i/ "" t

NASA Contractor Report 178255

L

II*

DEVELOPMENT OF A TAKEOFF PERFORMANCE

MONITORING SYSTEM

(_ASA-CB-178255) DE¥_LC}_E_t C_ A TAKEOFF

_E_FGIiflANCE SCBIIOBIRG S¥S_£_ 9h.D. Thesis.

Ccntractor Be_ort, Jam. 1984 - Jun. 1985

(Kansas Univ. Cente_ for Besearch, Inc.)

2C8 p CSCL 01D G3/06

Raghavachari Srivatsan

David R. Downing

N87-202£4

Unclas

45171

THE UNIVERSITY OF KANSAS CENTER FOR RESEARCH, INC.

Lawrence, Kansas

Cooperative Agreement NCC1-79

March 1987

NASA

National Aeronautics and

Space Administration

LangleyResearch Center

Hampton, Virginia 23665
PREFACE

The development of the takeoff performance monitoring system described

here was carried out under Cooperative Agreement NCC 1-79, between the

University of Kansas and NASA Langley Research center. Dr. David R.

Downing, of the Department of Aerospace Engineering at the University of

Kansas was the Principal Investigator on the project and Raghavachari

Srivatsan, served as the Research Assistant. The work was done at NASA

Langley Research Center in Hampton, VA.

The work was started under a one year agreement covering the period 15-

June-1983 through 14_June-1985, and continued under an extension for the

period 15-June-1984 through 14-June-1985. The project was accomplished

in two phases. The first phase consisted of conducting a detailed survey of

existing flight management systems and a comparison to those that were

available on the Transport Systems Research Vehicle (TSRV) Boeing 737 at

NASA Langley Research Center. This survey resulted in the identification of

three areas needing attention. In phase II one of the identified areas was

chosen for detailed development. This report documents the efforts of

phase II.

The authors wish to thank Dr. Paul E. Fortln for his help with the

administrative aspects at the University of Kansas, and his help with

proposals and renewals, and Mr. Wayne H. Bryant, contract monitor at NASA

Langley, for his support, availability for discussions, and in the

preparation of this document.

Thanks are also due to Mr. William E. Howell and Mr. Ray V. Hood of NASA

Langley for their periodic review of work and suggestions. The author also

wishes to acknowledge the technical assistance provided by Mr. Richard M.
Hueschen, Mr. Wiiliam T. Bundick of NASALangley, and the programming

assistance provided by Mrs. Jessie C. Yeager, and Mr. Melvin L. Bailey of

PRC,and Mr. Carey S. Buttril of TAI. To Ms. Danette Barrett, Mrs. Jessie

Yeager, Mrs. Beth Lee, and Ms. Louise Richardson thanks are expressed for

their assistance in the preparation of this document.

The authors also wish to thank Mrs. Nancy Hanson, of the University of

Kansas - Flight Research Lab, for converting this document from a thesis to

a report format and Mr. David B. Middleton, of NASALangley Research Center,

for his considerable help in the genesis of this contractor report.

ii
TABLE OF CONTENTS

PREFACE ................................................. i

LIST OF SYMBOLS ......................................... iv

LIST OF TABLES .......................................... xiii

LIST OF FIGURES ......................................... xv

SUMMARY ................................................. xxiii

I INTRODUCTION ....................................... I

2 TAKEOFF PERFORMANCE MONITOR ALGORITHM DEVELOPMENT .. 7

3 SIMULATION MODEL ................................... 42

4 TAKEOFF MONITOR ALGORITHM EVALUATION ............... 56

5 SENSITIVITY AND FAILURE MODE ANALYSIS .............. 117

6 CONCLUSIONS AND RECOMMENDATIONS .................... 156

LIST OF REFERENCES ...................................... 161

163 APPENDIX A:

APPENDIX B:

APPENDIX C:

DISCRETIZATION OF FIRST ORDER SYSTEMS ......

FORMULATION OF A SECOND ORDER COMPLEMENTARY

FILTER .....................................

PROGRAMMING FLOW CHARTS ....................

167

172

iii
LIST OF SYMBOLS

SYMBOL DEFINITION DIMENSION

A

A0 , A I , A 2, A3

a

b

CAS

CD

CL

C

m

m

C

cg

D

DRWY

DZ

EPR

{E}, [E]

F

F

nz

Speed of Sound

Acceleration Cubic Polynomial Coefficients

Along Track Acceleration

Wing Span

Calibrated Airspeed

Airplane Drag Coefficient

Airplane Lift Coefficient

Airplane Pitching Moment Coefficient

Mean Aerodynamic Chord

Center of Gravity Location

Aerodynamic Drag

Runway Length Used

Engine Moment Arm Along Z-axis

Engine Pressure Ratio

Euler Transformation Matrix

Force

Z Directional Load Factor

iv

feet/second

feet/second 2

feet

feet/second

knots

m

feet

ibs

feet

feet

lbs
LIST OF SYMBOLS (continued)

SYMBOL

Gear

g

M

g

H

HCG

H

cg

HRWY

HRUNWAY

H

r

IYY B

i H

L

LG

M

M

DEFINITION

10 for landing gear retracted

=I for landing gear extended

Acceleration due to gravity

Gravitational Acceleration Vector

Height of the airplane (mean sea level)

Height of the airplane center of gravity

above the runway

Height of the airplane center of gravity

above the runway

Height of the runway (mean sea level)

Height of the runway (mean sea level)

Height of the runway (mean sea level)

Moment of Inertia about the body Y - axis

Stabilizer incidence

Aerodynamic Lift

Landing Gear related Force/Moment

Airplane Pitching Moment

Mach Number

DIMENSION

feet/second 2

feet/second 2

feet

feet

feet

feet

feet

feet

slug-feet 2

degrees

lbs

lbs or

ft-lbs

ft-lbs

v
SYMBOL

m

nZ

P

q

R

R

Rad

r

T

TAS

THRUST

REVERSE

Th

LIST OF SYMBOLS (continued)

DEFINITION

Airplane Mass

Normal Load Factor

Roll Rate

Pitch Rate

Dynamic Pressure

Acceleration Due to Body Rates

Radious of the Earth

Radious of the Earth

Yaw Rate

Wing Area

Engine Thrust related Force/Moment

Iteration Time Step/ Sampling Interval

True Airspeed

Thrust Reverse Yes/No

Engine Thrust

vi

DIMENSION

slugs

g's

deg/second

rad/second

deg/second

rad/second

lbs/feet 2

feet/second 2

feet

feet

deg/second

rad/second

feet 2

Ibs or

ft-lbs

second

feet/second

knots

lbs
LIST OF SYMBOLS (continued)

SYMBOL

Ttotal

T0, T I , T 2, T 3

t

ramp

uW

V

V I

V2

V R

Vw

v

v G

v T

v T

rotate

W

w

XB

DEFINITION

Total Temperature

Thrust Cubic Polynomial Coefficients

Ramp Time to reach Maximum value

X-axis Velocity

Runway Wind Velocity

Velocity

Decislon Speed

Second Segment Climb Speed

Rotation Speed

Wind Vector

Y-axis Velocity

Ground Track Speed

True Airspeed

True Airspeed for Rotation

Airplane Weight

Z-axis Velocity

Aerodynamic Forces along Body X-axis

DIMENSION

o Kelvin

seconds

feet/second

feet/second

knots

feet/second

knots

knots

knots

feet/second

feet/second

feet/second

feet/second

feet/second

ibs

feet/second

Ibs

vii
SYMBOL

XBToT

xT

YB

YBToT

ZB

ZBToT

zT

B

F

Y

ACD

ACL

As

AT

At

Ag

6

a

6 E

LIST OF SYMBOLS (continued)

DEFINITION

Total Forces Along Body X-axls

Engine X-moment arm

Aerodynamic Forces along Body Y-axis

Total Forces Along Body Y-axis

Aerodynamic Forces along Body Z-axis

Total Forces Along Body Z-axis

Engine Z-moment arm

Airplane Angle of Attack

Airplane Side Sllp Angle

Discrete Control Effectiveness Matrix

Airplane Flight Path Angle

Incremental Drag Coefficient

Incremental Lift Coefficient

Computed Distance per Step

Iteration Time Step/ Sample Interval

Computed Time Interval

Difference in Friction Coefficient

Aileron Deflection

Elevator Deflection

viii

DIMENSION

ibs

feet

lbs

ibs

lbs

lbs

feet

degrees

degrees

degrees

feet

second

second

m

degrees

degrees
LIST OF SYMBOLS (continued)

SYMBOL

6

e

6F

_FLAPS

6FSP

6GSP

6GEAR

6R

6SP L

6SP R

6STAB

_th

e

eB

eRWY

p

DEFINITION

Elevator Deflection

Flap Deflection

Flap Deflection

Flight Spoiler Deflection

Ground Spoiler Deflection

Gear Up/Down

Rudder Deflection

Left Spoiler Deflection

Right Spoiler Deflection

Stabilizer Deflection

Throttle Position

Pitch Related

Body Pitch Attitude

Runway Inclination

Latitude

Rolling Friction Coefficient

Discrete Transform Multiplier

Air Density

ix

DIMENSION

degrees

degrees

degrees

degrees

degrees

degrees

degrees

degrees

degrees

degrees

degrees

degrees

degrees

degrees

slugs/feet 3
SYMBOL

T

_RUNWAY

B

brake

D

E

FI

FSP

fr

G

GSP

left

LB

LIST OF SYMBOLS (continued)

DEFINITION

Longitude

Discrete State Matrix

Bank Angle

Yaw Angle

Runway Heading

Superscripts

Time derivative

Estimated quantity

Subscripts

Body Axes

Due to braking

Down direction

East direction

From the first filter network

Due to Flight Spoilers

Friction

Ground

Due to Ground Spoilers

Left Side

Body Axis Rolling Moment

x

DIMENSION

degrees

degrees

degrees

degrees
LIST' OF SYMBOLS (continued)

SYMBOL

iB

M

MB

max

mB

N

NB

n B

0

r

right

S

step

T

T

total

XB

XS

ZB

DEFINITION

Subscripts (continued)

Body Axis Rolling Moment

Measured

Body Axis Pitching Moment

Maximum value

Body Axis Pitching Moment _

North direction

Body Axis Yawing Moment

Body Axis Yawing Moment

Old value

Relative

Right side

Stability Axes

step size

True

Engine Thrust line

Total Force/ Moment

Along Body X-axis

Along Stability X-axis

Along Body Z-axis

xl

DIMENSION
LIST OF SYMBOLS (continued)

SYMBOL

ZS

DEFINITION

Subscripts (continued)

Along Stability Z-axis

For a rolling friction coefficient ofu

DIMENSION

xii
LIST OF TABLES

TABLE TITLE PAGE

2.3

3.1

4.1

4.2

4.3

4.4

4.5

4.6

5.1

5.4

Parameters needed for the Pretakeoff Segment .......... 10

Flight Conditions for the sample Pretakeoff

Calculations .......................................... 21

Parameters needed for the Real-Time Segment ........... 27

Noise and Bias Characteristics ........................ 46

Normal Takeoff Test Cases ............................. 57

Summary of results for Case I with Perfect

Sensors ............................................... 73

Summary of results for Table 4.1 Cases with

Noisy Sensors ......................................... 88

The Effects of Actual versus Measured

Calibrated Airspeed on Case II ........................ 89

Summary of results from the Engine EPR

Failure runs .......................................... 96

Summary of results for the Thrust Failure

Runs .................................................. 112

Baseline Flight Conditions for Sensitivity

and Failure Analysis .................................. 119

Effect of Wind Speed Error ............................ 120

Effect of Wind Speed Error with a

Wind Estimator ........................................ 126

Effect of Ambient Temperature Errors .................. 129

xiii
LIST OF TABLES (continued)

TABLE TITLE PAGE

5.5

5.6

5.7

5.8

5.9

5.10

5.11

5.12

5.13

Effect of Gross Weight Errors ......................... 133

Effect of Flap Setting Errors ......................... 134

Effects of Aerodynamic Degradation .................... 135

Effects of frequency of calls to the

algorithm ............................................. 136

Effects of Accelerometer Bias ......................... 142

Effects of Accelerometer Scale Factor ................. 149

Effect of EPR sensor Bias ............................. 150

Effect of EPR sensor Scale Factor ..................... 155

Effect of Ground Speed Sensor Failure ................. 155

xiv
List of Figures

FIGURE

NUMBER

1.1

2.1

2.2

2.3

2.4

2.5

3.2

3.3

4.1a

4.1b

4.1C

4.1d

TITLE

The Instantaneous Forces Acting on an Airplane During

Takeoff Roll ..........................................

The Pretakeoff Segment ................................

The Axes System .......................................

Engine Model, Inputs, and Outputs ........ . ............

Landing Gear Dynamics Model, Inputs, and Outputs ......

Acceleration versus True Airspeed Data from

the Pretakeoff Segment and the Corresponding

Cubic Polynomial Curve Fit ...........................

The Real-Time Segment .................................

Flow Diagram for the Six Degree of Freedom TSRV B-737

Batch Simulation ......................................

Block Diagram of the Engine Model .....................

Aircraft Dynamics Module ..............................

Runway Used Time History for Case I with Perfect

Sensors ...............................................

Ground Speed Time Histories for Case I with Perfect

Sensors ...............................................

Engine Pressure Ratio Time Histories for Case I with

Perfect Sensors .......................................

Predicted Runway Required Time History for Case I

with Perfect Sensors ..................................

PAGE

NUMBER

4

9

12

18

19

22

24

43

48

51

58

59

6O

61

XV
List of Figures (continued)

FIGURE

NUMBER

4.1e

4.1f

4.1g

4.1h

4.1i

4.1j

4.1k

4.11

4.2a

4.2b

4.2c

4.2d

TITLE

Raw Sensor and Ideal Sensor Acceleration for Case I

with Perfect Sensors ..................................

Acceleration Time Histories for Case I with Perfect

Sensors ...............................................

Calibrated Airspeed Time Histories for Case I with

Perfect Sensors .......................................

True Airspeed Time Histories for Case I with Perfect

Sensors ...............................................

Measure of Goodness of Prediction from Algorithm for

Case I with Perfect Sensors ................... ........

Stopping Distance Time History for Case I with

Perfect Sensors .......................................

Negative of Estimated Acceleration Bias for Case I

with Perfect Sensors ..................................

Estimated Error in Ground Speed for Case I with

Perfect Sensors .......................................

Runway Used Time Histories for Case I .................

Ground Speed Time Histories for Case I ................

Engine Pressure Ratio Time Histories for Case I .......

Predicted Runway Required Time History for

Case I ................................................

PAGE

NUMBER

62

63

64

65

66

67

68

69

75

76

77

78

xvi
List of Figures (continued)

FIGURE

NUMBER

TITLE PAGE

NUMBER

4.2e

4.2f

4.2g

4.2h

4.2i

4.2j

4.2k

4.21

4.3a

4.3b

4.3c

4.3d

4.3e

Raw Sensor and Ideal Sensor Acceleration for

Case I ................................................

Acceleration Time histories for Case I ................

Calibrated Airspeed Time Histories for Case I .........

True Airspeed Time Histories for Case I ...............

Measure of Goodness of Prediction from

Algorithm for Case I ..................................

Stopping Distance Time History for Case I .............

Negative of Estimated Acceleration Bias for

Case I ................................................

Estimated Error in Ground Speed for Case I ............

Engine Pressure Ratio Time Histories for the

85% EPR Case ..........................................

Calibrated Airspeed Time Histories for the

85% EPR Case ..........................................

Runway Used Time Histories for the 85% EPR Case .......

Acceleration Time Histories for the 85% EPR

Case ..................................................

Goodness of Runway Requirement Prediction for

the 85% EPR Case ......................................

79

8O

81

82

83

84

85

86

91

92

93

94

95

xvii
List of Figures (continued)

FIGURE

NUMBER

TITLE PAGE

NUMBER

4.4a

4.4b

4.4C

4.5a

4.5b

4.5C

4.6a

4.6b

4.6C

4.7a

Engine Pressure Ratio Time Histories for the

85% EPR Case with Command Generation ..................

Ground Speed Time Histories for the 85% EPR

Case with Command Generation ..........................

Acceleration Time Histories for the 85% EPR

Case with Command Generation ..........................

Engine Pressure Ratio Time Histories for the

115% EPR Case .........................................

Acceleration Time Histories for the 115%

EPR Case ..............................................

Goodness of Runway Required Prediction for

the 115% EPR Case .....................................

Engine Pressure Ratio Time Histories for the

115% EPR Case with Command Generation .................

Acceleration Time Histories for the 115% EPR

Case with Command Generation ..........................

Calibrated Airspeed Time Histories for the

115% EPR Case with Command Generation .................

Acceleration Time Histories for the 85%

Thrust Case ...........................................

98

99

tO0

101

102

103

104

105

106

108

xviii
List of Figures (continued)

FIGURE

NUMBER

TITLE PAGE

NUMBER

4.7b

4.7c

4.8a

4 .Sb

4.8c

5.1a

5.1b

5.2a

Predicted Runway Required Time History for

the 85% Thrust Case ...................................

Goodness of Runway Requirement Prediction

for the 85% Thrust Case ...............................

Acceleration Time Histories for the 115%

Thrust Case ...........................................

Predicted Runway Required Time History for

the 115% Thrust Case ..................................

Goodness of Runway Required Prediction for

the 115% Thrust Case ..................................

Calibrated Airspeed Time Histories for the

Wind Speed Error Case - Assumed uW = 20 k,

Actual uW - 0 ........................................

Runway Required Time History for the Wind

Speed Error Case - Assumed uW = 20 k,

Actual uW _ 0 ........................................

Calibrated Airspeed Time Histories for the

Wind Speed Error Case -- Assumed uW = 20 k,

Actual uW - 25 k ......................................

xix

109

110

113

114

115

120

121

123
List of Figures (continued)

FIGURE

NUMBER

TITLE PAGE

NUMBER

5.2b

5.3a

5.3b

5.4a

5.4b

5.5a

5.5b

Runway Required Time History for the Wind

Speed Error Case - Assumed uW : 20 k,

Actual uW : 25 k ......................................

Acceleration Time Histories for the Weight

Error Case - Assumed W = 88,504 lbs,

Actual W : 98,504 lbs ................................

Runway Required Time History for the Weight

Error Case - Assumed W = 88,504 lbs, Actual

W : 98,504 lbs .......................................

Acceleration Time Histories for the Weight

Error Case - Assumed W = 88,504 lbs, Actual

W = 78,504 ibs ........................................

Runway Required Time History for the Weight

Error Case - Assumed W = 88,504 lbs, Actual

W = 78,504 ibs ........................................

Ideal and Raw Sensor Outputs of Acceleration

for an Accelerometer Bias of 2.32 ft/sq, second .......

Complementary Filter Estimate of the Negative

of Bias for an Accelerometer Bias of

2.32 ft/sq.second .....................................

124

126

127

130

131

137

138

XX
List of Figures (continued)

FIGURE

NUMBER

TITLE PAGE

NUMBER

5.5c

5.5d

5.6a

5.6b

5.60

5.6d

5.6e

5.7a

5.7b

Acceleration Time Histories with an

Accelerometer bias of 2.32 ft/sq, second ..............

Ground Speed Time Histories for an

Accelerometer Bias of 2.32 ft/sq, second ..............

Ideal and Raw Sensor Outputs of Acceleration

for an Accelerometer Scale Factor of 85% ..............

Complementary Filter Estimate of Bias for an

Accelerometer Scale Factor of 85% .....................

Acceleration Time Histories for an

Accelerometer Scale Factor of 85% ....................

Ground Speed Time Histories for an

Accelerometer Scale Factor of 85% .....................

Runway Required Time History for an

Accelerometer Scale Factor of 85% .....................

Estimate of the Ground Speed Error from the

Complementary Filter for a Ground Speed

Sensor Output of 250 feet/second ......................

Acceleration Bias Estimated by the

Complementary Filter for a Ground Speed

Sensor Output of 250 feet/second ......................

139

140

142

143

144

145

146

150

151

xxi
List of Figures (continued)

FIGURE

NUMBER

TITLE PAGE

NUMBER

5.7C

5.7d

Ground Speed Time Histories for a Ground

Speed Sensor Output of 250 feet/second ................

Acceleration Time Histories for a Ground

Speed Sensor Output of 250 feet/second ................

152

153

xxii
SUMMARY

An algorithm was developed to monitor the performance of the airplane

during the takeoff phase to improve safety in that flight phase. The

algorithm is made up of two segments: a pretakeoff segment and a real time

segment.

One-time inputs of ambient temperature, pressure, runway wind, airplane

gross weight, selected flap and stabilizer setting are utilized by the

pretakeoff segment in generating a set of standard acceleration performance

data in an offline condition.

The real-time segment, in addition to the above one-time inputs,

requires the runway length available for rotation, the runway length

available for stopping and an estimated runway rolling friction coefficient.

The real-tlme segment also utilizes instantaneous measurements of throttle

position, engine pressure ratios, calibrated airspeed, along track

acceleration, and ground speed. The input values and the measured

parameters are used in computing engine parameters and airplane

acceleration, keeping track of the runway used, runway remaining, and in

predicting the runway needed to achieve rotation speed, and the runway

needed to stop the airplane. A comparison of measured and predicted values

is utilized in detecting performance deficiencies. These comparisons and

the runway length computations lead to Go/Abort signals. With the algorithm

operating in a command generation mode these signals are transformed into

commands to the airplane systems. An important feature of the algorithm is

the one-time estimation of the runway rolling friction coefficient early

into the takeoff run. The instantaneous measurements and computations of

the real-time segment are carried out ten times a second.

xxiii
The algorithm has been evaluated using a six degree-of-freedom nonlinear

airplane simulation as the plant for several design point test cases and two

types of engine malfunctions. The algorithm does not cause any false alarms

and the error in the predicted runway required to achieve rotate speed is

within 5 percent of the runway actually used. The algorithm is not capable

of detecting engine failures that do not affect the Engine Pressure Ratio,

but even for this type failure the runway predictions are within 5 percent

of that used. Engine malfunctions that cause the Engine Pressure Ratio to

be affected are identifled as engine failures early into the takeoff run.

Sensitivity analysis of the algorithm to errors in one-time inputs

indicated a high sensitivity to errors in runway wind inputs. An onboard

wind estimator overcomes this sensitivity. The algorithm is also highly

sensitive to errors in ambient temperature inputs. The algorithm is capable

of adjusting for errors in other one-time inputs as long as these errors do

not cause the flight manual recommended rotation speed to be different.

Failures of the accelerometers resulting in bias and scale factor errors in

their outputs are sensed and compensated for by the algorithm. Bias and

scale factor errors in the Engine Pressure Ratio sensors of more than 15

percent of nominal values causes abort signals to be generated. Failures of

the ground speed sensor resulting in an unchangedoutput also results in the

generation of abort signals.

xxiv
CHAPTERI

INTRODUCTION

The percentage of initiated takeoffs that have resulted in accidents is

very small. Looking at this same data in a slightly different manner,

however, it is seen that accidents in the takeoff phase account for about

12% of all aircraft related accidents (Reference I). Looking at it from yet

another perspective, fatal accidents in the takeoff phase amount to about

15% of all fatal accidents (Reference I). Reference I also indicates that

while the accident rate in the other flight phases has been decreasing in

recent years, those in the takeoff phase have remained almost constant.

Most of these accidents are related to some kind of performance degradation

and a vast majority of these could have been averted had there been some

system to monitor the progress of the takeoff roll of the airplane and warn

the pilot of such a degradation.

Based on their investigation of accidents in the takeoff flight phase,

agencies such as the National Transportation Safety Board (NTSB) and the

Civil Aviation Authority of U.K. (CAA) have strongly recommended the

development of such a system (Reference I). The Society of Automotive

Engineers (SAE) has felt it important enough to create a committee to

prepare a set of standards for the development of such a system.

The concept of takeoff monitoring is nothing new. Almost since the

beginning of regulated aviation operation, this phase of flight has been of

concern. A history of takeoff monitoring has been given in reference I.

One of the methods proposed was based on checking the speed of the airplane

at a predetermined point on the runway (Reference 2). Another simple

approach found in the literature is a check on the time required to attain a
specified speed. Other more involved procedures as well as some elaborate

ground based systems were proposed and are described in Reference I.

A typical takeoff run

A typical takeoff run goes as follows. Once the airplane has been

configured for the takeoff run, approprite thrust is applied. After brake

release, the airplane begins to accelerate. If there is an engine failure

before the decision speed, VI, is reached, the pilot elects to abort the

takeoff and stops the airplane. Once past the decision speed, even with an

engine failure, the pilot is required by the Federal Aviation Regulations to

take the airplane through rotation.

At any point during the takeoff roll, the amount of runway required to

achieve rotation speed is a function of the instantaneous speed of the

airplane and how well it will accelerate until rotation speed. The

instantaneous acceleration of the airplane is given by

Th - D - _ (W - L )

a = -- (1.1)

m

where

a = acceleration (feet/sec/sec)

Th= thrust (lbs)

D = drag (ibs)

= rolling friction coefficient

W = weight

L = lift

m = mass = W/g

(ibs)

(ibs)

(slugs)

2
g = gravitational acceleration

(feet/sec/sec)

Figure 1.1 shows the forces acting on the airplane. The thrust varies with

the airspeed of the airplane; drag and lift are functions of the square of

the airspeed and the friction coefficient depends on the runway condition.

Properties of a good takeoff monitoring system

A takeoff monitoring system, to be useful to the pilot as a decision

tool or as a command system needs to continuously evaluate the status of the

airplane and detect any performance deficiencies. This system also needs to

keep track of the runway used to that instant and the runway available which

can be used to achieve rotation speed. The monitor should have the ability

to adapt to the prevalent loading and ambient conditions such as weight,

temperature, pressure altitude, runway winds and rolling friction

coefficient. This monitor can be either a ground based or an aircraft

system.

Study Goal

The goal of this study is to develop a takeoff performance monitoring

system that meets the following requirements.

* The system must be self contained. By having the entire

system on the airplane, its operation becomes airport

independent.

* The system must detect performance deficiencies by comparing

the airplane's present performance with a nominal performance

for the given conditions.
000

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o_1

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i-i 0m0

_0

.t-I

mLl-i

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4
* The system must keep track of the airplane's position on the

runway. By computing runway used, the runway remaining for

further action is known.

* The system should have the ability to predict the runway that

would be required to achieve rotation speed or to bring the

airplane to a complete stop.

* The system should be capable of operating in both an

informative mode and in a command generation mode.

Method Options and Difficulties

The nominal performance mentioned above can be obtained in two ways.

The first calculates the performance for all possible combinations of

ambient conditions (pressure altitude, temperature, runway winds, and

rolling friction coefficient), loading conditions (weight and center of

gravity), and airplane configuration (flap setting). Also to be included in

this list is the possibility of reduced thrust takeoffs. The resulting

performance figures could be stored in a computer memory for later lookup

and comparison. This is clearly seen to be impossible because of the large

number of combinations of the parameters.

The second approach is to have a good model of the aircraft available so

that for each takeoff run the scheduled performance can be calculated in

real time and thus available for comparisons. The model must include the

dynamics of the airplane as well as the engines. Ideally the engine model

will include parameters that when checked against measured values will serve

as a check on engine health.

Two major problems that must be overcome in the development of the

monitor system are the evaluation of the runway rolling friction coefficient
and an estimation of the thrust developed by the engine. As seen from

equation 1.1 these two parameters affect the acceleration performance of the

airplane significantly. Yet these are two of the most difficult to

estimate. No sensor is available to directly measure either the thrust

developed by the engines or the rolling friction coefficient. The runway

rolling friction coefficient plays an important part in determining the

runway needed (Reference 3) but is a very difficult parameter to estimate

(Reference 4).

Document Outline

The Takeoff Performance Monitoring System developed during this effort

is described in Chapter 2. Chapter 3 gives a brief description of a six

degree of freedom simulation model of the Transport Systems Research Vehicle

Boeing 737 airplane used to test the algorithm. The normal performance of

the algorithm is evaluated in Chapter 4. The test cases include ten

combinations of ambient and loading conditions and two types of engine

malfunctions. Chapter 5 explores the sensitivity of the algorithm to errors

in inputs, and the effects of failures of sensors. Conclusions and

recommendations for further work are detailed in Chapter 6.

Appendix A describes the technique used to model a first order lag

network in the discrete domain. Appendix B details the development of a

second order complementary filter network. Appendix C includes detailed

flow charts of the real-time segment of the algorithm.

Details of the project organization, finances, and scheduling are

described in Appendix D.
CHAPTER2

TAKEOFF PERFORMANCE MONITOR ALGORITHM DESCRIPTION

2. I Introduction

The method used in this study for monitoring the takeoff performance of

an airplane is to continuously compare the plane's actual performance with a

nominal performance. A prediction of the runway needed to attain rotation

speed, the runway required to stop the airplane, and the runway remaining

augment this method. In chapter I, it was discussed that the generation of

"nominal performance" data covering all possible situations and the storage

of this information for real time reference is impractical. In addition,

chapter I points out that thrust is not directly measurable on board the

airplane.

This chapter discusses a takeoff monitoring algorithm which overcomes

the difficulties of generating and storing scheduled performance data

covering all possible situations, the measurement of thrust aboard the

airplane and the uncertainty associated with the assessment of runway

rolling friction coefficient.

2.2 The Takeoff Performance Monitor Algorithm

The takeoff performance monitor algorithm consists of two segments: a

pretakeoff segment and a real-time segment. The pretakeoff segment

generates the nominal acceleration performance data prior to the start of

the takeoff roll. During the takeoff roll, the real-time segment compares

the measured acceleration with the scheduled acceleration performance data,

predicts the runway length required to either attain rotation speed or to

stop the airplane, and based on these generates Go/Abort signals or

commands. These segments are described in the following two subsections.
2.2.1 The pretakeoff segment

The airplane's acceleration performance is predicted for two extreme

values of rolling friction coefficient: one being a low value (_=0.005) and

the other being a high value (_=0.040). The algorithm consists of three

parts as shown in Figure 2.1 and can be run off-line in the onboard

computers or in ground support computers with the results down loaded to the

airplane computers.

The first step, using airplane weight, center of gravity, runway

pressure altitude, ambient temperature, and selected flap setting obtains

from the flight manual the recommended engine pressure ratio for takeoff,

the static throttle setting to achieve the engine pressure ratio, decision

speed (VI) , and the rotation speed (VR).

The second step of the pretakeoff algorithm computes the airplane's

nominal acceleration and true airspeed performance time histories using an

iterative process with a time step of 0.05 second.

In the third step, a least squares cubic polynomial curvefit is

performed on the true airspeed-acceleration data computed in the second

part. The coefficients obtained from the curvefit are stored for use by the

real time segment of the algorithm.

2.2.1.1 Data Requirements:

The pretakeoff segment of the algorithm requires several parameters be

input at the start of the calculations. These inputs are the Ambient

Conditions, the Loading Data, and the Vehicle Configuration summarized in

Table 2.1.
Start

Flight manual

lookup

il

Airplane

performance

for p = O.005

!

Curvefit

accelerationvs

true airspeed

Airplane performance

for p ---0.040

Curvefit

accelerationvs

true airspeed

Figure 2.1: The Pretakeoff Segment

9
Table 2.1: Parameters needed for the Pretakeoff Segment

AMBIENT CONDITIONS

Pressure Altitude

Ambient Temperature

LOADING AND CONFIGURATION INFORMATION

Airplane Weight

Center of Gravity location

Selected Flap Setting

2.2.1.2 Airplane Performance Computation

The airplane nominal acceleration performance is generated using a

detailed model of the airplane that includes an aerodynamic model, an engine

model and a landing gear dynamics model. These three components are used in

an iterative procedure with all variables being initialized to nominal

values for the first pass. The procedure is summarized in the next

paragraph.

The aerodynamic package is used to compute the lift, drag, and pitching

moment coefficients. These coefficients are used to calculate the forces

and moments in the stability axis system and are then transformed into the

body axis system. These body axis forces and moments are combined with the

thrust and landing gear forces and moments to obtain the total forces and

moments on the airplane. These forces, combined with the acceleration due

10
to gravity, result in linear and angular accelerations along the three body

axes. These accelerations and velocities are numerically integrated to

yield new velocities, linear positions and angular orientations. These new

positions and velocities are used in computing new aerodynamic coefficients

and the whole process is repeated until rotation speed is achieved. The

equations are developed in detail below.

Figure 2.2 details the axis systems used in this development

(Reference 5). The center of gravity of the vehicle is the origin for both

the body and stability axis systems. The body X-axis (XB) is along the

longitudinal axis of the airplane, with positive direction towards the nose.

The body Y-axis (YB) is parallel to the wing span and the positive direction

is to the right in the top view. The stability Y-axis (Ys) coincides with

the YB axis. The positive body Z-axis (ZB) points downward and is

perpendicular to both XB and YB' The stability axis system is another

right-handed coordinate axis system obtained by rotations from the body

axis system. The stability X-axls (XS) lies along the projection of the

velocity vector onto the XB-ZB plane. The positive direction of the

stability Z-axis (ZS) points downwardand is at right angles to the XS axis.

The airplane angle of attack (_), the pitch attitude angle (8), and the

flight path angle (_) are also illustrated in Figure 2.2.

The aerodynamic coefficients, stored as part of the aerodynamic data

base for the airplane, are functions of motion variables (_, _, q, nz) and

control positions (6E' 6F) (Reference 5).

CL = f(_' _' q' nz' 6E' 6F' iH' HCG'Gear) -- (2.1a)

11
X B

Z B

YB' YS

Figure 2.2:

ZBO ZS

The Axes System.

12
CD = f(CL, HCG , Gear ) -- (2.1b)

Cm = f(a, q, n z, 6E, 6F' iH' HCG' Gear) -- (2.1c)

The angle of attack (a) is initialized to the nominal static pitch attitude.

All angular rates and linear velocities are initialized to zero. The

stabilizer setting (i H) is obtained from the flight manual lookup. The

height above the runway (HcG) is initialized to the static center of gravity

height with normal gear compression. The load factor (nz) is initialized to

unity. The flap deflection (6F) is chosen by the pilot and is an input to

the flight manual segment of the non-real time algorithm

The dynamic pressure (q) is calculated as follows:

where

e = %B - eRWY

vT = /(u B + uW cos e )

- I 2

q=_P vT

+ (w B + uW sin e )21

eB = pitch attitude angle

8RWY= runway slope (positive for an up slope)

vT = true airspeed

uB = body X-axis inertial velocity

w B = body Z-axis inertial velocity

uW = runway wind (head wind is positive)

-- (2.2)

-- (2.3a)

-- (2.3b)

13
The aerodynamic coefficients, the computed dynamic pressure, and the

airplane geometric constants (c, S) are used in the following equations to

compute the forces along the stability X and Z axes and the pitching moment.

FXs-- -q S CD

FZs = -q S CL -- (2.4)

MS -- q S c Cm

where c = meanaerodynamic chord

S -- reference wing area

The two forces and the momentare then transformed into the body axis by

= - Cos_ Sin FXB FXS - FZs

FZB= FXsSin _ + FZs Cos e -- (2.5)

MB = MS

Engine thrust (Th), engine pitch attitude (eT), and the X and Z engine

momentarms (xT, zT) are used in computing the engine forces and moments

along the body axis, as follows:

where

TXB= Th Cos eT

TZB= - Th Sin 8T

xT TMB= - TZB + TXB

-- (2.6a)

-- (2.6b)

zT

-- (2.6c)

Th = engine thrust, generated by the manufacturer's engine

mathematical model

14
Forces and moments produced by the landing gear (obtained from the

manufacturer supplied gear dynamicsmodel) are represented by the variables

LG ,LG ,LG •

XB ZB MB

The resultant forces acting through the center of gravity along the body

X-axis and the Z-axis are obtained by

FX + + LG

Btotal = FXB TXB XB

FZ + ÷ LG -- (2.Ta,b)

Btotal = FZB TZB ZB

The resultant momentabout the body Y-axis or pitching momentis denoted by

= MB + LG -- (2.7c)

MBtotal + TMB MB

Using these forces, moments, and bodyX and Z components of gravitational

acceleration, the airplane accelerations along the body axes are computedas

UB=(Fx /m) -g Sin 8B

Btotal

WB= (F z /m) - g Cos 8B

Btotal

HCG = uB Sin 8 - wB Cos 8

+ (rB VB - qB WB)

+ (qB UB - PB VB) -- (2.8)

In the above equation, the angular rate about the body X-axis (pB) and

that about the body Z-axis (r 8) are assumed to remain unchanged at zero. In

addition, the angular rate about the body Y-axis, and the linear velocities

15
about the body X, Y and Z axis (uB, vB, wB respectively), are initialized to

zero.

Combining these speeds and accelerations, the rate of change of angle of

attack is calculated as

2 2

a = (u B wB - wB uB) / ( uB ÷ wB ) -- (2.9)

The pitching moment combined with the body Y-axis moment of inertia

(obtained from the aerodynamic data base as a function of weight), results

in pitch acceleration.

qB = MBtotal/ IYY B -- (2.10)

Rate of change of pitch attitude is written as

eB = qB -- (2.11)

The flight path'angle (Y) and the ground speed (v G) are computed as:

-- eB - a -- (2.12)

vG = /(UB 2 + WB2) i COS Y -- (2.13)

The parameters (e B, UB' HRWY' WB' qB' v

) are integrated using the G

second order Adam-Bashworth numerical integration scheme (equation 2.14) to

obtain new values for (8B, UB, HRWY, WB, qB' DRWY)"

+ AT

Xn+ I = xn _- ( 3 xn - Xn_ I) -- (2.14)

The thrust forces used in this model are generated using the

manufacturer supplied engine mathematical model. Throttle position, true

16
airspeed, ambient temperature, ambient pressure, and present engine pressure

ratio are inputs to this model. The outputs are engine pressure ratio,

engine thrust, compressor and turbine stage rotation speeds, fuel flow rate

and exhaust gas temperature. This information is summarizedin Figure 2.3.

A nominal throttle movement time history that duplicates typical

operational procedures was selected . This involves moving the throttle to

an intermediate setting and waiting until the engine pressure ratio attains

a prescribed value, and then moving the throttle to the suggested takeoff

setting. This throttle movementis replicated by the model.

The commandedthrottle position is processed by a throttle servo before

being input to the engine mathematical model. This throttle servo is

represented by a first order lag with transfer function

6th (S) a -- (2.15)

6th_S) S+a

which, after discrete transformation (based on References 6 and 7 and

described in Appendix A) is written as

6th(nT) = _ _th[(n-1)T] + (I-_) 6thc(nT) -- (2.16)

where _th(nT)

th C

T

= servo output at time "nT'

-aT

= e -- 0.60653

(nT) = throttle command at time "nT'

sampling interval _ 0.05 second

The landing gear forces and moments are also generated by a manufacturer

supplied mathematical mode_i. The inputs to this model and the outputs from

it are illustrated in Figure 2.4.

17
Q3

I,... CO

Z_ZZ_

_.. ¢ID

q3

E

=m_=$

o _- .._,=

A A A A A _ A

Q.)

_ _ *_

m

0

E

°_

E

C

,..,.

°_

0

'0

H

¢1)

0

Z

._

18
_o

r-

_Z

A O

r- tD

CZ

r- f- ,-_

OoE

._ >':-'_ ._

C O "--

-_'__"_,_-2 ,@_,.E

°_

_Q

_J

=1

0

Itl

_U

H

0

.,-I

(1)

I1)

.,,.t

19
2.2.1.3 Curve Fitting

The next block of the algorithm pretakeoff portion deals with curve

fitting the airplane true airspeed ,VT, (the independent variable) and the

along track acceleration ,a, (the dependent variable) to generate a set of

coefficients for a "scheduled performance" data set for the takeoff run.

The curve fitting process is chosen to minimize the memory requirement to

store nominal performance data and to facilitate the process of estimating

the runway rolling friction coefficient. A least square error cubic

polynomial curvefit method (Reference 8) is utilized to generate

a = A0 + A1v T + A2 VT2 + A3 VT3 -- (2.17)

This process is carried out twice; once for a low friction coefficient

(_ = 0.005) and a second time for a high friction coefficient (_ = 0.040).

The low friction coefficient value is chosen to be slightly lower than the

nominal lower bound suggested in Reference 9. Similarly the high value is

chosen to be higher than the nominal upper bound suggested in the same

Reference 9.

Table 2.2 summarizes the flight conditions for a typical takeoff case.

Figure 2.5 illustrates the acceleration versus true airspeed curves obtained

from the pretakeoff computations for the conditions of Table 2.2. It is

seen from the figure that the curve-fit matches the computed curve only

after the peak value of acceleration has been attained. This is because the

monitor algorithm comes on-line after the dynamics due to the throttle has

died out.

20
Table 2.2 : Flight Conditions for the sample Pretakeoff Calculations

Weight _ 88504 lbs

Center of Gravity _ 19% c behind LEMAC

Flap setting _ 5 deg

Pressure Altitude _ 32 feet

Ambient Temperature _ 75 deg F

where LEMAC _ leading edge of mean aerodynamic chord

2.2.2 Real Time Segment

The monitor system's real time segment is used I0 times per second in

the flight control or navigation computer during the actual takeoff run.

This segment performs the following functions.

I) Initially commands the throttle to the required throttle

setting for takeoff

2) Monitors the engine in terms of its engine pressure ratio

3) Monitors the performance of the airplane in terms of its

acceleration performance

4) Estimates the runway rolling friction coefficient

5) Predicts the runway required to achieve rotation speed

6) Predicts the runway required to stop the airplane and

7) Generates go or abort signals.

It also has the capability to command the application of brakes and reverse

thrust. To accomplish these tasks, the algorithm requires a number of

aircraft parameter measurements. Prior to use by the system, aircraft

sensor data is passed through a filter network. The airplane performance is

21
u_

0

00

II II

IE0

,--0 (J

(.} -._ < _

22

o

o

ffl oE

L.

I--

o

--

--0

4J

u_0

(_ -,-I

._ (_

{J

-,t

,--t

_0

_U

.,.-I

_Um t_ •,-.I .,-4

_4

m_

_0

m_

I1) I1) •_t _

tlJ

,-t

Ill U

_4

I]j
computed utilizing the filtered sensor data in a point mass formulation for

motion along the runway. This computed performance figure is compared with

the sensor measured values. The difference is used either to estimate a

rolling friction coefficient - a one time operation, or is utilized in the

generation of Go/Abort signals. Measured and calculated values are employed

during each iteration to predict the runway length required to achieve

rotation speed and to bring the airplane to a stop. A comparison of the

available and required runway lengths is also used to generate a Go/Abort

signal. A functional flow diagram is shown in Figure 2.6 and a detailed

programming flow chart of the real time segment in included in Appendix C.

2.2.2.1 Data Requirements

The real-time segment requires several input parameters. Some of these

are one-time inputs while others are continuously needed inputs. The

one-time inputs include: ambient temperature, ambient pressure, runway

winds, airplane weight, stabilizer setting, and flap selection. All of the

above values are obtained from the pretakeoff segment. Three additional

necessary one-time parameters are runway available for rotation, runway

available to stop the airplane, and a nominal rolling friction coefficient.

The parameters needed on a continuous basis are supplied by sensors and

include: left and right throttle position, left and right engine pressure

ratio, ground speed, along track acceleration, and calibrated airspeed.

The data requirements for the real time segment are summarized in

Table 2.3

23
|

I

Intitialize

variables, constants

|

|

!

Atmospheric

calculations

12.2.2.21

II

(I

!

Generation

of basisfor

scheduled performance

(2.2.2,3)

I

I

Table lookup

(2.2.2.4)

I

1

Filtering of

sensedparameters

(2.2.2.5)

I

I

I

I

Onepass

path

Figure 2.6:

Throttle command

(2.2.2.6)

The Real-Time

I

Continuous

passpath

Segment.

24
!

!

Enginepressure

ratio prediction

(2.2.2.7)

|

|

|

Thrust estimation

(2.2.2.8)

I

I

Point massperformance

estimation

(2.2.2.9)

I

!

Estimationof

rolling friction

coefficient

(2.2.2.10)

II

Figure 2.6: Continued

25

I
C

Predict

runway required

to stop

(2.2.2.12)

Generate

go/abort

signal/command

(2.2.2.13)

Figure 2.6: Continued.

26
Table 2.3: Parameters needed for the Real Time Segment

ONE-TIME INPUTS

Ambient Temperature

Ambient Pressure

Runway Wind

Weight 1

Flap Selection

Stabilizer Setting

Obtained from the

Pretakeoff segment

Runway Available for Rotation

Runway available for Stopping

Nominal Rolling Friction Coefficient

NEEDED CONTINUOUSLY

Left & Right Throttle position

Left & Right Engine Pressure Ratio

Ground Speed

Along Track Acceleration

Calibrated Airspeed

27
2.2.2.2 Atmospheric Calculations

In this block, the pressure altitude and ambient temperature inputs are

used with ideal gas laws to calculate air density, temperature and pressure

ratios, and the speed of sound. This is a one-time operation and is used

during the first pass through the real-time segment.

2.2.2.3 Generation of Scheduled Performance Basis

In the pretakeoff segment a cubic curve fit was performed to obtain

acceleration as a function of true airspeed as given by equation 2.17. This

was done for two rolling friction coefficients. In the present section a

set of coefficients is obtained for the nominal rolling friction coefficient

by linear interpolation as indicated below:

A0 (_2 - _ ) + A0 (_ - _I )

U1 _2

A0 = (_2 - _I ) -- (2.18a)

AI (_2 - U ) + AI (U - _I )

_I _2

AI = (_2 - _I ) -- (2.18b)

A2 (_2 - U ) + A2 (U - _I )

_I _2 •

A2 = (_2 - _I ) -- (2.18c)

A3 (W2 - W ) + A 3 (_ - U1 )

_1 u2

A3 = (u 2 _ _I ) -- (2.18d)

28
where

_I = low rolling friction coefficient

_2 = high rolling friction coefficient

= present estimate rolling friction coefficient

The basis for scheduled acceleration performance becomes

a = A 0 + AI vT + A2 VT 2 + A 3 VT3 -- (2.19)

This procedure is carried out one time at the beginning of the real-time

segment using the pilot input friction coefficient for _, and a second time

with the algorithm estimated friction coefficient (section 2.2.2.10).

2.2.2.4 Table Lookup..

Three table lookups are performed in this block. In the first table

lookup, a stabilizer setting (iH) is obtained as a function of the center of

gravity position and could be displayed in the cockpit. Also the nominal

lift and drag coefficients (CL, C D respectively), increments in llft and

drag coefficients with full flight spoiler deflections (ACLFsP, ACDFsP), and

increments in lift and drag coefficients with full ground spoiler

deflections (ACLGsP, ACDGsP), are obtained as functions of flap deflection.

The ground effect is accounted for by assuming a nominal gear compression.

The second table lookup is a repeat of the flight manual lookup carried

out during the pretakeoff segment. Using airplane weight, runway pressure

altitude, ambient temperature, and selected flap setting, the decision speed

(V I), and the rotation speed (V R) are obtained from the flight manual.

29
The third table lookup identifies the recommended takeoff engine

pressure ratio (EPR) setting and the corresponding throttle setting, and the

throttle setting necessary to achieve the intermediate EPRvalue (for the

nominal throttle movementof section 2.2.1.1). All of these are functions

of ambient temperature and pressure.

2.2.2.5 Filtering of sensed parameters

The measured acceleration and ground speed values are processed through

a second order complementary filter to estimate the bias present in the

acceleration signal. The details of this complementary filter

implementation are described in Appendix B (Reference 10). The final

equations are

_n+1 _ _ --nX+ F -nU -- (2.20a)

where

= [-°18 84 0464

r = 0.1416 0.0464

0.09287

0.9976_

0.0928_

-0.0024_

vG -- x(1) -- (2.20b)

aF1 = aM + x(2) -- (2.20c)

During the first pass through the real time segment, x(1) is initialized

to the measured ground speed and x(2) is initialized to zero. The filter

3O
output for both ground speed and acceleration is the measuredvalue Itself.A

new set of values is then calculated for the x's. During subsequent passes

the x values used are from the previous pass and after use they are updated.

The acceleration output from the complementary filter above, and the

measuredvalues of EPRleft and right, calibrated airspeed (CAS), and true

airspeed (TAS) are passed through a first order lag filter ,to remove noise,

as depicted below.

a = _ aO + (I - _) aF1

fhtt .PRo + (I M

left rl g_t ir_f_t

CAS = _ CAS O + (I - E) CAS M

TAS = _ TAS O + (I - E) TAS M

-- (2.21)

with _ = 0.7304026

where the subscript "O" stands for old and the subscript "M" stands for

measured sensor data.

During the first pass

aO = aFt

and the other old values are set equal to the measured values. For

subsequent passes the old value is the filter output from the previous pass.

2.2.2.6 Throttle Command

This throttle command is identical to the throttle command system in the

pretakeoff segment. This involves moving the throttle to an intermediate

setting and waiting until the engine pressure ratio attains a prescribed

value, and then moving the throttle to the suggested takeoff setting.

31
2.2.2.7 Engine Pressure Ratio Prediction

An empirical model of the steady state behavior of the Engine Pressure

Ratio (EPR) is extracted from the manufacturer supplied engine model and is

used in the real time segment to predict what the EPR should be. The

transients caused by throttle movement and engine spool up are neglected in

this model.

where

^

EPRleft = f(6thl_ , Ttota I ) -- (2.22) rlg_t f_t

^

EPRleft = left & right estimated EPR

rlg_t

6thleft _ = left & right measured throttle position

rlg_

Ttota I = total (stagnation) temperature

2.2.2.8 Thrust Estimation

In a fashion similar to the EPR computations, thrust calculation is

performed with an empirical relation extracted from the manufacturer

supplied engine model. Thrust estimation is based on measured EPR and

^

computed Mach number (M)

A A

T = f(EPR , M) -- (2.23)

_t _t

2.2.2.9 Point Mass Performance Estimation

The developments of this section are based on Reference 9.

True airspeed is the sum of wind speed and filtered ground speed.

^

vT = vG + uw -- (2.24)

32
The estimated true airspeed is used in estimating a Mach number, and

with the density computed by the atmospheric calculations, a dynamic

pressure is calculated. Using this dynamic pressure, and nominal lift and

drag coefficients from the table lookup, the lift and drag forces are

estimated. A friction force is estimated using the estimated rolling

friction coefficient (pilot input value until the algorithm estimates it as

described in section 2.2.2.10 and after that the algorithm estimated value),

weight of the airplane (assumedto remain constant), and the estimated lift

force. Using this information an acceleration is estimated. An estimate of

the ground speed is obtained by performing a rectangular integration on the

estimated acceleration. An estimate of the runway used is obtained by

performing a rectangular integration using the filtered ground speed. The

equations pertinent to these estimations are as follows:

where

^ ^

M = vT / A -- (2.25a)

A = Speed of sound

- I ^ 2 -- (2.25b)

q = _ P vT

L = q S CL -- (2.25c)

A

D = q S CD -- (2.25d)

Ffr= _ (W - L) -- (2.25e)

a = (Tleft ÷ Tright- D - Ffr) / m -- (2.25f)

vG = VGo ÷ AT a0 -- (2.25g)

DRWY = DRW Y + AT vG -- (2.25h)

33
with AT = 0.I second

2.2.2.10 Estimation of rolling friction coefficient

As discussed earlier, rolling friction coefficient is not easily

assessed. In the real time segment, the difference between the estimated

and measured acceleration is used to estimate a rolling friction

coefficient. This is done as follows. First, thrust is represented as a

cubic in true airspeed

T = TO + T I vT + T2 VT 2 + T3 VT3 -- (2.26)

Then using equations (2.25b) through (2.25e) and (2.26), the acceleration

equation (2.26f) can be rewritten as

a = g((T 0 - _ W) + T I vT + (T 2 - _pSC I D + _ppSCL)V I T2 + T3VT 3) / W

-- (2.27)

At any given true airspeed for two given runway friction coefficients

the two acceleration expressions are represented as

^a = g((T 0 - ^_i W) + TIVT + (T2 - _pSCDI + 2P11^pSCL)VT 2 + T3VT 3) I W

-- (2.28)

a = g((T 0 - _2 W) + T1v T + (T 2 - I_pSC D + _p2PSCL)VT I^ 2 + T3VT 3 ) / W

^

Subtracting a from a

a^ - a = g( W - _I pSCLVT2 ) (_2^ - Ul^ ) / W

or solving the above equation for the difference between the friction

coefficients

Ap....= U 2 -WI = (a - a) / (g ( W - I_ p S CL VT2 ) / W ) -- (2.29)

34
where

A

_2 = estimate of the actual runway friction coefficient

A

_I = assumed friction coefficient

AU = estimated amount by which the friction coefficient has to

be adjusted

Thus the actual runway friction coefficient can be estimated as

_2 = _I + A_

-- (2.30)

The above procedure is a one time operation carried out early into the

takeoff run. Immediately after this process the basis for scheduled

^

performance (section 2.2.2.3) is repeated with _2 as the present estimate of

the friction coefficient.

2.2.2.11 Prediction of the Runway Required

The runway required to achieve rotation speed is computed by a numerical

integration scheme. The difference between the present speed and the

rotation speed (true airspeed for rotation) is divided into ten equal

velocity increments.

Vstep-- (vT -v T) / 10 -- (2.31a)

rotation

The speed at the center of the first interval is

v -- vT + Vstep / 2 -- (2.31b)

The variation of acceleration with speed is accounted for by using the

scheduled performance equation (equation 2.19) with the v calculated above

(equation 2.3!b).

a = A0 + AI v + A2 v2 + A 3 v3 -- (2.31c)

35
The time for each speed interval is given by

At -- Vstep / a -- (2.31d)

and the distance needed for each interval can be approximated as

As = At (v - uW)

= Vstep (v- uW) / a -- (2.31e)

The center speed of the next interval is computed by adding Vstep to the

present center speed. This whole process is repeated ten times to cover the

entire speed range. The sum of all the As's gives a prediction of the

runway required to achieve rotation speed. A detailed flow chart of this

mechanization is included in Appendix C.

2.2.2.12 Prediction of Stopping Distance

To calculate stopping distance, the takeoff monitor system simulates the

effect of a series of commands to the airplane in order to determine the

distance required to stop the vehicle if these actions were actually taken.

No commands are actually passed to the airplane to bring the vehicle to a

stop.

Computation of stopping distance is based on the following assumptions.

I) The flight spoilers are commanded through servos modelled as a

first order lag.

2) The ground spoilers are commanded through servos modelled as a

first order lag.

3) With full braking the rolling friction coefficient is

increased by a constant amount over the prevalent value.

4) Maximum wheel braking is achieved in a ramp fashion per given

time period.

36
5) Thrust is assumed to vary linearly with throttle position

(based on present thrust and throttle position).

6) The changes in lift and drag coefficients produced by flight

and ground spoilers are assumed to vary linearly with

deflection.

The variation of llft and drag coefficients per unit deflection of the

flight and ground spoilers is computed.

ACLFs P ACLFSPmax

= -- (2.32a)

6FSP 6FSP

max

ACDFs P ACDFSPmax

_FSP 6FSP

max

-- (2.32b)

ACLGs P ACLGSPmax

6GSP _GSP

max

-- (2.32c)

ACDGs P ACDGSPmax

6GSP 6GSP

max

-- (2.32d)

where subscript "FSP" stands for Flight Spoilers

subscript "GSP" stands for Ground Spoilers

The variation of thrust per unit deflection of the throttle are calculated.

+ T -Tleftidle-Tri Tleftpresent rightpresen t ghtidle

= 2 * ......

6 +

thleft _thright

-- (2.32e)

37
where

^

= estimated thrust for zero throttle

Tleft

rlg_tidle

Next the rate of increase of braking is computed.

APbrak e APbrakema x

t t

ramp

-- (2.32f)

where A_brake = maximum increment in rolling friction coefficient

max from full braking

= 0.45

and t

ramp

= ramp time for full braking

= 0.6 second

A throttle command to zero, and flight and ground spoilers being

commanded to their full deflections are simulated. These simulated

movements are slaved through their respective servos.

6th = _th 6th

new old

-- (2.33a)

6GSP = _GSP 6GSP + (I - _GSP) 6GS P -- (2.33b)

new old max

_GSPne w = _GSP 6GSPold + (I - _GSP) 6GSPmax

-- (2.33c)

with _th = 0.36788

_FSP = 0.36788

_GSP = 0.13534

Based on the simulated throttle position and the assumed linear

variation of thrust with throttle position, a simulated engine thrust is

computed.

38
Th . _T_ 6 -- (2.34)

_th th

Using the simulated flight and ground spoiler positions and the nominal

values for the lift and drag coefficients, simulated lift and drag

coefficients are computed.

ACLFsP

ACLFsP - 6FSP 6FSPnew -- (2.35a)

ACDFsP

ACDFsP = _FSP _FSPnew -- (2.35b)

ACLGsP

ACLGsP = 6GSP 6GSPnew -- (2.35c)

ACDGsP

= -- (2.35d)

ACDGs P 6GS P 6GSPne w

CL = CLnominal + ACLFsP + ACLGsP

CD = CD +

nominal + ACDFsP ACDGsP

-- (2.36a)

-- (2.36b)

The increase in rolling friction coefficient is computed as a product of the

braking rate and the time elapsed (initialized to zero for the first pass).

A_brake

APbrake = t t

iC A_brake > APbrak e

max

then APbrake = APbrak e

max

-- (2.36c)

39
The net rolling friction coefficient is computedas the sumof the unbraked

rolling friction coefficient and the increase due to braking, calculated

above.

where

_ _nominal + A_brake

t I t + At

At I integration time step

These lift and drag coefficients, the net rolling friction coefficient, and

the weight of the airplane are used in a point massperformance calculation

similar to that in section 2.2.2.9. The acceleration is integrated over a

time step to determine the change in ground speed. The time elapsed is

incremented by the time step. Newpositions for the throttles, and flight

and ground spoilers are computedand the performance calculations repeated.

This process is carried out until the ground speed reaches zero. The total

distance used in bringing the airplane to a stop in this simulated stopping

is the stopping distance. Appendix C includes a program flow chart for the

computation of the stopping distance.

2.2.2.13 Generation of Go/Abort Signal/Command

The engine pressure ratio (EPR) is used as a check on engine health.

Sufficient time is allowed for the transients caused by throttle movement to

die out. After this, the measured and predicted EPRs are compared. If they

are different by more than a preselected limit then an engine failure flag

is set.

I EPRleft - EPRleft I

EPRleft

> EPRerro r limitS> E. Failleft

-- (2.38a)

40
A

EPR

right

> EPRerro r limit=> E. Failright

-- (2.38b)

with EPRerror limit = 0.15

After the instant at which the rolling friction coefficient is

estimated, any difference between the measured and the predicted

accelerations causes a performance failure flag to be set.

A

.[.a -at> a

a error limit => PER. Fail -- (2.38c)

with a = 0.15

error limit

The following conditions result in a Go signal/command:

I) No engine failure flag or performance failure flag is set and

the runway available is greater than the runway required to

attain rotation speed.

Only one engine failure flag is set and the runway remaining

is less than that required for stopping the airplane.

Performance failure flag is set without either engine failure

flag being set and there is insufficient runway length for

stopping.

2)

3)

The following conditions result in a Abort signal/command:

I) Runway length available for achieving rotation speed is less

than that required.

2) Both the engine failure flags are set.

3) One engine failure flag is set and there is sufficient runway

length available for stopping.

4) Performance failure flag is set and sufficient runway length

is available for stopping.

21
CHAPTER3

SIMULATION MODEL

3.1 Introduction

The previous chapters dealt with the development of an algorithm and the

data requirements for that algorithm. Before the algorithm can be

implemented on an actual airplane, it has to be validated in a test

environment as close to the real operational environment as possible. To

accomplish this initial testing and validation of the algorithm, a good

model of the plant (in this case the airplane in ground roll) is required.

This chapter describes the model used in this testing and development.

The parameters computed by the model are treated as the actual quantities.

Section 3.2 describes the model used and outlines its main components.

3.2 The Model

The plant model proposed for use in testing the algorithm is the six

degree of freedom nonlinear batch simulation model of the Transport Systems

Research Vehicle (TSRV) B-737 (Reference 11) which is available on the

computer system at NASA Langley Research Center. This batch simulation is

implemented to run at the rate of 20 iterations to a second. This gives an

iteration time step of 0.05 second.

The batch simulation uses a combination of inertial and wind axes

systems in all its computations. Figure 3.1 shows an outline of this batch

simulation. The aircraft variables are first initialized as needed for the

particular run. The airplane is then trimmed for a steady state flight

condition. Once the airplane has achieved trim for the given steady state

flight condition, it is then put in the operate mode. In this mode, the

42
Start

Initialize airplane

variables

Initialize user

systemrelated

variables

Trim airplane

(3.2. li

Lookup inertias

computeEULERtransform

matrix, airspeeds,ground

speed, MACH number,

aerodynamicangles,

accelerationdue to gravity

and angular rates.

(3.2.6.1)

I

Compute,path,vertical

and alongbodyaxis

accelerations

(3.2.6.6)

I

Airplanesensor

package

(3.2.2)

Figure 3.1 : Flow Diagram for the Six Degree of Freedom TSRV

B-737 Batch Simulation.

43
I

User implemented

control system

(3.2.3)

I

Processinput

commands

(3.2.4)

I

Computeengine

parameters

(3.2.5)

Aircraft dynamics

(3.2.6)

Intergration

(3.2.7)

Run

ermination requirement

satisfied

Figure 3.1: Continued

44
control systems implemented by the user are brought on llne. These systems

become effective in perturbing the airplane from the trimmed steady state by

generating new control inputs. The states of the airplane, control inputs,

and constants pertinent to the simulation run serve as inputs to the

aircraft dynamics module. The computations in the aircraft dynamics module

result in new values for the state derivatives. These state derivatives are

then numerically integrated to obtain new states. Control then passes back

to the module which contains the user generated control laws. This

procedure continues until the simulation is halted because of some parameter

having reached a desired value. Each of the modules shown in Figure 3.1 is

discussed below.

3.2.1 Trimming the Airplane

Airplane trimming is accomplished using a modified secant iteration

method which solves a nonlinear system of equations of the form

where

fi(x) = 0

x = (x I ,

i=I, ,n

,xn ) -- the independent trim variables

-- (3.1)

with fl is a set of n airplane force and moment equations

The trimming process is accomplished by iteratively computing a new

n-dimensional vector of independent trim variables satisfying an

n-dimensional vector of dependent trim constraints to within a preselected

tolerance level.

3.2.2 Aircraft Sensor Package

This module is utilized to simulate real sensors mounted on an actual

aircraft with all their attendant noise and bias values. A pseudo random

number generator is utilized to superimpose zero mean Gaussian noise signals

45
with any chosen standard deviations on any of the sensed parameters. This

module also includes the capability of adding a constant bias value to the

measuredparameters. Table 3.1 summarizes the noise characteristics used in

this study and represents a set of typical sensor noise characteristics.

where

Table 3.1 :Noise and Bias Characteristics

All noises are Gaussian with standard

deviations as indicated below

PARAMETER

Along track Acceleration (ft/s 2

Pressure Altitude

Calibrated Airspeed (kts)

True Airspeed (fps)

Throttle Position (deg)

Engine Pressure Ratio

Engine N I RPM

Exhaust Gas Temperature (°C)

Fuel Flow Rate (lb/hr)

SIGMA BIAS

O. 32 O. 32

0.0 0.0

2.0 0.0

2.0 4.0

O.2 -0.4

0.01 0.02

0.01 0.02

0.01 0.02

0.01 0.02

SIGMA

BIAS

-- Standard Deviation

-- Constant Bias value

46
3.2.3 User Implemented Control Systems

This is the module where the control system designed by the user will be

implemented for testing. This is the module where the Takeoff Performance

Monitoring Algorithm developed in the previous chapter will be implemented.

3.2.4 Process Input Commands

The commands generated by the user implemented control system are passed

through their respective servos to generate actual positions of control

surfaces, and throttles. Any inner loop control systems that are required

on the airplane, such as a yaw damper, pitch control system, or a roll

control system are included in this module. Any measured inputs to such

control systems are affected by the sensor package noises of section 3.2.2.

3.2.5 Compute Engine related Parameters

Figure 3.2 shows the engine module block diagram. The throttle position

input to this module is converted into a cross shaft angle. This cross

shaft angle is also a function of the difference in the throttle positions

between the present and previous iterations. The cross shaft angle position

along with the engine inlet stagnation temperature and the Mach number are

utilized in computing a commanded engine pressure ratio (EPR). In this

process an idle EPR value is computed as a function of a bleed valve

controlled by the Mach number and altitude. This bleed valve position (open

or closed) is also a function of the EPR value from the previous iteration

and whether or not the engine is going through start up. The commanded EPR

goes through an EPR dynamics loop which is controlled by the rate at which

the EPR is commanded to change. The resulting EPH directly determines the

thrust developed by the engine, the fuel flow rate, the compressor stage and

47
--_) r A

_t k_

0

e-

¢j

¢Y

IlJ

0

llJ

0

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g_

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°°° h _j

bO t._

...J bO I--

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,'," bJ ._J

0

C.J i., UJ

Z

Z Z

k:. ILl bJ

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r',

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r_

t/)

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rvr_ Z

_-- ,,,

"r- _-o

I-'-

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1,1

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49
turbine stage revolution rates (N I and N 2 respectively), and the exhaust gas

temperature.

3.2.6 Aircraft Dynamics

Figure 3.3 shows the detailed block diagram representation of the

aircraft dynamics module used in the simulation. The aircraft dynamics

model implemented in this simulation follows the developments of Reference

12. The inertial velocities of the airplane are transformed to the three

airplane body axes. The velocities relative to the airmass, the angle of

attack, sideslip angle, true airspeed, calibrated airspeed, Mach number, and

the stability axis body angular rates are computed. The airplane stability

derivatives are obtained from the aerodynamic data base and the forces and

moments along the stability axis are computed. These forces and moments are

then transformed into the airplane body axis. The forces and moments

generated by the landing gear and the engines along the body axis are

computed. The sum of the body axis forces and moments along with the

components of the acceleration due to gravity gives the net body axis linear

and angular accelerations. The present states, the resultant forces and

moments, along with the Euler transformations are used in computing the

derivatives of the states:

= F ( x , u ) -- (3.1)

where x = State vector

u-- Controls

50
IIIII1IIIIIIIIIIIIIIIIIIIIIIIIII1III

51

,-4

Ul

.,-4

:>I

14-4

oo

-,-4
The state vector is made up of the following parameters:

H

VN

VE

V D

PB

qB

rB

O

Airplane Latitude

Airplane Longitude

Altitude of the Airplane Center of Gravity

Velocity North

Velocity East

Velocity Down

Body Axis Roll Rate

Body Axis Pitch Rate

Body Axis Yaw Rate

Yaw Angle

Pitch Angle

Bank Angle

The controls vector consists of

Flap Deflection

Stabilizer Deflection

Gear Up or Down

Aileron Deflection

6FLAPS

6STAB

6GEAR

6

a

6 R

6

e

6SP R

6SP L

Rudder Deflection

Elevator Deflection

Right Spoiler Deflection

Left Spoiler Deflection

Euler Angles

52
THRUST Yes or No REVERSE

A brief description of each of the segmentsof the aircraft dynamics module

is given in the following subsections.

3.2.6.1 Landing Gear Forces and Moments

The landing gear forces and moments segment computes the forces and

moments along the body axis. These forces (L G , L G , ) and moments

XB YB LGZB

(L G , L G , L G ) are based on the pitch attitude and bank angles, pitch

L B MB N B

and roll rates, body axis velocities, computed gear spring forces (based on

computed oleo compression), and gear damping forces (based on gear

compression forces). The rolling friction forces and the braking forces

generated at the gears are also computed in this segment. These forces are

transformed into body axis forces and moments.

3.2.6.2 Aerodynamic Forces and Moments

The aerodynamic forces and moments acting on the airplane are computed

in this segment. This is accomplished in three steps. First the values for

the aerodynamic derivatives (CL, CD, Cy, Cm, CI, C n) are computed by

utilizing a table lookup based on the aerodynamic angles, proximity to the

ground, control surface deflections, and Mach number. Using the dynamic

pressure, and airplane constants (mean aerodynamic chord, reference wing

area, and wing span), the forces and moments along the stability axis are

calculated. These stability axis forces and moments are then transformed to

the body axis.

53
3.2.6.3 Engine Forces and Moments

The engine thrust forces (generated from the engine model) are combined

with the engine orientation in the body axis system to calculate the forces

and moments produced by the engine along the body axis.

3.2.6.4 Miscellaneous Equations of Motion

This segment includes equations of motion not covered in any of the

other segments. The Euler transformation matrix computation, airplane mass,

table lookup for moments and products of inertia, sines and cosines of the

longitude and latitude, airplane velocities relative to the airmass in the

inertial frame and their transformations to the body axis system,

computations of the aerodynamic angles (a, B), true and calibrated

airspeeds, dynamic pressure, Mach number, body angular rates along the

stability axis and their nondimensional equivalents, components of the

acceleration due to gravity along the body axis, and acceleration due to

body rates are computed in this segment.

3.2.6.5 Sum of Forces and Moments

The forces and moments generated from the different segments described

above are added in this segment to generate the net body axis forces and

moments acting on the airplane. The total body axis forces are also

transformed into the inertial coordinate frame relative to the airmass.

3.2.6.6 Accelerations

The accelerations caused by the total forces acting on the airplane

(section 3.2.6.5) are computed using the force-mass relationship. The net

accelerations in the body frame are computed as a sum of force generated

accelerations, the components of the acceleration due to gravity and the

accelerations resulting from the body angular rates (section 3.2.6.4). The

54
along track, cross track, and vertical accelerations are computed as

functions of inertial velocities and accelerations.

3.2.6.7 State Derivatives

The state derivatives are computed using the properties of the inertial

and wind axis systems. These are based on the total forces and body angular

rates (section 3.2.6.5), the mass of the airplane and the gravitational

forces (section 3.2.6.4), and the states themselves.

3.2.7 Integration

The state derivatives are integrated using the Adam-Bashworth numerical

integration scheme of equation (2.14). The fuel flow rate along with the

iteration time step is used in computing the amount of fuel used and hence a

new weight for the airplane.

3.3 Model limitations

The model does not allow the airplane to be trimmed at zero equivalent

speed. This necessitates the takeoff run to start at some small non-zero

airspeed such as true airspeed of 0.5 knot. Similarly, the model can not be

brought to a complete stop on abort. The model does not provide for varying

the runway friction force from zero until the limiting frictional force

value, and hence if an adequate forward thrust is not provided, the

frictional force will cause the airplane to move backwards.

The simulation model can not handle sloped runways.

55
CHAPTER4

TAKEOFF MONITOR ALGORITHM EVALUATION

4.1 Introduction

A takeoff performance monitoring algorithm was described in chapter 2.

Chapter 3 described a plant with which to evaluate this algorithm. This

chapter describes the evaluation of the algorithm using the Transport

Systems Research Vehicle (TSRV) B-737 model. Section 4.2 describes the

setup of the batch simulation for this evaluation. Section 4.3 presents

normal takeoff test cases and two performance degradation cases are

considered in section 4.4.

4.2 The Batch Simulation Setup

The batch simulation of the takeoff performance monitoring algorithm is

a two part process. The first consists of running the monitor system

pretakeoff portion and culminates with the storing of nominal performance

data. At the completion of the first part, the batch simulation of the TSRV

B-737 begins with the input of ambient conditions and airplane loading

information from the same input file as the first part.

The batch simulation is updated every 0.05 second (20 times a

second) while the takeoff performance monitoring algorithm is executed ten

times each second. This is accomplished by calling the algorithm every

other iteration. The simulation is stopped after the calibrated airspeed

from the batch simulation model of the airplane reaches the flight manual

recommended rotation speed for the given airplane loading.

4.3 Normal Takeoff Test Cases

To demonstrate the algorithm operation ten cases are presented. Each of

these ten cases represents one possible combination of ambient and airplane

56
loading condition and are listed in Table 4.1. An actual airplane, for

these cases, would have gone through takeoff roll and successfully rotated

off the runway after reaching the flight manual recommendedrotation speed.

CASENO

I

II

III

IV

V

VI

VII

VIII

IX

X

Table 4.1: Normal Takeoff Test Cases

PRESSURE

ALTITUDE

(feet)

AMBIENT

TEMP.

(o F)

RUNWAY

WINDS

(knots)

WE IGHT

(ibs.)

32. 75 •

O. 75.

I00. 75.

32. 0.

32. 100.

32. 75.

32. 75.

32. 75.

32. 75.

32. 75.

O. 885O4.

O. 88504.

0. 885O4.

O. 88504.

O. 885O4.

I0. 885O4.

2O. 885O4.

O. 885O4.

0. 885O4.

O. 98OOO.

RUNWAY

FRICTION

COEFF.

(-)

.015

.015

.015

.015

.015

.015

.015

.025

.007

.015

Figures 4.1 shows the time histories obtained from the simulation run

for case I, assuming perfect aircraft sensors. Figure 4.2 shows the time

histories for the same case with realistic sensor noises as detailed in

Table 3.1.

57
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69
In Figure 4.1a "runway used" computed in the simulation model and the

algorithm predicted "runway used" numbers are plotted against time. Towards

the end of the takeoff run, the simulation model computed runway used is

about a hundred feet more than the algorithm predicted runway used.

Figure 4.1b shows ground speeds from three sources plotted against

time:(1) the sensor output from the simulation model after filtering;

(2) the algorithm predicted value; and (3) the ideal sensor output from the

simulation model. The filtered sensor plot and the ideal sensor plot are

seen to be indistinguishable, whereas the predicted ground speed is seen to

lag behind the other two values. This is caused by the first order lag

filter that initializes the predicted ground speed to the measured value

during the first pass through the algorithm.

Figure 4.1c illustrates the Engine Pressure Ratio (EPR) time histories.

This figure shows that there is practically no difference between the

measured and predicted engine pressure ratios after 10 seconds. Prior to

this time the steady state engine model used in the algorithm is not

expected to follow the output from the simulation which accounts for the

transients caused by throttle movement. This is acceptable, since the

algorithm does not perform an engine health check until after ten seconds

into the takeoff run.

The algorithm predicted runway length required to achieve rotation speed

is plotted against time in Figure 4.1d. At every instant the runway length

requirement is predicted as a function of the filtered measured ground

speed, the scheduled acceleration performance, and the ground speed required

for rotation. For the present case, the initial runway requirement starts

at about 3200 feet and goes down to zero as the airplane speed increases.

7O
Figure 4.1e shows the difference between the ideal sensor value and

the actual sensor value of acceleration. As this run assumes perfect

sensors, the two curves are on top of each other. Plotted in Figure 4.1f

are the filtered sensor output, predicted value, and the ideal acceleration.

Even though no sensor noise is included in this run, the effect of the

filtering can be clearly seen from the acceleration plots. Below about 10

seconds, the three values of acceleration are seen to be distinct. In this

interval the ideal sensor output is the highest at any given instant,

followed by the filtered sensor output and the predicted value. At the 10

second point the difference between the measured (filter output) and the

predicted value is used to estimate a runway rolling friction coefficient.

This causes the filtered value and the predicted value to be identical at

that point. After the 10 second point, the filter dynamics does not

significantly affect the measuredacceleration in that the filtered and the

ideal sensor value are nearly the same. The predicted value of acceleration

is seen to be slightly on the high side after the ten second point. At

about the rotation speed, the algorithm is seen to overpredict the

acceleration by about one tenth of a foot / second 2 .

Filtered sensor output, predicted value, and an ideal sensor output of

calibrated airspeed are plotted against time in Figure 4.1g. The effect of

the first order lag filtering is seen to cause the filtered sensor output to

be lower than the ideal sensor value. The predicted value of true airspeed

is seen to be almost identical to the filtered sensor output.

The filtered sensor output and the predicted value of true airspeed,

plotted in Figure 4.1h, are seen to be identical. The predicted true

airspeed value plotted here is used in the aerodynamic computations in the

algorithm, but not for any decision making or signal generation.

71
In Figure 4.1i, the sum of the algorithm predicted runway length

requirement and the computedrunway used is plotted against time. This sum

is a measure of the goodness of the runway length requirement prediction by

the algorithm. For an ideal runway length requirement prediction, the sum

will be invariant with time. Locating the point on this curve corresponding

to a time of 10 seconds and drawing a line parallel to the time axis through

this point it is seen that at about the rotation time, the goodness llne is

above the horizontal llne by about a hundred and fifty feet.

Figure 4.1j shows the stopping distance time history obtained from the

algorithm.

The next two figures illustrate the estimates of errors obtained from

the complementaryfilter. Figure 4.1k shows the negative of the estimated

bias in the acceleration signal and Figure 4.11 shows the estimated error in

the ground speedmeasurement. Becauseof the ideal sensor assumption in this

run the filter estimates almost a zero bias in the acceleration (Figure

4.1k) and almost no error in the ground speed (Figure 4.11).

Table 4.2 summarizes the results for run I. These results are obtained

from the output listings that accompany the plots discussed above. The

second column in this table represents the filtered value of the sensed

calibrated airspeed. The third column shows the instantaneous value of the

algorithm predicted runway required to achieve rotation speed. The positive

value in this column shows that the algorithm computed calibrated airspeed

has not yet reached the flight manual recommended rotation speed. The

fourth column gives the runway requirement predicted by the algorithm

immediately after the 10 second adjustment of runway friction coefficient.

The fifth columnshows the runway used to that instant as computed by the

simulation model. The sixth column gives the error in prediction of the

72
runway length required to achieve rotation speed based on the prediction

immediately after the friction coefficient adjustment (column 4) and the

actual runway used (column 5). The negative number in this column indicates

that the runway used was more than the algorithm's prediction and represents

an under prediction by the algorithm. The last column (seventh) shows the

updated runway rolling friction coefficient after the 10 second adjustment.

The 0.010 value shown in this columnrepresents a 33%change from the 0.015

used in the simulation. This large change is caused by the presence of the

filter network in the absenceof noise.

Table 4.2: Summary of results for Case I with Perfect Sensors

CASE NO. MEASURED

CAS

at rotation

PRE DI CTE D

RUNWAY

REQUIRED

PRE DI CTE D

RUNWAY

RE QUI RE D

RUNWAY

USED

RUNWAY

PRE DI CT ION

ERROR

UPDATED

FRICTION

COEFF.

(knots)

I 128.O

at rotation

(feet) (feet)

21. 31!9.

overall

(feet)

31 50.

(feet)

-31 .

( - )

0.010

I

Note: The measured Calibrated Airspeed (CAS) is the filtered sensor

output

The simulation run is stopped based on a measured calibrated airspeed.

However, as the measured value reaches 128 knots (which is the flight manual

recommended rotation speed for this case) the actual calibrated airspeed

obtained from the simulation model is 129.1 knots. Backtracking through the
output listing, the simulation model is found to have reached a calibrated

airspeed of 128.3 knots at 31.9 seconds into the takeoff run. The runway

used (computedby the simulation model) at this point is 3106 feet. Thus

the algorithm is seen to have over predicted the runway required by 13 feet.

The reason that the algorithm predicts a residual runway required figure at

the end is the lag introduced by the filters in the measuredground speed

and acceleration.

Figures 4.2a- 4.21 depict the results from the simulation run for case I

in the presence of realistic sensor noises. It is seen from Figure 4.2a

that the filtered sensor data and the predicted data for ground speed are

closer together than in the ideal sensor run (Figure 4.1a). The

modification of the sensed data by the filter in the absence of noise causes

the difference in Figure 4.1a. The same effect is also observed in the

ground speed plots of Figure 4.2b. The EPRcurves of Figure 4.2c differ

from Figure 4.1c only in the sensor noise effect. The runway length

required to achieve rotation speed is seen to go negative in Figure 4.2d.

This is the result of the simulation model taking more runway to achieve

rotation speed than that predicted by the algorithm. Figure 4.2e shows a

comparison of the ideal sensor output and the unfiltered noisy sensor output

of the acceleration. Figure 4.2f shows better agreement amongthe filtered

sensor output, the predicted value, and the ideal sensor values of

acceleration. Residual effects of the sensor noise, after the filter, are

as seen in this figure. Figure 4.2g shows that the filtered sensor output

of calibrated airspeed does not lag behind the ideal sensor output as much

as in Figure 4.1g. The residual effects of the sensor noise, after

filtering, are discernable in this figure also. Figure 4.2h, whencompared

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to Figure 4.1h shows the effect of sensor noise. Figure 4.2i shows the sum

of the predicted runway length required and the runway used against time.

This curve is seen to remain practically horizontal until very near the end,

and then slopes upward. This upward sloping is an indication that the model

needed more runway to achieve rotation speed than the algorithm had

predicted. Figure 4.2j shows a time history of the required runway length

to stop the airplane, as predicted by the algorithm. It is seen from Figure

4.2k that the complementary filter estimated a bias error of about .3 feet

per second square, which is close to the sensor bias introduced. The

effects of the Gaussian noise on the the ground speed, as estimated by the

complementary filter is depicted in Figure 4.21.

Results obtained from the simulation outputs for all ten cases, with

sensor noises are summarized in Table 4.3. Looking at the column titled

runway prediction error in the above table, the largest absolute error is

seen to be 142 feet (case If). For that case, the table indicates that the

simulation model needed more runway than was predicted by the algorithm, to

achieve rotation speed. As was indicated for the ideal sensor simulation

for the conditions of case I, the filter has the effect of introducing a

time lag on the measured calibrated airspeed. For the worst error condition

in Table 4.3, the actual calibrated airspeed, when the measured (filtered)

value reaches 128.3 knots, is 131.3 knots. Again looking through the output

for the instant the actual calibrated airspeed exceeds 128 knots, it is seen

that the simulation model needed 3088 feet. The algorithm is seen to over

predict the runway requirement, that is the algorithm predicted runway

requirement for attaining rotation speed is more than what is actually

needed. These figures are summarized in Table 4.4.

87
Table 4.3: Summary of results for Table 4.1 Cases with Noisy Sensors

CASE NO.

I

II

III

IV

V

VI

VII

VIII

IX

X

MEASURED

CAS

at rotation

(knots)

128.1

128.3

128.6

129.1

129.4

129.1

128.8

128.2

128.1

138.1

PRE DI CTE D

RUNWAY

REQUIRED

at rotatio

(feet)

-21 .

-21.

-19.

-12.

--6 •

--5.

-5 •

--8.

-10.

-11.

P RE DI CTE D

RUNWAY

RE QUI RE D

I

(feet)

31 32.

3124.

31 49.

2682.

3625.

2690.

2289.

3246.

3045.

41 42.

RUNWAY

USED

overall

(feet)

3262.

3266

3277.

2740.

3603.

2685.

2300.

3272.

3O85.

4155.

RUNWAY

PRE DI CT ION

ERROR

(feet)

-130.

-142.

-128.

-58.

+22.

+5.

-11.

-26.

-40.

-13.

UPDATED

FRICTION

COEFF.

(-)

0.017

0.017

0.017

0.017

0.018

0.017

0.018

0.027

O. 009

0.017

Note: The measured Calibrated Airspeed (CAS) is the filtered sensor

output

It should be pointed out here that any system implemented on an airplane

can only perceive the measured quantity indicated above, and not the actual

value calculated in the simulation. This leads to the conclusion that the

errors caused by using the measured parameters are unavoidable. Looking at

88
the error quantity, it is seen that the magnitude is well within 5% of the

runway used and hence should be acceptable.

Table 4.4: The Effects of Actual versus Measured Calibrated Airspeed

on case II

CASE NO. MEASURED

CAS at

ROTATION

(knots)

II 128.3

ACTUAL

CAS at

ROTATION

(knots)

131.3

128.1

PRE DI CTE D

RUNWAY

RE QUI RE D

(feet)

31 24.

3124.

SIMULATION

RUNWAY

USED

(feet)

3266.

3O88

ERROR

in

PREDICTION

(feet)

4.4 Al_orithm Detection of Engine Malfunctions

The ability of the algorithm to detect engine malfunctions and signal

deficiencies in the performance of the airplane are illustrated in this

section. Two types of engine malfunctions are simulated for this

illustration, as listed below:

I) Engine does not develop hand book EPRs

2) Engine does not develop hand book thrust

89
The section 4.4.1 discusses the first malfunction, and section 4.4.2 deals

with the secondmalfunction.

4.4.1 Engine EPR Failure

The simulation of an engine not developing hand book EPR values can not

be simulated directly without affecting the overall simulation run because

of the implementation of the engine subroutine. This effect is simulated as

follows:

i

ii

iii

Compute the correct EPRs.

Reduce the EPR by a constant factor.

Compute the compressor and turbine stage speeds, engine

thrust, and the Exhaust Gas Temperature (EGT) based on the

reduced EPRs.

iv Restore the EPRs to their original values for use during the

next iteration.

Two types of engine EPR failure are simulated. One case where the EPR

developed is 85% of the nominal value and the other case where the EPR

developed is 115% of nominal. The first case is directly seen to be a

degraded performance case. The second case is also treated as such here

because it represents a deviation from nominal and could be interpreted as

an indication of impending failure.

Figure 4.3a-4.3e show the results for the run with the EPR reduced to

85% of nominal and the algorithm operating in the signal generation mode.

From Figure 4.3a, it is seen that the predicted steady state EPR is higher

than than the measured value throughout the run. Comparing this figure to

Figure 4.2c , it is seen that the second step climb in EPR is missing.

Since the measured EPR value does not reach the recommended intermediate

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setting, the throttle is not commanded to the takeoff setting. The

calibrated airspeed plot of Figure 4.3b shows a very slow increase to about

45 knots in 50 seconds. Figure 4.3c shows the runway used time history and

shows that the airplane has used up about 2500 feet of runway in 50 seconds.

Figure 4.3d shows that the measured (and filtered), predicted, and the

perfect sensor accelerations are practically identical. Figure 4.3e shows

the sum of runway-used-plus-required against time.

The output listings from the simulation run indicate that the algorithm

caused the engine failure flags to be set immediately following the 10

second point, and caused an abort signal to be generated. As the abort

command sequence was turned off during this run, the simulation model

continued its takeoff roll. Within the next few iterations, the performance

failure flag was also set (based on the difference between the measured

(filtered) and the predicted accelerations). These results are summarized

in Table 4.5.

Table 4.5: Summary of Results from the Engine EPR Failure runs

TYPE OF

SIMULATED

FAILURE

85 % EPR

115% EPR

PERFORMANCE

FAILURE

ENGINE

FAILURE

Set

Set

FLAG FLAG

TIME

(seconds )

10.1

10.1

96
Figure 4.4a shows the EPRtime history for the above run with the abort

commandgeneration enabled. It is seen from this figure that the EPRvalues

begin their downward trend after the 10 second mark, at which point the

abort commandis generated. Figure 4.4b shows the ground speed curves,

which after the initial increase until the 10 second point, begin dropping

off. The simulation run is stopped before the ground speed actually reaches

zero. The acceleration curves of Figure 4.4c are identical to Figure 4.3d

until 10 seconds, after which they rapidly go towards zero due to braking

and the reduction in engine power.

Figures 4.Sa-4.5d show the time histories for the case where the EPR

developed is 115%of nominal. The measuredEPRvalues are seen to be higher

than the predicted values in Figure 4.5a. Figure 4.5b shows the

accelerations obtained from this run. The measured, predicted and the

perfect sensor values are seen to start with a non-zero value (2 feet/sec2).

The plot of runway-required-plus-used, shownin Figure 4.5c, is seen to be a

curved line as opposed to a horizontal straight line. This shows that the

prediction of the runway required is not consistent. Again it needs to be

pointed out that the algorithm caused the two engine failure flags to be set

immediately after the 10 second point and a abort signal was also generated.

These results are also included in Table 4.5.

Figures 4.6a-4.6c depict the time histories for the 115%EPRcase with

the abort commandgeneration enabled. The EPR curves of Figure 4.6a are

identical to those of Figure 4.5a up to the 10 second point. After that

time the EPRvalues (both measuredand predicted) begin decreasing. After

leveling off between 16 and 18 seconds, the measuredvalues are seen to go

up. This is the point where the reverse thrusters come on. Figure 4.6c

shows the calibrated airspeed time histories.

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Malfunctions in engine thrust are simulated by making a modification to

the FORTRAN source code in the simulation model's engine deck. The thrust

equation is multiplied by a constant factor to degrade or augment the thrust

developed by the engine. Two cases are considered here. In the first case

the thrust developed by the engine is forced to be 85% of the nominal value,

and in the second case it is forced to be 115% of the nominal value.

Figures 4.7a-4.7c are representative time histories obtained for the 85%

of nominal engine thrust case. Figure 4.7a shows the acceleration time

histories generated from the simulation run. Before the 10 second point,

the predicted acceleration is higher than the measured (filtered) value. At

the ten second point, the difference between the measured and predicted

accelerations are used to estimate a new runway friction coefficient. After

the 10 second point, the measured and predicted values of acceleration are

practically coincident, except towards the end of the run where the two

values begin to separate. Figure 4.7b plots a time history of the runway

required prediction from the algorithm. At the 10 second point, the runway

required prediction is seen to go up by about 600 feet. This increase

corresponds to the newly estimated higher rolling friction coefficient at

that instant. From Figure 4.7c, it is seen that the sum of runway required

and the runway used remains constant after the 10 second adjustment of the

rolling friction coefficient. This run did not set any engine failure or

performance failure flags. The outputs from this run indicate that the 15%

reduction in the thrust output from the engine is interpreted as an increase

in the rolling friction coefficient from 0.015 to 0.063 . Table 4.6

summarizes the results from this run. It is seen from this table that

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rotation speed is only 35 feet, relative to the no engine malfunction case

(100% Thrust case), the change in the prediction error is 165 feet. This

seeming improvement in the performance of the algorithm has resulted because

of the 10 second adjustment to friction coefficient. The table indicates

that the adjusted friction coefficient for this case is 0.063, which falls

outside the nominal range of free rolling friction coefficient values used

in this development (0.005 - 0.040).

Table 4.6: Summary of results for the Thrust Failure Runs

CASE

85%

Thrust

i00%

Thrust

115%

Thrust

MEASURED

CAS

at

rotation

(feet)

128.4

128.1

128.4

PREDI CTED

RUNWAY

RE QUI RE D

overall

(feet)

RUNWAY

USED

(-)

UPDATED

FRICTION

COEFF.

(feet)

RUNWAY

PREDICTION

ERROR

3738.

3132.

2689.

37O3.

3262.

2732.

0.063

-0.028

-0.028

(feet)

35.

-13o.

-43.

CHANGE

IN

PREDICT.

ERROR

165.

O.

87.

Note: The measured Calibrated Airspeed (CAS) is the filtered sensor output

111
Figures 4.8a-4.8c summarize the time histories obtained for a run where

the thrust developed is 115% of the nominal value. In Figure 4.8a the

predicted acceleration is below the measured value until the 10 second

point. At the 10 second point the prediction is adjusted upward by the

newly estimated low runway friction coefficient. After the 10 second point

the measured, predicted, and the ideal sensor accelerations are practically

identical. The time history of the algorithm predicted runway requirement

is plotted in Figure 4.8b. The shift downward of about 500 feet at the 10

second point is caused by the adjustment to the runway friction coefficient

at that point. Figure 4.8c, where the sum of runway required and the runway

used is plotted, also shows this Jump at the 10 second point. In addition,

there is an upward movement of the curve Just before rotation speed. As

explained before, this is caused by the lags introduced in the measured

calibrated airspeed by the filtering process. No engine or performance

failure flags are set during this run. Just as for the 85% thrust case, the

absolute error performance of the algorithm seems to have improved to a mere

-43 feet from a -130 feet for the no engine malfunction case. The 15%

increase in engine thrust is interpreted by the algorithm as a decrease in

the runway friction coefficient, from a value of 0.015 to -0.028, which is

an invalid quantity. Table 4.6 includes the results from this run also.

112
tb.

0

(n

L- L

m

_um

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oo0

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115
4.5 Summary of Results

The algorithm is seen to function very well for all the 10 combinations

of ambient and loading conditions. The algorithm is also able to identify

engine failures that affect the Engine Pressure Ratio (EPR). The algorithm,

as it is set up, is unable to distinguish between engine performance

degradations that do not affect the EPR and discrepancies in the input

runway friction coefficient. Looking at the friction coefficient data of

Table 4.6 suggests that a check on the adjusted friction coefficient may be

used as an additional check on airplane performance anomalies during the

takeoff run.

116
CHAPTER5

SENSITIVITY AND FAILURE MODE ANALYSIS

5.1 Introduction

The previous chapter dealt with evaluating the Takeoff Performance

Monitoring System. The algorithm was shown to work under several different

ambient conditions during normal takeoff runs. A few performance

degradation cases were also demonstrated. All the simulation runs in that

chapter dealt with design point cases, that is, the inputs to the algorithm

were the actual ambient conditions. In this chapter, the sensitivity of the

algorithm to off-design cases and the effects of sensor failures are

explored. The sensitivity analysis is done by forcing selected inputs to

the algorithm and the simulation to be different and comparing the

algorithm's predictions with the true values generated by the simulation

model.

The failure analysis is carried out by causing the sensor outputs from

the simulation model to be in error and again comparing the algorithm's

predictions with the simulation model performance.

The algorithm can function in a closed loop mode where it generates

command inputs to the airplane systems, or it can function in an open loop

mode where it generates Go/Abort informative signals for use by the pilot.

Both modes of operation are discussed here.

Section 5.2 deals with sensitivity studies and section 5.3 evaluates the

effects of different failures. The chapter ends with a summary of results.

All of the parameter variations are for a base line case as listed in

Table 5. I.

117
Table 5.1: Baseline Fli_ht Conditions for Sensitivity and Failure Analysis

Runs

PARAMETER

Pressure Altitude

Ambient Temperature

Runway Winds

Runway Friction Coefficient

Gross Weight

Flap Setting

VALUE

32.

75.

O.

0.015

885O4.

5.

UNITS

feet

o F

knots

Q

ibs.

degrees

5.2 Sensitivit_ Analysis

As has been noted before, the algorithm consists of a pre-takeoff and a

real-time segment, both of which require a set of one-time inputs. In this

section the sensitivity of the algorithm to errors in some of these inputs

are explored. Such errors could occur in parameters such as runway winds,

ambient temperature, airplane weight and the flap setting selected for

takeoff. Effects of aerodynamic contamination and a reduction in the

frequency of calls to the algorithm are also considered.

5.2.1 Sensitivity to errors in inputs.

This section discusses the sensitivity of the algorithm to errors in the

one time inputs.

The first parameter considered is runway winds. The algorithm is forced

to use an assumed runway wind condition while the simulation model is run at

the true wind speed. This is accomplished with changes to the FORTRAN

118
source code for the algorithm. The effects of wind speed errors are

summarized in Table 5.2. Figure 5.1a shows the calibrated airspeed time

histories obtained for a run with an assumedwlndspeed of 20 knots but an

actual wind of 0 . The predicted value in this plot is 20 knots higher than

the filtered sensor and the ideal sensor values. This reflects the 20 knot

error introduced in the one time inputs.

Table 5.2: Effect of Wind Speed Error

WIND SPEED PERFORMANCE

L..

ASSUMED

SPEED

(knots)

10.

10.

10.

20.

20.

20.

20.

ACTUAL

SPEED

(knots)

MEASURED

CALIBRATED

AIRSPEED

(knots)

PREDICTED

RUNWAY

REQUI RE D

(feet)

RUNWAY

USED

(feet)

ADJUSTED

FRICTION

COEFF.

PRE DI C- !

-TION

ERROR

(feet)

.

10.

20.

O.

10.

20.

30.

128.1

129. I

128.7

128.1

129.1

128.7

128.0

2645.

2690.

2742.

2204.

2241.

2283.

2330.

3260.

2685.

2295.

3262.

2685.

2295.

1902.

0.O1 2

0.017

0.022

0.007

0.012

0.017

0.023

-615.

5.

447.

-1058.

-444.

-12.

428.

CHANGE

IN

PREDIC-

-TION

ERROR

(feet)

-620.

O.

442.

-1046.

-432.

O.

440.

119
"0

0.

Oum0

0C

120
Iiii iiiiC

Io

c_0

q,--

I

Q

O0

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0oo

r_

1.4 0

ecj

-el

U

0

O_

w_

•,..4 r_

°__

w

2_

121
Figure 5.1b shows the runway required prediction from the algorithm.

It is seen from this plot that there is a small adjustment at the 10 second

point, caused by an adjustment to the runway friction coefficient, after

which it steadily decreases to zero. At about the 27 second point, the

predicted runway required reaches zero, and after that a negative value is

predicted. Because of the initial runway wind input of 20 knots, the

algorithm computes a ground speed required to rotation which is 20 knots

below the value actually needed, causing the runway required prediction to

!

go negative after the algorithm computed speed has been attained.

Figure 5.2a is the calibrated airspeed time history for a run with an

assumed wlndspeed of 20 knots and an actual windspeed of 25 knots. Here all

three calibrated airspeeds start at non-zero values. The predicted value is

5 knots below the measured values, reflecting the 5 knot error in wind speed

input. The runway required plot of Figure 5.2b does not reach a value of

zero. The algorithm, because of the 5 knot error in wind speed, predicts

that a nonzero runway length is required to attain rotation speed.

The above sensitivity analysis indicates that the algorithm is highly

sensitive to errors in runway winds. No Abort signal is generated by the

algorithm. To explore the effects of an onboard wind estimator a simple

runway wind estimator is implemented in the algorithm. At the 9.9 second

point, the computed calibrated airspeed is subtracted from the measured

filtered calibrated airspeed to form a one-time estimate of the runway wind

which is usea throughout the rest of the run. Table 5.3 summarizes the

results obtained from this run for the runway wind error case which assumes

a wind of 20 knots, when in reality there is no wind. It is seen from this

table that the error in the predicted runway required is reduced from an

underprediction of 1058 feet to an under prediction of 139 feet.

122
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im<Q

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I I L n I i L

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Q

0

II

"0

,-4

u

0 0

in II .,-t

l:ci

(u

_ _ ._i,_

-,-I

I1_ IU

-,,4
Table 5.3: Effect of Wind Speed Error with a Wind Estimator

WIND

ASSUMED

SPEED

(knots)

20.

SPEED

ACTUAL

SPEED

(knots)

O.

MEASURED

CALIBRATED

AIRSPEED

(knots)

128.1

PERFORMANCE

P RE DI CTE D

RUNWAY

RE QUI RE D

(feet)

31 23.

RUNWAY

USED

(feet)

3262.

PREDICTION

ERROR

(feet)

-139.

The effect of errors in the ambient temperature inputs is summarized in

Table 5.4. Two cases considered, for this analysis, assume an ambient

temperature of 50 °F, whereas the actual temperatures are 25 °F and 75 °F

respectively. From the table it is seen that the error in the ambient

temperature inputs does not cause the estimated friction coefficient to

change. For an assumed temperature of 50 °F with an actual temperature of

25 °F the algorithm is seen to overpredict by 347 feet. With the error

going in the other direction, it is seen that the algorithm underpredicts by

505 feet. Thus it is seen that the algorithm is sensitive to errors in

ambient temperature inputs.

Errors in the gross weight of the airplane are considered next. The two

cases assume a gross weight of 88,504 pounds and actual weights of 98,504

and 78,504 pounds respectively. Figure 5.3a shows the acceleration time

histories for the run with an actual weight of 98,504 pounds. Due to the

assumed weight being 88,504 pounds, the algorithm predicted acceleration is

higher than the measured values until the 10 second point. At that time,the

125
o

o

ouO I , I I

c- oo

m

00 I 0m I

L_0

.iJo

111o'_

II

IlJ

ed_ m ,-t

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-- 4.1,-t •,-t ,_

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_g

--_ -,"t O0

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126
• m

_ _ o

5.

em

:3

0

U

0

PI

_J,_r

(Z)Qo

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.E__

.IJ

_ o

g_

•,-t ,.Q

llJ,_

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c_

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2_

r_

127
Table 5.4: Effect of Ambient Temperature Errors

TEMPERATURE PERFORMANCE

ASSUMED ACTUAL

TEMP. TEMP.

(o F) (o F)

50. 25.

50. 50.

5O. 75.

MEASURED

CALIBRATED

AIRSPEED

(knots)

PRE DI CTE D

RUNWAY

REQUIRED

(feet)

RUNWAY

USED

(feet)

ADJUSTED

FRICTION

COEFF.

PREDIC-

-TION

ERROR

(feet)

128.6

128.2

128.1

2964.

2975.

2986.

2617.

3015.

3491.

0.017

0.017

0.017

347.

-40.

-5O5.

CHANGE

IN

PREDIC-

-TION

ERROR

(feet)

387.

O.

-465.

difference between the predicted and measured accelerations is interpreted

as being caused by discrepancies in the assumed runway friction coefficient.

A new friction coefficient is estimated based on this difference. This new

friction coefficient causes the two acceleration values to be the same.

Figure 5.3b illustrates the variation of predicted runway required with

time. The runway friction coefficient update at the 10 second point shows

up as an increase in the predicted runway requirement of about 400 feet.

Another important effect of this error, which does not show up in either the

plot or the outputs from the run, is that the rotation speed of 128 knots

chosen by the algorithm is based on the 88,504 pound gross weight. The

flight manual recommended rotation speed for the 98,504 pound gross weight

is 138 knots. The effect of an actual weight of 78,504 pounds is similar

but in the opposite direction. Figure 5.4a shows the predicted acceleration

128
getting adjusted upward at the 10 second point, resulting in a reduction of

the estimated friction coefficient. Figure 5.4b shows a corresponding

reduction in the predicted runway requirement. In this case, the airplane

remains on the runway longer than needed. The flight manual recommended

rotation speed for a 78,504 poundairplane is 119 knots, but the algorithm

required a speed of 128 knots (rotation speed for a 88,504 pound airplane)

to be reached. This results in the airplane remaining on the runway for 387

feet more than needed. Neither case generates Abort signals. Table 5.5

summarizes the results from the simulation outputs.

The next parameter considered is Flap setting. As indicated in

Table 5.6, the assumed flap setting is 5 degrees. The two actual flap

settings chosen for this run are I degree and !0 degrees. For the I degree

setting the flight manual recommendedrotation speed Is 133 knots, and for

the 15 degree setting it is 123 knots. The simulation run for the first

case reaches only 128 knots. For the second run, the measuredcalibrated

airspeed is higher than 123 knots 2828 feet into the takeoff run. But the

airplane is kept on the ground until the calibrated airspeed exceeds 128

knots, the recommended rotation speed for 5 degrees flaps. Thus the

airplane remains on the ground 437 feet more than required.

5.2.2 Sensitivity to aerodynamic degradation

The sensitivity of the algorithm to contaminants on the airplane body

which alter the aerodynamic characteristics are considered here. Ice

formation on the wings is one example of such contamination. The effects of

such contamination is simulated by reducing the llft coefficient and

129
=l.._

ono

l I

ol

c- O000 I 0 I I

cO

e,i (1)

rJ

o_

-IJo

-_1 Go QJr-.

II

(1)

4.1

_o_ q-_4J

-,-I

OJ:l

(1_

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II

O_

-,-I

U'< U

130
I

,I,I,,I I I

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I..

Im

_r

Q)

r_-

¢..

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{E

.4--'

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w

I

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o

{jo

_n

4J,_

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,=

4J:_

I--.o

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o

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11/

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.,_

131
Table 5.5: Effect of Gross Weisht Errors

WEIGHT

ASSUMED

WEIGHT

(lbs)

885O4.

885O4.

88504.

ACTUAL

WEIGHT

(ibs)

78504.

88504.

98504.

MEASURED

CALIBRATED!

AIRSPEED

(knots)

128.1

128.1

128.5

PERFORMANCE

PRE DI CTE D

RUNWAY

REQUIRED

(feet)

2747.

3132.

3510.

RUNWAY

USED

(feet)

2802.

3262.

3449.

ADJUSTED

FRICTION

COEFF.

- .021

0.017

0.048

PREDIC-

-T ION

ERROR

(feet)

-55.

-130.

61.

CHANGE

IN

PREDIC-

-TION

ERROR

(feet)

75 •*

O.

191 .*N

For the actual weight of 78,504 lbs., the flight manual

recommended rotation speed is 119 knots. For this run, the

output indicates that this speed is reached at 2415 feet of

runway used.

For an actual weight of 98,504 ibs., the flight manual

recommended rotation speed is 138 knots.

132
Table 5.6: Effect of Flap Setting Errors

FLAPS PERFORMANCE

ASSUMED

SETTING

(deg.)

Q

5.

5.

ACTUAL

SETTING

(deg.)

•

5.

15.

MEASURED

CALIBRATED

AIRSPEED

(knots)

128.7

128.1

128.5

PREDICTED

RUNWAY

REQUIRED

(feet )

3123.

3132.

3121.

RUNWAY

USED

(feet)

3278•

3262.

3265•

ADJUSTED

FRICTION

COEFF.

0.017

0.017

0.017

PREDIC-

-T ION

ERROR

(feet)

-155.

-130.

-144.

CHANGE

IN

PREDIC-

-TION

ERROR

(feet)

-25. *

0.

-14.**

* For the actual flap setting of I o the flight manual

recommended rotation speed is 133 knots.

For an actual flap setting of 15 o

recommended rotation speed is 123 knots.

, the flight manual

For this run, the

output indicates that this speed is reached at 2828 feet of

runway used.

increasing the drag coefficient. Two such cases are considered here. The

first involves a 10% reduction in the llft coefficient and simultaneous 10%

increase in the drag coefficient. The second case considers the effect of a

15% simultaneous change in the lift and drag coefficients. The results are

summarized in Table 5.7. The effect of the increase in the drag coefficient

133
is accommodatedbut the effect of the reduction in the llft coefficient on

the rotation speedof the airplane is not. This effect can be approximated

as follows:

/

vR = vR * /I I(I- d) -- (5.1)

new original

where VR

new

= rotation speed with contamination

VR = rotation speed without contamination

original

= fractional reduction in llft coefficient

Table 5.7: Effects of Aerodynamic Degradation

DEGRADATION

LEVEL

(percentage)

O.

10.

15.

MEASURED

CALIBRATED

AIRSPEED

(knots)

128.1

128.1

128.8

P RE DI CTE D

RUNWAY

REQUI RE D

(feet)

31 32.

3134.

31 35.

PERFORMANCE

RUNWAY

USED

(feet)

3262.

3274.

3291.

ADJUSTED !

FRICTION

COEFF.

0.017

0.018

0.018

PREDIC-

-TION

ERROR

(feet)

-I 30.

-I 40.

-156.

CHANGE

IN

PREDIC-

-TION

ERROR

(feet)

O.

-10.

-26.

134
5.2.3 Sensitivity to reduced frequency of calls to the al$orithm

In this section the effects of calling the takeoff performance

monitoring algorithm 5 times a second, instead of the usual 10 times a

second, are investigated. Results from this run are summarized In

Table 5.8. The algorithm Is seen function under this reduced frequency of

use also. Because of the increased time between calls, the speed increase

between time steps is also higher and hence the excess speed over the

required speed is also higher. This time interval increase also causes a

difference in the predicted runway requirements, because of the difference

in the integration interval. It is observed from Table 5.8 that when the

frequency of calls to the algorithm is reduced from 10 calls per second to 5

calls per second, it has an adverse effect on the estimated runway friction

coefficient. The estimated value is seen to go from 0.017 to 0.002 with the

simulation using a value of 0.015.

Table 5.8: Effects of frequency of calls to the algorithm

FREQUENCY

OF

CALLS

(per second)

10

5

MEASURED

CALIBRATED

AIRSPEED

(knots)

128.1

129.5

P REDI CTE D

RUNWAY

REQUIRED

(feet)

31 32.

3078.

PERFORMANCE

RUNWAY

USED

(feet)

3262.

3283.

ADJUSTED

FRICTION

COEFF.

0.017

0.002

PREDIC-

-T ION

ERROR

(feet)

CHANGE

IN

PREDIC-

-TION

ERROR

(feet)

O.

-75.

135
5.3 Failure Analysis

Effects of sensor failures on the algorithm are considered in this

section. The failures are simulated for the accelerometer, the engine

pressure ratio sensors, and the ground speed sensor.

The effects of accelerometer failures are considered first. Two types

of accelerometer failures are considered. The first biases the

accelerometer output by a constant value. Figures 5.5a- 5.5d show the time

histories obtained from a run with a bias value of +2.32 feet/second 2. The

negative bias superimposed on the measured signal is seen as a standoff

between the ideal sensor output (noise and bias free signal) and the raw

(unprocessed) sensor output. The bias estimate from the complementary

filter is shown in Figure 5.5b. This is the negative of the actual bias.

It is seen from this figure that the filter takes about 6 seconds to fully

estimate the bias present in the signal. The estimated bias quantity from

the complementary filter is added to the measured signal to obtain a bias

free, but noisy signal. This noisy signal is processed by a first order lag

network and the result is plotted in Figure 5.5c as the filtered

acceleration. Initially, the filtered acceleration signal and the ideal

sensor value differ by the bias value. As the estimate of the bias

improves, the filtered acceleration value approaches the ideal sensor value.

The predicted acceleration, it is seen, is very close to the ideal sensor

value. Filtered ground speed value is the other output from the

complementary filter. Figure 5.5d shows a standoff between the filtered and

ideal sensor outputs on the one hand and the predicted value on the other.

This is caused in the initial few seconds where the filtered acceleration

output is in error. Effects of a bias of -I .68 feet/second 2 are similar but

136
OnI

o

oo

_a

_o< C

_0

o_

g_

v.4

_0

--_0C

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I

I/I

137
I

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gmm00L00< I

-J, I N0

138

I!

I

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!

.og00

ui0

0

_nO

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ul

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I1/

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In_40

r_

>_

u_

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t_

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on<>

I

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139

mf_ 0

"4"

CW

-_"0

G_

w-I

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4-I

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.__.

.,-I

•,-40

O_

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.,-I

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-,-I

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-,'-I

r_
k. L

0 0

M

_-OUl

_uu

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LLr_ t'_

oo<>

i i I

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o4

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8

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0

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0

I"- G,I (_b ,,-

140

o

o

(I)

(I)

L)

L)

C.i

•_ .,-4

4..1 m

m_

•,-t 4-1

-- _ ._.

Ili

0

_4

4_

-,-I
in the opposite direction. Results of these two runs are summarized in

Table 5.9. It is seen that the algorithm has the capability to estimate

such bias values. Abort signals are not generated.

The effect of a scaling failure of the acceleration measurement is

considered next. Figures 5.6a - 5.6e are the time histories for a run with

a scale factor of 0.85 (reduction of 15%) in the acceleration measurement.

The ideal sensor output and the measured (defective) signals are plotted in

Figure 5.6a. The bias estimate from the complementary filter is shown in

Table 5.9: Effects of Accelerometer Bias

ACCELEROMETER PERFORMANCE

BIAS

(ft./second2)

2.32

0.32

-I .68

MEASURED

CALIBRATED

AIRSPEED

(knots)

128.1

128.1

128.1

PREDICTED

RUNWAY

REQUIRED

(feet)

3112.

3132.

3132.

RUNWAY

USED

(feet)

3262.

3262.

3262.

ADJUSTED

FRICTION

COEFF.

0.016

0.017

0.018

PREDIC-

-T ION

ERROR

(feet)

-I 50.

-130.

-I 30.

CHANGE

IN

PREDIC-

-TION

ERROR

(feet)

.

Nominal case

141
O1"I I

0

c_! O

I OI O! OI OI Of O

c- O

C3O

k.. q3 O q)

.<

II

r,O

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146
Figure 5.6b. It is seen from this figure that the complementary filter

perceives this scale factor as a bias which changes with time. The bias

estimate decreases with time after the 12 second peak. The filtered

acceleration, predicted value and the ideal sensor output are plotted in

Figure 5.6c. This figure shows the ideal sensor value and the prediction to

be very close before the 10 second point. But the filtered value lags the

other two. At the 10 second point, the difference between the predicted and

the filtered values is used to estimate a new runway friction coefficient.

This causes the predicted acceleration value to drop after the 10 second

adjustment. In the mean time, the filtered acceleration value increases and

comes closer to the ideal sensor output, causing the predicted value to lag

behind. This effect is also seen in the ground speed time history plots of

Figure 5.6d, where all three values of ground speed start identical, but the

predicted output increasingly lags behind the other two. The adjustment in

the runway friction coefficient is also clearly seen in the predicted runway

required time history plot of Figure 5.6e. The effect of a scale factor

error in the opposite direction (115%) produces results in the opposite

direction. These results are summarized in Table 5.10. The 115% scale

factor error case produces an error in the prediction of runway required of

-253 feet. At the beginning, due to the high acceleration (scale factor of

115%) the runway required is predicted to be 3009 feet, but the actual

runway used turns out to be 3269 feet. It is seen from Table 5.10 that the

estimated friction coefficient after the 10 second point is significantly

different from the simulated O.015, even though within the range of values

chosen as acceptable for this study.

147
Table 5.10: Effects of Accelerometer Scale Factor

ACCELEROMETER

SCALE FACTOR

(percentage)

MEASURED

CALIBRATE_

AIRSPEED

(knots)

PRE DI CTE D

RUNWAY

RE QUI RE D

(feet)

PERFORMANCE

RUNWAY

USED

(feet)

ADJUSTED

FRICTION

COEFF.

PREDIC-

-TION

ERROR

(feet)

85

IO0

115

128.1

128.1

128.1

3269.

3132.

3009.

3262.

3262.

3262.

0.029

0.017

0.006

.

-130.

-253.

* Nominal case

CHANGE

IN

PREDIC-

-TION

ERROR

(feet)

137.

0.*

-123.

Introducing a bias error of -0.3 in the engine pressure ratio

measurement (16% of the nominal EPR of 2.0 subtracted from the nominal

sensor bias of 0.02) causes an engine failure flag to be set at the 10

second point and hence an abort signal to be generated. If command

generation is enabled, full brakes are commanded and the throttle is

commanded to full reverse thrust position. An EPR bias of +0.34 (a bias of

0.32 added to the nominal sensor bias of 0.02) also causes identical actions

to be taken. Table 5.11 summarizes the results of these two cases.

The other simulated EPR sensor failure pertains to scale factor error

caused by the sensor. Two scale factor errors are simulated here. In the

first case the sensor reads 15% higher than actual (sensor output is 115% of

148
Table 5.11: Effect of EPR sensor Bias

EPR

BIAS

(-)

-0.30

0.02

+0.34

PERFORMANCE

FAILURE

FLAG

ENGINE

FAILURE

FLAG

u Nominal case

Set

Set

i

TIME

(seconds )

10.1

-

10.1

actual). In the second case the sensor reads 15% lower than actual (sensor

output is 85% of actual). In both cases, the algorithm sets an engine

failure flag at 10.1 seconds. Both cases result in the generation of Abort

signals. This condition, with the command generation turned on, initiates

the abort command procedure. Table 5.12 summarizes these results.

The next sensor considered here is the ground speed sensor. The output

from this sensor is forced to remain at a constant level and its effect on

the algorithm investigated. The three different values considered for the

sensor output are 0, 100, and 250 feet/second. All three cases result in a

performance failure flag being set at 10.1 seconds and hence an abort signal

being generated. These results are summarized in Table 5.13.

Figures 5.7a - 5.7d are time histories obtained for a ground speed sensor

output of 250 feet/second with command generation enabled. The estimate of

the ground speed error from the complementary filter is plotted in

Figure 5.7a.

149
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153
Table 5.12: Effect of EPR sensor Scale Factor

SCALE

FACTOR

(%)

115

85

PERFORMANCE

FAILURE

FLAG

EN GINE

FAILURE

FLAG

Set

Set

TIME

(seconds)

10.1

10.1

Table 5 13: Effect of Ground S p.eed Sensor Failure

SENSOR

OUTPUT

(ft./sec)

O,

100.

250.

PERFORMANCE

FAILURE

FLAG

Set

Set

Set

ENGINE

FAILURE

FLAG

TIME

(seconds)

10.1

10.1

10.1

The estimate of the bias in the acceleration is plotted in Figure 5.7b.

These two figures indicate that the complementary filter is unable to handle

this type of error. The resulting Ground Speed time histories are shown in

Figure 5.7c. The actual ground speed is depicted by the perfect sensor

plot, and the filtered value and the predicted are offset by about 250

feet/second. The acceleration time histories are shown in Figure 5.7d.

154
5.4 Summary.

The sensitivity analysis indicates that the algorithm is highly

sensitive to errors in runway wind inputs. This points to a need for an

onboard wind estimator.

The algorithm is also found to be sensitive to errors in ambient

temperature inputs. An error of about 25 °F in the temperature inputs

causes errors of about 400 feet in the prediction of runway requirements to

achieve rotation speed.

The algorithm is able to adjust its operations by changing the runway

friction coefficient to compensate for input errors in gross weight, and

flap setting. This is true as long as the error does not shift the airplane

to a different rotation speed category in the flight manual.

The effects of aerodynamic degradation are similar to errors in flap

setting inputs.

Cutting down the frequency of calls to the algorithm from 10 times a

second to 5 times a second causes large errors in the estimated runway

friction coefficient. The estimate is changed from 0.017 to 0.002 with the

simulation using a value of 0.015.

The algorithm can function well under failures of the acceleration

sensors that cause a bias of up to +/- 2 feet /second 2. The algorithm

handles failures in the acceleration sensors that cause scale factor errors

in the range of 0.85 to 1.15 by changing the friction coefficient value.

Failures of the EPR sensors that cause bias failures of magnitude 0.5

and scale factor errors of 15% cause abort signals, as this is the only

source of engine health check.

Failures of the ground speed sensor that cause its output to be remain

unchanged also cause abort signals.

155
CHAPTER6

CONCLUSIONS AND RECOMMENDATIONS

6. I CONCLUSIONS

A Takeoff Performance Monitoring Algorithm has been developed and was

tested using the six degree of freedom non-linear batch simulation of the

Transport Systems Research Vehicle B-737 on the NASA Langley computer

network. The conclusions are clustered into cases that resulted in normal

takeoffs and those that resulted in abort signals.

6.1 Normal Takeoffs

Ten cases consisting of different ambient and loading conditions were

utilized in testing the algorithm. All of these cases resulted in normal

takeoffs. The runway required was predicted to within +/- 150 feet.

The engine malfunction test case affecting only the thrust output did

not cause an engine failure flag to be set. Since none of the other

conditions for aborting the takeoff run were satisfied, the algorithm

generated a Go signal. The algorithm compensated for the difference in

thrust level by adjusting the runway friction coefficient to a value outside

the nominal range of values used in this study.

The algorithm was found to be very sensitive to errors in the runway

wind inputs. A 10 knot error in the runway wind input (assumed wind speed

10 knots; actual 0 ) caused the error in the predicted runway required to

change by -620 feet. A 20 knot error (assumed 20 knot; actually no wind)

caused the runway prediction error to change by -1046 feet. The addition of

a simple runway wind estimator eliminated this sensitivity. Using the

estimator a 20 knot error in the runway wind (assumed value of 20 knots when

actual 0 ) resulted in a change in the prediction error of -127 feet.

156
The algorithm was also found to be sensitive to errors in ambient

temperature inputs. A temperature input 25 °F below the actual value (of

50 °F) caused a change in the prediction error of -465 feet. An input which

was 25 °F above the actual value (of 50 °F) caused the prediction error to

change by 387 feet.

For a gross weight input of 88,504 ibs., which is I0,000 ibs. greater

than the actual, the error in runway prediction changed by 75 feet. This

change in the prediction error was 191 feet when the weight input of 88,504

Ibs. was 10,000 Ibs. less than the actual value. The rotation speed choice

was made based on the erroneous input to the algorithm. These errors also

resulted in an adjusted friction coefficient which was outside the nominal

range Of values.

using a I degree flap setting instead of the 5 degrees input to the

algorithm caused the error in the predicted runway required to change by -25

feet. Using a 15 degree flap setting, for the same assumed value caused the

error to change by -14 feet. Again the rotation speeds chosen were based on

the input flap setting.

A 10% reduction in the lift coefficient and a 10% increase in the drag

coefficient caused errors in the prediction of runway required to change by

-10 feet. A 15% change produced error changes of -26 feet. The rotation

speeds here were based on the uncontaminated surfaces.

Utilizing the algorithm 5 times a second instead of 10 times a second

caused the error in the prediction of runway requirement to change by -75

feet. The runway friction coefficient estimated at the 10 second point

turned out to be less than the lower limit of the range of values used in

this development.

15'7'
An accelerometer bias error of 2 feet/second 2 over nominal caused the

runway prediction error to change by -20 feet. A -2 feet/second 2 bias (over

nominal) did not change the prediction error.

An accelerometer with an output that is 85% of actual caused a change in

the runway requirement prediction error of 137 feet. An accelerometer with

a 115% output changed the error by -123 feet. In both cases the friction

coefficient was changed, but remained within the chosen range.

6.1.2 Aborts

The engine malfunction test case that affected the engine pressure ratio

caused engine failure flags to be set and resulted in Abort signals being

generated 10.1 seconds into the takeoff run.

Failure of the engine pressure ratio sensor that results in a bias of

+/- 0.32 (over nominal), resulted in the engine failure flags being set at

10.1 seconds, and hence an abort signal.

Failures of the engine pressure ratio sensor resulting in a scaling of

85% and 115% also resulted in the engine failure flags being set at 10.1

seconds and hence an abort signal.

Errors in the ground speed sensor that caused constant outputs of O,

100, and 250 feet/second resulted in performance failure flags being set at

10.1 seconds and thus in abort signals.

6.2 RECOMMENDATIONS

This implementation of the algorithm does not check the friction

coefficient estimated at the 10 second point. It is seen that the friction

coefficient is changed substantially in the presence of errors in the input

gross weight, and in the engine malfunction test case (the case which does

not affect the engine pressure ratio). These two cases result in Go signals

158
from the algorithm even though the takeoffs should have been aborted. The

performance of the algorithm could be improved by checking the estimated

friction coefficient against a predetermined reasonable range to flag

performance deficiencies.

In the current algorithm the runway rolling friction coefficient is

estimated at the 10 second point. This time was chosen to allow for the

transients caused by a changing throttle position ( as it is being commanded

to the takeoff setting) to die out. This estimate of the runway rolling

friction coefficient is used throughout the remaining part of the takeoff

roll. In reality the rolling friction coefficient varies with speed. The

validity of estimating the friction coefficient at the 10 second point needs

to be investigated.

In computing the runway required to bring the airplane to a complete

stop it has been assumedthat with the application of brakes, the friction

coefficient increases by a constant amount above the prevalent free rolling

friction coefficient. This might not hold true, especially for contaminated

runways. There is no data available to correlate the free (unbraked)

rolling friction coefficient with what can be achieved with braking, with an

antiskid mechanism. A literature search failed to come up with any such

information. Such information is important to realistically predict

required stopping distances.

Another important point needs to be mentioned here. If this system were

used as an advisory system then what time delay factor should be introduced

in computing the stopping distances? Additional research is required to

determine this value. Additional work is also needed to develop formats and

methods of displaying this information to the pilot.

159
This implementation does not use the flight manual provided decision

speed (VI). The concept of VI evolved from an engine failure consideration

and needs to be addressed from the present context. Another related item is

the way in which the runway requirements are specified in the flight manual.

The flight manual tabulates only the balanced field length, that is the

runway required to either go through rotation and clear a 35 foot obstacle

or abort the takeoff at VI and bring the airplane to a complete stop. Only

the ground roll part of the balanced field length can be used to achieve

rotation speed, whereas the full length could be used to bring the airplane

to a complete stop. The full potential of the takeoff performance

monitoring algorithm can be realized only if such information is available.

The margin of safety to be built into these lengths needs to be investigated

and decided upon.

160
LIST OF REFERENCES

I. Minutes of the First Meeting of the SAE Takeoff Performance Monitoring

Ad Hoc Committee of the Aircraft Division of the Aerospace Council: May

15-16, 1984, Washington, DC.

2. Small, MaJ. J. T.; Feasibility of Using Longitudinal Acceleration (N X)

for Monitoring Takeoff and Stopping Performance from the Cockpit;

Proceedings of the Twenty-Seventh Symposium, Beverly Hills, CA,

September 28 _ October I, 1983, Pages 143-154; (A84-16157 05-05).

3. Foxworth, T. G.; Marthinsen, H. F.; Another Look at Landing and Stopping

Criteria; AIAA Paper No. 74-956; August, 1974.

4. Home, W. B.; Yager, T. J.; et al; Preliminary Test Results of the Joint

FAA-USAF-NASA Runway Research Program, Part II - Traction Measurements

of Several Runways under Wet, Snow Covered, and Dry Conditions with a

Douglas DC,9, a Diagonal-Braked Vehicle and a Mu-Meter; NASA TM X-73910;

1977.

5. Roskam, Jan; Airplane Flight Dynamics and Automatic Flight Controls

Part-I; Roskam Aviation and Engineering Corp.; 1979.

6. Franklin, G. F.; Powell, J. D.; Digital Control of Dynamic Systems;

Addison-Wesley; June 1981.

7. Oppenheim, A. V.; Schafer, R. W.; Di$ital Signal Processing; PrenticeHall; 1975.

8. Central Computing Complex Document N-3; Mathematical and Statistical

Software at Langley; NASA Langley Research Center; April 1984.

9. Lan, C-T., E.; Roskam, J.; Airplane Aerodynamics and Performance; Roskam

Aviation and Engineering Corp.; 1981.

161
10. Pines, Samuel; Terminal Area Automatic Navigation, Guidance, and

Control Research Using the Microwave Landing System (MLS): Part 2-

RNAV/MLS Transition Problems for Aircraft; NASA Contractor Report 3511;

January 1982.

11. Guenther, A. D.; Martin, D. J.; TCV/User Oriented FORTRAN Program for

the B-737 Six DOF Dynamic Model; Report No. SP-170-021; Sperry Support

Services; March 1981.

12. Etkin, Bernard; Dynamics of Atmospheric Flight; John Wiley & Sons;

Sixth Edition, 1967.

162
1)

2)

Thus

APPENDIX A

DISCRETIZATION OF FIRST ORDER SYSTEMS

A.I Introduction

This appendix describes approaches taken in modelling a first order

system in the discrete domain. Section A.2 describes the rules used in the

translation of a servo actuator and also a simple first order recursive

filter. The sampling interval is represented by T (also AT) and the digital

equivalents have frequency response characteristics which are periodic in m

with period 2_/T and the plots have symmetry about the Nyquist frequency of

_/T.

A.2 The First Order Lag

The first order lag Is represented in the S plane by

a -- (At)

H(S) = S+a

The technique used to transform this is a pole-zero mapping technique

(Reference 8) with some changes.

ST -aT

The pole at s = -a is mapped into a pole at z = e = e .

The zero at s =_ is mapped into a zero at z - O.

KZ -- (A2)

Hpz(Z) = -aT

(Z - e )

Choosing S = 0 and z = I to match gains, the gain K is computed to be

K = I - e-aT -- (A3)

Hence

Z(I - e-aT)

-- (A4)

HPz(Z) _ (Z - e-aT )

163
-aT Letting e =

That is,

Hpz(Z) Z(1 - _! = I - ___ s Y(Z)

m (Z - 6) I - Z-I_ X(Z)

Y(Z) = z-IY(z) _ + x(z) (I - _)

Using the properties of the Z-transform (Reference 9),

y(nT) - _ y[(n - I)T] + (I - 6) x(nT) -- (AS)

A.3 A typical implementation

For a cut off frequency of 5 radians/second (a = 5) and a sampling

interval of 0.1 second (T = AT = 0.1), the following results:

5

H(S) = (S+5)

Nyquist Frequency = 31.4 radians/second

Period = 62.8 radians/second

= 0.6065

y(nT) = 0.6065 y[(n-1)T] + 0.3935 x(nT)

Figures AI depict the magnitude and phase plots for the above example.

164
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mD

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oci

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166
APPENDIX B

Formulation of a Second Order Complementary . Filter

B. I Introduction:

This appendix briefly describes the equations involved in the

development of a second order complementary filter. The developments of

this appendix are based on the methods of Reference 10. The inputs to the

filter are the measured along track acceleration of the airplane and its

ground speed. The outputs from the filter are the negative of the bias on

the acceleration measurement and an estimated ground speed.

B.2 The Formulation:

A block diagram of the second order complementary filter is shown in

Figure B.I . The two states and their derivatives are given by the

following set of equations:

A

e_ oo

_I = KI(X - Xl ) + x - (B.I)

°,

where x = estimated acceleration .

x = measured ground speed

The estimated acceleration in the block diagram is obtained as

°, °.

x = x + x 2 - (B.2)

using (B.2) in (B.I),

°.

Xl " KI(X - xI) + x + x2 - (B.3)

The derivative of the second state is given by

.%

x2 " K2 (x - x 1) - (B.4)

167
P-4

X

.X

:× -I×

,-'4

C

0

0

C

0

U3

0

0

,-4

168
which can be rewritten as

xI = x _2/K2

Equation (B.5) on differentiation yields

..

.°

Xl = X - x21K 2

Substituting equations (B.5) for Xl, (B.6) for Xl in (B.3),

x - x2/K 2 _ K I (_2/K2) + x + x2

Rearranging the terms,

x2 + KI x2 + K2 x2 s K2

°.

°.

(x-x)

- (B.5)

- (B.6)

- (B.7)

Due to the discrete nature of the acceleration measurements, the value

remains a constant in the time interval 0<time<T . If the measurement

consists of a bias value added on to the actual acceleration then the right

hand side of equation (B.7) is seen to be a constant in each time interval.

Thus the characteristic equation of the system is given by

x2 + K I _2 + K 2 x2 = 0 - (B.8)

This characteristic polynomial can have either two real roots or a

complex conjugate pair of roots. Taking the Laplace transform of (B.8) with

zero initial conditions, one obtains

X(S){S 2 + 2_m n S + m2n }

Comparing terms one obtains:

K I = 2 _ _n

and

= 0 - (B.9)

- (B.10)

169
2

K2 = mn

B.3 Implementation:

The equation for the continuous implementation of the filter is given by

i=Fx+Gu - (B.11)

with

X= [x1] X2

F = -K_i(2I

G= K2

(B.12)

where xI = filtered speed

x2 = filter estimate of the negative of the bias

In discrete notation the filter implementation becomes

=]Xn+- = ¢ --n x + F --n u

- (B.13)

FT

where @ = e

- (B.14)

IT I" = eFndn G

0

- (B.15)

and T = sampling time interval.

B.4 A numeric example

For a system with K I -- 1.5 and K 2 = 0.5 (this results in a

characteristic equation with two real roots):

F= .5 O0
e m

Thus for T = 0.1

.8584046

0.1416 0.0464

O. 0928]

0.9976]

0.0928]

-0 0024]

171
APPENDIXC

PROGRAMMING FLOW CHARTS

This appendix includes programming flow charts for the real-tlme segment

of the algorithm. Section C.I depicts the flow chart for the overall

real-tlme segment. Subsection C.I.1 contains the flow chart for Predicting

the runway required to achieve rotation speed. The flow chart for

predicting the stopping distance is included in subsection C.I.2

172
C.I Real-Time Segment

173
No First

Yes

Initialize

Time = 0

Throttle Com =0

I.!=0. 015

Stopdist = 0

I

Obtain basis

for scheduled

performance

Throttle.

R I. No

Yes

Throttle. Corn

= T/OSetting

ComputeEPR

Using actual

throttle position

Figure C.i: Programming Flow Chart for the Real-Time Segment

174
EPRNt-EPRPI• li

'es

Set engine

failure flag

Computethrust

using measured

EPR

No

Compute true

airspeed,lift,

drag, acceleration

using measuredGS

No

me>-5

Yes

line = 5 No

Yes

Adjust p basedon

accelerationmeasuredpredicted

Figure C. 1: Continued

175
1

Recomputebasis

for scheduled

performance

>li

Yes

Setperformance

failure flag

Compute runway

used

Computerunway

required

No

Figure C. i= Continued

176
C.I.1 Prediction of Runway Required to Achieve Rotation Speed

PRECEDING PAGE BL./_( NOT FiL_EO

179
Initialize

USTEP= (UROTATE-UPESENT)

/10

USH = USTEP/2.

U = UPRESENT+ USH

RWYRQD= O.

ACCEL = 2 3

A0+AIU+A2U +A3U

RWYRQD= RWYRQD+

USTEP'(U-UWIND)/ACCEL

U = U+USTEP

U<UROTATE Yes

?

No

Return

Figure C.2: Programming Flow Chart for Predicting the Runway

Needed to Achieve Rotate Speed

"180
C.I.2 Prediction of Stopping Distance

181
Figure C.3:

STPDIS

No

IR

Yes

DDCLFSP = DCLFSP/40

DDCFSP = DCDFSP/40

HRHOS = 0.5*RHO'S

XMASS = WGHT/32

EAT = EXP(-TSTEP*IO)

EAGSP = EXP (-TSTEP/.05)

OMEAT = 1.-EAT

EAGSP = 1. EAGSP

BRKRMP = .45/. 6

FIRST =.FALSE.

THRPD = TH!UST/THROTTLE

DTH = THROTTLE

FSP = O.

GSP = 0

Time = TSTEP/2.0

XMB - O.

V = VPRESENT

STOPD = O.

QS = HRHOS VEL'VEL

1

Programming Flow Chart for Predicting the

Stopping Distance

182
DTH= EAT*DTH+

OMEAT*(-60)

THR= THRPD*DTH

< No

Yes

THR = O.60*THR

FSP = EAT'FSP+

OMEAT*40.

GSP = EAGSP'GSP+

OMEAGSP* I.

XMB = XMB+TIME*

BRKRMP

>

?

Yes

XMB = .45

No

Figure C.3 : Continued

183
DCL = CL+DDCLFSP*FSP

+ DDCLGSP*GSP

DCL = CD+DDCDFSP*FSP

+ DDCDGSB*GSP

LIFT= QS'DCL

DRAG= QS'DCD

XM = XMU+XMB

FORCE= -XM'(WGHT-Lift) THR-DRAG I

I

STOPD = STOPD+V'TSTEP

V = V+ACCLN*TSTEP

TIME = TIME+TSTEP

Yes

Figure C.3:

184

Cont inued
Standard BibliographicPage

1. NAsARep°rt cR-N°" 1 78255 2. Government Accession No.

4. Title and Subtitle

Development of a Takeoff Performance Monitoring System

3. Recipient's Catalog No.

5. Report Date

March 1987

6. Performing Organization Code

8. Performing Organization Report No.

KU-FRL- 629-1

10. Work Unit No.

11. Contract or Grant No.

NCC1- 79

7. Author(s)

Raghavachari Srivatsan and David R. Downing

9. Performing Organization Name and Address

The University of Kansas Center for Research,

Lawrence, KS 66045

12. Sponsoring Agency Name and Address

National Aeronautics and Space Administration

Washington, DC 20546

Inc.

13. Type of Report and Period Covered

Contractor Report

14. Sponsoring Agency Code

505-66-41-05

15. SupplementaryNot_ Raghavachari Srivatsan, Project Manager of NCC1-79, performed

and documented this work as his doctoral dissertation. David R. Downing, Principal Investigator, was his advisor at the University of Kansas.

16. Abstract

This document discusses the development and testing of a real-time takeoff

performance monitoring algorithm. The algorithm is madeup of two segments: a

pretakeoff segment and a real-time segment.

One-time inputs of ambient conditions and airplane configuration information

are used in the pretakeoff segment to generate scheduled performance data for

that takeoff.

The real-time segment uses the scheduled performance data generated in the

pretakeoff segment, runway length data, and measured parameters to monitor the

performance of the airplane throughout the takeoff roll. Airplane and engine

performance deficiencies are detected and annunciated. An important feature of

this algorithm is the one-time estimation of the runway rolling friction

coefficient.

The algorithm was tested using a six-degrees-of-freedom airplane model in

a computer simulation. Results from a series of sensitivity analyses are also

included.

17. Key Words(Sugg_tedby Authors(s))

Algorithm Safety

Airplane Performance Monitor

Runway Pretakeoff

Takeoff Real-time

Aborted Takeoff Friction

Acceleration

19. Security Classif.(of this report)

Unclassified

18. Distribution Statement

Unclassified - Unlimited

Subject Category 06

20. Security Classif.(of this paw) 21. No. of Pag_ ] 22. Price Unclassified 209 1 AIO

For sale by the National Technical Information Service, Springfield, Virginia 22161

NASA Langley Form 63 (June 1985)