NASA Contractor Report 3073

Investigation of Aircraft Landing in Variable Wind Fields

Walter Frost and Kapuluru Ravikumar Reddy

CONTRACT DECEMBER

NASS-29584 1978

NASA Contractor Report 3073

TECH LIBRARY KAFB, NM

Investigation of Aircraft Landing in Variable Wind Fields
Walter Frost and Kapuluru Ravikumar Reddy The University of Tennessee Space Irzstitute Tdahoma, Temessee

Prepared for George C. Marshall Space Flight under Contract NASS-29584

Center

MSA
National Aeronautics and Space Administration
Scientific and Technical Information Office
1978

AUTHORS’ ACKNOWLEDGMENTS

The work reported herein was supported by the National Aero-

nautics and Space Administration,

Marshall Space Flight Center,

Space Sciences Laboratory, Atmospheric Sciences Division , under

contract number NAS8-29584.

The authors are indebted to Mr. John H. Enders of the

Aviation Safety Technology Branch, Office of Aeronautics and Space

Technology (OAST), NASA Headquarters, Washington, D. C., for his

support of this research. Special thanks also go to Dr. G. H. Fichtl

and Mr. Dennis Camp of the Marshall Space Flight Center who were

the scientific

monitors of the program.

ii

TABLE OF CONTENTS

CHAPTER

I. INTRODUCTION. . . . . . . . . . . . . . . . . . . . . . . . . . 1

II. AIRCRAFT LANDING MODEL. ....................

6

1. Equations of Motion ....................

6

2. Incorporation of Wind Shear ................

11

III. MATHEMATICAL MODELS FOR VARIABLE WIND FIELDS. .........

15

1. Atmospheric Flow Over a Homogeneous Terrain ........

15

2. Atmospheric Flow Over Buildings ..............

15

3. Atmospheric Flow Associated with Thunderstorm Gust Fronts . 25

IV. AUTOMATIC CONTROLSYSTEM. ...................

29

1. Mode Selector .......................

33

2. Altitude Hold Mode. ....................

36

Capture Mode. .......................

38

1: Glide-Slope Tracking Mode .................

40

5. Flare Mode. .........................

42

6. Calculation of the Feed-Back Controls ...........

46

V. RESULTS AND DISCUSSION. . . . . . . . . . . . . , . . . . . . . 51

VI. CONCLUSIONS . . . . . . . . . . . . . . . . . . . . . . . . . . 76

BIBLIOGRAPHY. ............................

77

APPENDIX. ..............................

80

. . .
111

LIST OF FIGURES

FIGURE

PAGE

1. Relationship between the various forces acting on an

aircraft [121. .......................

7

2. Logarithmic wind profile ..................

16

3. Definition of flow zones near a sharp-edged block [22] ...

18

4. Description of flow region considered for a block

building [22]. .......................

19

5. Description of flow region considered for a long, wide

building [23]. .......................

20

6. Vorticity contour [22] ...................

21

7. Streamline patterns [22] ..................

22

8. Velocity profiles over an obstruction on the surface [22]. . 23

9. Velocity profiles over a step geometry long, wide

building [23]. .......................

24

10. Overall block diagram of control system. ..........

31

11. Automatic landing geometry using ILS ............

34

12. Mode control logic .....................

35

13. Altitude hold mode .....................

37

14. Glide slope capture mode ..................

39

15. Glide slope tracking mode. .................

41

16. Flaremode .........................

44

17. Feedback loop-thrust ....................

47

18. Feedback loop-elevator angle ................

49

19. Fixed control landing over a block building. ........

52

20. Fixed control landing over a step. .............

53

iv

FIGURE

21. Fixed control landing in the atmospheric boundary

layer,.

..........................

22. Fixed control landing in thunderstorm gust front ......

23. Wind.distribution

over a block building along the flight

path ............................

24. Wind distribution

over 6 long; wide building along the

flight path. ........................

25. Wind distribution

in the thunderstorm gust front along

the flight path. ......................

26. Automatic landing in atmospheric boundary layer, ......

27. Automatic landing over block building. ...........

28. Automatic landing over a long, wide building ........

29. Automatic landing in the flow associated with thunderstorm gust front. ...................

30. Controls required for landing over a block building. ....

31. Controls required for landing over a step. .........

32. Controls required for automatic landing in thunderstorm

gustfront

.........................

33. DHC-6 landing through atmospheric flow over a block building ..........................

34. Automatic landing reference trajectory ...........

PAGE
55 56
57 58
59 60 61 62
63 65 66
67
68 70

NOMENCLATURE

cD

Drag coefficent, D/(l/2)pV2S

cL

Lift coefficent, L/(l/2)pV2S

C m

Pitching-moment coefficent, M/(l/2)pV2SE

E

Wing mean aerodynamic chord, m

cl, c2 l . . cy Constants

D

Magnitude of aerodynamic drag, N

FT
G(s)

Magnitude of thrust, N Filter transfer function

9

Magnitude of acceleration due to gravity, 9.8 m/sec2

h

Altitude of aircraft measured from ground, m

hr

Reference altitude, m

hf

Initiation

altitude

the flare, m

of the feedback control law in

Altitude at which the predictive begins, m

pitch ramp command

h step

Altitude at which the predictive begins, m

pitch step command

ILS

Instrument Landing System, standard radio guidance

installed at major airports

I

Aircraft moment of inertia around y-axis, kg-m2

YY

K

Filter gain constants

L

Magnitude of aerodynamic lift force, N

L'

Vertical extent of major vertical updraft relative to

the flight path

i

Monin-Obukhov stability length

m

Airplane weight, N

vi

u*
V
'a
wX
wz
X Z 2 a Y YILS 6e
9 P -I
Tl
TO
-+ ('>

Pitch angular velocity, radians/set

Wing reference area, m2

Laplace transform operator

Sampling Friction

time interval, velocity given

set by u,

r-iTO =-It T

Magnitude of aircraft m/set

velocity with respect to ground,

Magnitude of airspeed, m/set

Magnitude of x-component of wind speed in earth axis, m/set

Magnitude of z-component of wind speed in earth axis, m/set

Horizontal coordinate, m

Vertical coordinate, m

Z-transform operator

Angle of attack, radians

Flight path angle, radians

ILS glide path angle, radians

Elevator deflection, radians

Glide slope error angle, radians

Pitch angle, radians

Air density, g/m3

Filter constant

Filter constant

Surface shear stress

Designates vector

Time derivative

vii

CHAPTER I

INTRODUCTION

Wind is an important consideration in the analysis of airplane

flight in the atmospheric boundary layer, both because of short-scale

gusts or turbulence and because of large-scale variations of the mean

wind. In the planetary boundary layer the mean wind decays toward the

ground and has considerable horizontal variations due to irregulari-

ties in terrain.

Thus, both spatial and temporal variations occur in

near surface winds encountered along ascending and descending flight

paths,

Previous analyses of airplane motion that have been carried out

[1, 2, 31 consider, in general, only constant winds and thus neglect

the effects of wind shear. This report, however, investigates the

influence of variable mean wind fields and discrete gusts on the

dynamics of aircraft during terminal flight operations,

Mathematical

models of the winds are introduced into the equations of aircraft

motion, both with fixed and automatic controls; computer solutions of

the resulting motion are carried out.

As an aircraft descends on its glide slope, a sudden change in

horizontal wind or vertical wind, or both, will instantaneously affect

the velocity of the aircraft relative to the air mass. If the shear

is such that the relative velocity of the aircraft increases, the lift

force will increase and the aircraft will tend to rise above the glide

slope. If the shear causes a sudden decrease in the relative

velocity, the aircraft will respond by falling below the glide slope,

and a hazardous condition may result.

Several reports have been published which link short and long

touchdowns to a sudden wind shear occurrence during final approach

C4, 5, 6, 71, Recent accident reports also have found wind shear to
be at least a contributing cause for several accidents [8, 91. In

addition, it is believed that wind has been responsible for many other

accidents, though it remained undetected at the time [lo, 111. The

problem of quantitatively

defining the effect of shear of given magni-

tude on an aircraft during descent has not been completely resolved.

Noteworthy studies that have-investigated

wind shear and/or turbulence

during landing include References 3, 6, 7, and 10 through 14.

Although a very complete development of the system of equations

governing airplane motion is available [1, 21, most analyses reported

to date reduce the equations to those for a constant wind or employ a

linearized model which requires the assumption of a uniform wind field

and is not applicable for non-uniform winds.

Ramifications of the airplane motion due to the effects of

temporally and spatially varying mean winds are studied in this

report, Analyses of flight paths through changing mean wind fields

reported in the literature are primarily two-dimensional and deal only

with vertically varying horizontal winds (i.e., having a component

parallel to the flat earth only).

Etkin [1] has a very complete development of the general

equations of unsteady motion. Normally, the wind components of

velocity are not included in the equations since it is assumed that

2

no wind is present. Luers and Reeves [7] developed a system of

equations in two dimensions which incorporate only horizontal wind.

Later in this report, a general form for the two-dimensional equations

of motion is developed. This accounts for both vertical and horizontal

mean wind components with both time and spatial variations.

Using this later set of equations, analyses both with fixed and

automatic feedback control were carried out. In the fixed control

simulation, the aircraft is trimned at an altitude of 91 m and on a

glide slope of -2.7 degrees. The corresponding throttle setting and

elevator angle setting are then fixed for the remainder of the

landing. These fixed control landing simulations were carried out for

several different wind fields and the deviations in the glide slope

and touchdown points are compared. In the cases with high wind shear,

the deviations are very large and in some cases the aircraft

trajectories

with fixed controls are not realistic.

To overcome this difficulty

an automatic control system was

developed for the same two-dimensional system of equations. Every

phase of the flight of an aircraft can be regarded as the accomplish-

ment of a set task, i.e., flight on a specified trajectory.

That

trajectory may simply be a straight horizontal line traversed at

constant speed or it may be a turn, a transition from one symmetric

flight path to another. All of these situations are characterized by

two corrPnon features, namely, the presence of a desired state and the

departures from it, designated as errors. These errors are, of

course, a consequence of the unsteady nature of the environment.

3

The correction of errors requires a method of measuring the error

or the desired state. Some of the state information needed (i.e., air-

speed, altitude, rate-of-climb,

heading, etc.) is measured by standard

flight instrumentation.

This information is not generally sufficient,

however, when both guidance and altitude stabilization

are considered.

For this case, the state information needed may include [1, 161

position and velocity vectors relative to a suitable reference frame,

vehicle altitude, aerodynamic angles, etc. A wide variety of devices

are used to measure these and other variables, and range from pitot-

static tubes to sophisticated inertial-guidance

platforms.

Gyro-

scopes, accelerometers, magnetic and gyrocompasses, angle-of-attack

and sideslip vanes, and other devices, all find applications as

sensors. The most common form of output is an electrical signal, but

fluidic devices [17] are receiving increased attention.

In this study we assume that the desired variable can be measured

independently and linearly, which is of course, an idealization.

Since every sensing device, together with its associated transducer

and amplifier, is itself a dynamic system with characteristic

frequency response, noise, nonlinearity and cross-coupling,

these

attributes cannot be ignored in the final design of real systems,

although one can usefully do so in preliminary work [l].

In the automatic control simulation, the aircraft is tritnned

initially

at an altitude of 91 m on a straight horizontal line

trajectory and is automatically controlled by actuation of thrust and

elevator angle. In this first phase the aircraft remains in an

altitude hold mode until it intersects the Instrument Landing System

4

(ILS) guidance beam, It then switches to the glide-slope capture mode

which actuates the thrust and elevator controls so as to capture the

-2.7 degree glide path specified by the ILS guidance beam. As soon as

the specified glide path is captured, the third phase, glide-slope

tracking mode, becomes effective.

In this mode the controls are

actuated such that the aircraft remains on the glide path. At an

altitude of approximately 18 m, flare initiation

altitude along with

other necessary parameters are calculated to begin the flare mode.

The flare mode is switched on as soon as the aircraft reaches the

flare initiation

altitude.

The aircraft remains in this mode until

the final touchdown.

For this investigation,

the scope of the automatic landing

problem was restricted in two ways. First, the aircraft simulation

equations are restricted to three degrees of freedom by considering

the longitudinal axis only. This restriction

is reasonable in the

light of the accident statistics

compiled in References [8, 91,

which conclude that accidents due to longitudinal more often than accidents due to lateral errors.

errors are fatal Second, the system

guidance information was assumed to come from error-free sensors and

an error-free ILS beam. This is beneficial to maintain simplicity of

the automatic control subroutines, since the objective of this study

is the effects of wind shear, and not a study of ILS system errors.

5

CHAPTER II

AIRCRAFT LAND1NG MODEL

1. Eauations of Motion

The two-dimensional model for aircraft motion presented in this

section follows the general form developed by Frost [12]. It accounts

for both vertical and horizontal mean wind components having both time

and spatial variations.

The aircraft trajectory model employed in this study was derived

based on the following assumptions:

a) The earth is flat and non-rotating.

b) The acceleration of gravity, g, is constant (9.8 m/sec2).

c) Air density is constant (1.23 kg/m3).

d) The airframe is a rigid body.

e) The aircraft is constrained to motion in the vertical plane.

f) The aircraft has a symmetry plane (the x-z plane).

g) The mass of the aircraft is constant.

h) Initial flight conditions are for steady-state flight.

Figure 1 illustrates

the forces acting on the aircraft.

These

include:

iT thrust of the engines L lift

d drag

fi wind velocity

4 gravitational

force.

6

FRL /
-+

-.
+ D &
_______! Z

'?L X

Figure 1 Relationship between the various forces acting on an

aircraft

[lZ]

7

The figure shows the orientation of the forces with respect to

the ve1ocit.v relative to the earth (c), the velocity relative to the

air mass (Ta), and the fuselage reference line (FRL) of the aircraft.

The x-axis in Figure 1 is parallel to the surface of the earth and the

z-axis is perpendicular to the surface of the earth (positive down-

ward).

From a direct force balance along the direction c and along the

direction perpendicular to 3, respectively,

it follows from Figure 1

that

mi = - L sin 6 - D cos 6 - mg sin y + FT cos (6T + a)

0)

and

mV+ = L cos y - D sin 6 - mg cos 6 + FT sin (6T + a) .

(2)

The aerodynamic forces and the thrust from the engines exert a

pitching moment on the aircraft.

The equation describing the momentum

balance about y is

2 ;I=d=-

FTLT - M

(3)

dt2 'yy + IYY '

where the dot refers to the derivative with respect to time, and !3 is the magnitude of the acceleration of gravity, V is the magnitude of the velocity relative to the earth, Y is the angle between 3 and the x-axis (the flight path angle), FT is the magnitude of the thrust vector, m is the aircraft mass,

8

6T is the angle between the thrust vector and the fuselage reference line (FRL),
a is the angle between 3 and the FRL, 6 is the angle between ia and ?, 4 is the time derivative of the pitching rate, q, LT is the effective moment arm of the thrust vector, M is the pitching moment, and I yy is the moment of inertia about the symmetry plane of the
aircraft.

By considering a different coordinate system in which the x-axis is along the vector qa, called "wind" frame of reference by Etkin [l], similar force equations can be developed by summing up the forces parallel and perpendicular to Ta. These are

m(\ja + fix ) + mq, Wz = F.,- - D - mg sin y'

(4)

W

W

X W

and

mljz - ww(Va + W, ) = FT -L+mgcosy'

.

(5)

W

W

z W

It is convenient to express these in terms of the wind components relative to an earth fixed coordinate system, since most wind correlations from the meteorological literature are expressed in such coordinates.

wX W’ = Wx cos y' - W, sin y' ,

(6)

wz= Wx sin y' + W, cos y' .

(7)

W

Taking the time derivative

of Wx , we get
W

= Ij,
9X W

cos y'

- AZ sin

y'

- Wx sin

y'

ddty'

- wz cos y'

$$

.

(8)

Then, since q, = -ddyt-' ,

iX W = W, cos y'

- iz

sin

y'

- W, q,
W

.

(9)

Also, since
= FT cos(bT + a') , and
FTX W
= FT sin(bT + a') ,
FTz W
Equation (4) becomes
m\j, = FT cos(AT + CL') - D - mg sin y' - m(i, cos y' - iz sin y') . (10)

From Equation (7), taking the time derivative

of Wz , we get
W

% = ix sin y' + W, cos y' + w, cos y' g- - Wz sin y' *d' ,

(11)

W

and Equation (5) becomes

- mV, q, = - FT sin(6T + a') - L + mg COS y'

- m(dx sin y' + Wz cos y') .

(12)

The moment equation remains the same as Equation (3). The governing force equations in "wind" frame of reference are thus

10

mSa = FT COS(~~ t cl') -r D - mg sin y'.

- m(rjx cos y' - tiz sin y') ,

(13)

mV,+' = FT sin(6T + a') t L - mg cos y'

t m(cix sin y' + Pz cos y'i ,

(14)

qw=r FTLT + -3M

(15)

YY

IYY

where Wx is the horizontal wind speed, W, is the vertical wind speed, and ~1' (the angle of attack) is the angle between ca and the FRL.
2. Incorporation of Wind Shear The wind is seen to enter the equations in the form of a gradient
or wind shear ix and fiz. The expanded form of these equations is:

lj,=+-- aw or

awx dX -a-wx dZ
ax d-t ’ az dt

fix = -a-gw-X+ v [ cos y -aawx)(- si.n Y -a1awz,X

(16)

and, similarly,

aw

aw

aw

iz = +tV[cosy$-siny-$].

(17)

Thus, both spatial variations and tempo;-al variations motion influence the equations in the wind coordinate

in atmospheric system.

11

Generally, care is needed in evaluating aazwX and aazwZ since the

wind speed is normally expressed in terms of altitude measured upward

from the surface of the earth, whereas in aerodynamic coordinates, Z

is measured downward. Additional kinematic

relationships

necessary to solve for the

aircraft motion are as follows: The relative velocity as a function

of inert ial and wind velocity

is

= [ (i - wx)2 + (i - wzj2 1l/2
'a

,

08)

and, in turn, V= wx cos y - Wz sin y + [(Wz sin y - Wx cos y12

l/2

t vz - (w2 + Wf, 1 X

*

(19)

The angle between ? and ca is given by

Wx sin y + Wz cos y

sin fS=

.

(20)

va

Other angular relationships

are

a ’ = e-y-6=0-y’,

(21)

a =e-y.

(22)

The derivative of a' is

a*I =f? -i/L

q - ;’ )

12

where y' is given by Equation (14), hence,

a*I =q-

FT sin(6T + a')

L

--

mVa

mVa

+ 9 cos y' tf

[Ox sin y' + iz cos y'] .

(23)

va

a

Also required for solution aerodynamic coefficients

of the preceding equations are the

cL = cL b', &E, va' q, 4') ,
$, = CD b’, $ va’ q, i’, cL) 9

cm = cm b’, 6E’ va’ 93 i’> ,

(24)

where 6E is the elevator deflection angle. As indicated above, the

aerodynamic expressions

coefficients

are functions of a number of variables.

The

for CL, CD, and Cm, along with the stability

derivative

data and aircraft physical data are given in the Appendix.

The equations of motion discussed in this chapter can be solved

for the flight of an aircraft flying through spatially and temporally

varying two-dimensional wind fields.

In this study we have used three

different wind shear models,

1) atmospheric flow over homogeneous terrain,

2) atmospheric flow over buildings, and

3) atmospheric flow associated with thunderstorm gust fronts.

The initial conditions used in this simulation are for that of a

pitch stabilized aircraft,

given by

13

Altitude = 91 m

'a

= 70 m/set

'a

= 0

Y.I

=

0

;r

=

0

‘4

= 0

a*I

= 0.

Under these conditions the initial values of thrust, elevator angle and angle of attack were calculated from Equations (13), (14) and (15).

14

CHAPTER III

MATHEMATICAL MODELS FOR VARIABLE WIND FIELDS

1, Atmospheric Flow Over a Homogeneous Terrain

The mean velocity in the region of the atmosphere near the ground

is described by a logarithmic function of altitude.

The surface

roughness characteristic

of most natural terrains is generally

described in terms of a vertical scale, Zo. For a neutral atmosphere,

experimental evidence [18, 191 confirms that the mean wind velocity in

the region near the ground can be described by a logarithmic wind pro-

file (Figure 2). The logarithmic wind profile is thus [20], given as

a function of altitude Z,

z t z.

Wx(z) = : In ( z ) ,

(25)

0

where Z. represents the surface roughness, and K is von Karman's

T

constant.

u, is the friction

velocity given by u, =I/- $ , where ~~

is the surface shear stress, and p is the air density. Observed

wind profiles up to 150 m, over reasonably level and uniformly rough

terrain, with neutrally stable conditions, obey this law reasonably

well [20].

2-.- Atmospheric Flow Over Buildings Since the wind shear models for the flow over a block building
and a step are completely described by Sheih, et al. [22] and Bitte

15

Z
Figure 2 Logarithmic wind profile 16

and Frost [23], respectively,

only a cursory description of the models

is presented here.

The distorted shear flows approaching and passing over a building

can be divided into a displacement zone, an upstream bubble or down-

wash zone, and a wake zone which includes the rear separation bubble

or cavity zone (see Figure 3). The effect of shear in the approaching

flow creates a downwash on the front face and a swirling flow in the

wake or cavity zone. Undisturbed, neutrally stable atmospheric wind

perpendicular to the axis of the building is assumed far upstream and

far downstream of the obstacle (see Figures 4 and 5). The atmospheric

wind field is analyzed by using the Navier-Stokes equations with a

two-equation model, one for the turbulence kinetic energy and the

other for turbulence length scale. In this approach, the partial

differential

equations for the vorticity,

stream function, turbulence

kinetic energy, and turbulence length scale are solved by a finite-

difference technique.

Both vorticity contours (Figure 6) and streamline patterns

(Figure 7) confirm the experimental evidence of a small downwash zone

near the front lower corner and a large recirculation

zone behind the

obstruction.

Figures 8 and 9 show the computed velocity profiles at

selected X-stations in the region close to the wall. The flow is

decelerated as it approaches the obstruction and is accelerated as it

passes over the obstruction.

In the region above the recirculation

zone, the flow is accelerated because of the displacement of the flow.

The flow re-attaches near X = 12.3H and the logarithmic boundary

17

Upstream separation bubble or down wash zone

Rear separation bubble or cavity zone

Approaching

'

velocity

profile I

Redeveloping, boundary layer I

Reattachment flow zone Figure 3 Definition of flow zones near a sharp-edged block [22]
18

Z = 6.0 H
l I
El 2 Neutrallv stable inflow

Upper Boundary

z 0.75 H

r

Block geometry obstacle

X = -10.0 H

Wall Boundary

I I
X = 20.75 H

Figure 4 Description of flow region considered for a block building [22]

Z = 9.0 H

Upper Boundary

c Velocity Profile

X = -10 H

X=lOH

Figure 5 Description of flow region considered for a long, wide building [23]

Vorticity

-9.97 -7.97 -5.97 -3.97 -1.97

0.03 2.03 Horizontal

4.03 6.03 8.03 10.03 12.03 14.03 16.03 18.03 20.03 Distance X/H

Figure 6 Vorticity contour [22]

-1.97

0.03

2.03

4.03

6.03

8.03

10.03

12.03

14.03

16.03

18.03

20.03

Horizontal Distance X/H

Figure 7 Streamline patterns [22]

Z/H t
6.0

0 5 10 m/set

N w

-10.0

-1.25

0 0.75 2.75

5.75

9.75

17.0

20.0

X/H (H = 3.2 m)

Figure 8 Velocity profiles over an obstruction on the surface [22]

Scale 0 10 , . *

20 Cm/set) for u* = 0.75 m/set I

Horizontal

Distance X/H

Figure 9 Velocity profiles over a step geometry long wide building [23]

layer begins to re-establish downstream. These results seem to agree

very well with the limited experimental data available.

The velocity distributions

of the atmospheric flow around

buildings are especially important in the design and operational pro-

cedures for helicopters and V/STOL aircraft operating in large

metropolitan areas.

& Atmospheric Flow Associated with Thunderstorm G-u~s-t Fronts Gusty winds are undoubtedly the most hazardous for an aircraft to

negotiate.

One of the most common causes of significant

wind shear is

the gust front associated with thunderstorms.

The thunderstorm gust

front is believed responsible for several accidents [S, 221. The

severe wind shear accompanying thunderstorms is generated by a

vigorous rain-cooled downdraft, which spreads out horizontally

from

the storm cell as it approaches the ground. The cold outflow is led

by a strong, gusty wind which often occurs as much as 16 km ahead of

the storm, called the gust front.

Mathematical schemes for computing wind fields associated with

thunderstorm gust fronts are still in the formative stages. After

extensive study of gust front characteristics

and the available gust

front data, Fichtl and Camp [26] have presented a mathematical model

which describes updrafts and downdrafts associated with gust fronts

along a given approach path. This model incorporates both scaled vertical wind speeds along a -2.7 degree glide slope from the gust

front data of Goff [27], and the vertical wind speeds reconstructed

from the digital flight data record of Eastern 66 [8]. The sequence

25

of vertical wind speeds encountered by an aircraft given by the following:

during landing is

Major downdraft:

X -X

wz = - P1 A sin (r

9

q1

; z. 1 z > zr

Major updraft:
(1- 2q,)U-$J3+(1- 3qpx - XJ2 + (2q, - 3q@ - $1
wz =A - s;bl, - u2

; Zr)Z,Zr

- L’

Minor downdraft:

wz = - P2 A sin (K 'r -1-x 42

> ; (Z,-L)

> z -> (zr-(1+q2)L')

Minor updraft:

wz = P2 A sin(n where

'r -1-x 92

1 ; c zr - (1 + 42) L’l ’ z 2 I: zr - (1 + 2q2) L'l

x, = p'r- ; x=3.

The various quantities in the above equations are defined as follows: W, = thunderstorm cold air downdraft, Z = vertical coordinate, ZD = altitude of the top of the major downdraft,
26

'r = altitude zB = altitude A = amplitude

of the top of the major updraft, of the bottom of the minor downdraft,
of major vertical velocity updraft,

L' = vertical extent of major vertical velocity updraft relative

to<he flight path,

p1 = ratio P2 = ratio

of major downdraft of minor downdraft

to major updraft or minor updraft

velocities, to major updraft

velocity,

q, = (Zr - Z,VL’,.

q1 = (Zr - Z&L', q2 = (Zr - ZB - L')/L'.

The values for the cold air outflow lation study are that of typical vertical provided by NOAA/NSSL [27]:

parameters used in this simuwind speeds derived for data

L' = 91 m ZR = 152 m A = 15.0
P1 = 1.2
P2 = 0.35
90 = -0.36
q1 = 2.0 92 = 2.3.

In this wind shear model, the vertical winds due to the thunderstorm gust front described above are superimposed on a stable

27

atmospheric boundary layer. ditions is given by

The mean wind velocity

under stable con-

Wx(z) = 2

1 z + z.

ln(

z ) + 5.2 ; ,

0

where i is the Monin-Obukhov stability length.

28

CHAPTER IV

AUTOMATIC CONTROLSYSTEM

The two principal quantities that need to be controlled in

symmetric flight are speed and flight path angle, i.e., the vehicle

velocity.

To achieve this, control forces are needed both parallel

and perpendicular to the flight path. Parallel force is provided by

thrust or drag control, and perpendicular force by lift control

achieved via elevator deflection.

It is evident from simple physical

reasoning (or from the equations of motion) that the main initial

response to opening the throttle (increasing the thrust) is a forward

acceleration,

i.e., speed control,

The main initial response to

elevator deflection is a rotation in pitch, with subsequent changes

in angle of attack and lift, and hence, development of ;, a rate of

change of flight path angle. When the transients that follow such

control actions have died away, a new steady state is achieved.

In this section the longitudinal automatic landing system will be

described, and some of the design considerations will be given.

It has been shown in Reference [24] that turbulence causes larger

deviations from the desired flight path than the errors in ILS

guidance. This study, therefore, concentrates on the effect of wind

shear on safe automatic landings. assumed to come from an error-free

The system guidance information is

ILS beam and altimeter.

Reference

[S] has an excellent discussion on longitudinal automatic landing and

aircraft control laws. The overall control system can be represented

29

I-

in the form of a block diagram as shown in Figure 10. The flight

control laws are segmented into control modes for different portions

of the approach and landing,

In the various control modes the linear filters are described by

transfer functions.

The filtering

function, however, is actually per-

formed in the digital computer by solving difference equations.

Simulating a linear system with the appropriate difference

equation is more efficient than solving the differential

equations

directly by numerical integration.

Numerical integration would be

rather a lengthy process and may be unstable for large sampling

intervals [3]. The difference equation for one of the linear filters

used in this simulation can be derived as follows:

---Y- (s) - KS Gk4 - x(s) s+a '

The response of the filter to a unit step input is

y(S) = &$=

Ks+a or y(t) = K eBat 6(t) .

Taking the z-transform,

Y(Z) = zD:aT

'

Factoring the z-transform of a unit step function from y(z),

y(z) = K '-'

--? .

z-e-aT Z-l

30

Initial conditions

t

Aircraft

5

dynamics

Position

W L

Mode Selector

1

Figure 10 Overall block diagram of control system

Since the response to a general input is wanted, replace the step input by a general input x(z). The actual input is approximated by a linear combination of unit step functions and is equal to the general input at the sampling points,

y(z) = K '-'

x(z) .

z - ewaT

Cross-multiplying, (z - e -aT) y(z) = K(z - 1) x(z) , Dividing throughout by z,

-)Y(z)

= K (1 - t, x(z) .

Transforming to the discrete time domain,

-aT Y, - e yn-l

= K$,

- xnml) 9

and rearranging, the final form of the difference equation is obtained,

yn = eBaT ynel + K(x, - x,,-~) .

At the sampling points the difference equation is the exact solution for the response of the equivalent analog system. The difference equations for the various filters were compared to those obtained using numerical integration (fourth-order Adams-Bashford); it was concluded that the computation efficiency of the difference

32

equations is better nique [3].

than that of the numerical

integration

tech-

1. Mode Selector

The mode selector automatically selects the proper control mode

in sequence (i.e., the altitude hold, glide slope capture, glide-slope

tracking, and flare mode) according by the desired flight path.

to predetermined

criteria

defined

In accordance with conventional practice [25], the control modes

operate on the velocity and pitch stabilized aircraft and therefore

operate with only two command variables:

speed command, Vc, and

pitch angle command, 8,.

The mode selector is best described by considering a landing

approach (see Figure 11) and the flow chart (Figure 12). The aircraft

approaches the ILS glide slope at a constant altitude of 91 m until

the aircraft intercepts the ILS beam. During this time the mode

selector maintains Mode 1, i.e., the altitude hold mode. As soon as

the aircraft penetrates the ILS beam, the mode selector compares the

aircraft position to the point of intersection of the horizontal

flight path and the ILS glide slope; when the aircraft reaches that

point it switches to Mode 2, the capture mode. The capture mode is

timed and the flight path angle is compared with the desired glide slope; as soon as the desired glide slope is reached the mode selector

switches to Mode 3, the glide-slope tracking mode. Glide-slope

tracking proceeds to a preselected altitude, at which point the sink rate and velocity of the aircraft are used to calculate the flare

33

Altitude

Glide-slope capture
hold 1

I Flare I I I

Figure 11 Automatic landing geometry using ILS 34

Altitude hold

Calculate

initiation

\/

altitudes

F

F

1

T

Glide-slope

5 tracking

Glide-slope capture
Y To next subroutine
Figure 12 Mode control logic
35

Flare

initiation

altitude (hstep ) and other initiation

parameters described

in the flare-mode selection.

The mode selector then switches to

Mode 4, the flare mode, when hStep is reached.

Notice that no automatic go-around mode is provided; the simu-

lated aircraft is forced to land so that the conditions can be found

that result in unsatisfactory

landings.

2. Altitude Hold Mode

A simple hold mode incorporated in the system keeps the aircraft

flying at a constant altitude.

The digital control was modeled after

the representative analog system shown in Figure 13. The system con-

sists of a differencing circuit for calculating the altitude error,

Ah, followed by a low pass filter, a gain, and a low gain integrator.

For comparison, digital equivalent equations are as follows:

8
3

= c1 OCjBl

+ c2 ecje2

t

c3 Ahj

+ cy AhJ.-1

’

Ahj = h.J - href ,

8. J

= cl

‘j-1

+ ~2 Ahj-1 3

8, = ec t k2 ej t c3 ejml .

j

j-l

These equations are solved once each computation cycle. The constants, cl, c2 and c3, are given by

36

h 4 +
IAh
t K1
s+a 1 -
Typical values K1 = 0.1 al = 1.0 K2 = 0.05 a2 = 0.1

K2

*

1+ ya-2

Figure 13 Altitude hold mode

37

c1

=e

alT ,

c2 =qk”l -cl) ,

c3 = k2 (a2 T - 1) , where T is the sampling interval.

3. Capture Mode

The capture mode (Figure 14) provides for a smooth rotation from

level flight to the glide-slope angle. In this mode a step pitch

angle command, A0 is applied to rotate the airplane. P'

The magnitude

of the step is based upon the glide slope angle of the beam to be

captured. In addition, an inertial vertical velocity error signal is

generated to increase the sink rate for a given glide-slope angle.

The error signal, 8e, is then integrated and filtered to produce the

pitch angle command. The integrator provides an error signal pro-

portional to the altitude error. Since the sink rate reference value

is the proper sink rate of the aircraft on the glide slope, the

resulting altitude reference is a parabolic curve that smoothly

intersects the glide slope.

The difference equations are as follows:

8EJ. =hc-h., 3

% j = ‘1 ‘Cj_1 - ‘2 ‘Cj-2 + ‘3 ‘Ej-1 + ‘4 ‘~j-2 + aBp ’

38

@E *

K3 s

5

K4

-rls + 1

Typical values
K3 = 0.05 K4 = 0.01
T1 = 0.01

of capture

Figure 14 Glide slope capture mode

Rate limiter

39

where = 1 + ,-T/-c ,
c1

c3 = k3 k4 C T + y k2 - 1) 1 , c4 = k3 k4[T - c2 (T + T)] .

4. Glide-Slope Tracking Mode

After glide-slope capture the aircraft remains in the glide-slope

tracking mode (Figure 15) until flare. The glide-slope error angle,

E, is passed through a low-pass filter, a gain, and then a low-gain

integrator.

In addition, two differencing circuits are used which

estimate the approximate altitude error for the next step and give

pitch error signal, 8. This extension is a pitch altitude command,

eCy proportional

to h-h, and also 6 - Gc, where hr is the reference

altitude and Lc is the proper sink rate for the given glide slope.

The digital equivalent equations are as follows:

= Yj - yref '
3

8. = k4 (hj - hr) + kg (~j - ~c) )
J

ePj = '1 epj-l + '2 ‘j-1 ’

8E.
J

=

8
'j-1

’ k6 epj ’ ‘3 epj-l

’

8 2

= ej + ‘E.J ’

40

r

e

E

L

53

-c2 s+a 2

P * K6

Typical values
K3 = 1.0 K4 = 0.05 K5 = 0.00325 K6 = 0.00125

T2 = 0.01 a2 = 1.0 a3 = 0.01

c 1+y a3

%

Figure 15 Glide slope tracking mode 41

where

-- a2T

cl=e

T2 ,

c2 = qk3 (1 - Cl) 3

c3 = k6 (a3T - 1) .

5. Flare Mode The flare mode controls the traditional
The flare has three boundary conditions,

exponential flare [25].

hf initiation

altitude of feedback control law,

Lf initial

sink rate,

desired vertical touchdown velocity.

A flare law that satisfies these boundary conditions is developed

by Neuman and Foster [3]. A modified version of this flare law is

used in our simulation.

The equation that satisfies the boundary

condition is:

-t/a4

hr(t) =[hf - a4 if ]e

+ a4 i)f, ,

(26)

0

and a4 is calculated as

a4 = hf/(if

- r;, ) .
0

(27)

42

The reference sink rate is the derivative of Equation (26),

‘hr = - (l/a41

-t/a4 (hf - a4 lif > e

.

(28)

0

The predictive portion of the flare law (Figure 16) has two sections,

a step command in pitch, A8 which causes the aircraft P'

to begin to

rotate, an-d a ramp pitch command, AeR, which begins somewhat later.

With no other disturbance, the predictive flare commands will

generate an approximately exponential flare. Feed-back is used to

overcome disturbance.

Equation (26) is the solution of the following

differential

equation:

hr.+ a4 (t!~ - if ) = 0 ,
r 0

(2%

with the boundary conditions hr = hf at t = 0, and ir = if at h = 0.

The feed-back version of the flare law generates a correctgve signal

when Equation (29) is not fulfilled

by the actual altitude, h, and

sink rate, 6, in place of hr and ir. The corrective signal is (see

Figure 16):

'fb = Kf[l+

$][h+a4

(i - if) 1 3

(30)

which is added to the predictive pitch comnand. Hence, no correction signal is applied when the reference path is followed.
When the flare subroutine is entered for the first time, the sink rate is used to calculate decision altitudes for the predictive flare law connnands. The altitudes at which these initial calculations are made are somewhat above the highest value at which the flare may be
43

-

h
+ t T Kf
"fb -
2 1. of Ae,blO 2. If ABfb<O

h step h
ramp
hf 8

. = 1050 +

= 0.6 = 0.8 = 0.9

h step
h .steP Q

= CO.255 4 - 0.000132)T

= 0.00024 Kf

K

= 2.0

a4

= 5.0

a5

= 0.00333

a6

= 4.0

a5
1 -s

a5

2

Closed

'fb

h=hf

\

I

KS S + a6

Figure 16 Flare mode 44

started. The step command altitude is proportional to the flight-path

angle, y z i/v. The ramp begins at a proportionally

lower altitude.

Since the aircraft does not begin to deviate from a straight-line

glide path instantaneously , upon receiving the pitch step command, the

altitude for the corrective feed-back to begin is also selected pro-

portionally lower than the step command altitude.

After these

calculations are completed, the flare mode transfers the authority

back to the glide-slope tracking control.

When the step command altitude,

hstep' is reached, the flare

control mode takes over completely and from the sink rate, fi, dalcu-

lates and executes A0 Then the ramp increment, AOR, and the feedP'

back gain constant, a4, are calculated.

At this point the mode

controller is switched to its final submode.

In the final submode the predictive ramp pitch command is added

to the corrective feed-back flare command. The summed signals are

transmitted as the pitch change command, Bc.

Under disturbances, the feed-back term in the flare law does not

attempt to guide along a path fixed in space, or even hold h(t) and

e(t) at given values: As long as the feed-back signal of Equation

(30) is zero no correction is made. Disturbances, therefore, tend to

cause translations of the touchdown point rather than large maneuvers

to meet a given touchdown point, which would often cause hard

landings,

45

6. Calculation of the Feed-Back Controls

To control the flight path of an airplane automatically,

it would

be desirable to control the flight-path

angle, y, directly.

However,

there is no output control variable that controls y. In linearized

models [1], the steady velocity, d, at which the airplane flies is

governed by the lift coeff;cient;

which is in turn fixed by the

elevator angle, implying that a constant AE gives a fixed ?. Also,

the flight path angle, y, at any given speed is controlled by the

thrust in the long term, implying that the ultimate result of moving

the throttle at fixed elevator angle is a change in y without change

in speed. But, by physical reasoning [l], we know that initial

response to opening the throttle is a forward acceleration,

and

initial response to elevator deflection is a rotation in pitch; hence,

the short term and long term effects of these controls are quite

contrary.

The total picture of longitudinal

control is clearly far

from simple when we represent the aircraft motion with a non-linear

system of equations.

To make short and long term responses agree, the aircraft is

stabilized in the following manner. The speed of the aircraft is kept

nearly constant throughout the landing operation and flight path is

controlled by means of both throttle and elevator angle deflection.

The thrust control loop maintains constant airspeed by generating a

thrust command signal to drive the throttle servo (Figure 17). The

thrust command signal is derived from airspeed error, horizontal and

vertical acceleration,

and the pitch command signal. These four

signals are processed by passing through variable gains and a

46

‘a

D

K
T1

. x V
F T C
Figure 17 Feedback loop-thrust 47 -_-

differencing circuit so as to generate a thrust command signal of

correct magnitude. The elevator control loop generates an elevator

angle command signal to drive the elevator angle servo (Figure 18) so

as to maintain air velocity constant and control the flight path. The

elevator angle command signal is also derived from airspeed error,

horizontal and vertical acceleration,

and the pitch comnand signal,

and then passed through variable gains. The thrust command signal and

elevator angle command signal are given by

FTc = KT1 "a
6EC = KDIVa

.

.

- KT2 v'+K T3 'v + KT4 ec ,

.

.

- KD2 ; - KD3 f + KD4 ec ,

where KT1 and KD1 are the variable gains calculated from the system Equations (13), (14), and 15) under zero wind conditions, given by

Gil

-G12

0

0

-D2

0

-1

0

7
H9 H1O , L H1l

KD1
KD2 -1
KD3 -! KD4

-G1o Gil

= -D2

0

-

0

-D2

0

-1

-

I iH6 H7
c H8 -1
48

V a

c

K D1

% C -i

KS
hS+al) [(S+a212+b2] I-

Figure 18 Feedback loop-elevator angle 49

where

G1 = D7 G2 = - (C1+C2 a) cos(y' -y)-C3

sin(y' -y)

G3 = - C4 sin(y' -y)

G4 = D6 cos(6T+c) G5 = C3 cos(y' -y)-(C1+C2 G6 = c4 cos(y' -y) G7 = D6 sin(6T+a) G8 = C5

cd) sin(y' -y)

G9 = c6 G1o = c7vacos(y' - y)+(C8Va+C9q+ClD&')sin(y'-y) Gil = (C8Va+Cgq+Clo~')cos(y'-y)-C7Vasin(y'-y)

G12 = Cl1 va+c12q+c13c? H1 = G6G1 - G7G9 H2 = G5G1 - G7G8 H3 = G5Gg - G6G8 H4 = G2H1 - G3H2 + G4H3 H5 = vf H4 H6 = Hz/H5 H7 = (G2G1 - G4G8)/H5 H8 = (G2G7 - G4G5)/H5 H9 = H3/H4 H10 = (G2Gg - G3G8)/H4

Hll = (G2G6 - G3G5)/H4 ,

with the Cn values provided in the appendix.

50

CHAPTER V

RESULTS AND’DISCUSSION

The two-dimensional equations of motion, Equations (l), (2), and

(3), for the aircraft discussed in Chapter II were solved on a digital

computer using a fourth-order Runge-Kutta technique. Wind models

incorporated into the governing equations include (1) atmospheric flow

over simulated buildings, (2) atmospheric flow in the absence of

buildings, and (3) atmospheric flow associated with thunderstorm gust

fronts. The influence of these wind fields on the aircraft landing

under different conditions of terrain roughness is investigated,

The

aircraft characteristics

used in the simulation are that of the DC-8

and the DHC-6, specifications

of which are given in the Appendix. The

initialization

conditions for the simulated landings of the aircraft

with fixed controls are trimmed conditions on a -2.7 degree glide

slope, with the descent beginning at an altitude of 91.4 meters (300 feet).

This corresponds to a touchdown point of 1939 meters (6361 feet),

down range from where the descent begins. Any variation in

winds will cause the aircraft to deviate from the glide slope. The

deviation in touchdown point for fixed control conditions is defined as

the distance between the actual touchdown point and the intended glide

slope touchdown point.

Figures 19 and 20 show the descent trajectories

of the aircraft

into a wind blowing over a two-dimensional bluff-type body, similar to a block building, and a step, similar to a long, wide building,

51

zO = 0.2 m

0

zO = 0.4 m

D

zO = 0.8 m

0

Horizontal distance X (II-I) Figure 19 Fixed control landing over a block building

zO = 0.45 m -0 zO = 1.0 m -0

Horizontal

360 distance

X (m)

Figure 20 Fixed control landing over a step

respectively.

The heights of the simulated block building and the

step building are of 20 m and 10 m, respectively.

Figure 21 shows the

trajectories

of the aircraft in identical wind conditions without the

presence of the building (i.e., the neutral atmospheric boundary

layer), and Figure 22 shows the descent trajectories

of the aircraft

into the wind fields characteristic,

of a thunderstorm gust front.

Figures 23 and 24 show the winds, both horizontal and vertical,

that were encountered during the descent of the aircraft through the

building-disturbed

winds --a block building and a long, wide building,

respectively.

Figure 25 shows the horizontal and vertical winds that

were encountered by the aircraft during descent through the thunder-

storm gust front. Three flow conditions were used in each simulation

of the wind fields for the flow over the block building, for the

atmospheric boundary layer flow without the building present, and for

the thunderstorm gust front. The surface roughness parameter, Zo, was

parametrically

assigned the values of 0.2, 0.4 and 0.8 m, with corre-

sponding friction velocities,

u,, of 1.25 m/set, 1.4 m/set, and

1.6 m/set, respectively.

These combinations of friction velocity and

surface roughness give wind speeds of 12.3 m/set, 11.4 m/set, and

10.4 m/set, respectively,

at an altitude of 10 meters. For simu-

lation of flow over a long, wide building, surface roughness values of

0.45 meters and 1.0 meters were used, with an assigned wind speed of

10 m/set at an altitude of 10 meters. This corresponds to friction

velocities of 1.27 m/set and 2.5 m/set, respectively.

Figures 26, 27, 28 and 29 show the landing trajectories

of the

aircraft with automatic controls, through the atmospheric boundary

54

zO = 0.2

0

zO = 0.4 -D

zO = 0.8-

0

10'00

2600

Horizontal distance X (m)

Figure 21 Fi'xed control landi‘ng in the atmospheric boundary layer

26bO

1 1000

I 2000

1
2600

Horizontal

distance X (m)

Figure 22 Fixed control landing in thunderstorm gust front

24222018-
X

2.0

zN

a

1.0

.5
3

= 0.4 zO

-a

zO = 0.8 -0

Figure 23 Wind distribution flight path

over a block building along the

57

21.0 14.0
7.0 0.c

zO = 0.45 m

a

X

Z 0 = 1.0 m

0

Figure 24 Wind distribution the flight path

over a long, wide bui'lding along

58

3x 21-

423

l-l 14-

J

0"

.:

7-

g
X

0

X

14-r

2 -r: .E

aBN 7-

.35

7

.:

:s:

0

-3.5zO = 0.2 m-o

0 a

Cl

zO = 0.4 m-6

\ X
zO = 0.8 m-0

Figure 25 Wind distribution the flight path

in the thunderstorm gust front along

59

zO = 0.2

0

zO = 0.4-

0

zO = 0.8-

0

1000

2000

2600

Horizontal

distance X (m)

Figure 26 Automatic landing in atmospheric boundary layer

I -c-nI

zO = 0.2

0

zO = 0.4

a

zO = 0.8

0

10-00 Horizontal

distance X (m)

Figure 27 Automatic landing over block building

zO = 0.45 m

a

zO = 1.0 m

0

1600

2000

2600

Horizontal

distance X (m)

Figure 28 Automatic landing over a long, wide building

-

loo-/

z. s 0.2

0

za 3 0.4

a

z. s 0.8

0

m W

lQO0 Horizontal

distance X (JII)

2QQQ

26QQ

Figure 29 Automatic landing in the flow associated with thunderstorm gust front

layer without the presence of the building, flow over a block building,

flow over a long, wide building, and a thunderstorm gust front,

respectively;

The same wind field simulations that were used in the

landjng simulation with the fixed controls are applied here also.

Figures 30, 31 and 32 show the controls, thrust and elevator angle,

that were actuated by the automatic control system to track the glide

slope through the block building, the long, wide building, and the

thunderstorm gust front disturbed wind fields, respectively.

Addi-

tionally, Figure 33 shows the trajectory of an aircraft with the

characteristics

of a DHC-6 Twin Otter with automatic controls landing

through the atmospheric flow over a block geometry building.

The deviations from the touchdown point in the different wind

fields are presented in Table 1, Note that a positive deviation

indicates a long landing and a negative deviation indicates a short

landing. The deviation point for the automatically-controlled

air-

craft was taken as the difference between the actual touchdown point

and the touchdown point determined by the prescribed trajectory.

This value is computed, as illustrated

in Figure 34, by adding X = 3h,,

the specified condition for capture to begin, AX = 0.02hr required
cap for the glide slope to be captured, Z, cot yo, the horizontal distance

covered while on the glide slope, and 0.2hr cot yf, the horizontal

distance traversed during flare. The value of yf is specified as

1.35 degrees.

One observes that the aircraft made short landings in almost all

cases with fixed controls.

By comparing the landing of the aircraft

in the atmospheric

boundary layer,

with and without
64

the presence of the

w

0

2

-2

lFa

8

-4

4J

kz

-6

rl w

-8

2 - arl
x
LCD -mlJ 2 i2

1.81.40.910.45-

x

zQ =1 Q.2 m

0

zQ = 0.4 m

0

zO = 0.8 m

0

FPgure 30 Controls requi,red for 1andi:ng over a 61ock bui‘ldi‘ng

65

1.6

E 0.32-

X

zO = 0.45 m

n

= 1.0 m zO

0

Fi‘gure 31 Controls requi.red for landing over a step 66

-6 -8

* 2.70 d x 1.8-
B
b4 0.914J 3
X

zO = 0.2 m

0

zO = 0.4 m

n

zO = 0.8 m

0

Figure 32 Controls required for automatic landing in thunderstorm gust front

67

100 91.4

N

z

-34

50

x 4

zO = 0.4 m U* = 1.4 m/set
Wspeed = 11.42

m/set

at 10 m altitude

Horizontal

distance X (m)

Figure 33 DHC-6 landing through atmospheric flow over a block building

Table 1. Deviation from touchdown point

Wind Condition

With Fixed
Controls (meters)

With Automatic Controls (meters)

I. Flow over a building

(1) Block geometry

a. Zo=0.2m u,=1.25m/sec

-198

4-35

b. Zo=0.4m u,=1.4 m/set

-309

-30

C. Zo=0.8m u,=1.6 m/set

-415

-5

(2) Long step geometry

a. Zo=0.45m u,=1.27m/sec

-147

-15

b* Z0' =l.Om u,=2.5 m/set

-185

+ll

II. Flow without building present

a. Zo=0.2m u,=1.25m/sec

-313

-14

b. Zo=0.4m u,=1.4 m/set

-328

+7

C. Zo=0.8m u,=l.6 m/set

-350

+6

III. Flow associated with thunderstorm gust fronts

a. Zo=0.2m u,=1.25m/sec

-223

+19

b. Zo=0.4m u,=l.4 m/set

-80

+8

C. Zo=0.8m u,=1.6 m/set

+505

-27

69

-O.O2h,
T
3 = 0.78h 1:

0.2hr

t- 3-o --i-e

z1 cot Y. -----+-

0.2hr cot Yt --I

X

Hold Capture

Track

Flare

Figure 34 Automatic landing reference trajectory

building, one can observe the effect of complex wind patterns caused

by the presence of the large bluff objects. The aircraft lands

approximately 300 meters short of the touchdown point in the atmospheric

flow without the building, which is a direct result of the decreasing

head wind with elevation.

However, this is a predictable effect and

all landings are within 37 meters of one another, as shown by Figure 21,

page 55. Landing through the same atmospheric flow over buildings,

however, causes larger variations in touchdown point between the

different wind conditions.

With a surface roughness value of 20 cm

the aircraft lands approximately 200 meters short, whereas for a Z. of

80 cm the aircraft lands approximately 400 meters short.

This variation in touchdown points can be explained by looking at

the winds encountered by the aircraft along the flight path; see

Figure 23, page 57, and Figure 24, page 58. The aircraft encounters

an increased head wind (positive horizontal shear) and a downdraft

just before the building.

An increasing head wind during approach

with fixed controls causes the aircraft to be high on the glide slope.

This effect is absent in the undisturbed atmospheric boundary layer

because of the continuously decreasing head wind, which causes the

aircraft with fixed controls to always be below the glide slope. The

aircraft does have a slight downdraft, but this is not sufficient

to

overcome the head wind influence.

Just past the building, there is a

sudden drop in horizontal wind and a sudden increase in updraft. This

reverses the previous effect and forces the aircraft to go below the

glide slope. Thus, competing wind effects occur relative to the

71

undisturbed wind field case, resulting in an unpredictable deviation

from touchdown.

One observes that the magnitude of the positive horizontal

(tail wind) shear is largest for the case of Z. = 20 cm and smallest

for the case of Z. = 80 cm. Thus, landing under the conditions of

Z. = 20 cm and Z. = 40 cm creates sufficiently

high positive hori-

zontal shears and updrafts to force the aircraft higher during part of

the approach than the case with no building present, resulting in

shorter deviation from touchdown. The case Z. = 80 cm does not create

as large a positive horizontal shear and updraft and the influence of

the decreasing head wind and downdraft in the wake of the building

produce a shorter touchdown than occurs with the undisturbed wind

field.

In the case of landings through the flow over the long building,

the aircraft lands 147 m short for the case Z. = 45 cm and 185 meters

short in the case Z. = 100 cm. One should notice that in this case the

descent starts from an altitude of about 33 meters. Therefore, these

touchdown points cannot be compared with the touchdowns in the

landings through the atmospheric boundary layer without the building.

However, by looking at the winds encountered by the aircraft

along the flight path, one can observe the similarity with the block

building case. Just as the aircraft passes over the edge of the

building, there is a sudden drop in horizontal wind which causes the

aircraft to go below the glide slope, and thereby resulting in an

unpredictable deviation from touchdown. One can observe that the dif-

ference between the case of Z, = 100 cm and Z. = 45 cm is that the

72

initial head wind is higher and decreases more rapidly. Also, the aircraft encounters a smaller updraft than in the former case which tends to decrease the sink rate. Both of these wind effects result in a shorter touchdown, as indicated by the results in Table '1, page 69.

In'the case of landings with automatic controls, the deviations

from the touchdown points are very small for landings through the

atmospheric flow without the building, as well as with buildings

present. Even though the deviations from the touchdown point are not

significant,

one can see that complex wind patterns created by the

presence of large buildings do create larger deviations in touchdown.

Moreover, a significant

factor on the safety of aircraft operations is

the rate at which the controls must be operated to track the glide

path. Figure 30, page 65, shows that the thrust must be reduced

significantly

as the aircraft passes over the building to compensate

for the sudden excursions in the horizontal and vertical winds.

Thrust was cut almost 50% in the case for Z. = 80 cm. Figure 31,

page 66, shows the controls that were used in the case of flight over

the long, wide building.

In this case the elevator angle changes

quite rapidly to compensate for the effects of changing winds.

Figure 22, page 56, and Figure 29, page 63, show the aircraft

landing trajectories

in the flow associated with a thunderstorm gust

front with fixed controls and with automatic controls, respectively.

In the case of fixed control landings, the deviations between touch-

down points are large, as much as 725 meters variation from the case

for Z, = 20 cm and for Z, = 80 cm. Figure 22 shows that there are

73

very large deviations from the flight path itself and thus would

result in unsatisfactory

landings.

Figure 25, page 59, shows the winds encountered by the aircraft

along the trajectory.

Initially,

there is high vertical updraft which

increases to approximately 13 m/set and then suddenly drops to almost

zero. Thus, the aircraft is initially

blown above the glide slope and

then suddenly this wind dies out, resulting in a high sink rate. In

the case for Z. = 20 cm, the head wind remains almost constant and

then starts decreasing very rapidly; at the same time the vertical

updraft suddenly drops to zero, creating a strong turning moment on

the aircraft which results in a shorter landing. For landing under

the conditions of Z. = 80 cm, head wind and vertical updraft remain

constant for a longer period of time, thus keeping the aircraft above

the glide path for a longer period of time.

In the case of landings with automatic controls through this wind

field, the deviations from the flight path are small, but the

influence of these severe winds is to cause rapid changes in the

controls.

Figure 32, page 67, shows the controls that were applied to

maintain the flight path. Here thrust starts out initially

at a high

magnitude, increases slightly and then drops very suddenly to almost

one-third of the initial value. This is because the pitch angle is

maintained constant in automatic landings, a vertical updraft causes a

larger angle of attack and increased drag. Therefore, when the

vertical updraft suddenly goes to zero, the angle of attack decreases

and drag drops, hence thrust is reduced to prevent going high on the

74

glide slope. The elevator angle also changes very rapidly from 0 to -6 degrees in the process to compensate for the sudden drop in vertical wind and counterclockwise moment produced by the vertical wind, since a negative elevator setting corresponds to a counterclockwise rotation with the airplane traveling in positive x-direction,
Figure 33, page 68, shows that the aircraft with the characteristics of a DHC-6 on a 6-degree glide path behaves basically the same as a DC-8. For the landing of this aircraft, few changes were required in the automatic control system. In the glide-slope capture mode the reference flight path angle was changed from 2.7 to 6 degrees and' the gain constant, k3, from 0.05 to 0.1. In the glide-slope tracking mode the constant, a3, is changed from 0.01 to 0.02, and in the flare mode the constant, a6, is changed from 4.0 to 5.0. These changes in different control modes increase the response of pitch angle command variable, ec,
75

CHAPTER VI

CONCLUSIONS

The two-dimensional aircraft landing simulation study has pro-

vided some basic results concerning the problems of wind shear due to

the presence of large buildings or other bluff geometries. The air-

craft encountering a strong wind shear caused by the edge of a

building is drawn towards the building,

With fixed controls,

deviation in touchdown point in excess of 400 m resulting from

variation of the horizontal wind during the final 100 m of descent has

been computed under wind shear conditions that may realistically

be

encountered around buildings or bluff terrain features.

Wind shear due to thunderstorm gust fronts can cause very severe

departures from the glide slope during landing. Although thunderstorm

gust fronts are not encountered too frequently, landing through such a

gust front can be very hazardous and requires rapid changes in the

controls required to maintain the flight path. Based on the model of

thunderstorm field investigated in this report, changes in the controls

at the rate of 7 degrees of elevator angle and 9072 kg of thrust per

one-half second for the DC-8 were required.

Although the surface roughness parameter, Zo, shows little

influence on touchdown points during the landings through the atmospheric flow over level terrains, it does have considerable effect on

aircraft landing when large buildings or bluff objects are present

near the airports. 76

BIBLIOGRAPHY

1. Etkin, B., Dynamics of Atmospheric Flight. Inc., New York, 1972.

John Wiley & Sons,

2. Blakelock, John H., Automatic Control of Aircraft John Wiley & Sons, Inc., New York, 1965.

and Missiles.

3. Neuman, F., and J. Foster, “Investigation

of a Digital Augo-

matic Aircraft Landing System in Turbulence," NASA

TN D-6066, October, 1970.

4. Melvin, W. W., "Wind Shear on the Approach," Shell Aviation News, 393:16-21, (1971).

5. Kraus, K., "Aspects of the Influence of Low-Level Wind Shear on

Aviation Operations," International

Conference on Aerospace

and Aeronautical Meteorology, Washington, D. C.,

May 22-26, 1972.

6. Camp, D. W., W. Frost, and W. A. Crosby, "Flight Through Thunderstorm Outflows," to be presented at 11th International Congress of ICAS, Lisbon, Portugal, September
10-16, 1978.

7. Luers, J. K., and J. B. Reeves, "Effect of Shear on Aircraft Landing," National Aeronautics and Space Administration CR-2287, George C. Marshall Space Flight Center, Huntsville, Alabama, July, 1973.

8. 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.

9. National Transportation Safety Board, “Iberia Lineas Aereas de

Espana (Iberian Airlines), McDonnel Douglas DC-10-30,

EC CBN, Logan International

Airport, Boston, Massachusetts,

December 17, 1973," Aircraft Accident Report No. NTSB-AAR-

74-14, National Transportation Safety Board, Washington,

D. C., November 8, 1974.

77

10. Frost, W,, and D, W. Camp, "Wind Shear Modeling for Aircraft

Hazard Definition."

Interim report No. FAA-RD-77-36 prepared

for U. S. Department of Transportation,

Federal Aviation

Administration,

Systems Research and Development Service,

by FWGAssociates, Inc., Tullahoma, Tennessee, March, 1977.

11. Haskins, G. L., "The X in WX," Aerospace Safety, April, 1969.

12. Frost, Walter, "Flight in Variable Mean Winds," Report in preparation for NASA Contract No. NAS8-29584.

13. Gera, J., "The Influence of Vertical Wind Gradients on the Longitudinal Motion of Airplanes," NASA TN D-6430, September, 1971.

14. Johnson, W. A., and D. T. McRuer, "A System Model for Low-Level Approach," Journal of Aircraft, December, 1971.

15. Farrell, J. L., Integrated Aircraft New York, 1976.

Navigation.

Academic Press,

16. Bosman, D., "Aircraft Flight Instrumentation

Integrated Data

Systems," AGARD Conference Proceedings Number Six,

November, 1967.

17. Tanney, J. W,, "Fluidics,"

Progress in Aeronautical

Volume 10. Pergamon Press, Oxford, 1970.

Sciences,

18. Blackadar, A. K., "The Vertical Distribution

of Wind and

Turbulent Exchange in a Neutral Atmosphere," Journal of

Geophysical Research, 67:3095-3102, April, 1962.

19. Lettau, H. H., "Wind Profile, Shear Stress and Geostropic Drag Coefficients in the Atmospheric Surface Layer," Advances in Geophysics. Academic Press, New York, 1962.

20. Frost, W., J. R. Maus, and W. R. Simpson, "A Boundary Layer

Approach to the Analysis of Atmospheric Motion Over a Surface

Obstruction,"

NASA CR-2182, January, 1973.

21. Panofsky, H. A., "The Atmospheric Boundary Layer Below 150 Meters, ‘I Annual Review of Fluid Mechanics, Vol. 6, 1974.

22. Shieh, C. F., W. Frost, and J. Bitte, "Neutrally Stable Atmos-

pheric Flow Over a Two-Dimensional Rectangular Block,"

Report prepared under NASA Contract No. NAS8-29584, The

University of Tennessee Space Institute,

Tullahoma,

Tennessee, December, 1976.

78

23. Bitte, J., and W. Frost, "Atmospheric Flow Over Two-Dimensional

Bluff Surface Obstructions,"

NASA CR-2750, October, 1976.

24. Johnson, W. A., and D. T. McReur, "Development of a Category II Approach System Model," Technical Report 182-1, Systems Technology, Inc., December, 1969.

25. Osder, S. S,, "Avionics Requirements for All Weather Landing of Advanced SST's," Volume I, NASA CR-73092, 1967.

26. Fichtl, G. H., and D. W. Camp, Memo to Mr. Frank Coons, ARD 451, FAA, 2100 2nd Street, S. W., Washington, D. C., 20590, March 22, 1976.

27. Goff, R. C., "Thunderstorm Outflow Kinematics and Dynamics," NOAA Technical Memo ERL NSSL-75 (1975).

79

APPENDIX 80

APPENDIX

The aircraft characteristics

used in this simulation study are

for that of a DC-8 and a DHC-6. The initial conditions and aircraft

physical data are given as follows [7]:

DESCRIPTION

DC-8

DHC-6

H(m)

Reference altitude

91

91

V,(m/seC)

Initial velocity

70

46

v&d W(kd Iyy(kg-m2)

Initial flight path angle Aircraft weight Moment of inertia

-2.7 90700 5.3 x lo6

-6.0 4985 3.2 x lo4

LT(m)

Moment arm of thrust vector

1.2

-0.91

GT(dd 34 45

Angle between FT and FRL

3.15

0.0

Chord length

7

2

Wing area

256

39

The expressions aircraft are:

for the aerodynamic coefficients

of the DC-8

cL=cL +cL cx’+cL

0

a

6E+j+ a Lq

c,=c,

+cm a’+Cm 6E+gc

0

a

6E

a

mq + -a2v,

c
mAI

'

81

where the usual notation is used for the various stability derivatives.

The values of the stability derivatives are given as follows:

DC-8

DHC-6

cLO
cL a cL
"E cL
9 cL*ci
cDO
cDa 'Da2

0.90 5.30/rad O.O053/deg
7.68/rad 0.0 0.140 0.50l/rad 1.818/rad2

0.86 6.109/rad 0.5236/deg
2.152/rad 0.0 0.32 0.9832/rad 0.0

'm
0
'm cx C
m6E C
mq Cmae

-1.01 -l.O62/rad -O.O16l/deg -12.30/rad -4.Ol/rad

0.0/rad2 -2.026/rad -2.068/deg -28.76/rad -8.663lrad

The various dimensionless groups (normalizing factors) used in this

study are provided below:

D =P?!! 1 2w

D2 = e&! 'a2

82

H2 D3 = 7 a

D6 =

-3!L

2 w

v

a

LTD3 D7 = Iyy

The following are the "C" coefficents

and 6 :

FTC

EC

c1

= D, CD a

c2 = Dl 'DC,2

c3

= D, CL a

c4 = D, CL "E

c5

= D5 Cm a

‘6 = D5 Cm "E

c7 = Dl 'Do

used in variable gain computations of

‘8 = D1 CL0

c9 = Dl D4 CLq 83

clO = D, D4 Cc;

= D5 Cm

cll

0

= D5 D4 cm

52

9

cl3 = Dg D4 Cma.'

1. REPORT NO,
NASA CR - 3073 a TITLE AN0 SUBTITLE
Investigation of Aircraft

2. GOVERNMENT ACCESSION NO.
Landing in Variable Wind Fields

3. RECIPIENT’S

CATALOG NO.

5. REPORT DATE
December 1978
6. PERFORMING ORGANIZATION

CODE

7. AUTHOR(S)
Walter Frost and Kapuluru Ravikumar

9. PERFORMING ORGANIZATION

NAME AND ADDRESS

Reddv

The University of Tennessee Space Institute TuIlahoma, Tennessee

12 SPONSORING’ AGENCY NAME AND ADDRESS
National Aeronautics and Space Administration Washington, D. C. 20546

6. PERFORMING ORGANIZATION

REPOR r

10. WORK UNIT, NO.
M-272
11. CONTRACT OR GRANT NO.
NAS8-29584
19. TYPE OF REPORi’ 8: PER100

COVERE

Contractor
1.1. SPONSORING AGENCY CODE

y SUPPLEMENTARY

NOTES

Prepared under the technical monitorship of the Atmospheric Sciences Division, Space Sciences Laboratory, Science and Engineering, NASA/Marshall Space Flight Center
16. ABSTRACT
This report describes a digital simulation study of the effects of gusts and wind shear on the approach and landing of aircraft. The gusts and wind shear are primarily those associated with wind fields created by surface wind passing around bluff geometries characteristic of buildings. Also, flight through a simple model of a thunderstorm is investigated.

A two-dimensional model of aircraft motion was represented by a set of nonlinear equations which accounts for both spatial and temporal variations of winds. The landings of aircraft with the characteristics of a DC-8 and a DHC-6 are digitally simulated under different wind conditions with fixed and automatic controls. The resulting deviations in touchdown points and the controls that are required to maintain the desired flight path are presented. The presence of large bluff objects, such as buildings in the flight path is shown to have considerable effect on aircraft landings.

7. KE’r WOROS
Aviation Safety Aircraft Motion Simulation Low-Level Wind Wind Shear Turbulence
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