- 

NASA Contractor Report 3342 

- - 

NASA 

CR 

3342 

C-1 

Pilot-Aircraft System 

Response to Wind Shear 

Barry S. Turkel and Walter Frost 

CONTRACT NAS8-33458 

NOVEMBER 1980 

i 

.1 

,i 

ib 

NASA Contractor Report 3342 

Pilot-Aircraft System 

Response to Wind Shear 

Barry S. Turkel and Walter Frost 

F WG Associutes, Iuc. 

Tzdhhomn, Terzuessee 

Prepared for 

Marshall Space Flight Center 

under Contract NAS8-33458 

National Aeronautics 

and Space Administration 

Scientific and Technical 

Information Branch 

1980 
ACKNOWLEDGMENT 

The authors are grateful to A. Richard Tobiason, John H. Enders, 

and Solomon Weiss for the support of NASA under Contract NAS8-33458. 

Technical inputs provided by Mr. Dennis W. Camp, NASA Marshall Space 

Flight Center, Atmospheric Sciences Division, Huntsville, Alabama, and 

Dr. John McCarthy, University of Oklahoma, Norman, Oklahoma, are also 

gratefully acknowledged. 

TABLE OF CONTENTS 

SECTION PAGE 

1.0 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . 1 

2.0 WIND SHEAR STUDIES . . . . . . . . . . . . . . . . . . . . . . 3 

3.0 THE PHUGOID OSCILLATION . . . . . . . . . . . . . . . . . . . . 6 

4.0 THE PILOT MODELS . . . . . . . . . . . . . . . . . . . . . . . 8 

5.0 RESULTS AND DISCUSSION . . . . . . . . . . . . . . . . . . . . 13 

5.1 Simulated Queen Air Flight Through Queen Air Flight 17/ 

Run 2 Wind Field . . . . . . . . . . . . . . . . . . . . . 13 

5.2 Simulated Boeing 727 Flight Through Queen Air Flight 17/ 

Run 2 Wind Field . . . . . . . . . . . . . . . . . . . . . 31 

5.3 Simulated B727 Flight Through Sinusoidal 6 m/s Amplitude 

Wave Near Phugoid Frequency . . . . . . . . . . . . . . . 36 

5.4 Simulated B727 Flight Through Sinusoidal 14 m/s Amplitude 

Wave Near Phugoid Frequency . . . . . . . . . . . . . . . 49 

5.5 Simulated B727 Flight Through Full Sinusoidal 10 m/s 

Amplitude Wave Near Phugoid Frequency . . . . . . . . . . 69 

6.0 CONCLUSIONS . . . . . . . . . . . . . . . . . . . . . . . . . . 76 

7.0 REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . 78 

APPENDIX A--Derivation of Thrust and Elevator Angle Control 

Functions (FT,6E) . . . . . . . . . . . . . . . . . . . 80 

APPENDIX B--Characteristics of Aircraft Used in Numerical Flight 

Simulations . . . . . . . . . . . . . . . . . . . . . . 86 

iii 
LIST OF ILLUSTRATIONS 

FIGURE TITLE PAGE 

1 Eulerian Glide Slope Wind Profile Measured by Doppler Radar 

During Queen Air Flight 17/Run 2 . . . . . . . . . . . . . . 14 

2 Simulated Fixed-Stick Trajectory of a Queen Air Flown 

Through Queen Air Flight l-//Run 2 Wind Profile . . . . . . . 16 

3 Simulated Trajectory of a Queen Air Under Autopilot Control 

Flown Through Queen Air Flight 17/Run 2 Wind Profile . . . . 17 

4 Autopilot Elevator Inputs to Queen Air in Flight Through 

Queen Air Flight 17/Run 2 Wind Profile . . . . . . . . . . . 18 

5 Autopilot Thrust Inputs to Queen Air in Flight Through Queen 

Air Flight 17/Run 2 Wind Profile . . . . . . . . . . . . . . 19 

6 Elevator Angle Sign Conventions . . . . . . . . . . . . . . 20 

7 Simulated Trajectory of a Queen Air Controlled by a 70 

Percent Performance Rated Pilot Flown Through Queen Air 

Flight 17/ Run 2 Wind Profile . . . . . . . . . . . . . . . 22 

8 Elevator Inputs by 70 Percent Rated Pilot to Queen Air Flown 

Through Queen Air Flight l-//Run 2 Wind Profile . . . . . . . 23 

9 Thrust Inputs by 70 Percent Rated Pilot to Queen Air Flown 

Through Queen Air Flight 17/Run 2 Wind Profile . . . . . . . 24 

10 Simulated Trajectory of a Queen Air Controlled by an 8 

Percent Performance Rated Pilot Flown Through Queen Air 

Flight 17/Run 2 Wind Profile . . . . . . . . . . . . . . . . 25 

11 Elevator Inputs by 8 Percent Rated Pilot to Queen Air Flown 

Through Queen Air Flight 17/Run 2 Wind Profile . . . . . . . 26 

12 Thrust Inputs by 8 Percent Rated Pilot to Queen Air Flown 

Through Queen Air Flight 17/Run 2 Wind Profile . . . . . . . 27 

13 Simulated Trajectory of a Queen Air Controlled by a 5.5 

Percent Performance Rated Pilot Flown Through Queen Air 

Flight 17/Run 2 Wind Profile . . . . . . . . . . . . . . . . 28 

14 Elevator Inputs by 5.5 Percent Rated Pilot to Queen Air 

Flown Through Queen Air Flight 17/Run 2 Wind Profile . . . . 29 

iv 
FIGURE TITLE PAGE 

15 Thrust Inputs by 5.5 Percent Rated Pilot to Queen Air Flown 

Through Queen Air Flight 17/Run 2 Wind Profile . . . . . . . 30 

16 Simulated Fixed-Stick Trajectory of a B727 Flown Through 

Queen Air Flight 17/Run 2 Wind Profile . . . . . . . . . . . .32 

17 Simulated Trajectory of a B727 Under Autopilot Control Flown 

Through Queen Air Flight 17/Run 2 Wind Profile . . . . . . . 34 

18 Autopilot Elevator Inputs to B727 in Flight Through Queen 

Air Flight 17/Run 2 Wind Profile . . . . . . . . . . . . . . 35 

19 Autopilot Thrust Inputs to B727 in Flight Through Queen Air 

Flight 17/Run 2 Wind Profile . . . . . . . . . . . . . . . . 37 

20 Simulated Trajectory of a 8727 Controlled by a 70 Percent 

Performance Rated Pilot Flown Through Queen Air Flight 17/ 

Run 2 Wind Profile . . . . . . . . . . . . . . . . . . . . . 38 

21 Elevator Inputs by 70 Percent Rated Pilot to B727 Flown 

Through Queen Air Flight 17/Run 2 Wind Profile . . . . . . . 39 

22 Thrust Inputs by 70 Percent Rated Pilot to B727 Flown 

Through Queen Air Flight 17/Run 2 Wind Profile . . . . . . . 40 

23 Simulated Trajectory of a B727 Controlled by a 5.5 Percent 

Performance Rated Pilot Flown Through Queen Air Flight 17/ 

Run 2 Wind Profile . . . . . . . . . . . . . . . . . . . . . 41 

24 Elevator Inputs by 5.5 Percent Rated Pilot to B727 Flown 

Through Queen Air Flight 17/Run 2 Wind Profile . . . . . . . 42 

25 Thrust Inputs by 5.5 Percent Rated Pilot to 8727 Flown 

Through Queen Air Flight 17/Run 2 Wind Profile . . . . . . . 43 

26 Simulated Fixed-Stick Trajectory of a B727 Flown Through a 

6 m/s Amplitude Sinusoidal Wave at the Phugoid Frequency . . 45 

27 Simulated Trajectory of a B727 Under Autopilot Control 

Flown Through a 6 m/s Amplitude Phugoidal Sine Wave . . . . 46 

28 Autopilot Elevator Inputs to B727 in Flight Through a 6 m/s 

Amplitude Phugoidal Sine Wave . . . . . . . . . . . . . . . 47 

29 Autopilot Thrust Inputs to B727 in Flight Through a 6 m/s 

Amplitude Phugoidal Sine-Wave . . . . . . . . . . . . . . . 48 

30 Simulated Trajectory of a B727 Controlled by a 25 Percent 

Rated Pilot Flown Through a 6 m/s Amplitude Phugoidal Sine 

Wave............................ 50 

V 
FIGURE TITLE PAGE 

31 

32 

33 

34 

35 

36 

37 

38 

39 

40 

41 

42 

43 

44 

45 

46 

Elevator Inputs by 25 Percent Rated Pilot to B727 Flown 

Through a 6 m/s Amplitude Phugoidal Sine Wave . . . . . . . 

Simulated Trajectory of a B727 Controlled by a 5.5 Percent 

Rated Pilot Flown Through a 6 m/s Amplitude Phugoidal Sine 

Wave............................ 

Elevator Inputs by 5.5 Percent Rated Pilot to B727 Flown 

Through a 6 m/s Amplitude Phugoidal Sine Wave . . . . . . . 

Thrust Inputs by 5.5 Percent Rated Pilot to B727 Flown 

Through a 6 m/s Amplitude Phugoidal Sine Wave . . . . . . . 

Simulated Trajectory of a B727 Under Autopilot Control Flown 

Through a 14 m/s Amplitude Phugoidal Sine Wave . . . . . . . 

Autopilot Thrust Inputs to B727 in Flight Through a 14 m/s 

Amplitude Phugoidal Sine Wave . . . . . . . . . . . . . . . 

Autopilot Elevator Inputs to B727 in Flight Through a 14 m/s 

Amplitude Phugoidal Sine Wave . . . . . . . . . . . . . . . 

Simulated Trajectory of a B727 Controlled by a 50 Percent 

Rated Pilot Flown Through a 14 m/s Amplitude Phugoidal Sine 

Wave............................ 

Thrust Inputs by a 50 Percent Rated Pilot to B727 Flown 

Through a 14 m/s Amplitude Phugoidal Sine Wave . . . . . . . 

Elevator Inputs by a 50 Percent Rated Pilot to B727 Flown 

Through a 14 m/s Amplitude Phugoidal Sine Wave . . . . . . . 

Simulated Trajectory of a B727 Controlled by a 25 Percent 

Rated Pilot Flown Through a 14 m/s Amplitude Phugoidal Sine 

Wave............................ 

Elevator Inputs by a 25 Percent Rated Pilot to B727 Flown 

Through a 14 m/s Amplitude Phugoidal Sine Wave . . . . . . . 

Thrust Inputs by a 25 Percent Rated Pilot to B727 Flown 

Through a 14 m/s Amplitude Phugoidal Sine Wave . . . . . . . 

Simulated Trajectory of a B727 Controlled by a 5 Percent 

Rated Pilot Flown Through a 14 m/s Amplitude Phugoidal Sine 

Wave............................ 

Elevator Inputs by a 5 Percent Rated Pilot to B727 Flown 

Through a 14 m/s Amplitude Phugoidal Sine Wave . . . . . . . 

Thrust Inputs by a 5 Percent Rated Pilot to B727 Flown 

Through a 14 m/s Amplitude Phugoidal Sine Wave . . . . . . . 

vi 

51 

52 

53 

54 

56 

57 

58 

59 

60 

61 

62 

63 

64 

66 

67 

68 
FIGURE TITLE PAGE 

47 Simulated Trajectory of an Autopilot-Controlled B727 

Through 10 m/s Amplitude Phugoidal Sine Wave . . . . . . . 70 

48 Simulated Trajectory of a B727 Controlled by Pilot A 

Flown Through 10 m/s Amplitude Phugoidal Sine Wave . . . . 71 

49 Elevator Inputs by Pilot A to B727 Flown Through 10 m/s 

Amplitude Phugoidal Sine Wave . . . . . . . . . . . . . . . 72 

50 Thrust Inputs by Pilot A to B727 Flown Through 10 m/s 

Amplitude Phugoidal Sine Wave . . . . . . . . . . . . . . . 73 

51 Simulated Trajectory of a B727 Controlled by Pilot F 

Flown Through 10 m/s Amplitude Phugoidal Sine Wave . . . . 75 

vii 
NOMENCLATURE 

cD 

cDo 

cD 

a 

cDa2 

cL 

cLo 

cL 

q 

cL 

a 

cL* 

a 

CL6E 

cm 

c" 0 

cm 

crnq 

a 

C me 

a 

cm6 E 

c 

D 

FT 

HA 

I 

YY 

L 

LT 

Drag coefficient, D/(l/Z)pViS (dimensionless) 

Drag parameter (zero angle of attack) (dimensionless) 

Drag derivative (rad-') 

Drag derivative (rad-*) 

Lift coefficient L/(l/Z)PViS (dimensionless) 

Lift parameter (zero angle of attack) (dimensionless) 

Lift derivative (rad-') 

Lift derivative (rad-') 

Lift derivative (rad-') 

Lift derivative (deg-') 

Pitching-moment coefficient, M/(l/Z)PVzSc (dimensionless) 

Pitching-moment parameter (zero angle of attack) 

(dimensionless) 

Pitching-moment derivative (rad-') 

Pitching-moment derivative (rad-') 

Pitching-moment derivative (rad-') 

Pitching-moment derivative (deg-') 

Wing mean aerodynamic chord (m) 

Magnitude of aerodynamic drag (N) 

Magnitude of thrust (N) 

Reference height (m) 

Aircraft moment of inert 

Magnitude of aerodynamic 

ia around y-axis (kg-m' > 

lift force (N) 

Moment arm of thrust vector (m) 

viii 
m Aircraft weight (N) 

M Pitching moment (kg m*/s*) 

q Pitch angular velocity (rad/sec) 

V Magnitude of aircraft velocity with respect to the ground 

(m/s 1 

'a Magnitude of airspeed (m/s) 

'a Magnitude of initial airspeed (m/s) 

0 

X Horizontal coordinate (m) 

Z Vertical coordinate (m) 

Greek Symbols 

a 

a’ 

Y 

6 

6E 

5 

*h 

A= h 

E 

% 

P 

Other 

(7 

( Jo 

Angle of attack between ground velocity vector and aircraft 

fuselage reference line (FRL) (rad) 

Angle of attack between airspeed vector and aircraft FRL (rad) 

Flight path angle (rad) 

Angle between airspeed vector and ground speed vector (rad) 

Elevator deflection angle (deg) 

Angle between thrust vector and aircraft FRL 

Glide slope positional error (- aircraft above, + aircraft 

below) (m) 

Aircraft descent rate error (- slower, + faster) (m/s) 

Glide slope error angle (rad) 

Pitch control variable (m rad/sec*) 

Air density (g/m3) 

Time derivative 

Initial value 

ix 
1 .O INTRODUCTION 

Encounter with wind shear during approach and takeoff has gained 

recognition within the past few years as a major hazard to flight safety. 

Several accidents and near accidents have now been officially attributed 

to wind shear. There were probably many more prior to instruments and 

basic knowledge of the atmosphere which made identification of wind 

shear as a contributing factor possible. These accidents and near 

accidents have been mistakenly resolved as pilot error. The most notable 

accident with wind shear as a major cause involved the Eastern 66, 

Boeing 727, which crashed on approach in a thunderstorm wind environment 

at John F. Kennedy International Airport on June 24, 1975, resulting in 

113 fatalities Cl].* A more recent incident took place on August 22, 

1979, in Atlanta as Eastern 693, also a Boeing 727, was forced to abort 

approach and initiate a go-around after a relatively severe loss of 

altitude and airspeed [2]. 

Wind shear is a spatial or temporal gradient in wind speed and/or 

direction. It has many sources in the atmosphere. A common but 

generally benign example is the logarithmic wind profile associated with 

boundary layer flow over homogeneous terrain. A vertical shear exists 

in the longitudinal wind-- the wind velocity has some magnitude wx at 

height h which decreases logarithmically to zero at the ground. Other 

sources of shears are cold and warm fronts, thunderstorms, and perturbed 

flows around obstacles. 

To illustrate the effects of wind shear on an aircraft, two simple 

examples are examined. Since an airplane's flight depends on horizontal 

airflow (relative airspeed) over its wings to generate lift, any changes 

in the relative airspeed will alter the balance of forces that keep the 

aircraft in straight, unaccelerated, level flight. Therefore, a tail 

wind shearing to a head wind will increase the relative airflow over the 

*Numbers in brackets correspond to similarly numbered references in 

the List of References. 
wings, increasing the lift force, and causing the aircraft to ride high 

on the glide slope. In the case 0f.a head wind shearing to a tail wind, 

the relative airflow over the wings will decrease, the lift will decrease, 

and the aircraft will fall below the glide slope. This is a particularly 

hazardous condition since reaction time and engine spool-up time become 

relatively small as the plane approaches the runway threshold; premature 

ground impact may result. Escape from this hazardous situation depends 

on the severity of the wind conditions, the physical and performance 

characteristics of the aircraft, and the skill, experience, and reaction 

time of the pilot. If a trained pilot recognizes his decrease in airspeed and deviation below the glide slope, he can apply the necessary 

thrust and elevator controls to perform a go-around or land the plane 

safely. 

2 
2.0 WIND SHEAR STUDIES 

Previous computer simulations of aircraft flight through wind shear 

have suggested that the phugoidal oscillations of commercial jetliners 

are excited when the wind spectral frequency approaches the phugoidal 

frequency. 

McCarthy, Blick, and Bensch [3] used aircraft measured thunderstorm 

environment winds as input to their numerical aircraft flight simulation 

model. They used a two-dimensional linear system of aircraft motion 

equations to perform fixed-stick (constant thrust setting and elevator 

deflection angle) flight simulations with an aircraft characteristic of 

a Boeing 727. The results of the simulations show that horizontal gusts 

at approximately the phugoidal frequency are responsible for most of 

the flight path deviation and airspeed oscillation. It was also noted 

that flight simulations through a wave-form longitudinal wind profile 

representative of the winds encountered by Eastern 66 [I] resulted in 

poor approaches. 

Frost and Crosby [4] numerically simulated fixed-stick and automatic controlled flight of aircraft characteristic of a DC 8, Boeing 

747, DHC-6 Otter, and STOL (short takeoff and landing) through thunderstorm wind fields. They used a nonlinear two-dimensional three-degreesof-freedom model. Two-dimensional thunderstorm wind field data were 

provided in tabulated format with a computer lookup routine. The 

longitudinal and vertical wind component data used in the study were 

measured with an instrumented 500 m tower at the National Severe Storms 

Laboratory at Norman, Oklahoma. Time history measurements were converted 

to a horizontal spatial coordinate grid using Taylor'; hypothesis for 

use in the computer lookup routine. Frost and Crosby's simulations 

revealed highly amplified phugoidal oscillations along flight trajectories 

through these storms. 

Extensive work was done in simulated automatic controlled flight 

through boundary layer shear, perturbed wind fields around buildings, 

3 
and thunderstorm gust fronts by Frost and Reddy [5]. A feedback control 

loop was developed which passes airspeed error, horizontal and vertical 

acceleration, and pitch command signals through variable gains to drive 

the throttle and elevator controls. A detailed discussion of this automatic control system appears in Appendix A. 

The aforementioned work has established a relationship between aircraft response to longitudinal thunderstorm gusts; however, the fact 

remains that influence of a human pilot has not been included. The 

fixed-stick method is not likely to be flown in a thunderstorm environment,whereas the automatic control system is too perfect. To achieve a 

more realistic simulation, this study examines the response of the 

pilot-aircraft system to hazardous wind environments. 

The work of Frost and Reddy [5] is expanded to include a human 

pilot as controller. Computer-simulated flight through variable winds 

measured along typical flight paths is carried out. The wind data were 

measured along the glide slope with a Doppler radar. Simultaneously, a 

Queen Air aircraft made controlled approaches along the glide slope. 

The measurements were carried out as part of the SESAME '79 program, 

April and June, 1979, in Oklahoma. 

The overall objective of the flight experiment program is to test 

the feasibility of a Doppler radar wind shear warning and detection 

system. The operational system concept is to aim a 10.2 cm pulsed 

Doppler radar along the glide slope at commercial airports and thus 

supply air traffic control personnel with real-time wind information on 

the approach path. The Doppler radar system is capable of making a 

complete scan along the glide slope from 3.5 km (minimum range) to 22.5 

km (maximum range) and obtain almost instantaneous wind information in 

150 m steps. Such a system would be extremely beneficial in detecting 

hazardous shear conditions for any aircraft landing on a monitored 

approach path. Air traffic control personnel can monitor worsening wind 

shear conditions between takeoffs and landings of various aircraft. 

Also, a real-time spectral analysis can be performed on the Doppler wind 

data to determine if phugoidal frequency shear waves particularly hazardous to a given aircraft type exist. The phugoid oscillation is discussed 

in Section 3.0. 

4 
In order to compare the effects of the Doppler-detected wind fields 

on aircraft other than a small commuter-type Queen Air aircraft, an 

aircraft having characteristics of a Boeing 727 was also flown through 

one of the wind fields. In addition, the aircraft was flown through 

sinusoidal longitudinal wind waves having a frequency near the phugoid 

frequency of the aircraft. The wind field was constructed to have a 

head wind shearing to a tail wind,thus giving an effect similar to 

flying directly through the downburst region of a thunderstorm cell. 

5 
3.0 THE PHUGOID OSCILLATION 

An aircraft responds to a longitudinal disturbance with oscillations in speed, vertical height, and pitch rate. The oscillatory motion 

can be broken down into two components: the short-period oscillation 

and the long-period phugoid oscillation. The short-period oscillation 

is heavily damped, and its associated pitch rate changes "wash out" 

shortly after the disturbance is encountered. The aircraft is then left 

with a long-period,low-damped phugoid oscillation which produces slow 

changes of speed and height. This is usually not a serious problem for 

a pilot to control since the speed and height changes are not severe and 

the time period is long. It is insidious, however, when the pilot's 

attention is directed to other factors. Moreover, encounter with a 

large wavelength longitudinal disturbance (horizontal wind shear) may 

exaggerate the phugoid mode, causing a control problem for the pilot. 

Analysis of the phugoid oscillation assumes small pitch-rates, 

constant angle of attack, negligible drag effects, and a constant sum of 

potential and kinetic energy. A simple example involves an aircraft 

encountering a head wind gust. The initial response is an increase in 

lift, a pitch-up of the nose, and an increase in height; kinetic energy 

is converted to potential energy, causing the airspeed to drop and the 

nose to pitch down. Potential energy is converted back to kinetic 

energy as the plane begins to descend, picking up airspeed until it once 

more begins to climb. The kinetic energy of descent is converted to 

potential energy of height. This simple harmonic motion will damp out 

after some time. 

From Dickinson 1-61 the degree of phugoid damping for a particular 

aircraft depends on the aerodynamic derivative xu, which is the rate of 

change of force in the x-axis (direction of flight) due to changes in 

forward speed. This is related to the drag characteristics of the 

aircraft. Also known as the speed damping derivative, xu is usually 

negative and proportional to -CD where CD is the drag 

6 
coefficient. If the aircraft is disturbed in such a way as to increase 

its forward speed, lift will increase as well as drag, which will eventually reduce the speed back to its initial value. 

From McCarthy, Blick, and Bensch [3] the exponential phugoid damping 

period, or the time for the oscillation to decay to l/e of its initial 

amplitude, is given by T = Va,/g(CL,/CD,) where Va, is equilibrium 

airspeed (m/s), g is the gravitational acceleration (m/s*), and CL, and 

CD0 are the lift and drag coefficients for the particular 

aircraft. Thus, the high approach speed (Va,) and high lift-to-drag 

ratios of commercial jet transport aircraft contribute to a large exponential phugoid damping period. This simply means that the phugoid 

oscillation of a jet transport will not damp out as quickly as that of a 

smaller aircraft. This adds significance to the observation that smaller 

aircraft have escaped longitudinal gusts that later caused large commercial aircraft to crash. 

7 
._- ..-.. . -.--. --.--_----. 

4.0 THE PILOT MODEL 

The pilot models used in the computer-simulated flights are 

described in this section. 

For the preliminary study, a parametric study of pilot performance 

rating was carried out. The pilot performance rating model was incorporated into the control loop of Frost and Reddy [5] in the following 

manner. The automatic feedback control system as described in Appendix 

A evaluates the difference between the actual and desired state of the 

simulated aircraft on approach. The system monitors airspeed, horizontal 

ground speed, vertical velocity, flight path angle deviation and displacement from the glide slope and processes these parameters through variable 

gains to determine the necessary signals to the throttle and elevator 

servos. The servos adjust thrust and elevator angle to bring the aircraft 

back to the desired state. A pilot, who is assumed to be monitoring 

these same parameters at the same rate as the autopilot, would not be 

able to respond as fast as the autopilot to the information he receives. 

Thus, the pilot would not move the servos to correct the plane's deviations as efficiently as the autopilot. In effect, the pilot is always 

lagging the autopilot. Thus, the pilot's control signal inputs are 

reduced by a performance rating or "perfection percentage" gain where 

Initial 

Conditions 

1 

Thrust and 

Auto-Control ) Pilot Lag I__t Elevator e 

Aircraft 

Dynamics m 

Controls Position 

A 

. 

Feedback Va, 2/V, 

i/v, eCkJhJ$ 

8 
0 percent corresponds to zero inputs (fixed-stick) and 100 percent 

corresponds to "perfect" autopilot control. This is accomplished in the 

program by use of the difference equation 

where y, and y,,, are the control signal outputs for the present and 

previous time steps, respectively, x, is the input control signal for 

the present time step, and k is the "perfection percentage" gain. The 

pilot constantly attempts to return the aircraft to the des-ired state, 

but this occurs at a slower response rate than the "perfect" automatic 

control system. 

#Classifying pilot response by means of a performance rating encompasses the many intangibles encountered in pilot modeling which are too 

complex to simulate. These intangibles include pilot personality, 

training, knowledge and warning of the encountered wind shear, as well 

as the element of surprise. Hence, a pilot with a low performance 

rating (for example, 0.03, which corresponds to a minimal control input) 

may be classified as poorly trained, slow-to-react, unknowledgeable, or 

uninformed of the imminent wind shear. Clearly, more work needs to be 

done on pilot modeling specifically to determine pilot response to the 

wind shear environment. However for purposes of this study, the proposed 

pilot's "perfection percentage" gain gives useful results. 

In addition, two runs were carried out using human pilot transfer 

function data taken during simulator experiments by Adams and Bergeron 

[7]. They tested six pilots (ages 30 through 47) and two test engineers 

in a flight simulator equipped with an oscilloscope and control stick. 

Pilot workload was created by filtering computer-generated noise to 

obtain a simulated flight disturbance. .While viewing the disturbances 

on the oscilloscope, the subjects were instructed.to keep the oscilloscope signal aligned with a marked reference point by moving the control 

stick. Adams and Bergeron measured the subjects' static gains, lead and 

lag time constants throughout the runs,examining variations between the 

subjects for given controlled dynamics (degree of vehicle controllability). 

The general form of the human pilot transfer function is 

9 
where 

6 = analog pilot output produced by moving the control stick (volts) 

D= input disturbance sensed visually by the pilot (volts) 

T = lag time constant (see-') 

k,/T = static gain (volts/volts), k, units are volts/(volts)(sec) 

k2/-c = lead time constant (set), k2 is dimensionless 

S = Laplace operator (set-') 

This transfer function is useful for describing a pilot in a linear 

single-axis attitude control system in.a compensatory tracking task 

( i.e., glide slope tracking) and provides a representative model for 

analysis purposes. 

Throughout the runs Adams and Bergeron [7] noted that k,, k2, and T 

stabilized within 30 seconds to near constant values for the remainder 

of the run. Thus, k,, k2, and T form a constant gains transfer function 

representative of a given pilot for a given run with specified controlled 

dynamics. A sample transfer function for pilot F (Table 1), assuming 

control dynamics = 1 (easily maneuverable and controllable aircraft), 

with k, = 3 volts/(volts)(sec), k2 = 1, and 'C = 4 see-' is 

The complete pilot-aircraft system response to a disturbance (in 

this case wind shear) is obtained by multiplying the pilot transfer 

function by the controlled system transfer function. For example, from 

Adams and Bergeron [7], multiplying the pilot transfer function 

and control system dynamics 

e 1' -= 

6 

10 
TABLE 1. Transfer Function Data of the Eight Pilots Investigated in 

Reference [7]. 

Controlled 

System 

Dynamics 

_ -.i 

1 

1 

1 

1 

1 

1 

1 

1 

-- _ ~. = ..- _-- 

Pilot 

Identifier 

kl volts 

(volts)(sec) 

8.0 8.0 0.0 

6.5 7.0 0.0 

9.0 11.0 0.0 

5.0 5.5 0.5 

9.0 10.0 0.0 

3.0 4.0 1.0 

5.5 6.0 0.5 

3.0 3.0 1.0 

‘T 

set-1 

k2 

(dimensionless) 

where 8 is the aircraft system output response (volts) to pilot output 

which is input to the system yields 

The general form of the pilot-aircraft transfer function 

can be rewritten as 

A transfer function of this form multiplied by a step response, l/s, can 

be z-transformed into a difference equation of the form 

yn = (C~)Y,-, + (C*)Y,-~ + (Dlh,-, + 0*)x,-, 

(Neuman and Foster [8]) where y, is the output signal, ynW2 and y,-, are 

the signal outputs of the last two previous time steps, respectively, 

11 
and x, 2 and x, , are the signal inputs of the last two previous time 

steps, respectively. The constants for this difference equation (Neuman 

and Foster [8]) are 

C* = -e-2Tt 

Dl = 5 + ,-rt kl 

-c (k,k2 - kT)t - T I 

and 

D2 = 

kl 7 (eDTt - 1) - (klk2 - k,)t eeTt 

1 

The response time t is set equal to 0.01 corresponding to the sampling 

interval of the computer program used in the flight simulations. 

12 
5.0 RESULTS AND DISCUSSION 

Doppler radar-detected glide slope longitudinal wind data for the 

twelve Queen Air SESAME approaches supplied by McCarthy and Elmore of 

the University of Oklahoma consisted of three sets of data for each 

flight. Two sets of data were Eulerian or "frozen" glide slope wind 

scans taken by the Doppler radar before and after the approach of the 

Queen Air down the glide slope. The third set of data was obtained 

with the ground-based Doppler radar sampling the wind just ahead of the 

aircraft as it flew down the glide slope. 

In the following simulations, only the Eulerian data sets are used. 

The raw Eulerian Doppler wind data were recorded in terms of slant range 

from the radar location and were then converted by McCarthy and Elmore 

to time history data by Taylor's hypothesis using the average approach 

speed of the Queen Air. Thus, 24 cases of time history wind data are 

available as input to the nonlinear flight simulation program. These 

cases were initially run in the fixed-stick mode to determine which 

cases, if any, had any significant wind shear to cause airspeed and 

flight path deviations. Generally, the wind shear in most cases was not 

severe enough to cause major deviations, but two cases revealed 

phugoidal-type oscillations in the aircraft's approach trajectory. One 

of these cases is selected for detailed examinations where the original 

fixed-stick trajectory is compared with autopilot- and pilot-controlled 

trajectories. In addition, the simulated flights of a B727 flown 

through sinusoidal phugoid frequency longitudinal wind waves of varying 

amplitude are presented. 

5.1 Simulated Queen __-- Air Flight Through Queen Air Flight 17/Run 2 Wind 

Field 

.____ 

The longitudinal winds measured during the SESAME Queen Air Flight 

17/Run 2 are used as input to the flight simulation program. Figure 1 

shows the head winds encountered during the flight as a function of 

13 
s 

*-* 

a I I I I I 1 

0.00 20.00 40.00 60.00 50.00 100.00 120.00 

X/HA 

Figure 1 Eulerian glide slope wind prof 

during Queen Air flight 17/run 

ile measured by Dopp ler radar 

2. 
horizontal distance traveled. The initial increase and subsequent drop 

in head wind appears as a wave-form similar to those observed by 

McCarthy, Blick, and Bensch [3] and Frost and Crosby [4] which cause 

airspeed and altitude deviations during approach with fixed stick. 

Figure 2 shows the simulated fixed-stick trajectory of an aircraft 

having the characteristics of a Queen Air with the phugoidal-type oscillations clearly observable. This is by no means a dangerous approach 

,since the maximum deviation from the glide slope, occurring primarily at 

the beginning of the approach, is approximately 17 m. The wavelength of 

the initial wave in the aircraft trajectory measures approximately 2,300 

m (peak to peak), with the remaining waves approximately 1,400 m. The 

phugoid period of the Queen Air (approach speed Va, = 56 m/s) as determined by T = aTVa,/g from Etkin [9] is 25.5 seconds. The Queen Air 

phugoid wavelength is X = Va,T or 1,438 m. However, since this is an 

approximate value and since a pure sine wave at the Queen Air's phugoid 

frequency is not specifically input, the exact Queen Air phugoidal 

wavelength is not expected. The phugoidal-type oscillations are augmented primarily by the initial increase in head wind from 7.21 m/s to 

8.84 m/s and subsequent decrease to 4.91 m/s. The increasing head wind 

causes the initial rise above the glide slope and an initial increase 

and then decrease of airspeed. Shortly after the airspeed begins to 

decrease, the head wind begins to decrease and the airplane descends 

through the glide slope. The initial encounter with this wave sets off 

the subsequent oscillations where the aircraft descends and picks up 

airspeed, then begins to ascend until it once again loses airspeed and 

begins to descend again. 

Figure 3 shows the trajectory of a simulated Queen Air under autopilot control descending through the same wind field (Queen Air 17/2). 

Predictably, the trajectory is perfectly aligned with the glide slope 

and all phugoidal-type oscillations are removed. Figures 4 and 5 show 

the minor elevator and thrust control inputs necessary to maintain the 

approach along the glide slope. The sign conventions for elevator angle 

are shown in Figure 6. Since the autopilot represents a flight path 

optimization control system, the initial increasing head wind is 

countered with slightly increased thrust to maintain ground speed and an 

15 
I I I I I 1 

0.00 20.00 40.00 60.00 00.00 100.00 120. 

X/HA 

Figure 2 Simulated fixed-stick trajectory of a Queen Air flown through 

Queen Air flight 17/run 2 wind profile. 

00 
0.00 20.00 40.00 60.00 50.00 100.00 120.00 

X/HA 

Figure 3 Simulated trajectory of a Queen Air under autopilot control 

flown through Queen Air flight 17/run 2 wind profile. 
‘,” .+-I--- ----. -- ---r--------- I-------- r--- --1 

0. km 2i;l.rDQ 40.00 60.80 BE. 00 10Q. 00 120.00 

X/HA 

Figure 4 Autopilot elevator inputs to Queen Air in flight through 

Queen Air flight 17/run 2 wind profile. 
0. mm 20. II0 40.00 60.00 

X/HA 

60.00 100.00 120.00 

Figure 5 Autopilot thrust inputs to Queen A 

Air flight 17/run 2 wind profile. 

,ir n flight through Queen 
f 

Elevator Down 

Elevator Up 

Figure 6 Elevator angle sign conventions. 
elevator setting moving from negative to positive to pitch the nose down 

to counter the increased rise above the gl-ide slope. As the head wind 

begins its. drop from 8.84 m/s to 4.91 m/s, the initially added thrust is 

removed to maintain ground speed and the nose is pitched up to arrest 

descent. The airspeed is still high due to the previously added airspeed 

due to the thrust increase during the increased head wind. 

Throughout the flight, the autopilot tries to closely monitor the 

aircraft's state (airspeed, ground speed, descent rate, and glide slope 

alignment) and retrim the aircraft following the changes in the wind. 

Figures 7, 8, and 9 show trajectory, elevator angle, and thrust 

setting for a simulated Queen Air flown by a pilot with a 70 percent 

performance rating. The control inputs are small and similar to those 

of the autopilot. This is reasonable since the wind shear in this case 

is neither large nor severe. Again the aircraft is flown straight down 

the glide slope with no discernible deviations. Next, a pilot having a 

lower performance rating of 8 percent is examined. Figures 10, 11, and 

12 show the aircraft trajectory and the elevator and thrust control 

settings. The pilot attempts to retrim to the changing wind trend, but 

due to slower response time, the control excursions are larger than 

those of the autopilot and the 70 percent rated pilot. The trajectory 

shows that the pilot cannot adequately counter the initial head wind 

increase,and a small rise above the glide slope can be seen. However, 

the pilot manages to get back to the glide slope,suggesting that the 

main concern in maintaining control is the initially encountered wave 

and that controlling the remainder of the run is relatively straightforward. Finally, a simulated Queen Air commanded by a pilot having a 

5.5 percent performance rating was flown through the wind field. The 

performance rating in this case appears to be the threshold of minimum 

control because, as shown in Figure 13, the pilot is unable to counter the 

effects of the initial wave. The aircraft oscillates about the glide 

slope until finally near the end of the run the pilot is able to bring 

the plane back to intercept the glide slope. The elevator and thrust 

control inputs are presented in Figures 14 and 15, respectively. 

21 
1 

6; r 

0.00 

I I I I I I 

20.00 40.00 60.00 00.00 100.00 320. 

X/HA 

Figure 7 Simulated trajectory of a Queen Air controlled by a 70 percent 

performance rated pilot flown through Queen Air flight 17/run 2 

wind profile. 

00 
a Q 

ri I I I I I I 1 

0.00 20.00 40.00 60.00 60.00 100.00 120.00 

X/HA 

Figure 8 Elevator inputs by 70 percent rated pilot to Queen Air flown 

through Queen Air flight 17/run 2 wind profile. 
Es! 

6; I I I I I 1 

0.00 20.00 40.00 60.00 50.00 100.00 120.00 

X/HA 

Figure 9 Thrust inputs by 70 percent rated pilot to Queen Air flown through 

Queen Air flight l-//run 2 wind profile. 

- 
fii i 

.\. 

. 

. . 

II- -- I I 

0.00 2Ld. 00 40.00 61b.0@ eO.OO 100.08 120.00 

X/HA 

Figure 10 Simulated trajectory of a Queen Air controlled by an 8 percent 

performance rated pilot flown through Queen Air flight 17/run 2 

wind profile. 
v).(oB xJ.00 40.00 60.08 

x/t-m 

e0. eu 

Figure 11 Elevator inputs by 8 percent rated pilot to Queen Air flown 

through Queen Air flight 17/run 2 wind profile. 
- 

q, /------- --.^------ -_-_, --Ls-m/.d /---- 

.\/’ 

2 

Id- . 

-____ _.. _ I I__-..----- - r -- -- -- ---I-'-~' _-._. --. - r---.. -__- T-------7 

0.00 20. GJB G0.W 60.00 e0.00 100.00 17rD.W 

X/HA 

Figure 12 Thrust inputs by 8 percent rated pilot to Queen Air flown through, 

Queen Air flight 17/run 2 wind profile. 
B. t40 20. QQ 6d. 00 60,QB 100.. riw 12Ln.LWJ 

X/HA 

Figure 13 Simulated trajectory of a Queen Air controlled by a 5.5 percent 

performance rated pilot flown through Queen Air flight l-//run 2 

wind profile. 
- 

u Eg - v. Gi - A---- ‘k,, 

W 

Lo 

\.\p/(-.L~~-..d ---, -L\/ .,,---/‘---\-. 

z 

A--- 

---- -_--__ 

- 

I -.-.- .--- - I 1’ 1 

8.08 20.00 V0.0Q 60. Q0 eO. 00 100.00 1 m. km 

X/HA 

Figure 14 Elevator Inputs by 5.5 percent rated pilot to Queen Air flown 

through Queen Air flight 17/run 2 wind profile. 
Es I 

c-4 1 

E 

e 

hB q/y /--L-.---J’------+ .-..- -./--. .),_ 

I 

I 

;I I I --I---- --l-- -~--r-- ‘1 

I%. Lm 20.00 w. 00 60. CC tic. 0i5 100. cc 120.0~ 

X/HA 

Figure 15 Thrust inputs by 5.5 percent rated pilot to Queen Air flown 

through Queen Air flight 17/run 2 wind profile. 
The results of this simulation show that,although the aircraft is 

disturbed by the wind field in the fixed-stick case, the shear does not 

appear to be strong enough to cause any difficulty to a human-controlled 

vehicle. This is verified by the extremely low performance rated pilots 

who are able to make excellent approaches. 

5.2 Simulated Boeing 727 Flight Through Queen Air Flight 17/Run 2 

Wind Field 

An aircraft having the characteristics of a Boeing 727 is flown in 

simulated flight through the same wind field that the Queen Air encountered. The time history wind data, which have been converted from range 

data using the Queen Air's average airspeed, were reconverted to range 

data so that both aircraft encounter essentially the same wind field. 

The approach speed used for the B727 runs is 72 m/s as opposed to 56 m/s 

for the Queen Air. 

Figure 16 shows the fixed-stick flight of the simulated B727 through 

the Queen Air wind field. As with the Queen Air, the B727 encounter with 

the initial increasing and decreasing head wind results in a phugoidaltype oscillation in the trajectory. These oscillations are of higher 

amplitude and lower damping than those of the Queen Air. This is in 

direct agreement with McCarthy, Blick, and Bensch [3] and Frost and 

Crosby [4],who suggest that large commercial transports will experience 

greater difficulty in flight through wind shear than smaller aircraft 

due to the effects of higher landing speed and higher lift-to-drag ratio 

influence on the exponential phugoid damping period. Table 2 shows 

comparative calculations for the B727 and Queen Air exponential phugoid 

damping periods. The greatest deviation from the glide slope in Figure 

16 is approximately 43 m. The phugoid time period for the B727 given by 

T = JZrVao/g is 32.5 set and the wavelength x = VaoT is 2,341 m as 

compared with the 2,743 m (peak to peak) waves of the simulated trajectory. 

The trajectory of a simulated B727 flown by autopilot through the 

wind field is shown in Figure 17. Predictably the flight is smooth and 

perfectly aligned with the glide slope. In Figure 18 it can be observed 

that the response of the autopilot to the initial head wind increase is 

31 
8. 0 

1 

6: 

0. 0 20. 0 40. 0 60. 0 80. 0 100.0 120.0 

X/HA 

Figure 16 Simulated fixed-stick trajectory of a B727 flown through Queen 

Air flight 17/run 2 wind profile. 
TABLE 2. Comparison of Exponential Phugoid Damping Periods (T) of Queen 

Air and Boeing 727. 

T= the time for the phugoid oscillation to decay to l/e of its initial 

amplitude. 

'a 'L 

T= 0 

*$a 

0 

where 

Boeing 727 Queen Air 

'a = approach airspeed (m/s) 72.000 56.000 

0 

9 = gravitational acceleration (m/s2) 9.800 _ 9.800 

cLO = lift coefficient (dimensionless) 1.360 0.639 

cDO = drag coefficient (dimensionless) 0.139 0.080 

T= exponential phugoid damping period (set) 71.700 45.900 

33 
8. 

6. 

5 4. 

2. 

0. 0L............I.....1...,...,.1......-................,1......,........,,-.............,. 

0. 0 20. 0 40. 0 60. 0 80. 0 100.0 120.0 

X/HA 

Figure 17 Simulated trajectory of a B727 under autopilot control flown 

through Queen Air flight 17/run 2 wind profile. 
2. 0 

1 

+.pj~...,..............~uuluu..-uuu-u.U~~ 

0. 0 20. 0 40. 0 60. 0 80. 0 100.0 120.0 

X/HA 

Figure 18 Autopilot elevator inputs to B727 in flight through Queen Air 

flight 17/run 2 wind profile. 
a positive deflection in elevator angle. This pitches the nose down to 

counter the nose-up attitude caused by the increased head wind. However, 

in Figure 19 it is noticed that the autopilot optimization control loop 

has decreased thrust when encountering the increased head wind at the 

beginning of the run. With the Queen Air, thrust was increased to 

maintain ground speed. In the case of the B727, the higher approach 

airspeed into the increasing head wind causes too much additional lift 

which tends to force the airplane above the glide slope. Thus, the 

thrust was cut back to prevent the climb above the glide slope. It 

should also be noted that the elevator and thrust control inputs to the 

B727 are of larger magnitude than those of the Queen Air. 

The trajectory of an aircraft controlled by a pilot with a 70 

percent performance rating is given in Figure 20. The aircraft flies 

straight down the glide slope,. Figures 21 and 22 provide the elevator 

and thrust control inputs which are similar in magnitude to those made 

by the autopilot. 

The flight of an aircraft flown by a pilot with a low performance 

rating (5.5 percent) is next considered. The flight profile (Figure 23) 

shows that this pilot is unable to fully counter the initial increased 

head wind and the aircraft rises slightly above the glide slope at the 

beginning of the run. Following a slight descent below the glide slope 

due to the decreasing head wind, the pilot manages to correct and maintain a near-perfect approach. Note that the elevator and thrust controls 

(Figures 24 and 25) show less "fine tuning" than those of the 70 percent 

rated pilot. 

This above-described simulation shows that although the aircraft 

oscillates due to the wind shear for the fixed-stick run, there is no 

problem in maintaining an excellent approach in a piloted aircraft even 

for a pilot with a low performance rating (5.5 percent). 

5.3 Simulated B727 Flight Through Sinusoidal 6 m/s Amplitude Wave Near 

Phugoid Frequency 

A simulation is carried out flying the simulated B727 through a 6 

m/s head wind shearing to a 6 m/s tail wind. This wave disturbance is 

36 
- 

0. OLL 

0. 0 20. ia 40. 0 60. 0 80. 0 100.0 120. 0 

Figure 

X/HA 

19 Autopilot thrust inputs to B727 

flight 17/run 2 wind profile. 

in flight through Queen Air 
0. 0l...................1................. 

0. 0 20. 0 40. 0 

X/HA 

Figure 20 Simulated trajectory of a B727 controlled by a 70 percent 

performance rated pilot flown through Queen Air flight 17/ 

run 2 wind profile. 
2. 0 

1 

0. 0 20. 0 40. 0 60. 0 80. 0 100.0 120.0 

X/HA 

Figure 21 Elevator inputs by 70 percent rated pilot to B727 flown through 

Queen Air flight 17/run 2 wind profile. 
2.01 

I 

1.0’ 

0.0LPp 

0. 0 20. 0 40. 0 60. 0 80. 0 100.0- 120.0 

X/HA 

Figure 22 Thrust inputs by 70 percent rated pilot to B727 flown through 

Queen Air flight 17/run 2 wind profile. 
8. 03, 

2. 0 

t 

4. 0. 

\ 

2. 0. 

. . 

0.0\uuuubuuUP 

0. 0 20. 0 40. 0 60. 0 80. 0 100.0 120. 

0. 0* -u0. 0 20. 0 40. 0 60. 0 80. 0 100.0 120. 

X/HA 

0 

Figure 23 Simulated trajectory of a 8727 controlled by a 5.5 percent 

performance rated pilot flown through Queen Air flight l-//run 2 

wind profile. 
2. By 

I 

X/HA 

Figure 24 Elevator inputs by 5.5 percent rated pilot to 8727 flown through 

Queen Air flight 17/run 2 wind profile. 
3. 0, 

2. 0 

t 

0. 0 I Lw~..lr,rru--~Llsu.,Luuuuurrkurl~~u~~ &4J.u.&-dIsb4 

0. 0 20. 0 40. 0 60. 0 80. 0 100.0 120.0 

X/HA 

Figure 25 Thrust inputs by 5.5 percent rated pilot to B727 flown through 

Queen Air flight 17/run 2 wind profile. 
similar to that of the Queen Air 17/2 case except that a wave at approximately the B727's phugoid frequency is encountered by the aircraft. 

Such a wave disturbance is used to simulate the thunderstorm cell wind 

environment which has been the cause of either an accident or, at 

minimum, an incident to several aircraft which encountered similar 

waves. An aircraft flying through a thunderstorm initially flies into a 

head wind (the thunderstorm cell outflow). This longitudinal head wind 

component diminishes to zero as the aircraft flies through the central 

down draft region of the cell and becomes a tail wind as the aircraft 

flies into the outflow on the other side. 

Figure 26 shows the fixed-stick trajectory of the simulated B727 

flying into a constant 6 m/s head wind which begins to decrease at 

X/HA = 8.3 to become a 6 m/s tail wind at X/HA = 21.2. The aircraft 

drops below the glide slope and loses airspeed until X/HA = 74.8 when 

the airspeed starts to increase again. However, since the head wind is 

still decreasing, the aircraft continues to fall as the airspeed continues 

to build up. Finally, the aircraft then begins to climb at X/HA = 33. 

The encountered wave disturbance thus sets off phugoidal oscillations in 

the trajectory. Since the sinusoidal wind velocities are computed using 

a time scale based on aircraft position along the glide slope and average 

approach speed, the sine wave is approximate since the aircraft does not 

travel collocationally along the glide slope during the wave encounter. 

The flight path of a simulated B727 flown by the autopilot is given 

' in Figure 27. The beginning of a very slight descent below the glide 

slope occurs at X/HA = 11, which is the same location that the fixed-stick 

aircraft (Figure 26) begins to drop. The autopilot, however, quickly 

begins to pitch the aircraft nose-up (Figure 28) and increases the thrust 

(Figure 29) to counter the 'loss of airspeed and deviation below the 

desired glide path. The aircraft comes back up, to intercept the glide 

slope and continues the approach through the remaining 6 m/s tail wind 

without deviation. Note that the retrim for maintaining flight through 

the tail wind requires a higher thrust setting than for the initial head 

wind as well as an elevator angle setting of approximately -8". Once 

again it can be observed that by correct countering of the wave-form wind 

44 
X/HA 

Figure 26 Simulated fixed-stick trajectory of a B727 flown through a 6 m/s 

amplitude sinusoidal wave at the phugoid frequency. 
0. 

X/HA 

Figure 27 Simulated trajectory of a B727 under autopilot control flown 

through a 6 m/s amplitude phugoidal sine wave. 
10. 0 

F 

5.01 

. 

- c 

X/HA 

Figure 28 Autopilot elevator inputs to B727 in flight through a 6 m/s 

amplitude phugoidal sine wave. 
3. 0 

1 

2. 0 1 

0. 0 20. 0 40. 0 60. 0 80, 0 100.0 120.0 

Z/HA 

Figure 29 Autopilot thrust inputs to B727 in flight through a 6 m/s 

amplitude phugoidal sine wave. 
disturbance,-the oscillations of the fixed-stick case can be almost completely eliminated. 

Simulated landings with pilots of various performance ratings were 

flown down the same sinusoidal wave. Figure 30 illustrates that a pilot 

with a 25 percent rating can easily negotiate the disturbance with only 

a slight dip below the glide slope. The wave-like "humps" in the elevator 

control setting (Figure 31), observed from X/HA = 0 to 4 and from X/HA = 

35 to 80,represent pilot inputs to counter the aircraft's slight natural 

phugoidal oscillation in the steady 6 m/s head wind before the wave and in 

the tail wind after the wave, respectively. 

Figure 32 shows the flight path of an aircraft controlled by a 

simulated pilot with a 5.5 percent performance rating. Passing through 

the shear wave, this pilot does not react quickly enough to the decreasing 

airspeed caused by the decreasing head wind, and the aircraft falls a 

maximum of 23 m below the glide slope. The pilot then regains control and 

applies step inputs to the elevator and throttle (Figures 33 and 34) to 

get back on the glide slope. In general, the pilot's approach is fairly 

good. 

The results of this simulation show that a 6 m/s thunderstorm 

environment phugoid wave is not very severe from the standpoint of pilot 

control,as even a pilot with low performance capability can make the 

approach without too much deviation from the glide slope. However, had 

the deviation below the glide slope occurred relatively close to the 

runway threshold, the 5.5 percent rated pilot would have been forced to 

execute a go-around. 

5.4 SimulpteclB727 Plight Through Sinusoidal 14 m/s Amplitude Wave Near 

Phugoid Frequency 

In the following simulations, the 8727 is flown through a longitudinal wave disturbance representative of a very strong thunderstorm cell 

wind profile. A 14 m/s amplitude wave is chosen based on longitudinal 

thunderstorm wind data analyzed by Frost, Camp, and Wang [lo]. The aircraft is initially trimmed for flight in a steady 14 m/s head wind which 

49 
X/HA 

Figure 30 Simulated trajectory of a B727 controlled by a 25 percent rated 

pilot flown through a 6 m/s amplitude phugoidal sine wave. 
10.0” 

-10.0Lya. 0 20. a 40, 0 60. 0 80. 0 100.0 120.0 

X/HA 

Figure 31 Elevator inputs by 25 percent rated pilot to B727 flown through a 

6 m/s amplitude phugoidal sine wave. 
8. 0 

r 

X/HA 

Figure 32 Simulated trajectory of a 8727 controlled by a 5.5 percent rated 

pilot flown through a 6 m/s amplitude phugoidal sine wave. 
10. 

5. - 

-5. 

0, 

i 0, k 

i 

Figure 33 Elevator inputs by 5.5 percent rated pilot to B727 flown through a 

6 m/s amplitude phugoidal sine wave. 
X/HA 

Figure 34 Thrust inputs by 5.5 percent rated pilot to B727 flown through a 

6 m/s amplitude phugoidal sine wave. 
shears as a wave at approximately the aircraft's phugoid frequency to a 

steady 14 m/s tail wind for the remainder of the run. 

The simulated trajectory of an autopilot-controlled aircraft is shown 

in Figure 35. The aircraft encounters the decreasing head wind at approximately X/HA = 8 and begins to fall below the glide slope. The autopilot 

increases thrust (Figure 36) and moves the elevator to full negative 

deflection (Figure 37) to pitch the aircraft nose-up. The aircraft falls 

a maximum of 75 m below the glide slope until it responds to the added 

controls and pulls out of its descent at X/HA = 74. Due to the added 

controls, the aircraft ascends above the glide slope to a maximum of 23 m 

at X/HA = 30. The autopilot then decreases thrust to allow the aircraft 

to gradually fall back and recapture the glide slope and finish with a 

near perfect approach. While it is unlikely that an aircraft would 

execute an approach in a 14 m/s tail wind, note that the autopilot trims 

the aircraft with full nose-up elevator deflection and twice the initial 

thrust to maintain flight in this tail wind. 

Figure 38 shows the simulated trajectory of an aircraft controlled by 

a pilot with a performance rating of 50 percent. The aircraft drops 

approximately 18 m below the glide slope when it encounters the decreasing 

head wind. Again, thrust is increased (Figure 39) and elevator angle is 

increased to full nose-up deflection (Figure 40) to counter the effect of 

the decreasing airspeed. However, due to the farther drop below the glide 

slope and slower response time of the pilot as compared with the autopilot, the aircraft does not rise as high above the glide slope as it did 

under autopilot control. Thrust is then decreased so that the aircraft 

can descend to intercept the glide slope and maintain an excellent 

approach through the remaining tail wind. 

The flight profile and control inputs of an aircraft controlled by a 

25 percent rated pilot (Figures 41 through 43) are examined next. During 

the encounter with the shear wave, the aircraft falls a maximum of 23 m 

below the glide slope. This would obviously create a hazardous situation 

had the aircraft encountered such a wave in the immediate vicinity of the 

runway threshold. Because of the large drop below the glide slope and 

slow response of the pilot, the aircraft rises only slightly above the 

55 
8. 

6. 

X/HA 

Figure 35 Simulated trajectory of a 8727 under autopilot control flown 

through a 14 m/s amplitude phugoidal sine wave. 
X/HA 

Figure 36 Autopilot thrust inputs to 8727 in flight through a 14 m/s 

amplitude phugoidal sine wave. 
Figure 37 Autopilot elevator inputs to 13727 in fl 

amplitude phugoida 1 sine wave. 

X/HA 

ight through a 14 m/s 
- 

- 

i&J 4. 

N 

2. 

Figure 38 Simulated trajectory of a B727 controlled by a 50 percent rated 

pilot flown through a 14 m/s amplitude phugoidal sine wave. 
X/HA 

Figure 39 Thrust inpu-ts by a 50 percent rated pilot to B727 flown through 

a 14 m/s amplitude phugoidal sine wave. 
Figure 40 Elevator inputs by a 50 percent rated pilot to B727 flown 

through a 14 m/s amplitude phugoidal sine wave. 
X/HA 

Figure 41 Simulated trajectory of a B727 controlled by a 25 percent rated 

pilot flown through a 14 III/S amplitude phugoidal sine wave. 
30. a, 

20. 

1z. 

0. 0 

-10. 0 

-2z. z 

-30. 

- 

fi? 

-0 

- 

W 

W 

X/HA 

Figure 42 Elevator inputs by a 25 percent rated pilot to B727 flown through 

a 14 m/s amplitude phugoidal sine wave. 
X/HA 

Figure 43 Thrust inputs by a 25 percent rated pilot to B727 flown 

through a 14 m/s amplitude phugoidal sine wave. 

- 
glide slope as it pulls out of its descent. Thrust is decreased at X/HA 

= 21 to return the aircraft to the glide slope where it remains for the 

length of the run. 

Finally, 'the performance of a 5 percent rated pilot in an aircraft 

encountering the 14 m/s shear wave is examined. Figures 44, 45, and 46 

show the flight profile and the elevator and thrust inputs, respectively. 

As the aircraft enters the decreasing head wind, the airspeed decreases 

and the aircraft begins to descend. The pilot's response is extremely 

slow, allowing a very high sink rate to build up. Because of the large 

lag on the controls and severe change in the wind, control of the aircraft 

is lost. The initial loss of control builds up to the point where the 

control loop starts to decrease thrust between X/HA = 13 to X/HA = 17 

(Figure 46). At this point there appears to be a small"bug"in the control 

loop. The thrust should not decrease with increasing sink rate even 

though the aircraft is experiencing an increasing speed. 

It is believed that a small correction to the gain on the vertical 

velocity deviation in the pitch control variable eC, which has been kept 

constant for all previous cases, will correct this slight anomaly. 

However, the severity of this wind field and the low performance rating 

used in this case is apparently responsible for this effect. The proper 

setting of this gain will require further investigation. Nevertheless, 

the aircraft does eventually begin to regain thrust control and pull out 

of its descent at approximately X/HA = 18 when the vertical velocity 

peaks, compensating for the low gain. Thrust is eventually increased to 

a higher setting (Figure 46) and step inputs are made to both elevator and 

thrust to return the aircraft to the glide slope. The response of the 

aircraft to the step inputs is shown by the wave-like trajectory in 

Figure 44 from X/HA = 20 to X/HA = 75. 

The results of this simulation illustrate the severity of strong 

thunderstorm-related shear in the horizontal wind. The autopiloted and 50 

percent rated pilot-controlled aircraft maintained fairly good approaches 

but not without significant deviation below the glide slope. The 25 

percent rated pilot-controlled aircraft experienced a fairly large drop 

below the glide slope of such magnitude that a go-around would have had to 

65 
8. 

6. 

5 4. 

2. 

0. 

Figure 44 Simulated trajectory of a B727 controlled by a 5 percent rated 

pilot flown through a 14 m/s amplitude phugoidal sine wave. 
- 

X/HA 

Figure 45 Elevator inputs by a 5 percent rated pilot to B727 flown 

through a 14 m/s amplitude phugoidal sine wave. 
X/HA 

Figure 46 Thrust inputs by a 5 percent rated pilot to B727 flown through 

a 14 m/s amplitude phugoidal sine wave. 
I - I 

be executed had the shear wave been encountered relatively close to the 

runway threshold. Finally, the inability of the low performance 5 percent 

rated pilot to negotiate the high rate of descent caused by the shear wave 

shows the danger of slow response and failure to properly recognize the 

effects of wind shear on approach. 

5.5 Simulated B727 Flight Through Full Sinusoidal 10 m/s Amplitude Wave 

Near Phugoid Frequency 

In the final simulations the B727 is flown through a full 10 m/s 

head wind to tail wind sinusoidal phugoid frequency wave. The wind 

increases from 0 m/s to become a 10 m/s head wind which shears to a 

10 m/s tail wind and then returns to zero wind for the remainder of the 

run. 

Figure 47 shows the trajectory of a simulated B727 under autopilot 

control flown through the sinusoidal wind field. The aircraft is forced 

slightly above the glide slope when it encounters the increasing head 

wind and drops slightly below the glide slope as it enters the increasing 

tail wind. The aircraft then rises above the glide slope as the tail 

wind diminishes to 0 m/s. The autopilot eventually returns the aircraft 

to the glide slope to land on target. 

Figures 48, 49, and 50 show the simulated flight path, elevator 

inputs, and thrust control inputs, respectively, for a piloted B727 

flown through the phugoidal sine wave. The pilot model used for this 

run was based on the data for pilot A from Adams and Bergeron [7] 

(Table 1). This pilot was rated relatively high based on high static 

gains, high lead time constants, and low lag time constants. The 

aircraft rises above the glide slope when encountering the increasing 

head wind. The pilot cuts thrust to zero and pitches the nose down to 

counteract the rise above the glide slope. The aircraft then encounters 

the head wind to tail wind shear and drops below the glide slope, due 

to the previously decreased power, necessitating a thrust increase and 

pitch-up of the nose. Eventually, the aircraft is brought back to the 

glide slope and retrimmed for the zero wind condition for a safe landing. 

69 

II 
5 

N 

4. 

2. 

0. 

Figure 47 Simulated trajectory of an autopilot-controlled B727 through 10 m/s 

amplitude phugoidal sine wave. 
6.0, 

4. 0 

2 

2 

2. 0 

0. 0 u&.bbbUP 

0. 0 20. 0 40. 0 60. 0 80.0 100.0 

Figure 48 Simulated trajectory of a 8727 controlled by pilot A flown through 

10 m/s amplitude phugoidal sine wave. 
10. 0 

f 

5. 0; 

X/HA 

Figure 49 Elevator inputs by pilot A to 8727 flown through 10 m/s amplitude 

phugoidal sine wave. 
X/HA 

Figure 50 Thrust inputs by pilot A to B727 flown through 10 m/-s amplitude 

phugoidal sine wave. 
Figure 51 shows the trajectory of a simulated B727 flown through the 

shear wave by pilot F. As shown from the data of Adams and Bergeron [7] 

in Table 1, this pilot is of relatively low skill due to a low static 

gain, low lead time constant, and high lag time constant. The aircraft 

as controlled by this pilot rises highest above the glide slope and 

drops farthest below the glide slope due to higher response lag time. 

The pilot is unable to bring the aircraft back to the glide slope and 

lands short. The wave-like humps in the trajectory represent attempts 

to stabilize the approach angle. 

This simulation compares the relative degrees of control applied to 

an aircraft landing through a phugoidal shear wave. The optimization 

autopilot rapidly corrects for the wind changes with low lag time 

and maintains the tightest control. Pilot A possesses higher lag than 

the autopilot and illustrates the danger of decreasing thrust when 

encountering a head wind to tail wind shear. The aircraft dropped below 

the glide slope but the pilot was able to regain control and recover the 

approach. The lower skilled, higher' lagged pilot F was unable to safely 

counter the shear and landed short. 

74 
4. 

2. 

0. 

0. 0 20. 0 40. 0 60. 0 80.0 ’ 100.0 

X/HA 

Figure 51 Simulated trajectory of a 8727 controlled by pilot F flown through 

10 m/s amplitude phugoidal sine wave. 
.-..-. 

6.0 CONCLUSIONS 

The purpose of this study was to evaluate the response of the 

pilot-aircraft system to wind shear. This was carried out by performing 

a parametric study of pilot performance rating and by use of actual 

pilot data. Performance ratings ranged between 100 percent autopilot 

control (perfect pilot) and "hands off" or 0 percent control (fixed-stick), 

with the human pilot having any performance rating in this range. Fixed- 

. 

stick, autopilot, and manned performance of both a simulated B727, a 

medium-sized commercial transport, and a simulated Queen Air, a small 

commuter-type aircraft,flown through a glide slope longitudinal wind 

profile detected by Doppler radar were compared. The wave-form wind 

disturbance was shown to excite the phugoid oscillations of both aircraft when flown in the fixed-stick mode but presented no control problems 

for manned aircraft. The fixed-stick simulations also showed agreement 

with the theories of McCarthy, Blick, and Bensch [3] and Frost and Crosby 

[4] stating that the oscillatory effects of a shear wave are greater on 

transport aircraft than on smaller aircraft as pred,icted by aircraft 

stability theory. 

A simulation was also carried out flying the fixed-stick, autopilot 

controlled, and manned aircraft with characteristics of a B727 through a 

6 m/s amplitude head wind to tail wind phugoid frequency shear wave 

representative of the thunderstorm cell wind environment. This case also 

revealed phugoid oscillations but clearly illustrated that this shear 

wave was not a serious problem to a manned vehicle. 

However, in the stronger disturbance of a 14 m/s head wind to tail 

wind phugoid frequency shear wave, significant deviation from the glide 

slope was noted for the autopilot, 50 percent rated pilot, and 25 percent 

rated pilot flight simulations. The low performance,5 percent rated pilot 

initially lost control of the aircraft and dropped farthest below the 

glide slope. However, thrust was eventually increased to bring the 

aircraft back up to the glide slope. 

76 
In flight simulations through a full 10 m/s phugoidal sine wave, 

comparisons were made between autopilot control and control by simulated 

pilots of varying skill. The autopiloted aircraft executed the best 

approach,while the high-skilled pilot descended below the glide slope but 

was eventually able to bring the aircraft back onto the glide path. 

However, the low-skilled pilot could not maintain adequate control and 

landed short. 

The four wind profiles utilized in this study do not by any means 

limit the severity or variety of conditions to be found in the atmosphere. 

However, this research provides a better understanding of pilot-aircraft 

response to longitudinal wind shear and serves as an important input 

toward the development of a Doppler radar wind shear warning and 

detection system. 

77 
7.0 REFERENCES 

1. National Transportation Safety Board. "Eastern Airlines, Inc., 

Boeing 727-225, John F. Kennedy International Airport, Jamaica, 

New York, June 24, 1975,” Aircraft Accident Report No. NTSB-AAR-76-8, 

National Transportation Safety Board, Washington, D.C., March 12, 

1976. 

2. National Transportation Safety Board. "Eastern Airlines, Inc., 

Boeing 727-25, Atlanta Hartsfield International Airport, Atlanta, 

Georgia, August 22, 1979," Aircraft Incident Report No. NTSB-AAR80-6, National Transportation Safety Board, Washington, D.C., 

May 28, 1980. 

3. McCarthy, J., E. F. Blick, and R. R. Bensch. “Jet Transport Performance in Thunderstorm Wind Shear Conditions," NASA CR 3207, December, 

1979. 

4. Frost, W., and W. A. Crosby. "Investigations of Simulated Aircraft 

Flight Through Thunderstorm Outflows," NASA CR 3052, September, 

1978. 

5. Frost, W;, and K. R. Reddy. "Investigations of Aircraft Landing in 

Variable Wind Fields," NASA CR 3073, December, 1978. 

6. Dickinson, B. Aircraft Stability and Control for Pilots and Engineers. 

London: Sir Isaac Pitman and Sons, Ltd., 1968. 

7. Adams, J. J., and H. P. Bergeron. "Measured Variation in the Transfer 

Function of a Human Pilot in Single Axis Tasks," NASA TN D-1952, 

October, 1963. 

8. Neuman, F., and J. Foster. "Investigation of a Digital Automatic 

Aircraft Landing System in Turbulence," NASA TN D-6066, October, 

1970. 

9. Etkin, B. Dynamics of Atmospheric Flight. New York: John Wiley and 

Sons, Inc., 1972. 

10. Frost, W., D. W. Camp, and S. T. Wang. "Wind Shear Modeling for 

Aircraft Hazard Definition," FAA-RD-78-3, February, 1978. 

78 
APPENDICES 

79 
APPENDIX A 

DERIVATION OF THRUST AND ELEVATOR ANGLE 

CONTROL FUNCTIONS (FT,6E) 

The three degrees of freedom of the two-dimensional aircraft motion 

model are given by the following equations from Frost and Crosby [z] 

cj = D7FT + D&C, (J> 

iv = D6 sin (6T + a)FT - D2 cos y + D,Vs(CL cos 6 - CD sin 6) (2) 

\i = DG cos (6T + cr)FT - D2 sin y - D, Vi(CL sin 6 + CD cos 6) (3) 

Equations 1, 2, and 3 represent pitch motion about the y axis, vertical 

motion along the z axis, and longitudinal motion along the x axis, 

respectively. The axis system has the origin fixed at the airplane's 

center of mass with the x axis oriented along the ground speed vector. 

Expanding Cm, CL, and CD plus adding an arbitrary pitch control variable, 

ec, to Equation 2 yields 

;I = D7FT + O&(Cm + Cm Al' + Cm "E + (D4Cm /v,h + (D,C,./V,)~') (4) 

0 a &E 9 a 

TiV = D6 sin (6T + cr)FT - D2 cos y + DJVs(CL 

0 

+ CL a' + CL 6E 

cl 6E 

+ (D4CL /V,)q -I- (D,C,./V,)i') cos 6 - DJV;(CD 

q 

+ CD CY' 

a 0 a 

+ CD ~1~) sin 6 - 8 

a2 c 

i = D6 cos (6T + a)FT - D2 sin y - D,Vi(CL + CL a' + CL 

0 

6E 

a 6E 

+ (D4CL /Va)q + (D,C,./V,)i') sin 6 - D,Vi(CD (r12) 

q 0 

+ CD a' + CD 

w. a. a2 

x cos 6 

80 
Collecting coefficents of F,-, ~1', and 6E in the three equations and 

setting all time derivatives to zero 

D7 V;D5CItl 

a 

II6 sin (CS~ + a) - V$(D,CD + D,CD 

a2 

cl') sin 6 + DICL Vi COS 6 

ct a 

D6 cos (+ + a) - Vg(D,CD + D,CD a') cos 6 - D,CL Vg sin 6 

a '32 ct 

- DIV;CL s 

"E 

Next, separating the remaining terms of the three equations, gives 

-(D,C, 

' -0 

V, + DJD4CL q + DJD4CL.i') cos 6 f D,CD Va sin 6 

q a 0 

-(D5Cm V, + 

0 

D5D4Cm q + D5D4Cm.~') 

q a 

0 

D2 

1 

(DICL V, + DJD4CL q + DJD4CL.&') sin 6 + D,CD V, cos 6 

0 q a 0 

- D2 

0 

0 

(7) 

(8) 

81 
For computational convenience and clarity, 

r 

Gl .G& 

, I 

G9v$ FT 

\ 

G7 

,G4 

G5v: G6Vi a' = [Va ;&] 

G2v: G3v:, \'E, 

we write Equations 7 and 8 as 

-G12 -GJl Glo 

\ 

0 0 -D2 

0 D2 0 (9) 

0 1 0 , 

To solve for FT and ~5~' we take the inverse of the 3x3 matrix on the Jefthand side of Equation 9 which is 

I 

(G5G3 - G2G6)V; -(G8G3 - G2Gg)V; 

& -(G7G3 - G4G6)V; tGlG3 - G4Gg)V; 

,(G7G2 - G4G5)V; -(G,G2 - G4G8)v; 

where the determinant, DET, is equal to 

(G8G6 - G5Gg)V; 

-(G,G6 - G7Gg)V; 

(G,G5 - G7G8)v; 

(G,G~G~ + G~GSG~ + ~~~~~~ - ~~~~~~ --G~G~G~ - G~G~G~)v; 

= [G2(GgG7 - G6Gl) + G3(G,G5 - G7G8) + G4(G6G8 - G5Gg)lV; 

= -(G2tiJ - G3H2 + G4H3)V; 

= -(H4)V; 

= -(H5)V; 

Multiplying both sides of Equation 9 by Equation 10 yields 

I \ 

FT 

c 

HJJ -H10 H9 

-l f 

-G12 O 0 I f O 'a 

\ 

a' = --- --- 

,'E, ,-H8 H7 

-mm -Gil O D2 1 i/V 

-H6~ iGIO -D2 0 0, i/v 

Since we are solving for FT and &E, the terms of the second row of the 

inverse corresponding to a’ were not derived. Solving for FT, 

and 6E gives 

82 

(10) 

II II
I 

. . 

FT = KT1va + KT2 v 

' + KT3 t+ KT4 0C 

. 

"E = KDIVa + KD2 v 

' + KD3 ;+ KD4 ec 

where 

I 

KTJ 

KT2 

KT3 

cKT4 

and 

I 

KDJ 

KD2 

KD3 

,KD4 

= 

I 

= 

I 

Equations 

section. 

-HllGJ2 + HlOGJ1 + H9GJC 

-H9D2 

-HJOD2 

-HJO 

H8G1 2 - H7Gll - H6G10 

H6D2 

H7D2 

H7 

(12) 

(13) 

I 

(14) 

I 

(15) 

for Gi, Hj, Dk' and Cn appear in detail in the following 

Equation Form of Gi, H., Dk, and Cn 

-- 

Gl = D7 

G2 = -(C, + C2a’) cos 6 - C3 sin B 

G3 = -C4 sin 6 

G4 = D6 cos (6T + CL) 

G5 = c3 cos 6 - (C, + C2a') sin B 

G6 = c4 cos 6 

G7 = D6 sin (6T + a) 

83 
G8 =c5 

G9 = c6 

Glo = 

c7va cos 6 +.(c8va + c9q + cJ&i') sin 6 

G, J = (c$, + Cgq + Cl,;') cos 6 - C7Va sin 6 

‘12 = 

c,,v, + $24 + C,3i’ 

Hl = G6Gl 

- G7G9 

H2 = G5Gl 

- G7G8 

H3 = G5Gg 

- G6G8 

H4 = G2tiJ - G3H2 + G4H3 

H5 = V;H4 

H6 = H2/H5 

H7 = (G2Gl - G4G8)/H5 

H8 = (G2G7 - G4G5)/H5 

H9 = H3/H4 

H10 = (G2Gg - G3G8)/H4 

H,, = (G2G6 - G3G5)/H4 

D1 = b/2) (SHA/m) 

D2 = kW/V~) 

D3 = (HAW;) 

D4 = (F/2HA) 

D5 = b/2) (SrHA2/s Iyu) 

D6 = (gHA/mVi) 

D7 = ($D3/Iyy) 

The following are the "C" coefficients used in variable gain computations 

of FT and sE: 
- 

5 = D,CD 

a 

c2 = DlCDa2 

c3 = DICL 

a 

C5 = D5Cm 

a 

‘6 = D5Cm 

6E 

c7 = DICDo 

‘8 = DICLo 

C9 = DJD4cL 

9 

c1o = D,D4CL. 

a 

c11 = D5Cmo 

c12 = D5D4Cm 

'7 

‘13 = D5D4Cm. 

a’ 

85 
APPENDIX B 

CHARACTERISTICS OF AIRCRAFT USED IN 

NUMERICAL FLIGHT SIMULATIONS* 

Reference (scale) altitude HA (m) 

Initial approach airspeed Vao (m/s) 

Initial flight path angle y (deg) 

Aircraft mass (kg) 

. . Moment of inertia Iyy ( kg-m2) 

Moment arm of thrust vector LT(m) 

Angle between FT and fuselage reference 

line (deg) 

Chord length c (m) 

Wing area S (m2) 

cLO 

cL a 

cL 

6E 

cLq 

Boeing 727 Queen Air 

91.4 91.4 

71.9 56.4 

-3.0 -3.0 

63,945.6 3,469.2 

6.1 x lo6 7.8 x lo3 

0.0 0.0 

0.0 0.0 

5.0 1.8 

145.0 27.3 

Boeing 727 

1.360 

5.04/rad 5.28/rad 

O.O07/deg O.O07/deg 

9.3/rad 2.9/rad 

Queen Air** 

0.639 

*Courtesy of E. F. Blick, Professor of Aerospace Engineering, 

Department of Engineering, University of Oklahoma, Norman, Oklahoma. 

**Based on approach speed of 62 m/s. 

86 
cL* 

a 

cDO 

cD a 

‘Da2 

C 

mO 

'rn a 

C 

m6E 

'rn 

q 

C mm 

a 

6.6 

0.139 

1.245/rad 

O.O/rad' 

0.0 

-1,47/rad 

-O.O25/deg 

-29.5/rad 

-1.77/rad 

1.08 

0.08 

0.33/rad 

O.O/rad' 

0.0 

-l.O/rad 

-O.O25/deg 

-8.7/rad 

-3.24/rad 

87 
1. REPORT NO. 2. GOVERNMENT ACCESSION NO. 3. RECIPIENT’S CATALOG NO. 

NASA CR-8842 

1. TITLE AND SUBTITLE 5. REPORT DATE 

November 1980 

Pilot-Aircraft System Response to Wind Shear 6. PERFORMING ORGANIZATION CODE 

7. AUTHOR(S) 6. PERFORMING ORGANIZATION REPD!X 

Barry S. Turkel and Walter Frost 

3. PERFORMING ORGANIZATION NAME AND ADDRESS 

FWG Associates, Inc. 

R.R. 2, Box 271-A 

Tullahoma, TN 37388 

2. SPONSORING AGENCY NAME AN0 ADDRESS 

10. WORK UNIT, NO. 

M-307 

11. CONTRACT OR GRANT NO. 

NAS8-33458 

,S. TYPE OF REPOR;’ 8: PERIOD COVERI 

Contractor Report 

National Aeronautics and Space Administration 

Washington, D.C. 20546 1.1. SPONSORING AGENCY CODE 

5. SUPPLEMENTARY NOTES 

NASA Marshall Technical Monitor: Dennis Camp 

Interim Report 

6. ABSTRACT 

The nonlinear aircraft motion and automatic control computer model of Frost 

and Reddy has been expanded to incorporate the human pilot into simulations of 

aircraft response to wind shear. The human pilot is described by a constant gains 

lag filter. In addition, two runs are carried out using pilot transfer functions 

from the experimental data of Adams and Bergeron. Fixed-stick, autopilot, and 

manned computer simulations are made with an aircraft having characteristics of a 

Queen Air (small commuter-type aircraft) flown through longitudinal winds measured 

by a Doppler radar beamed along the glide slope during the SESAME '79 experiments 

in Oklahoma. Simulations are also made flying an aircraft characteristic of a 

Boeing 727 through sinusoidal head wind and tail wind shears at the phugoid frequency 

to evaluate the response of manned aircraft in thunderstorm wind environments. 

7. KE’, WORDS 

Wind Shear 

Flight Simulation 

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