode labels to transfer function factors is sometimes a problem in other axes as well.

One aspect shown in Table III-1 is the effect of off-axis regulation, i.e., roll and yaw regulation, on the primary pitch response. Except for the BO-IO_ there is consistently a degradation of phngoid damping as roll and yaw loops are closed. For the OH-6A the largest source of degradation appears to be the yaw loop regulation; however, in the other three examples it is the roll loop which destabilizes the phugoid. Knowledge of how the off-axis regulation affects primary control response (in this case pitch) 8S I "Z. .

v I I '4 o i-4 E.-I _1 c_ _r • ° o i :s o : X< • 3 .Zi --: ca _._ H b_ _ -_ _ ,

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H

,£ff

e8 s_@ I H j_" q_ v I I I _ j'2_ ¸ _ _ o .

_a _,-,,._, B : _° _c _ _,_ _'_ o I o T _ t:_- _ T

i

I sq b I U_ _c "3" "T c: H -_ _ o H I--t • . .:,_, ._:s _7 0 _,G C :, > _ ,_

X_

I' I F3 is a direct benefit of the six-degrees-of-freedom model, i.e., coupled longitudinal-lateral-directional equations of motion. It is believed that additional information concerning such indirect cross-coupling effects would accrue from use of higher order equations of motion which included rotor flapping degrees of freedom, althot_gh the effects would likely be limited to the very short term effective control lag features. Data was not avail- able to verify this, however.

Closed-loop pitch attitude control has been analyzed in a number of earlier efforts (e.g., Refs. 15, 16, and 19). The cases considered here indicate that the classical form is still a valid way of viewing direct pitch response although there are effects from off-axis regulation. For the purposes of this report it is nevertheless useful to consider briefly pitch axis regulation in a closed-loop context. This can be done rela- tively easily if we rely on a pilot model consisting of a pure gain feed- back of pitch attitude to longitudinal cyclic control. The essential features of pitch attitude loop control in hover are summarized in Table 111-2 which shows that the important stability derivatives in the pitch loop are simply Mq and M u (and to a minor extent, Xu).

Note that the open-loop pitch response, without control lags, is approximately: e _B s -- - (III-11)

8B [s2_ _j(S_Mq)

P PD The accuracy of this approximation for the vehicles in Volume One is shown in Table III-3, i.e.: • The phugoid frequency, _p, is compared to _gMu/-M q • The pitch damping mode, I/TsP2, is compared to--Mq Where there is a fair level of pitch damping (e.g., OH-6A and BO-10_) the separation of modes is wide, and the approximations are good.

TABLE 111-2

ESSENTIAL FEATURES OFPITCH ATTITUDE CONTROL

IN HOVERING FLIGHT

TRA_NS FER FUNCTION: _B P PD APPROXIMATE FACTORS: M I A ____q + g u - -M 2M q TsP2 4 q 2 L gMu L -gMu

% - 1-/'_p2 Mq

2_,, - -x -M - 0

Dp_p u q Tsp 2 ._]_1. "- -X + _ XSB M - 0 Te 1 u M6B u A e = MSB 0d b- o,1 u_o O O o o .% ,% Cq E-I .r'-t ,--t ._ kD o_ t.cx O O t--4 .11 H o ,._ ..p O © O cH _..bCH i O O', co I-I O4 o_ o4 t.f'x t-4 t-4 O o o r_ oll v 4-_ O O O o ,,D '7 O o I.-I 4_ P_ o b- r_ .-,d- co rj o O o O 0 ,e...- ,e--

£

(D o .p © _ _ o _ r_ oj .t._ E-'t o-t !

For the helicopter examples considered, the phugoid frequency at hover falls within the range between 0.3 and 0.5 rad/sec. Thus, for the G/5 B transfer function to be like K/s, the pitch damping mode (hence --Mq) should be at least as large or somewhat greater than the desired crossover frequency, Wc_. This condition is met by the OH-6A and B0-I05 examples. In the remain- ing three cases the pitch damping is low, and it is not surprising that stability augmentation is employed by each.

A way of viewing the quality of the _/5 B response is to consider the phase margin in the region of crossover. According to experimental measure- ments, a phase margin of about 30 deg is usually present in the open-loop pilot-vehicle transfer function. Since the phugoid normally involves low damping, its phase contribution at I to 2 rad/sec is small. Thus, the approximate phase margin for a pure gain pilot is: "- tan- I --Mq (III-12) Wc8 If we use 30 deg phase margin as a rule of thumb for a minimum required level, then the required pitch damping must be: (III-13) --Mq _> 0.58 w% The combined effect of pilot delay and control lag can be added by assuming an effective delay, Te: --M (III-14) _M e " tan-1 _____ Wc8 _e_co This function is plotted in Fig. 111-I for a phase margin of 30 deg to show the approximate relative importance of pitch damping and combined delay.

The Ref. 20 requirement for pitch damping as shown in Fig. III-2 contrasts with the level of pitch damping required to allow the pilot to operate with pure gain compensation with I < Wc0 < 2 rad/sec and _m > 30 deg. The require- ment is a function of pitch moment of inertia. While it may be adequate for -Mq = Wce tan (_T/6 + r_c8) ¢.)

Minimum value Q.)

of neuromuscular delay assumed to /2 o" !

be .2 sec _ V ¢- °_ ¢L E C3 r- cJ ,.Ik.- Q.

.w I rad/sec o tj.Ic _ = IJJ

I

0 I I !

0 .I .2 .3 Effective Control and Pilot Lag, T e sec) Figure 111-I. Required Pitch Damping to Provide 30 deg Effective Phase Margin for a Given Control and Pilot Lag

MIL-H-8501A Requirement: _7

gM

> 8Ty ft-lb/rad/sec

gq -

-Mq

(I/sec)

I

O' 1 I

I00 I000 I0000 I0 _

Iy(slug-ft z)

Figure 111-2. Existing Pitch Damping Requirement small vehicles (e.g., OH-6A), it is clearly inadequate for larger ones. The level suggested in Ref. 21, i.e., -Mq > 2.5/sec, is more realistic; however, an important implication of Fig. III-I is that the level of pitch dampin_ required is tied to the amount of effective control la_ _resent.

In view of the importance of pitch damping, it is worthwhile to recall briefly the key factors which produce it, especially in connection with the vehicle examples considered here.

Reference 22 illustrates that, for those helicopters included in Volume One, the key rotor system parameters affecting rotary damping are flapping hinge offset, _, and blade Lock No., 7. Figure 111-3 shows a sketch of the relationships. Shaded areas indicate approximately where various rotor hub types are situated. In view of the parameters shown in Table 111-4, this qualitatively explains the large difference in Mq between the hingeless B0-I05 and teetering AH-IG and UH-IH. The difference between the articu- lated examples, OH-6A and CH-53D, can be traced to a combination of Lock No.

and vehicle size (inertia).

Hinge Offset,

O

O

Teetering

J

Hingeless

t-

"_ _ Lock NO., 7"

(Based on material from Ref. 2 2)

Figure III-3. Pitch Damping as a Function of Rotor Hinge Offset and Lock Number _o L_ o o

q E

o .rll o _q 0 kO o _D 4-) kO (D _q b.1 bD T.O .r-I o oJ o (D o -p (1) L_ © © E_ Irk l I.-I _.Q

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CO H * _ o © oh _D © .-d" OJ © (1) O

_P

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o _

o_ .p o .._

_ _ _o

4o 0 F_ © OJ 0 _ .-, _0 0 0 [_ D_ _ .,-I l © (i) bD _ _ 0 ,ii .r'l Given the background regarding the pitch control response and closed- loop pilot-vehicle aspects, we shall consider two hovering examples which span a fairly wide range of characteristics: • B0-I05 • AH- 1% SCAS off A Bode root locus is shown for each in Figs. III-4 and III-5. The most prominent difference is in the phase margin in the region of pitch attitude regulation which is primarily due to the disparity in pitch damping.

The phugoid is a prominent feature in both cases cited above. Note that as long as a_p is well below the region of crossover the phugoid is subject to bein_ effectively damped by closure of the pitc h loop. This implies that a direct upper limit might be placed on phugoid frequency to insure effec- tive damping with reasonable regulation of pitch attitude.

b. Forward Flight As forward velocity is increased the pitch attitude dynamics transition to those of a conventional airplane so long as the sign of Mw is negative.

According to Ref. I the m_in features of the pitch response in forward flight have the following dependency on airspeed:

_sp 2 _ Mqz w-v • _ (III-1_)

2_sp_sp - -- Zw -- Mq (III-16) 2 g MU (III-17)

% -

+V-- -Mq Z w M g u

+ .-- (Ill-18)

2_p "- - Xu 2

C%p I

I

II

i

o o .r-t

I I

,-t D [] 13 0 Q I"1 rl 1 I N r_ H I l

A

I I--4 H I-4 © ._-I o o

• o

o _ __

© !

• r-_ .

I !e + Io

I

q

Od El- M .M % 0 0 0 " bO .,-I [] ._ _,

\ /

++ _oo 0 .M

I I 1

I

[] El rl [] Iq _ 1 1 H N I !

M M H , _ _ © < -N

- - × (TII-I' )

Tel u I -" - Z (I11-20) T@2 w Thus, in forward flight we should expect to see: • Pitch damping and heave damping combining to form an overdamped short period • Increased phugoid frequency • Increased phugoid damping.

As shown in Table 111-5, the 60 kt pitch dyna_lics are characterized by a phugoid mode, not much different from that in hover, and a highly damped short period mode. As with the hover condition, the transfer function is composed of two parts -- one with dominant response poles and zeros, the other with approximately cancelling dipole factors (only the former is shown in Table 111-5).

In forward flight it is reasonable to assume only pitch and roll loops.

Yaw regulation is largely unnecessaryas we shall discuss shortly. For the reasons stated previously, perfect roll regulation is a valid assump- tion when considering the pitch response transfer function. (Again, the conditions for validity are stated in Table II-I.) For the 60 kt examples shown in Table 111-5 there are various effects of roll regulation. The most prevalent are increases in short period damping and decreases in phugoid damping.

The most important feature in each of the 60 kt pitch response transfer functions shown is that, compared to hover, there is a net increase in phase margin in the expected vicinity of crossover (I to 2 rad/sec). This can be deduced by inspection from the shift in the pole-zero combination involving short period and heave damping. The significance is that pitch attitude response in forward flight should be correspondingly less critical than in hover.

• _

_;._o

c_ -_ _°.I_

._ _

T'I_.

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o_

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_,j o _J t-- T -a_

• _ _

..

m

__ I_

According to the approximate factor relationships, pitch damping shows up as the prime differentiating feature in pitch response dynamics at the hover and 60 kt conditions considered. Figure III-6 shows that for a given vehicle the magnitude of pitch damping, Mq, does not vary significantly over the entire range of low speed flight conditions. Inspection of the data in Volume One also shows that Mq does not vary with vertical velocity or altitude.

c. Summar_ Prior to considering roll regulation, let us summarize the important features of the direct control response of the pitch axis with regard to the five helicopter examples: • The essential @/8 B controlled element features can be factored from a high order transfer function The essential features can be identified in conven- tional terms (e.g., phugoid, pitch damping, short period, etc.)

Approximate numerator ratios can be used to imbed off-axis regulation in the direct control response and, at the same time, to simplify the transfer function, i.e., __9 _._ B P in hover 5ASp

and in forward flight (111-21)

Sequentially constraining off-axes can produce second- order effects in primary control response features, e.g., for the AH-]G in hover, SCAS off, m vs

(l_l-_)

shows that roll regulation destabilizes the phugoid.

0 C)

o_

T, i

ooao_

0 rl

o _ a4, r_ .H -.o 0

0 0

o .H

<1

I H t---t H (1)

[]

-@<1 0

El

I

0 .I

0 rl

_r

I

I

In those examples considered, the prime differentiating feature in pitch control is pitch damping, i.e., -Mq.

2. Roll Axis The predominant features of the roll axis, just as in the pitch axis, can be summarized in terms of the general form of transfer function as given in Section Ii, i.e., for hover: Appr ox imat ely Cancelling Dipoles

I le oS

8A [ ]( )l 1 (III-23 PL R for forward flight, App r ox imat ely Cancelling Dipoles

I e- os

(ii1-24

S R a. Hovering Flight For hover, the form shown for roll response is the same as for pitch response. The primary factor differentiating roll and pitch derivatives in hover is the ratio of roll inertia to pitch inertia_ ix/ly. Hence_ M L' - q p ix_y ( III-29 -M L'v - ix_y (111-26 -MSB and L{A A ix_. Y (III-27)

_6

Therefore, there is a general increase in roll damping over pitch damping, little change in the phugoid, and the same angular rate sensitivity. If the roll response examples in Table 111-6 are compared with those in Table 111-I (pitch response), the above generalities hold fairly well except that the lateral phugoid frequency and damping tend to be slightly higher. The effects of other inner loop closures (pitch and yaw) are not as large for the roll axis as for the pitch axis.

The numerical requirements on damping should apply in roll as in pitch if the control lags and desired crossover frequency and phase margin are the same (as they are in the experimental data of Ref. 7). Thus, the same plot in Fig. 111-I could be used to describe required roll damping, I_.

However, Ref. 21 is in variance to this and suggests that a minimum level of roll damping be _/sec vs 2._/sec for pitch damping.

b. Forward Flight In forward flight the roll damping time constant remains and the lateral phugoid disappears and is replaced by a spiral mode. So long as the spiral mode is well below the roll crossover frequency range and the roll mode is above, then the controlled element will appear like K/s and will permit easy regulation.

Table 111-7 shows a survey of bare airframe roll dynamics at 60 kt for the five helicopters studied. The transfer functions themselves are all numerically similar to hover except for the disappearance of a lateral phugoid and emergence of a spiral mode.

Roll damping, the main determining factor in roll response is plotted as a function of airspeed in Fig. 111-7. Like pitch damping, it does not vary significantly for a given vehicle. The same is not necessarily true for varying vertical velocity, however.

Where the basic value of roll damping is low (as in the teetering rotor examples which include the AH-IG and UH-IH), there is a significant varia- tion of L_ with vertical velocity. This is illustrated in Fig. 111-8.

?

j u C_ t:,m' ,_ ,-H o I.-I E-t o I" -2 .... _ .8 "" _ ._ S__, _ 2 .

E-I .r O I" I" r,q H '-Z,r_ _ _ _, 4_ I % b;

_ _

E-I _ . _.i _

% I" I" Z ' t.2 P_ 4_ O _,, _ +_ o _ _ : ,_._ o ° rs_ a _ .2

,4

!

H I'_ 2, t.--I _ z2 c, -d

-)

I % n _:4 - -tl ,,t X C_2 _8 co v .p 0d b.0_H r_ ._.1__,"- _ O

d d

O E-I

,g

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H H m 0 _ I Lr_ I At some light weight conditions the roll damping stability derivative, _, even becomes positive. This is most apparent in the UH-IH and AH-IG data but the trend is apparent also in the OH-6A and B0-IO5 (all CH-53D flight conditions are level flight).

Roll response for varying vertical velocity was analyzed by considering the _/_A transfer function, first completely open loop, then with pitch attitude regulated. Three flight conditions were compared ranging from autorotation to level flight to maximum power climb, all at 60 kt, for the AH-IG aircraft with SCAS off. Table 111-8 shows tabulation of roll to lateral cyclic transfer functions for each of these cases. For the completely open-loop dynamics (first column) as rate of climb increases, dutch roll damping decreases and becomes approximately netural at maximum rate of climb. This trend can be observed in flight test data; however, what cannot be observed directly is a variation in coupling among the roll, spiral, and dutch roll modes. For level flight, the coupling is nearly zero, but for non-level flight the coupling takes on differing forms.

Figure 111-9 shows dutch roll root locus along with roll and spiral for various rates of climb_ h, based on the data from Volume One.

The pitch-regulated roll response in column 2 of Table 111-8 helps us to sort out the modes more easily. The same trends are visible in the roll, spiral, and dutch roll modes for increasing rate of climb, that is, the roll and spiral modes tend to become more coupled and the dutch roll less damped. The effect of pitch regulation on lateral-directional modes in general is to reduce dutch roll damping and to alter roll-spiral modes somewhat.

The implication of the high rate of climb effect on roll response is illustrated by the closed-loop step responses in Fig. 111-10. These show that for pure gain regulation of roll attitude in the presence of good pitch regulation there is no problem in level flight, but for maximum climb, a troublesome dutch roll oscillation is present. The deterioration of dutch roll damping with increased rate of climb is observable in the AH-IG, SCAB off according to the flight data presented in Ref. 26.

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5_

c. Summary Based on the analysis presented, the key points regarding roll control response are therefore: The predominant roll control response features and procedures for analyzing them are strongly analogous to those of the pitch axis.

The essential _/5 A controlled element features can be factored from a high order transfer function and identified in conventional terms (e.g., lateral phugoid, spiral, and roll damping).

Appropriate numerator ratios can be used to imbed the effects of off-axis regulation, but the impact of pitch on roll response is generally less than for roll on pitch response.

Roll damping, LS, is the prime differentiating feature in roll response among vehicles. Like pitch damping it is invariant with airspeed but, unlike pitch damping, does vary with vertical velocity.

3. Ya_ Regulation Yaw regulation through use of rudder pedals is required when sideslip stiffness is inadequate such as in hover or backward flight. In addition, yaw control is involved in providing turn coordination when needed.

The general form of the W/Sp transfer function varies somewhat depending on whether roll and pitch loops are closed. If we consider the case of roll and pitch inner loops closed, W/_p is relatively simple in form and allows some degree of insight, i.e., _r _ 0 5p " ©, ¢ N_SASB LD in hover (III-28) (o)( liD ( and in forward flight [ ] D Note that the numerator form is the same between hover and forward flight. The denominator also is actually the same form if we recognize it as the quadratic containing yaw damping, N' and sideslip stiffness, r' N_ (= VNv). This can be shown with a set of reduced equations of motion having only r and v degrees of freedom: (III-29)

I s- 'v rs Y ][i] IY ]If

Thus, ___ _-" NSp v

(III-3o)

P s Is2 --(N$ + Yv ) s + VN' + N' Y.]

V r V or, more simply, if we neglect small terms

N_ (s - Yv)

s Is 2-N_ s +VN_]

The last expression is instructive for it shows that the yaw control varies primarily as a function of airspeed to the extent that Nip , Yv' N_, and N$ are invariant which can be confirmed by inspection of the compiled data in Volume One.

The above form is useful in computing the relief from the need for yaw regulation as forward velocity is increased from a hover flight condition.

Consider the two root loci in Fig. III-11 for the second order portion of the _/Sp denominator, one corresponding to a pure gain regulation of _, and the other corresponding to a forward velocity-induced variation: V>O jo] jr.D \ \ \ VN' K N_p

\

\ \ Yaw Yaw Damping Damping

\

V<O X c<0 0 N' N' r r a, Pure Gain Regulation of b. Forward Velocity-Induced Oscillation Yaw Angle Root Loci for the Dutch Roll Figure 111-11.

These show an equivalence in terms of the effect on the _/Sp denominator T although not in terms of active yaw regulation (VNv represents active sideslip regulation rather than yaw angle regulation). Nevertheless, we can utilize this to compute the forward velocity for which active yaw regul_tion becomes unnecessary.

Assuming a pure gain pilot, we can directly estimate the K_ for a given crossover frequency, e%, according to:

_N_p

(III-3]) ] = YpYcl

s2 - N_s + Wv

S:j_ C or 2 2 + N r _c_ 2

)( )'

Hence, for hover:

2 + N,2 (III-33)

KsN_p & _c$ _c$ r Thus_ the forward velocity which yields the equivalent directional stiff- ness is: 2 N,2 _% % + r V A (III-34) N !

v Figure 111-12 shows a plot of sideslip stiffness, N_, versus airspeed, V, for the five helicopters studied. Superimposed are approximate levels of equivalent yaw regulation at hover. In the case of the 0H-6A a forward velocity of 22 kt provides a level of directional stability equivalent to a pilot-generated yaw crossover frequency equal to I rad/sec at hover.

Thus, if _c$ = I rad represented the desired level of yaw regulation, active regulation would be unnecessary above 22 kt. Note that the two examples having the lowest level of N_ utilize yaw stability augmentation (the effect of which willbe discussed in Section VI).

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A survey of approximate yaw control response in hover is shown in Table 111-9. A progression of off-axis regulation includes _/Sp with open loops, with e ---_ 5B, and finally with _ --_ 5A as well. One feature common to all cases is that heave damping appears coupled to yaw response.

This is most directly observable in the ?/Sp response with perfect C and reg_lation. In the case of the OH-6A ? ---_ 5 degrades heave damping and P in the UH-IH and AH-IG it enhances heave damping. In the case of the B0-I05 any effect is obscured because heave damping and yaw damping cannot be distinguished positively. Finally, in the CH-_3D we have an example of how off-axis regulation (_ --_ 5A) noticeably improves the predominant yaw response mode from about 0.3 rad/sec to 0.4 rad/sec.

The essential features of the yaw controlled element at hover or very low speeds are analogous to pitch and roll. That is, the controlled ele- ment in each case is like a K/s system which is bandwidth limited by the respective rate damping level. Thus, for yaw control to be good, yaw damping, i.e., N' should be commensurate with the desired crossover r' frequency range and whatever effective control lags are present.

Reference 21 suggests that the minimum yaw damping level for NOE operation be about 5/sec. While this would provide a good controlled element, it is in sharp contrast with the lower levels indicated by the data from Volume One.

C. CROSS COUPLING The term cross coupling can refer to a variety of specific features connected with helicopter dynamics. The limit on this variety is depen- dent only upon the model degrees of freedom. The features to be considered here, of course, fall within the range of a six-degrees-of-freedom quasi- static description, but the general approach could be applied to more complex systems.

Cross coupling can manifest itself in at least two ways. First, it can alter the direct primary control response by changing dominant mode characteristics. For exampl% in the preceding subsection, roll regula- tion was shown sometimes to affect dominant modes involved in pitch and

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yaw response. A second form of cross coupling is the direct production of unwanted motion from a given control or commanded motion. The most common example of this in a helicopter is the unwanted yawing motion due to a collective control input.

To a large extent we have addressed the first of the above coupling effects in Subsection B, for it is closely connected with direct control response itself. Therefore, in the following pages our attention will center on the "unwanted response" aspects of cross coupling. We shall address the procedures for computing it and demonstrate examples relevant to helicopter vehicles.

One way of systematically approaching the many kinds of cross coupling possibilities is to consider various motions resulting from various controls.

Ideally, a pure, direct motion should be produced from each of the four flight controls, i.e.: • Heave from collective • Pitch from longitudinal cyclic • Roll from lateral cyclic • Yaw from rudder _edais Table 111-10 shows how these four motions can be produced in ways other than from the respective direct control. Note that the desired level of cross coupling is not always zero, however. Good turn coordination, for example, requires that a yaw rate be produced for a given bank angle in the propor- tion of g/V. Also, vertical velocity due to pitch motion should be equal to V, especially where flight path is controlled by pitch attitude.

In the following pages we shall address three of the twelve interactions identified in Table 111-10. The first two include roll-due-to-pitch control and pitch-due-to-roll control and represent cross coupling phenomena which require for their description at least the complexity of a six-degree-of- freedom quasi-static model. It will be demonstrated that selected stability O O _1_> II I1 II

->1_o °

-_-IcD o-:_ O O l O i-q II II O I--I E-I O O O O C D E-_ 11 II II

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I-t H I--1 CDI_ CD I--:-_ t--I D_ o I_oCJ I-I _:> O O II II II i "_II cD "_l& .,el I-:> H C_ C; C_ -,-I ,-I 4_ O ,q .,-I b0 ,-q © 4_ -p O O O derivative parameters, while providing insight, do not completely describe important coupling effects. The third form of cross coupling we shall consider is uncoordinated yaw due to roll command. In this case multiloop effects are more easily reduced to a few key derivatives.

I. Pitch-Roll Cross Coupling We shall consider the mutual cross coupling effects between pitch and roll axes in the context of multiloop manual control. Thus, instead of viewing coupling terms of a control response, say q0/GB, let us look at coupling relative to a commanded response, i.e., _/e c. This will be not only more direct in terms of visually perceived relationships, but also mathematically simpler and more general.

To the extent that cross coupling does not meet the ideal levels shown in Table III-10, the pilot must minimize it through compensatory tracking or by utilizing appropriate pursuit control erossfeed paths. An example involving pitch regulation with roll cross coupling is shown in Fig. III-13.

Regardless of the pilot control strategy, the key transfer function to describing cross coupling is the appropriate modal response ratio. For example, for roll-due-to-pitch we would compute: - (III-35) 8 8 This expression is relevant to the compensatory tracking strategy because it represents the unwanted off-axis response which must be regulated out by the roll loop. In the pursuit crossfeed situation, the above numerator indicates the crossfeed required to minimize uncommanded roll. To see thisj consider the general transfer function for _/Oc: :D A Y "i VEHICLE + _B C u a. Compensatory Loop Structure Zero VEHICLE Ye c b. Compensatory Loop Structure _mith Pumsuit Crossfeed Figure 111-13. Block Diagrams Comparing Compensatory Loop Structures with and without Pursuit Crossfeed for Pitch and Roll Control For $/8 c to be zero, YsN_B (Iii-37) Yc f Y_SA But, according to the crossover model:

: s

(III-DS)

s YsN_B _c8 -Tee s and _ e (111-39) A s Substituting these into the crossfeed expression gives: °Jce N_B -(_es-Te_) (III-40) Ycf - _Ocq ) N_ e Note that the effective delays cancel, if Te8 = _e_.

If, in addition_ the pitch and roll loops were closed at the same cross- over frequency, then the pursuit crossfeed required to decouple the roll from pitch would be exactly: _B Ycf = - 7 (III-41)

NN

exactly For strictly compensatory tracking the level _/0 c cannot be made zero_ rather the effect is minimized depending upon the tightness of the roll loop. This can be shown by substituting crossover model functions into the general equation for q_/$c" For the sake of simplicity the effective delays can be neglected, without loss of generality, and reinstated later if desired; therefore:

(iiI-4a)

YGN_B _ _cG and

(III-43)

A S Thus: e N_B YoN_B N_ B A + + YQY_NSBSA ] + -- A A £ (III-44) or, after eliminating higher order effects ___ _ N_5 B c%(9 S

(III-%5)

Bandpass Filter Between _c_ and _c_ Note that for no active roll regulation (_c_ = O) the amount of _/9 c is exactly equal to the numerator ratio out to the pitch crossover frequency (as shown previously in Section II).

Again, the main point to be made is that for roll due to pitch the numerator ratio N_G_/N L describes the level of coupling which must be overcome regardless of the pilot's control strategy--whether purely compensatory or involving a pursuit crossfeed.

A general survey of cross coupling in terms of roll-due-to-pitch and pitch-due-to-roll was made for the various subject helicopters in order to search for consistent trends and to try to develop simple approximate factors relationships for this variety of cross coupling. Hover and 60 kt flight conditions were considered. The modal response ratios used as indicators were: 8c N_ B for forward flight (III-46) In hover, where yaw regulation must also be provided, we constrain _, thus: -% = _ for hover (111-47)

e¢

c NSBgp Similarly, for pitch-due-to-roll: for forward flight 8_ = (III-48)

_e e

for hover

hSp

By considering a time history corresponding to a unit step input_ we obtain a direct indication of the magnitude of unwanted roll excursion which must be countered by the pilot.

Figures III-14 and III-15 show step input time histories for the two varieties of coupling. This covers each subject helicopter at hover and 60 KT HOVER .4 OH-6A .2 .2 0 0 -2 -.2 .2 .2 BO- 105 I I 0 0 j -2 --.2 .4 .4 SCAS Off AH- IG

NO

NSA_p .2 AS Off _A_p STEP . CSCAS On ! I 0 0 .4 .4

//_ UH- I__.__HH

.2 .2 /_ _With Stabilizer Bor _ Stabilizer Bar _VVithout Stabilizer Bar / I __1 With Stabilizer Bar I 1 0 0 .4 .4 S Off CH-E3D .2 .2

o6 O0 _'_

2 4 t (sec) t (sec) Figure III-14. _c_9 Cross Coupling Effect 7O 60 KT HOVER t (sec) t {sec)/ 2 4 6 0 0 0 0 l I f I -.2 OH - 6A -2 -.4 -.4 BO- 105

f

0 I T , , 0 l I I f

_BB___2 OH - 6A

-2 - _ -2 N e V' BO- IO5 NSB I STEP 8BSp STEP -.4 - -.4 I 0 i I i 0 -2 - AH- IG -2 SCAS On / SCAS -4 On -.4 _/SCASOff I SCAS Off I I I i1 ' ' ' 0 - UH - I H -.2 SAS Off Without +_itizer Bar -4 er / , - Without Stabilizer Bar SAS On 0

@/' ' CH-53D =2 -2

_j_ SAS Off -.4 -4 Figure III-15. 0 -.-_-_ Cross Coupling Effect c 60 kt_ with and without augmentation.

For pitch-due-to-roll (qo c _ @) in Fig. 111-14: • Hover involves more coupling than 60 kt • The sense is nose up for right roll except for the BO- Io5 • Augmentation is effective in reducing the coupling.

For roll-due-to-pitch (_c -_ _) in Fig. III- 15: • 60 kt is worse than hover • The sense is left roll for nose up (again, except for the BO-I05) • Augmentation reduces coupling • The magnitude is generally larger than for pitch- due-to-roll.

The results obtained in the foregoing exercise are generally represen- tative of the respective main rotor designs involved. According to Ref. 22 the roll-due-to-pitch and pitch-due-to-roll depend upon various rotor system parameters discussed previously in connection with pitch damping. A sketch of the effects of hinge offset and Lock No. on important cross coupling stability derivatives is shown in Fig. III-16. Recall that the level of roll-due-to-pitch and pitch-due-to-roll ranged from one extreme with the teetering designs (UH-IH and AH-IG) through articulated (OH-6A and CH-53D) to the other extreme with a hingeless design (B0-705).

It is convenient to express the roll-due-to-pitch and pitch-due-to-roll in terms of appropriate stability derivative ratios as done in Ref. 22 For example, roll-due-to-pitch could be expressed in terms of:

Lp°rMq Lp

An alternative_ however# is to utilize the appropriate numerator ratio with some sacrifice in computational ease but with added value in terms of -J !

&.

O _r

k_ - Teetering

.J

ticulated

o.

O Q_ O &.

O

O! _geless

4--

"_Lock No., 7"

&.

r-

Hinge Offset, e

Figure 111-16. Sketch of How Key Rotor System Parameters Affect Inertial Cross Coupling (Based on Material From Ref. 22)

?3

pilot-vehicle effects. Figure 111-17 illustrates roll-due-to-pitch coupling as a function of airspeed using three parameters: • MSB Lq M L q P L • ---_ L P • Peak _ following a unit step e (with and without regulated), c Note that the two stability derivative-based parameters show a reasonable trend in the low speed range but do not reveal the extreme level of coupling in hover nor the increasing level of coupling at higher airspeeds.

The above is a demonstration of how cross coupling can be put in a multiloop manual control context such as _/e c or e/_ c . Key stability derivatives such as M and L' are used in a supporting role to indicate P q origins of the phenomena, but the derivatives themselves may not necessarily adequately describe the overall effect.

2. _ Coordlmmtlom Another form of cross coupling which we shall consider is turn coordina- tion or lack thereof. According to Ref. 2_ adverse yaw (turn coordination) can be especially detrimental to hOE operation if too extreme. In this variety of coupling it is possible to identify the potential problem source well enough to speclLlate on how it may arise for given rotor system designs_ particularly the hingeless variety.

None of the helicopter examples from Volume One exhibit significant adverse yaw, however, their characteristics are used to verify a simplified form of the closed loop transfer relationship.

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The closed loop dynamic response relationship considered most meani_4ful is _/_ since we have only to check how closely it equals g/V with use of roll and pitch controls only. Hence, the appropriate transfer function is:

(zII-50)

The above expression contains all the cross coupling effects among longitudinal, lateral, and directional axes describable by the basic six- degree-of-freedom model. In addition, it represents the pilot's crossfeed between roll and yaw loops if he were to apply manual coordination. (This is analogous to the pursuit crossfeeds of e/9 and e/_ modal response ratios discussed previously.) This is illustrated in the following block diagram: Yc where Ycf - s N_A_ B j (111-51) To gain insight we can solve for an approximation of _/_ using a simplified set of directional equations of motion similar to that introduced in the discussion of yaw control response, i.e., -0 g

o

V (III- 52) _A s(s-_{) -L, r -N' s s-N' p r The approximation is:

--g o

V __ . A

(II1-DD)

s 0 1

_A

-L_ I -L' r -N_ N_A/LgA s-N$

_gA s3 _gA_, 13

s -N'r s +N_ I N_A L_I << IN!_I (III-55)

if _AA

and ZoA r -- both are valid assumptions according to the data in Volume One. Equation III-5] can be further manipulated into the following useful form if N_ > 0_ l T ] T N; - (LSA/%a,L) < o _d (_ /L_)P -o: A . /_.

( N A)(s )()

i - L -7 a s+a

s N' + N r where g (III-57) Thus, the @/_ transfer function is composed of a high frequency gain equal to N_ - (NgA/LgA)L_, a non-minimum phase zero, a denominator consisting of the dutch roll approximation, and a low frequency gain equal to g/V. There- fore the magnitude of N_ - (NgA/LgA)L _ directly determines the adverse yaw excitation of dutch roll. If N_ -(NgA/LgA)L _ equaled g/V, an unlikely occurrence, then @/_ would be very nearly g/V in the dynamic sense. Let us consider, then, the composition of [71 - { _J J' ]_l :, _• _i:__ _A' p" First, let us view the adverse yaw in terms of unprimed derivatives, i.e._ N' NSA L 1 - N + -- L - L (III-58)

_ __ _z "gA

P L_A P P z p L_A p According to the compiled d&ta the first and third terms above are norn_lly small. It is the second term,(Ixz/Iz)Lp, which could be potentially trouble- some if the cross product of inertia and basic roll damping were both large.

The first condition is strictly a function of mass distribution, but the second one is heavily dependent on the rotor system design. We would expect L to be large for, say, hingeless rotors. It is not surprising, then, that P the adverse yaw problems encountered in the NOE flight tests reported in Ref. 2 5 involved a hingeless rotor helicopter. Unfortunately data describing inertial and roll damping characteristics were not available.

It is important to note that the B0-I05 hingeless rotor data compiled in Volume One did exhibit a very large L' but did not involve a non-zero P Ixz , therefore the adverse yaw characteristics of the modeled vehicle are probably unrealistically low.

A survey of the turn coordination of the various helicopters is shown in Fig. III-18. Time histories of _/_c are plotted for a step _0 c and an assumed roll crossover frequency of I rad/sec. The dashed line in each plot represents g/V • _/_c' i.e., perfect turn coordination. When the solid line is below the dashed line, inadequate turn rate (adverse yaw) is present and, conversely, when above it, excessive turn rate (proverse yaw).

Note that the AH-IG SCAS tends to produce worse adverse yaw than the bare airframe, but the CH-53D SAS produces perfect coordination. These features will be further discussed in Section VI.

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SECTION IV OUTER LOOP KEGULATION A. BACKGROUND In this section we shall explore the closed-loop dynamics of the outer manual control loops involving position or translational velocity.

The ability to control a vehicle's position in space or its flight path is an important factor in completion of its mission. The traditional handling qualities parameters that pertain to position and/or velocity control such as stable stick force characteristics with respect to velocity, positive effective dihedral (stable spiral), etc., are often parameters defined by static or open-loop vehicle characteristics. However, it is possible to view position 8rid/or velocity as the outer loops of our six- degrees-of-freedom model, and to evaluate the total dynamic and static characteristics for each case. The benefits to be gained by doing so are an increased understanding of the total vehicle response and a better understanding of the parameters which may affect the vehicle's response.

In segregating the six parameters of our model into inner (_ _, _) and outer (5, #, _) loops, we have to appreciate fully the impact of the inner loop closures on outer loop responses: that the basic modes of the outer loop responses are derived largely from the inner loop closures. Thus_ outer loop characteristics such as response time constants, steady state gains, and damping ratios, are strongly affected by inner loop closures.

In this study, many of the outer loop characteristics will be examined for the cases where inner loop regulation is assumed because it removes the complexities of pilot behavior while retaining the key vehicle-related characteristics.

B. PRI_ CONTROL RESPONSE According to the overall pilot-vehicle loop structure in Section II, the primary outer loop controls are:

• Collective stick for heave

• Pitch attitude for surge (or forward speed)

• Roll attitude for sway(or lateral flight path).

Weshall begin our discussion of these by developing a general expression

for outer loop responsegiven the regulation of inner loops with finite

bandwidth. This will be followed by specific applications to surge_ sway, andheave control.

The main objective in the following pages is to demonstratethe use of

appropriate numerator ratios in estimating outer loop control response.

Let us begin by considering the exampleof surge control (X/_c) for forward

flight specifically including the effects of pitch and roll regulation but

neglecting yawregulation.

I. Surge (Longitudinal) Control

The general expression for _/8 c can be written directly from the block diagram_ i.e.j _c _-_ <_ Yc

A I I

i

(iv-i)

C

After rearranging and expandingcoupling numerators, we have

° _n _B _c 0 _SBSA N_A @ A A NSB (IV-2) Under the conditions of weak cross coupling, i.e., (Iv-3)

%%

and Y_N_ B -N_SB_A A (IV-5) then @c a _ N_AI Y_ + -- A Notice that explicit terms involving q0 - 8A disappear_ and only @ -- 8 B terms remain. After substituting an appropriate crossover model approxi- mation such as (Y@N_B/A) - (:OcJS) (we can choose to neglect the effective delay :e_ since it is a high frequency effect) we have

x 4B_A I

(IV-6)

N_B_ for J<

Using a similar argument, if roll and yaw loops are closed: "m,

. B ASp

_t N_SB_AGP provided Isl <

<%+i)

(IV-?)

The foregoing is important because it essentially separates all inner loop features from outer loop ones except for the primary inner loop cross- over frequency (Wc@ in the case of X/_c)" Similar relationships can be developed for the other outer loops• 2. _way (Lateral) Control In the case of lateral position control: #e #0 NgA8 B I NSASB provided isi < We@ _A% (_+I) N_SA % (IV-8) or, with pitch and yaw loops: NYj0* provided ISl < Wc_ _c _qoo, -SASB8 p Pitch loop effects can usually be assumed negligible because they enter in the form of higher order effects as shown previously for the X/@c transfer function. Yaw regulation, however, may involve a less negligible cross coupling effect. It can be included, though, in a direct way:

_oSB+ I

8 _' 6p 5B_SASB yN_ a ] ICBA5BN5_o 5 B

(iV-lO)

_e BA6B_ + Y N_/ 3 \

+<)

Thus, to the extent that _ responds to rudder pedals, ? responds to lateral cyclic, and a yaw loop is closed, there will be a corresponding modification of the first order sway control response.

3. Heave Control Heave response due to collective control requires consideration of an inner pitch loop, i.e., N _ i e 5c + Ye NScSB c + Ye N_B e 1 • -- + _ i

e 1 N_NSc

8 i NSe8 B NGBN6 c (ZV-11) or, with _ and _ regulated

8_

+ and if pitch-heave coupling is low with collective and longitudinal cyclic controls, i.e., N 0 _ _ N _ _ Y << N 0 _ _ N_ _ _ (IV-15) 6c5A5 p 5BSA5 p _SBSA6p-Sc6ASp N z 0 _ i 6cgBSA6p (IV-14) then -- 1 provided Isl < Wc 0 5c NO _ * -_5A5 p C. ANALYSIS USINO APPROXIMATE FACTORS The expressions shown for outer loop primary control response appear more formidible than they really are, especially when approximately can- celling dipoles are omitted. For example, consider the AH-IG at 60 kt including SCAS effects. While seven first order roots and two second all approximately order roots are present in the denominator (N_A), they cancel except for the following:

. {B_A - -7.6(o.8_)[o.o2m.1] _ -32.3

_ e m - (o.oo7)(o.9o) (o.oo7) (TV-]5)

NSB5 A NbAbB 1 73[0.03;4.3] 31.4

- - " - (zv-16)

(o) -

_#. e cp nScSBSA - -14.4(0.009) ,_ -14.4 (IV-17) O q) (0.9)(0.007) - 6c NSB 6A The simplicity of the above expressions can be shown more formally by considering reduced order longitudinal-vertical and lateral-directional equations of motion, i.e., Longitudinal-Vertical Equations of Perturbed Motions -0 "-0 -0 (IV-18) (IV-I 9) 0 J SD HD

_Zw = (S-Xu)(S-Zw)

and

" = -g (s - zw)

(IV-20) -g 0 I HD Zc_ s - Zw -g whence (IV-21 )

(s - Xu)

SD SD Ni u Likewi s e _c "- (IV-22) = Z_c (s- xu) s-X -Z Z5 c _. Z5c whence (Iv-23)

- ; 5 c (s - Z w

HD Lateral-Directional Equations of Perturbed Motions V I _y (iv-2_) S - NrS + s v Y_ A or s-Y s D - N'Sr + N_ (Iv-as) and (IV-26) M 2 N' s s - s+N r whence (IV-27) s and, if _ is constrained _Y .__ g (zv-28) s -Y LD The accuracy of the above approximations is demonstrated in the survey of outer loop control characteristics shown in Table IV-I. Further, the validity over a range of forward velocities is shown in Table IV-2 using the OH-6A as an example.

a. Surge Re6ulation. The nature of outer loop regulation is easily shown using the foregoing relationships along with a crossover model for the inner loop regulation by the pilot. First, consider the surge loop.

T e I --_-s

x - -g iv-2q

e e s s -X u s +I +-_s The root locus is thus: \ Predominant low frequency surging + Xu T -_C8 - --

\

e motion is oscillatory and divergent . __ "_ce _k X T e Te u This sketch indicates that surge control is essentially a K/s 2 system in which the attitude loop tightness, represented by _cB , plays a relatively weak role. According to the root locus some degree of lead or velocity feedback is required for a stable loop closure as shown in the sketch. This lead requirement is effectively addressed by the extended crossover model described in Ref. 12 in which the parameter _ represents a lead compensation zero placement.

'l.c

• II °II °II IEx I (.)

H E-I e-.- I.-I P_ F_ E-I rj r_ 'T

°,S

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'K

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0 °K

i 4p.

'l_

r_ r.Q .II °If .n •I_ I_ c_ 9o .RIo.

'_ '1£

I°

s/o

----_ U:) Cl E.)

I--I E--t cO .-._, 0 o C.)

,-M "0

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'K ,.5

I21 v r.q Od I

I °

Od F ,._ cO

S_

£1o.

a 'K

o o

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°WI o -q3

jdD Predominant low frequency surging motion is oscillatory, but damped _ _2 _a_c9 _ c_ X _2 T e / U T e Low frequency lead equalization in surge must be supplied either by the pilot at great cost in workload or by automatic surge velocity-aided augmentation If velocity rather than position were being regulated as in forward flight, the controlled element would be more like K/s and the closed loop bandwidth would exhibit a stronger dependence on _ce , i.e., Te e _g I - .-.-_- s m (Iv-5o) The corresponding root locus is shown in the following sketch.

j_

/

Predominant surge \ / velocity perturba-k k moderate bandwidth _/ 2 X - _c@ T U -[ e e

According to Ref. 11 the difference betweenK/s2 and K/s(s+1) or K/s(s+2)

controlled elements (henceposition versus velocity) can amountto one or

two points on the Cooper-Harperrating scale.

b. Sway Re_tlation. The above discussion of longitudinal control

applies equally to lateral position and velocity control, since the respec- tive controlled elements for both axes are essentially the same in hovering flight. Hence, lateral position,

g(1

_y_ ._ 2 (Iv-51) _--_ 1 1 + 2 s (Iv-32) r with _ regulatio I y is like K/s 2.

Lateral velocity (also lateral flight path angle), s-_-s + I I + Te_ s c_ 2 is a K/s(s+1) or K/s(s+2) controlled element, and therefore somewhat easier to control than lateral position.

The x and y axes do not involve strong aerodynamic effects. Only X u and Yv appear explicitly, and they are both very small. For example Xu represents an inverse time constant for surge damping which is typically mnch less than the crossover frequency for x-axis regulation. Only in the z-axis does a significant vehicle aerodynamic effect appear.

c. Heave Regulation. From the simplified _/5 c transfer function we see that the heave damping, Zw predominates_ i.e., _. ._ Z6c 6 s - z (Iv-3_) c w According to Ref. 14 the value of Z in hover is inversely proportional w to the square root of disk loading*. As airspeed is increased heave damping grows as shown in Fig. IV-I for various helicopter examples.

The essential features of the manual pure gain compensation heave loop are shown in the following root locus sketch for: z ZSc

'- -

ICO // with effective time delay A / Heaving motion is very well damped / with bandwidth /

\

approaching -Z w X ! • Z w Note that the heave loop is primarily bandwidth-limited by Zw. This implies that a somewhat higher crossover frequency is possible for vertical position regulation than for horizontal position in either the x or y axis.

Ref. 14 indicates the Zw - O m GO O _ O [] CO i © _r © > t_ O I O cN O CI CIo<I --I O O O o TI I _H d. Surmnary. The outer loop control features which have been exposed by the application of multiloop analysis and interpretation by simplified pilot-vehicle equations of motion are summarized by the following: • Outer loop control characteristics can be effectively divorced from inner loop vehicle d_cs by use of appropriate numerator ratios.

• For x and y-axis regulation the controlled element is primarily like K/s 2 with the respective inner-loop crossover frequencies acting as effective control lags -- aerodynsm_ic effects (surge and sway damping) are neglible.

• For z-axis regulation the controlled element is bandwidth limited by heave damping, a characteristic determined mainly by disk loading and airspeed.

The helicopter examples considered demonstrate the relative invariance of outer loop control response which is suggested by the various generic approximations.

To a limited extent, outer loop regulation is aided by good inner loop control characteristics. For example, x-axis regulation benefits from a tight G loop which reduces the surge control lag and which, in turn, depends upon easy manual regulation of 9 or effective automatic regulation.

This indirect impact of inner loop control on x and y-axis outer loop control is the means by which current handling qualities specifications (MIL-H-8_OIA and MIL-F-83300) address outer loop control features. The weakness of purely aeroydnantic effects (surge and sway damping) appears to be acknowledged in the current specifications.

In the z-axis the very important aerodynamically-determined heave damping is subject to some variation due to disk loading. Unfortunately it too is not addressed by current handling specifications although it should be.

For operation in the NOE environment it may also be advisable to assess the need for explicit outer loop control requirements, namely, by specifying effective levels of augmented surge, sway, and heave damping. This could have the effect of imposing direct x, y, and z-force augmentation.

aE_T.O_ Y A. I_I_ODUCTIO_ The purpose of this section is to take advantage of the foregoing method of closed-loop pilot-vehicle analysis in order to expose some properties of coupled longitudinal-lateral-directional helicopter dynamics.

Two specific topics are considered. First, we shall explore the relative effects of individual gust components on each of the inner loop states.

This will reveal the nature of interactions between the normally partitioned longitudinal and lateral-directional dynamics. The second topic we consider is related to outer loop states. In particular, we treat the interaction of the pilot-vehicle combination with terrain-dependent disturbances and find that helicopters are susceptible to the disturbances under certain conditions.

The compiled data in Volume One contain gust numerators for flight conditions at hover and 60 kt forward flight. In addressing the two topics just mentioned we shall demonstrate the use of the gust numerators given.

Note that the compiled data are broken down into translational and rotary gust components. That is, the effects of qg and rg components are not imbedded in the u and v transfer functions as is traditionally done g g (e.g., Ref. I ). Therefore, it is unnecessary to apply the frozen field gust assumption (Ref. 27 ). This allows the introduction of rotary gusts at zero airspeed without a singularity appearing in gust numerators.

Another feature of the compiled data is that gust components are taken with respect to an earth-fixed reference frame, not the usual body-fiixed reference frame. This was believed to be of more general use in a low speed, low altitude environment especially where gusts can be terrain-dependent.

Presently there appears not to be a completely satisfactory gust model for nap-of-the-earth environment especially at or near hover. Nevertheless, the MIL-F-878_B turbulence model (Ref. 28 ) is frequently applied in this flight regime, and we shall make limited use of it here for the purpose of estimating the size of various gust components and their relative frequency content. In addition, we shall make use of simple deterministic gust inputs such as step translational gusts and step rotary gusts. The main objective in doing so will be to establish the important gust components in each of the inner and outer loops for a given vehicle and flight condition.

B. _ LOOP G_T _PO_E In the following pages we demonstrate the method for obtaining gust response relationships for the inner-loop regulated variables (pitch, roll, and yaw). This method is then applied to an example to investigate the gust sensitivity in low speed flight and especially the nature of axis cross coupling.

We begin by describing the insertion of pilot feedback loops, compute a set of gust transfer functions, then apply two kinds of gust inputs. In one case a random gust model is used to show rms motion excursions, in the other case step inputs are applied for each gust component. These results are correlated with stability derivatives to provide for a method of easily estimating significant gust components in each inner loop axis.

Computation of inner closed-loop gust responses can be accomplished by making the following assumptions: I. Outer loops are open (no position or velocity regulation).

2. Off-axis inner loops are perfectly regulated (e.g., in considering 8 response, _ and possibly _ are constrained).

3. A realistic pilot loop closure is adopted for regulation of the axis in question (e.g., for e response to gusts, assume a pure gain feedback of e _5 B at a given crossover frequency).

These steps, each of which was justified in previous sections, permit an easy formulation of a gust transfer function from the data presented in Volume One.

Consider an example. The 0H-6A open loop 8/ug transfer function in the presence of perfect roll and yaw regulation and without outer loop regulation (Steps I and 2 above) yields: ._ _U_6ASp = 0.0409(0)(0.022)(0.37) -3.27(0.022) (0.36) (I .85)[-.125;0.471 ]

F -

_ggqo,_ 5ASp LD HD PD P Note that this response is unstable. Clearly, any consideration of gust characteristics must account for the effects of the pilot to regulate divergent responses. This forces us to model the pilot's pitch attitude regulation. We shall assume that the effects of pilot compensation can be suitably modeled by a pure gain set for a I rad/sec crossover frequency.

This type of pilot model retains the basic features of a human pilot, while keeping the model simple enough to use without ambiguity. Thus, the closed loop e/Ug_ transfer function is:

N g ASp + ' ug JA p

l e _6 B Ye *'6B6ASpl = - I at s = J_ee = j I rad/sec I _T e _ I where N_A@Sp I Table V-I lists the gust transfer functions which result from assuming each primary axis to be closed by a pure gain at I rad/sec and the other two axes perfectly regulated.

By using the transfer functions of Table V-I and the gust power spectral density models of MIL-F-8785B, we can compute the rms gust responses which are shown in Table V-2 and determine the predominant gust components in each axis.

IO0 f _ % 0 o o -t- 99 o o ._ "&" , o.

0 _ _ 0 o o o o _" _ _" _" _" o o o 0 m _ o _ o 0 0 0 • o 0 I I 0 0 0 o u'N M3 0 .'-'- o_ _ _ o o _ _ o m_ o _ _ o o Ox o o o _ _ _ o b- _ 0 0 0 -g ed To o_ o 0_ _ o 0 i o 0 I _ I / H o ".g _0

C:; £

_0 O_ & 0 0 o So _ o = _, o o _ o 6 o _ o_ o _ s_ o. o o _ _% o o ,..-t bD O_ O _ _ I01 TABLE V-2 R_S GUST RESPONSE (MZL-F-8785B Dryden model applied to OH-6A in hover at 40 ft altitude, ou = 4.5 ft/sec and mean wind 10 ft_sec) COMPONENT

(deg) % (deg)

o .8 o .65 4.9 u g I .0 0.07 0.6 v g 0.05 0.5 I .2 g 2.o o .6 o .6 Pg o .5 I .3 o.I qg 0.02 0.2 1.9 r g Considering the translational gusts first, we see that B is most in- fluenced by Ug and Wg; _ by Vg; and _ by Ug. The only real surprise in this data is the large effect of u on _. For the rotary gusts, we see g that pg has a strong effect on _, 8, and _.

As an alternative to examining inner loop gust sensitivity by applying random gust inputs, a systematic application of deterministic gust inputs was also considered. The same example was used, i.e., the OH-6A in hover flight condition.

The procedure for viewing the response to deterministic gust inputs was to consider one inner loop axis at a time and to apply a unit step for each of the six gust components. For example, in the roll axis, pitch and yaw were assumed to be perfectly regulated and a I rad/sec crossover fre- quency was used for roll loop regulation. Time histories were then generated for the closed-loop _ response resulting from a I kt step input of Ug, Vg, and Wg, then a I kt per rotor diameter step in pg, qg, and rg. The same procedure was then applied to the pitch axis and finally to the yaw axis.

Results are plotted in Fig. V-I.

A third and much simpler way of estimating the significant gust compo- nents in each axis is to compare directly the appropriate stability deriva- tives. For example, the relative effect of Ug, Vg, and Wg on pitch attitude should be visible from the relative values of Mu, My, and Mw_ respectively.

The danger in using stability derivatives in the manner suggested is that axis transformations (body axis to earth axis) are not strictly accounted for, and the effects of predominant response modes are neglected.

Nevertheless, reasonably good agreement with the two previous methods is obtained. Table V-3 shows the relative magnitudes of gust response computed using random gusts, deterministic (step) gusts, and stability derivative ratios. Thus, any one of three methods could be used to determine the main gust component contributions for each axis.

1o3 @ OH-6A, hover • _ regulated at I rad/sec • 0 and ¢ constrained • I kt step input of Ug, Vg, and Wg (deg) I -"---'---5 -- I0 Time (see) u g a. 7 response to translational gust components Figure V-I. Attitude Response to Step Gust Inputs • OH-6A, hover • _i._ regulated at I rad/sec • S and ,_, constrained • I kt/rotor diameter step input of pg, qg, and rg Pg qg rg I 0 I Time (sec) b. _ response to rotary gust components Figure V-1 (Continued) • 0H-6A, hover • _ regulated at ] rad/sec • _ and T constrained • ] kt step input of Ug, Vg, and Wg 9 (deg) Time (sec) 5 10

\

v g u g c. _ response to translational _ust components Figure V-1 (Continued) Io6 • OH-6A, hover • e regulated at I rad/sec • _ and _ constrained • I kt/rotor diameter step input of qg, and r Pg' g e (deg)

/rg

I 5 I0 Time (sec) Pg d. e response to rotary gust components Figure V-I (Continued) _o7 • OH-6A, hover • _r regulated at I rad/sec • _ and q: constrained • I kt step input of Ug, Vg, and Wg u g 2O ( deg

\ 10

v Time (sec) g e. T response to translational gust components Figure V-I (Continued) lo8 • OH-6A, hover • W regulated at I rad/sec • 8 and _ constrained • I kt/rotor diameter step input of pg, qg, and rg I kt S _$.

_& 1 rotor dia.

(26.33 ft)

(deg)

Pg qg

I

IO 0 Time (sec) 5 f. _ response to rotary gust components Figure V-I (Concluded) I09

TABLE V-3

RELATIVE EFFECT OF INDIVIDUAL GUST COMPONENTS FOR RANDOM GUSTS/DETERMINISTIC (STEP) GUSTS/AND STABILITY DERIVATIVES (OH-6A, It)VER ) O ,¢

u o.1/--/-- _ I/I/I I/1/I

g v I/I/I 0.1/--/0,2 O. I/--/0. I g --/--/-- o. 7/0.3/0.

0.3/0.8/1.2 g

I/I/I o.Vo.3/o.2 o.3/o.V1.2

Pg

O. 2/0.3/0.2 I/I/I o.1/o.1/o.2

qg

r --/--lo.1 o.2/o.1/-- 1/I/I

g Each element shows the magnitude of motion for one gust component relative to the predominant gust component. The order of numerical entries in each element, set off by slant lines, is: Relative rms /Relative peak /Relative moment from stability from MIL-F-878_B/due to /derivatives corresponding model /step gust / to each element For the specific example considered, namely the 0H-6A in hover, the response to on-diagonal gust components is direct as expected. Significant off-diagonal results include: • Roll response due to qg • Pitch response due to pg • Yaw response due to ug, Wg, and pg.

In general, any given vehicle would require a survey to determine im- portant gust components for an individual axis. Based on the foregoing, however, such a survey could easily be conducted by a direct comparison of stability derivatives with reasonable assurance of success.

C. 0UTER IDOP GUBT F_P0_E In order to observe the effects of atmospheric disturbances on outer loop states it is necessary to stabilize inner loops suitably. And, in doing so we can develop simplified expressions for outer loop gust transfer fkuuctions in a manner similar to that used for expressing outer loop control response.

To illustrate the general approach for obtaining the essential outer loop gust response, consider heave motion due to a horizontal gust component with pitch attitude regulation: = Ug + Ye NSBUg Tggl N_ 0 _ e _5 B Z_ + Y0 N_B or, with the addition of _ and_ regulation: I I _ZO i_ G iV I n

N_B5 Al_p _g_A l_p/

5BSA' 8p t YoNSBMSA 15_ l +I

: _g_B_l _

N_B_AI_ p

i

if

NUg_AI5 p NSB_AISp <<NSBSAI5 p NUgSAI5 p

I I I I

This applies similarly to _/Wg if we replace Ug with Wg numerators. Further, _/Ug, _/Wg, and #/Vg transfer function relationships can also be so inferred and are listed in Appendix A.

It is advantageous to express the simplified longitudinal and lateral equations of motion to reveal generic properties and to compare with the complete quasi-static six-degree-of-freedom transfer functions. Following the form_ used in Section IV, we can write: * If yaw regulation is not involved, the vertical dashed line partitions the _-constrained numerators from the y-constrained numerators.

I12 Longitudinal-Vertical EQuations of Perturbed Motion Wg -O S-Xu or A -

= (s_x)(s_z )

-Z s-Z u w -'0 u

= -x(s_z I

-Z s-Z u 0 0 = 0 -Z s-Z _g w s-X -X 11 U -Z -Z u u s-X O u

: _z (s_x)

-Z -Z u and, -X

_B_Altp

I

"0 I

" 0 NSB_AI _p

I

_ u i -Z s

N_B_Altp

I

- W • _g g

I

Lateral-Directional EQuations of Perturbed Motion = _ y

s(s_ N')r

v and ± - .

Vg s 2 - N'r s + N _,6ASBI6p

I

Based on the relative magnitudes of predominant stability derivatives, the two major outer loop disturbance transfer functions in the above list are: and u w g g The first of these is of particular interest because of the relative importance of height re@_]ation and the likelihood of strong Ug gust or shear components when near the ground. In fac% a significant degree of CS_l contri- _/Ug sensitivity occurs in a critical range of airspeeds which bute to an adverse pilot-vehicle-gust interaction.

Reference 29 describes a hypothetical situation for CTOL aircraft flying in an altitude-dependent wind shear where a significant level of destabilization can occur in closed-loop flight path response modes. The relationships are shown in block diagram form in Fig. V-2. A direct analogy can be made for a helicopter operating at low altitudes where a terrain-dependent wind shear can occur from the wind shadowing effect of trees or other obstacles.

A simple example of pilot-vehicle-gust interaction is shown in Fig. V-3. We consider a helicopter hovering in a spatially-dependent wind consisting of a linear shear with altitude. If the pilot is simply regulating his height_

o

H H E-_

I

I

[a r.D -p Bq > ,-t

%

-r-I o

S

o tH

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Ed oo _.) r.D F=a E-_ P.

B

q:ff

B

_o

,-'4 ca_ I > .,-I

_° i

_o

h

BLOCK DIAGRAM PILOT-VEHICLE u Z g U WIND_uSHEAR _h ROOT LOCUS jcD _u I I / -_h (_okt_-_) e Te l

\

10 20 30 X q I --" f -.4 -.2 .2 .4 o (_ad/s_c) Figure V-3. Hover in a Spatially-Dependent Wind Z h u u g where 1/T01 and I/T02 are the closed loop pilot-vehicle modes dominant in surge and heave, respectively.

The wind shear can act to modify the pilot-vehicle stability as shown in the block diagram and root locus plot of Fig. V-3. Note that the stability derivative Z combines with the wind shear gradient 8u/Sh to produce a u divergence -- a feature which can be directly associated with additional pilot workload.

Several factors make the above example interesting: • The value of Z is most critical for helicopters u (approximately -0.2/sec in magnitude) at airspeeds of 20 to 30 kt as shown in Fig. V-4 • The critical shear corresponds to a headwind decreasing with altitude • A shear such as this can be found in the altitude segment between the ground and the top of a canopy formed by trees as indicated by wind tunnel velocity profile measurements from Ref. 30.

cd o _ El r_ c_ r._

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o o c_ .,-4 > cd

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t'N n Oo I o-_0 I I N 8ETION V_ AUGMENTATION SYST_4S Of the five vehicles included in the data compilation in Volume One, three employ forms of stability and control augmentation systems. The examples involved span the range of complexity from a simple mechanical, two-axis stability augmentor (UH-IH stabilizer bar) to a three-axis ele- tronic rate and attitude feedback with command augmentation and turn coordination (CH-_3D). A system having an intermediate degree of com- plexity involves angular rate damping about three axes with command augmentation (AH-IG). In the following pages we shall describe each of the three examples in order of their increasing complexity. Then, we shall briefly examine how each augmentation system example influences the basic handling qualities by considering the inner loop and outer loop relation- ships as described previously in Sections III and IV.

A. B_TIM3D_C_PTIO_ Each of the three augmentation systems is described in Volume One by a system block diagram and each was implemented in the equations of motion accordingly. Some additional discussion of important features, however, will aid in our examination of resulting handling qualities.

I. UH-IH Stabilizer Bar The stabilizer bar employed by the UH-IH is a mechanical stability augmentor which operates at all times. As described in Ref. 1 7 the Bell stabilizer bar is pivoted to the rotor shaft and coupled with a viscous da_per. Gyroscopic, inertial, and damping torques are involved, but only the last two directly determine feedback angles to the main rotor feather- ing controls.

A derivation of stabilizer bar equations of motion is given in Table VI-I. From this, it is apparent that the stabilizer bar senses pitch and roll rates relative to the main rotor shaft axis, and that by gearing the 4J o _H _ % f'_ 0 o O O 4_ _ ,--I _ N 4._ _ N O O + 4_ _ ,c_ O °,-I _ O _ ,--t o ,_ 04J O ._ N 'd r/l ,13 % "_; II g O_ _]II _]II ._II _II o O d ct_ o .el ¢ .... °.o.... ......... °°..°° ......

H O3 o "T H _ e 1::I _ o O _ -._ + 0 _ _ o _ _ _ -- _ ._ :_ ,, _ + °° % + % . o + • II • II _) % _ od 4-_ _ IE--, + _ E--t • II • II _. •

r "1 _ _ ,_ o o

i _ I[--' + _ eJIE_ _ 4- + ? .

._ oi# oi_ _

o

_._ _2

4* @ II II ,d o o "T H > 4- g_ 0 m • , _I [_ ,_ _, , _ _ :, , II II ._ + + o + _ t_ _ "_ _> _'mJ 1E-_ + b.1 _I['_ <_I_ _11 _ + _o _ ' "° 5 _'_ + _

_ _ o _

o. _ _ _

stabilizer bar directly to main rotor feathering controls, rate feedback can be effected. Finally, the lag in rate feedback can be adjusted by the time constant in viscous damping between the main rotor shaft and stabilizer bar.

The stabilizer bar equations of motion involve high frequency d_cs and some pitch-roll cross coupling. These effects, however, are clearly negligible within the constraints of this study. For the normal 324 rpm of the UH-IH rotor, the natural frequency of the oseillatory mode occurs far outside our range of interest at 69 rad/sec. The cross coupling is small compared to the direct feedback effect as shown by the following stabilizer bar tip path plane modal response ratio: d -2_s - -.015 s ± o (vz-4) c (3s+I) In analyzing the effects of the stabilizer bar feedback it is conven- ient to take advantage of closed loop analysis methods, especially where high order equations of motion are involved. For example, to examine the effects of the pitch augmentation loop (qm+B1s) on the pilot's pitch response we shall use the following: (vz-5) + _,B1s6A6p where Yqm is the stabilizer bar feedback compensation, ZkB1/qm. This minimizes complication of lateral-directional effects. One further simplifying step is to recognize that qm = _ and B1s = K 5B. Hence: 0 am o,, _Is --" = o (vl-6) and

o.. = Ks

In other words_ only the 8/_ B denominator is modified, and we can make direct use of the tabulated transfer function data in Volume One. The roll axis is analogous.

The effect of the stabilizer bar can be demonstrated by considering each According to the relationships stated above in Eq. VI-6, response in hover.

Eq. VI-5 becomes: =0 __8 - (VI-7) Thus, the 8/5 B numerator is unchanged, but the denominator does vary.

The following root locus shows how the denominator is modified by the stabilizer bar: I /Oscillatory i _short term I mode 1 Phugoid Damped _X V phug°id k \y A Pitch Stabilizer Speed Damping Bar Time Damping Constant

The phugoid is stabilized by the washout and speed damping zeros, the pitch dsmrping mode couples with the stabilizer bar pole and becomes oscillatory.

This general trend occurs in both pitch and roll axes and for hover and forward flight conditions. We shall consider specific results shortly in Section VI.B.

The basic feedback loops involved in the pitch and roll axes can be rearranged from Volume One to the following forms shown in Fig. VI-I.

The stabilizer bar provides a lagged angular rate feedback_ or alternatively, a washed-out attitude feedback. Because of the relatively large time con- stant (3 sec) the latter interpretation is perhaps more meaningful.

2, AH-IG SCAB The AH-I G SCAS involves angular rate feedback and control feedforward about all three axes. The nature of compensation, however, varies among the axes.

a. Pitch Axis. The pitch axis involves feedback and feedforward loops as shown in Volume One. The feedback consists of a pitch rate-to-longitudinal cyclic path which is compensated to emphasize the mid-frequency region near 0.4 rad/sec, i.e., BI s

t

- K (0.42)(0 q Hence, the system augments the basic vehicle pitch damping which, in hover, • Increases the frequency of the pitch damping mode • Decreases the frequency of the phugoid mode • Increases the damping of the phugoid mode.

This is shown in the following comparison of the SCAS off and SCAS on 12p LONGITUDINAL BARE AIRFRAME _- 8 (deg) 5 B (in.) --_ S TAB I LIZERBAR I LATERAL AIRFRAME 6 A (in.) ----_ q) (deg) 0.104(0) STABILIZER BAR I (o.33) Figure VI-I. Approximate Equivalent Feedback Loops for UH-1H Stabilizer Bar Pitch Response in Hoverin_ Flight: SCAS Off: SD HI) -.I 46(-.001 )(0.39) - [-.43;0.28] [0.90 ;0.47] (VI-9) P HD PD SCAS On: From Feedforward SD /Compe_tion -.146(-.001 ) (0.07) (0_ (2.6) (VI-10) [-.16;O.1p 3] (O_26)(O_)(OHD ._)(2.5) From Feedback Compensation The Bode root locus plot for each condition is shown in Figs. VI-2 and VI-3.

Note that the net favorable effect of the longitudinal SCAS is to separate phugoid and pitch damping modes and to create a controlled element more nearly like K/s.

In forward flight the AH-IG pitch SCAS also augments pitch dsmrping and produces the same general effects as in hover. In fac% the effect of the SCAS on pitch response in forward flight is nearly identical numerically to that of the hover condition. (Cf. Eq. VI-12 with VI-IO.)

Pitch Response in Forward Flight at 60 kt: SCAS Off: SD HI) (VI-11) "- [- .15;0.32] [0.84;0.79] I -.16(0.01 )(0.91 ) 5B qo p SP SCAS On:

_

(VI-12) [-.04;0.14] (0.26)(0.68)(I .2) -H _D .H ID _0 o I

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_29 b. Roll Axis. The AH-IG roll axis SCAS, as in the pitch axis, involves feedforward and feedback loops. There is an important difference, however, in the form of feedback compensation, i.e., a low frequency washout.

A_s : K (0)(3.6) (v_-13)

p (0.37)(I)

The result is that, in hover, the lateral phugoid is not improved; in fact, it is slightly degraded. But, the ability to damp manually the lateral phugoid remains effective and, most importantly, roll phase margin is im- proved in the region of crossover as shown in the comparative roll response Bode root locu_ plots in Figs. VI-4 and VI-5.

In forward flight the lateral SCAS provides the same controlled element as in hover, just as did the pitch SCAS.

Roll Response in Hover; SCAS On:

. o._(o)(o.o6)(_.7_)

_L (VI-14) [- .28;0 .I9] (0. I5)[0.79;3.3]

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8,# SCAS On: Roll Response at 60 kt;

I . o.48(o)(o.o6)(_.<5)

5_A e,* [-.28;0.19](0.19)[0.79;3.3] c. Yaw Axis. The AH-IG yaw axis SCAS is similar in form to the pitch and roll axes with a combination of feedforward command augmentation, feedback stability augmentation. The feedback loop in the yaw axis consists of compensation which is very nearly a washout followed by a lag.

8T___R = K (0.04)(3.3) (VI-16) r (0.94)(0.59) o % o o !

H .,-t

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i --_ < The effect of the yaw SCAS is to augraent the yaw damping from approxi- mately 0.5 rad/sec to over 2 rad/sec. At forward velocities the yaw SCAS follows the pattern of the other two axes in that the essential features of the response remain relatively unchanged from that of the hover flight conditions.

Yaw Response in Hover: SCAS Off:

-.83(o.o2)(o.39) -.8

(VI-17) (0)(0.07)[0.99;0.45] - (0)(0.5) SCAS On:

. -.83(o.o2)(o.o8)(4) = -.8(4)

(VI-18) (0)[0.84;0.05][0.64;2.3] (0)[0.64,2.3] Yaw Response at 60 kt: SCAS On: -.96(o.q8)(4) (VI-19) [0.63;0.27][0.63;2.7]

3. c_-_3DSAS

The CH-53D employs a number of augmentation devices. In hover the aircraft is attitude-stabilized with velocity-command-like control in all translational axes. At forward speeds of 60 kt and above, attitude stabilization remains effective, except during l_teral maneuvering, at which time roll attitude feedback is dropped and a turn coordination system is activated.

a. Pitch Axis. The pitch SAS consists of a pitch attitude feedback

loop with lead compensation and a longitudinal cyclic stick feedforwmrd loop. Pitch damping is not provided by an angular rate feedback of q; rather_ an Euler angle rate, G, is used. This otherwise avoids a pitch axis error signal in a steady turn. The net result of the 8 and 0 feed- back is to damp the phugoid effectively and to hold pitch attitude. Thus, the pilot is relieved of active inner loop regulation in longitudinal control of the vehicle. As we shall see shortly, the longitudinal cyclic stick with SAS on is essentially a velocity-command control.

b. Roll Axis. The roll SAS provides roll rate damping and roll attitude stabilization in hover and when the pilot's feet are off the pedals at airspeeds above 60 kt. If the pilot's feet are on the pedals above 60 kt, the roll attitude feedback is anulled, and the conventional roll rate damping remains effective.

At low speeds where roll attitude is stabilized, the lateral cyclic stick is essentially a #-command control just as longitudinal cyclic is an i-commmnd control.

c. Yaw Axis. The yaw SAS contains elements to: @ Increase yaw damping • Coordinate turns above 60 kt • Hold heading (except when the pilot's feet are on the pedals).

The first two items are reflected in the compiled data; the third is not because the pilot's feet are assumed to be on the rudder pedals, i.e., that he is actively maneuvering laterally.

Yaw damping is provided by washed out yaw rate. Turn coordination, when active, involves roll rate and lateral specific force feedbacks. Note that the roll rate feedback, in effect, augments the derivative N' in such P a sense as to counteract adverse yaw:

- :-.o81 : o.32 (I/sec)

1 34 The a feedback yaws the vehicle so as to eliminate any residual lateral Y specific force.

B. n_EC_ ON HANDliNG The effect of augmentation systems on the various aspects of handling qualities can be observed by applying the identical multiloop analysis procedures outlined in Sections III, IV, and V. Specifically, we can utilize the same transfer function relationships along with appropriate loop constraints in order to examine direct control response, cross- coupling effects, and gust response in both inner and outer loops. In the following pages the comparative effects on roll axis dynazLics are discussed for the three augmented vehicles.

Table VI-2 lists the direct roll attitude response for the augmented helicopters in hovering flight. The responses in this table can be compared directly to corresponding un_ugmented cases in Table III-6. Some of the important features shown in Table VI-2 are: • Additional modes are evident which can be attributed to the dyrmm_cs of the augmentation systems (these are identified_ where possibl% by the label "A").

• Regulation of pitch and yaw axes has an effect on predominant roll modes in the case of the AH-IG and UH-IH (where attitude stabilization is not involved).

• Regulation of pitch and yaw axes does not have a significant impact on the roll response of the CH-53D.

The Bode root locus plots in Figs. VI-6 through VI-9 further illustrate roll response features and compare cases with and without augmentation devices. The following discussion considers each vehicle separately.

1 , A_IG The SCAS shifts the phugoid to a lower frequency and increases the effective roll damping. Recall from the discussion in Section III.B.I and III.B.2 that such features help to facilitate good attitude regulation.

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a. UE-IH The stabilizer bar significantly alters roll response by (i) damping the lateral phugoid and (ii) coupling the roll damping mode with a stabilizer bar mode. The resulting Bode root locus plot shown in Fig. VI-7 depicts a low frequency drooping tendency in amplitude ratio which ordinarily would aggrevate regulation. The degree of the problem is suspected to be some- what less in the actual vehicle than in the mathematical model, however.

According to the measured vehicle characteristics reported in Ref. 29 the control derivative L'AI (or L_A ) is approximately 75_0 of that modeled s here. Hence, the high frequency osci_atory mode would be slightly better damped (_ " 0.3_) and at a slightly lower natural frequency (_ " I .4 rad/sec).

Correspondingly less compensation would be required; therefore, the drooping tendency in amplitude ratio would be less. The same rationale would apply to the pitch axis dynamics which suffer a low frequency droop also.

Regardless of the problem cited, the stabilizer bar is beneficial in increasing the net phase margin (compare the _m in Figs. VI-6 and VI-7) and in stabilizing and damping the phugoid. The net result is a reduction in workload for the pitch and roll axes.

Where the AH-IG and UH-IH augmentation systems only tend to stabilize and damp the phugoid, the CH-53D augmentation system fully stabilizes roll attitude (as well as pitch attitude and heading) and provides complete hands-off stabilization capability. In effect, the roll SAS eliminates the need for active roll regulation (a difficult task with SAS off as shown in Fig. Vi-8) and provides direct outer loop control of lateral position and velocity through the lateral cyclic control. We can observe this from the closed loop lateral velocity transfer function: i.e., the lateral cyclic stick commands lateral velocity with an open loop bandwidth of 0.35 rad/sec. This is a system which permits easy and precise regulation of lateral position in the likely range of crossover frequencies.

Other outer loop controls are improved also. The surge response in hover is similar to the lateral response although with a lower bandwidth:

(vl-21)

VgW_

SAS ON SAS ON In heave, with roll and pitch SAS on, the basic heave damping prevails, and: _c . -6.4 (VI-22) _c SAS ON SAS ON

SECTION Vli 00_LUBIONS AND REOOMMEZ_DATI0_ In this volume we have demonstrated procedures for effectively reducing coupled longitudinal-lateral-directional equations of motion to forms which expose specific features of helicopter handling qualities in a closed-loop, pilot-vehicle context. In so doing we have utilized the compiled data from Volume One to form a realistic quantitative frame of reference. Thus beyond just a demonstration of methods, we have also a survey of several handling- qualities-related features for a variety of single rotor vehicles.

It was shown that a general compensatory manual loop structure could be applied to the coupled longitudinal-lateral-directional helicopter equations of motion with two important results: (i) Key handling qualities features in a single loop could be examined direetly with simple but appropriate constraints on other loops.

(ii) The overall mathematical complexity could be reduced from that of the basic vehicle model while retaining the significant effects of longitudinal-lateral- directional cross coupling.

The examples considered in this study demonstrated these results in the cases of basic inner loop vehicle attitude stabilization and outer loop translational control. The following is a summary of conclusions and recommendations ensuing from this work.

A. BASIa ANALYTIQAL APPROACH The analytical approach used herein to examine specific handling qualities features consisted of: Selecting a closed-loop transfer function relationship which addresses the handling quality feature as directly as possible (e.g., one direct measure of the quality of pitch attitude control can be taken to be the response of pitch attitude to longitudinal cyclic stick displacement with roll and yaw loops closed).

Expressing the closed-loop transfer function in terms identifiable as (i) strictly vehicle components and (ii) combined pilot-vehicle components.

@ Substituting crossover model approximations for the combined pilot-vehicle components and taking advantage of the simplification ensuing from neglecting higher order terms.

The fortuitous result which makes this procedure useful is that attitude- constrained relationships frequently predominate, reduce mathematical complexity, and enhance physical insight.

The steps outlined above were used successfully to examine: • Direct control response for inner loop states -- pitch and roll attitude and yaw.

Inner loop cross coupling-- pitch-due-to-roll, roll- due-to-pitch, and turn coordination.

Direct control response for outer loop states -- translational velocity and displacement components.

Determination of significant inner and outer loop gust response components.

Augmentation system effects on inner and outer loop gust response components.

Augmentation system effects on inner and outer loop control response.

In each of these areas it was possible to determine the relative influence of various pilot-vehicle loops, determine important vehicle features, and estimate the relative success in closing the primary control loops.

Summaries of some notable examples follow.

Primary inner loop control response was analyzed in the presence of appropriate off-axis regulation, and it was found that perfect regulation of off-axis states is a generally valid assumption. It results in about the same net effect on the primary inner loop control response as a moderate 1 44 degree of relation of off-axis states. As an example, open-loop pitch response can be expressed simply in terms of ratios of coupling numerators, _T _ q_ i.e., 0 - *"SBSA6P (VII-I)

5B

This formulation carries along, from the pilot's point of view, the signifi- cant cross coupling effects among roll, pitch, and yaw axes (as described by six-degrees-of-freedom equations), and it minimizes mathematical complexity (by reducing transfer function order by at least two). As an added feature, the roll and yaw pilot model elements in the above example do not appear explicitly, but their effects are a_propriately imbedded in the pitch transfer function. Similar results were obtained for primary control response in roll and yaw loops.

The above analytical procedure also has implications for the formulation of handling qualities metrics and for the flight test determination of them.

The key issue is how one correctly introduces the effects of pilot-furnished vehicle control when examining and measuring various stability and control features. For example, should open loop pitch response be prescribed and ultimately measured in flight with some regulation of roll and yaw? As demonstrated in Section III, such off-axis regulation can modify the handling characteristics in the axis under consideration. Further, one might claim justifiably that these modified characteristics are more relevant to the pilot. Resolution of how and to what extent control strategy should be applied in formulating handling qualities metrics and testing for them is considered to be a worthwhile task.

The six-degrees-of-freedom models used in this study offered an opportunity to explore some of the various closed-loop cross coupling effects inherent in helicopters. Roll-pitch cross coupling was one such effect considered. Two means of characterizing the closed-loop roll-pitch cross coupling effects at low forward speeds were shown to be the modal

responseratios representing roll dueto a pitch conm_aud andpitch due to

a roll command with yawmotion constrained via pedal control,

i.e., 8

e_

c NSB_p

0_

and e - N_A_ (VIl- 3)

Analytically, these relationships were shownto be significant for either

an exclusively compensatory pilot-vehicle loop structure, or one involving

additional pursuit crossfeeds to off-axis controls (e.g., a precognitive

application of lateral cyclic to minimize uncon_nanded roll responsewhen

regulating pitch). The magnitudeand senseof the closed-loop cross-

coupling relationships expressedaboveagree with what is expectedin

specific rotor systemtypes -- teetering, articulated, andhingeless.

Furthermore, as in the case of direct control response, implications for

cross-coupling-related handling metrics and test proceduresarise from the

analysis applied here. Theseimplications involve not only howandwhen

manualcontrol strategy should be considered, but also howcross-coupling,

per se, should be classified and categorized. Pursuant to this, the matrix

of cross coupling features shownin Table III-10 provides a systematic check

list of characteristics which could be considered one-at-a-time in a rational

closed loop context. In turn, this list suggestsa form for handling

qualities design specification and testing.

D. PRINARY COI_'aOL _3:01_Z l_ T_ OUT_L LO0_I

Analysis of outer loop controlled elements was approached in a manner similar to that for the inner loop elements. But while the inner loops involve a variety of aerodynamic effects dependent on the specific vehicle design, the outer loop characteristics are, by contrast, rather invariant.

The only outer loop control response subject to any significant variation is heaveresponse,whichis mainly a function of disc loading and airspeed.

But even this feature is remarkably similar among the vehicles studied.

In view of the inherent restriction on outer-loop responseproperties

it is somewhat understandablethat specific flying qualities requirements

have not been well established. At the sametime it is conceivable that

a severe NOE operating environmentcould demand a level of outer loop

responsesuperior to that occurring naturally in the basic helicopter

vehicle. This would, in turn, necessitate the use of additional force

generation and would require prescribing levels and forms of surge, sway, or heaveresponse.

E. Gt_T F_P0_E

The important atmospheric gust induced responsecomponents for a heli-

copter model including longitudinal-lateral-directional cross coupling were

examined. Closed-loop analysis was applied but was shownto give about

the sameresults as simply considering the relative magnitudesof appropriate

aerodynamicstability derivatives.

The sensitivity of helicopters to spatially dependentwind shear was

illustrated by considering the closed-loop interactions among the pilot,

vehicle, and terrain. Basedon the predominantgust derivative, Zu, the

peak gust sensitivity was found likely to occur at forward velocities of

approximately 20 kt. This could be critical in an NOE environmentif a

significant headwindcomponent were to exist above tree level and decay

nearly linearly betweenthe tree tops and groundlevel (as compared to a

natural planetary boundarylayer logarithmic decay). Velocity profile data

fromwind tunnel tests suggest that just such a low level wind shear condi-

tion is possible. It is recommended that not only the hazard potential be

further studied, but that the necessity for including such effects in manned

simulation be considered.

F. EFFECTS OF VEHICLE AUGMENTATION For vehicles having the added complexity of stability and control augmentation systems, the same procedures described previously were applied.

Even with the appearance of additional response modes, the resulting dynamics were expressed with about the same degree of simplicity as for the unaugmented vehicle. This is a significant result and leads to the following notion.

G. APPLIGATION TO M0_E COMPLEX MATHEMATICAL MODELS In this study the unaugmented vehicle equations of motion were limited to six-degrees-of-freedom, quasi-static. The complexity of any vehicle augmentation was commensurate with the vehicle complexity. It is important to recognize, however, that the analysis procedures applied in this study lend themselves to system models involving the addition of rotor system and structural degrees of freedom just as they lent themselves to the additional complexity of control augmentation. Therefore, it is recommended that these procedures be considered as aids to reducing higher order rotor- craft systems to their essential properties within a pilot-vehicle context.

2F2EP_NCES 1. McRuer, Duane, Irving Ashkenas, and Dunstan Graham, Aircraft D_namics and Automatic Control, Princeton University Press, Princeton, N.J., 1973.

2. McRuer, D. T., and E. S. Krendel, Mathematical Models of Human Pilot Behavior, AGARD AG-188, Jan. 1974.

"Effect of Nap-of-the-Earth Requirements on Aircrew Performance During Night Attack Helicopter Operations," The Guidance and Control of V/STOL Aircraft and Helicopters at Nisht and in Poor Visibility, AGARD CP-148, Paper No. 4, May ]975, PP. 4-1 to 4-]0.

4. Dooley, Larry W., "Handling Qualities Considerations for NOE Flight," J. of the American Helicopter Society, Vol. 22, No. 4, Oct. 1977, pp. 2o-27.

D. McRuer, D. T., and D. Graham, "Pilot-Vehicle Control System Analysis," Guidance and Control --, Eds. R. C. Langford and C. J. Mundo, (Progress in Astronautics and Aeronautics, Vol. 13), Academic Press, N.Y., June ]964.

.

Teper, Gary L., An Assessment of the "Paper Pilot" --An Anal_tical Approach to the Specification and Evaluation of Flyin 6 Qualities, AFFDL-TR-71-174, June 1972.

, Ringland, R. F., R. L. Stapleford_ and R. E. Magdaleno, Motion Effects on an IFR Hoverin_ Task --Analytical Predictions and Experimental Results, NASA CR-1933, Nov. 1971.

8. Allen, R. W., W. F. Clement, and H. R. Jex, Research on Display Scanning, Sampling, and Reconstruction Usins Separate Main and Secondar_ Tracking Tasks, NASA CR-I_69, July 1970.

.

Clement, Warren F., R. Wade Allen, and Dunstan Graham_ Pilot Experiments for a Theory of Integrated Display Format, JANAIR Report 711107, Oct. 1971 10. Stapleford, Robert L., Samuel J. Craig, and Jean A. Tennant_ Measurement of Pilot Describing Functions in Single-Controller Multiloop Tasks, NASA CR-1238, Jan. 1969.

11. McRuer, Duane, and Dunstan Graham, Human Pilot Dynamics in Compensator_ Systems, AFFDL-TR-65-15, July 1965.

]2.

Clement, Warren F., and Lee Gregor Hofmann, A Systems Analysis of Manual Control Techniques and Display Arrangements for Instrument /_ndin_ Approaches in Helicopters 2 Volume I: Speed and Height Regulation, JANAIR Report 690717, July 1_69.

]3. Hunsaker, J. C., and E. B. Wilson, Report on Behavior of Aeroplanes in Gusts. Part I -- Experimental Anal_sis of Inherent Longitudinal Stability for a T_ical Biplane. Part II -- TheolU/ of an Aeroplane Encountering Gusts , NACA Report No. 1, 1915.

14. Wilson, Edwin B., Theory of an Airplane Encountering Gusts 2 II, NACA Report No. 2!, 1716.

]>. Wolkovitch, Julian, and Richard P. Walton, VTOL and Helicopter Approxi- mate Transfer Functions and Closed-Loop Handling Qualities, Systems Technology, Inc., TR-]28-I, June 1965.

T6.

Craig, Samuel J., and Anthony Campbell, Analysis of VTOL Handling Qualities Requirements_ Part I: Longitudinal Hover and Transition, AFFDL-TR-67-179, Pt. I, Oct. ]9689 and Craig, Samuel J. and Anthony Campbell, Analysis of VTOL Handling Qualities Requirements_ Part II: Lateral-Directional Hover and Transition, AFFDL-67-179, Pt. II, Feb. 1970.

]7. Br_mwell, A. R. S., Helicopter Dynamics, John Wiley and Sons, N.Y., ] 976.

]8. Seckel, Edward, Stability and Control of Airplanes and Helicopters, Academic Press, N.Y., ]964.

19. Walton, R. P., and I. L. Ashkenas, Analytical Review of Military Heli- copter Flying Qualities, Systems Technology, Inc., TR-145-I, Aug.

1967.

20. Military Specification_ Helicopter Flying and Ground Handling Qualities_ General Requirements for, MIL-H-850]A t Amendment ], 3 Apr. ]962.

2].

Edenborough, H. K., and K. G. Wernicke, Control and Maneuver Requirements for Armed Helicopters, American Helicopter Society Twentieth Annual National Forum, Washington, D. C., May 13-I_, ]964.

22.

Chen, Robert T. N., and Peter D. Talbot, An Exploratory Investisation of the Effects of Large Variations in Rotor System Dynamics Design Parameters on Helicopter Handling Characteristics in Nap-of-the- Earth Fli_ht, American Helicopter Society 33rd Annual National Forum, Washingtion, D.C., May ]977.

23. Rade, M., "Requirements for Operation of Light Helicopters at Night and in Poor Visibility," The Guidance and Control of V/STOL Aircraft and Helicopters at Night and in Poor Visibility, A_ CP-7_8, Paper No. 7, May ]975, PP- 7-I to 7-12.

15o 24. Hohenemser, K. H., Hingeless Rotorcraft Flight Dynamics, AGARD AG-197, Sept. 1974 .

25.

Kelley_ Henry L._ Robert J. Pegg_ and Robert A. Champine, Flying Quality Factors Currently Limiting Helicopter Nap-of-the-Earth Maneuverability as Identified by Flight Investigation, NASA TN D-4931 3 Dec. ]968.

26.

Finnestead, Rodger L., Ralph J. Pelikanj Donald P. Wray_ and Marvin W.

Buss, Engineering Flight Test_ AH-IG Helicopter (Hueycobra)2 Phase D I Part I_ Handling Qualities, USAASTA Project No. 66-06, Dec. 1970.

27.

Chalk, C. R., T. P. Neal, T. M. Harrisj F. E. Pritchard, and R. J.

Woodcock, Back[round Information and User Guide for MIL-F-878_B(ASG)I "Military Specification --Flying Qualities of Piloted Airplanes," AFFDL-TR-69-72, Aug. 1969.

28.

Chalk, Charles R., Dante A. DiFranco, J. Victor Lebacqz, and T. Peter Neal, Revisions to MIL-F-878_B(ASG ) Proposed by Cornell Aeronautical Laboratory Under Contract F_61_-71-C-12_4, AFFDL-TR-72-41, Apr. 1973.

29.

Lehman, John M., Robert K. Heffley, and Warren F. Clement, Simulation and Analysis of Wind Shear Hazard_ Systems Technology, Inc., TR-I063-3, Dec. 1977.

30. Maynard, Harry W., Wind Tunnel Modeling of Velocity Profiles of the Atmospheric Surface. Layer, ECOM-6019, Apr. 1966.

APPENDIX

SUMMARY OF CL08ED-LOOP HELICOPTER

TRANSFEE FJNCTIONS

The following tables are presented as a guide to computing various

pilot-vehicle response quantities using the data compiled in Volume One.

The relationships listed contain primarily first-order effects. Where

significant second-order effects are suspected a more thorough derivation

should be made in the manner illustrated in the foregoing sections of this

report.

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1. Report No. 2. Government Accession No." 3. RecJplent's Calalog NO.

NASA CR-3145

4. Title and Subtitle 5.

Report Date

August 1979

A COMPILATION AND ANALYSIS OF HELICOPTER HANDLING _.

Performing Organization Code

QUALITIES DATA. Volume Two: Data Analysis

7. Author(s} 8. Performing Organlzat_on Report No.

TR 1087-2

Robert K. Heffley

10. Work Unit No.

9. Performing Organization Name and Address Systems Technology, Inc. tl. Contract or Grant No.

2672 Bayshore-Frontage Rd., Suite 50 5 NAS2-9344

Mountain View, CA 94043 ,3.

Type of Report and Period Covered 12. Sponsoring Agency Name and Address

Contractor Report

National Aeronautics and Space Administration

Sponsoring Agency Code

Ames Research Center 14

Moffett Field, CA 94035

i5. Supplementary Notes 16. Abstract

A compilation and an analysis of helicopter handling qualities data

are presented. Volume One contains a collection of basic descriptive

data, stability derivatives, and transfer functions for a six-degrees-of-

freedom, quasi-static model. This, the second vo!_me, analyzes those

data using multi-loop manual control methods. A general compensatory

loop structure is applied to coupled longitudinal-lateral-directional

equations in such a way that key handling qualities features can be

examined directly. But the overall mathematical complexity is reduced

from that of the basic vehicle model. Extensive use is made of con-

strained state variable relationships and approximate factors in order

to gain physical insight.

18. D;slributJon Statement 17. Key Wor_ (Suggested by Auth,|s))

0H-6A

Helicopters

UNCLASSIFIED - UNLIMITED

BO- 10'

Handling Qnalities

AH-I G

Gust and Wind Shear Response

Star Category - 08

Manual Control

UH-IH

Pilot,Vehicle Analysis Cg-5_])

22. _ice* 20. Security Classif. (of this "page) 21. No. of Pages 19. Security Oa_if. (of this report)

Unclassified 1 76 $9.0o

Unclassified

*For sale by the National Technlcallnformation Service. Springfield, Virginia 22161 NASA-Langley, 1979