Technical Report No, 143-

ANALYTICAL fV5 -OF~ WWJA1~YEUI; PTR #LYING QUAL-iEza

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Teckniical Report Fi. itj.5-l

AwzaLT~A 1wm or x3w~IA inJ n FL!m wALZT(Final Report)

R. F. WaltonI. L. Ashkenas

Systems Technology, Inc.Hawthorne, California

August 1967

(First draft submitted November 196.5)

Distribution of this document is unlimited.

Under Contract No. NOw 64-o6oi-f to

DEPARTMENT OF THE NAVYNAVAL AIR SYSTEMS COMMAND

WASHINGTON, D. C.

This report is directed at analysis and review of the current militaryhelicepter flying qualities specification, 3t-E-5 61A, and of the relevantpublished literature. T!e analytical approact rests primarily on servo-analysis of closed-loop piloting tasks and secodarily on - ve-loop responseconsiderations, and such analysis and consideraeions are used as the basisfor correlating and "explaining" the available data. This process delineatesthose flying qualities criteea (either in the specification or proposed inthe literature" -Aich are valid, and establishes bases for additional experi-mets in inadequately explored critical areas. The reaults are specificallyapplied to an itemized critique of KEL-H-8501A (excluding autoration, wiscel-laneous, izstrument flighit, and vibration characteristics).

4t

i-

.1 .. .mw~c .II. IWIVIDUAL CiARACf fISTICS OF BUZL*PR AND PILD

W1I I 0'M ON TO CLMO6-LOOP MACKflx TASK .... 3

A. Aircraft Equations of Notion and the StabilityDerivative ............. . 3

B. Introduction to Pilot-Vehicle Closed-LoopTrackI Tsk ..... .... . 7

C. Eample of Closed-Loop Considerations for the I

Sinple Pitch Closure ..... . 10

D. Analytical Implications of Gust Inputs andNultiloop Control ......... ..... . 13

III. CL0E -IOP AALYS. ........... . . . 16

A. Krver Over a Spot ...... ...... ... 16

B. Lateral-Directiomal Control D-ring Approach . . . . 31

C. Forward Flight Longitudinal Considerations . . . . 41

IV. OPEN-LOOP ANALYSES .......... . . . 48

A. A Note on Control Positien Stability ..... .48

B. The "Concave Downward" Requirement for ManeuverStability (Item 3.2.11.1 of Ref. 1). . .... 49

C. Open-Loop Responses to 8A Step Inputs. . . ...... 5

D. Sensitivity and Control Power ...... .... 54E. Sum ry of Important Analytical Results from

Open-Loop Considerations ....... .... 60

V. CRITIQUE OF SPECIFICATION..... ...... 61

A. Collected Specific Results of Experimenta:/AnalyticalCorrelations . ........... . 62

B. Specification-Related Conclusions 64

C. Detailed Review of Specification MIL-H-8501A. . 69

REFEWECES .. . .. ............. 112

APPENDIX A - APPROXIMATE FACTORS. . ...... ... 116

APPENDIX B - METHOD OF APPROACH FOR CLOSED-LOOP ANALYSES .12

AP-PENDIX C - SURVEY TRIP NOTES ON HELICOPTER HANDLINGQUALITIES SPECIFICATION MIL-H-8501A...... . 1'

TR- 143- 1iii

F-

A Polynomial coefficient

b Airplane -wing span

B Polynomial coefficient

C Polynomial coefficient

D Polynomial coefficient

E Polynomial coefficient

g Acceleration due to gravity

G(s) Loop transfer function

h Altitude perturbation

hl Altitude response in one second

Ix, I' Iz Moments of inertia about x, y, and z axes

Ixz Product of inertia

K Transfer function low frequency gain

L Integral scale of turbulence

L Rolling moment/I x

Lr /6

IXZ+-x + Nx1x where X refers to any motion or input quantity

Ixaz

m Mass of the aircraft

TR-145-1 iv

M Pitching ncment/i

MU ()4/aq

q!

N Yawing moent/I!

Nr a/r

Ixzl + -v'" LX

x+- lx Y where X refers to any motion or input quantityI

IxIz

N(s) Transfer function numerator

p Roll rate

MOR ox PR Pilot's r'ating

q Pitch rate

r Yaw rate

R Rotor radius

s Laplace operator, s = a + jw

LTime

T Thrust

TI Human pilot lag time constant

TL Human pilot lead time constant

TN Human pilot neuromuscular time constar'

T), Time constant of X zero or pole

TR-143-1 v

u Perturbation velocity along x-axis

Ug Gust velocity along x-axis

Uo Steady state velocity along x-axis

v Perturbation velocity along y-axis

Vas Steady state airspeed

w Perturbation velocity along z-axis

W Gross weight

x Horizontal displacement in direction of x-axis

X Force in x-direction divided by aircraft mass

Xq 2X/bq

x6 ax/28

y Side displacement in direction of y-axis

Y Force in y-direction divided by aircraft mass

IYp /aYr BYIar

Y(s) Transfer function

Human pilot transfer function, particularized with respectYP~x)t to general variable

Z Force in z-direction divided by aircraft mass

Zq Z/6q

zu nzlau

7-w Z/Cav

M Angle of attack

f3 Sideslip angle of attack,

TR-145-1 v-i

Flight path

71 Lock number

b Control deflection (Positive: forward stick, right stick,right pedal)

ek Pilot's error, particularized with respect to general variable

A Transfer function denominator

AX Incremental change in X

Damping ratio of X zero or pole

9 Pitch angle

00 Angle between (untwisted) blade no-lift chord line and plane ofrotation

01 Pitch angle response in one second

K Transfer function high frequency gain

XGeneral variable (u, v, w, 0, fp, #, etc.)

Uo/R

Real part of s

Root-mean-squared value of x

Time delay

'Te Effective pilot time delay, r plus neuromuscular time constant

TRoll angle

INM Phase margin

1PI Roll angle response in one second

xX power spectrum

4Yaw angle

Yaw angle response in one second

0Imaginary part of s

We Crossover f-equency

a)) Undamped natural frequency of X zero or pole

0 Rotational speed (rad/sec)

TR-145-i vii

-

Special Subscrt -s:

A Poll control (Lateral cyclic pitch)

B Pitch control (Longitudinal cyclic pitch, differential thrust, etc.)

c Collective pitch

d Dutch roll

o Basic (unperturbed) condition

p Phugoid or pilot

r Yaw control (tail rotor or diffezential lateral cyclic)

R Roll subsidence

s Spiral

sp Short-period

T Thrust

X General variable (u, v, w, e q, , etc.)

Mathematical Symbols:

< Less than

> Greater than

Much less than

Much greater than

/ Not (e.g., $, not equal to)

Approximately equal to

- Fed to; approaches

Partial derivative

X/5 Generalized transfer function, (s)/8(s)

TR- 145-1 viii

I

The work reported here has been directed at conducting an analytical

review of certain aspects of the current military helicopter flying

qualities specification, MIL-H-8501A (Ref. 1), with the aim of laying a

rational foundation for handling qualities design criteria for this class

of vehicles. The review has not been confined solely to the contents of

the present helicopter specification, but has been broadened to include

all relevant published material; to delineate those criteria (either in

the specification or proposed in the literature) which are valid.; and to

establish a theoretical basis for additional experimental effort where

critical areas are found to be inadequately explored. The analytical

approach rests primarily on servo-analysis of closed-loop piloting tasks;

and secondarily on open-loop response considerations.

The need for more rational flying qualities requirements establisAied

on a combined experimental analytical basis can be seen in the much

exercised controversy which exists regarding the applicability of certain

empirical relationships contained in the specification. Where possible,

empirical relationship based on statistical data should be kept to a

minimum, e.g., many of the requirements based solely-on a size effect

provide little in the way of a handling qualities desi-r. guide to an

individual case.

A logical step towards achieving rational criteria is the approach

taken in this report wherein the helicopter requirements are based upon

experimentally validated theoretical considerations. The primary effort

then has been collecting, analyzing, evaluating and correlating existing

handling qualities data. The evaluation effort involves the theoretical

analysis of both closed- and open-loop control tasks and One correlation

of these results with available data. By this process a more unified

set of criteria can be evolved which can "explain" trends in the handling

qualities data and predict significant effects.

TR-143-1

Secie I 1 instrofces; the dy icchrac stics of the controlled

element (the he~lio.eri Aloo with eqations of motion -tich are

sufficient -or rost of the closed-loop and oren-loop analyses in the report.

The ranges of the stab'ly 6erivatives are given for the tandem awl

single rotor configurat Ion as a finetion cf speed. Aos vith-the air-

craft characteristics the describing fuaction of the pilot is discussed

in terns o~f his perfor-mnce -and adjustment riales in order to ccuplete

the overall pIcture of the pilot-vehicle control loop. An exaTle of

closed-loop contzro! is given for the sieple wvtU studied. case -here the

corntrol element is K/s (s +1 I T)~

Section II contains the analyses of four closed-loop cases which

are representative of the multiple-loop situation where a pilot in a

comnesator" task maniv.lates one input by observing the error in t-

outputs o- the syste- The cases studied include hover over a

spot as well as lateral-directional control during landing approaches,

and were analyzed with and without gust input disturbances. The results

of these analyses are used to explain certain phenomena in experimentally

derived data, and these data in tur are used to define the good and bad

regions for the analytically-derived critical parameters.

Section IV presents certain of the open-loop analyses used to gain

a better understanding cf some of the miscellaneous maneuver tasks which

can be analyzed and include control stick stability, "concave downward"

requirement, roll responses, etc.

Section V interprets the specification in terms of the analytical

results. This then becomes the specification critique which also includes

recozmaendations as to further experimental effort in critical areas.

TR-14,h-i 2

CII, ~ ~ C E= m 8 llCcMM AMDpn

j IA. AMTO cwm-M OF TR A I

MME STAB=ZI DCRIVA=V

The linear equatious of motion, Ref. 2, were fcund sufficient to

handle all the situations encountered in the specification review. In

this part, the equations required for hover and forward flight are dis-

cussed and the equivalence between lateral and longitudinal hover is

shown. The key point of this discussion is to show and compare a typical

set of stability derivatives for the tandem and the single rotor heli-

copters. In the process of analyzing closed-loop control, the most

critical situations become the hover and the forward flight approach.

The terms which are usually small and do not contribute to the under-

standing of these control situations are omitted, an. the equations of

motion can be written:

Longitudinal

s U0 g ]-MU MVs 2 _ me] 01 Y%

Lateral-Directional

[sYV s2L~ -+ {10 (2)

II --N 0 s - Nr r N3

TR-1 43 -1I

For the case of hover the pitch longitudinal equations of motion simply

become

With the proper changes of symbols, Eq. 3 represents the lateral hover

equations of motion in roll.

uXu Yv X5 "

Because of t.1s identity in form, the reminder of the hover work willuse only the longitudinal terminology and symbols, but the results will

apply to the lateral hover as well. From Eqs. 1 and 2 and the usual kine-

matic relationships, h = Uoe-w, = r, etc., the vertical and yaw equations

at hover (Uo =0) are given by the single-degree-of-freedom expressions:

h -cror

a s(s-Zw) = s(s -Nr) (4)

Control situations having this transfer function form for the controlled

element have been studied extensively as regards closed-loop pilot control

e.g., Refs. 2-5. This same form also applies to the pitch and roll hover

equations when the speed stability derivatives can be neglected (Mu= -Lv 0).

e MbB or Lt)Sor L8A

B = s(s - Mq 5A s(s -Lp)

Although the speed stability derivatives can be rather large, they still

can be neglected for purposes of closing the attitude loop only In the

absence of external disturbances (see Section III-A). For orientation

purposes, the ranges of derivatives are given for the single- and tandem-

rotor helicopters (see Fig. 1). These derivatives represent the basic

airframe without augmentation and the sketches indicate the trends for

TR-143-i 4

Dampingl

S-RMq -3.0 -3.0 -3.0 -3.0

(1/sec) p Nr-2.0 -T-R -2.0 -2.0 -2.0-

T-R-1.0 S-R -1.0- -1.0 - -I.0 - T-

T-RS0 1''. 0 1', 0 0 liI!

0 .2 .4 0 .2 4 0 .2 4 0.2 4L Uo /D R

[Speed Stabi/ity!

SR.06- .06 - .06 -Mu - -Lv / N v

(I/f t-sec)(I .04 - .04 04

S-R.02 -R .02 T-R .02

S-R0 I 0 0', 0

.4 0 .2 .4 T-R- .4-.01 - ' ---. 1 - F

Cor,,rol Sensitivit S-RJAngle of Attock SR2

S-R NRUoMw - M88 .6 -L86 -. 0

(1/sec) -- A T-R4.0 (rod/sec2) T R

n -T-R

2.0 " T-R .2 S-R .2 .2-

0 i t I f o _ ._0 .2 .4 0 2 .4 0 .2 .4-1.0 - "

(with tail) - - -

Figure 1. Variational Trends of the Stability Derivativeswith Speed for the Tandem and Single Potor Helicopter

TR-143-1 5

average values with restnect to each con'.igraticn. Wegh or size was

n&,t found to be pri:s-ary in estab-izhir'g the tre.nds even though the

veights differed by a factor of five fobr so-ce con--igurrations.

Demping

A coarison of the rotary daz-ming derivaltives of Fig. 1 shows the

longitudinal darr-ping of the t.and--=a to be greater than that of the single

rotor. The situation is reversed for thne lateral-directional £i Ding

where both ID and Hi, of the single rotor are greater thnthe tanden-.

While the rotary deanni-!s are fairly conszant. with sneed, the vertical

daemping, Z., decras abrupty near hover and bcesaippro.xirately

equal. to -.3 (1/sec) at hover.

Speed Stability

These derivatives (Mu, LL,, and IIv) are largely responsible for the gust

sensitivity about the three aircraft axes; the longitudi I~ derivative, i4U,

is also directly proportional to the stick position stability, dbBJdu.

!~is always positive at hover, but in the case of the tandem the derivative

becomes negative after transition unless certain modifications such as swash

plate dihedral are made to prevent the sign change. For the single-rotor

the derivative is usually smll, positive, and relatively constant withspeed. This indicates a stable stick variation with speed about any trim

condition; however some single-rotor helicopters have a low speed stick

reversal problem, possibly due to nonlinear power effects in going from one

trim condition to another. For the roll and directional axes the single-

rotor configuration leads to high -Iv and liv, while the tandem has a high

II,/NvI ratio (due to the low liv) which is associated with a large cj/j5

ratio. All these characteristics are essentially constant with Speed

except for A, of the tandem and L, of the single rotor near hover.

Angle of Attack Stability

As showni in Fig. 1, the pit~hirng moment due to angle of attack is

liss~ally made stable for tha single rotor by the addition of a small

-,ail plane, whil~e the tandern requires r.ore sophisticated modifications

TR- I -I6

ave-rage values with respect to each config;aation. Weight or size was Jnot found to be pri -ar- in establ-is. the trends even though the

-eights differed by a factor of five for sore cnf--uratons.

A ccm-erison ef the rotary da __ing -derivatives of Fig. I shows the

longitudinl daTing of the tandem to be greater than that of the single

rotor. The situation is reversed for the lateral-directional damping

where both L, and Nr of the single rotor are gr-ater than the tandem.

Waile the rotary da=-i-7_ s are fairly consrant with speed, the verticaldamdig, c, ecreases abrautly near hover and beccmes approximtely

aqual to -. 3 (1/sec) at hover.

Speed Stability

These derivatives (Mu, Iv., and Nv) are largely responsible for the gust

sensitivity about the three aircraft axes; the longitudinal derivative, M.,

is also directly proportional to the stick position stability, d6B/du.

M is always positive at hover, but in the case of the tandem the derivative

becomes negative after transition unless certain modifications such as swash

plate dihedral are made to prevent the sign change. For the single-rotor

the derivative is usually small, positive, and relatively constant with

speed. This indicates a stable stick variation with speed about any t-rm

condition; however some single-rotor helicopters have a low speed stickreversal problem, possibly due to nonlinear power effects in going from one

trim condition to another. For the roll and directional axes the single-

rotor configuration leads to high -I, and Nv, while the tandem has a high

ILv/NvI ratio (due to the low Nv) which is associated with a large '/.3

ratio. All these characteristics are essentially constant with speed

except for lI of the tandem and Iv of the single rotor near hover.

Angle of Attack Stability

As shown in Fig. 1, the pitching moment due to angle of attack is

'tsLally made stable for the single rotor by the addition of a small

tail plane, while the tandem requires more sophisticated modifications

TR-145-i 6

reaction time delay, and the neuromuscular lag which in this report are

combined into an effective transport lag, -re = T +TN- For the purpose

of constructing root locus and Bode plots, the transport lag has been

incorporated into the phase and magnitude parts as

-jK e- e I(P'r = -jTe ; K =

Returning to the adjustment rules, in general they can artificially be

divided into two categories -adaption and optimalization. Broadly speak-

ing, adaption is the selection by the pilot of a specific form of Eq. 6.

For all cases considered in this work the closures at most require pilot

lead, so the applicable form of the pilot transfer function reduces to

Yp = Kpee(TLS+I) (7)

Such adaption has been fairly well established for the controlled element

forms in the present applications, and is consistent with providing good

low frequency closed-loop response and absolute stability of the system.

As for opt.alization of the parameters Kp and TL, they have been shown

(Ref. 7) to be roughly compatible with the minimization of the rms error.

The pilot rating can be a function of many factors both of an open-

and closed-loop nature, but a basic assumption of the theory presented

here is that overall ratings will be most affected by flight situations

requiring precise control and close attention in control modes akin to the

compensatory tracking task. Consequently, as a first approximation, one

can synthesize a functional relationship between pilot ratings and the

primary system factors, i.e.,

PR = fn(a., ab, Kp, TL, TI) (8)

The first factor, a., has to do with the system performance the pilot can

achieve, and this is of primary importance. If performance is poor, then

the remaining factors, even if favorable, will not result in a favorable

rating. However, when performance in a closed-loop system is good, the

pilot still wants to keep his physical output responses (if he is con-

trolling more than one output) at some sort of a ninimum; and., obviously,

the smaller (within limits) his physical activity, o5, the better he will

TR-Ihj-I 8

rate the pilot-airframe system. Similarly, the ast two factors have to

do with the pilot's mental or data-processing activity and here again

the very best pilot ratings occur when his equalization requirements are

minamm, i.e., TL = TI = 0 (T I J 0 does not have an important effect on

rating), and Yp = KPe . This "best-opinion" form of the pilot describ-

ing function is appropriate when the effective vehicle characteristics in

the region of crossover have the transfer function form Yc " Kc/s. How-

ever, even such favorable situations will be poorly rated if the pilot's

gain, Kp, is too high (as in a sluggish system) or too low (as in a

sensitive system). Because the pilot attempts to keep a constant cross-

over frequency, a, which in this case is just equal to KpKc, a Kp-induced

variation of pilot rating can be demonstrated simply by -arying the con-

trolled-element gain, Kc. The result will show that an optimum gain exists,

and that either increasing or decreasing this gain results in a degraded

rating. The crossover frequency, a, defined from the Bode plot as the

highest frequency intersection of the open-loop transfer function with

the zero-db line, is a good approximation to the domirant response

frequency and the bandwidth of the closed-loop system. For good system

performance, c must be at least as large as the input disturbance band-

width and must also come up to the pilot's expectations with regard to the;dominant response time of the system. In practice the latter requirement

leads to more or less constant a's for given classes of tasks and simple

controlled elements. For complex controlled elements the attainable "ah

depends on the total usable gain, which in turn depends on the provision

of adequate gain and phase margins (about 6 db and 300, respectively).

These margins are necessary to insure adequate nominal stability and are

consistent with pilot describing function measurements (extrapolated to

the lower ao's of interest here) and with good servo practice. There is

nothing really sacred about either figure, and in scme instances one

margin or the other my be reduced for reasons associated with a specific

situation. However, in most cases analyzed here at least one margin

(6 db gAin or 300 phase) was maintained.

c. sx)xZ3 07 OVUD-LOOP Z=1 C7MAI C SDim= PITC 0OO

To illustrate the age of the pilot model and at the same time to set

damping requirements, corisider the simple, ideal, one-degree-of-freedom

pitch to longitudinal cyclic control (e -- 5B ) transfer function:

e ____ (B)8B s(s - ) -)

s q Ts

This form applies to most all hover situations (see Eqs. 4 and 5) when

the speed stability derivatives are zero (Mu = -Lv = Nv = 0). It serves

as a logical point of departure for later considering the implication of

the outer-loop closures in position. Contrcl of pitch is the primary

piloting task necessary for maintaining or changing the position in

hover. Regulation of the pitch angle to maintain position is a compen-

satory tracking task wherein the pilot applies cyclic control to change

attitude as a function of his observed position error.

In exploring the closed-loop implications of ideal pitch control,

the pilot's activities are characterized by his experimentally observed

transfer function (Refs. 5 and 6) fitted to the simple form of Eq. 7.

Accordingly, the complete open-loop transfer function in its simplest

applicable form is given by Eq. 10.

Ype =Kpje,- (TLs + (114B 0)6 ss + I

Tsp

For low values of Tsp, corresponding to high pitch damping, the controlled

element dynamics, Yc - e/5B, approach the simple Kc/S form (i.e., in Eq. 9

for Ts- -O, e/8B--I.1B/s). Under these conditions pilot lead is unnec-

essary for good closure, i.e., YpYc I KpKce-TeS/s, and the only pilot

adaption requires is on the value of gain, Kp. For this simplest of all

closed loops, the open-loop gain determines the gain-crossover frequency,

wc; i.e., KpKc = . The corresponding phase margin is given by

TR-143-I 10

Ii

186 0 -4YDYc= 900 57. ( (11)

Since the required pilot adaption is a minimum, pilot opinion of the

Kc/s-like controlled element is invariably good provided the value of

i is in some optimum region, and provided the system bandwidth, deter-

mined by (c, is greater than the input disturbance bandwidth. Both of

these auxiliary requirements demand some knowledge of the possible or

likely values of a)" There are a number of measurements of varying

validity (Refs. 5 and 6) which indicate that, for single-loop attitude

closures, values of wn are 2 ± 1/2 rad/sec for K/s controlled elements;

and these values are essentially constant with varying input bandwidths

provided these bandwidths are less than a).

The basic data of Ref. 7 show additionally that regardless of thecontrolled-element form the complete open-loop describi-ig function,

pYc, can be approximated in the crossover region by

(YPYc) KpKcees (12)

In view of the basic desirability of K/s-like crossovers (for either

automatic or manual control), the pilot's lead adaption for closed-loop

control of pitch will be to effectively cancel the pitch subsidence mode;

i.e., for TL Tsp, Eq. 10 looks like Eq. 12 (see Fig. 2). Obviously,

the pilot cannot generate sufficient lead to allow TL to follow Tsp as

it approaches infinity (Yc - .Kc/s 2) but will, instead, be limited to

a mximum value of TL around 5 (Ref. 8). Also, TL will not follow T.

as it approaches zero (Yc -m4Kc/s) but will, instead, precede it and

approach zero when the phase lag contributed by Tsp at wc becomes

permissibly small (at a value of Tsp below about .5).

The outcome of the pilot's adaptive behavior is that the closed-loop

perforrmnce is relatively insensitive to variations in Tsp, i.e., the

pilot adapts in such a way as to effectively cancel Tsp and thereby makes

all systems look like Ko/s. Therefore, provided uL is greater than 04i

and Kc is selected at its optimum gain, the pilot's opinion changes with

Tsp is a function only of the required TL adapted by the pilot. From

TR-1 3-1 ii

KP Ma S 4Ti+)eTYPYC ( ) IGI I

0 db

II 0.10 1.0 10r T, t rod

w sec

Figure 2. Sketch of Pitch Closure for TL I Tsp

pilot opinion ratings obtained with the experiments surveyed in Ref. 8(single-loop pilot-vehicle systems with random forcing functions), an

average rating increase (degraded opinion) of about three Cooper points

was observed in going from best Kc/s to best Kc/s2 (i.e., gain, Kc, for

best opinion). Thus the rating increment associated with a finite value

of Tsp will depend on the pilot-adapted value of TL and will vary with Tsp

roughly as shown .*n Fig. 3. For in'7reasing Tsp, the degradation of the

rating first appears at a value of Tsp somewhere around 1 .0, the point,

roughly, at which lead generation first becomes necessary. These simple

tasks which employ random input forcing functions offer the most direct

3

2 For Optimum Control

] Rating Sensitivity, M 8

0OI.1 1.0 10

T5 p (sec)

Figure 3. Rating Change as a Function of the Time Constant, Tsp

TR-143-1 12

means of determining the valid effects of pitch damping (-Mq = 1/Tsp) on

pilot rating trends for vehicles subject to external disturbances. This

result has been shown in Ref. 8 to be consistent with the notion thatclosed-loop tracking tasks are generally more demanding as iegards system

dynamics than open-loop tasks. Reference 8 also presents data which show

that pilot rating trends with damping are essentially the same for all

axes (i.e., pitch, roll, and yaw).

For vehicles which are not exposed to external disturbances, the rating

increments (and the absolute ratings) are lower than those discussed above, Ipresumably because closed-loop regulation activities are considerably

reduced. For example, ;he lunar lander of Ref. 47 showed ratings of aboat

3.5 for a pure inertial characteristic (Tsp -a-) and about 2.0 for a value

of Tsp - 0.8. The corresponding absolute ratings for similar dynamics

subject to external disturbances are about 6.5 and 2.5, respectively (Ref. 8).

D. ANMI!CAL Z3G7. OOF 0? WT ED= AM MWZILOOP C01MB0

Using the pilot model, an analysis was made to determine the closed-loop

system responses to gust disturbances. When the pilot's task includes flying

in gusty air, he becomes concerned with the variations in position (or head-

ing), attitude, and control deflection due t, the gust disturbances. For

analytical purposes it is desirable to have an input spectram that is

simple in form but which adequately represents the gust phenomena. Such

a model, derived from Refs. ? and 10, is given, and its use to obtain

pilot-vehicle rms responses described, in Appendix B.

The pilot-vehicle system most often assumed in these studies is given

by the block diagram of Fig. 4 and is probably one of the simplest of all

multiloop systems because a single input is used for controlling two out-

Puts. This system is classified as a single-point controller. The basic

case depicted is for longitudinal control in a 'hover-over-a-spot" situa-

tion, but the block diagram applies, with suitable changes in the motion

variables, to lateral control in hover (i.e., substitute ( and y for 0 and x);

to elevator control of the flight path in forward flight (substitute h for x);

and, as shown parenthetically in Fig. 4, to aileron control of heading Jn

approach (p and * for e and x).

TR-1k3-1 13

ug

I X(. ) I -'-

Helicopter

86I +Y+

L J __,, _,

Inner Loop

Outer Lnip

Figure 4. Block Diagram for Typical Multiple-Loop Closuresof Hover Over a Spot (or Latera]-Directional Approach)

Extension of the single-lcop pilot model to multiloop systems is

5 discussed in Ref. 7 and the results obtained by the application therein

can attest to the usefulness of such an extension. In the analyses the

inner loop is treated first as a single-loop closure usually involving

the higher frequency stabilization task (crossover frequencies from

2 to 4 rad/sec) of attitude control for which the expression of Eq. 7 is

adequate. Since the outer loop, usually referred to as the "path loop,"

is closed at a relatively low frequency where lead is difficult for the

pilot to generate (on the order of 0.2 to 0.4 rad/sec), a pure gain pilot

model is used. For the position closure, the general pilot transfer

function is

YPPee (15)

In the closed-loop analyses to follow, contrcl situations are reviewe!d,

and the resulting implications on handling problems are correlated with

experimental data, when available, to give metrics which will aid in the

TR- 143-1 14

unification of helicopter handling qualities. The multiloop situations of

hover over a spot and lateral-directional approach are considered in the

absence of external disturbences to yield information on danping require-

ments and good dynamic stability characteristics in these two critical

I flight regimes. These same two exercises are repeated in the peesence of

gusts to give further information on control activity, additional damping

Ito cope with gusts, and the effects of other stability derivatives.

T 3

TR-1435-11

UMO ni

CUM-10' ANLYM

The pilot-vehicle systems for three broad areas of closed-loop control

are analyzed to determine the critical handling qualities factors in longi-

tudinal and lateral-directional control situations. The piloting problems

selected are mostly those situations where some experimental data are

available in terms of the stability derivatives (dynamic characteristics)

and pilot opinion or coments. The most representative of these problems

4 are encountered in the performance of an ILS approach or in hovering over

a spot. Various measures of the handling qualities difficulties were con-

sidered as appropriate, depending on whether system performance was good or

bad, and these were correlated with pilot opinion. From these correlazionsthe criteria for good handling qualities can be established. Although it

is optimistic to generate generally applicable criteria from one or two

sets of data, it appears, because of the strong theoretical backing, that

major influences can be described in fairly simple terms.

The three situations of interest are:

e Hover over a spot

* lateral-directional control during approach

* Longitudinal control during approach

The coverage given these three situations includes the effects of stability

derivative variations on the open-loop factors (Section IV) as well as on

the closed-loop system and on the pilot's closed-loop performance in the

presence of gust inputs.

A. EMVM OVE A SPOT

The longitudinal dynamics of a hovering vehicle in pitch are completely

specified by Eq. 5 and its five stability derivatives. In the handling

qualities analysis of the closed-loop situation, the effects of control

TR-143-I 16

sen itility -%B are not considered, and the resulting conclusions are

only valid for situations in which M5B is adjustei to its optium value,

i.e., degradations in pilot rating due to too high or too low a control

sensitivity are not ecosidered to begin with. Of the five derivativres, Mqand MU are recognized as the most important. Consequently, the major emhasiswill be on the effects of these two derivatives; that and XY/B are

of secondary importance is demonstrated in Appendix B. Figure B-I of

Appendix B illustrates the effects of M. and Mq on the characteristic

roots for a tenfold change in the two derivatives taken one at a time.

Increasing M increases the phugoid frequency at nearly constant damping

ratio and increases I/Tsp. increasing the pitch damping (M. more negative)

increase the phugoid damping at roughly constant frequency and also

increases I/T.p Additional information on the effects of the derivatives

on the open-loop dynamics is readily obtained via the approximate factors

of Appendix. A.

i 1. Pitch Closure 0 --a- B

In Section II-C the hover pitch closure for the simple case where

Mu = 0 was given as an example. For the more general case (Mu J 0), where

the control mode is characterized by the hover cubic, the vehicle transfer

function Yc = e/8B can be written from Eq. 3.

(_)

T(14where 1 _X6B

and approximations for the cubic factors are given in Appendix A.

The pilot closure of 0 -pN for the general cubic case of Eq. 14 is

much the same as that for the simple hover expressions of Eq. 9.

TR-145-1 17

To =derstand the siilaritty co--ae tre = 0 case of :-Pig. 2 "ith the

a. 0 cases of Pig. 5. , the latter cases, incresing Pilt gain

increases the d:--ng o-f the mstable _hugoid a for !. valrmes of gain,

K S (the sy ! * lo-ates the closed-loop poles). h- effect of .M, is

il ustrated by com--ring the pilot closure of -- for the ti-o configu-

rations of Pig 5 (cases 2 and 11 of RefiI). The (short-period) -periodic

-odes, I/Tsp, associated with the darping, -M, for both cases are in the

good region with regard to tilot lead requirements (1 /Ts > 1, see example

of Section TI-C). Accordingly the pilot vifl select his crossover frequencyfro- 2-3 rad/sec in a K/s region, with his lead frequency, 1iTL, appro-d-

mately equal to 1/Tsp. Ehe Bode plots of Fig. 5 shaw that the frequency

characteristics of the tw;o situations are practically identical in the region

of crossover. This suggests that the pitch closure is not critical with Yu

in the absence of gusts. The experients of Ref. 11 verify this result in

that 14, is not imortant from a dxmamic standpoint unless trim effects are

included.

One significant effect of pitch damping, l4<q, on the inner-loop closure

is the same as given by the simple example case of Section II-C. if the

damping. !q, is increased above a minimum corresponding t6 I/Tsn> 1 .0 sec -I,

the pilot lead requirements are practically eliminated. The reduction in

pilot lead requirements will be accompanied by an improvement in pilot's

rating, provided system perforiance is good and the pilot gain required for

crossover is "optimum."

2. Position Closure x

The performance obtained in the position or "x" loop closure, Fig. , is

a strong function of the kind of dynamic characteristics attainable

with the closure of the inner, attitude loop. Most important of these is

the achievement of positive damping of the phugoid and a large 1/Tsp (the

prime indicates the factor after the rirst closure). The latter refers

to the location of ]/Tsb with respect to the crossover frequency. Since the

outer looD is closed at a relatively low frequency, it is difficult for

the ,Ilot to ,yenerate low frequency leads and such action would, in any

event, croduce a poor rating. it is easier for the pilot to adapt lead

-IJ' - I

3.0

2.0

Y18

Wp 2.0

3. 2.0 -1.0 T 0.1 1.0 10.0

Figure H.itch Hoe Cure,~

xI

-3.0

\.4k 2.0

Tip

-3.0' -2.0 -1.0 I0

0.1 1.0

a) High Mu

~jW

4.0 10 db

3.0

-2.0

-1.0 -180*

-3.0 -2.0 -1.0 0.I .

b) Low M.

Fi ,u r e .Position Hover Closires, X-

T R 1 120

in the faster inner loop than in the slower outer loop. On the basis of

these observations, we can safely assume that lead is not used in the outer

loop. The difficulties a pilot would have if he did not choose to close

his attitude loop when attempting to hold his position over a spot is best

illustrated by Fig. 7. In the sketch of Fig. 7a, it is impossible for the

pilot to stabilize his phugoid mode without adapting more lead than he cal

easily accommodate. This was experimentally shown to be the case in Ref. 12

where the pilot was unable to "hover" the simulator given only position

information. Having stabilized the phugoid with an attitude closure (Fig. 7b),

the controlling modes of interest become the low frequency poles near the

origin; and the q- modes associated with high inner-loop gain (Fig. 5)

are little affected by the low gains used in the position closure.

With regard to the specific effects of stability derivatives, the per-

formance obtained in the displacement closure is probably more dependent on

Mu than on the other derivatives. As shown in Fig. 5, the large I/Tip is

associated with the high Mu. Figure 6 gives the outer-loop closure for the

two inner-loop cases of Fig. 5. The low Mu case of Fig. 6b is an example

of a K/s2 situation where the small I/Tap combines with the free s of the"x" closures. The pilot would be critical of this situation if higher

performance tracking were required, since the achievable bandwidth would be

too low to cope with fast inputs without the pilot supplying large amounts

of lead. The tracking performance of the high Mu case, Fig. 6a, is improved

due to the higher system bandwidth and the K/s characteristics in the region

of crossover. The pilot can now achieve a desired crossover frequency

without going unstable and at the same time obtain lower rms position errors

(see Fig. 9). A minimum desirable outer-loop crossover frequency of approxi-

mately 0.5 rad/sec is indicated in the Appendix B analyses. At this time

there is very little experimental data to support this value beyond the

limited data of Ref. 17.

In a similar way, the larger the closed-loop factor I/T' (Fig. 6), the

smaller its phase margin contribution in the position closure. This factor

is set by 1/Tsp (Fig. 5) and therefore responds favorably to either increased

Mu or Mq, as shown in Fig. B-I. Raising the minimum I/Tsp above about 1 .)

(based on 0.3 rad/sec crossover) will probably benefit the performance of

TP-143-i 21

3 +

+- N

33%W 3

c -Ii-+

+

00

C f6 D00 Q

E- u >

44,

*r-20% zS

0

~. V-1

>~ 3 Q)

"I +

3 N+ 3 1

+ N

"011

06

TR- 14 5-1 22

outer closure, but this requires experimental verification. However,

increasing separation of both the 1/-,' and I/T-p modes from the low frequency

control mode of the position closure will always improve the phase margin.

Another factor which can make a significant contribution to the outer-

loop performance is the zero, 1/Te1 , of the pitch closure. If the zero

had a minimum value of 0.3 to 0.5 rad/sec, it would guarantee a K/s char-

acteristic in the desired crossover region of the x--B closure. This can

be seen in Fig. 8 where the zero, 1/Tea, represents the minimum value that

1/Tsp can have; in turn, this 1/T'p sets the maximum outer loop crossover

frequency for a pure gain closure-provided all other factors are optimally

located. The usual approximate factor for this zero is given in Eq. 16

Swhere, for the single rotor, Xb is nonzero but I/Tel is still very small

(near zero). In the case of a tandem employing only differential collec-

tive pitch for the longitudinal stick control, the factor becomes equal to

-X u . However, large Xu'S derived aerodynamically will not be as satisfac-

tory as those obtained through inertial feedbacks (see Ref. 12) because of

the detrimental gust effects. Since special means (inertial sensors) are

required to obtain a good location of the 1/T6 , factor, this criteria would

not be practical in specifying good handling qualities.

WU

- "-- o" I'.0 / 1.--0 1.01

' " , sp, Tel¥ T;P

Figure 8. Effect of the Zero, 1/Tel, on the Outer-Loo) Closure

TR-1 3-I 2,-)

. Hoer Stea ness Without Oust

The ability of the pilot-helicopter combination to hover over a spot

within a given maximum control deflection is currently specified as a

measure of the handling qualities at hover. This criterion is difficult

to analyze since the inputs to the pilot-vehicle system are not easy to

identify or describe. In the absence of external gusts, the inputs must

be considered to be either internal to the pilot and the helicopter, such

as the pilot's own noise or remnant, or due to aerodynamic turbulence

generated in the rotor downwash.

The use of the analog fixed-base simulator is about the best means of

obtaining some representative data in this area. The results of F . 9

show the pitch, displacement, and control responses to the internyl noise

input of a human pilot in a fixed-base simulated hover. The figure demon-

strates the Mu effect on the outer-loop closure. The "x" error was reduced

by a factor of three for a tenfold increase in Mu. The improved "x" per-

formance for the high Mu case was predicted qualitatively in the study of

the outer-loop closure. It is also important to note that the control

responses were also reduced by about the same factor as the "x" displace-

ment error. This presents a potential danger if the specification is

interpreted to mean that the smaller the control deflection in still air,

the better the helicopter handling qualities. As proved in Ref. 11, the

pilot would rate the two configurations of Fig. 9 the same. This means

that the pilot in these tests is willing to trade performance (response

errors) for stabilicy. The high Mu case has better closed-loop hover per-

formance, as already shown, but the low Mu case has less negative damping

of the phugoid mode and is therefore more stable open-loop. Also, in the

presence of gusts the low Mu case is superior because of its lower gust

sensitivity. This is the primary subject of the following section, but

the point to be made here is that the pilot may be more critical of the

handling qualities in the presence of gusts than to his hover performance

in still air.

TR-1 I-t 24

(f t/sec)

+20 ~ ~ e

+201- w

mu.0089 Mu '105Mq -. mq=-4.95

Figure 9. The Effect of MU on Hover Steadinessin Still Air

TR-143-1 2

I

,. Effect of Oust Disturbances an Closed-Loop oyer Task

The preceding haniling qualities discussions have to do with a pilot

hover-ing in still alr. Wen the above task includes gusty air, then the

pilot is also concerned wdith the variations in poiItion, atttte, and

control deflection as influenced by the gust disturbaces. The purpose of

this section is to discuss the results of a rather comlete analysis of

hover in the presence of random u-jgust disturbances. The detailed stady }which exa ines the effects of gusts on pilot closures is presented in

Appendix B. The results presented here are primurily concerned with the

effects of changes in pilot pitch and position closure gains and of changes

in the stability deriv.atives on the rms x, 8, and 6B responses with both

loops closed.

The min point of the hover analysis contained in Appendix B is anK e>anination of four corbinations of derivatives; two values of both Hu and

1k. The two values for each derivative differ by a factor of ten and the

total of four vabies selected adequately covers the range of the critical

root positions (see Fig. B-1 of Appendix B).

For the hover work the gust spectrum is given by Eq. B-1, where the

gust break frequency, cqg = (3/2)(Vas/L), was chosen as 1.0 radisec (this

corresponds to an L of 30 ft and a mean wind speed of 20 ft/sec). The rms

gust responses were not found tc be strongly dependent on ag.

&. Effect of Gains. The rms values of ax, Ge, and %BOB.D weredetermined for variations in the e and x loop gains withboth loops cloned, but only one gain varied at a time, withthe other held fixed at the nominal values. The sketch ofFig. 10 shows typical variations in the a's as a function0 and x closure gains about the nominal. The nominal gainswere selected according to the pilot adjustment rules forgood handling qualities as outlined in Section II. It canbe seen in Fig. 10 that these nominal gains provide a reason-able compromise as to a composite minimum among the various"a" values. The most significant result shows Ge and axa decreasing function of their respective gains, Ke and Kx;however, the remining a's in each case are usually anincreasing function of the loop gain, e.g , the pilot's con-trol utilization, M6BOB , and the position response, xaincrease with "e" gain as do the pitch response, oa, and

146B05B with "x" gain.

TR-143-1 26

iI

I IB

0" '--I I, 1 M

01IWI

Nominal NominalKe Kg

Figure 1o. Sketch of a Variations About .3nminal Gains

b. Effect of the Stability Derivative. Having verified the

suitability of the nominal pilot gains, the effects of

changes in the two most important stability derivatives

Mu and Mq on the rms responses can be analyzed. Figure 11

displays the analytical performance results obtained as

well as the experimental pilot rating data of Ref. 11. The

four analytical cases are defined as follows:

VALUE OF DERIVATIVE-%lftsr (I/sec)

Low Mu' Low Ma .0088 0.15

High Mu , Low M .088 0.15

Low Ma, High Mq .0088 1.5

High Mu, High Mq .088 1.5

The analytical results (Fig. Ila) show little variation of

the a's with respect to I, except for MaBO8B at the high Mu.

This result is consistent with the flight test data of Fig. l1b,

i.e., pilot opinion rating (PR) is not a strong function of Mq.

This follows also from the Fig. 3 trends and the observation

that the range of tested Mq's in Ref. 11 corresponds to values

of Tsp < 1, where the pilot lead adaptation is minor. For the

smaller values of Mq analyzed, the restlts of Fig. 3 would

indicate a sharp increase in rating; but the analysis (Fig. Ila)

shows no general decrement in performnce. This result is in

line with the Section II discussion where we concluded that

the rating increment should be ascribed to changes in pilot

equalization, TL, rather than to system performance, and that

significant changes in TL would occur only for Tsp > 1.

TR-143-1 27

Note: Top graphs only show trends - variationsbetween data points are unknown

50a- 4T5ft/scC U 5 f t/sec

30-

20- M(degdg/sec 2

MU .008810 x lo-x(fl) [X (xv

g)(eg0 1.0 2.0(eg 0 .05 M ~ L

(a) Ef fects of Ma on a- 's (c) Effects of Mv on a- sfrom Analysis from Analysis

M=-41rad/sec2

10- 8 in M = Const = .41 rad/sec96~ .3 ft/sec 8i

8 - Mu =.105 =2.

M=.035

MU 5

C~~ 5..20000

(b Ef fe- of oqR()Efcso ~OlP

ioi

The effect of changing K, by a factor of 10 is shown by

plot "c" of Fig. 11, and the results can be sunmarized asa negligible effect on qX, a large change in ae (roughly afactor of 3), and a very- large change in ZBabB (roughlya factor of 10). The latter change appears to be directlyproportional to Mu . In fact, an approxisate formula relat-,ing the response spectra in M6BPB to the gust input spectrum(see Appendix B-I) is simply

Mf~a -- 1.'-muou rad/sec (195)

Accordingly, the control power required to combat the maxi-mum gust expected (4a value) is easily estimated as

45.614aou (16)

Thus, for the values of Mq tested, Mu emerges as the moresignificant parameter on the basis of boh the analyticalresults and the experimental evidence in Fig. 1Id.

Combining the results of plots "c" and "d" of Fig. 11 sug-gests a strong correlation between the flight test pilot'sopinion rating data and the computed pilot's control actii-ity, MbB0B, in the presence of gusts. This is consistentwith the functional relationship of Eq. 8 and the observa-ticn that, for the test conditions, neither performance,ax and ae, nor equalization, TL and TI, variations occur;therefore, pilot rating should be reflected in controlactivity, ab. This is also suggested by Ref. 13, where themeasured control response, oo, is roughly related to thepilot rating for constant M6 . But if aa does reflect pilotrating, then a desirable or optimum level of mv (correspond-ing to a given optimum value of %g, say) should be linearwith Mu according to Eq. 15. This expected result is con-firmed by the experiments of Ref. 14, where the optimumsensitivity is defined on an Mq-Mb plot for a number ofgust sensitivities, Mu, and for a representative ghust. Thelimited results of the experiments in Ref. 14 show that theoptimum control sensitivity, Mbopt, is a function of thedamping, Mq, the -elocity stability, Mu, and the value ofXu which has a direct effect on I/Te1 (Eq. 14). For valuesof -Xu appropriate to helicopters (generally less than 0.05)and for the ranges of Mq and Mu covered, the optimum valueof M8 is fitted 'Cy the approximate relationship

Mopt = 0.23 - 0.03q + 6Mu rad/ec2 (17)

in. (7

for I <-mq < 6 ; 0 < Mu < 0.031

The expected variation with Mu is clearly shown by thisrelationship. The variation with mq< is "explained" laterin connection with the open-loop analyses of Section IV.

TR-14 - 2

B.8 u7 of oRftant Am7tim1 Remats fbi Uwz Ovez a tf

a. To reduce the pilot's lead requirements to where they have anegligible effect on rating, the minimau damping about allaxes in the absence of gust should be greater than 1 sec - i

(p. 1 3)- For mltiloop control such as attitude stabiliza-tion and hovering over a spot, the minimum da ming shouldprobably be increased to 1._5 sec-I (p. 21).

b. For pitch control in still air, Mu is relatively unimortantfrom a dynadic standpoint; increasing k, imro cc the abilityof the helicopter to haver over a spot (still air only) byproviding a larger crossover frequency in the position closure(pp- 18, 21, 2)

c. Increasing the numerator factor 1/T% through nonaerodynamicaugmentation improves the precision hover performance, ox, inboth still and gusty air (p. 22).

d. Selecting e and x pilot-closure gains according to established"adjustment" rules provides a good composite minimum to aq,ax, and oSB responses in gusty air (p. 26).

e. In gusty air the rms control response, ob, is roughly propor-tional to 1uau (p. 29).

f. An increase in Mq above the minimum of Item a produces smallfavorable changes in attitude responses, ae, and controldeflection, o, in gusty air (p. 29).

g. Correlation of pilot rating data in hovering over a spot withanalytical results (f the attitude and position manual closuresindicates that pilot rating is primarily a function of controlactivity, b, provided the Item a condition is met (p. 29).

h. Analysis of recent experiments shows the optimum control sensi-tivity, 14, to be a function of Mu, as well as Mq, in thepresence of gusts. The optimum M8 is a simple function of bothdamping, Mq, and the velocity stability, Mu (p. 29).

i. The control power required to cope with the maximum gust expectedcan be specified on the basis of the rms control deflectionsfor random gust inputs, for example (p. 29),

am x = 4 at

j. All the foregoing apply also to lateral and directional controlin hover with appropriate modifications in the motion quantitiesand derivatives, i.e.,

Mq - DLp Nr M6 - Lb N5 X -'y

Mu -Lv Nv - -

5

IS. XIMAL-DMMMISL CO1nWL T Lim APFTRrO

The in-flight model sirulator experiments of Refs. 15 and 16 study the

laterul-directional handling qualities of tandem-rotor and single-rotor

configurations, respectively. In some cases the range of parameters isgreat enough that the characteristics of the simulatrs are overlapping.

Thc- two experiments were designed to determine the requirements on direc-

tional speed stability, Nv, and damping, Nr, but the flight environment and

the piloting techniques were different enough to require two separate arlyses.

In the NASA test (Ref. 15) the pilot task was to null the localizer and glideslope indicators on an ILS approach, while in the NRCC tests (Ref. 16) the

pilot maintained a ground track and glide slope through visual alignment of

a ground-fixed indicator. In the face of the varied conditions of the

simulators and test conditions, our approach has been to analyze appropriate

closed loops with and without external disturbances and to correlate the

data with the appropriate analyses.

In the first section the lateral-directional analysis without gust

disturbances will be perfomed and correlated with those experimental data

which are not strongly influenced by gusts. Under this category the dynamics

of the airframe are the primary influence on the pilot's ating on the

handling qualities. In order to nullify the influence of the large canned

gust inputs (through Nv) to the NRCC experiments, only those configurations

with 'lhe lowest value of Nv are considered to be correlative with the NASA

tests. Because of the large differences in geometry and weight, It is

instructive to find dynamically similar situations (i.e., same transferfunction factors) to compare NASA and NRCC pilot ratings.

1. Control of Reding With "Ailerons"

To track the localizer beam through deviations displayed on his ILS

instrument, the pilot closes the loop by maneuvering the airplane to zero

the deviation, preferably by using "ailerons" alone to make corrections.

The control of lateral offset and heading through aileron is considered

long term or outer loop control; and since it is generally impossible for

the pilot to follow the proper ground track by just "zeroing" the meter

deviation, he must provide a good speed of response in turning through

TR-1(45-1 1

I

another aileron closure of the roll inner loop. The lateral-directional

loop (y-'-8A) is not considered as a separate factor here because this

closure is normally of very low bandwidth which is set primarily by the

bandwidth of the heading clcsure (Ref. 17)- If the aircraft has good

heading control, the lateral deviation control will be good. Accordingly,

two basic loop closures are considered in evaluating the handling qualities

of the various configurations:

a. Bank angle to lateral cyclic stick, cp-BA

b. Heading to lateral cyclic stick, *---BA

The criteria used for closing the cp-a.--A loop are simple and involve

the pilot's desire to obtain good system performance with minimum lead,

and at the same time achieve good damping of the dutch roll as shown in

Fig. 12a. As for the ideal pitch case of Section II-C, the q-b-5 A closure

will involve pilot lead, TL, adaption which effectively cancels the roll

subsidence mode, i.e., TL" TR (see Fig. 12a). In these experiments the

roll damping was not on trial (-Lp /TR) because TR was always on middlo

ground, 0.25 < TR < 0.67; therefore, selecting 1/TL identically equal to

I/TR was not critical and provided a good basis for comparison. In fact,

there is no improvement in rating for TR below 0.5 to 1 .0 as borne out by

the discussion of Section II-C.

The important effect to be demonstrated here is the influence of the

numerator damping, , which is just beginning to be recognized (Ref. 3)

as a basic metric of heading control performance not necessarily limited to

helicopters. The oscillatory numerator case of Fig. 1 2a is typical of many

of the NASA configurations tested in Ref. 15 where t" was always greater

than or approximately equal (Lv = 0) to tda. The t" effect can be

appreciated by studying the heading closure *1' 6A, wheze the prime again

indicates that the inner (m) loop has been closed. Referring to the heading

closure of Fig. 12a, it can be seen that the maximum damping that 4 can

achieve depends on t" of the roll numerator; and for the roll-closure gain

required (indicated by the symbol 1) to give a crossover of approximately

2 to 3 rad/sec in the inner loop, (Qd%)' of the heading closure approximately

equals t". The maximum usable gain in the heading closure is limited in

this case by stability considerations of aU" (i.e., having adequate gain and

TR-145-1 32

(0 e-4

00 1I?

40 -

+'c e.Iy

3 PR4

II NI

33

11 -N

A-B.

TR- 43 -1

I

phase margins). More specifically, the extent to which the heading gain

(and crossover frequency) can be increased depends on the value of

which in turn is most strongly influenced by the basic value of too. In

effect, the heading loop crossover frequency (or bandwidth or dominant

response frequency) is determined by the value of ton, which in turn is

approximately given by (Appendix A)

9fv -NrS 2--Yv-N (18)2

The other terms associated with this approximation (such as li, Lr, L'Sr ,

and NBA) are either negligible or were not present in the simulator.

Figure 12b shows a similar dependence of the achievable heading response

speed (or crossover) on 1/T for situations where the (p/8A numerator is

nonoscillatory, i.e., approximately when 4Np < (Yv-Nr)2 , most likely to

occur for tandems, which have low directional stability, N1 (see Fig. i).

In this case the most critical loop in the beading closure is the closed-

loop pole of the roll closure, which becomes almost equal to 1/Tq1 . As

seen by the heading closure of Fig. 12b, this pole, 1/TdI, sets the cross-

over of the heading control. The approximate factor for this zero, for the

above condition on No is

1 -Y + No (19)

Tv Yv - Nr

Figure 13 shows the correlation obtained using the above basic

(p-numerator characteristics as metrics. In this figure all the NASA data

of Ref. 15 and three NRCC cases (lowest value of Nv = 0.01/fto-sec was used

to nullify gust effect) of Ref. 16 are plotted to establish a boundary value

of tot (or 1/T") 0.4/sec associated with the 3-1/2 rating. This value

for . (or i/TT), which, as explained above, is to be taken as a measure

of the heading response, converts to a crossover frequency between about

0.25 to 0.3 rad/sec. For crossovers less than 0.25 to 0.3 rad/sec, the pilot

will begin to complain that the aircraft will not follow into a turn using

"aileron" control. These results are in good agreement with the conclusions

reached in Ref. 17 where the supersonic transport configurations studied are

very much different in size arid approach speed. In fact, the two in-flight

simulators of Refs. 15 and 16 are themselves much different in size and weight

TR-143-i 34

E0.101

0 4-)

.c .

0

cr. to0

c 4400

4; 4, cr -. s

04 0

CP0 (z) Zo . D

0 Z C~ 0 N '-

34 0 d d d

,*0 -- 14013

(see Appendix B, p. 147), but the pilot ratings of similar dynamic situations

in the two aircraft gave surprisingly good agreement, as indicated in Fig. 13.

For a more detailed study of the foregoing results, Appendix B contains

a configuration review of several representati-ie situations taken from

Refs. 15 and 16. Appendix B gives the closure details using the pilot

models of Section II together with the transfer function data for +he example

cases. The pilot comments are also discussed with re3pect to the closure

characteristics when these comments are available.

2. OmtrZo of Dieotlaml Distuxb es With "Rudder"

In the experiments discussed above, the pilot was controlling his long

term lateral deviation from a ground track which reduced to the control of

heading with 6A. Also, the influence of gust disturbances was slight. In

this section the investigation is concerned with pilot control of gust-induced

heading disturbances with "rudder," 5r. Because the gust disturbances are

only directional in nature (Lv = 0) and the vehicle's roll characteristics

are suppressed (high -Lp), the pilot is interested primarily in the single-

loop regulation of heading with pedals. As opposed to the previous study,

the value of Nv is never less than 0.01, and increasing values of Nv change

the disturbance level directly. The purpose here is to analytically determine

the closed-loop performance and other factors for the approach situations of

the NRCC data, and then to correlate the results with the pilot ratings.

The pilot-vehicle control loop has the form shown in Fig. 14.

Pilot Helicopter*

vg-2 r , f o vl -

2d d o /Tdl I/Td2 ' -Nr (Yv very small relative to Nr)

a or I/TdiTd2 " UoNv

Figure 1L. Heading Closure *-w-br

TR-14 7-1 36

The gust input spectrum of Eq. B-I was a simple approxination to the

actual "canned" gust used in the experiments when g was chosen at

0.5 rad/sec.

Appendix B contains a detailed examination of twelve *-*-8 r pilot

closures representative of the NRCC-approach test of Ref. 16. The twelve

combinations contain five variations in yaw damping, Nr, and four varla-

tions in yaw speed stability, Nv.

a. Effect of Gain. Variations in pilot gain had much the sameeffect on the rms responses in * and Nbrbr as was shown in

Khovering over a spot. A typical _ult is depicted inFig. 1,5a where the a response varies as an inverse function 2

of closed-loop gain and the control response Nbrabr variesmore or less as a direct function. As in the hover case,the nominal gain selected on the basis of the conventional"rules" produced a good compromise between performance, G*,and the pilot's control activity, abr.

0oj, 1 degFvg-

N 8RBR ,deg/sec2

~ I 'Vg ft/sec

5.0 E)

Nominal N7 =-.II No o-r 4.0 -1.0 0Or Or

I1 -2.0I9 3.0 N,/--1

2.02 .03 .04 .5

KA i 0 .01 .02 .03 .04 5Nv(llft-sec)

a) Typical 0- 's vS Kj , b) o" s for Typical Closures vs Nv ; Nr

Figure 15. Analytically Derived Closed-Loop Performnce

TR- I11; 3-1I 37

Fignure 15b gIves t.;:- analyically deri-,ed rm-s resacnse in4and Rbl as a ft-ction of N., and U.. tbe angy two viarables;-e-ired to def-ine- the characteristic roots. - ese resultsshoaw both G' s to be a strong fAmction of 57, but mly Gtobe a stramg fun-ction and a wres- function Off Thr-

b. COm aoywth Zz-rDmta1 Tih analytical resultsare correlate! -with the expwerzentei data in Fig. 1t6 to pro-vide directioepal humdbi qualities criteria. The pilotrating cases s horwm in Fig. 16(a are those for an __

Smin, N5, (Table B-7-1), !uiiih is t:-e -best opdnion"2 gain forthe narticular malues of !iv and Nr. 71he co=uted v-alues of

or thbese fiu'i~?r's and the c muted values of-I(whnich are independent of iror) are plotted versus the corre-sooniing experirental pilot ratings in Fig. 10-0. On thebasis of these relationshi~s and the obser-mation tI-It leadadaptation is genezrnliy smli (Table B-X_1) , it appears thatthe Dilot. may be eqimlly, sensitive to syster errors, cl, andcontrol activity, oa. Since G5. is little affected by theValue of Nr (Fig. 1,5), i appears that the optirun value of!N&r is selected to reduce G5. to an acceptable level; i.e..for ratings better (less) than 3.5, Obr 131st be less thanabout 0.22 in. (Fig. i6b). The plot of Fig. 17 shows that suchvalues of Nr are essentially linear w.ith Nv. However, thecorbinations of Nv anld !R5r whi-Ch produce the desirable levelof Gb,. will not be considered satisfactory unless at~ is alsoreAu"ed to values below about 20 (1Fig. 16b).- But the onlyreal influence on cy- for a given H7v is 11r (Fi-g. 15b), which=1st therefore be int.- ;ased, withn increasing liv, to reduceaF to accevtaole levels. The appropriate level of I,-. rustalso be such to produce acceptable open-loop responses tocontrol inputs (discussed later).

The similarities and differences between the above resultsand those obtained in the analysis of the longitudinal hovertask are worth delineating. Both sets of calculations showthat the rms attitude changes (aij, (;) are similar functionsof the damping N? N I~) and speed stability (Mud) or direc-tional stability (liv); also that control activity (14808, '-'4r0,50is primarily influenced by the gust excitation, which is pro-portional, respectively, to the speed andi directional stability.However, the pilo0t's chief concern regarding system performancein the longitudinal case is a.~, and this is not stronglyinfluenced by either damping or speed stability. Thereforethe ce performance, while about the same as the cV performancein the heading control case, has a much smaller influence onpilot ratings. Furthermore, because 1% was held constant(Figs. 1ib, lid) the resulting pilot activity, %ye' wasstrongly influen'ted by Msu and thus emerged as tne importantpilot rating factor In contrast, for the tested headingcontrol task both Gbr and ao appea2r to be eqiiai'y importanta-, pilot rating factors.

To8.9 f t/sec

6 V Inc Nr

4-

0 .01 .02 .03 .04 .05

a) Pilot Ratings for 1M ptimum"A(N

8 8-

7- 0 7-

Rating 0 06- 0 &-

5 50 0

4- 4-

3 0.

.2 .3 .4 .5 .6 0 1 2 3 4 5a,(in) 0, (deg)

b.) Pilot Ratings vs a- j~

Figure 16. Correlations with Pilot Rating

2.4Nr = -0.1 X

-1.0 E"2.2 -2.0 +

2.0-5.0 -10.0 -Pilot rotings ore shown

"opt' Nr Le1. beside each point.

1.6rod/sec2/in // _ _4.50

1.4 - 03.0

1.2Approximate* "Optimum"

1.0 NBr for PR <3.5; All Conditions

0.8 +3.52.9+ E0 5.0 +7.5

0.6 3.0E +6.0

0.4 X6.5 x 7.0 038.0

0.2

0

0 0.01 0.02 0.03 0.04 0.05Nv

Figure i7. "Otimum" N-r Variations with Nv and Nr

T-0

S. S3n7 of Iq~wtat Analytical Results forZatrz..-D~retonaJ Control Dart*g Approh

In tracking the MI localizer with aileron:

a. Based on consideration of Ref. 17 results, the aircraft wIll

have good lateral-deviation control, y 6A, if the headingcontrol is good, *--BA.

b. Acceptable aileron-only heading control requires a closed outer-loop crossover frequency greater than about 0.3 rad/sec or, forthe test conditions analyzed, gqaV or 1/Tcp1 greater than 0.4/sec(Fig. 13) in addition to minimnu roll damping, - > 1.5 sec.

For the control of gust-induced heading disturbances with "rudder" at

approach speeds:

c. The pilot's rating is a strong fianction of the direc-tional damping, fir (unlike longitudinal hover), as wellas the directional stability, Nv, and rudder effective-ness, Nbr (Fig. 6a).

d. The pilot's rating shows a strong correlation with rmsheading response, o , and with rms control deflection,

Tbr (Fig. 1 6b)

e. The optimum control sensitivity, N5r. is a functiononly of Nv for a given gust input (Fig. 17).

f. The directional damping, Nr, requirements are a strongfunction of Nv and the design gust level, cOVg, asreflected Jn the value of o, (p. 38).

C. 1F AWtLII C3MMAm oIS

Analytically, hover is an easy flight regime to study since most motions

decouple into simple modes; and for pitch the dynamics are completely

expressed by two to three stability derivatives which are simple to esti-

mate. Likewise, a variety of experimental data are available from hover

flight and fixed-base simLlator studies. On the contrary, there is a

paucity of data and information in the low speed transition range. In this

region the motions become coupled and the derivatives are influenced by

complex interactions which are not easy to treat analytically. This could

also be said of the high speed range above 150 kt where little data exist,

either analytical or experimental, in regards to handling qualities.

The tiansiticn region (hover to forward flight) is an important regime

because it encompasses approach conditions and is commonly characterized

TR-145-i 41

If

by sign reversals in eithe- or both M!u and 14g. Tue industrj approach has

been to solve these problems with stabiity azxgzenters if the problem is

serious enough or just to neglect it if the trcublesome speed is low or

the region of re7ersal small enough. However, the region and its associ-

ated handling qualities can be important if the approach speed happens to

lie in it or if the hc Ucopter has to stand plane guard off a carrier at

the reversal sneed.

I. Dymideal C¢esdftstifts Wito't Guat

Fortunately the rotary damping requirements in forward flignt have been

found to be, for all practical purposes, the same as those determined for

hover. In this regard there appear to be sufficient helicopter data (e.g.,

Ref. 18) which, however, do not usuialy include information on the other

derivatives of potential importance.

For phugoid-type instabill ties (14I < Q) there are some non-helicopter-

oriented data in Ref. 19 (T-. le V) for a fixed-base simulation. The cases

of interest had aperiodic phugoid modes of the form (s-I/Tp)(s +/Tp 2 )

with zero total damping; i.e., I/Tp1 +i/Tp2 = 0 as shown by the sketch of

Fig. 18. For these situations the rating was 3-1/2 for an aperiodic"frequency" of 0.2 rad/sec

I (1/Tp2 = -/T = 0.2). This is

Wprobably no worse than an unstable(Sp spiral mode for which the loop

iW closure problem is very similar;

and spiral divergence rates of

about 4 sec to double amplitude

(/T" -0.17) are not considered

unacceptable for conditions other

than cruise or landing (Ref'. 48).I I I I-- '' T -T However, from a practical stand-

To \ point the configuration is notO111 " -" typical of the helicopter having

Mu and IMI, proble:s in the low

Fieire 18. Phugoid Instability speed range: for example, the

TR- 1 - 42

separation of the short period and the nhugoid is not as great in the

helicopter as in the airplane.

If the short period and phugoid are separable, then the short period

dynamics can be treated by the raneuver ,argin criteiion or equivalent in

terms of the "concave downward" requirement (the two have been shown to be

equivalent in Ref. 20. These open-loop requirements will be discussed

further in Section IV.

Several examples of possible configuretions where the modes are

inseparable are given in Ref. 2, and thez.. same situations are shown not

to be amenable to the concave downward requirement as discussed in Ref. 21

(p. 84). One such open-loop transfer function is depicted by the sketch

of Fig. 19. For this configuration it is difficult to physically separate

the modes, and the labeling in

the sketch is for identifying

purposes only. Airplane rating

data somewhat representative I I Pof the above situation are To2 sp 2 X sp I

found in Refs. 22 and 23 for C XI Inegative values of naneuver

margin, < O. The results T8 2 X TO1

of these data would, except Figure 19. Typical Example of

for emergency situations, Mu and M Instability

forbid any negative values of the aperiodic I/TspI • For example, it was

not possible to obtain a rating better than 4 despite high "short period"

* - damping (1/Tsp I +1/Tsp2 ). However, the short period approxi ations, appli-cable in these tests, replace the two y, poles and the I/Te1 zero with a

single pole at the origin (free s). This is a much more difficult config-

uration to stabilize than those shown in either Fig. 18 or Fig. 19. In

fact, if the positive 1/Tel zero shown in Fig. 19 is at least 0.1 rad/sec,

the pilot closure can be made with relatively little difficulty or at least

with the same ease as for the oscillatory divergent phugoid case pictured

in Fig. 18.

Unfortunately, the number of situations similar to that of Fig. 1 9

(poor separation of modes), each having a problem peculiar to the specific

TR-143-1 43

II

pole-zero locations, can be large. This makes it rather difficult to

establish a general criterion to cover all situations, particularly with-

out experimental data with which to relate to handling qualities ratings.

This, then, is an area thit requires further analytical-experimental

effort if more realistic r'i-ements are to be obtained.

2. Lo gitudim1 Gust Responses In Forward Flight

This section considers the gust esponses in pitch for approach condi-

tions. Longitudinal situations are investigated for several combinations

of the stability derivatives which encompass only the stable values of Mu

and Mw. The pilot adaption rules are applied in order to obtain optimum

performance by closing a single attitude loop, and the effects of the

stability derivatives on the rms attitude response and the rms control

activity are determined. Since pilot opinion data in defined gusty environ-

ments is nonexistent for the subject closures, the results presented are

based only on analytical findings.

The Gust Model

The gust input speccrum is that represented by Eq. B-1. The integral

scale of turbulence, L, is generally set at 1000 ft for altitudes above

1000 ft and equal to the altitude below 1000 ft. For low speed aircraft

the gust break frequency is generally between 0.2 rad/sec and 1 .0 rad/sec,

and in the absence of flight test data the choice of (% has been set at

0.5 rad/sec -the same value that was found appropriate for the directional

approach case of Subsection 3. This is equivalent to an average approach

altitude of 225 ft as given by ag = (5/2)(Vas/L) in Eq. B-I.

* Langitad±ml Forward Plight

In this section the rms pitch response, ae, and the rms control activity,

%aBO8B, are examined separately for the horizontal. u gust (oug) and for the

vertical w gust (awg) inputs. The aircraft equations are given by Eq. 1,

and the following parameters are held constant at the given values:

Uo = 75 ft/sec Mq = -1.5/sec Zw = -1.0/sec

Xu = -0.13/sec XbB/MbB =-5 ft ZbB = 0

TR-I143-1 44

The gust-sensitivity parameters, Mu and Mw were varied as follows

(the Mu variations are identical to those used in the hover analysis):

S0.0088/ft-sec -. 002/ft-se

For the 0-m-5B closire, the pilot model is as represented by Eq. 7,

where the pilot lead is adjusted to give a phase margin of at least 300

for a crossover frequency of 2 rad/sec. The gains for closure at these

conditions are called the nominal gains.

The rms gust responses in ae and MlBG6B were computed for the horizontal

and the vertical awg gust inputs. The purpose of these computations

is to compare the relative magnitudes of these disturbances (on the pitch

angle and control activity) with those obtained in hover, and also to

examine the effects of changes in the Mu and M1, stability derivatives on

the two responses, ce and abB. The rms responses were computed using the

techniques outlined in Appendix B.

A comparison of the rms responses at hover with those in forward flghs

is given in Table I, where the gust break frequency is I .0 rad/sec in hover

comppred to 0.5 rad/sec in forward flight at the approach altitude.

TABLE I

COMPARISON OF RMS RESPONSES TO ug AND Wg GUSTSIN HOVER AND FORWARD FLIGHT

ore (deg) M6bca B (deg/-sec2)

Low Mu 1 .40 0 3.0 0

HoverHigh Mu 4.o 0 29.0 0

Forward Low Mu 0.55 0.085 2.6 0.-40fl'ight, .. ..

low MU High Mu 5.9 0.095 23.0 0.38

Forward Low 14 0.54 0.85 2.4 5.7,,light, ..

High Mu 0.95 19.0 3.3

TR-143-1 45

I

For all cases it appears that the control activity, M8BabB, in response

to u gusts is greater for hcver; and except for the high Mf cases in forward

flight, the pitch response to u-gusts is also greater for hover. The

latter exception is not serious since the survey of Fig. 1 shows that

the xariation of Mu with soe_ would place its most probable value at

the low r.nge of N, in the above comparison. Thus the hover situation

is generally worse than the forward flight condition.

The observed effects of N and M4v on the forward-flight rms responses

to a ul Est can be sunarized as follows:

a. Increasing Y4, by a factor of 10

1) Increases ae by a factor of 10

2) Increases MbBU8B by a factor of approximately 8.5

b. Increasing M. by a factor of 10 has a negligible effect ona6 ead am B8B.

Similarly, the effects of Mu and Mw on the rms responses to a HE gust

are sumarized as follows:

a. Increasing Mu by a factor of 10 has a negligible effect on

ae and '%BoB

b. increasing M, by a factor of 10

I) Increases ae by a factor of 10

2) Increases MbBa5b by a factor of 9

The computed responses to w gusts are however considered unrealistic since

tight attitude control under such circumstances gives a very hard ride;

that is, the rms vertical accelerations tend to approach

" "- O"92 o.16Anz 32 .2

The pilot more probably elects to "loosen" the e closure (lower tlhe pilot

pitch gain) to allow natural "weathervaning" to reduce the vertical response.

Under such circumstances control activity in response to w gusts is minimal

and the pilot simply lets the aircraft "ride" tte disturbance provided he

has sufficient ground clearance. In any event, whether a control is tight.

or loose, the Paan contributor to stick motions a. attitude excursions i.

T, - 5_1I

due to Muug disturbances, except for low Mu, high Mw combinations (see

Table I). For the latter, the high probability of loose control for v gusts

invalidates the significance of the w gust values given ir -able I.

-e foregoing remarks indicate that while control responses and control

margin requirements computed by pitch closure considerations are probably

adequate for ordinary cruise flight, they my be inadequate for terrain-

following requirements in gusty air. Very probably such requirements willbe set in practice by the automatic control philosophy used to implement

operational terrain-following systems. In any event, such requirements

will depend on both assumed terrain and gust input characteristics.

3. Binv-y of lortant Aaltcl Rsultsfro r B Speed Forward Plight oetit

a. At low approach speed (Uo < 100 ft/sec) the open-loop longitu-dinal roots are not always easily identified or separable intolong- and short-period modes. A possible criterion (needsexperimental verification) to achieve acceptable pitch controlrequires that there be no unstable aperiodic roots less thanabout -0.2 rad/sec (p. 42).

b. Control motions (from trim) required to counteract gusts arelargest at hovez based on the fact that Mu is greatest athover and that Zw never becomes much greater than I/sec (p. 45).

1

MOTION IVf

OPEN-LOOP AM

A. A NOTE ON 0OM1 L POS ON BTU Y

There seems to be some confusion as to the meaning of "control position

stability" as used in the specification (Ref. 1). Speaking precisely, the

phrase refers to the change in stick position for a unit change in speed

about a trim condition; i.e., it is the ratio of change in BB to a change

in u about a trim point at Uo for all other controls remaining fixed. This

is not to be confused with the slope of the curve connecting the level

flight (y =0) trim points of stick position versus velocity (see Fig. 20).

Fwd Fwd

Stick SickY

Unstable

Stable

U U

(a) This (b) Not This

Figure 20. Control Position Stability for y = 0

In the latter cace the collective pitch is usually changed in going from

one trim point to another. The spteification neither refers to nor is

intended to imply the use of the latter case. If the motion of the vehicle

can be described by the linear equations of motion about a trim point, then

the slope is the steady-state part of the transfer fuiction of u to 6 B as

given in Ref. 2:5B IE

os 0)

where E : g(ZuYw-MuZwj) and Du = g(M8BZW-ZMW)

TR-145-1 48

For the flight ranges of the two example helicopters considered in

Ref. 2, the control position stability can be represented by the approxi-

mation

"- (20)

Since MbB is usually nearly constant over the speed range of the heli-

copter, the static stability is primarily determined by Ma variations

with speed when the above relationship, Eq. 20, is valid. The condition

for validity of Eq. 20 depends on the inequalities

ZaMw << MUZW

5Bw<< 6

Since the "concave downward" test was first introduced as a measureof maneuver margin, several attempts (see Refs. 20, 21, 24, 25) have been

made to translate this requirement on the transient behavior of normalacceleration into more easily understood relationships in~volving the

stability derivatives or the charazteristic factors. The most noteworthy

attempt is the approach presented by Seckel (Ref. 20). This approach

reduces the requirement to bondaries in the "s" planes -which define the

corresponding regions for the characteristic short-period roots or factors

(see Item 3.2.11.1 of Section V-B).

2or Iq + Zw

st Tsp1 Tsp2 (21)

1~ 1or I " Zw -UoMw

. P TsPl T sp 2

Although the short-period mode is fairly representative of helicopter

characteristics at forward speeds, there are conditions involving negative

Mu and/or positive M, where short-period dynamics, as such, do not exist.

The concave downward test in this instance can give a false indication of

the handling qualities.

TR- 14.- 3- o

An eample of such a situation is Wow frc. Ref. 2 where, over the

forward speed range investtiated (up to t20 ft/sec), the tandeu-rotor

confi-aticn possesses a positive * and a oderate Ma of neative

sign, but with I'ki << *,. Under these circumstances the characteristic

long1Maiz l roots il lie alsmg t root locus (Fig. 21) of G(s) + 1,

Sketch of typical Values

and chosures. Arrow indicates jWincreasing Mu.

:1P Ii

I. -o -I_- 10

Tsp, TSP2

Figure 21. Intermediate Modes ArisingThrough Sah Negmtve M. and Postive Mv

where G(s) is obtained from an approximtion to the characteristic deter-

mingnt (Ref. 2):

Ggs) = - ZW+ (22)G(s) = s2[.2 + (-Z, - Mq)s - Uo.N + MqZ] (22

Typical results of the closure are indicated by the I symbols which

become the roots of the characteristic quartic. The two short-period

poles (poles are X in Fig. 21) could have positive maneuver margins

(MqZw -Uo14 w > 0) and satisfy the "concave downward in 2 sec" requirement.

However, undesirable handling could result due to the large divergent

factor shown as 1/TsP2 in Fig. 21. The transient response of such a

configuration is similar to that shown in Fig. 22. It should be recog-

nied that the time history depicted is not considered satisfactory

TR-1 143-1 50

-equires tat the response "...rejin concave downvard until the attain-

ment of wnxImm acceleration." This portion of the specification there-

fore proibits negative mlues of 1/Tsp2 .* ii

* 9L05

nz

II

1.00 1 2t 2 3

Figure 22. Transient Due to Negative Ma with Positive Ai

However, there are indications, e.g., in Ref. 19 discussed previously

on p. 42, that divergent (negative) values of the aperiodic mode as high

as 0.2/sec are acceptable (rated 3-1/2). At zero stati, margin (UoMw = 0),

the minimum damping of Section III-A (-q = 1.5), and a typicale value of

-Zw - 1 for forward flight, it is estimated that to limit the divergent

factor to -0.2/sec means the equivalent of M. "-0.0021 at zero angle of

attack stability (UoM( =0). It appears possible, therefore, to have

situations in which neither the complete "concave _-nward" reqturement

nor that for control position stability are met, but which are considered

z ceptable.

C-. OUI-ILOP TO PA OW MM

The roll rate response to a bA unit step is usually a first-order lag

(assuming no dutch roll excitation) where the time constant, TR, is

approximately equal to .1 i-Lp:

p(t) = L-IF$ oA I (23)

TR-143-1

3nd the steaty-state roll rate ilor a. uui szez: ~.io

th- control ser ittlity to the roa di;... e f: the RASh

cz ,tgurations of Ref. i5 where tbe spirp[ =e (1/Ts) is appreciable

and sometimes equ. :t, the roll subsidence ( /At),

P(t) = -' + '1 ( T_.), (24)

In the latter case the steady-state rolling response is zero and a steady

b3nk angle is obtained for stable spiral modes. The pilots in the NASA

test of Ref. 15 gave these situations a good rating, which would seen to

contradict -good handlJ qualities requirements for conventional air-

craft. The steady-bank angle of the XRSA test was smosthL and

_uiday attained, and since heading rate is proportional to bank angle

(for mU sideslip), the effect was to mike heading to ailerm almost a

pure rate system. Under these circumstances the vehicle steers like an

automcbile and there is no basic objection to such - respouse. Such

responses have, in fact, been proposed as more desirable than tie conven-

tional roll-rat-a response, but there axe other aspects which Ndst be

considered. For example, precise control of lank angle in ,ty air

MSY be more difficult - not a major probie in the NASA tests.

The computed roll, rofl-rate, and sideslip time 1_istories for the

NASA and NRCC configurations of Appendix B are shown in Fig. 23. High

sideslip occirs independently of the type of "p" response (1fTs large or

smal) and this is consistent with the pilot's complaints of high f even

for the best rated configuration. Of course as sreed reduces, sideslip

is not a good indication of discoordination. For example, at hover a

given bank angle produces a side velocity only, therefore, a 900 side-lip

angle; but there is no lateral net force on the pilot who judges the maneuver

to be perfectly co-ordinated, In view of such considerations, -it might

have been more aspropr);-:te to compute the lateral acceleratio rather than

sideslip angle time responses for the Fig. 25 cases.

TR-143-1 52

p- .2 -

(rad/sec) J 2

00~ 5 O"1 - lo)-, O:!-.2-$ C

*pLOj 2

(red) 00 0 p00 11 1 0 5 10g-

a)NASA 1(A) PR:6 d) NASA 16(E*) PR:3

(red/sec) .

.0 5 l0--

.3

I (rod) .5 .5

0 1*1.5-

' -. 0 b) NASA 4(0) PR 5.5 e)NRCC I FR:3

.3-2P .2 ..

0(rod/se) 0s

(rod) / - - 0 5 I01.0

(od1 5 10

c) NASA f)NRCC 2 PR:60 AS I(t) PR 2.5 _____________________

Figure 2-5. Open-Loop Rebpoises to 1-Inch 5tep

F TI1 -l>

As for '.e bank-angle and rol -rate time histories, there is a clear

distinction between the right and left columns as regards the type of

response. Obviously the right set represents roll-raLe control in accord-

-ance with Eq. 23, whereas the left set, governed by Eq. 24,, show examples

o bank angle proportional to input. However, if the steady bank angle

is achieved reasombly fast and has suall residual oscillations (Fig. 23c)

the pilot ratings are about the sam as for the "ideal" roll-rate cases.

Notice that such good. ratings are delivered despite the obvious roll-rate

reversals that must occur to limit the bank angle. Such reversals, clearly

an integral part of the maneuver, cannot be bad. On the other hand, con-

sidering roUl-rate control, reversals that car occur due to dutch roll

interactions excited by wpJ1 dJ 1 (Ref. i4) are undesirable.

The cause of the Uarge difference in pilot rating between Figs. 23d,

23e, and 23f is not evident from the time tzaces shown. However, if ve

consider head i g response (not depicted) to be given by (for Yv -O, as was

the case) r = (g/U00 )- , then it is clear that the characteristics corre-

* sponding to Fig. 23f are inch worse than those of Figs. 23d and 23e. For

exlpzple (for Uo 5-- 50 ft/sec), i:t appears that for the former case the

heading does not respond in the desired direction for about the first 3 sec.

*This poor heading response carries over, of course, into the closed-loop

situazion already discussed in connection with Fig. 13, where the compari-

sons clearly show the inferiority of the ARCC 2 configuration.

D. 85n V= AMD 15111 PC=

General.ly speaking, it has been very difficult to obtain any sort of

handle on sensitivity or control power requirements either by analytical

means or from experimental data sources. For the closed-loop analyses of

Section III the sensitivity was always assumed optimm and the control

poer required for the closed-loop tasks was always found to be a small

percentage of the total power usually available.

There appear to be many examples in the literature, Section V, where

the specification requirements are considered inadequate and most refer-

ences seem to feel that control sensitivity and power shoald be specified

as a function of mission instead of weight, although there is veiy little

TR-14-i 54

i-nformtion as to what the mission or mneuver requirements should be in

terms of either control sensitivity or power.

I. La m tultzai 0%ftoI Smamti it

From the closed-Ioop analyses of Section III-A there is some evidence

that the optimum longitmdinal control sensitivity has the form of Eq. 17:

a basic value plus a term dependent on the gust sensitivity. Experiz:ntal

evidence from Ref. 14 indicates that for the longitudinal hover case the

optinm sensitivity, 6., is dependent on Mu az Nq, whereas in the direc-

tional approach case of Ref. 16 the optimum N5 sensitivity for gust

disturbances appeared almost directly proportional to Nv (see Fig. 1 6b).

The term independent of Mu In Eq. 17 is best "explained" from open-loop

considerations. Taking "optimum" 3(5 versus Mq data from longitudinal

examles for Mu = 0 show these data to correlate with an angular response

±n 1 ziec time. This ccrrelation ir given in the presentation of Fig. 24

where the optimm sensitivities are replotted on the V-BBversus Tsp (1NA~)grid (see Ref. 3) for 8B = 1 inch. For unit stick step inpu'-s the ordinate

2.0l- MU<2 tm ftec A Ref. IU o so

|t/sec 0 Ref. 14 "opt M8 8

x Ref. 50 for 8-Il

o1.0 Note: A, assums a O2sec;;M3 Iromp elevoor which is

(rod /sec 2 ) 9- =8 1 rod (ref) freated as an effective0Q1sec delay

09 81 0.075 rod

0.2-

0.1 0.2 0.5 1.0 2.0 5.0 10.0Tsp" I/Mq (sec)

Figure 24. Optimum Longitudinal Control Sensitivity for Low Mu

RJL- 1 4,3-1 55

becomes the optimum control gain, NB. Lines of constant pitch angle in

1 sec, 61 , and steady pitch rate, qo, are parallel to the heavy refer-

ence lines shown. We see that 01 = 0.075 ad = 4.30 represents the kind

of Ditch response the pilots find most desirable for these configurations.

The points in Fig. 24 represent data obtain-A from both flight test and

fixed-base simulator for best-opinion Ne. where Mu is known to be small.

On this basis the optimum gain in still air is set by the damping level

to give a desired attitude displacement in 1 sec. This means that the

miniMm control sensitivity for M. = 0 and for the minimum acceptable

damping of 1.5 (Tsp = -I/Nq = 0.67) is approximately 0.25 (rad/s c2liinch

five Fig. 24. An adtioal a above this basic value is required for

4gust sensitivity (M.) effects and possibly for extra mission -requirements.

However, because Ma is unknown for much of the longitudi1al data on Mq

versus N5, it is bard to obtain enough data to establish t#e "additional"requirement.

9. eetUeM, 0mtUV NOMIUV~ty

The results of Ref. 16, already discussed in the preceding section in

connection with the heading control task, also seem to support a response

in 1 sec criterion. For example, the data points lying along the "over-all

optimum" line of Fig. 17 are shown in Fig. 25 on a grid similar to that of

Fig. 24. It my be seen that the "over-all optimum" NBr versus Nr points

correpond closely to "0.19 rad 10.90. Of course the actual responses

are somewhat dependent also on the value of UoNv, which varies with Nr

(Fig. 17), but is not included in the simplified calculations on which

Fig. 25 is based. However, the errors involved. in neglecting this effect

are small (less than about 10 percent) for the tested values of Nv

(Uo 50 ft/sec) and are probably less than the uncertainties involved in

identifying the optimum Nbr's-

We must remember that these results were obtained in simulated gustiness

corresponding to aVg = 8.9 ft/sec and that the responses are probably greater

tian those that would be considered optimum for a nongusting environment.

This follows from the notion, explored above (p. 38), that the pilot-selected

values of "optimum" NBr reflect his desire to reduce pedal activity, in the

TR-43i 56

10.0- x Ref. 16 "Opt" NSr3r for 8r=I"

5.0Note I*usswrie a 0 2 sec

.Nar romp rudder wNch is, freated as a7 effective

(rcmd/sec 2 ) 0sec delay

0.2

2.0-

~~Nr

TR-143-I 57

presence of gusts, to an acceptable level. Incidentally, the over-anl

optimum Nbr values shown in Fig. W7 and plotted in Fig. 25 are essentially

the same for either the hover or circuit-flying (Uo < 40 kt) tasks of Ref. 16.

3. lateal C stral 8"itLvity

Figure 26, taken from Ref. 3, shows-the variation of optimum roll power

for a iumber of lightweight (2500-4500 lb) flight-tested VTOL configura-

tions. As noted in Ref. 3, these data are probably more indicative of

desirable control sensitivity than of control power because the control

actions used by the pilots were all in the small deflection range. For a

:1 mximum stick displacement of 5 inches (as in the X-1 4) the optimum value

of qp per inch is about 0.15 rad 8.60.

If we discount slightly the values of 4I, noted above, because of the

quite gusty environment in which they were obtained, we see that, roughly,

;he optimum control sensitivities are in the ratio

e1 :I :(p " 1 :2:2

We can compare these with the ratios specified by MIL-H-8501A which are

given as el : *1 : (p/2 = 45 : 110 : 27

To effect a direct comparison we convert qP/ 2 , the bank angle attained in

1/2 se,, to qp by multiplying by a factor of 4. (For the 0.1 sec effective

time delay assumed, the actual factor varies from 3.9 at TR = 0.5 to 4.4

at TR = 1 .0.) Then the, MIL-H-85O1A-speciffied ratios are approximately

01 : *1 : ) I I 1 : 2.45 : 2.4

These values are in reasonable agreement with those based on the data

presented above.

On the other hand, simulator experiments, Rrfs. 27 and 49, tend to show

that the desired 1 sec response about the various axes is about equal if one

takes into account the speed stability associated with the axis (Mu, Lv,

and Nv). However, flight test results tend to agree with the preceding

sensitivity ratios, possibly because the pilot has other criteria which

TR-143-1 58

10.0 Ref. 47

Numbers in Parentheses

I

H- (Refrence)

ii ZX214 .75rad

S-Irad/sec1.0 t -(Reference)

OW2X-14

Note: 0/ assumes a 02 secromp aileron which istreated as an effective0sec delay

0. , i i I I i lil i I i I i l

0,1 10 10.0TRFigure 26. Optimum Lateral Control Power

lead to a different sensitivity between the longitudinal and the lateral-

directional axes. One such criterion could be associated with maintaining

zero side velocity on the landing gear.

As regards the absolute values of the desired response in 1 sec, more

data are required to firmly establish the general validity of the above

numbers, especially with respect to the possible influence of size or

mission. In terms of the above discussion, the question of size effects

boils down to whether pilots will accept degraded 1 sec performnce as size

TR-143-1 59

tI

increases. There is little in the auove dat to reject or verify such a

possibility.

2. SON= wr XucMu AUI=A mm uRM O i-1 CW7.ANK

I. The static igtd l stick stability wJLth speed is given (p. 149)for any trim speed by the approximate expression

u 3%

vhose validity depends aostly on the inequality

2. The "concave doun.mrd" requirement of the specification mybe unduly restrictive (p. 51), considering tolerable valuesof neative Na (approxiately -0.002).

3. These negative values of Nu can result in unstable wriationsof stick position vith speed which, amlin, appear to be

*tolerable.

i. For helicopters with low Nv and a large spiral mode, lateralstick inputs co-- nd bank angle and associated heading ratesrather than roll rates (pp. 53 and 51), but such character-istics can be acceptable.

). The desirable level of control sensitivity in still air con-ditions and at the min mm required damping, 1.0 to 1 .5/see,is approximately 0.25 rad/sec2/inch for the pitch axis,reflecting a 61 of about 4.50, and about twice this valuefor the yaw and roll axes (p. 56). Additional control sensi-tivity is required for gusty air, depending on the velocitystability.

TR-143-I 60

$

This section is an evalmtcon of the specification in light of the

results which vere obtained fron the open- and closed-loop aly-,es of

the preceding sections. These amlyses form the basis for the selection

rZ criteria vhich can be used to make eaninul correlations amcng the

pertinent experimental data. In many instances the correlations, while

good, are of limited Impact on a specification because they are of limited

scope despite the great amount of extent hand1lg qualities experinental

data. Unfortunately, the great majority of such documented experiments are

incomplete and are not useful in the approach taken in this study because

they do not exhibit the following:

* A description of the mathematical model (i.e., the stabilityderivatives)

* Carefully controlled test environment, such as gust andpurity of task

* Reliable pilot ratings for each indiv-.dual task

These three requirements elimimte almost all of the early work on heli-

Tter handling qualities before the late fifties (pre-Cooper rating) as

candidates for the types of correlations presented in this report. The

best sources of data were the variable-stability helicopter tests conducted

by Princeton (EWP-1), NASA-langley (Vertol 107), and the Canadian Research

Council (Bell H-1 ).

Despite this relatively weak experimental base, it is possible to pin-

point consistencies and inconsistencies, and to translate these into tenta-

tive reco-mendations for acceptance, rejection, or modification of a spec

item. In this process, and because of the limited amount of complete

correlatable data, as discussed above, we also consider other data, experi-

ences, etc., as pertinent inputs to the specification critique. This is

consistent with our standard practice of ch-cking all applicable experience,

whether directly analyzable or not, against the implications of analytically

based correlations. Most of such "incidental" experience used to guide the

TR-14 3-1 t

critique bas already be- cited in the foregoing sections. However, be-cuse

many of the spec item are of a detailed ature, not aenable to general

discussions, some of the "Incidental" experience is cited in situ. This

is especially true of comments and ideas expressed during a survey conducted

by the authors and documnted in Appendix C.

A. 00U3 IB O= uZRi ,, ,iAZ _,5WZC._ : O(,,

The sumary statements previously given in Sections M and IV are

collected here for easy reference, as follows:

1. To reduce the pilot's lead requ rements to vhere they have a negli-gible effect on rating, the minium damping about all axes in the

absence of gust should be greater than 1.0/sec (p. 12). For iugtiloop con-trol such as attitude stabilization and hovering over a spot, the minimumdamping should be increased to 1.5/sec (p. 21).

2. For pitch control in still air, Mu is relatively unimportait froma dynawic standpoint; increasing MU improves the ability of the

helicopter to hover over a spot (still air only) by providing a largercrossover frequency in the position closure (pp. 18, 21, 24).

3. Increasing the numerator factor I/T6 through nonaerodynamicaugmentation improves the precision hover performance, Cx, in both

still and gusty air (p. 23).

1 . Selecting e and x pilot-closure gains according to established"adjustment" rules provides a good composite minimum to Ce, ax,

and 08B responses in gusty air (the same is true for the lateral case inhover) (p. 27).

5. In gusty air the rms control response, a8 , is roughly proportionalto Muoug (p. 29).

6. An increase in Mq above the minimum of Item I produces smallfavorable changes in attitude responses, ae, and control deflec-

tion, 08, in gusty air (p. 29).

7. Correlation of pilot rating data in hovering over a spot withanalytical results of the attitude and position manual closures

indicates that pilot rating is primarily a function of control activity,.provided the Item 1 condition is met (p. 29).

8. Analysis of recent experiments shows the optimum control sensi-tivity, M6 , to be a function of Mu; as well as Mq, in the presence

of gusts. The optimum 14 is a simple function of both damping, Mq, and thevelocity stability, Mu (P. 30).

TR-I -1 - 62

I

9. te cmtrol pouer requi-ed for the mxian2 gust orqmcted can bespecified on the basis of the rus control deflecti s for random

oust inputs; for example (p. 29),

10. All the foregoing apply also to lateral and directional controlin hover with appropriate modifications in the notion quantities

and derivatives, i.e.,

11. In tracking the IIS localizer with aileron, the aircraft will havegood lateral-deviation control, y --8 A if the heading control

is good, * 8 A (p- 32).

12. Acceptable aileron-only heading control requires a closed outer-loop crossover frequency greater than about 0.3 rad/sec, or, for

the test conditions analyzed, CODV or 1/Tq greater than 0.4/sec in additionto inimum roll damping, -p>1 .5,(Fig. 13.

13. For the control of gust-induced heading disturbances with "rudder"at approach speeds, the pilot's rating is a strong function of the

directional damping. -4r (unlike longitudinal hover) as well as the direc-tional stability, Nv, and rudder effectiveness, Nbr (Fig. 16a).

14. In the Item 13 task the pilot's rating shows a strong correlationwith rms heading response, o3, and with rms control deflection, Obr

(Fig. 16b).

15. For the approach tdsk of Item 13 the *)ptimum control sensitivity,Npr, is a function only of Nv for a given gust input (Fig. 17).

16. The directional damping, Nr, requirements, based on the controltask of Item 15, are a strong function of Nv and the design gust

level, ovg, as reflected in the value of Ga (p. 38).

17. At low approach speed (Uo < 100 ft/sec) the open-loop longitudinalroots are not always easily identified or separable into long- and

short-period modes. A possible criterion (needs experimental verification)to achieve good pitch control requires that there be no unstable aperiodicroots less than -0.2 (p. 42).

18. Control motions (from trim) required to counteract gusts are largestat hover, based on the fact that Mu is greatest at hover and that

Zw never becomes much greater than I/sec (p. 45).

TR-14-i 6-5

I19. The static longitilzal stick stability with speed is given

(p. 49) for any trim speed by the approximte expressio

whose validity depends mostly oc the inequality

7WuN <-<M19a.

20. The "concave douvard" requiement of the specification my beunduly restrictive (p. 50), considering tolerable values of

negtive Ma (approximtely -0-002).

21. These negative vianes of N. can result in unstable variationsof stick pcsition with speed, which, again, appear to be

tolerable.

g. For helicopters ith low N and a large spiral mode, lateralstick inputs coinnd bank angle and associated heading rates

rather than roll rates (pp. 53 and 54), but such characteristics can beacceptable.

93. The desirable level of control sensitivity in still air condi-tions and at the minlimman required damping, 1.O to 1.5/sec, is

approximately 0.25 rad/sec2 /inch for the pitch axis, reflecting a 0l ofabout 4.50, and about twice this value for the yaw and roll axes (p. 56).

. Additional control sensitivity is required for gusty air, depending on thevelocity stability.

3. SP3CD'ICA Z0-DALD C0EU3IO

Before delving into the individual specification items, it is expedient

and desirable to summarize and express the foregoing results in a way that

relates them more directly to the specification, as follows:

1. Rota daMIM about all axes should be a minimum of about -1 .0 to

-1 .5/sec. Such values appear necessary to avoid degraded opinion due to

excessive pilot lead generation.

Applicable to the following MIL-H-8501A items (see pp. 80-109):

3.2.11 3.3.5 3.3.153.2.13 3.3.6 3.3.183.2.14 3-3.7 3.3.19

TR-14h3-1 CAI

2. OMt' iMI tvt

2. * di " uoptlMi" values appear to be associated with the

maneuver response criteria expressed in tems of the angular displacement

achievble in 1 sec. For a 1 Inch steD control displacement, "optimum"

values ae &1 " 4.50 and about twice ths value for q, and *1-

b. The unlin- -%;Lues of control effectiveness (rad/sec2 -inch),

corresponding to Items 1 and 2a, my result in relatively large rms controlinputs, %, cud position errors, ae, if the gust excitation (Maug, Lvvg,

[vvg, etc.) is sufficiently high. general, an additional increment in

control effectivenp:s proportional to the gust sensitivity derivative (MU,

Lv, Nv, etc.) is required to limit control activity and/or attitude or

translation errors to acceptable values. Where attitude rather than trans-

lation errors are of primry importance, increaiid rotary damping above the

level specified In Item 1 above ill have a small beneficial effect.

a. If the additional required effectiveness due to Item b above

results in appreciably increased 1 sec responses, the rotary damin must

be increased to reduce the now-oversensitive response to no more than about

150 percent* of the nouial Item a values.

:1 Applicable to the following NInL-H-8501A items (see pp. 72-106):

3.2.2 3.3.3 3.3.7 3.3.183.2.13 3.3.5 3.3.15

. Oo}t"'ol pwer must in general be sufficient to:

a. Trim the aircraft about all axes over the desired normal andand emergency operating conditions, including atmosphericwinds.

b. Maintain or recover control in gusty air

c. Perform required maneuvers consistent with the aircraft'seffective utilization

The Item 3c requirement demands consideration of the aircraft's

specific mission and intended use. Such considerations are beyond the scope

of this study, but they usually seem to involve normal force and performance

*A rough estimate based on data in Ref. 18; also supported by Fig. 25,

which shows optimum $ relatively invariant for various Nv'S.

TR-3-165

camacity rather than control power, per se. That is, generally speaking,

twie time spent in, aneuvering by pulling load factor or accelerating,

climbing, etc., is usually mich longer than that spent in changing attitude

(e.g., Ref. 8).* &Ice the foregoing Item 2 seiisitivities are pilot-selected

to give him adequate response Rnd control for relatively sll ccntrol inputs

(recall the relatively small os shown in th Section II analyses), it seems

likely that maximum maneuver response requirezments will be less than those

obtainable by linearly extrapolating the desired sensitivities to full

throw. A suitable factor my be something of the order of 60 percent of

full throw, corresponding to about 3 inches of stick (lateral and longi-

tudinal) and about 2 inches of rudder. Applying such deflections To the

Item 2 sensitivities results in maneuvering capabilities of:

el 13.50

*1 =180

Whether such figures would be generally applicable to all helicopters

is of course very unlikely. The real maneuvering requirement must be a

:1 function of the vehicle's mission and expected use. For example, *I = 180

is obviously an inadequate maneuver capability fo- an armed helicopter

requiring quick turnaround at low speeds. On the other hand, (p= 270 .y

be overstating the roll maneuverability requirement for very large heli-

copters, since a corresponding requirement for large airplanes in the approach

condition is less than about 60 (Ref. 8).

Once maneuvering requirements are established on the basis of the

helicopter's mission, etc., it would then be possible to add to these the

requirements imposed by considerations of trim and gusts. Such stperposition

to be ccrrect should employ a suitable probabilistic model encompassing

maneuvers and gusts and their interactions. Of course the specific gust

sensitivity, terms (Mu, Lv, Nv, etc.) of the individual designs would govern

the agnitude of such additional requirements, as they apparently also do

for the desired control sensiLivity (i.e., Items 2b and 2c).

*Quick turnaround in hover is an obvious exception.

TR-143-1 66

To the extent that missions, expected usage, and governing gust-sensitive

derivatives are a function of size and geometric configuration, logical

control power requirements must also reflect such dependence. To lump such

dependence into the factor W + 1000 as in MN.-H-8501A seems a gross over-

simplification. More reearch .1n the area of mission effects on maneuvers,

and in the proper superposition of the individual control power components,

Items a, b, and c above, is needed.

Applicable to the following MIL-H-8501A items (see pp. 88-106):

3.2.13 3.3.1 3.3.3 3.3.5 3.3.83.3.2 3.3.4 5.3.6 3.5.18

.Ad control with ailerons in approach. Good flight path control

during approach appears to be synonymous with good heading control without

the use of rudders. Furthermore, this translates into a requirement for a

reasonable bandwidth, Z 0.3 rad/sec, for closed-loop control of heading with

aileron, using a closed inner loop of bank angle to aileron. In general

there are a variety of bank angle and heading transfer function numerator

characteristics (as well as the usual dWaominator dynamics) which enter into

the complete picture. However the data analyzed in Section III minimize

heading numerator effects because the associated zeros were always favorably

located. The resulto of the analyses were therefore compactly expressible

in terms of requirements on only the q numerator, ta or 1/T" .

The open-loop consequences of the closed-l)op requirement need more

complete analysis before they can be stated in simple flight-test-producible

terms. For example, it my be possible to judge control adequacy by con-

sidering, as with current requirements on conventional airplanes, the side-

slip excursions following a step aileron input. However, in this case, both

the magi.itude of the sideslip and its phasing with respect to the input must

be taken into account. Furthermore, a requirement expressed in such terms

provides, at best, an indirect indication of the apparent piloting problem.

A more direct approach may be to consider the nature of the heading time

response and, for e.ample, to specifj limits on the time required to achieve

initial heading rate in the correct direction. More wo-k in th 4s area, ex1com-

passing a wider variety of heading and roll transfer function characteristics,

is needed before desirable open-loop properties can be formulated. In the

TR-145-i 6-

'II

meantim suitable closed-loop properties have been identified and can beIuzed, at least analytically.

Applicable to the following IUL-H-801OA items (see pp. 98-100):

3.5.8 3.3-9.1 3.3.9.2

P10 11 dyie etcs are usually such to produce a steady

roll-rate in response to a step aileron input. However, for low speed flight

where the spiral mode, 1I/Tsl, can be large, the steady-state response in

such cases approaches a constant bank angle. These situations are appar-

ently acceptable from the standpoint of roll response, provided the steady

bank angle is smoothly and quickly attained. In effect, the vehicle steers

like an automobile, requiring a constant wheel or stick deflection to hold

a steady turn rate (proportional to bank angle). When considered for con-

ventional airplane roll-control systems, such characteristics are sometimes

downrated because the pilot becomes unhappy about holding an aileron

deflection throughout a long high speed turn. However, for low speed

flying the turn rate is high (r - gp/Uo) and the time spent in turns is

sufficiently short to apparently alleviate this complaint.

Applicable to: 3.3.9.1

6.~~~ Lo6t~ maneuver1Ig wA spW. stablity abaiatsftstics. Asdiscussed in Section IV, the "concave downward" requirement, Item 3,2.11.1,

defines acceptable maneuvering characteristics to exclude mildly divergent

aperiodic modes. However, there is some evidence (p. 42) that such modes,

having time constants greater than about 5 sec, are acceptable. UnfL tun-

ately there is little definitive data on this point and the question needs

experimental resolution. Ftrthermore, since such unstab.e aperiod. cities

will in most practical instances be associated with negative Mu and/or

positive Mm, the resulting control position variation with speed (Eq. 20)

will be slightly unstable. Similar instabilities, incidentally, are rather

common on conventional propeller-driven aircraft in high power climb, where

slipstream effects and direct forces on the propellers can combine to give

unstable Mu's sufficiently powerful to overcome fairly respectable static

margins. Provided control force variations with speed are stable, the

unstable control position variations resulting from such effects are not

TR- 14 5-1 68

normally considered unacceptable; whether they would be for extended

operating times (e.g., cruise) is a moot point.

The entire question of allowable negative Mu, considering both

dynamic and static aspects, needs further research.

Applicable to the following NIL-H-8501A items (see pp. 78-86):

3.2.10 3.2.11.1 3.2.11.2

0. AZID fum W SNXA! 3 -81A

The above conclusions, based on the specific analyses and correlations

conducted during the present study, reveal certain inadequacies in the

applicable specification items -and in the background state of art. These

inadequacies can be translated, almost by direct inference, into a set of

recommendations. However, there is a considerable amount of applicable,

but so far uncorrelated, data and experience which was also reviewed and

which has some bearing on the final recommendations. The fornat used to

compactly encompass all the considerations involved is to present them in

tables which contain the following columns:

8pecification Item: The review is confined to those specification itemsassociated with the fundrmental stability and control aspects of the heli-copter and does not cover such items as vibration, instrument flight,stability augmentation, etc.

Applable Itersature: The results and conclusions of the pertinentpublished saterial are listed.

0mnts: This column contains comments on conflicts between thespecification item and the applicable literature and within the literatureitself. Also, the results of the Government and Industry Survey (Appendix C)are cited here when applicable.

Discussi=o an4 Recomenatons: A discussion of the reasonableness ofthe specification item based on the foregoing and on the specific conclu-sions listed in Section V-A and V-B above, with recommendations for accept-ance, rejection, modification, or additional research.

TR-145-1 69

wMARMm

1. SCOPE1.1 Tis specification covers the desig re-

quircments for flying and ground handling qual-ities of U.S. military helicopters.

2. APPLICABLE DOCUMINT8There are no applicable documents.3. REQUIREMENTS3.1 General3.1.1 W~ith the exception of 3.6, section 3

contains the requirements for the flyiug qual-ities, and for cetain relevant ground-handlingcharacteristis, of all helicopters procured bythe Department of the Army, the Departmentof the Navy, and the Department of the AirForce, that are required to operate under visualflight conditions. Paragraph '4.8 applies tohelicopters required to operate under instru-ment flight conditions. The iequired charac-teristics are those which are considered, on thebasis of present knowledge, as tending to insuresatisfactory handling qualities and are subjectto modification as indicated by new informa-tion. Every effort shall be made by designersto provide additional desirable characteristicswhich have been omitted as specificrequirements.

3.1.2 Unless otherwise specified, the require-ments of section 3 shall apply at all normalservice loadings over the operating rotor speedrange and all operational altitudes and tem-peratures. For the purposes of section 3,normal service loadings shall include all com-binations of gross weight and center of gravitylocations that could ordinarily be encounteredin normal service operations.

3.2 Longitudinal characteristics.CORMaL POWER 33 7=82~t X37AR Aa MW (Re .13), IM PAPE 61-60

3.2.1 It shall be possible to obtain steady, One- to three-axis fixed-base simulator. Repre-smooth flight over a speed range irom at least sentative of 35,000 lb duct-fan VTOL. The study30 knots rearward to maximum forward speed emphasized measuredas lirniid either by power available or by pilot's stick activity ,.¢roughness due to blade aerodynamic limit&- and performance (posi-tions, but not by control power. This speed tion error) for IFR hover 4 u., .

range shall be construed to include hovering in still and gusty air. ,*,

and any other steady state flight condition, The standard deviations .

including steady climbs and steady descents. of the fluctuatingThroughout the specified speed range a sufi- velocity were a percentciont margin of control power, and at least of the mean wind, as 6 (4)adcquate control to produce 10 percent of the listed (p. 72). R 45 O~eplacemen+

TR-143-1 70

-I-

ing to determine "normal service load- tions, although its intent, to provide acceptable2ings." Industry is concerned over characteristics for all "normal" flight condi-

this general operational clause because tions, is clear.I the aircraft are not tested to theseconditions under the demonstration Recommeondation: The conditions for which hand-specs. Satisfying these altitude and ling qualities are to be demonstrated should be

Itemperature requirements could compro- more cl.-arly delineated, perhaps by reference to2mise over-all diisign. type specs or to a demonstration spec.

The cited literature (IAS 61-C A does The applicable analytical results, summarized innot -orovide a deterministic means of Paragraphs J5, 4, 5, 7, 11, and 18 of Section V-A,

otining the control power require- show that pilot rating is I.roportional t tcments for gusty air, i.e., for the activity, in turn proportional to the pitchiniggraph shown, ab versus aD, the impor- moment disturbance level, Muaug; and that minimumltant factor, Mud, is missing. Also, longitudinal power required for control of cuthe vertical gust component is on the gusts (not including pilot remnant) is approx-low side for approach altitudes over mately given by50 ft.

rad sec2M6BGF)B 1 .Muqu 9 i't sec _

TR-

3.2.1 ...... Cotinued KX Iar and Craig (Ref. 13) o.. Cctinued

mm saa ie pacting moment ihov- T= : 1/5 VV (m)ering shall be asailble at esch end to amt(t~sdec~sd , itaF 1 1/1 : /tVv (mean)

Sthe effects of longitudinal distranes. Iisrequirement shall apply At omly to p .redflight, but sim to autorotve t at fwrd Qmlekel of disp Vy bentficial In still &Lr.speeds between sere ad the msmam fwad Ro good wder gust eaditins.

speed for autorotatimn. Withia the liits ufspeed specified in &M1 and during the trauui- A.. Gtbons between hovering aind th e" e x -Lr ttuas, the mtrk and the hdicopter itm Specifies tht the control required to returnshall be fee from o a, iba the aircraft to trii after a 5 knot or 0.2gsoo, br gm.. ob se ed in a e7.L aceeationor 50 /sec disturbance should not

exceed one-half of the control ncsent availablefrom trim to stops.

LOMMMIA 5& DB IOUUDINI 10" aMu wA u (set. 13,), Iii PA~iR 61-6D

3=2 The helicopter da be reasonaly Correlates pilot ratingsteady while hovering in sill air (winds up to with stick disp acement. 4 t,

3 knotw), requiring a minimum movement of The lover the stick dis-the cyclic controls to keep the machNe over a placement, the lovergiven spot on the ground, for all terrain dear- (better) the rating. -fanes up to the d of round efect.In any come, it shall be possible to aacmpiulathis with 1e than 2.04ock movument of thecyi cntols

_R- 14 3-1 72

!-

Cm D M AM

Further, results shad the hover task to be the

most demanding of control power (from trim) evenvnen vertical gusts are considered in forwardflight.

Recommendations: The control margin require-ments portion of this item should be modifiedto reflect the disturbance response character-istics of individual helicopters to a design

Recognizes that the blanket 10 per- gust (random or deterministic) of specified

cent margin in 3.2.1 is not realis- form and intensity.tic; and that margin should be based

on (gust) disturbance be . Research is needed to define design gusts andto establish flight test procedures for demon-

strating compliance.

The correlation of pilot rating with The applicable analytic-l results are sunmarized

pilot's activity in the cited liter- in Paragraphs 2, 3, and 7 in Section V-A.datiroes not specify the wind con- The spec could lead to trouble if it were inter-

rthe speed stbil- preted to mean that the smaller the control

ity, M .- activity in still air, the better the handlingqualities. Increasing Mu in still air willgreatly reduce control activity, but willstrongly increase control activity in gusty air(see Section III-A-3). Tests have shown that

pilot rating is much mor. sensitive co controlactivity in gusty air. Nevertheless, still aircontrol should provide a good indication ofvibration, buffeting, ground effects, etc.; butspecifying the stick movements without a corre-sponding specification on hover position

accuracy is too loose.

Recommendations: To be a meaningful spec,hovering accuracy (depending on expected use)as well as control displacement should be speci-fied. In addition, item should be expanded tocover hover accuracy and control in a specifiedgusty environment. Again, the question ofdesign gusts (random in this case) needsresearch attention.

TR-143-1 73

Z grogWJOM e W i - aM A M3MM (Bef. 29), AN 2ME AiMUAL

3.1 For all conditios and speeds specified They recomnd that all llngitu l and lateralin 3.2.1, it shall be p i trim systems be continuous-trim type so that theflight to trim steady, leingitudinal ontro fore control forces never fall to zero instantane-to sew. At thes trim conditions, tw contros ous3y. A hover switch could be used tostie. Stick jump" whs trim i actuastlit de-energize trim spring.

undedrble

L_011PT Q DW J O PAD CM -A AMMAM (Ret. 29), AU 200 AlfM A

3.2-4 At all trim conditions and speeds They recommend that designer select his forcespecified in 3.2.1, the longitudinal force gradient gradients on premise that if force applied willfor the first inch of travel from trim shall be indicate the response, then the force should beno less than 0.5 pound per inch and no more proportional to steady-state angular velocitythan 2.0 pounds per inch. In addition, however, and would be similar from one aircraft tothe force produced for & 1-inch travel from trim another - suggest 20/sec/lb pitch.by the gradient chosen shall not be leo than New rotorcraft have demonstrated, maneuveringthe breakout force (including friction) exhibited stability. Stick force mneuver stabilityin flight. There shall be no undesirable di- s t tcontinuities in the force gradient, and the slope should be 20 g for typical 3.5g helicopter.

of tho curve of stick force versus displacementshall be positive at all times with the slope for XUR wa MM (We. 1 3), ZAU FAPZR 61-60the fz t inch of travel from trim grmter than or High stick force gradients were desired for IF,equal to the lope for the remaining stick travel. although pilots were satisfied with zero stick

feel for VYR in actual helicopter.

j 11aSM (Ref . 30), XaIIST OF AVIATION RPT.

Results for "Whirlwind" show that pilots like1.5 lb/in. longitudiml and 0.54 lb/in. lateralstick gradients.

ACCLSL AT- Z ATZ

3.2.5 With the helicopter trimmed in steady,level, horizontal flight at maximum forwardspeed, it shall be possible readily and safely tobring the machine to a quick stop and hover.WVith the helicopter trimmed in hovering flight,it shall be possible to accelerAte rapidly to maxi-mum forward speed, maintaining approximatelyconstant altitude.

TR-I -1 74

II

Cited literature suggests a switch to Recommendation: No change; spec seems reason-

de-energize trim spring in hover, but able.means must be provided to maintainservo augmenter backups.

SThe consensus of opinion from survey No experimental support for a universal gradient

trip was that the gradient forces of based on steady rate. The conclusions of See-Table II were about right, except yaw tion V-B-2 indicate that pilot desires correlategradient possibly too low. NATC, with angle response in 1 sec rather than withPatuxent River, claimed forces too steady rate.low in all cases.

Recommendation: No change of longitudinal forceOf course, the survey comments would o rmrqieet.Hwvr osdrto

be dependent on many factors, such as or trim requirements. However, consideration

typeof issin, tabiityof lng- should be given to expanding or augmenting thistype of mission, stability of long- item to include specification requirements for

a longitudinal stick acceleration-force feel forDuring the survey trip, many pilots helicopters.expressed a desire to add g-forcefeel to the stick. NATC pilots even

found it helpful on low speedapproaches.

While the spec is not too instructive and thereis very little to meet, it serves as a checkitem.

Recommendation: No change.

R -143-1 75

im ii

M 00 IMan M W 2),M,, 9M

3±6 WiOU h , tm k oRecomnmend the followvfg liit forces as aginstcontrol foare required to doUm anyU trim 8 lb per spec:and powe conditio to any ther trim sad a" mnLticn cnutsepowCr condition speci-- ed in table 1, or for - C

perfornance of dthe mnaeuvesu uased in 3.2A Icg. axis .... 10 lb 3D lb 40 lbmid 3.5.4 or any other nermal helicopter ma-neuvers, shall not exceed the vIms given ia Kiher for boost, SAS, or "feel- system fail-tablo Ii. ures.

MESA= IC M r I and NA (3sf. 29), AN 20M AMJAL

3.L7 With the conta-l trimnmed for wo Free ply or "slop" sho(lf not exceed 1 percentforce, breakout forCeS, iucluding fet i thM of total travel. Frictin and breakout forceslongitudinal control system, shall confin with should be as shown.the values given in table H wi mmmred in Target Vlueeflight.

ionetudlina ......... 0.5 to 2.5 o.5 to 1.5Collective ........... 1.0 to 3-0 1.0 to 3-0Throttle ............. 1.0 to 3.0

3.2.8 The controls shall be free from objec-tional transient forces in any direction follow-iig rapid longitudinal stick deflections. Duringand following rapid longitudinal displacementof the control stick from trim, the force actingin a direction to resist the displacement shallnot at any time fall to zero. Longitudinal con-trol displacement shall not produce lateral con-trol forces in excess of 20 percent or pedal forcesin excess of 75 percent of the associated longi-tudinal force. For helicopters employing power-boosted or power-operated controls, there shallbe no lateral or directional control forcesdeveloped.

LONGOMMSAL REM= W M ad wTM (Ref. 29), AS20 M LNATIOA lam

3=9 There shell be no objectionable or The response delay shall not be objectionablevxcessiv delay in he development of angular if in this time, T1 , a specified threshold valuevelocity in response to control displement, in the proper direction is reached for a stepThe angular acceleration shall be in the properdirection within 0.2 second after longitudinalcontrol displacement. This requirement shail threshold my be or nz, depending on speed.apply for the speed range specified in 3.2.1. The recommended target value for T1 is 0.1 sec

and a maximum of 0.4 sec to reach either= 0.50/sec or nz = 0.01g.

TR-143-1 76

Forces seen high for uzma oDe-hand Recamendation: No change.•control. AD data in Itef. 29 to '

"based on recent research flight tests

mde by industry, the AM' and otherGovenmnt agencies." I

I it

In general agreement with spec; no Reconmendation: No change. jdata to support suggested cIangas.

Recoianendat 4on: No change; spec seems reason-

t S

if *

ii i

I : able.

The literature appears to be in The high frequency lag of an articulated rotor

essential agreement with spec except can be approximated by a pure time delay (goodfor mximum, value =0.4 see (Ref. 29). up to 10 rad/sec, as shown by Fig, 51 of Ref. 2)This seems unreasonably high when it given by 1is considered that such delays add

i directl to pilot's own delay,

toAl

-- '0.2 to04see. FrteaeaeICCO.elthstimedela isless than 0.1 sec. The product of L.c. iwier,

7,and rotor speed Len'ds to reai rciativelyconstant with 6ize; i.e. , wita increasing sizte,7 increases while Q decreases. Thus, the

R-1 '4 - 77

3.2.9 (continued) NM (Ref. 27), W A NT. 1-162For hover, results show control system responsetime characteristics have a large effect on HQ'sin roll and pitch, but none in yaw. Controldelays and lags increase damping required mostwhen control sensitivity is high.

Z~ImwL FTZ &ZL= OI WAn NAMTW (Rsf.- 29), ASS 2MT AIWAL(PBI AVI ) SM. OEAL 11 011

Recommend control forces should be indicative of3.2.10 The helicopter shall, at all forward the aircraft's forward velocity. Claim rotor-

speeds and at all trim and power conditions craft have not demonstrated this in the past.specified in table I, except as noted below, They farther suggest that in providing static andPoecss positive, static longitudinal control dynamic stability about all axes, the stick-freeforce, and contol posion stbility with respect or stick force stability is the more important.to speed. This stability shall be apparent in Stick-fixed or stick position characteristics arethat at constart throttle and collective pitch- important only if relatively large stick motions,control settings a rearward displacement of and either stable or unstable, are required as longpull force on the longitudinal-control stick shall as stick force characteristics are stable.be required to hold a decreased value of steady,forward speed, and a forward displacement and SAM aM APOM (Ref. 18), NS TN D-58push force be required to hold an increasedvalue of speed. In the speed range between Authors conclude that stick force gradients are15 and 50 knots forward, and 10 to 30 knots secondary.rearward, the same characteritics ar3 desired,

bu', a moderate degree of instability may be -TAIA aM COLVIN (Ref. 31), =Tc-T.-63-32permitted. However, the magnitude of thechange in the unstable direction shall not Authcrs state in their tests of the HH-43B heli-exceed 0.5 inch for stick position or 1.0 pound copter that slightly negative or neutral speedfor stick force. stability with respect to control position is

3.2.10.1 The stability requirements of 3.2.10 not objectionable, provided the control forceare intended to cover all steady flight condi- is positive.tions in which the helicopter might be operatedfor more than a short time interval. As a DLMIELL (Jef. 2 ), ARC PM 3104guide for the conditions to be investigated, thetabulation of pertinent conditions in table I Points out that the desirability of a positivemay be utilized, all referred to the most critical static margin is not so straightforward for thecenter of gravity positiot,. helicopter as for the fixed-wing. Due to diver-

3.2.10.2 The helicopter shall not exhibit gent phugoid with the helicopter, the relation-excessive longitudinal trim changes with varia- ships between static and dynamic stability aretions of rate of climb or desceat at constant opposite to fixed-wing aircraft. For fixed-wingairspeed. Specifically, when starting from aircraft the Mu term is regarded as negligibletrim, at any combination of power and air- and static stability depends on Mw. Increasingspeed within the flight envelope, it siall be Mw provides positive static margin and improvespossible to maintain longitudinal trim with a dynamic stability. For the helicopter the MWlongitudinal control displacement of no more term is usually small and Mu large; therefore,than 3 inches from the initial trim position as increasing Mu is responsible for divergentthe engine power or collective pitch, or both, phugoid, so that positive static margin impliesare varied throughout the available range. dynamic instability.Generally, the airspeeds needing the mostspecific investigation of the above character-istics include V, and the speeds between zeoand one-half the speed for minimum powe.r.

TR-1 3-I 78

comZOe=ZO AND DOCI6 A!O

',(con.zaued from 77"Apparently time lags are more critical additional time delay caused, for example, bythan time delays (compare Fig. 9 with powered control system aynamics m-st be held toFig. 11 of Ref. 27). less than about 0.1 sec, which is not unreason-

able.Recommendation: No change.

Stick force stability is difficult to Ianalyze for the nonboost helicopter,because the blade forces are hard topredict and can be highly nonlinear.

Ref. 18 appears to conflict with The applicable analytical conclusions are summa-Refs. 29 and 31 on whether stick force rised in Paragraphs 19-21 of Section V-A, andor stick position stability is more are further discussed in Section V-B-6. Theseimportant. The discrepant results are are in basic agreement with the suggestions ofmost likely due to differences in the Refs. 29 and 31 that negative speed positiontask and the inherent stability of the stability is tolerable provided the force speedaircraft. stability is positive.

Spec item 3.2.10.1 gives emphasis to Recommendations:those flight conditions of 3.2.10 Consideration should be given to amendingwhere the helicopter is operated for along period of time. This, in effect, Item 3.210 to permit a limited amount ofties item 3.2.10 to the mission. unstable speed position variation. The limiting

degree of instability should be the subject of

Reference 25 has good summry of the an experimental investigation.effects of the stability derivatives Items 3.2.10.1 and 3.2.10.2 appear reasonable asand coefficients of the stability apply to item 3210 no chanquartic with respect to 3peed. How- they .. 0 ng.ever, one must become familiar withthe British nondimensional process.

TR-143-I 79

MWO I= = MUM and ANOO (ef,. 18), 1M 2K D-0

3.211 The helicopter shall exhibit satis- Three-axis test of S-51 (Uo~ = l45 knots).factory dynamic stability characteristics fo- e. pigmlile /.1•3 ielowing longitudinal disturbance. in forward ""p ulile 12 ,3 *.,5 ie

light. Specifically, the stability character- basic.istics shall be unacceptable if the following are Results show handling quai- lnot met for a singlo disturbance in smooth air: ties are improved for

(a) Any oscillation having a period of leas increased danping, but arethan 5 se-onds shall damp to one- also dependent on controlhalf amplitude in not more than 2 sensitivity. L "cycles, and thero shall be no ten- 16. LS.144

dency for undamped smali ampli- AINAM and I f (Ref. 3 ), AEO. ING.tudo oscillations to persst.

(b) Any oscillation having a period greater Simulator results near hover correlate pilotthan 5 seconds but less than 10 rating and control sensitivity with dampingseconds shall be at least lightly factor. For a given control sensitivity, thedamped. pilot ratings are shown to be primarily a func-

(c) Any oscillation having a period greater tion of tcz) rather than .

than 10 seconds but les than 20seonds shall not achieve double ' 1.2racl/seeamplitude in leas than 10 seconds. PK. 5M4?u'e

I 5/54t 4

-. I 30 ,3 - . IS - . 1i

3UL(Ref. 27), GRWB(A MT. RE-1 62

Presents results from moving-base simulator usedto study a tilt wing's handling qualities instill air at hover and during transition (tran-sition results not applicable here). Compareshis results on rate damping versus control sensi-tivity for roll, pitch, and yaw with otherinvestigators and finds that results dependstrongly upon the maneuvering task.

LURRY ead KAMMD (Ref. 29), ABS 20TH AMIUALNATIONAL FORUM

Show boundaries appli-cable to longitudinal, ,n.<:1 41 .lateral, and directionaluncoupled motions. Curve Lbased on capabilitiesand desires of typical 'I pilot. .,'W, rod/sec

TR-I 43-i 80

Of the literature presented here, only The basic problem with this item is that it is ahalf (Refs. 29, 33) is directly appli- blanket specification which covers conventionalcable to the question of acceptable phugoid and short-period modes, and also hover-cycles or time to damp. The other ing oscillatory modes. The frequency and damp-half is concerned with the pitch damp- ing characteristics of these modes vary stronglying derivative, Mq, which is specifi- as a function of Mu and Mq for the usually smallcally covered by item 3.2.14; accord- values of McL pertinent to most present-day heli-ingly the literature and commentary copters (see Table A-II, Appendix A, for approx-for item 3.2.14 is also "applicable," imate relationships). Desirable levels of Mq as

indirectly, here (see discussion in a function of Mu (and assuming optimum Mb) are,*Inext column). however, not consistently expressed in terms ofI The boundaries suggested in Ref. 29, or tc-i.e., these parameters are not, by

I wthemselves, good correlators of handling quali-which require considerably more damp ties. The M8, Mq, Mu relationship for goodIng than the spec, are not supported hovering control is analyzed in the text andby any data shown there. The bound- summarized in Section V-B-1, -2. Some of thearies in AGARD Rept. 408A (Ref. 28), basic experimental data (Ref. 11) used for thewihrqieicessi ovr correlations involved sho~w that acceptablewhich require increases in over

* those of the spec of roughly 0.1 and ratins involv ed th tabe t10.2 for "single-failure" and "normal ratings (PR = 3.5) were obtained for times to

.f .2t" oniions-f repective, anrel double oscillation amplitudes between aboutJ flight" conditions., respectively, arep y a10 and 25 sec fir periods which varied only from!.ialso unsupported by any presentedabu12t14scs an uicrse

idata. about 12 to 14 s as -4 and gM4 increased

The Influence of turbulence on from 2 to 6 and 0.6 to 1.5.

T he influencef33) tu ngs i no t For levels of -Mq 1 1, considered acceptableSA'Harrah's (Ref. 33) ratings is not for small Mu (Section V-B-i), conventionalclear, although 0ug = 5 ft/sec was short-period oscillations, as well as the hover-check-tested. At any rate his results ing aperiodic mode, will automatically beare at odds with Seckel's (Ref. 11, reasonably well damped (i.e., tspaso 1, foritem 3.2.14) which are all for

= 6.3 ft/sec, and large positive Zw + M& " -1; 1/Tsp2 -Mq=Mu Seckel, et , conclude that Recomendations:"...it is impossible to express pilot

ting as a simple function of The (a) and (b) portions of this spec should be

deleted and covered under item 3.2.14 concerning!pitch damping (-Mq) requirements. The (c) por-tion my have validity for unattended operationand should be retained and possibly extended tocover divergent aperiodic modes associated withpermissible -Mu's (see 3.2.10 and 3.2.11.2).

The entire area needs further experimentationand analysis.

Z-141-I 81

iImAzar CATO -= APPICABLE I AM

L8D~~A NAUVE S!AXI! AM (Ref. 24l), NACA WT. 1200

$1.II The following is intended to insure Results of analysis (peaking of A at t = 2.0)acceptable maneuver stability characteriatics, are presented in chart form which shows boundaryThe normal acceleration stipulations are in- separating combinations of longitudinal stabilitytended to cover all speeds above that for mini. ity derivatives that result in satisfactorymum power required; the angular velocity maneuver stability from combinations that dostipulations shall apply at all forward speeds, not. Good prediction for both single-rotor andincluding hovering. tandem-rotor in flight test.

(a) After the longitudinal control stick issuddenly displaced rearward fromtrim a sufficient distance to generate 0 ca 0.2 radian/sec. pitching rate within2 seconds, or a sufficient distance todevelop a normal acceleration of1.5 g within 3 seconds, or 1 inch, O Modified "" parameterwhichever is less, and then heldfixed, the time-history of normal BBC= (Ref. 20), OTAB= AN CMWOL OF AIR-acceleration shall become concave PLOW AND MLICOPRdownward within 2 seconds follow- On pp. 363- 365 he finds boundary of the "con-ing the start of the maneuver, and cave downward" requirement (H in t = 2.0) inremain concave downward unt the terms of short-period roots in the s-plane.attainment of maximum accelera-

tion. Preferably, the time-historyof normal acceleration shall be con-,cave downward throughout the pe-riod between the start of the ma- "' -*nuever and the attainment of maxi-mum acceleration. Figure I(a) isillustrative of the normal accelera- Concludes that "concave do nwi" requirement istion response considered acceptable. a specificati on maneuver margin since a

(b) During this maneuver, the time-historyof angular velocity shall become reasonable acceleration trim gradient will meet

ofcave a wn ar d withall 2. criteria. If trim acceleration gradient (foroncave downward within 2.0 constant fl and ec under varying Q) is unstable,ensfollowing the start of theondsf ng the attainmet of maxi- then maneuver margin is nebative and "concavenouver and the n iio downward" requirement is not satisfied.mum anglar velocity. Fir (b)is illustrative of the angulir velocityresponse considered acceptble. B1 _ (UoMw - Mq) .I

nU 0 ZawM - MZB "

Numerator negativ, ' -t'1 efor stability

Continued

TR-143-1 82

I

coa r ntMrM,= AND

I fThe analysis of the "concave downward"requirement by Amer is based on satis-lying certain functions of the stabil-ity derivatives which are rather messyand not very instructive. Althoughthe approach is more informative thanthe spec, it requires a knowledge of Ithe stability derivatives. I

Seckel's analysis reduces specifica- See page 85.tion to a simple requirement on themaneuver margin, the maneuver marginbeing a simple expression of thestability derivatives, qZw - UoMw.

Continued

TR -1451

3.2.11.1 ................... contlinued 1 (Ie. 1,), AN 2M AIWAL T 7.

Criteria were adopted in part becase of thedifficulty in determining stick position versusacceleration in turn maneuvers. Also, theyprovide a sWIpl easure of inportant charac-teristics fo-nd in norml nlight - not anoscillatory stability criterion. Claimscriterion similar to statility in accelerationflight criteria for the airplane.

=AMU (5s. 21 ), UZ sM. YAVAL

Study shows downwash imterference of tandem-rotor causes a reversal of stick position withspeed, with an associated divergence in dynamicstability. May be elimnated by swashplatedihedral angle at the expcnse of increasing -Maat hover where downwash effect is absent.

States that the tandem can satjfy the NACA"concave downward" requirement, but does notnecessarily indicate ae-ceptable raneuverability.Claims the RACA criterion was based on measure-ments of nz for a single-rotor helicopter whereM. usually has a small positive value and nopurely dive,-gent mode. Suggests that responseis determined by dynamic stability and that goodresponse will occur if there is good tsp and ifthe phugoid is no worse than slowly divergent.

WAZI (We. 25), ARC R AM) X 310

Develops a maneuver theory analogous to conven-tional aircraft and claims that tre coefficient"C" in the stability quartic gives a good indi-cation of helicopter handling characteristics.The larger the C, the more rapidl3y the heli-copter will reach steady-state.

An example (S-51) without tail failed to satisfythe "concave downward" requirement at all speedsfor which the maneuver mrgin is negtive anidMu positive. Author states that the mneuveringqualities are vastly improved with a tail whichprovides negative Mw and inereases Mq. Furtherstater that the :'E" coefficient my becomenegtive at high Uo, lead-ing to divergence.

TR-,4 -1

-DUICMI A3D U OTIO3

Tapscott says that aeeeleration trimgradients are hard to detera.ne.,vhereas Seckel (Ref. 20) claimw itis easier than masuring the dynsuLcreonse.l ~UThe applicable conclusions of this study are

su mrizid i.n Section V-B-6, which calls atten-tion to the fact that slow aperiodic divergenceswhich are apparently not objectionable (e.g.

Ref. 21) are specifically prohibited by this

item. Since the intent of this spec is toBramwell is another reference which insure constant-speed maneuvering stability,points out that the "concave down- some modification of the maneuver or the specv trd" requirement does not neces- language to suppress the effects of speedsarilv indicate acceptable maneuver- changes should be considered. For example, theability. Also infers that the corresponding conventional airplane requirementrequirement on dynmdc stability will for stick position and force variations withdetermine the response. normal acceleration specifies that the maneu-

vers be performed at constant speed.

Recommendation: Consideration should be givento modifying this specification to eliminate,or recognize the acceptability of, slowdivergences due to speed changes.

Bramwell demonstrates that themaneuver margin (coefficient "C")and the "concave downward" require-ment yield the same result for thesingle-rotor helicopter.

In regard to his concern for thecoefficient "E" becoming negative, abrief survey of single-rotor helicop-ters shows the sign of "E" is alwayscontrolled by Mu for Uo < 200 ft/sec.

E o ZU -and

IjM ZI >> IMWZUI

____________________________________ ______________________________________________

II

BflZIZATZN (AICA LTIMA!T

L~~IGmuL NA eUVUn 00131M and~ m M M 8 (Be. 29), AM 20TH AIIALNZAO YME

3.11.2 To insure that a pilot has reason- To evaluate transient characteristics, they con-able time for corrective action following uuod- sider the aircraft short-term response to a stepcrate deviations from trim attitude (,s, for or pulse.example, owing to a gust), the effect of anartificial disturbance shall be determined.When the longitudinal control stick is suddenly __ 0-5_to_1.__sec _,

displaced rearward from the trim, tihe distance Idetermined in 3.2.11.1 above, and held for at The characteristics of the response which areleast 0.5 second, and then returned to and held considered i ortant in achieving good handlingat the initial trim position. the normal accel- consies fortat inpchie :eration shall not increase by more than 0.25 g qualities for the above input are:within 10 seconds from the start of the disturb- ._L

anee, except 0.25 g may be exceeded during the e or n r - --period of control application. Further, during (depending on speed) 3- tthe subsequent nosedown motion (with thecontrols still fixed at trim) any accelerationdrop below the trim value shall net exceed0.25 g within 10 seconds after passing through TI = 0.1 to 0.4 for 0 = 0.50/sec or n = 0.Olg

the initial trim value. = 0.1 to 1 .0 sec; target 0.5 sec

Op = 0.05 (b or n)steady.state

as presented under spec item 3.2.11 bysame authors

3.2.12 The response of the helicopter to JEW (Ref- 35), AMS 20TH AIIAL NAT. RMmotion of the longitudinal control shall besuch that in the maneuver described in 3.2.11.1, Good mneuverability - high speed, low bladethe resulting normal acceleration always in- loading and power loading.creases with time until the maximum accelera- Present spec contains little .0tion is approached, except that a decrease not informtion on stability andperceptible to the pilot may be pernmitted. handling qa] ities based on

mission (weapons here) ormaneuvers (turns, sustained nz).Suggests criteria for nmneuverability - abilityto pull and sustain a noinul load factor.

WE I I IMM AND WWI= (Ref. - 6), AUB 2MTAMUL NAT. FWUM

nz characteristics are found to be most impor-tant longitudinal requirements. Two types ofnz -maximum (constant ec) quickie; sustained(constant u, P, and h, variable Gc) turns.

T0

TR-145-1 86

c DISMOWIOKAND

There are no data in Ref. 29 to Item 3.2.11.2 seems extraneous in view of othersupport the proposed response char- requirements on dynamic and static staoility.acteristics; also, tne desired char- Furthermore, as stated, it is not indicative ofacteristics are not definitely the problem it is supposed to address- the

associated with the intent of pilot's ability to (comfortably) correct dis-3.2.11.2 "...to insure...reasonable turbances due to gusts. The closed-loop analyses.time for corrective action... owing to and .correlations discussed in the text are

a gust...." specifically concerned with regulation againstgust disturbances - ard the resulting require-

ments on M and M5 should adequately cover thisquestion.

On the other hand, the item seems to recognizethe possibility of acceptable slowly divergentaperiod or oscillatory modes.

*Recommendation: Combine with recommendedchanges to 3.2.11(c).

IReference 35 is concerned with the Item 3.2.12 is an additional specification ondevelopment of criteria based on the shape of tht "concave downward" time history

weapon systems considerations, which (5.2.1.I1) designed, apparently, to prevent

are beyond the scope of this study. initial reversals in the time resporse- seeiasreasonable.

Recozmendation: No change.

Reference 36 is concerned with liftand performnce rather than stabilityand control.

A. ~ -i4-1 ky

in III IWOL I To 2APOOON (Reft. 37), lAS PAPE 6D-51iMIAD YAIMM (Or C POUR)W L ft" if Dh kes results of ESA TN D-58 and scales them to

various types (helicopters and VTOILs) and sizes3=13 Longitudinal control power shall be (weights). Control power and damping given as a

such that when the helicopter is hovering in function of weight.still air at the maximum overload gro weightor at the rated power, a rapid 1.0-inch step displacement from trim of the longitudinalcontrol shall produce an angular displacement jai.

at the end of 1. second which is at least 6.W. C..

.W+ 1000 degrees. When maximum avail-able dispkccement from trim of the longitudinal !AIOI (Iet. 34), AN 20TI AWAL RAT. I =Wcontrol is rapidly applied, the angular displace- Ament at the end of 1.0 second sliall be at least Defends the size-dependency W 7 + 1000 1 for

1SO angular accelerations, since he considers thevTV+ 1000 degree.. In both expresbons W control response parameter scale in such a man-

represents the maximum oveoad pes weight ner as to maintain approximately the same linearof the helicopter in pounds. acceleration at the extremities for a given

control input for larger sizes.

0 n A lEMrIC (3sf. 36), ARS 20TADUAL NAT. FOM

Suggest control effectiveness for weapons heli-copters to give -"/mq (618)r -' to 20/sec/in.

LMu (,: . 38), AS PAPER 62-63

The mission or type of operation defines controlrequirements where criteria independent of sizeand configuration are defined for helicopter-type operation.

Develops criterion which agrees with damping vs.control sensitivity plots. Criterion is a pulland recovery maneuver where minimum acceptablevalue of e/I and D/I can be defined by precisionmaneuver and pilot minimum response time.

NIINAR and aAIG (Ref. I), IM PAPER 61-60

Findings show that dynamic scaling of controlsensitivity and damping with size (as indicatedin IAS Paper 60-51) did not apply for the largevehicle (35,000 lb). Minimum leve.s of totalcontrol power recommended in the spec were foundto be adequate in pitch and yaw, but not forroll, particularly under gusty conditions. How-ever, it was felt that total control power isscalable dynamically with inertia and weight.

- ,4 3-1 88

'I ccOE~~~rB I D~CN3ION ANiDO~~DTO

The variation of requirements withweight suggested in Refs. -37 anais ba~sed on specious arguments whichare not supported by present data(see Section V-B-2,5)

§

Type of mission appears to be more See page 91.important than size or weight.

The authors found the minimumrequirements as basea on weight aidnot apply to their situation, butfailed t*o realize at this time thatthe primary factor in determiningcontrol sensitivity or power was thespeed stability, M., in the presenceof gust.

m APPLICABtZ LITERAVa

3.2.13 ..................... Continued (e 39), MBA TND-2786

VFR investigation of low speed control reqlire-ments with Langley variable-stability helicoptershowed control power to be the primary factorinflencing over-all pilot rating. However, forprecision hover task, wide variations in eithercontrol power or sensitivity had no appreciableeffect on pilot rating. However, these resultswere obtained in the absence of trim changes andgust effects (Mu =Lv Mv 0).

IV M (Ref. 27), mom Um. Rz-iQ

Author concludes that the minimum acceptablecontrol sensitivity (in still air) appears to beindependent of task

NO OI~tAL DAWZN9 WLIA (Ref. 5), AG A m REP. 471

3.2.14 To insure satisfactory initial response Simulator used to measure pilot's transfer func-characteristics following a longitudinal control tion in pitch attitude hover control with Mu = 0input and to minimize the effect. of external (Eq. 9) and gusts injected through Mw:disturbances, the helicopter in hovering shall e = o.0175exhibit pitch angular velocity damping (that eis, a moment tending to oppose the angular Wg s(s-Mq) (wg)rms = 5.1 ft/secmotion and proportional in magnitude to the Results of closed-loop airplane-pilot system hasangmlar velocity) of at least 8 (,)" ft4b/rad/ shown a lower bound of airplane damping oflice, where I, is the moment of inertia about 0.75/sec (I/Tsp) to insure tolerable closed-loopthe pitch axis expressed in slug-ft'. stability for IFR. Optimum gain of approximately

10 in./md of attitude error. To a first approxi-mation, au -2 rad/sec over wide range of damping.

BZ=L, ET AL (Ref.- 11) PRIN~oNREPTm. 594

Flight test of variable-stability HUP to deter-mine effect of stability parameters on precisionhover tasks in canned turbulence. The effect ofMu was found to be of particular importance inthe presence of gust. Control trim gradient anddynamic stability were found to be of secondaryimport. Their results disclosed greater controlsensitivity and higher damping required overother findings (NASA TN D-58)

TR-1I43-IJ0

BDIBCU8 ON AD MOOM M=00

The Ref. 39 results are not unexpected On the basis of the applicable results of Para-when the control power available is graphs 5, 8, and 9, Section V-A a id V-B-2 and -3limited to levels lower than that the parameter involved in this criteriondesired by the pilot. (response in 1 sec) is a good one, but its vahe

as a functiQn of mission is inadequately expres-sed by the I'W+lOOO factor; also, no considera-tion is given to the effects of gust sensitivity(MU) which strongly influence the desired Mr,(but maybe not the desired 1 Eec response- seediscussion item .3-5.).

Recommendations: Consideration should be givento rewriting this item to more adequatelyreflect mission and gust sensitivity effects onrequired response. Continued experiments andanalyses are required.

Breul's optimum control sensitivityline on plot of Mq versus M6 givesconstant Mb - 0.2 to 0.3 rad/sec2 /in.(infinite slope). Value consistentwith, but slope at odds with, otherinvestigations.

The single-loop attitude control See page 93.problem of Ref. 5 my not be trulyrepresentative of the pitch controlin hover for Mu / 0. However, theresults show the same trends as dothe more complete analyses ofSection III.

The test of Ref. 11 was one of thefirst to give pilot ratings for theclosed-loop hover task, and to showthe importance of Mu in the presenceof' gust.

TR-i43-

SPEOZYICATION X APPLICA3I, LZORA

3.2.14 ...................... Con.iiued M ad CIAMK (Ref. 14 ), ADA PAPER &-618

Fixed-bpse UAC simulator study reveals factorswhiich define the slope and intercept of optimumsensitivity control line on Mq versus M pilot

rating contours for hover.

For coiensatory hover with gust inputs, theslope (approxiwately 32) is independent of gustlevel and the intercept is mostly a function ofMu and gust level and, to a lesser extent, Xu .(Roll dynamics fixed in good region with low Lv.)Concluded that the oscil- -0 sem ielatory mode dynamics Q .co) are of minor importance ,sjope 7aq-3Zw'thin the satisfactory MCIrange of handling quali- (ulsec) T .. -ties for both compensa- " Tc/- s. PRtory and pursuit trackingtasks 6.rd /Sc-

SDnECTIONAL-IATERAL

DMCTIONAL CONTROL ON THE GROUND

3.3.1 Direct iomnl control shall he 8uffi-

ciently powerful, in order that its use ii. -on-junction witi the otier normal controls wilpermit easy exiecution of all normal taxiingmaneuvers witl, wheel gear on land and floatgear in water using normal rotor speeds. Inparticular, the following ground handling con-ditions shall be met:

ta) It shall be possibli, without tie useof brakes. to maintain a straightpath in any direction in a wind of35 knots.

(b) It shall be l)OSdil)le to make a conl)leteturn in either direction by pivotigon one whcel in a wind of 35 knots.

TRANSLATIONAL VELOCITY OF 35 KNOTS3.3.2 From the hvering ('codition, it shall

be possible to obtai, .,ady. level, translatioiilflight at a sidewise velocity of 35 knots to b,)ththe right and the left. At the sl)ecifiIl side-wise velocity ail (luring the transition fromhovering, the controk and the helicopter it.elfshall be free from oIIjeclionable shake, vibra-tioli, or rouglns.s ii speiied in 3 7 1

TR-143-I

OCH D:OU DZ3WZO AND isaOC DAIOIMThis work is a further verification The results of this study, summarized in Para-of the results Seckel obtained a.bove, graphs 1 and 6 of Section V-A and in V-B-i,only on a fixed-base simulator. More indicate that a minimum pitch damping of aboutdetailed information is given on the 1-Mq - is required independent of mission oreffects of Mu and Xu in the presence size; and values greater than this may be neces-of gust. sary, depending on the values of Mu and M8. For

vehicles not subject to gust upsets (of academicinterest to a helicopter spec), Mq my be allowedto approach zero.

Recommendation: This item should be modified toreflect a minimum requirement, regardless ofsize or inertia, of Mq -1/sec.

No comments were recorded concerning Recommendation: No change; spec item seemsthe contents of this spec on survey reasonable.trip.

No comments were recorded concerning Recommendation: No change; spec tem seemsthe contents of this spec on survey reasonable.trip.

TR-1 45-I j

. Te requirements of 3.2.2 shall be See literature under Items 3.2.2, 3-3.5, and

applicable to lateral as well as to longitudinal 3.3.6.control motions. It slhal be possible to meetthis requirement with leow than ±4-nch move-

went of the directional control.

M CommL PCU (omMLaMW AVAflAMA)

3.2.4 In all normal service loading condi- See literature under item 3.2.1tions, including those resulting in asymmetricallateral center of gravity locations and steadyflight under the conditions specified in 3.2.1(including autorotation) and 3.3.2, a sufficientmargin of control effectiveness, and at leastadequate control to produce 10 percent of themaximum attainable hovering rolling momentshall remain at each end.

* D~IREI L YAW UPOME TO UM~ AM) A 'ARARM MAndIIAX (Ref.- 33), AnO. UG.W4AIDI.D (OwMML PC=u) 0013L amD

Has single-loop sina tor results of Nr versus3..5 Directional control power shall be N~r for single degree of freedom in hover.

such that when the helicopter is hovering instill air at the maximum overload gros weight 200 t %or at rated takeoff power, a rapid 1.0-inch step , vdisplacement from trim of the directional con- ZOtrol shall produce a yaw displacement at the descC. 1 I

110 in Z1 I .0 10.0

end of 1.0 second which is at least 4rW+iOOO .ier (S44degrees. When maximum available displace-ment from trim of the directional control is TAPBOOM (Ref. 37), Z S PAPIR 60-51rapidly applied at the conditions specifiedabove, the yaw angular displacement at the end Scale6 Nr versus N~r results of NASA TN D-58 to

33, any size.of 1.0 second shall be at least !W+1000

degrees. In both equations W represents themaximum overload gross weight of the heli- (-copter in pounds. (r/seIcee

in5 10 6S 5 i0 s

Wlooo W1,ooo

DW (Ref. 16), MCC Uni. LR-4WO

See text, Sections III and IV.

TR.43-1 ,

CONK=I DNMUSZON AND IOOA!

See comments under items 3.2.2, 3.3-5, The applicable conclusions of this study areand 3.3-6. sunnarized in Paragraphs W0, 2, 3, and 7,

'Section V-A.

Discussion and Recommendations for item 3.2.2apply here as well.

See comments under item 3.2.1 Discussion and Recommendations for item 5.2.1apply here as well.

t "!

The ratings of this reference were The applicable analytical results are summrizedtaken at hover in still air as spec in Paragraphs 10, 13, 14, and 15 of Section V-A,suggests. However, the ratings are and in V-B-2 and -3 (also see item 3.2.13). Theindependent of weight and inertia interesting thing about the V-B-2(c) conclusionjust as any handling qualities test is its implication that the optimum response inconducted in a simulator must be. 1 sec uer inch of rudder is largely un.affected

by gust sensitivity, so that this metric appar-ently has some general validity, independent ofthe derivatives involved. Discussion given for3.2.13 is also applicable here.

Recommendations: Some as for _3.2.13.

The results were not obtained athover as the spec requires, and thedynamics of the remaining axes(longitudinal and lateral) were notoptimally set. The latter factcould have a significant influeniceon the pilot's rating about thedirectional axis.

Fully discussed in Scetions IIIand IV.

'2-~ ' 5-I

SP!CICATION TiC APPUCMAM L T AT

DMMDTOM C4WdJ 36LIM POR Dw fnd Y~m (.L. - 16), vT. LR-"W

XWUT V33D AT! ===CA D=MT2I-he a runt of rudder necessary to hover cross-

3.136 It shall be possible to c.iute a coam- vine is a direction function of 15V A n r,plete turn in each direction wh'&l hovcripg overa given spot at the maxinum overload gross Vovweight or at takoff power fin and out of ground o -

effect), in a wind of at least 35 knots. To "insure adequate margin of control during theserneAivern, sufficient control slall remain at Roughly speaking, configurations requiring fullthie most criti d azimuth angie relwtive to the rudder to hover in a I , knot crossvnd werewind, in order that, when starting at zero rated 6.5; those --equiring 1 inch of rdderyawing velocity at this ale, th, rapid applica- pedal "were eligible for a 3.5 rating prov-idingtion of full directional control in the critical dymmics were acceptable.diection results in a corresponding yaw

110 LYI (Pef. - 8)o IAS PAE 62-bdisplacement of at least WTIO degrees in C ef nthe firt second, where W represnts th ma-i- Concludes that definition of yaw controlmum overload weht of ts h mi- criteria and the interpretation of related testsin pounds. must involve consideration of the gust sensi-tivity and the operational wind conditions.

tIPS of LIM .S. ,-¢i / w7nf~eu.Ee C.rit~ct

30

S 3 A

For the example shown in the figure, with windsabove 15 ft/sec, the maneuver criteria falloutside the desirable region which would bereflected in the pilot's rating.

[ - 5-;"

This item combines requirements for trim andmaneuverability in a fairly logical way, and theform of this specification is basically good.However, the required maneuverability as a func-tion of mission is probably inadequately speci-fied by the chosen numerical function of weight.

Recommendations: Same as 3.2.13, i.e., the

criterion values should be specified in terms ofmission and/or gust sensitivity rather thanweight.

The consensus of opinion from the

survey trip was that the 35 knotsidewind set the maximum controlpower in yaw.

The criteria as proposed by Lynn foryaw control sensitivity agrees withthe result found by Daw in the pre-ceding literature, i.e., the controlsensitivity must not only combinewith the proper damping, but mustconsider the speed stability, Nv

(gust sensitivity), and availablecontrol in the presence of wind.

M

SPVECICATION ID( APPLICABO ll ATME

YAZDCD D~IP==W BM5ITVI=f 0 D w V NIQ (Ref . 36), ASS 20THfLN HDVE, LMMTST NOEKAL SliVCE AIM=UAL T. YOMWIDADuNG

For precision ya4 control (weapons fiing) a3.3.7 The response of the helicopter to shoit response time is needed, which implies a

directional-control deflection, as indicated by rate type of control. Points out that heli-the maximum rate of yaw per inch of sudden copters, especially during hover, approach apedal displacement from trim while hovering pure acceleration control. Suggest controlshall not be so high as to cause a tendency for sensitivities of the order of 30o- 50/sec/in.the pilot to overcontrol unintentionally. In and response times -1/Nr < 0.2 sec for hover,any case, the sensitivity shall be considered depending on weapons system.excessive if the yaw displacement is greaterthan 50 degrees in the first second following asudden pedal displacement of 1 inch from trimwhile hovering at the lightest normal serviceloading.

C0= MZA=ED W3 A IN O =ON

3.3.8 It shall be possible to make coordi-nated turns in each direction while in auto-rotation, at all autorotation speeds.

IAT L STA=L~ - N, , 8r, baVMUS I LIEAR; 10 PJM= YARGIN321 LATW" COZR0L

3.3.9 The helicopter shall possess positive,control fixed, directional stability, and effectivedihedral in both powered and autorotativeflight at all forward epeeds above 50 knots,0.5 V.,, or the speed for maximum rate ofclimb, whichever is the lowest. At theseflight conditions with zero yawing and rollingvelolity, the variations of pedal displacementand lateral control displacement with steadysidt-slip angle shall be stablo (left pedal andright stick displcement for right sideslip) upto fdl pc(lal displacement in both direclions,but not necessarily beyond a sideslip angle of15 degrees at V.,,, 45 degrees at the low speeddeterI.ined above, or beyond a sidcslip angledetermined by a linear variation with speedbetwecii these two angles. Between sidesliptingles or ± 15 degrces, the curve of pedal dis-lphecnient anl ltteral control displtcent

plotled agninst sideslip angle shall be approxi-niately linear. In all flight conditions specifiedabove, a 10 percent. margin of both lateral andl 1itudinid control effectiveness (as defined in:3.2.! irid 3.3.4) shall remain.

TR- 1,3-1 98

Single rotors, due to higher damping, Recomendation: No change; the spec appearsdo appear to be a rate control at reasonable.hover, but with a time constant of

X to 4 sec. Tandem rotors are moreof an acceleration type of control

, with approximately zero damping inyaw. These are typical of basicvalues without augmentation

Reconmendation: No change; reasonable require-ment.

Recommendation: No change; the present require-ments for linearity, sign, etc., are appropriate.

TR- --- )

SPZCI NI~ APPLICAM2 LIZMLUA"

MUMW KMVR OF P 0& DMJIB wA~ NORIM (hRf - 4), WMD-R-59-13

3.3.9.1 At the conditions specified in 3.3.9, The amourit of Dutch roll appearing in the roll-it shall be possible to make complete turns in ing motion following a step aileron dependseach direction with pedals fixed, by use of cyclic priarily on departure of (c.au) 2 from unity.control stick alone. At all speeds specified in Shows figure for incipient "?" reversal, assum-3.3.9, no reversal of rolling velocity (i.e., return ing long spiralthrough zero) shall occur after a small lateral mode time con- N R.ves.step displacement of the control stick is made stant, Ts, and 2.5 oevs

with pedals fixed. The stick deflection chosen low dutch roll (_Pshall be such ihat the maximum angle of bank damping, td- Wdreached during 6 seconds is approximately 30 0 .I I.0degrees. This requirement is intended to WTa

apply to angular velocity type controls.

T. 196oAmong other things, they show that acceptableconventional aircraft pilot ratings areobtained (in a fixed-base simulator) only forIP1 I/IPssl < 0.045; where p, is the amplitude ofroll oscillation at the first overshoot followi-ing a step aileron input.

rOicEO (!Wf. 42), HOC REP?. IR-39

Results from airborne simulator show goodhandling qualities region confined to the leftplane where right 8 r produces left rollingmoment. Lv negative and Nv positive.

3.3.9. Durb, pedal fixed roiling maneu- or cen-ol Ao

vera, there shall be no objectionable adverse , withO. ton

tlob,+ c.p_,irable qudraflor rudder control

in turns

Pedal-fixed considerations are given by thehandling qualities along the Nba axis (Lbr 0).

Note: Nbr is positive for right rudderan- Lba is positive for rightaileron.

GAMP a XLLY (Ref. 15). RAUTN D-277

DAW (Ref. 16), Hcc RPm. LR-4O0

See Section 11I.

TR1 +-I 1 G

Co DI3CBMS AM

The references cited here, except for The applicable analytical results are sumuarizedthe last two (Refs. 15, 16) apply to in Paragraph 22 of Section V-A and in V-B-5-.both requirements. A limited survey shows the single rotor generally

Reference 4 relates incipient roll Aas roll rate control, whereas the tandem config-reversal (for rate control situations) uration has roll position control with lateralto the aileron yaw characteristics stick inputs commanding bank angle and associated

through turn rate instead of roll rate. The latter char-

" (a )2 _1 - (N/Lb) LjNv) acteristics involve roll rate reversals which areacceptable provided bank angle oscillations are

For ad) < 0..5, implying negative small and initial response is reasonably fastN~a/ (adverse yaw) for normally (see Fig. 25a, b, c).negative Lv/Niv, reversals will occurfor ldutch rversaswll oinIf the spec is intended to apply only to rollfor small dutch roll damping, rate control situations, as implied by the lastReferences 51 and 42 indicate that the I entence, it seems reasonable, but incomplete inlimit of acceptability occurs before view of unacceptable roll rate oscillations ofactual reversal and i a function of either sign shown in the literature.the relative magnitude of the rolloscillation which is related to Recommendations: Consideration should be givendeparture.; of a/cqd from 1 .0. For to revising the language to clarify intendedexample, the Ref. 42 resx1.ts can be area of application (i.e., rate control) andconverted (for Lbr =0) into the expanding to cover generally undesirable rollfollowing trend!: rate oscillations; also expanding to cover

bank-angle-commanded (rather than roll rate)Ke dynamic situations.

0 0.5 /.O 2.0

These trends are consistent with thoseI for conventional aircraft collected The spec is OK as a check item, but is non-in Ref. 3. instractive and indefinite.

* 1 Finally, Refs. 15 and 16, as analyzed Recomendations: Spec should be rewritten toin Section III-B, indicate that con- Rec omm e ction abe yaw be r erit ics,

siderations other than adverse aileron specify "objectionable" yaw characteristics,e.g., in terms of allowable sideslip or allow-

yaw are important in achieving good able time delay in achieving heading rate inheading control during approach. correct direction (see Section V-B-h).

TR-145-1 101

2r

?I

8ATMI A E3NMOMO

3.&10 For all conditions and speeds speci-fled in 3.2.1 and 3.3.2, it shall be possible insteady flight to trim steady lateral and direc-tional control forces to zero. At these trimconditions, the controls shall exhibit positiveself-centering characteristics. Stick "jump"when trim control is actuated is undesirable.

ZA!UA AS D0TOEA 0 and XATEWS (let. 29), AN 20MH AWJAL2Mn Sol=Z NATICEAL YW.J

They recommend higher limit forces for the3.3.11 At all trim conditions and speeds directional control than the spec.

specified in 3.3.10, the lateral force gradient forthe first inch of travel from trim shall be no Hover Transition Cruiseless than 0.5 pound per inch and no more than lateral ........ 7 lb 15 lb 20 lb2.0 pounds per inch. In addition, however, theforce produced for a 1-inch travel from trim by Directional.... 0 lb 60 lb 100 lbthe gradient chosen shall not be less than thebreakout force (including friction) exhibited inflight. The slope of the curve of stick forceversus displacement shall be positive at alltimes and the slope for the firet inch of travelfrom trim shall always be greater than or equalto the slope for the remain'ng stick travel.The directional control shall have a limit forceof 15 pounds at maxinium dellcion With ,Ulinear force gr'adiezt from t,'iii posit ion. Th ero

shall be no und.*siralle discontinuili s in citherthe lateral or directional force gralients.

UA!RAL ANqD D18=I0NAL AWAR PIT. 408 (Ref. 28)

Recommends the following breakout forces:3.3.12 From trimmed initial conditions, the

lateral and directional control forces required Boost

for the performance of the maneuvers discussed Nomial Failure

in 3.2.6, 3.3.1, 3,3.2, 3.3.4, 3.3.5, :3.6, 3.3.8, lateral ............... 0.5-2.0 < 4and 3.3.9.1, shall conform with tile values given Directional............1.0-10 < 15in table II.

TR-145-1 102

Recommendation: No change; spec is reasonable.

A n

lii inTbe1 1 b)apastolw

The literature suggests higher limit Recommendation: Amend requirement to permitforces for directional control than larger directional control forces.those of spec. This suggestion

Icoincides with comments obtained onthe survey trip.

As noted above, the directional control forcelimit in Table II (1.5 lb) appears too low.

Reconmmendation: Amend Table II to show larger

permissible directional control forces.

103

SPSCIYCATIQN ITD( APPLICAKtZ -L-AT=~

LAMM"L AIM DU=0IONAL AM ESPI. 408 (Ref. 28)WMEAlC0 FORES! CM #Ad YXATTWB (Reft. 29), AH8 20TH AJIITALNA. IOEN

3.3.13 With the controls trimmed for zero

force, the breakouL forces including friction in Both reccaumend the following breakout forces:

the latral and directional control systens shall Boostconform wilh the values given in table II when Normal Failureiiiea.sured in iight. Lateral........., 0.5-2.0 < 4COTOL FORCE CROSS-COUPLING Directional...... 1.0-10 <15

3.3.14 The controls shall be free fromi oh-jectionable transient forces in any directionfollowing rapid lateral stick or pedal deflections.During and following a rapid lateral displace-ment of the control stick from trim or a rapidpedal displacement from trim, the force actingin a direction to resist the displacement shallnot et any time fall to zero. Lateral controldisplacement shall not produce longitudinalcontrol forces in excess of 40 percent or pedalforces in excess of 100 percent of the associatedlateral force. Pedal displacement shall notproduce longitudinal control forces in excess of8 percent or lateral control forces in excess of6 percent of the associated pedal force. Forhelicopters employing power-boosted or power-operated controls, there shall be no longitudinalcontrol forces developed in conjunction withlateral or directional control displacement.

MAX= (JlP/Inch ba Sfld.WM = (Ref. 36), AHS 20THANUL NAT. FOXIM

3.3.15 Tie response of the helicopter tolateral-contrul deflction, as indicated by the Claim the roll response requirement establishedf or an armed helicopter is 140 - 20°/see/in.maximuin r.,e of roll per inch of sudden con- are hencote is notrol deflection from the trim setting, shall not sd Tin tesbe so I to cause a tendency for the pilot specified in the spec

to overcontrl unintentionally. In any case, L and the maximum leit• is considered because

at all level ifighL speeds, including hovering, se1 ofthe control effectiveness shall be considered o p arid its

excessive ii ;ze maximum rate of roll per inch I__ 1_1 _1 effect on easeof stick disp.ucement, is greater than 20 degrees _4 = .ke- of trim during

pe steady flight.per becond.

3.3.16 Tl,,'ro siadl be no objectionable orexcessive dch, y irn the development of angularvelocity in response to lateral or directionalcontrol displacement. The angular accelera-tion shall be in the proper direction within 0.2 See literature under item 3.2.9.second after control displacement. This re-quirement shall apply for all flight conditionsspecificd in 3.2.1, including vertical autorotation.

TR-143-1 1o4

COOrI! DZSCO AND UOODTon

The values recommended in the litera- Recomendation: No change warranted on basis ofture extend slightly the "normal" available data; spec appears reasonable.values given in Table II.

I •,

Recommendation: No change; spec appears reason-able.

I

I

Excessive control sensitivity will always lead to

able; however this spec limits roll rates todeadediotrating ando thse limi isnestir-a

Reference 56agrees with maximum roll valecosdrby eowtsefron ninarat ofspe, bt lsosugest afighter aircraft -i.e., for 5 inches of full I

stick, 3.5.15 results in Pmax = 1000/see, whereasjminimum maneuvering requirement foi- an Ref. 51 requires 1000 in 1 sec and considers thearmed helicopter. However, maximum limit to be 2200/sec. While such rates appearlimit appears to involve low 4, con- excessive for helicopters, they can apparentlysiderations which are not appropriate be'cmcae ~hut vroto ednisto this spec item.beacmoaewihu vrotltndces

Recommendation: Amendment of the limiting value,jespecially for high speed conditions, should beconsidered.

See comments under item 3.2.9.Sedicsonfitm52,.

Recommendation: No change.

T'R-I 45-1 10

BPCYIA I =I~ APPLICAXI MMA MI~

IAUDAL Tfl( MUWM DM TO POW TAP8COTT (Ref. - 3), ASS 20TH ANNAL NAT. IORTA

Analysis of a large helicopter (30,000 ib)

3.3.17 The helicopter shull not exhibit ex- showed that the factor comlete3l overriding anyctssive lateral trin- clages with changes in maneuver consideration was the need to cancelpower or collective pitch, or both. Specifically, yaw moments brought about by power clanges.when starting from trim at any combination of

*power ,ti;d airspeed within the flight, envelopeof the helicopter, it shall be possible to main-tin lateral trim with t control displacementamounting to no more than 2 inches from theinilial trim position as the engine power orcollective pitch, or both, are varied either slowlyor rapidly in either direction throughout theavailablo range.

A RAL ROIL ME8PE0ME T UNIT A1DMAXDM (caMUaoL POER) COIOL STEP

3.3.18 Lateral control power shall be such See literature under item 3.2.1 3.that when the helicopter iq hovering in still airat the maximum overload gross weight or at the ABS MAB (Ref. 3), AGM RUP-. 5rated power, a rapid 1-inch step displacementirom trim of the lateral control shall produce Shows that best opinion in-flight roll poweran angular displacement at the end of one-half for helicopters/VTOLs corresponds to

27 - 0.75 rad. For tests where maximum deflec-second of at least --- degrees. Wien tion was not used, converting to qcp per inch

maximum available displacement from trim (assuming 5 inches of cockpit travel) gives

of the lateral control is rapidly applied at the 0.15 rad " 100 (see Section IV).

conditions specified above, the resultingangular displacement at the end of one-half

81secoi d shall be at least -, -- _-_o0 degrees.

In both expressions W represents the maximumoverload groso weight of the helicopter inpounds.

IATERAL AND DniECIOA DAMPING

3.3.19 To insure satisfactory initial response See applicable literature under items 3.2.14characteristics following either a lateral or and 3.5.5.directional control input and to minimnizothe effect of external disturbances, the heli- ASHEIA (Reft. ), AGAD IMP. 3copter, in hovering, shall exhibit roll angularvelocity damping (that is, a moment tending Correlates desirable levels of rcll and yaw

to oppose the angular motion and proportional damping (1p, Nr) for single-degrce-f-freeorn

in magnitude to the rolling angular v.ocity) cituations (as in hover) and findz acceptable

of at least 18(I,)"' ft-lb/rad/scc., where I. is levels to be near -1 .0 (same as fc fil)

TR-143-1 lo0'

IIDZIOBMZO A1D DOSI 3WO

It would seem, from the Ref. 54 com- Recommendation: Requirements, similar in word-ment, that similar limits should be ing, etc., to present spec, should be added to Uplaced on the directional controls. cover pedal control limits.

ii

See Section IV. The applicable conclusions of this study aresummarized in Paragraphs 10, 5, 8, and 9 ofSection V-A and in V-B-2 and -3.The use of a 1/2 sec, rather than a 1 sec,response criterion, places a premium on ailerondeflection rate, is not consistent with thecorrelations of Ref. 3 presented in Section IV,and represents a difficult flight test procedure.

The discussions and Recommendations ofitem 3.2.13 apply here as well.

See applicable comments under See applicable results imder items 3.2.14 anditems 3.2.14 and 3.3.5. 3.3.5.

TR-i 43,-1 107

3.3.19 ..................... Continued G w U OW. 1), KM 2 D4 77

the moment of k tiabou the tall ai imsu.. in ad.ziio to thoe given in the text,expressed in slug4. The yaw angular vd.ty text, az as folows: hould be > 0.3. Mini-damping should prderably be at least 27(IT m satisfactory 4r ad Sr are in agreemntftblrad/c., where , is tbe i minmt d imeia vith current criteria (Fbr 1 0.2 and Jr 1 -1).about the yaw axis exprmedm in dg-t. For opt iou characteristics at s k > 0.3,

add sufficient fr to Aeld 0.8 < < 0.1.(* defined as Xr/2i% -)

For IFR, reduced Lv results in improvedhandling qtelities due to less disturbancesand/or oscillatiors; for VFR. pilot - insensi-tive to L4 effect.

DAW an XcQF9M (uei. 16), Vc WT. W-4,00

In addition to results discussed in text, theyshow that tA versus dutch roll period, Pd (seebelow), tends to be meningless, since thepilot's min objection as damping is decreasedis based on al- L Cthe disturb- LR 400 -tu$

ances and .6-

not on the S', AGARD 408,pe "-; odic"nat._ ! of the "motion. o _.

-.z--Per'o P, Se .

*GONZALSS i(Ref. -4o), PBII(CM0 U. BXlT. 4i5TGoIB~~ (Ref. i)M PRIN~C umI. BFm. 4d96

PmflCO VAiABI4BT T mUP (m,-1)IN MOM AIR

For gooa handling qualities, %d should be welldamped. 1ITs my be slightly unstable, but highpositive stabiLity desired if Dutch roll dampingis low.

Therefore, desirable spiral characteristics aredependent on d" W .Z

, -43-1 Z.7

TR )I.-i 1

MIN yo- I I m A31

Thedeiralelevels of yaw and roll The basic retary dacping reqWirements do notdaping (the subject of this spec appear to be significantly size-, mission-, or ,

item) are nasked in the results cited weight-dependent. Basic reqa.-re ents for sini- Ihere which are expressed in ter=s of D O ard N. appear to be about -1. but thesedutch roll frequency and dam-in= , ny be low for high -iant sensitivity and corre-

Dutch roll damping by itself has not spondingly high control effectiveness.

been fond to be a good metric of The spec currently does not address questionshandlJg qualities in the listed of a deqite d4-ping and freuency for oscilla-literature. The use of t* (Ref. i) tory lateral modes, although the Iit era tu = sis limited, for it does not indicate a nuber of attemted correlations (insuccess-.Door rests when N becomes small Pal in general) based on these or relateddue t loss of the *-i-ba effective- parameters. Also, AGARD Rept. 408 reco=-endsness in turns (see Section III for the same damping-frequency relationships forother correlations of these data)- lateral as for longitudinal oscillations.

The requirement for minimum N (from All this is very reminiscent of the discussionsRef. 15) uy not be associated with concerning items 3.2.11 and 3.2.14 which apply

dutch roll frequency and damping, equally well here, with suitable cha ges inbut rather with turn coordination axes.questions (Fig. 14 of text).

* Recommenat.Lons: This item snould be modifiedi Spiral characteristics are of course to reflect minimum requirements, regardless ofinfluenced by R4 and Wr; the desirable size or inertia of LD UJr -1 /sec.properties shown in Refs. 40 and 41

, may be due to good roll angle response: characteristics as discussed in

Section IV and 5.5.9.1.

10-

• 10

BOLL Dm = 2Q=u See 5.5.19.

VCMA, fl3A okJ (Bet. 4.3), NASA TN D-14

3.4.1 It shan be pasible to maintain posn- shows iso-opinion plcts for Zw vs. Z5. Optimum

tive control of altitude within 31.O jot by value between 0.25g/in. for Zw = I to 0.159g/in.

use of the colectivo-pitch control while boverin for Zw = 0. If Z., is high, good iandling

at ODtt rotor rpm under the conditions o@ qualities for T/W ! 1 .08; if

3.2.2. This rhall be accomplidwd with a mini- 3 T/W is high, good handling

1u1U mount of collective ac motion 1.0 qualities for -Zw - 0.2.

wruircd. atn in any et3l ishail be poible to - Increasing time delay resultsa-ccmnplih this with kin than +% imch move- LO- in deterioration of control-iutnt of the collective stick. Whn gvuois mpoyeh theae . bem o oveon lability. Regardless ofis employed, there sa be no oijectiona, damping, -r > O.4 gave poorver eronM t diimg frosma la pvg m- control.response. - control

ANMWMA. X TMI (Re. 33), AERO. EM.

Results show optimum gains, Z5, less than

O.3g/in. for damping less than 1 (-Zw I sec- 1 )

3.4.2 Tho cd1ecti °e-pitch control shll re-

Wain fixed ,lt &II ti2ll.e ialthSS Ioved !,y tiepilot and shall not tend to creep, whether ornot cyclic or directional controls aro moved.

The z,:1xinnan effort required for the collectivecoitt'ol Shall1 11oi exceed tie values specified

in t'd,le I. The breakout iorcc (including

* fri,'tion:) shll be Within the acceptable limits,IS " . ,' i , , li, ta llc 1 1.

COLIZC'MIV TO CYCLC O030MM BA

3.4.3 Movement of the collective-pitch con-trol shall not produco objcctionablo ferces inthe cyclic control; in no case shall these forccpexcced 1 pound. In hclicopters where power-ope-ated or powcr-boosted controls are uti-lized, there shall be no control force coupling.__

TR-I43-, 11

See 3.3.19. There is no lateral-directional spec equivalentto the item 3.2.11.1 longitudinal maneuveringcriterion, so that the question of minimum"stiffness" or frequency is not treated in thecurrent svec.

Recommendation: Research and analysis be con-ducted to define the minimum acceptable dutchroll frequency.

The closed-loop situation is similar to thesingle-degree-of-freedom hover mode in pitch,

Both references tend to shour optimum roll, and yaw; but values of -Zw < 1, while notcontrol sensitivity, Z6, at about "optimum," appear acceptable (PR < 3-5);O.25g/in. for the typlcal rotor damp- Recommendation: No change; spec is reasonable.ing of -d" 0.5 sec -l. However, the -

optimum damping appears to be greaterthan 1 sec- 1 (-Zv > I) in hover, con-sistent with corre]ftions in Ref. 5.

The optimum control line in this casealso indicates a constant altitude in

! sec, h.j•

Reconunendation: No change; spec appears reason-

able

Recommendation: No change; spec apipears reason-Sable.

TM-1 43-51 l

1. Helicopter Flinjg and Ground Hndlng Qualities; General Requirementsfor, MIL-H-8501A, 7 Sept. 1961.

2. Wolkovitch, J., and R. P. Walton, VTOL and Helicopter ApproximateTransfer Functions and Closed-Loop Handling u ties, SystemsTechnology, Inc., Tech. Rept. 12d-1, June 1965.

3. Ashkenas, I. L., Some Open- and Closed-Loop Aspects of AirplaneLateral-Directional Handling Qualities, AGARD Rept. 533, 1966.Note: This is a condensed version of Ref. 8.

4. Ashkenas, I. L., and D. T. McRuer, The Determination of LateralHandling Quality Requirements from Airframe/Human-Pilot SystemStudies, WADC-TR-59-135, June 1959.

5. Lollar, T. E., A Rationale for the Determination of Certain VTOLHandliig Qualities Criteria, AGARD Rept. 471, 1963.

6. Durand, T. S., and H. R. Jex, Handlin Qualities in SingLe-LoopRoll Tracking Tasks: Theory and Simulator Eaperiments,ASD-TDR-62-07, Nov. 1962.

7. McRuer, D. T., D. Graham, E. Krendel, s-nd W. Reisener, Jr., HumanPilot Dynamics in Compensatory Systems- Theory, MOdels, andExDeriments with Controlled Element and Forcing FunctionVariables, AFFDL-TR-65-15, Jan. 1965.

8. Ashkenas, I. L., A Study of Conventional Airlae Handling QualitiesRequirements, Part I, Roll Handling Qualities; Part II, Lateral-Directional Oscillatory Handling Qualities, AFFDL-TR-5-158,Parts I and II, Oct. 1965.

9. Etkin, B., Dynamics of Flight, John Wiley and Sons, Inc., New York,1959.

10. Klinar, W. J., id S. J. Craig, Jr., Gust Simulation as Applied toVTOL Control Problems, 3AE Preprint 570C, 1961.

11. Seckel, E., J. J. Traybar. and G. E. Miller, Longitudinal HandlingQualities for Hovering, Peinceton Univ., Dept. of Aeron. Eng.,Rept. 594, Dec. 1961.

12. Ellis, David R., and Gregory A. Cart.-r, A Preliminary Study of theanamic Stability and Con+rol R-sponse Dezired for V/STOLAircraft, Princeton Univ. Pept. No. 611, June 1962.

15. Klinar, W. a., dn S. T. Craig, Stuffy of .'TOL Control RequirementsDurini, ov'-ring and Low-St) -i Flight Und,r !FR Conditions, IAS

1'.r. -, O, .Trtn. 1)f 1 .

P-I -- r

TIP - :1 5 -

14. Miller, David P., and James W. Clark, Research on MethodsPresenting VTOL Aircraft Handling Qualities Criteria,AIM Paper No. 64-618, Aug. 10-12, 1964.

15. narren, John F., Jr., James R. Kelly, ajid John P. Reeder, Effectsof Gross Changes in Static Directional Stability on V/STOLHandling Characteristics Based on a Flight Investigation,NASA TN D-2L77, October 1964.

16. Daw, D. F., D. G. Gould, and D. M. McGregor, A Flight Investigationof the Effects of Weathercock Stability on ViSTOL AircraftDirectional Handling Qalities, National Research Council ofCanada Rept. UI-LOO, may 196.

17. Stapleford, Robert L., Donald E. Johnston, Gary L. Teper, andDavid H. Weir, DeveloDment of Satisfactory Lateral-DirectionalHandling Qualities in the Landing Approach, NASA CR-259, July 1965.

18. SalJmirs, Seymour, and Robert J. Tapscott, The Effects of VariousCombinations of Damping and Control Power on Helicopter HandlinQualities During Both Instrument and Visual Flight, NASA TNOct. 1959.

19. Saunders, T. B., Handling Qualities of Aircraft with MarginalLongitudinal Stability, British Aircraft Corporation ReportNo. Ae. 197, Jan. 19Ei.

20. Seckel, Edward, Stability and Control of Airplanes and Helicopters,Academic Press, Inc., New York, 19-L.

21. Bramwell, A. R. S.. The Longitudinal Stability and Control of theTandem-Rotor Heliconter, RAE Rent. No. Naval 5, Nov. 1959.

22. Sadoff, Melvin, Norman 14. McFadden, and Donovan F. Heinle, A Studyof Longitudinal Control Problems at Low and Negative Dampingand Stabi ywith hasis on Effects of Mction Cues, NASA Tech.Note D-,48, Jan. 19t1I.

23. McFadden, Norman 14., Richard F. Vomaske, anj Donovan R. Heinle,Flight Investigation Using Variable-Stabilit Z Airplanes ofMinimum Stability Requirements for Hiih-Speed, Hiih-AltitudeVehicles, NASA Tech. Note D-779, Apr. 19' 1.

24. Amer, Kenneth E., 1ethod for Studying Helicopte LongitudinalManeuver Stability, NACA Rept. 1200, 19'..

25. Bramwell, A. R. S., Lcnitudinal Stability %.in Control of theSingle-Rotor H, licozt.r, Arron. R-o. Coumil F -ni 1. 310",Janutary 1957.

26. Rolls, L. Stw'w-.rt, m- F. J. Drinw.ater, III, A Fligh'. De"errairation ofthe Attit de- Control ow, r i'n,. " P r... - '" . t.nt -'or 'i Viu'iHovering T in t, '",riY4 .'t'd ilit ro, *A-1... . .. rchVhicl ,- , 7:A?;. Tc .C .ct, 1'-I-' ,,

• R -i I 11'

27. Breul, Harry T., Sinrulator Study of Tilt-Wing Handling qualities,Grunman Aircraft Eng. Corp. Rept. RE 162, Mar. 1963.

28. Recommendations for V/STOL Handling Qualities (With an Addendum

Containing Coirnents on the Recommendations), AGARD Report No. LO8A,A ARD Flight Mechanics Panel, Oct. 19- 1 .

29. Curry, Paul R., and James T. Matthews, "Advanced Rotary-Wing HandlingQualities," Proceedings of the Twentieth Annual National Forunm,May, 1964.

50. Fisher, I. A., An Investigation Into the Desirability of ArtificialSpring Feel in the Cyclic Pitch Controls of a Helicopter,Aeroplane ani Armaxent Exper. Estab. Rept. AAEE/Res/506,Dec. 1960.

51. Tanaka, Frank H., and Gene L. Colvin, Cater ory II Stabilit and

Control Tests of the HH-43E Helicopter, AFFTfC-TDR-63-32.May 1964.

52. Jenkins, Julian L., Jr., Trim Requirements and Static-StabilityDerivatives from a Wind-Tunnel Investigation of a LiftingRotor in Transition, NASA TN D-2655, Feb. 1965.

55. A'Harrah, R. C., and S. F. Kwiatkowski, "A New Look at V/STOL FlyingQualities," Aerospace Engineering, July 1961.

54. Tapscott, Robert J., "Review of Helicopter Handling-Qualities Criteriaand Sunmary of Recent Flight Handling-Qualities Studies,"Proceedings of the Twentieth Annual National Forum, May 1964.

55. Jenny, David S., Robert Decker, and Richard G. Stutz, "ManeuverabilityCriteria for Weapons Helicopters," Proceedings of the TwentiethAnnual National Forum, May 1964.

36. Edenborough, K., and K. Wernicke, "Theory and Flight Research on Controland Maneuverability Requirements for Nap-of-the-Earth HelicopterOperation," Proceedings of the Twentieth Annual National Forum,May 1964.

37. Tapscott, Robert J., Criteria for Control and Response Characteristicsof Helicopters and VTOL Aircraft in Hovering and Low-Speed Flight,Institute of Aeronautical Sciences Paper No. 60-51, Jan. 1960.

38. Lynn, Robert R., New Control Criteria for VTOL Aircraft, Instituteof the Aerospace Sciences Paper 62-63, Jan. 22-24, 1962.

39. Kelly, James R., John F. Garren, and John P. Recder, A Visual FlightInvestigation of Hlovring and Low-Speed VTOL Control Requirements,NASA Tech. Note D-2788, Apr. 1965.

WR-1+5 -1 11

hO. Gonzalez, E., An Investigation of the Influence of the Later-1 DynamicsCharacteristics of a Heliconter on Pilot Opinion and Pilot Effort,Princeton University, Aeronauti al Engineering Department, ReportNo. 457, 1959.

41. Goldberg, J. H., and R. C. Gangwish, Required Lateral Handling Qualitiesfor Helicopters in Low-Speed Instrument Flight, Princeton UniversityAeronautical Engineering Department, Report No. L96, Feb. 1960.

42. McGregor, D. M., An Investigation of the Effects of Lateral-DirectionalControl Cross-Coupling on FLying Qualities Using a V/STOL AirborneSimulator, National Research Council Report LR-390, Dec. 1963.

43. Garren, John F., VTOL Height-Control Requirements in Hovering asDetermined from Motion Simulator Study, NASA Tech. Note D-1488,Oct. 1962.

44. Ashkenas, I. L., and D. T. McRuer, Approximate Airframe Transfer Func-tions and Application to Single Sensor Control Systems, WADD TR 58-82,1958.

45. Stapleford, R. L., J. Wolkovitch, R. E. Magdaleno, C. P. Shortwell, andW. A. Johnson, An Analytical Study of V/STOL Handling Qualitiesin Hover and Transition, AFFDL TB 65-73, Oct. 1965.

46. Newton, George C., Jr., Leonard A. Gould, and James F. Kaiser,Analytical Design of Linear Feedback Controls, John Wileyand Sons, Inc., New York, 1957.

47. Matranga, G. J., H. P. Washington, P. L. Chenoweth, and W. R. Young,Handling Qualities and Trajectory Requirements for Terminal LunarLanding, as Determined from Analog Simulation, NASA TN D-1 921,Aug. 1963.

48. Flying Qualities of Piloted Airplanes, Military SpecificationMIL-F-8785(ASG), Wright-Patterson AFB, Ohio.

49. Breul, H. T., A Simulator Study of Low Speed VTOL Handling Qualities

in Turbulence, Grumman Research Rept. RE-238, Feb. 1966.

50. Faye, Alan E., Jr., Attitude Control Requirements for HoveringDetermined Through the Use of a Piloted Flight Simulator,NASA TN D-792, Apr. 1961.

51. Crone R. M., and R. C. A'Harrah, "A New Modified Acceptance Criterionfor Lateral-Directional Flying Qualities" Aero. Eng., Sept. 1 )60,pp. 24- 29.

TR-1j.5-I 11

!APPEOX A

APPOXD4ATZ FCArS

The formulation of approximate factors for helicopters is more compli-

cated than for conventional aircraft. The extra complexity stems from

the addition of low speed flight. In this flight regime certain important

stability derivatives differ greatly from their values at conventional

aircraft speeds and also differ substantially from one type of helicopter

to another. As a result it is necessary to use several sets of approximate

factors to adequately cover the speed range and the types of vehicles.

This Appendix contains a summary of the best approximations currently

:1 known. In several high speed cases the conventional airplane factors of

Refs. 44 are used. Most of the factors unique to helicopters were

taken from Refs. 2 and 45.

The conditions below list the configurations and forward speeds which

were used to check the validity of the approximate factors. In all cases

UoVehicle (Uf/sec)

H-19 single-rotor helicopter

70

115

HUJP-1 tandem-rotor helicopter 80

120

the approximate factors were within 5 percent of the exact values. The

general forms of the transfer functions are given in Table A-II. Tables

A-I and A-V list the denominator approximate factors for the single rotor

and tandem rotor helicopters. Tables A-III to A-IV list longitudinal and

Tables A-VI to A-VII list the lateral approximate factors for the numer-

ators of the single and tandem rotor hclicopters. All the approximate factors

TR- 15 3-1

are for straight and level flight and for stability axis derivatives. If

toe conditions of validity are met, the approximate factors should gen-

erally be acc-irate within -10 percent of the magnitude of the root, i.e.,

for a seconc- ,;!er pair the errors in the real and imaginary parts o' the

roots should be less than 10 percent of their frequency.

TR- 1143-1 117

TABLE A-I

TBAINSFER FUNCTION FORMSH

GEHM'.L:

6(s) = =I

L.()=(2 + 2

p~Ds + S22 * OP + -?P)

or

+ A- s +

= ~ +

N.,( S) =. T,; Tw2 ) +T-L3

or

2+ 2 t, w 4,s+ 2

or

(~2 )

(2+or+2

hcos +"I

IATERAL:i=(S TS TO Y-)KI +s 4)

= (2 + + 2)

+ or L

+ + ~-(

v T v

11 .V

-i 2

0: 0

C 0 0

'.4

TR 143 -

TABL A-Il

MIML ROM~ ELICOPMN APM~IMM lONGITUIN M3WA= MOMSP RIMTION

AIIKMkO 11 VALMhI '

r~ r;

U 0LO(at U 0 , 0.)

ZI~ -Ni - b z -

+ L,~ . U4,+0X .1 « I h

h7 -Z jU 0 (a Or 0 0 j 0)c s . Z /-

v = 18- 1 r 1

Me Me No 0 (Note.- Pe -0 at Uo *0)

F~~~LO 0[or U -0, l/T)c~s -, ar iaegie b atoso

oro I U 0 < 10 , I (

lb< 01l literall factorsmt formue beon Mosn foreenb

ii TANZ A- IV

I 511TAX= O ROM iO u AMP NO ! LOGTD N UMEATOR TRANSMN FUNCTIONS

OW- IAiNDMM AM VALrDZY CMMMlS'1 1 VDUfl0flAL I . 1D A ?) - 72(xUW. - 1X6) * 1(X., - ZU1x6)

I flzam IMS.zu=IC Om

1..

Izvl - lINIl

X3 7v 1Z. 1 * -

I bb .7,(wf - NZS (uz9,~,j 16(f -IA ai(. N.

2C- 4 % - O4l BPkmz)+% -ub

N0 A 0

8 1A -X P,, «w IX I lz

b -ZC or iK M', >>

Tu-, Yuo r. X. Mc -0

TR-1O 0'1 2

I r

I Ml *O MI

JJII

TR- ~~ 1431

i "N-1 I -I1.o~

TAN.E A-VI

SMOMRoz afformLATM.b UMMO TRJMM iiE

W4MJii CD.APM0I3M FACOR VAL!D1TY CMflIONS

flTM (AIDm) 24ft -Y - X I,', '

I1 44< 4X4 - _y , r

I 2 a* N - 5!s) -qX'3.

r 4 Expressions are exact for X6 - 0

Q? 2 4X6L0 introduces tbird root and cJsugeuWN -Y-,--Irlfirst coefficient to WE

VSimpl-t generally valid forms are

Tv r

TAL IM - . Z= Y -rPr=a (RLiI7F5) T-,y r !y4<«IN6' L4O..1'):

* , Y~ ,bttwee,' -Y.,~ Nr' anad %NIL/)Lr; fence,

atn It04ccrc I o

r Is~ 1 typleally of the order of 0.02 to 0.05,Nt I but no simple. approxination for t has been

found

0

TV 0,U<~Tv, TV2

TV, Y. of the orderr o~f 0.02 typ~c..ily

(Uox 9 r i .th I'2.r of '0 typicallyTv L21 Y6 YUN.g I

TR14- 12

TAKEZ A-Il

TAX=U ROM JGLCOPT3 APMoxM& WEuR 1 NMMuAT MANSr AMwi7 =-

tI

wamIi n. APPROXDPM PACT= VALIDITY CWITIUB

IARA crzM i CYCICH = %r, *Ix ,O l0O

jyb(Lrlv + LvlN) - .t(UOTr + r)

16 2C <1NX + YvyNr)

-yy-rFor UO10, use 1tpI -NrTO,___ T92, +-y fYhIs

r 19 C 0~&.for <O 022!Tr lip NO

2t a~,or -- + U0 gy8.Tv2 TV,1 11Y6 A;

PITCH DRI) X; Yr 0 i t

2C ~ 7V jL vNr For UO - 0, see text

9 2C^

Ti N6 TrWoI

v _Uo fl' T2 0At U0 6 0, nurerator becomes first-order

-- 21 [jLU TI g [1(a- Nr) + I4I4J

iTR-i43-1 1 24

I*

m IAPPIDIX 3

U1M 07 APPROACH Ot CM )-LoP ANALYS

I. EDR OVU A SPOT V=T GMS DISMBhANCE

Hovering in gusty air, the pilot is concerned with the variations in

position, attitude, and control deflection as influenced by the gust

disturbances. It is the purpose of this Appendix to present the approach

used to examine the effects of riudom u-gust inputs on pilot closures and

to calculate the effects of changes in the stability derivatives on the

rms (root mean square) x, e, and MbBBB responses with both the 0- and

x-loops closed. In particular, variations in the pilot gains, leads, and

time delay from the nominal values of' Scdtio3r !I will be shown. The

nominal gains will be shown to be reasonable in terms of minimizing the

compos'te rms responses in e. x, and M5 B. Likewise the various stab.lity

derivative effects will be analyzed to determine those parameters which

have the most influence on the attitude and position responses to u-gust

and on the control power requirements for hovering in gusty air.

The five stability derivatives, Xu, XbB, Mu, Mq, MbB, completely

specify the longitudinal dynamics (excluding the plunging mode) of a

hovering vehicle. In the handling qualities analyses which follow, the

effects of control sensitivity, MB, will not be considered. The analysis

method considers only the pilot-vehicle transfer function pole-zero loca-

tions and total loop gain (product of pilot gain and control sensitivity).

The resulting conclusions are therefore only valid for situations in which

MBB is at'usted to it4 optimwn value for the selected values of the other

terms. !, other words, degradations in pilot rating due to too high or

too low a control sensitivity are not considered here.

Eliminating M8B, we will consider the four quantities:

Xu , XB/M u , Ma

TR-14'3-1 1 '

I

Of these, Mu and M are generally recognized as the mst important. Con-sequ-ntly, the major emphasis here will be on the effects of these two

derivatives; that Xu and XSB/ 8B are of secondary importance will be

demonstrated. The main point of the analysis is aui -lnation of four

combinations of derivatives; two values of both Mu and Mq for set values

of Xu and XbB/M5B. These values of Mu and Mq were selected to bracket

the most critical region ever to be expected with the helicopter.

The stability derivatives for our representative sampling of helicopterj vehicles are given in Tables B-I and B-II. From this survey the following

values were selected:

Xu(Yv) = -0.13 sec- 1

XB /MA) = 0

Mu(-L,) = 10.8 (ft-sec)f1

Mq(Lp) = -i:1 sec-

The root positions for the hover cubic are shown in Fig. B-1 which also

includes the root locations for the surveyed vehicles. It can be seen

that the four values selected adequately cover the range of critical root

positions. For our present sampling none of the vehicle root positions

lie to the right or above the most critical boundaries.

Figure B-i also illustrates the effects of Mu and Mq on the character-

istic roots. Increasing Mu increases the phugoid frequency at nearly

constant damping ratio and increases 1/Tsp. Increasing the pitch damping

(Mq more negative) increases the phugoid damping at roughly constant

frequency and also increases I/Tsp.

Making Xu more negative (not shown in Fig. B-I) also increases phugoid

damping at roughly constant damped frequency wp -- p and increases

1/T s. The increases in tpap and 1/Tsp are approximately equal to one-

third the change in Xu (see Appendix A).

TR-143-1 126

Ii!TABLE B-I

SURVEY OF LONGITUDINAL iDVER DERIVATIVES

VEHICLE -*q -Xu -b -WT-A1D 1 -m~un -sc)- , - 1 st - SEC2 -IN)- FLB SLwc- (pT-SEC) SEC SEC s 2 nOF

H-19SINGI-oToR .oo61 .61 .03 .20 4.86,4o 9$640

S-58

SINGLE-ROTOR .005 .60 .03* .18 5.311,600 27,500

HUP-1TANDEM ROTOR .035 2.0 .019 .41 1.95,430 10,080

VERTOL 107TANDEM ROTOR .00082 1.34 .o18 .312 -.32

13,000 75,000

TABLE B-II

SURVEY OF LATERAL HOVER DERIVATIVES

VEHICLE -L V -Lp v LA LAWT AND Ix

LB SLUG-FT 2 (FT-SEC) - 1 SEC-1 SEC- 1 (SEC 2 -IN) - FT

H-19W 6,400 .052 3.18 .073 .87 1.1

Ix 2,188

HjP-1W = 5,550 .032 1.49 .028 .49 .82Ix = 9 7 1

S-58W = 11,600 .025 2.50 .03 .55 1.0*

=Ix 5,895

VERTOL 107W = 13,000 1011 1.00 .025 .c6 3.25Ix = 9,200

*Estimates - Not Given with Data Source

TR-143-1 127

410 x

Q 39

00

310~

4

0

0000

0- 0V

CPC

x x 0 > %

E) 0

TR-143-1 128

CU

4C

IIC3 IV

-40

0n 00

4.2

in V:

+ NY

121.

+ +

E if E If

r.r a-a

< 00

Tli 14 3-12

Of course XrB/.'bB has no effect on the characteristic roots, but does

influence the e!bB and X/8B numerators.

Additional information on the effects of the derivatives on +he open-

loop dynamics is readily obtained via the approximate factors of Appendix A.

Pitch Closure

The pilot model selected for this loop was a properly placed lead and

an effective transport lag of 0.5 sec. The pilot lead and gain are

generally adjusted for a crossover frequency of 2-3 rad/sec with

roughly 30 deg phase margin. The e -- 8 B closures for the four combina-

tions of Mu and Mq are illustrated in Fig. B-2; the key parameters are

listed in Table B-III.

TABLE B-III

ATTITUDE LOOP CLOSURE PARAMETERS

CLOSED-LOOP ROOTS HIGH D.C.CASE PHASE GAIN CROSS- PILOT FREQ. LOOP

MARGIN MARGIN OVER M IO., 1 LOO GAIN,FREQ. TL ~~ j '- ~ GAIN,I It Ke Ke

Mu Mq eg -b L'aTd ee rad sec-. se-1 radse e sec see

Low Low 33 9 2.0 1.0 0.59 2.1 0.33 2.3 -1.800.825

High Low 12 5 3.0 0.66 0.19 3.0 1.5 1.6 -2.66 0.184

Lo High 30 10 2.0 0.25 0.29 2.2 0.20 5.7 -1.10 2.02

]&High 26 6 3.2 0.46 0.33 3.8 0.77 2.2 -2.88 0.284

Note that for the high Mu , low Mq case the loop was closed at a lower

phase margin than for the other cases. This was done after it was dis-

covered that, for this case a 4O-deg phase margin closure resulted in gust

TR-1 5-! 1 ;6

responses which were very sensitive to the e-loop gain. Any condition

which places tight restrictions on pilot gain is bad because the pilot

cannot maintain his gain within narrow limits for extended periods. The

pilot will want to operate in a broad optimum region where his errors are

more or less minimum and his performnce is not overly sensitive to hisgain.

It can be seen from Table B-III that the most significant effect of

'!ncreasing the pitch damping is tc reduce the required pilot lead. This

is as expected since the lead produces a pitching moment proportional to

pitch rate (neglecting the lag introduced by the pilot's time delay). No

serious effects of increasing Mu are noted for high Mq, although there is

a subotantial increase in 1/Tsp (open-loop value was also increased).

Changing Xu shifts the open-loop parameters, tpa and I/Tsp, by approx-

imately one-third the change in Xu . Thus, realistic variations in Xu

have little effect on the )pen-loop poles, but more strongly influence

the e-numerator zero, I/Te1 , at -X u + MuXbB/MbB. As this zero is at a

relatively low frequency, it has little effect on the closed-loop phugoid

roots (see Fig. B-2). The effect on 1/Tsp depends on the d.c. gain of the

e-loop. For high d.c. gain 1/Tsp approaches the zero, so its change is

nearly equal to the change in-Xu. For low d.c. gain 1/T,p is only

slightly affected.

The e-loop is affected by changes in X8B/M6B only through the shift

in the numerator zero at -Xu + MuXB/M8B. As the shift is proportional

to Mu, the effect will b. most important for large Mu cases. The high Mu,

low M case was recalculated with a relatively large XB/MSE of -5 ft.qThe phase margin was increased from 12 to 20 deg and 1/T1 was reduced

-1Pfrom 1.5 to 0.65 sec . Neither of these changes is very important and

all others are negligible.

Outer-Loop Position Closure

The analyses of the position control, x-e 6n, loops use the 9--

closures of Table B-Ill as inner loops. As the x-loop can only be closed

at relatively low frequencies, a pure gain pilot model is used. At

TR-143-i

these low frequencies, pilot lead and transport lag tend to cancel and

neither is significant in the crossover region of the x-* 6B loop.

The key parameters for the x-* 6B closures for the four Mu, Mq

combinations are sumnarized in Table B-IV and the closures are illustrated

in Fig. B-3. For ease of comparison a crossover frequency of roughly

0.3 rad/sec was used for all cases; this gives a minimum phase margin of

about 30 deg.

TABLE B-IV

]POSITION LOOP CIOSURE PARAMETERS

CLOSED- OP ROOTS HIGH -W

C PHASE GAIN CR-SS- IEQ. FREQ.MMARGIN OVERI I, , , , " O Loop

P Cx 1 Cp amp MIN,

Mu. I deg rad rad rad se - r_see see sec af

Low low 3h 8 0.30 0.29 o.36 0.6 2.2 2.4 o.2o o.o6

High Lov 70 17 0.30 0.85 0.61 0.21 3.0 2.0 1.04 0.311

Low Higb 28 14 0.30 0.26 0.33 0.30 2.2 5.7 o-458 0.536

High High 66 2o 0.25 O.73 io.4 0.33 3.8 2.2 O.96O 0.263

It can be seen from Table B-IV and Fig. B-3 that changing Mq has

unimportant effects on the position loop. The dominant x-mode (w4) is

only slightly influenced by Mq. As before, increasing Mu has generally

beneficial effects on the position loop. For the constant crossover

frequency used, the phase and gain margins (also t and a) are

increased; for given margins, the crossover frequency could have been

iicreased. The beneficial effects are largely due to the increase in

1/T p which accompanies an increase in Mu .

TR-I143-1 132

*1 A 0

1CL

Ct Cu

90 *4. -1 N0

IICU

+me

fZf

co

I 0

E C00' I-0

CO

3 r4

2 3 7

IIN Q.CY

N(4.l

+. 340 0

r e , -0 0

CI 000

4 0 0 0 o lo

E

a .

TR- 143-1 3

Making Xu more negative has an advantageous effect on the position

loop because of the increase in 1/TAp. This allnws a higher gain, higher

bandwidth closure of the x-loop. However, for realistic variations in Xu

the effect is rather unimportant.

A nonzero X6B adds a second-order zero [2 MqS - (9M5B/X5B)J to the

x/8B transfer function. For realistic values of XYB/MBB this zero is at

too high a frequency to be of significant benefit, e.g., for X6/M6B =-9 ft

the zero is at 2.54 rad/sec. For the high Mu, low Mq case this is more than

offset by the lowered i/T~p mentioned earlier. For a crossover frequency

of 0.3 rad/sec this reduces the phase margin from 70 to 53 deg, reduces

t from 0.85 to 0.51, and 4 from 0.61 to 0.44 rad/sec. Thus, it appears

that, for realistic values, XB has a negligible effect on position control

if Mu is small and a detrimental effect if Mu is large. This fact is not

only borne at by the above dynamic effect, but is discussed further in

regard to control effects under gust responses on p. 142.1

i Out input Model

For analytical purposes it is desirable to have an input spectrum that

is simple in form but which adequately represents the gust phenomena. Such

a form, suggested and used in Ref. 45 and shown there to be adequate for the

calculations of interest here, is the simple gust spectrum

22g = +=UvU

(B-I)

where c)g = rms gust velocity

= (3/2)(Vas/L)

Vas = steady-state airspeed (for hover, Vas = average wind speed)

L = integral scale of turbulence

The input spectra of Eq. B-I are represented by the output of a linear

filter whose input is white noise. The simple first-order filter model has

the transfer furction

Yf - 2c = (B-2)

TR-1)13-1 1I~

i[s+

For the hover calculations the gust break frequency, g = (3/2)(Vas/L), waschosen as 1 .0 rad/sec (this corresponds to an L of 30 ft and a mean wind

speed of 20 ft/sec). However, to nake sure the results of the analysis

were not highly sensitive to this parawter, a frequency of 0.13 rad/sec was ,

also briefly considered. The effects of lowering mg from 1 .0 rad/sec to

0.3 ad/sec at the nominal gains for the high Mu, low Ma case are presented

in Table B-V. It may be seen that the rms gust responses are not strongly

dependent on c. Also, from other calculations, the slight difference

beween the a's shown ir Table B-V appear to be independent of pilot gin.

That is, the differences between the a's for ag = 1.0 rad/sec and

wg = 0.3 rad/sec remain roughly constant despite pilot gain variations from

the nominals. TABLE B-V

EFFECTS OF GUST BREAK FREQUENCY

- 1.0 rad/sec az - 0.3 rad/sec

C./N (see) .............. 2.0 2.9

q&/%g (deg/ft/see) ....... 0.81 0.68

OB/OuBI (deg/ft/sec)... 5.9 4.T

P Oust Reavonhes

The determination of the rms x, e, and M8B8B gust responses is outlined

below. The x-response provides a measure of the pilot's success in the

principal task: of hovering over a given point. The e-response describes

the attitude deviations of the vehicle; if the pitching variations are

large, the pilot ;,,ill not like the aircraft even if he is able to satis-

factorily maintain position. Finally, MbBO8B provides a measure of both

the required control power and the control effort exercised by the pilot.

The mean-squared values or x, 0, and M8BbB were calculated from the

response spectra

2

P us Ug for X = x, 0, or M ,p -)

TR-1 1 - 1

4

T is the gust spectrum of Eq. B-2 and X/ug(Jw) is the transfer PuctionUg

of X to u-gust inputs with both the 8- and x-loops c-osed. Equation B-3

can also be put into the form

q)= 1Y(iW)I (B-4i)

1[

where Y1(JW) = -(wy~wug

and Yf is given by Eq. B-1

The mean-squared values were computed by numerically integrating the

spectra from Eq. B-4 by the method of Appendix E of Ref. 46.

Choice of Pilot Gedne

The rms values of x, 0, and MBD were calculated for variations in pilot

x- and 6-loop gains from the nciml values shown in Figs. B-2 and B-3 and

Tables B-III and B-IV. The results for the two high Mq cases are given in

Figs. B-4a and B-4b; the trends in these figures also apply to the low Mq

cases. In the regions of interest, increasing pilot x-loop gain increases cg

and MSBVB, while cx decreases to a minimum value, then, while not shown,

increases as instability is approached at high Kx. As the x-loop gain

approaches zero, ax tends to infinity, and a6 and MBCaB tend to minimum values.

In the gain regions of interest, as pilot e-loop gain increases

a. ax tends to increase, although for low Mu therc isan initial region where it first decreases

b. a6 decreases

c. M8Ba5B increases

It can be seen in Figs. B-4a and B-4b that the nominal gains provide a

reasonable compromise among the rms values o" x, e, and MbBB . The 6-gain

gives a near-minimum 0-response without greatly increasing x or MfBbB.

The x-gain gives near-minimum x-response with only miodest increases in e

and MbBbB .

TR-I 3-1 136

ax (f

2

I M8,a 8(deg/sec)

vq(deg)

K9 -2 .2 4 .6 .8 IJD

(a) L ow Mu ,High Mq Case

7 7

7 -7 -- - -

6 6-

5I5

Illlllllliiiiin 'l'ljollll o m - - - - - - - - 2 - - - -I

nonan nominal

-2 3 - -5.1 .2 .3 4 .5

(b) High Mu ,High Mq Case

Figure P-14 . Va'r~itions of Gukst w ;os' ith P ~t

Moe o StabAl Delvatives

Having confirmed the validity of the nominal pilot gains, the effects

of the rms responses of changes in the stability derivatives can now be

assessed. However, because of the approximate nature of the nominal pilot

parameters, small percentage changes in the gust responses should be

ignored. Only gross variations can reliably be attributed to the effects

of the stability derivatives.

The rms vilues for aUg = 5 ft/sec for the four combinations of Mu and

Mq are sumarized in Table B-VI. The values all appear quite acceptable

to a pilot except pitch attitude and control power variations for the high

Mu cases. An attempt was made to compare these with results of an early

TABLE B-VI

RMS GUST RESPONSES

ax v(ft) (deg) (deg/seC2)

ow Mal Lev ................. 9 2.0 3.2

High Mu, LOW Nq ........ ....... 9 7.0 44

Lov Mu, High N4 .*.............. 7 1.4 3.0

High MU, High Mq .............. 10 4.0 29

-~u m5ft/sec

exploratory experiment on the STI fixed base simulator. Unfortunately, a

direct comparison could not be made because of differences in some para-

meters and the limited nature of the tests. For one thing, the random-

appearing sum of sinusoids used in the simulator tests was not comparable

in spectral characteristics to the assumed spectrum used in the calcula-

tions. Also, the test program was small with only one pilot participating

and then with only a minimum of training or learning time and without

benefit of any actual helicopter experience. Figure B-5 compares time

TR-143-1 158

Actual Pilot Simulated Pilot

- -0- -- --- - -

20-

VI N V- -.-- --

* - -- -~- -- --- - - - - -- - - - - -

B - . . . . . .- - - -. * .

.; .0 ~ .- .. .- ..

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

- 0

Fi0r B-3.LAN TieHARToxe ro. Simuate anIcull~~tR

for ~ ~ ~ ~ ~ ~ ~ ~ -1 -Uw Ud High ML aei ovrFxdBseS-ua

(in1.)113

histories of this pilot and the "optimum" pilot of Tables B-Ill and B-IV

for the low 1.u, high Mq case. Based upon a oUg of 5 ft/sec the actual

pilot of Fig. B-5 has the following responses:

a = 3.6 deg

ox = 10.1 ft

SB° B = 7.2 deg/sec2

Compared to the analytical pilot of Table VI

}e = 1.4 deg

Ix = 7.0 ft

M&B08B = 3.0 deg/sec2

The biggest discrepancies appear in the control responses where those of

the actual pilot are somewhat nonlinear. It is not known at this time

whether training could reduce this remnant or whether the remnant is

largely a result of the nature of the task. This is an area which requires

further work and should include experimental measurements of the pilot's

remnant.

To provide additional insight into the numerical rosults an attempt

was made to obtain approximate literal expressions for the response ratios

for MMbBaB/Oug, 0O/OUgv and ox/aug. One approximation does predict the

Mb a results of the four extreme cases of Table B-VI with an average error

of about 20 percent and is given by

2 2 c rad sec

u -_ +{ - ft s,+c 2?-5+

-I , 1

The_ brac:.eted term in Eq. B-5 vas evaluated for several cases including

variations in closure gain as -well as the stability derivative. The

resulingir values were essentially constant, leading to the linear relation-

ship given by

__M5 5 _ra/sec 2

af -. 41 Ka- -Nr-e

•I 1 degsec'or A 180] Mu -,

ft/-see

where the mean constant In the bracket was obtained by dividing Mu into

the actual MbBaSdaUg and not the approximate expression of Eq. B-5.

A fairly accurate approximation was developed for the mean square

variation in position (see Ref. 4 s)

ft, sec(B.-7)

An attempt to obtain a simple approximation for ce/OUg was unsuccessful.

The effects of Xu on 1x for the two high Mq cases and on ce for thehigh Mu, high Mq casewere evaluated by computing their partial derivatives

with respect to Xu. The results appear in Table B-VII. None of the

changes are very important, considering the extreme change in that

was used.

The gust responses are all for X&B . The rms values of x, , and

M5B6B were also calculated for the high Mu, low Mq case with 013,!MbB =5ft.The results were quite close to the rms values for X B = ; the maximum

change was 10 percent. Thus, realistic values of X6, appear to havelittle effect on the gust responses.

TR- I- 1q

TABLE B-VII

Xu on= ON Ow RESPoN'eS

a(xu) (ft)

Lo w ) High 14q .... ............ -1.3 -0.3 2.3

+Xig MU, Hig Mq .............. .-0.292 -0.3 o.44

()u((Nxj (deg)

+High M , High Mq .............. 1.09 -0.3 -1.6

*These changes are for u = ft/sec

*These were cM1culated at nominal Kx, but at K,, 1 . sec "1

TR-145-1 142

II. L&T3AL-DIWCTIONAL COOL WRING APRACKH

Configuration Review

Four NASA and two IRCC configurations of Refs. 15 and 16 respectively

were selected as being representative of most all situations in the two

experiments. The derivatives (obtained from the referenced reports)

and the computed transfer function factors are given in Tables B-VIII

and B-IX, respectively. Only the NRCC configurations with the lowest

value of Nv could be considered on a par with the NASA tests due to the

gust effects, as explained in Section III-B. For purposes of comparison

herein, it is assumed that the control sensitivity is alway at its

optimum value. That is, we are interested in the best ratings for a

given set of dynamics.

In general, the two model simulators were representative of their

respective classes, i.e., the tandem rotor configurations were low in

roll damping (Lp) and directional stability (Nv) as opposed to the

single rotor cases. Only in a few situations did the NASA model approach

a flight condition similar to the NRCC model. NASA's Condition E* (with

Lv = 0) and the HP.CC Condition 2 is one such overlap and the pilot ratings

were approximately the same. The lateral transfer functions are based

on the following equations of motior (the product of inertia effects

are considered negligible):

(s - Yv)V -gP +Uor = YbAbA

-L v v + s(s - Lp) q = L A8A (B-8)

-Nv v + (s - Nr)r = N6r~ r

The coupled moment derivatives (Lr and Np) and the cross-control deriva-

tives (Lbr and N5A) were said to be negligible.

*Actually, the pilot rating for this situation (Lv = 0) was notgiven in Ref. 15, but was obtained by telephone conversation with theauthor.

TR-143-i 115

TABLE B-VIII

SDIARY OF DEBIVATIVES FOR NASA AND URCC FLIGHT CONDITIOIN

C0NFIGUMT.NDDESIEALunvI E NASA NASA NASA NASA N1CC R(MI (A) 4(D) 11(K) 16(E*) I 2

v o o "- ,o "-0 "o

1.3 1.3 1.3 1.3 1.0 1.0

I -o.oi4 -o.oi4 -o.o4 o 0 0

('p) (-1.06) (-1.06) (-1.06) (0) (0) (0)

-1.-5 -1.5 -1.5 -1.5 -4.2 -4.2

LA0.40 o.4o 0.40 o. 4o o.41 o.41

Nv 0.0013 0.0013 0.013 0.0053 0.01 0.01

(Na) (0.10) (0.10) (1.00) (0.4) (0.506) (0.506)

Nr -0.2 -1.0 -2.0 --. 0 -1.0 -0.1

N8r 0.2 0.2 0.2 0.2 0.5 0.5

TR-1L3-1 1h

A

O0 II- n -

C ~ -t- 0- -t n r o0 w~

0 CI CVd 0n ~_________________________ _______r7 __________

0 .00 0 0 0 0 0 KN 0 0 0

cu t-l t - 8 C -

1880 0 0 u 00

Cl 1:

a, n. '.0 cmCVkc~ \D * ~ .31'

.- 0 0 0 - 0 t cu

o ~ ~ ~ ~ ~ t 114000 0~ )0U) 00

TR- 14 -1 145

The two experiments are defined as follows:

NASA (Ref . 15) DYRC (Ref. 16)

Task .............. IFR and VF 3 approach V 110 approach

Simultor ......... Tandem rotor Single rotorType .............. Vertol 107 H-13G

Approximate wt .... 13,000 lb 2,900 lbSpeed, Uo . . . . . . . . . 76 ft/sec 50.6 ft/sec

Wind .............. Wind from al directions, Flight path into wind5 to 15 knots with occa- with simulated 8.9 ft/secsional gusts to 25 knots rms side gust

For the configuration reviewvi which follow, all p-.- a closures were

made with pilot lead equal to roll time constant, TL = TR, and the gain was

chosen to give 30 deg phase margin with crossover frequencies greater than2 rad/sec and ain mrgins of approximately 5 db. In NASA Flight Condi-

tion 4(d) it was thought that the inner loop gain might be critical in

establishing the crossover frequency of the outer heading loop, but was

found later to be noncritical [see discussion under Flight Condition 4(D)].

In all closures the pilot's time delay (r) was selected at a loose 0.4 sec.

None of the above items were found to be critical and were selected as a

standard of comparison. INASA FLIGHT CONDITION 1(A)*, pi - 6

8A e Closure

Inner loop closure, Fig. B-6a, provides only a limited potential

(low t ) for damping the dutch roll. Damping t was only increased-1

to a positive 0.13 sec after the first closure (the symbol I locates

the closed-loop poles).

-~~- 8A Closure, with (P -5 A Inner Loop

The poor damping of w = prevents the attainment of a good

crossover frequency (Fig. B-6b), which is less than 0.2 rad/sec.

*The letter in parentheses is NASA's designation.

TR-143-11 I6

NASA LGT CONDITN -- 5-1/2

5p 8A Clostwe

Even though the basic dutch roll mode is unstable, the pilot with low

gain could obtain the characteristics he likes (see Fig. B-7a).

*-e~lBA Closure, with q -B 5A Inner Loop

The interesting aspect of this configuration is the poor heading

closure of Fig. B-7b. For a relatively large gain margin of 9 db, the

crossover frequency is a low 0.16 rad/sec at 30 deg of phase margin.

The primary reason for the low wc is the small 1/T%, zero of the P/ia

numerator. This is responsible for the pilot's comaent "aircraft will not

follow into desired turns using lateral control."

At first thought, it would appear that the performance of the heading

control with lateral stick would depend on the pilot's gain used to close

the inner loop. However, closing the inner loop at a much "-wer gain

(increasing the damping of the closed-loop pole nearest the origin, Fig. B-7a)

increased the crossover frequency (cc) of the heading to 0.22, but reduced

the gain margin to less than 5 db for the same 30 deg phase margin. There-

fore, heading control is little changed by the pilot's selection of inner

loop gain (this is consistent with the findings of Ref. 17).

NASA MMGH C014DITION 11 (K) ) PR - 2-1/2

p -- 8A Closure

Adequate damping is easily achieved in the roll closure due to the

large 1/TI of 0.76 (see Fig. B-8a).

B bA Closure, with c - &A Inner Loop

The large tAaz (due to the large I/T I), as shown in Fig. B-8b, provides

sufficient bandwidth to obtain a faster heading response than for most

other configurations, which correlates well with the piLot's comment"Good turning response to bank."

Th-143-1 047

NASA PLIM~ COIDITIN 163-3.,p

Jc~ --., 5A Cloture

Because of the aV, wd cancellation (Fig. B-9a), the dutch roll cannot

be damped with ba. In this case, the basic damping of this mode is accept-

able for a ;ood rating.

* - &A Closre, with (p 5A Inner "Loop

For the reason memtioned under the -- A closure, the value of

S(= dd ) is adequate to also obtain an acceptable rating for the

heading control. This outer loop closure, Fig. B-9b, has a crossover fre-~~quency o f wc = 0.3 •

a, FaIG CONDITION 1, Rt * 6

(P 6A Closure

The condition is typical of the configurations where the dutch roll

is poorly damped and the lateral stick cannot damp this mode. The closure

of Fig. B-10a looks the same as that given in Fig. B-9a because of the u

wd cancellation.

* -" 5A Cloure, with T - BA Inner Loop

As shown in Fig. B-IOb, the dutch roll goes unstable for very low gain.

The gain margin limits the crossover frequency to less than 0.1 rad/sec

in order to achieve a 5 db gain margin in a good K/s region.

*Refers to NASA Condition E with Lv = 0.

**This condition was selected because it is similar to NRCC Flight

Condition 1. The open-loop transfer functions, Table B-IX, are essentiallythe same except for the roll subsidence (" Lp), which is approximatelyone-third that used by NRCC. As it turns out, the closed-loop aspectsare identical even though the pilot would possibly be required to use0.67 sec lead in the (- -5 a closure as opposed to 0-0.25 sec leadin the NRCC condition. The difference in these lead requirements is adifference in rating of less than one-half a Cooper point (see Fig. 3).Although the ratings were the same, the difference of one rating pointis within the error of the Cooper rating system. This is an interesting

comparison since the two helicopters are vastly different in size andweight.

TR-1 43-114

~I 1MCC PTWCINITN2 ~

q) 5' A CIaure O

The closure of Fig. B-11a is identical to NASA Condition 16(E*) of

Fig. B-9a when the pilot 3elects his lead equal to the roll subsidence

0T 1/TL)

-5 5A Closure, with (P B 5A Inner Loop

The crossover frequency of the heading control *- 8A is an ample

0.4 rad/sec (Fig. B-Jib). The improvement (higher crossover frequency)

over the similar NASA Condition 16(E*) is due to the higher roll subsidence

of this condition.

*The hRCC Flight Conditions 1 and 2, as defined in Tables B-VIII and

B-IX were selected as being comparable to NASA conditions where Lv is zeroand Nv small. The NRCC ratings were taken as the best attainable at theoptimum gain. Only ratings from the circuit approach task (as opposedto the hover task) were considered comparable.

TR-143-1 i9

_~ _A__u

0f

T, T -r

TR 150 -

-Al

14-

1! ___

41 zRN 3

~L404 I -. _

II I! (0

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TR-143-1 156

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TR-143-i 15

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4 3-U

In. DTIlXNAL APPOACH TASK WITHV-SID GS

The purpose of this section is to present a detailed examination of

twelve 8 5r pilot closures representative of the approach task flown

in the tests of Ref. 16. This includes an analytical determination of

the rms heading response, a*, and the pilot's required control activity,

Nbrabr to the simulated gust environment of the NRCC experiment.

The equation of motion and the values of the stability derivative

used in this study correspond to those in Ref. 16. The NRCC experiments

of interest here reduce to the single closed-loop rudder control of the

heading disturbance. The control loop and the transfer functions have the

form shown in Fig. 15. Values of the pertinent parameters and the

stability derivatives for the approach conditions of Ref. 16 are

u. = 5o.6 ft/sec

II0.01 < v < 0.05 ft-sec

II

0.1 < INrl 10 1.... sec

The pilot model is assumed to be at most a gain, a time delay, and a lead,

Y yp*p = Kpe (s + 1

The choice of the pilot model is not obvious for some of the cases examined,

and a discussion of the considerations involved in choosing the pilot model

is given later.

Based on the results of Ref. 16, the cases of Table B-X were chosen for

study. Also listed are the dutch roll roots as well as the stability

derivative of the helicopter transfer Tunction.

TR- 143-1

iii

TABLE B-X. DIRECTIONAL CASES

td WdCASE Nv -Nr NbrL

NO. ( opt) (a )(i

1 .01 0.1 .4 .07 .711

2 .01 1.0 .6 .703 .711

3 .01 2.0 .7 (.296) (1.704)

4 .02 .1 .4 .050 1.01

) .02 1.0 .7 .500 1.01

6 .02 2.0 .8 1.00 1.01

7 .035 1 .4 .377 1.33

8 .035 2 .6 .754 1.33

9 .035 5 '.4 (.381) (4.62)

10 .05 2 .7 .630 1.59

11 .05 5 1.5 (.576) (4.42)

12 .05 10 2.3 (.26) (9.74)

Parentheses indicate that the factors are real

TR-143-i 1.3

Reading Closure

For the twelve cases the 4-o 6R loop was closed so that the crossover

frequency was 2 rad/sec and tha phase margin was at least 30 ° . A list of

the pertinent closed-loop quantities is given in Table XI. Root locusand Bode plots for a selected :grbup arce given in-Fig. B-12..

The importance of adequate yaw damping-as a means of reducing pilot

lead requirement is shown in Fig. B-1 2. In these cases the, damping of -the -

dut.ch1roll mde is directly related to Nr, Nr -2 d Tis i pposd 2

to the pitch attitude case where the odping factor of the p4imarymodeI (phugoid) appears little changed-by large changes-in pitch daTing, -Mo, as

shown- in Fg. B-i This , for daig e directional case

is further illustrated by closing- the loop with i siiple, pilot noddi- As

shown by Fig. B-12, increasing the loop gain primarily increases frequencyrather than damping unless the pilot adapts leads of the order of 1 sec

(which is accompauied by-arating degradation as large as 1 point). For

the pitch case the opposite is true' i.e., increasing the loop gain goes

primarily at first to increase the damping of the mode controlled (see

j Fig. B-2). This then is the reasoA: why pilot rating is a strong function

of damping in the directional case, and a weak function of damping in the

pitch case.

The effect of Nv on the pilot closure is small except that an increase

in Nv requires an increased Nr to maintain a given damping. Although

increasing Nv has little direct effect on the closure, its primary influence

is to increase the gust sensitivity as discussed in Section III-B-2.

te imtation of the tht inotion

In Ref. 16 the canned gust acted through Nv only. Due to this, one of

the principal results of the NRCC study (i.e., for satisfactory pilot

opinion at large values of Nv, Nr must be la'ge) may be misleading. If alarge portion of Nr was of aerodynamic origin, then the gust sensitivity cfthe simulator would be increased through Nr as well as Nv. Therefore, it

was decided to briefly investigate this effect. In the Canadian simulation,

only Nvvg was used as a gust input term. When Nr is of aerodynamic origin.,

TR-143-1 16h

0I 0ODO

cy 3 t0 I - 0

1j - cI .-. ', *it

5,P,

I T

to INI

0 0

TR- 147-

~I

a gust gradient term proportional to Nrg is important in determining

directional gust responses. Thus the simulation in Ref. 16 contains the

implication that Nv is totally aerodynamic and Nr is totally augmented.

A brief investigation compared the a/avg obtained by using Ref. 16

equations of motion with the qlav g obtained by using modified equationsin which Yvvg J O-and Nrsvg/Uo 0 0. The gust transfer function for

headirg, , becomes

I r ( s vU o v

Vg s + 2(t) s +

MirFor YvVg = 0 and Us Vg = 0 (the case of Ref. 16)

U0

! = Nv(s- yv)

v [ IS2 + () 21

Thus, when the aerodynamic portion of INrI is large (greater than 1.0),

the pilot ratings in an actual gust would be somewhat worse than those

reported in Ref. 16.

The Analtics. Gust Model

The gust spectrum in Ref. 16 is equivalent to passing white noise of

unity variance through the filter below

Yfl =- 0,,T

T__-1+43+-I 1)+ S +

TR- 143 -1 166

It was found that the simple gust model in Appendix B was qualitatively

nearly identical to the above when cg was chosen as 0.5 rad/sec. The main

discrepancies occur at frequencies below 0.5 rad/sec. Thus, for analytical

purposes, the gust model -chosen was the same as in the previous sections

(see Appendix B-I).

The Red nea t6 V-dust

The determination of the rms * and Nb85r gust responses uses the same

procedure as outlined in the hover case, Section B-I, of this Appendix.

The *-response provides a measure of the pilot's performance in the

approach task and Nbrabr provides a measure of both the control power

and the control effort required of the pilot.

The rms values of * and NFrC5r were calculated for variations in pilot

loop gins of Fig. B-12. The results for a medium Nv and the high Nv cases

are shown in Fig. B-I3. The trends also apply to the other eight cases.

It can be seen from these figures that the nominal gains provide a reason-

able compromise between tie rms values of tk and Nar 8 r . The *-gain gives a

near-minimum *-response for about the same control activity in each case.

Having selected the values of pilot gains, the effects on the rms

responses of changes in the derivatives are determined for the twelve

cases at the nominal gains. These values along with all pertinent closure

information are given in Table B-XI. The rms values of the response are

given as a ratio to the gust input. The correlation of these analytical

results with the pilot rating of Ref. 16 is discussed under Section III-B-2

of the text.

Selection of a Pilot Model

The closures of this section appeared to have certain shortcomings

when compared to the conventional adjustment rules for the human pilots

describing function. The worst of these is the low dc gain over a long

frequency region in the cases of low dutch roll damping. The dc gains

in cases 4, 7, and 10 are all below 5 db. This indicates poor low

frequency response to the primary forcing function (i.e., heading error).

TLR-143-1 167

3.0-

Case 6

2.0 Case 4 Ncr dge\2.

ov, 3.It/sec;)~(e/eR

1.0 I1.0 I

0I e deg

nmnlnominal ftse

L 0 2.0 0 0.2 0.4 0.6 0.8KI, Kip

(a) Medium Nv(02?), Low N, (-0.1) (b) Meditim Nv (.02), Medium N., (2.0)

/deg7-x 101f /e

6.0-Ov tsc 6.0I Case 12

5.0 -Case /0 15.0

I NB1oa8 (e c2 i4.0 - 4.0 - tse

N 8 Ov deq/ec2

2.0 2.0 / deg

lt1.0 nmI inl1.0 - oia Vq ft/sec

0 1.0 2.0 3.0 4.0 5.0 6.0 0 10 20 3040 50K 4, K* -1(4,

(c) High Nv (. 05), Mediumn N,, (- 2. 0) (d) High Nv (.05), High N, (NO)

J1 Figure B-13. Variations of Gust Responses with Pilot Gains

TR 13- 6

$4 L\ 0 ON 0 0 U-% 0 0 0 it\ U\

cu- $\ li - tu- ?(- Co- 0 - cu

0~

-: \0~ r- co --t \ t t 4

0 0 0 .- 0 . CU

N/ ,-. U'\ UN \ 0\ 0 4 cu -t \0 I

- 44 0 0c

' \ -t ~ tC-U-

<~ ~ (' CU CUCU CU Lr- - l - cui K\

101

- CU o- o~ C;t- U~.

r) \1- CU\00 'C 0\ CU CO 0i~

a' 0' 0- o a '0 ) A 0 C 0 0 co5-

Cl) \0 k U\ t- C 0 D 0

v______ nC 0t '0L\ n t \ \ C\ t

f7,~..1 t- .4% a\ -t U- l)c C

__"\D 4- -+r4C

0 0 0 0

_ _\ _l 6- 6r 06 0 0

1 60

Also, in case 10, the pilot is crossing over in a K/s 2 region and not in

the generally desired K/s region. To achieve the K/s crossover at the

same 2.0 rad/sec, a suffT3iently high pilot lead could be chosen. In

case 10 this would put the pilot lead zero in the range 1.0 to 4.0 rad/sec.

Any lead, however, will tend to worsen the already poor dc gain. Another

alternative is the use of low frequency .lag td improve dc gain and give

a good K/s region at a lower crossover frequency and then sufficient lead

to achieve good stability. When choosing a lower crossover frequency, it

is desirable to keep ac somewhat larger than the gust break frequency of

0.5 rad/sec. In cases I and 4 any lag will force the crossover frequency

we-l below 0.5. Thus, lag will not help these cases. In cases 7 and 10,

it is conceivable that lag will Improve the performance. Case 10 was

chosen for study since it had no K/s region and would (due to higher wd)

benefit the most from low frequency lag. The lag was chosen at 0.1 rad/sec

and a lead term at 2.0 was added to give adeqaate gain margin. The results

of this closure yielded a good K/s region in the vicinity of the crossover

freqtency (1.0 rad/scc); a phase margin of 530, a gain margin of 7.5 db

and a dc gain of 8.9 db. It would appear that this is a much better system

than the "nominal" used for comparison purposes. When the rms values

were computed, however, both a* and Nbrabr were larger than before and

a* had increasod considerably (i.e., from 0.53 to 0.8). Thus, the "better

looking" closure with high dc gain gave much poorer gust response.

To check further into the lack of importance of dc gain on rms behavior,

the case 10 was closed with a pilot lead at 1.0 rad/sec and no lag. Here

the dc gain was very low (0.75) but a* was close to the original value

while N rabr was greatly reduced (2.6 to 1.4). The summary of closed-loop

parameters and rms responses for the three pilot models is given in

Table B-XII.

Since the pilot can do so well with large lead and poor dc gain, one

might be tempted to conclude that the lead only case would most closely

represent the pilot model. The pilot, however, is first concerned with

good low frequency tracking of the primary signal, the heading error.

ThuS, the pilot will attempt to keep his crossover frequency high enough

to keep the rms responses low but use as little lead as possible to

achieve a good rating.

TR-I43-1 170

:10

______a

r-

CC)

0 ICu -c U

E-1~

WU

El-4) 0iI *

a - I

0'

U~c~co

TR-1 43-

saV TWX NCTES

WWZELMm CXL=W O 83oiA

Victor Holloway WO 1

James H. Nichols major

Don C. Jones Civilian

Edwin N. Clay Major

Charles E. Arnold Civilian

Vernon R. evas Captain

0. A. Buettner Civilian

Womcak WO

NAB -LAIA(l . . . . . . . .. 11 /12/64

J. Reeder

R. Tapscott

J. Kelly

R. Piper TRECOK

vEIiOL ........ . 11/u/64

Jim Smith Hugh McCafferty

John Kannon E. Diamond

Frank Duke, Pilot Section P. Sheridan

Bob Gangwish, Pilot Section B. Blake

Bob Stroub K. Landis

J. W. Berkeley

i 13TR-14-I172

Flight Test Division)

Lt. D. A. Beil NATC Flight TestCapt. P. L. James NATC Flight Test KrW. R. Powers NATC Flight TestR. C. rhnond NATC Flight Test

Lt. D. F. Mayers NA.C Flight TestBen Stein BuWeps

E. Carter D. Jenny W. KingJ. N eeden D. Cooper R. PerroneR. Baker J. Clark P. D'EstillioT. Kaplita D. Gardner

HUGHE ........ 10/29/64

K. Amer

C . Savant

LOCKHEE. . . . . . . . . . 10/28/64

Ford Johnson

Carl Friend

SISTEMS TECHNOLOGY, INC. RPRESENTATIVES

I. L. Ashkenas

D. Graham (Replaced Mr. Ashkenas at Sikorsky)

R. P. Walton

TR-i 43-1 173

I SPEC ITES MS'S

Do't-yet bave miltary type of vehicle, i.e.,carrier. Off-tbe-shelf not so good. -Want somthing'like a flying crane baving a pod attacbment for everymission. Want utility--not concerned with handligqualities, except for lousy sato A large rangeof trim attitues for fuselage.

Spec should be written only when there is a demon-strated need, e.g., for .M/&iu " bae stable s!opetakes lots of effort, but it's only in helicopterspec as a holdover from the airplane spec. Not

frequired for-hover. No evidence to show that-itIdoes improve hover characteristics.

3 3-1.2 Definition of Normal PAIM.SrcLa gNormal service loadings-spend a lot of time wonder-

Iing what this is.

3.2.1 Control Power in PI. WUnaccelerated Flightfor Distur ances Don't think any present helicopter will meet present

crosswind turn requirement but spec item OK, but not3.3.6 Directional Control sure would want to sacrifice power to achieve.

"brgin for I' Kt Windfrom Critical Direc- PA FItion

C ximum CP margin not specific-direction, c.g., G.W.3.2.13 Control Paver in

Terms of Response to Control power test OK. Tandems do not have preciseUnit and Maximum directional control, but meet control power require-

3.3.18 Control Step Input menb-large inertia, low damping.

For utility, most maneuvers limited to 309 bank.

For weapons, bank angles can go as high as 90

In attack, time-to-bonk/time-to-mneuver < constant.

Never have encountered longitudinal or lateral con-trol power deficiency.

Do limit controls because of accelerations they feel.

TR-143-1 174

PEC ITEMS C0O4ETS

3.2.1 Continued SDmU1I3.3-43-3-6 Cotrol sensitivity (i48) determined by CPm x and3.2.13 cockpit size: = Nmai/amax.3.3.58 If meet spec for trim in high speed and rearward

flight, then M5 may not be satisfactory.

Requirement for gain changers exists as speed rangebecomes greater, but Sikorsky opposed to, pinningdon. 6

Sikorsky basically accepts control power requiremnents.

M8 available for hover makes machines more agilethan they need to be.

S-61 can fly same envelope as smaller machine.

As to Mb8bm, - How is it measured or how can demon-stration be made of the 10% requirement?

Claim spec requires too much N8 .

VXTOL

For precise heading control they are presentlycriticized for-low sensitivity.

Their present yaw rate capability is less thanMIL-H-8501A; CH-46, 47 designed to -8501.

Sikorsky restricts to 3600/15 sec-too slow. Theygave customer 3600/10sec, which felt was veryadequate.

Rapid turning has lead to pitching motions--can leadto loss of pitch control.

Not important for transports, but could be veryimportant for Escort fighter.

HUGHE

Critical roll maneuver is probably obstacle avoidance.

Adequate CP first prerequisite, then gradient (Me,If3, etc.).

14aximum LBB - hovering in 30 kt crosswind andasymmetric loading more critical than roll in I sec.

Upsetting moment about all axes is proportional tocontrol power, as is damping, e.g., offset hingesincrease the upsetting moments in the saine propor-tion as the hinge increases the control power anddamping.

TR-143-I 17

*'

SPEC ITEMS COOMS

3.2.1 Continued

3 3.6 Gust sensitiity (Mu) increases with disk lbading

3.2.1.) (higher collective) and diia lading i reases ifith- size.

-3 3.183.5.1t% side wind Of f kfor -control izoke -critical

; _ than any maneuver req nt

3.2.2 Steadiness in Hover

j For hovering over spot, Canadians show gust effects.Thijr.tasks moving near gr-oun&dcneoing up to a spot

rather than hoyering over it - don't show gust effects.

Want to limit Mu to low value.

Think initial rotor tilt is helpful in translatingas opposed to Jet VTOL.

3 " Even without gusts, always disturbance due to hovering,e.g., recirculation disturbances, etc.

3.2.4 Longitudinal and VEROLLateral Force

3.3.11 Gradients Stick forces. Breakout and gradient-recognize valve

friction-artificial breakout force around 1 lb,3.2.6 Longitudinal and including valve friction.3.3.19 Lateral Trim Forces

They like the forces in Table Ilfor hover, except for

rudder. They equate desirable gradients with dis-3-9.T Breakout Forces placements required for holding-and frequency of3.3.13 occurrence.

3.2.10 Longitudinal Stick Around 60 kt, basic tandem has zero stick gradient.Stability (Position Therefore, had poor trimability (S.F.).and Force) Level flight stick stability not important (7 = 0)

As to stick forces versus stick position, they are

stick force men, not stick position

PATU X

Stick fo rces in Table II are too low in all cases.

Level flilt trim versus airspeed-want stable slopeto indicate speed charge.

Also say stick force gradient good on approach.

TR-143-1 176

SPEC ITEJ. COMM~ERME

3.2A4 Continued3-3.113.2.6 Control breakout forces, especially directional, too3.3.123.2.7j -5.1 Position tick gradients-are they necessary?

3.2.10 Sikorsky does not-always meet 3.2.10 at 50 kt,especially with large tail sizes. iSikorsky says LA Airways flies with no feel in VFR.They don't care about force gradient and they mynot care about position gradient (constant coliec;.tive, conslAnt throttle).

~Trim requirement:

7 lb maximum lateral stick force

2 to 2.5 lb maximum longitudinal forTxckheed helicopter

3.2111 Longitudinal Dyn=.c V RNOLoStabiltj

They prefer pulsing elevator and looking at a) and

With S they aim for w "1 3 radt, p " 0.7-0.8.

jOscillatory requirements-basically OK.IFR should extend over entire frequency range andnumbers should be reviewed from closed-loop basis.

Blade stall is limit of linear theory because largemotions (1" pull and hold) give nonlinear response,especially in high speed machines.

.2.11 .1 ILongitudinalManeuver Stability

The "concave" downward requirement was substitutefor minimim maneuver margin. Originally they couldnot hold V to do maneuver for maneuver margin.

pATUEqTManeuver requirements should be identical withmission, i.e., for attack the "concave" downwardrequirement should be similar to airplane spec.

Basic criteria OK - not sure about numbers (2 sec).

TR-143-1 w

SPEC ITEMS COMMENTS

3.2.11.1 Continued S U

Maneuver mrgin is perhaps better, or the accelera-tion trim gradient.

The "concave" downward requirement stiil consideredgood.

On "concave" downward--aperiodic divergence my comeafter first cycle of phugoid-a poor indicator.

3.2.11.2 Normal Acceleration O N1

Stay Within 1/4g 4After 1/2 SecondPulse

Believe exceedance of 1/4g should be measured asshown.

3 .2.14 Damping Required to

Insure SatisfactoryInitial Response and TR < 2, -1/Nr.> 4, for minimum right now, but Reederto Minimize the Effect thinks these * U come down.of Tl sturbances

1/Mq, 1/1 close to 0.8 for basic aircraft, but nogood because Mm is positive-when add SAS to pitch,increase effective Mq.

M6 15

SAS -4

0.5 2.0 Period

PATAMIT

Damping criteria difficult, to measure, since anattitude change starts aircraft to translate.

T-143-I1 178

SPEC ITEMS COE.T.NTS

3.2.14 Continued BDW a3.3.19

For Sikorsky ships, Nq is approximtely constantwith size: = 0.5 basic, = 1 .8 with ASE.

fr - Too much required. OK with ASE. Might meetwith nonlinear effects.

Rigid rotor. Lp 6, Mq 1- 1.8.

3.3., Directinnal Yaw Rum=ResponL. to Unit and1'amum (Control Yaw acceleration capability - pilot location for-Power) Control Step ward of c.g., therefore wouldn't subject self to

high linealr accelerations; therefore expect sizeeffect.

However would expect no size effect on the abilityto achieve a new heading in short time; and on theequivalent situation in roll - to move over laterallyin short time.

3.3.9 Positive Directional IT. RUCMStability, Np, andDihedral, p - br, Pedals no real use in most flying, except for taxi-B. versus P Linear ing, hovering, takeoff, and landing. Would like to-10% Control Margin fly without pedals most of the time--over 50 ftfor Gust in lateral altitude. Most pilots don't really learn to useControl pedals.

3.3.9.1 For Speeda Above VEOL

50 Kt or 1/2 V , o0Ctor~le tI2 With- 15 p requirement at Vmax designs their rudder control.Complete tums With-

out Pedals and With- There is no operating requirements--why is it in?out Rolling velocity 45 at 60 kt is too high for visibility -- e.g., plane

guard talik on carrier recoveries.

3.6.2 Extension of Above Question as to whether demonstrate with or withoutScstro Foncle autopilot - then what about stick-fixed stability?Control ForceStabilt', 10% in control power is better than old spec, which

called for 10% in position.

Maximum attainable (ambiguous)- neutral to extremerather than extreme to extreme; which is correctinterpretation?

PATUXEN

Linearity may not be desirable. Also, 15 lb too low-see conventional airplane spec.

E TR-1I h3-I 1,79

SPEC ITEME COMMN]S

3.6.2 Continued B ,C

Pedal force proportional to sideslip very questionablewith heading retention.

Artificial force may be desirable (to keep synchswitch closed).

3.-.17 Lateral Trim Changes PATUShall Not Be ExcessiveWith Changes in Power Rudder pedals required for transition into auto-or Collective Stick rotation in single rotor helicopter - should be reduced.

Throttle cross-tie - very troublesome.

. Safe Transition Into PATEMMAutorotation

Delay time for engine failure:

2nd failure - shorter time dehy

1st failure - 2 sec seems reasonable

1 sec for one recip. engine

Up to Vmax recovery from engine failure.

h-V diagrams usually drawn for level flight-wantsclimb with takeoff power.

As to delay times from unalerted testing

0.5 sec appears more realistic than the 2 secspecified.

3.5.7 Autorotative landings PATUFMat Speeds Less than

15 Kt Have trouble with 3-5.7.

Autorotative - 15 kt, one engine out, perhaps,but Sikorsky finds this difficult to achieve inpower-off landings.

3.).9 Use of SAS or ASE to IT. RMeet Spec Require-ments ASE lots of trouble in maintemnce. Fatigue without

ASE, but not mndatory for flight. Don't need ASEfor all jobs.

Basic machine - can't fly hands off. One hour inhelicopter is equivalent tc 3 hr in airplane.

iTR14-II

GENERMAL TOPICS CC °NTS

j30/see to 5O°/see per inch sounds high tot

them. Also question of high speed, i.e.,how limit speed to retain control? a

Flexible turrets will be used for areafire.

Consensus seems to be that Bell(Edenborough's 20th AHS Forum article)rates are too high!

W

Complain about weak rol. control power

versus high pitch - never use mximumroll control.

Harmony can be expressed in a number ofways, i.e., do you harmonize forces,displacement or maximum control power.More study needed in this area.

No spec on lateral-directional dynamicsfor VFR. If supply specified Nr and have

static directional stability, could havehorrible characteristics

Task--All axes under hood.

Lvel attitude during S-maneuver mostimportant. P low and high Dutch rolldamping.

High Np rough on passengers up thr-oughmoderate turbulence.Most helicopters don't have adverse yaw

(Np). Do on rigid rotor.8-10 sec to make maneuver back to course.Therefore if Dutch roll period in thisregion, pilots want more damping.Damping correlations a = Nr/2V ) onlyfoi, NE > 0.4 for TN D-24A77.

TR-143-I

§0.MAL TOPICS COME

Two types of PlO's have occurred: a

~Long period., large amplitude, fullthrow due to low damping and control

power

High frequency, high sensitivity

SCI, P1127--increased CP and sensitivity;:VZ-4. Low control power, low damping in

* a hover.

SC-I, VZ-4, P1127 cited; last improved

ith increased CP and sensitivity.

Flying crane PI due to cable and a/rev

• of rotor. Cured by vibration isolatoron cable.

Two basic problems--- lip < 0, actually unstable atcruiseexcept at forward c.g. (for

C.g. limit set by high speed and rotor

loading rather than stability or control.

L is high--to augment Np use static

pressure in nose--4p transducer for~v> 60 kt.

Can t use ay to get static stabity

in sense of 6r or T versus 13.irN 0.3 about as low as want to godfi cuit to control for low calues.

T H-g43-1 .

GENEPAL TOPICS CC0ES

RTICK M M G -contd

Doubt effectiveness at high speeds due toblade stall limitations.

?AX

SF/g difficult to get at low speed-ofopinion that one canno get much below50 kt; OK above minirmum power.

SF gradient for hover desirable to indi-cate forward velocity-a good airspeedindicator not available.

Kaman has a hydraulic bobweight -very Isuccessful at 15 lb/g; first serviceapplication he knows of. Tried bobweightstat NASA-Langley at about 60 kt-pilotsunenthusiastic. Ordinarily do not get

force signal until nz is achieved. Low 1spring gradient needed for hover.

Most helicopters have power actuators.If not stick forces are unpredictable.

LOMKME

SF/g is a good substitute for concave

downward criteria.

TR- IJ43- 7)

GEERAL TOPICS COMMENTS

sIZ T - contda aa ' From dimensional analysis, I cP c, c L,

W/A % L.

Desire large D/I to prevent gust upsetsbecause of small size (referring to rigidrotor dampi:ng). Also leads to higherrotor (Th) because of ground clearance.

si vim MISSIK M icMSuggest different spec for different

• missions.

Size effect was expedient at time spec

was written.

Minimums are ccmpronises.

iSTICK 7M MALOMM LOCKHM

Wants a stick force gradient as opposed

to none for light damping.STICK FORAE PER G IT. YUIIf

Kaman bobweight liked.

Bat sst have light forces around trim

because in gusty air, pilot is fightingthe rotor flexing.

Says SF/g good idea.

Do want maneuvering force- are planningwork in this area to get stick force (6F)proportional to (low speed), g (highspeed).

a az

Vlso important cue as well as lmiting

used 14t lb/g damper.

. Force cue desired--AGARD spec.

Ia

IIa

Ic7I ---- - - -- - - - - - - - - - - - - - -- - - - - - --- - - - -- - - - - -- - - - -

a a I

TR-a II I1

GEWB L TOPICS C0MMEI7S

Desires fast rol to keep flight path

shorter.High rotor inertia provides additional

power in turn.Cyclic + collective

long roll rolltime. shrdecel. accel.

rollaStime.

For obstacle avoidance -- just slowdown rather than increase roll cape-bility.On Lockheed, po = 350 to 450/sec.

Required to avoid obstruction -- getrotor around.

I II Tl_

Studying size effect by plotting rollresponse versus size.

D/ Sml

Targe

CS

Sizelarger

ff+ 1000 is rell supposed to be size

efect rather than weight.

Makes point about optimum TR versusminimum TR . These -oy indeed vary with

size.

2R-1 43-1

I

I

Unclassified

Secutity ClassificastionDOCUMENT CONITROL DATA - R&D

(Securifty classification of *tie. boOdy of abstract and kdaajnea nnotation, ,,tt be entered emsi th *4090i **Paf Is C184621104)

1. ORIGINATING6 ACTIVITY (Cooporale author) 20. REPORT SECURITY C LASIV3CATION

Systems Technology, Inc. UnclassifiedHamthorne, California Zb *v

N/A3. REPORT TITLE-

ANALYTICAL REVIW OF MILITARY HELICOPTE FLYIN1G QUALITIE

4. DESCRIPTIVE NOTES (Type of ropoat and inclusiv, date@)

Final ReportS. AU THOR( Lost name. fisat me. initial)

R. P. WaltonI. L. Ashkenas

S. REPORT DATE 7.. TOTAL. NO. OF PAGES 7b. No. OF Raps

February 1968 155$a. CONTRACT OR GRANT NO. $a. ORIGINATOR*$ REPORT NUNSEX(S)

NOw 64--060 -fIPROJECT NO. TR-143-1

C. 96b. OTHER REPORT NOS) (Any ethernianbes, thatmay be asatj~od

10. A VAIL AuILITY/Lli~TATION NOTICE

Distribution of this document is unlimited.

71. SUPPLEMENTARY NOTES 12. SPONSORING MILITARY AtCTIVITY

None Department of the NavyN~aval Air Systems Command

13. ABSTRACT

'I This report is directed at analysis and review of the current militaryhelicopter flying qualities specification, MIL-H..8,501A, and of the relevantpublished literature. The anaJ.yrtica. approach rests primarily on servo-analysis of closed-loop piloting tasks and secondarily on open-loop responseI considerations, and such analysis and considerations are used as the basis

4 for correlating and "explaining"' the available data. This process delineatesthose flying qualities criteria (either in the specification or proposed inthe literature) which are valid, and establishes bases for additional experi-ments in inadequately explored critical areas. The results are specificallyapplied to an itemized critique of MJ:L-H-8501A (excluding autoration, miscel-laneous, instrument flight, and vibration characteristics).

DD I J A 1-4 7341 Unclas ;ifie4

Security Classification

Unclassifijed -- ,.: - -

14. SeuiyKYW~SL14K A L164K6 b LINK C_____________________________________ ROLE WT lO.5 1 ROLE. "T

THelicopter Flying QualitiesIj Closed-Loop Tracking IGust Inpuits

A Miultiloop Control AClosed-Lcop Analyses _StabilityDynamic CharacteristicsControl Requiremtentsj

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