DOT/FAA/AR-05/21 

Office of Aviation Research 

Washington, D.C. 20591

Handling Qualities and Flight 

Safety Implications of Rudder 

Control Strategies and Systems in 

Transport Aircraft 

June 2005 

Final Report 

This document is available to the U.S. public 

through the National Technical Information 

Service (NTIS), Springfield, Virginia 22161. 

U.S. Department of Transportation 

Federal Aviation Administration
NOTICE 

This document is disseminated under the sponsorship of the U.S. 

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This report is available at the Federal Aviation Administration William J. 

Hughes Technical Center's Full-Text Technical Reports page: 

actlibrary.tc.faa.gov in Adobe Acrobat portable document format (PDF). 
 Technical Report Documentation Page

1. Report No.

DOT/FAA/AR-05/21

2. Government Accession No. 3. Recipient's Catalog No.

5. Report Date 

June 2005

 4. Title and Subtitle 

HANDLING QUALITIES AND FLIGHT SAFETY IMPLICATIONS OF RUDDER 

CONTROL STRATEGIES AND SYSTEMS IN TRANSPORT AIRCRAFT 6. Performing Organization Code

7. Author(s)

Ronald A. Hess 

8. Performing Organization Report No. 

10. Work Unit No. (TRAIS) 

 

9. Performing Organization Name and Address

Dept. of Mechanical and Aeronautical Engineering 

University of California 

Davis, CA 95616

11. Contract or Grant No.

 12. Sponsoring Agency Name and Address

U.S. Department of Transportation 

Federal Aviation Administration

13. Type of Report and Period Covered

 Final Report

Office of Aviation Research 

Washington, DC 20591

14. Sponsoring Agency Code

 ANM-100

15. Supplementary Notes 

The FAA William J. Hughes Technical Center Manager was Robert McGuire. 16. Abstract 

An analytical and limited experimental study was undertaken to assess the effects of rudder control systems and strategies in 

transport aircraft. The analytical study encompassed a pilot and vehicle analysis of possible feedback strategies that could be 

used by a transport aircraft pilot for lateral and directional control. The effect of control sensitivity was accounted for in

approximate fashion in the analyses. Pilot-induced oscillation tendencies were examined. The experimental study involves a 

desktop, human-in-the-loop simulation of the tasks used in the analytical study. A final comparison was undertaken involving 

pedal force/displacement characteristics for three transport aircraft and a helicopter. A simple index was proposed that can 

quantify the linearity of the force/displacement characteristics of any force/feel system. 

17. Key Words 

Rudder control, Feedback strategies, Transport aircraft, 

Human-in-the-loop simulation, Pedal force/displacement 

characteristics 

18. Distribution Statement 

This document is available to the public through the National 

Technical Information Service (NTIS) Springfield, Virginia 

22161.

19. Security Classif. (of this report) 

 Unclassified

20. Security Classif. (of this page) 

 Unclassified

21. No. of Pages 

 57 

22. Price

Form DOT F1700.7 (8-72) Reproduction of completed page authorized
ACKNOWLEDGEMENT 

The research reported herein was supported by a grant from the Federal Aviation Administration 

through the Airport and Aircraft Safety R&D Division at the William J. Hughes Technical 

Center, Atlantic City International Airport, NJ. The grant technical manager was Robert 

McGuire. 

iii/iv
TABLE OF CONTENTS 

Page 

EXECUTIVE SUMMARY xi 

1. ANALYTICAL STUDY 1 

1.1 Introduction 1 

1.2 Rudder Feedback Strategies for Manual Control 1 

1.2.1 Yaw Rate to Rudder 1 

1.2.2 Sideslip to Rudder 2 

1.2.3 Roll Attitude to Rudder 2 

1.2.4 Roll Attitude to Aileron 2 

1.2.5 Roll Attitude to Rudder and Aileron (Coordinated Control) 2 

1.2.6 Frequency-Domain Comparisons 3 

1.2.7 Handling Qualities Implications of Coordinated Control 5 

1.3 Pilot Models for Computer Simulation 7 

1.3.1 Introduction 7 

1.3.2 Pilot Model for Single-Axis Tracking 8 

1.3.3 Coordinated Aileron and Rudder Inputs 11 

1.3.4 Piloting Tasks for Computer Simulation 13 

1.4 Suggestions for Flight Simulator Investigations 22 

1.5 Summary of Section 1 22 

2. DESKTOP SIMULATION 23 

2.1 Introduction 23 

2.2 Visual Scene Representation 23

2.3 Inceptor 24 

2.4 Aerodynamic Model 25 

2.5 Control Law Implementation 26 

2.6 Test Subject 27 

2.7 Simulation Results 27 

2.7.1 Task 1: Large Roll Attitude Change 27 

2.7.2 Task 2: Wings-Level Sideslip Captures 32 

2.8 Summary of Section 2 35 

3. PEDAL FORCE/FEEL SYSTEM COMPARISON 35 

3.1 Introduction 35 

v
3.2 The Helicopter Comparison 37 

3.3 Comparing Pedal Force/Feel Characteristics 37 

3.4 A Computer Simulation 38 

3.5 Summary of Section 3 43 

4. SUMMARY OF RESULTS 44 

5. CONCLUSIONS 44 

6. REFERENCES 45 

LIST OF FIGURES 

Figure Page 

1 Bode Diagrams of s)( r

δ r

Without and With Yaw Damper 3 

2 Bode Diagrams of s)( δ r

β Without and With Yaw Damper 4 

3 Bode Diagrams of s)( δ r

φ With and Without Yaw Damper 4 

4 Bode Diagrams of s)(

K arr a δδ δ

φ

⋅=

With Yaw Damper for Kr = 0, 0.25, 0.5, and 

0.75, Including Aileron and Rudder Actuator Models 5 

5 Bandwidth and Phase Delay Definitions 6 

6 Bode Diagram of 

r a

ps

. a

y

s

a

δδ

δ

750

)(

=

 7 

7 The Structural Model of the Human Pilot 8 

8 Structural Pilot Model for Roll Attitude to Aileron Control 10 

9 Pilot/Vehicle System for Coordinated Use of Aileron and Rudder 12 

10 Bode Diagram of Open Loop Pilot/Vehicle Transfer Function With Kr = 0 13 

vi
11 Computer Simulation of Pilot/Vehicle System With Aileron Input Alone (Kr = 0) 

and With Coordinated Aileron and Rudder Inputs (Kr = 0.25, 0.50, and 0.75) 14 

12 Aileron and Rudder Inputs for Tracking Figure 11, Kr = 0 14 

13 Aileron and Rudder Rates for Tracking Figure 11, Kr = 0 15 

14 Aileron and Rudder Inputs for Tracking Figure 11, Kr = 0.5 15 

15 Aileron and Rudder Rates for Tracking Figure 11, Kr = 0.5 16 

16 Lateral Acceleration in the Cockpit for Tracking Figure 12, Kr = 0 and Kr = 0.5 16 

17 Lateral Acceleration in the Cockpit for Tracking Figure 12, Kr = 0, Kr = 0.5, and 

Kr = 0.35 With High Rudder Sensitivity 17 

18 Rudder and Aileron Inputs in Simulated PIO With Pilot Model Adopting 

Regressive Behavior (PIO frequency 3 rad/sec) 18 

19 Pilot/Vehicle System for Roll Attitude to Aileron and Sideslip to Rudder 19 

20 Bode Diagrams of Open Loop Pilot/Vehicle Transfer Functions for Roll and 

Sideslip Loops 19 

21 Computer Simulation of Pilot/Vehicle System to Alternating Sideslip Commands 20 

22 Aileron and Rudder Inputs for Tracking Figure 21 20 

23 Aileron and Rudder Rates for Tracking Figure 21 21 

24 Lateral Acceleration in the Cockpit for Tracking Figure 21 21 

25 Rudder and Aileron Inputs in Simulated PIO With Pilot Model Adopting 

Regressive Behavior (PIO frequency 2.9 rad/sec) 22 

26 Visual Scene Representation in Desktop Simulation 23 

27 Visual Scene Representation With Plastic Overlay 24 

28 Physical Simulation Setup 25 

29 Simulation Details in HPESIM 26 

30 Control Law Implementation Scheme in HPESIM (Longitudinal Axis Shown) 26 

31 Large Roll Attitude Change Task, Wheel Only Subject Inputs 27 

32 Aileron and Rudder Inputs for Task of Figure 31 28 

vii
33 Aileron and Rudder Rates for Task of Figure 31 28 

34 Large Roll Attitude Change Task, Wheel and Pedal Inputs 29 

35 Aileron and Rudder Inputs for Task of Figure 34 29 

36 Aileron and Rudder Rates for Task of Figure 34 29 

37 Comparison of Lateral Acceleration at Pilot’s Station (aps) for Tasks of 

Figures 31 and 34 30 

38 Large Roll Attitude Change Task, Wheel and Pedal Inputs, Performed With LowGain Tracking Behavior 30 

39 Aileron and Rudder Inputs for Task of Figure 38 31 

40 Aileron and Rudder Rates for Task of Figure 38 31 

41 Large Roll Attitude Change Task, Wheel and Pedal Inputs, Performed With 

Transient Rudder Inputs 31 

42 Aileron and Rudder Inputs for Task of Figure 41 32 

43 Aileron and Rudder Rates for Task of Figure 38 32 

44 Sideslip and Roll Attitude in Sideslip Capture Task 33 

45 Aileron and Rudder Inputs for Task of Figure 44 33 

46 Aileron and Rudder Rates for Task of Figure 44 33 

47 Modified Sideslip Capture Task 34 

48 Aileron and Rudder Inputs for Task of Figure 47 34 

49 Aileron and Rudder Rates for Task of Figure 47 34 

50 Pedal Force/Feel System Comparison of the A300-600 at 240 kts and the UH-60A 

Blackhawk Helicopter 36 

51 Pedal Force/Feel System Comparison of the B-767 and the UH-60A Blackhawk 

Helicopter 36 

52 Pedal Force/Feel System Comparison of the Airbus A300-B2-B4 and the UH-60A 

Blackhawk Helicopter 37 

53 A Simplified Computer Model of the Pilot/Vehicle System 38 

viii
54 Representation of the Pedal Force/Feel Systems A and B in the Computer 

Simulation of Figure 53 39 

55 Responses of the Computer Simulation System of Figure 53 for Different Pilot 

Gains for the System A Pedal Force/Feel System 40 

56 Responses of the Computer Simulation System of Figure 53, for Different Pilot 

Gains for System B Pedal Force/Feel System 40 

57 Pedal Force vs Pedal Displacement for Systems A and B in Figure 53 for Kp = 4 41 

58 Defining a Linearity Index 42 

59 Alternate Definition of Linearity Index 43 

LIST OF TABLES 

Table Page 

1 Bandwidth and Phase Delay for Systems of Figure 4 6 

2 Force/Feel System Summary 38 

ix
LIST OF ACRONYMS 

LI Linearity index 

PIO Pilot-induced oscillations 

PS Pilot’s station 

x
EXECUTIVE SUMMARY

This report contains five sections. Section 1 contains an analytical investigation of various 

rudder control strategies that could be employed by the pilot of a transport aircraft. A detailed 

mathematical model of the human pilot is used in a computer simulation to examine the closedloop nature of these strategies. It is shown that the coordinated or combined use of aileron and 

rudder inputs for roll-attitude tracking can exhibit poor performance and stability compared to a 

strategy using aileron inputs alone. It is also suggested that rudder force/feel systems with large 

sensitivities (low force gradients) can precipitate lateral/directional pilot-induced oscillations 

with coordinated rudder and aileron inputs due to large lateral accelerations being created at the 

pilot’s station. Similar large accelerations at the pilot’s station can be created in a sideslip 

capture task when large control sensitivities exist in the rudder control system. These 

accelerations can also serve as a trigger for pilot-induced oscillations. 

Section 2 involves a human-in-the-loop desktop simulation of the rudder control strategies 

examined in section 1. In particular, the handling qualities and potential flight safety problems 

of high-gain, closed-loop tracking using coordinated or combined aileron and rudder inputs 

predicted in section 1 appear in the simulations of section 2. 

Section 3 discusses a comparison of the rudder force/feel characteristics of three transport 

aircraft and a military helicopter. Significant differences in the force/feel characteristics of one 

transport compared to the remaining two and the helicopter are noted. A linearity index is 

defined to quantify the linear force/displacement characteristics of any force/feel system. A 

simple computer simulation of a closed-loop piloting task involving two of the force/feel systems 

differing most in linearity indicates that the nonlinear force/feel design leads to unpredictable 

vehicle responses and poor performance. 

Section 4 summarizes the major results of the study. 

Section 5 presents the major conclusions. 

Section 6 lists the references cited in this report. 

xi/xii
1. ANALYTICAL STUDY. 

1.1 INTRODUCTION. 

The Federal Aviation Administration has undertaken a four-phase research project to study 

airplane rudder control systems. The four phases include Literature and Database Review, Pilot 

Survey, Desk Top Simulation, and Real-Time Pilot Simulation. This report represents part of the 

third phase Desk Top Simulation. 

Recent incidents, like the crash of American Airlines Flight 587 in November 2001, have 

brought transport pilots’ use of rudder control under increased scrutiny [1-3]. This is especially 

true in large upsets caused by wake vortex encounters [4]. Rudder designs are typically driven 

by the following general requirements: (1) maintaining zero sideslip in turning flight, i.e., 

overcoming adverse yaw; (2) maintaining or minimizing sideslip in asymmetric power 

conditions, e.g., power loss in multiengine aircraft; (3) maintaining constant sideslip in 

crosswind landings; and (4) spin recovery. None of these requirements are directed toward using 

the rudder in closed-loop tracking control, an activity that will be of central importance in the 

research to be described. 

1.2 RUDDER FEEDBACK STRATEGIES FOR MANUAL CONTROL. 

Reference 5 presents a thorough treatment of various feedback strategies (or surveys) using the 

rudder as part of automatic feedback system, i.e., stability augmentation systems. Three systems 

were of particular interest to this study: feedback of yaw rate to rudder, r → δ ; sideslip to 

rudder, β → δ ; and roll attitude to rudder, φ → δ , particularly in combination with aileron to 

rudder, φ → δ , δ . Reference 6, published nearly 40 years ago, provides an analytical and 

experimental study of lateral directional manual control. This involved feedback of roll attitude 

to aileron, φ → δ , and yaw rate to rudder

r

r r

r a

a , r → δr. 

1.2.1 Yaw Rate to Rudder. 

The yaw-rate-to-rudder deflection transfer function for a typical transport aircraft can be given in 

symbolic fashion as [5] 

])[1(

][

2)[1( ]

2[ ] )( 2 2

2 2

dds

rrr

s ddd

r rrr

r ,T/

,A

ssT/s

ssA

s

r

ως

ως

ωως

ωως

δ = + ++

++ = (1) 

where the far right-hand side of the equation is expressed in shorthand notation. If a yaw damper 

is included in the system, mechanized with feedback of first-order, washed-out yaw rate, the 

general form of equation 1 is modified. A real zero is added (with a time constant equal to the 

washout pole) as well as a real pole with a slightly smaller time constant than the washout pole. 

In this case, δr would represent the output of the pedal force/feel system in the cockpit, with the 

yaw damper loop closed. No actuator dynamics are included at this juncture. 

1
1.2.2 Sideslip to Rudder. 

The sideslip-to-rudder deflection transfer function for a typical transport aircraft can also be 

given in symbolic fashion as 

])[1)(1(

)1)(1)(1( )( 1 2 3

r rrrs ,T/T/

T/T/T/A

s

δ ως

β βββ β = (2) 

Taken alone, feedback of sideslip to rudder can destabilize the spiral mode emanating from the 

root at s = -1/Ts [5]. If a yaw damper with feedback of first-order, washed-out yaw-rate is 

included, a modification similar to that for the yaw rate-to-rudder transfer function occurs. 

1.2.3 Roll Attitude to Rudder. 

The roll attitude-to-rudder deflection transfer function for a typical transport aircraft can be given 

in symbolic fashion as 

])[1)(1(

)1)(1( )( 1 2

r rrrs ,T/T/

T/T/A

s

ως

φ φ

δ

φ φ = (3) 

It should be noted that the zero 2

= −1 T/s φ will typically be nonminimum phase and can possess 

a relatively small time constant, i.e., on the same order as the roll subsidence mode. The addition 

of a yaw damper will have a similar effect as in the previous two cases. The appearance of the 

nonminimum phase zero and resulting reverse action in control response is attributable to the fact 

that the rudder induces yawing as well as rolling motion. Initially, a rudder deflection will 

induce a rolling motion opposite to the intended input. Quickly, however, a sideslip develops 

that induces the desired roll response. 

1.2.4 Roll Attitude to Aileron. 

The roll attitude-to-aileron deflection transfer function for a typical transport aircraft can be 

given by 

))(1)(1(

][1

a ddrs ,T/T/

,A

)s(

ως

ως

δ

φ φφφ = (4) 

The addition of a yaw damper will affect the transfer function in a manner similar to the previous 

cases. 

1.2.5 Roll Attitude to Rudder and Aileron (Coordinated Control). 

Here, one considers the possibility that the pilot may employ both aileron and rudder to control 

roll attitude. This might occur in a large roll upset where aileron control alone may appear to 

provide insufficient roll control power. In this case, one can consider 

2
K arr

r

r

a

a

sssss

δδ

δ

δ

φ δ

δ

φ φ

⋅=

⋅+⋅= )()()()()(

)()()( sKsss )( ar

r

a

a

δ

δ

φ δ

δ

φ φ ⋅⋅+⋅= (5) 

r

a a r

⋅+= Kss

δ

φ

δ

φ

δ

φ )()(

In equation 5, it is assumed that rudder inputs proportional to aileron inputs are commanded with 

the relation between the two inputs given by δr = Kr

.

δa. 

1.2.6 Frequency-Domain Comparisons. 

Figures 1 through 3 show the Bode diagrams of the transfer functions in equations 1 through 3 

for a generic transport aircraft. This aircraft is the DC-8 vehicle with stability derivatives 

defined for flight condition 8002 in reference 5, corresponding to an airspeed of 468.2 ft/sec and 

an altitude of 15,000 ft. Also shown are the diagrams that result when washed-out yaw rate is 

fed back to the rudder. The yaw damper transfer function is given by 

)50(

)0(141 )( .. s

r

r = δ rad/rad (6) 

with the gain being chosen as one which increases the damping of the dutch roll mode from 0.11 

to 0.4. The Bode diagrams in figures 1 through 3 clearly show the increase in dutch roll mode 

damping provided by the yaw damper. The magnitude and phase characteristics of figure 3 

clearly show the effects of the nonminimum phase zero, here at s = -2.56. 

FIGURE 1. BODE DIAGRAMS OF s)( r

δ r

WITHOUT AND WITH YAW DAMPER 

3
FIGURE 2. BODE DIAGRAMS OF s)( δ r

β WITH AND WITHOUT YAW DAMPER 

FIGURE 3. BODE DIAGRAMS OF s)( δ r

φ WITH AND WITHOUT YAW DAMPER 

Figure 4 shows the Bode diagrams for the system of the last of equation 5 for Kr = 0, 0.25, 0.5, 

and 0.75. The yaw damper of equation 6 is included in each of these systems as are two actuator 

models for aileron and rudder. These actuator models are given by 

]207070[

202

,. c ac

a

r

r == δ

δ

δ

δ rad/rad (7) 

4
As will be discussed in section 1.3, the value of Kr = 0.75 will produce the maximum-allowable 

rudder input when the aileron input is also the maximum allowable. 

FIGURE 4. BODE DIAGRAMS OF s)(

K arr a δδ δ

φ

⋅=

WITH YAW DAMPER FOR Kr = 0, 0.25, 

0.5, AND 0.75, INCLUDING AILERON AND RUDDER ACTUATOR MODELS 

For frequencies less than 1 rad/sec, the Bode diagrams in figure 4 show that an increase in roll 

control power can be obtained with the combined use of rudder and aileron. In the case of Kr = 

0.75, the increase is approximately a factor of 1.7. In addition, the magnitude and phase curves 

in this low frequency range show the K/s—like characteristics long associated with desirable 

handling qualities (180° should be subtracted from the phase curves to account for the sign 

definitions of positive rudder and aileron). The same cannot be said for higher frequencies 

however. The magnitude characteristics for all Kr values indicate a first-order lag appearing 

around 1 rad/sec. As Kr increases, however, phase lags beyond the 90° associated with a firstorder lag can clearly be seen. 

1.2.7 Handling Qualities Implications of Coordinated Control. 

So-called coordinated control of aileron and rudder may constitute the most challenging pilot 

feedback strategies in terms of vehicle handling qualities. Bandwidth and phase delay have been 

used extensively for handling qualities investigations, e.g., reference 7. While the particular 

values of these parameters would be dependent upon the particular aircraft model selected here, 

the relative variations in these parameters as a function of Kr can shed light upon the handling 

qualities variations that may occur with coordinated use of rudder and aileron. Figure 5 shows 

the definitions of bandwidth and phase delay [7]. The Bode diagrams in figure 4 indicate that the 

response is a rate-type system. Using the definitions given in figure 5, the bandwidth and phase 

delay results for the four transfer functions in figure 4 are given in table 1. 

5
FIGURE 5. BANDWIDTH AND PHASE DELAY DEFINITIONS 

TABLE 1. BANDWIDTH AND PHASE DELAY FOR SYSTEMS OF FIGURE 4 

Kr

Bandwidth 

(rad/sec) 

Phase Delay 

(sec) 

0 1.14† 0.06 

0.25 0.90 0.055 

0.5 0.792 0.054 

0.75 0.738 0.013 

† All bandwidths obtained from BWphase ω 

The most significant feature of the results of table 1 is the significant decrease in bandwidth as Kr

increases. It must be emphasized that the results of table 1 correspond to a hard-wired aileron 

and rudder linkage. In reality, this linkage is created by the pilot. Of particular interest to this 

study is the susceptibility of an aircraft to pilot-induced oscillations (PIO). Unfortunately, at 

present, no PIO boundaries have been established for bandwidth (as opposed to those for phase 

delay). As pointed out in reference 8, this is due to a lack of supporting data, not to any 

assumption as to the possible impact of roll bandwidth on PIO. Thus, a direct comparison with 

existing bandwidth and phase delay boundaries that delineate handling qualities levels, (e.g., 

reference 7) must be approached with caution. 

6
The small phase delays in table 1 are attributable to the shape of the phase curves in the 

frequency range beyond the point where the phase lags equal -180°. That is, the phase curves do 

not resume a steep roll off until frequencies associated with the bandwidths of the actuators are 

reached. 

If manual control of roll attitude through coordinated use of rudder and aileron is attempted, the 

resulting lateral accelerations at the pilot’s station (PS) are also pertinent to a discussion of 

handling qualities. The lateral acceleration to aileron transfer function then can be approximated 

as [5] 

arr

r

arr

ps

a K

psr

a K

v

a

y

s

r xKYs v Ys

a

δδ

δ

δδ δ δ δ = =

≈ )()( +⋅+ )( & (8) 

where xps is the x body-axis coordinate of the pilot’s station. Figure 6 shows the Bode diagrams 

of the transfer function of equation 8 for the example vehicle. Here, the yaw damper and rudder 

actuator are included and Kr = 0.75. 

FIGURE 6. BODE DIAGRAM OF 

r a

ps

. a

y

s

a

δδ

δ

750

)(

=

Figure 6 indicates that if a sinusoidal aileron input of δa(t) = 20sin(2t) deg with an associated 

δr(t) = (15) sin(2t) deg is applied, the resulting amplitude of the sinusoidal lateral acceleration at 

the PS will be approximately 9.2 ft/sec2

 or 0.24 g’s. 

1.3 PILOT MODELS FOR COMPUTER SIMULATION. 

1.3.1 Introduction. 

The fundamental manual control theory states that the pilot will provide whatever compensation 

is necessary to yield an open loop pilot/vehicle transfer function that resembles K/s in the region 

7
of the open loop crossover frequency [9]. This representation has been referred to as the 

Crossover Model of the human pilot and can be represented as 

s

e

YY

s

c

cp

e τ ω −

≈ (9) 

where Yp represents the pilot transfer function and Yc represents the vehicle for the control axis in 

question. Also in equation 9, ωc represents the crossover frequency and τe represents an 

effective delay. The latter encompasses true transport delays in the human central nervous 

system, delays that approximate the higher-frequency human neuromotor dynamics, and higherfrequency vehicle dynamics that may be omitted from Yc. In what follows, two different tasks 

and feedback strategies will be examined. First, coordinated use of aileron and rudder will be 

examined (including no rudder usage). Second, the piloted control of roll attitude with aileron 

and sideslip with rudder will also be examined. The first of these tasks might model the pilot 

using aileron and rudder to provide rapid roll attitude recovery from an upset. The second task 

could represent a situation in which the pilot is attempting to maintain a given heading with 

wings level, while a transient crosswind creates an effective sideslip angle. 

1.3.2 Pilot Model for Single-Axis Tracking. 

To create a realistic computer simulation of the pilot/vehicle system, a more complete pilot 

model than that implied by equation 9 is obviously needed. This will be accomplished by using 

the structural model of the human pilot, e.g., reference 10. Figure 7 shows the structural 

pilot/vehicle model appropriate for single-axis tracking of roll attitude, here with aileron inputs, 

alone. Thus, in figure 7, C ≡ φc, M ≡ φ, and δ ≡ δw, the displacement of the wheel (output of the 

wheel force/feel system). Referring to figure 7, the following pilot model elements can be given. 

FIGURE 7. THE STRUCTURAL MODEL OF THE HUMAN PILOT 

8
• Visual Gain Ye = Ke. The value of this gain is application-dependent and is selected to 

yield a desired open loop crossover frequency [9]. 

• Time Delay τ0. This delay is selected as 0.2 sec and models human delay sources 

exclusive of those associated with neuromuscular system operation. 

• Neuromuscular System Dynamics. These dynamics are modeled as 

2 2

2

1010)7070(2

10

+ + = s.s

YNM (10) 

and represent the actuation dynamics of the particular limb effecting control, e.g., arm in 

wheel motion and leg in pedal motion. 

• Proprioceptive System Dynamics. In this particular task, these dynamics are modeled as 

) 1 (

PF

PF

PF

T

s

K Y

+

= (11) 

This form is appropriate for the roll attitude dynamics of figure 4, since the pole in 

proprioceptive feedback dynamics will create a zero in the pilot transfer function located 

as s = -1/TPF. 

• Vestibular System Dynamics. For simplicity, no continuous vestibular feedback will be 

considered in the model, i.e., K . m& = 0

• Force/Feel System Dynamics. The dynamics of the force/feel system(s) will be of the 

form 

2 2

2

2

)(

FS FSFS

FS FS

FS

s s

K

sY

ωως

ω

+ +

⋅

= displacement/lbf (12) 

• Modeling Effects of Control Sensitivity. Control sensitivity, or its reciprocal force 

gradient, is one of the more important force/feel system parameters affecting handling 

qualities and particularly PIO susceptibility [11]. Unfortunately, the manner in which the 

gain KPF is chosen in the structural model removes all control sensitivity effects [10]. 

However, one important issue can be addressed, which is the ratio between maximum to 

breakout forces in the force/feel system. 

Figure 8 shows the structural model for a particular application (roll attitude to aileron 

feedback). 

9
FIGURE 8. STRUCTURAL PILOT MODEL FOR ROLL ATTITUDE TO 

AILERON CONTROL 

In figure 8, an approximation to the control force inputs is obtained by normalizing the signal 

that represents the model of the neuromuscular dynamics of the particular limb driving the 

cockpit controller (e.g., the arm moving the wheel). The normalization is defined by the gain 

value immediately following the neuromuscular system dynamics block in figure 8 (Gain 1 in 

figure 8). In what follows, inceptor refers to the cockpit controller, e.g., wheel, pedal, etc., and 

effector refers to the control surface, e.g., aileron, rudder, etc. The gain identified as Gain 1 is 

defined as 

Max Effector Deflection

Inceptor Force Correspond toing Maximum Effector Deflection K force = (13) 

A nonlinear threshold element follows Gain 1 and represents the breakout characteristics of the 

inceptor. Because of the preceding gain element, the breakout limits are expressed directly in 

terms of breakout force. Following the threshold element is another gain (Gain 2) defined 

simply as the reciprocal of the gain in equation 13. Thus, determination of the force applied by 

the pilot model is confined to three elements: Gain 1, breakout, and Gain 2. The inceptor 

displacement is calculated from the output of the force/feel system dynamics by multiplying by a 

gain (unit conversion in figure 8) defined as 

Maximum Effector Deflection

Maximum Inceptor Displacement Kdisplacement = (14) 

The threshold element has the effect of a gain reduction in the forward path of the loop closed 

around the pilot’s neuromuscular and force/feel system. By considering the Gaussian input 

describing function for the threshold nonlinearity that represents the nonlinear force/feel 

characteristics in the computer simulation [12], this reduced gain can be approximated as1

 

1

 It is assumed in equation 15 that 2σ for the Gaussian input to the nonlinearity is equal to Force|max. 

10
max

max

max

1

Force

Force Force

Force

Force

K breakout breakout

threshold

− −≈ = (15) 

Immediately before the nonlinearity in the Structural Model of the pilot, the reciprocal of the 

reduced gain is inserted to model the pilot’s attempt to compensate for the gain reduction due to 

the nonlinearity. This latter gain value can be approximated by a multiplicative factor on Ke, 

defined as follows: 

breakout

factor Force Force

Force

K − =

max

max (16) 

In equations 15 and 16, Force|max corresponds to Inceptor Force Corresponding to Maximum 

Effector Displacement in equation 13. Thus, if in equation 16, Force|max = 25 lbf and 

Force|breakout = 5 lbf, Kfactor = 25/20 = 1.25 and the gain Ke is multiplied by 1.25. Since the 

pilot/vehicle transfer function in any modeling application will have finite stability margins, 

Kfactor can induce closed-loop instability if the Force|breakout is of the same order of magnitude as 

Force|max. Finally, note that if no breakout force is in evidence, the procedure just described will 

not accommodate the effects of control sensitivity. 

1.3.3 Coordinated Aileron and Rudder Inputs. 

Referring to figure 4, one sees that, for this task, the pilot would be required to generate firstorder lead with a reciprocal time constant on the order of 1/sec, (the approximate location of the 

dutch roll poles with the yaw damper in place). Thus, in its simplest form, the pilot equalization 

would be 

 ) ≈ sKY +1( φ pp φ (17) 

It should also be noted that the form of equation 17 would be invariant with Kr values, since, 

with the exception of an increase in gain, the form of the various vehicle transfer functions in 

figure 4 varies only in phase lag. This fact does not bode well for closed-loop system stability at 

larger values of Kr. 

For coordinated use of aileron and rudder, a more complex model than figure 7, must be 

employed. The hypothesized model is shown in figure 9. Here, the block labeled Structural 

Model for φ-loop is essentially the model of figure 7. It is hypothesized that the command to the 

pedals is obtained from the input signal to the neuromuscular system for the pilot’s arm. The 

specific parameters for the various elements in figure 9 can now be given. 

• Proprioceptive Dynamics. In equation 11, 1/TPF = 1/sec. The parameter KPF is chosen as 

the value that yields a minimum damping ratio of 0.15 for any poles of the transfer 

function resulting when only the proprioceptive loop of figure 7 is closed. 

11
FIGURE 9. PILOT/VEHICLE SYSTEM FOR COORDINATED USE OF 

AILERON AND RUDDER 

• Neuromuscular Dynamics. YNM will be as given in equation 10 for both arm and legs. 

• Force/Feel System Dynamics. YFS for the wheel and pedals will be given by 

2 2

2

1010)30(2

1015

+ +

⋅ = s.s

YFS wheel wheel deflection/lbf (18) 

2 2

2

2020)30(2

2065

+ +

⋅ = s.s

YFS pedal pedal deflection/lbf (19) 

For the wheel, full deflection corresponds to a 80° wheel rotation and a 20° aileron 

deflection. For the pedal, full deflection corresponds to 1.5-inch pedal deflection and 15°

rudder deflection. The ratio of maximum rudder deflection to maximum aileron 

deflection is 0.75 and gives rise to the Kr = 0.75 value employed in section 1.2. The Kmax 

for the aileron is 15 lbf and 65 lbf for the pedals. The breakout forces for the wheel and 

pedal are wheel: 2 lbf; pedal: 13 lbf. 

• Delay. The delay in figure 9 is identical to that in the pilot model of figure 7, 0.2 sec. 

• Actuator Dynamics and Limits. The dynamics of the actuators for both rudder and 

aileron have been given in equation 7. The amplitude and rate limits of these actuators 

are as follows: 

 aileron: amplitude limit = ±20°

 rate limit = ±45°/sec 

 rudder: amplitude limit = ±15°

 rate limit = ±60°/sec 

12
Figure 10 shows the resulting Bode diagram for the open-loop pilot/vehicle transfer function 

with Kr = 0, and with Kfactor set to unity. The diagram is very similar in form to measured 

pilot/vehicle transfer functions, e.g., reference 9. 

FIGURE 10. BODE DIAGRAM OF OPEN LOOP PILOT/VEHICLE TRANSFER 

FUNCTION WITH Kr = 0 

1.3.4 Piloting Tasks for Computer Simulation. 

1.3.4.1 Task 1: Large Roll Attitude Change. 

The command roll attitude will be a filtered step command in which the pilot uses the aileron 

alone with no pedal inputs. Next, the same roll attitude command will be used, but this time, the 

pilot model will be employing coordinated aileron and pedal inputs. In the second scenario, 

various Kr values will be chosen, with the largest representing the ratio of maximum 

displacements of aileron and rudder, i.e., Kr = 0.75. 

The crossover frequency for the roll attitude loop with no rudder inputs will be chosen as 1.5 

rad/sec. The gain Ye = Ke selected for the first task will remain unchanged in the second task. 

The Kfactor for the aileron loop is from equation 16, Kfactor = 15/13 = 1.15. For the rudder loop, 

Kfactor = 65/52= 1.25. Figure 11 shows the simulation results. When the maximum Kr (0.75) is 

employed, the closed-loop pilot/vehicle system is unstable, with an oscillatory divergence 

exhibiting a frequency of 1.5 rad/sec. The results indicate that the dutch roll mode has been 

excited with the manual loop closures examined here. With Kr = 0 and 0.25, the closed-loop 

system responds well. The aileron and rudder inputs for each Kr = 0 are shown in figure 12. The 

residual rudder motion with Kr = 0 is attributable to the action of the yaw damper. Figure 13 

shows aileron and rudder rates. Figures 14 and 15 compare aileron and rudder inputs and rates 

for Kr = 0.5. Figure 16 compares the lateral acceleration in the cockpit for the two Kr values. 

Note that for Kr = 0.5, the lateral acceleration can reach 0.3 g’s. Figures 12 through 15 indicate 

that amplitude and rate limiting of both aileron and rudder occurs in these tasks. 

13
FIGURE 11. COMPUTER SIMULATION OF PILOT/VEHICLE SYSTEM WITH 

AILERON INPUT ALONE (Kr = 0) AND WITH COORDINATED AILERON AND 

RUDDER INPUTS (Kr = 0.25, 0.50, AND 0.75) 

FIGURE 12. AILERON AND RUDDER INPUTS FOR TRACKING 

FIGURE 11, Kr = 0 

14
FIGURE 13. AILERON AND RUDDER RATES FOR TRACKING 

FIGURE 11, Kr = 0 

FIGURE 14. AILERON AND RUDDER INPUTS FOR TRACKING 

FIGURE 11, Kr = 0.5 

15
FIGURE 15. AILERON AND RUDDER RATES FOR TRACKING 

FIGURE 11, Kr = 0.5 

FIGURE 16. LATERAL ACCELERATION IN THE COCKPIT FOR TRACKING 

FIGURE 12, Kr = 0 AND Kr = 0.5 

16
Figure 17 shows the lateral acceleration in the cockpit that occurs for Kr = 0 and Kr = 0.35 with 

nominal rudder sensitivity and Kr = 0.35 with high rudder sensitivity, defined here as K|force = 32 

lbf and K|breakout = 22 lbf. This yields Kfactor = 32/10 = 3.2 for the rudder channel. The increased 

rudder sensitivity has significantly increased the maximum values of aps. 

FIGURE 17. LATERAL ACCELERATION IN THE COCKPIT FOR TRACKING 

FIGURE 12, Kr = 0, Kr = 0.5, AND Kr = 0.35 WITH HIGH 

RUDDER SENSITIVITY 

The issue of whether a pilot would coordinate rudder with aileron, as was done in the computer 

simulation, is open to question. Obviously, continuous high-gain coordination is detrimental to 

tracking performance and stability. It is possible, however, that a highly sensitive pedal 

force/feel system might induce pilot activity of this nature. In addition, the large lateral 

accelerations that are predicted to develop could precipitate a PIO. This was suggested by the 

author when investigating the crash of American Airlines Flight 587 [11]. A PIO can be 

precipitated in the computer simulation by forcing the pilot model to adopt the so-called 

regressive tracking behavior as discussed in reference 10. In this behavior, the pilot is 

hypothesized to use roll rate rather than roll attitude as the fundamental visual cue. In addition, 

proprioceptive cues were assumed to be ignored. Figure 18 shows aileron and rudder inputs 

demonstrating the oscillatory vehicle responses that develop with this regressive behavior. Here, 

the minimum pilot gain was selected that yielded the oscillatory behavior. The nature of the 

aileron and rudder inputs indicate that amplitude and rate saturation of these devices occurred. 

The frequency of the PIO is approximately 3.0 rad/sec (0.48 Hz). 

17
FIGURE 18. RUDDER AND AILERON INPUTS IN SIMULATED PIO WITH PILOT 

MODEL ADOPTING REGRESSIVE BEHAVIOR (PIO frequency 3 rad/sec) 

It should be emphasized that this simulation does not imply that the vehicle chosen for study is 

PIO prone. Rather that an overly sensitive pedal force/feel system (low force gradient) could 

precipitate a PIO in a sudden upset by inducing large lateral accelerations at the PS. 

1.3.4.2 Task 2: Wings Level Sideslip Captures. 

In this task, demanding discrete sideslip captures are required while maintaining wings level. 

Referring to figures 2 and 3, one sees that for this task, the pilot would again be required to 

generate a first-order lead with a reciprocal time constant on the order of 1/sec, for both the 

aileron and rudder loops. Figure 19 is a block diagram representation of this task. Of course, in 

flight, sideslip deviations would not be sensed by the pilot as readily as a roll attitude. In a flight 

simulator, however, sideslip deviations could be presented to the pilot by artificial means. It is 

the possibility of using such feedback to investigate rudder control in a simulator that motivates 

this part of the study. 

The command roll attitude for this task will be zero, with the sideslip command consisting of a 

filtered doublet alternating between ±6° in amplitude. One physical interpretation for this input 

would be the aircraft experiencing a 30-kt wind that alternates between ±30° from the aircraft’s 

initial heading. Here, each alternating pulse lasts approximately 6 sec. 

18
FIGURE 19. PILOT/VEHICLE SYSTEM FOR ROLL ATTITUDE TO 

AILERON AND SIDESLIP TO RUDDER 

Since two loops are being simultaneously closed by the pilot, an iterative procedure is employed 

to determine the forms of the pilot models for each loop. First, the rudder loop is left open and 

the appropriate Structural Model pilot dynamics are selected for the aileron loop. As in the study 

with coordinated aileron and rudder, the general form of YPF for both loops is as given in 

equation 11. After selection of the aileron-loop pilot model, this control loop is closed and the 

appropriate Structural Model pilot dynamics are selected for the sideslip loop. The procedure is 

repeated until no significant changes in the pilot models occur. Figure 20 shows the Bode 

diagrams of the open loop pilot/vehicle transfer functions for each loop, with the remaining loop 

closed. 

FIGURE 20. BODE DIAGRAMS OF OPEN LOOP PILOT/VEHICLE TRANSFER 

FUNCTIONS FOR ROLL AND SIDESLIP LOOPS 

As was the case in figure 10, K/s-like dynamics are evident, and a common crossover frequency 

of 1.5 rad/sec is chosen. Once again, this crossover frequency was created with Kfactor = 1 in 

each loop. 

19
Figure 21 shows the responses in roll attitude and sideslip. Note the significant roll attitude 

excursions from the desired wings-level condition. Figures 22 and 23 show the aileron and 

rudder inputs and rates. Finally, figure 24 shows the resulting lateral acceleration at the PS. 

FIGURE 21. COMPUTER SIMULATION OF PILOT/VEHICLE SYSTEM TO 

ALTERNATING SIDESLIP COMMANDS 

FIGURE 22. AILERON AND RUDDER INPUTS FOR TRACKING FIGURE 21 

20
FIGURE 23. AILERON AND RUDDER RATES FOR TRACKING FIGURE 21 

FIGURE 24. LATERAL ACCELERATION IN THE COCKPIT FOR 

TRACKING FIGURE 21 

Increasing the sensitivity of the rudder system to high level resulted in incipient instability in the 

pilot/vehicle system. Lateral accelerations at the PS exceeded 0.5 g’s in one excursion. Again, 

such values are likely to serve as a triggering event for a PIO. Creating regressive behavior in 

the pilot model in both the roll and sideslip channels leads to the PIO shown in figure 25. The 

PIO frequency is approximately 2.9 rad/sec or 0.46 Hz. Again, significant amplitude and rate 

limiting are evident in the figure. 

21
FIGURE 25. RUDDER AND AILERON INPUTS IN SIMULATED PIO WITH 

PILOT MODEL ADOPTING REGRESSIVE BEHAVIOR (PIO frequency 2.9 rad/sec) 

1.4 SUGGESTIONS FOR FLIGHT SIMULATOR INVESTIGATIONS. 

Compared to those for wheel and column, rudder force/feel system designs have received little 

attention in the literature [13]. However, recent accidents, such as American Airlines flight 587 

and other rudder-related incidents with transport aircraft [14], have uncovered a need for firm 

design requirements for these systems. Given the inherent dangers of flight testing in which the 

possibility of excessive vertical stabilizer loading can easily occur, it would appear that groundbased flight simulators offer the most practical means for delineating acceptable force/feel 

characteristics. It is essential in defining the tasks that would be performed in such 

investigations that the recommendations of reference 15 be recalled. Specifically, any tasks 

selected for discerning the PIO susceptibility of force/feel system characteristics need to be 

sufficiently challenging and aggressive. The coordinated roll attitude capture and wings-level 

sideslip captures exercised herein via computer simulation may serve as two such tasks. This 

and other candidate tasks could undergo preliminary evaluation on simple desktop engineering 

simulators to assess their worth and practicality. One such investigation is discussed in 

section 2. 

1.5 SUMMARY OF SECTION 1.

The research described in this section has used a simple dynamic model of the lateral/directional 

dynamics of a transport aircraft. A system survey of possible manual loop closures was 

presented. Using a Structural Model of the human pilot, two tracking tasks were examined, each 

with an eye toward capturing possible pilot/vehicle behavior than could occur in large roll upsets 

and in deliberate sideslip excursions. The pilot model was extended to emulate the effects of 

control sensitivity. The coordinated use of aileron and rudder inputs for roll attitude tracking 

was shown to exhibit poor performance and stability compared to aileron inputs alone. In 

addition, it was suggested that rudder force/feel systems with large sensitivities (low force 

22
gradients) could precipitate lateral/directional PIOs with such coordinated strategies due to the 

large lateral accelerations at the PS that occurred. The sideslip capture task also suggested that 

large control sensitivities in the rudder control system could also lead to large lateral 

accelerations at the PS that could serve as a PIO trigger. Although simplified in nature, the 

analytical study emphasized the handling qualities and performance issues that can arise in 

continuous use of rudder inputs in flight control tasks. 

2. DESKTOP SIMULATION. 

2.1 INTRODUCTION. 

A desktop, human-in-the-loop simulation of the vehicle and tasks described in section 1 was 

conducted. The simulation itself used a simulation software package HPESIM from High Plains 

Engineering [16]. This package allows pilot-in-the-loop, five or six degree-of-freedom 

simulation of aircraft dynamics. A variety of visual scene representations are possible. Here, a 

head-up display was employed and will be described in the following. The simulation is 

nonlinear in nature, although linear stability derivatives provide the vehicle model. 

Nonlinearities arise since no small angle approximations are employed in solving the equations 

of motion, and actuator amplitude and rate limiting can be modeled. 

2.2 VISUAL SCENE REPRESENTATION. 

Figure 26 shows the visual scene representation used herein. The small aircraft symbol at the 

center of the display is a flight path symbol that was used in the sideslip capture task but was 

removed for the large roll attitude change task. For the two tasks discussed in section 1, a clear 

plastic overlay was placed over the terminal, as shown in figure 27. 

FIGURE 26. VISUAL SCENE REPRESENTATION IN DESKTOP SIMULATION 

23
FIGURE 27. VISUAL SCENE REPRESENTATION WITH PLASTIC OVERLAY 

The slanted lines in figure 27 represent 20° roll attitudes (the magnitude of the commands used 

in task 1 in section 1). The two vertical lines represent 5° sideslip excursions (the magnitude of 

the sideslip commands used in task 2 in section 1). The nominal eye-to-display distance for the 

simulations was 26 inches. The monitor size was 14.4375 by 10.875 in. HPESIM uses the 

monitor size to create a vertical field of view in the visual scene. 

2.3 INCEPTOR. 

Figure 28 shows the subject’s chair and the inceptor used in the simulation. The joystick shown 

allowed three-axis control. The desk shown in figure 28 allowed arm support during the tracking 

tasks. Aileron inputs were created by lateral stick deflection, with rudder inputs created by 

rotating the stick about a vertical axis. When viewed from above, a clockwise rotation of the 

joystick was equivalent to the right pedal being depressed. The desktop version of HPESIM 

requires inputs from a single joystick, thus separate pedals to provide rudder inputs could not be 

accommodated. Though not employed in the tasks examined here, elevator inputs were possible 

through longitudinal stick deflection. The inceptor incorporated a light return spring in all axes. 

To approximate the dynamics of the force/feel systems of equations 18 and 19, filters in the form 

of the transfer functions given by these equations were implemented in software in HPESIM. Of 

course, proprioceptive feedback reflecting these dynamics were not available to the subject. 

Displacement thresholds for wheel and pedal inputs were 20% and 10% of full deflections, 

respectively, again created in software. Although longitudinal aircraft dynamics were included 

in the simulation, no column inputs were allowed. The natural aircraft short-period and phugoid 

motions were mitigated by creating a high-gain, pitch-attitude stability augmentation system to 

be described. 

24
FIGURE 28. PHYSICAL SIMULATION SETUP 

2.4 AERODYNAMIC MODEL. 

As in section 1, the aerodynamic model employed in the simulation was taken from reference 5 

and represented a DC-8 aircraft with stability derivatives defined for flight condition 8002, 

corresponding to an airspeed of 468.2 ft/sec and an altitude of 15,000 ft. The stability derivatives 

in reference 5 are referred to as a stability axis system, whereas HPESIM requires a body-axis 

system, with the x-body axis aligned with the mean aerodynamic chord. To transform the 

derivatives from stability to body axes, the trim angle of attack is required. This information was 

not provided in reference 5, therefore, a trim angle of attack of 5° was estimated here. 

25
2.5 CONTROL LAW IMPLEMENTATION. 

Figures 29 and 30 show the general format available in HPESIM for setting up simulation details 

and for implementing control laws (shown for the longitudinal axis). 

FIGURE 29. SIMULATION DETAILS IN HPESIM 

FIGURE 30. CONTROL LAW IMPLEMENTATION SCHEME IN HPESIM

(LONGITUDINAL AXIS SHOWN) 

As mentioned in the preceding, a longitudinal SAS was designed to reduce the pitch attitude 

deviations in the vehicle. The SAS was defined as 

ss += )1(5)( e

θ

δ rad/rad (20) 

26
A yaw damper similar to that used in the analysis of section 1 was also implemented in the 

lateral directional axis. Because of the default transfer function forms available in HPESIM, this 

yaw damper took the form 

]50990[

]010990[114 )( .,.

.,. s

r

r = δ rad/rad/sec (21) 

This can be compared to equation 6 in section 1. No pure differentiation elements (s) were 

available in HPESIM, and only second-order numerator and denominator forms could be 

accessed. The form of equation 21 exhibits small amplitudes at low frequency (below 0.5 

rad/sec) and a constant amplitude of 2.28 for frequencies beyond 0.5 rad/sec, as does the transfer 

function of equation 6. 

2.6 TEST SUBJECT.

The author served as the test subject in this simulation. It must be emphasized that this 

simulation effort was an initial, exploratory effort aimed at a qualitative evaluation of the 

analytical results of section 1 and an assessment of possible tasks to be evaluated in other, more 

realistic simulation studies. For these reasons, no other test subjects were sought. 

2.7 SIMULATION RESULTS. 

2.7.1 Task 1: Large Roll Attitude Change. 

Figure 31 shows a 20° roll attitude change and corresponds to figure 11 with Kr = 0. Figure 32 

shows the aileron and rudder inputs that produced this response. Two points should be noted in 

figure 32. First, no amplitude limiting is actually occurring in the aileron input for this task. The 

flat portions of the input are due to signal quantization created by the joystick. Second, just as in 

the computer simulation of figure 12, the small rudder inputs are attributable to the action of the 

yaw damper, not to any inputs provided by the subject through the joystick. 

-10

-5

0

5

10

15

20

25

30

0 5 10 15 20

Time sec

phi deg

FIGURE 31. LARGE ROLL ATTITUDE CHANGE TASK, WHEEL ONLY 

SUBJECT INPUTS 

27
-30

-20

-10

0

10

20

30

0 5 10 15 20

Time sec

aileron and rudder deg

aileron 

FIGURE 32. AILERON AND RUDDER INPUTS FOR TASK OF FIGURE 31 

Figure 33 shows aileron and rudder rates for this task indicating significant aileron rate saturation 

occurring. Again, this result is similar to the computer simulation result shown in figure 13. 

-60

-40

-20

0

20

40

60

0 5 10 15 20

Time sec

aileron and rudder rate deg/sec

aileron rate 

FIGURE 33. AILERON AND RUDDER RATES FOR TASK OF FIGURE 31 

Figure 34 shows a 20° roll attitude change, including both wheel and pedal inputs. As opposed 

to the computer simulation study of section 1, no specific Kr value can be identified in this 

human-in-the-loop study. Nonetheless, incipient instability is evident in figure 34 much as was 

the case in figure 11 with Kr = 0.75. As in figure 11, the frequency of oscillation apparent in 

figure 34 is very near that of the dutch roll mode for this aircraft and flight condition. Figure 35 

shows the aileron and rudder inputs for this task, with figure 36 showing rates. Some aileron rate 

limiting is evident, and again, no amplitude limiting is occurring in figure 35 as the flat portions 

of the input are due to signal quantization created by the joystick. 

28
-10

0

10

20

30

40

50

0 5 10 15 20

Time sec

roll attitude deg

FIGURE 34. LARGE ROLL ATTITUDE CHANGE TASK, WHEEL AND PEDAL INPUTS 

-20

-15

-10

-5

0

5

10

15

0 5 10 15 20

Time sec

aileron and rudder deg

aileron 

FIGURE 35. AILERON AND RUDDER INPUTS FOR TASK OF FIGURE 34 

-60

-40

-20

0

20

40

60

0 5 10 15 20

Time sec

aileron and rudder rate 

deg/sec

aileron rate 

FIGURE 36. AILERON AND RUDDER RATES FOR TASK OF FIGURE 34 

29
Figure 37 compares the lateral acceleration at the pilot’s station (aps) for the tasks of figures 31 

and 34. Not surprisingly, the large roll attitude change task with both wheel and pedal inputs 

resulted in considerably larger accelerations than were obtained with just wheel inputs alone. 

-0.2

-0.1

0

0.1

0.2

0 5 10 15 20

Time sec

lateral accel at cockpit g's

aps from task of figure 34 

FIGURE 37. COMPARISON OF LATERAL ACCELERATION AT PILOT’S STATION (aps) 

FOR TASKS OF FIGURES 31 AND 34 

Figure 38 shows the large roll attitude change task with both wheel and pedal inputs now 

deliberately performed with a low-gain tracking approach. Figures 39 and 40 show the aileron 

and rudder inputs and rates, respectively, for this low-gain tracking. As predicted by the 

bandwidth and phase delay results of table 1, low-gain behavior (low bandwidth) is required for 

stable performance when both wheel and pedal inputs are used in the large roll attitude change 

task. 

-5

0

5

10

15

20

25

30

35

0 5 10 15 20

Time sec

roll attitude deg

FIGURE 38. LARGE ROLL ATTITUDE CHANGE TASK, WHEEL AND PEDAL INPUTS, 

PERFORMED WITH LOW-GAIN TRACKING BEHAVIOR 

30
-8

-6

-4

-2

0

2

4

6

8

10

0 5 10 15 20

Time sec

aileron and rudder deg

aileron 

FIGURE 39. AILERON AND RUDDER INPUTS FOR TASK OF FIGURE 38 

-40

-30

-20

-10

0

10

20

30

40

50

0 5 10 15 20

Time sec

aileron and rudder rate deg/sec

aileron rate 

FIGURE 40. AILERON AND RUDDER RATES FOR TASK OF FIGURE 38 

A final alternative tracking strategy for the large roll attitude change task can be considered, 

namely, one in which rudder inputs are employed but only in transient fashion. That is, rudder 

inputs are brought in to initiate and arrest roll motions, but are not applied in continuous fashion, 

i.e., closed-loop tracking with rudder is not employed. Figures 41 through 43 summarize 

simulation results for this strategy. The performance shown here is qualitatively superior to any 

of the previous results. 

-10

0

10

20

30

0 5 10 15 20

Time sec

roll attitude deg

FIGURE 41. LARGE ROLL ATTITUDE CHANGE TASK, WHEEL AND PEDAL INPUTS, 

PERFORMED WITH TRANSIENT RUDDER INPUTS 

31
-20

-15

-10

-5

0

5

10

15

0 5 10 15 20

Time sec

aileron and rudder deg

aileron 

FIGURE 42. AILERON AND RUDDER INPUTS FOR TASK OF FIGURE 41 

-60

-40

-20

0

20

40

60

0 5 10 15 20

Time sec

aileron and rudder rate 

deg/sec

aileron rate 

FIGURE 43. AILERON AND RUDDER RATES FOR TASK OF FIGURE 38 

2.7.2 Task 2: Wings-Level Sideslip Captures. 

Figure 44 shows the sideslip response to an attempt at ±5° sideslip captures. The term wings 

level refers to the desired task performance, and not that actually obtained just as was the case in 

the computer simulation of section 1. The subject found this task very difficult, as the roll 

attitude excursions evident in figure 44 indicate. Part of the difficulty may be attributable to the 

nature of the control inceptor, i.e., both wheel and pedal inputs are created with the joystick 

rather than with an actual wheel and pedals. Nonetheless, the subject found the transition from 

+5° to -5° very challenging. The roll attitude excursions are very large in the latter part of the 

maneuver where the -5° sideslip is being attempted. Figures 45 and 46 show the aileron and 

rudder inputs and their rates. Note that significant aileron rate limiting is occurring in the task. 

32
-20

-10

0

10

20

30

0 5 10 15 20 25 30

Time sec

sideslip and roll attitude deg

roll attitude 

FIGURE 44. SIDESLIP AND ROLL ATTITUDE IN SIDESLIP CAPTURE TASK 

-20

-15

-10

-5

0

5

10

15

20

0 5 10 15 20 25 30

Time sec

aileron and rudder deg

aileron

FIGURE 45. AILERON AND RUDDER INPUTS FOR TASK OF FIGURE 44 

-50

-40

-30

-20

-10

0

10

20

30

40

50

0 5 10 15 20 25 30

Time sec

aieron and rudder rate deg/sec

aileron rate 

FIGURE 46. AILERON AND RUDDER RATES FOR TASK OF FIGURE 44 

33
A much more reasonable task can be defined by requiring a wings-level sideslip capture of +5°, 

followed by a return to 0° sideslip and wings level. The results of employing this approach are 

shown in figures 47 through 49. For ease of comparison, figures 47 through 49 have been scaled 

identically to figures 44 through 46. 

-20

-10

0

10

20

30

0 5 10 15 20 25

Time sec

sideslip and roll attitude deg

roll attitude

FIGURE 47. MODIFIED SIDESLIP CAPTURE TASK 

-20

-15

-10

-5

0

5

10

15

20

0 5 10 15 20 25

Time sec

aileron and rudder deg

aileron 

FIGURE 48. AILERON AND RUDDER INPUTS FOR TASK OF FIGURE 47 

-60

-40

-20

0

20

40

60

0 5 10 15 20 25

Time sec

aileron and rudder rate 

deg/sec

aileron rate 

FIGURE 49. AILERON AND RUDDER RATES FOR TASK OF FIGURE 47 

34
An additional experiment was conducted to evaluate the effect of rudder sensitivity. Here, the 

displacement threshold for the pedal was increased from 25% to 50% of full deflection2

 and the 

sensitivity of the pedal was tripled. With these values, the subject could not successfully 

complete any wings-level sideslip captures. Particularly noticeable was the reverse action of the 

rudder inputs, wherein an attempt to capture a +5° sideslip angle with pedal inputs initially 

induced a negative (left wing down) roll response. This reverse action is attributable to the 

nonminimum phase zero in the transfer function s)( δ r

β and was touched upon in section 1 of the 

report. 

2.8 SUMMARY OF SECTION 2.

The research summarized in this section has served as a preliminary and exploratory human-inthe-loop desktop simulation of the vehicle and tasks analyzed in section 1. The simulation effort 

has qualitatively evaluated the analytical results of section 1. The handling qualities and 

potential flight safety problems of high-gain, closed-loop tracking using coordinated aileron and 

rudder inputs that were suggested in section 1 have also appeared in the simulation. The use of 

wings-level sideslip captures as an evaluation maneuver warrants further investigation. 

3. PEDAL FORCE/FEEL SYSTEM COMPARISON. 

3.1 INTRODUCTION. 

The graphs in figures 50 through 52 show three comparisons of three transport aircraft pedal 

force/feel systems and a helicopter. The helicopter was the UH-60A Blackhawk, and the 

transport aircraft were the Airbus A300-600 at 240 kts, the Boeing 767, and the Airbus A300-

B2-B4. The Airbus A300-B2-B4 was the immediate predecessor of the A300-600 and is very 

similar in size, weight, and configuration. The Blackhawk data were obtained from the research 

staff at the Army Aeroflightdynamics Directorate at NASA Ames. The A300-600, A300-B2-B4, 

and B-767 data were obtained as part of a report on the American Airlines Flight 587 accident. 

These plots involve straight-line approximations to the force/displacement characteristics with 

full control movement, with no cable stretch involved. It should be mentioned that, as opposed 

to the A300-600 and UH-60A data, the B-767 and A300-B2-B4 characteristics were obtained 

from tabular data that did not give specific force/feel characteristics within the breakout area. It 

should be noted that, as used here, maximum force is defined as the pedal force that yields a 

maximum pedal displacement without inducing cable stretch in the mechanical system. As 

shown, larger forces can be applied to the force/feel system. Finally, it is important to emphasize 

that the force/feel characteristics for the pedal system of the A300-600 are a function of airspeed. 

This is the reason for associating the particular data for this vehicle with the 240-kt airspeed. 

This is not the case for the UH-60A, A300-B2-B4, and B-767 vehicles, where the force/feel 

pedal characteristics are invariant with airspeed. Like the B-767, the A300-B2-B4 rudder system 

is a ratio system, whereas the A300-600 is a variable stop system. 

 

2

 It is important to recall that this threshold is a software threshold and is not reflected in the force/displacement 

 characteristics of the joystick. 

35
FIGURE 50. PEDAL FORCE/FEEL SYSTEM COMPARISON OF THE A300-600 AT 240 kts 

AND THE UH-60A BLACKHAWK HELICOPTER 

UH-60A 

B-767 

UH-60A 

FIGURE 51. PEDAL FORCE/FEEL SYSTEM COMPARISON OF THE B-767 AND THE 

UH-60A BLACKHAWK HELICOPTER 

36
FIGURE 52. PEDAL FORCE/FEEL SYSTEM COMPARISON OF THE 

AIRBUS A300-B2-B4 AND THE UH-60A BLACKHAWK HELICOPTER 

3.2 THE HELICOPTER COMPARISON. 

The primary reason for choosing a military rotorcraft for a benchmark case was that the vehicles 

can, and do, perform tasks in which precise heading/yaw rate control is obtained with pedal 

inputs. UH-60A flight tests are routinely conducted at NASA Ames that involve maneuvers 

from ADS-33E [17] in which precise heading control was required, e.g., reference 18. These 

maneuvers consist of hovering turns, pirouettes, lateral repositions, and sidesteps in which 

heading performance requirements are spelled out in a quantitative fashion [17]. Of course 

desirable handling qualities and task performance depend on more than just the characteristics of 

the force/feel system. However, acceptable force/feel system characteristics constitute a 

necessary condition for achieving these. Thus, the nature of the pedal force/feel system on the 

UH-60A is more than just a passing interest. 

3.3 COMPARING PEDAL FORCE/FEEL CHARACTERISTICS. 

Figures 50 through 52 clearly indicate significant differences between the pedal force/feel system 

on the A33.00-600 at 240 kts and those for the UH-60A, B-767, and A300-B2-B4. For the 

reason stated in the preceding paragraph, the common system selected for comparison in each 

figure is the UH-60A. The differences are summarized in table 2. In addition to the quantitative 

differences, it is apparent from the graphs that the system for the A300-600 at 240 kts is 

significantly more nonlinear than the UH-60A, B-767, and A300-B2-B4. The differences 

between the A300-600 and A300-B2-B4 force/feel characteristics are particularly noteworthy, 

37
not only for their force/displacement characteristics (compare the solid lines in figures 50 and 

52) but also because these two aircraft are nearly identical in size, weight, and general 

aerodynamic configuration. 

TABLE 2. FORCE/FEEL SYSTEM SUMMARY 

Vehicle 

Ratio of 

Maximum Force to 

Breakout Force 

Maximum 

Force 

(lbf) 

Maximum 

Displacement 

(in.) 

UH-60A 

B-767 

A300-B2-B4 

A300-600*

5.7 

4.71 

5.7 

1.45 

50 

 80 

125 

 32 

 2.8 

 3.6 

 4.0 

 1.3 

*240-kt airspeed 

The graphs invite the following question: Is the linearity of the force/displacement 

characteristics of the control inceptor, in this case the pedals, a useful metric for acceptability of 

these devices? Linearity is meant to be the ability of the pilot to minimize the nonlinear 

characteristics when precise control is involved, such as in tracking or disturbance regulation. 

The primary means by which this linearization occurs is through gain regulation by the pilot. 

3.4 A COMPUTER SIMULATION. 

The system in figure 53 represents a simplified pilot/vehicle system with a nonlinear force/feel 

system. Although the symbol for roll attitude (phi) was identified as the system input and output, 

the symbol was used merely for convenience here. Figure 53 represents any generic tracking 

task in which force/feel characteristics can be compared. 

FIGURE 53. A SIMPLIFIED COMPUTER MODEL OF THE PILOT/VEHICLE SYSTEM 

38
The pilot in figure 53 consists of a gain, a second-order transfer function modeling 

neuromuscular dynamics, and a 0.2-second time delay. This pilot model is considerably simpler 

than the Structural Model of the pilot offered in section 1. The vehicle is a simple integrator 

with an adjustable control system gain. By considering the product of the transfer functions of 

the pilot, force/feel system, and vehicle, it can be shown that the open loop/pilot vehicle system 

obeys the dictates of the Crossover Model of the human pilot [9]. Two force/feel systems will be 

considered. These systems correspond approximately to the systems on the A300-600 and 

A300-B2-B4 (shown in figures 50 and 52) and are referred to here as System A and System B. 

In this simulation, each of the force/feel systems will be capable of the same maximum 

amplitude command to the integrator (vehicle model) through the appropriate adjustment of the 

control system gain shown in figure 53. Figure 54 shows the force/displacement curves for 

systems A and B in the simulation. Note that in this simulation, the absolute magnitude of the 

forces and displacements involved are of no concern, therefore, no units are attached to the axis 

definitions in figure 54. 

FIGURE 54. REPRESENTATION OF THE PEDAL FORCE/FEEL SYSTEMS A AND B IN 

THE COMPUTER SIMULATION OF FIGURE 53 

A 5-second pulsive roll command was provided in the simulation. The units involved here are 

not important, given the simplified nature of the simulation. Figures 55 and 56 show the 

responses when systems A and B are used for the pilot gains Kp = 1, 2, 4, 6. As can be clearly 

seen from figure 55, responses of the high-sensitivity System A is much less predictable and is 

much more sensitive to the particular pilot gain chosen. Oscillations are apparent for all pilot 

gains at or above Kp = 4, whereas no such oscillations appear in figure 56 for System B. The 

inability of either system to respond with Kp = 1 is merely due to the fact that this gain value was 

not large enough to overcome the identical breakout forces in either force/feel system. 

39
FIGURE 55. RESPONSES OF THE COMPUTER SIMULATION SYSTEM OF FIGURE 53 

FOR DIFFERENT PILOT GAINS FOR THE SYSTEM A PEDAL FORCE/FEEL SYSTEM 

FIGURE 56. RESPONSES OF THE COMPUTER SIMULATION SYSTEM OF FIGURE 53, 

FOR DIFFERENT PILOT GAINS FOR SYSTEM B PEDAL FORCE/FEEL SYSTEM 

Figure 57 shows the plot of pedal force versus pedal displacement that occurred in the computer 

simulation, with Kp = 4. Interestingly, System A clearly shows that the pedal force associated 

with maximum pedal displacement was exceeded. The segment described as cable stretch in the 

40
figure denote these force exceedances. Cable stretch means the control cables would likely be 

stretched when forces exceeding those required for maximum control surface deflection are 

employed by the pilot. In an actual mechanical flight control system, some pedal motion would 

be associated with this cable stretch. That is, the segments denoted as cable stretch would not be 

vertical, but would, instead, have large slopes consistent with large forces, resulting in relatively 

small pedal motion. Again, it is worth emphasizing that the maximum attainable control surface 

deflections for both Systems A and B are identical. 

FIGURE 57. PEDAL FORCE VS PEDAL DISPLACEMENT FOR SYSTEMS A AND B IN 

FIGURE 53 FOR Kp = 4 

In comparing the results of the computer simulation, it must be emphasized that the two 

simulations have employed 

• identical vehicle models. 

• identical forms for the pilot models. 

• identical pilot model gains. 

• identical maximum control power. 

• identical command inputs. 

The nature of the vehicle responses were, however, very different. This fact can be attributed 

solely to the different force/feel systems that were modeled. In other words, in terms of a closedloop feedback structure that defines human pilot tracking behavior, there is a price to be paid for 

highly nonlinear force/feel characteristics. Such characteristics can and will produce 

unpredictable and unsatisfactory response characteristics in closed-loop control. 

41
As previously stated, the primary difference between the two force/feel systems that were 

modeled is their linearity, or lack of it. A simple way to quantify this property is shown in 

figure 58. 

A

B 

C

D 

E

F

inceptor displacement

inceptor force

force/feel system 

full-throw characteristics 

FIGURE 58. DEFINING A LINEARITY INDEX 

The heavy lines in figure 58 represent the full-throw force/feel characteristics for the inceptor in 

question. Line DB was drawn from the origin of the force/displacement graph to the point 

farthest from the origin. Based on figure 58, one can propose a nondimensional linearity index 

(LI) as 

)(

)()( 1

Area DEBFD

Area DABD Area DBCD LI + −= (22) 

Thus, if LI = 1 in equation 22, the force/feel system is completely linear. If LI = 0, the system 

could be called completely nonlinear. The simple formula above can easily be extended to 

force/feel graphs defined by curves rather than straight-line segments. Using the metric above, 

the LI’s for the force/feel systems defined as System A and System B compare as follows: 

• System A—LI ≅ 0.14 

• System B—LI ≅ 0.76 

System B is a factor of 5.4 more linear than System A using LI. 

It is useful to note, that for any force/feel system, once a satisfactory breakout force has been 

determined, the selection of the sensitivity of the system (or its reciprocal, the force gradient) can 

be based entirely on the value of LI. 

Obviously one can create an inceptor force/feel system with a high LI value, but it will prove 

unacceptable in use. This might involve inceptor force/feel characteristics with no breakout and 

with a range of applied forces that is far too small (or too large) for the particular human muscle 

group that is intended to create the forces with any accuracy. Thus, any criterion that might be 

developed based on some minimum value of LI should be regarded as a necessary, but not a 

sufficient, condition for the acceptability of the force/feel system. It would appear that small LI 

42
values should almost always be avoided in inceptors that can be used in closed-loop tracking by 

the human pilot. A low LI value almost invariably indicates an overly sensitive force/feel system 

in which the breakout and maximum inceptor forces are not sufficiently separated in magnitude. 

A final variation in calculating the LI should be discussed. This might apply to a force/feel 

design in which inceptor forces beyond that associated with maximum control surface 

deflections are permitted, including allowing proportional pedal motion, but not allowing the 

larger control surface deflection associated with this increased pedal motion. Essentially, beyond 

a certain point, pedal motion would not be reflected in control surface motion. The force/feel 

characteristics for such a system might be represented as in shown in figure 59. 

A

E B 

inceptor force

force/feel system 

full-throw characteristics 

D 

C

F

H 

I

inceptor displacement 

FIGURE 59. ALTERNATE DEFINITION OF LINEARITY INDEX 

In figure 59, the line segments BHIC represent that portion of the force/feel trajectory in which 

inceptor force and position result in no control surface movement. In this case, LI should be 

defined as 

)(

)()( 1

AREA DEBF

AREA DAHD AREA DHID LI + −= (23) 

That is, the normalizing area in the calculation of LI is just that associated with the inceptor 

force/displacement graph that produces control surface motion. Cases involving possible cable 

stretch should be treated as if no cable stretch were possible. 

3.5 SUMMARY OF SECTION 3. 

The research discussed in this section involved a limited comparison of existing pedal force/feel 

systems in three transport aircraft and an operational military helicopter. The helicopter was 

included since its pedal force/feel system has been shown to allow precise heading/yaw control. 

In comparing the pedal force/feel systems for three transport aircraft and a helicopter, the system 

for one transport was shown to be significantly more nonlinear than that for the remaining three 

vehicles. A simple computer simulation of a closed-loop piloting task involving two of the 

force/feel systems differing most in linearity was conducted. It was shown that the highly 

nonlinear force/feel design led to unpredictable vehicle responses and poor performance. A 

43
linearity index was defined to allow a quantitative comparison of the linearity of force/feel 

systems. 

4. SUMMARY OF RESULTS. 

• The handling qualities and flight safety implications of high-gain, closed-loop tracking 

using coordinated aileron and rudder inputs that were suggested in the analysis were 

reflected in the desktop simulation. 

• Transient use of rudder inputs, i.e., not relying on continuous closed-loop tracking using 

this control effector, resulted in improved performance in a large roll attitude task 

compared to when a continuous, closed-loop rudder control was employed. 

• The wings-level sideslip capture task, suggested in the analysis as a useful maneuver to 

investigate handling quality issues, was also supported by the limited desktop simulation 

study. Large rudder system sensitivity led to an inability to complete the sideslip capture 

task in the desktop simulation study and further supported the use of this task in a more 

realistic flight simulation to investigate rudder sensitivity issues. 

• The pedal force/feel systems for a helicopter (UH-60A) and two transport aircraft 

(Boeing 767 and Airbus A300-B2-B4) were compared and found to be significantly more 

linear in their force/displacement graphs, than that of a third comparison transport (A300-

600). The UH-60A was included in the comparison since its pedal force/feel system was 

shown to allow precise yaw/heading control in demanding handling quality-related 

maneuvers. 

• A simple computer simulation modeling a piloted, closed-loop tracking task clearly 

demonstrated that highly nonlinear force/feel systems produce poor response 

predictability and tracking performance compared to more linear force/feel designs. 

• A simple linearity index that can vary between zero and unity in value can be used to 

quantify the linearity of force/feel systems. Force/feel systems with small linearity index 

values will almost invariably be very sensitive, i.e., will exhibit a small difference 

between breakout and maximum forces applied to the inceptor. 

5. CONCLUSIONS. 

An analytical and limited experimental study was conducted to investigate the handling qualities 

and flight safety implications of rudder control strategies and systems in transport aircraft. The 

study focused on the dynamics of a single representative transport aircraft, a dynamic model of 

which is readily available in the literature. The preliminary and simplified nature of this study 

must obviously be borne in mind in interpreting the conclusions that follow. In addition, a 

limited comparison of existing force/feel characteristics of four aircraft was undertaken. Based 

on this study, the following conclusions can be drawn. 

44
• A system survey of possible manual loop closure that could be employed by the pilot, 

using rudder control, led to an examination of two tracking strategies that could occur in 

large roll upsets and deliberate sideslip excursions. These strategies were the coordinated 

use of aileron and rudder inputs and wings-level sideslip captures. 

• Using bandwidth and phase delay measures, the coordinated use of aileron and rudder 

inputs was predicted to result in low obtainable bandwidths in roll attitude control. 

Although no bandwidth boundaries were established for acceptable handling qualities in 

tasks involving coordinated use of aileron and rudder, the relatively small bandwidth 

values suggest poor handling qualities in such tasks in anything, save low-bandwidth 

operations. 

• The analysis suggested that rudder force/feel systems with large sensitivities (or 

equivalently, low-force gradients) could precipitate pilot-induced oscillations when a 

coordinated use of ailerons and rudder was employed. This susceptibility could be 

attributed to large lateral accelerations occurring at the pilot’s station. 

• The analysis suggested that wings-level sideslip captures might serve as a useful pilot-inthe-loop flight simulation task to investigate handling quality issues involving rudder 

control. 

6. REFERENCES. 

1. Dornheim, M.A., “Did Rudder Motions Snap Off A300 Fin?” Aviation Week and Space 

Technology, January 21, 2002, pp. 24-26. 

2. Dornheim, M.A., “Crash Probe Triggers Rudder Design Scrutiny,” Aviation Week and 

Space Technology, April 1, 2002, pp. 44-46. 

3. Dornheim, M.A., “Flight 587 Probe Shows Tails Have Been Overloaded Before,” 

Aviation Week and Space Technology, November 25, 2002, pp. 44, 49-51.

4. Fiorino, Frances, “Upset Events, Wake Vortices at Center of Flight 587 Probe,” Aviation 

Week and Space Technology, April 22, 2002, p. 39. 

5. McRuer, D., Ashkenas, I., and Graham, D., Aircraft Dynamics and Automatic Control,

Princeton University Press, Princeton, NJ, 1973, chapter 8. 

6. Stapleford, R.L., McRuer, D.T., and Magdaleno, R.E., “Pilot Describing Function 

Measurements in a Multiloop Task,” IEEE Transactions on Human Factors in 

Electronics, Vol. HFE-8, No. 2, June 1967, pp. 113-124. 

7. Mitchell, D.G., Hoh, R.H., Aponso, B.L., and Klyde, D.H., “Proposed Incorporation of 

Mission-Oriented Flying Qualities into MIL-STD-1797A,” WL-TR-94-3162, Wright 

Laboratory, Wright Patterson AFB, OH, October 1994. 

45
8. Preston, J.D., et al., “Unified Pilot-Induced Oscillation Theory, Vol. II, Pilot-Induced 

Oscillation Criteria Applied to Several McDonnell Douglas Aircraft,” WL-TF-96-3029, 

Wright Laboratory, Wright-Patterson AFB, OH, December 1995. 

9. Hess, R.A., “Feedback Control Models—Manual Control and Tracking,” Handbook of 

Human Factors and Ergonomics, G. Salvendy, ed., Wiley, New York, 1997, chapter 38. 

10. Hess, R.A., “Unified Theory for Aircraft Handling Qualities and Adverse Aircraft-Pilot 

Coupling,” Journal of Guidance, Control, and Dynamics, Vol. 20, No. 6, NovemberDecember 1997, pp. 1141-1148. 

11. Hess, R. A., “An Inquiry Into Whether a Pilot-Induced Oscillation was a Factor in the 

Crash of American Airlines Flight 587,” a report submitted to the National 

Transportation Safety Board, January 2003. 

12. Graham, D. and McRuer, D., Analysis of Nonlinear Control Systems, Dover, New York, 

1961, p. 228. 

13. Gibson, J.C. and Hess, R.A., “Stick and Feel System Design,” AGARDograph 332, 

March 1997. 

14. Anon., “STEADES—Safety Trend Evaluation, Analysis & Data Exchange System,” first 

interim report, December 20, 2002, Transport Category Airplane Rudder and Lateral 

Control Events, International Air Transport Association (IATA). 

15. Anon., Aviation Safety and Pilot Control—Understanding and Preventing Unfavorable 

Pilot-Vehicle Interactions, National Academy Press, Washington, DC, 1997, chapter 5. 

16. Smith, R.H., “Quick Start Manual for HPESIM,” HPE-MAN-QSSIM-0.1.01, High Plains 

Engineering, 1999. 

17. Anon., “Aeronautical Design Standard, Performance Specification Handling Qualities 

Requirements for Military Rotorcraft,” ADS-33E-PRF, U.S. Army Aviation and Missile 

Command, March 2000. 

18. Heffley, R.K., Hess, R.A., and Zeyada, Y., “Computer Modeling and Simulation for 

Helicopter Pilotage Task Analysis,” U.S. Army Aviation and Missile Command, 

Research, Development & Engineering Center, USAAMCOM TR 02-D16, June 2002. 

46