Aircraft Flight Dynamics Robert F. Stengel Lecture1 Introduction to Flight Dynamics

Aircraft Flight Dynamics Robert Stengel, Princeton University, 2012" Copyright 2012 by Robert Stengel.. Text and References• Principal textbook: – Flight Dynamics , RFS, Princeton Univ

Aircraft Flight Dynamics


Robert Stengel, Princeton University, 2012"

Copyright 2012 by Robert Stengel All rights reserved For educational use only.!

http://www.princeton.edu/~stengel/MAE331.html !

!   Dynamics & Control of Atmospheric Flight

!   Configuration Aerodynamics

!   Aircraft Performance

!   Flight Testing and Flying Qualities

!   Aviation History

Details

•   Lecture: 3-4:20, D-221, Tue & Thu, E-Quad

•   Precept (as announced): 7-8:20, D-221, Mon

•   Engineering, science, & math

•   Case studies, historical context

•   ~6 homework assignments

•   Office hours: 1:30-2:30, MW, D-202, or any time the door is open

•   Assistants in Instruction: Carla Bahri, Paola Libraro : Office hours: TBD

•   GRADING –  Assignments: 30%

–  First-Half Exam: 15%

–  Second-Half Exam: 15%

–  Term Paper: 30%

–   Class participation: 10%

–  Quick Quiz (5 min): ?%

•   Lecture slides –  pdfs from all 2010 lectures are available now at http://www.princeton.edu/~stengel/MAE331.htm l –  pdf for current (2012) lecture will be available on Blackboard after the class

Syllabus, First Half

!  Introduction, Math Preliminaries

!  Point Mass Dynamics

!  Aviation History

!  Aerodynamics of Airplane Configurations

!  Cruising Flight Performance

!  Gliding, Climbing, and Turning Performance

!  Nonlinear, 6-DOF Equations of Motion

!  Linearized Equations of Motion

!  Longitudinal Dynamics

!  Lateral-Directional Dynamics

Details, reading, homework assignments, and references at

http://blackboard.princeton.edu/ "

Syllabus, Second Half

!   Analysis of Linear Systems

!  Time Response

!  Root Locus Analysis of Parameter Variations

!  Transfer Functions and Frequency Response

!   Aircraft Control and Systems

!   Flight Testing

!   Advanced Problems in Longitudinal Dynamics

!   Advanced Problems in Lateral-Directional Dynamics

!   Flying Qualities Criteria

!   Maneuvering and Aeroelasticity

!   Problems of High Speed and Altitude

!   Atmospheric Hazards to Flight

Text and References

•   Principal textbook:

–  Flight Dynamics , RFS, Princeton

University Press, 2004

–  Used throughout

–  Airplane Stability and Control ,

Abzug and Larrabee, Cambridge

University Press, 2002

–  Virtual textbook , 2012

Stability and Control Case Studies"

F-100"

Flight Tests Using Balsa Glider and

Cockpit Flight Simulator

•   Flight envelope of full-scale

aircraft simulation

–  Maximum speed, altitude ceiling, stall

speed, …

•   Performance

–  Time to climb, minimum sink rate, …

•   Turning Characteristics

–  Maximum turn rate, …

•   Compare actual flight of the glider

with trajectory simulation

Assignment #1

due: Friday, September 21

flight behavior of a balsa glider

–  Everything that you know about the physical characteristics of the glider

–  Everything that you know about the flight characteristics of the glider !

Luke Nash s Biplane Glider

Flight #1 (MAE 331, 2008)"

•   Can determine height, range, velocity, flight path angle, and pitch angle from sequence of digital photos (QuickTime)"

Luke Nash s Biplane Glider Flight #1 (MAE 331, 2008)"

Electronic Devices in Class

you may leave the room to do so

•  American Institute of Aeronautics and Astronautics!

–  largest aerospace technical society!

–  35,000 members!

•  https://www.aiaa.org !

•  Benefits of student membership ($20/yr)!

–  Aerospace America magazine!

–  Daily Launch newsletter!

–  Monthly Members Newsletter, Quarterly Student Newsletter! –  Aerospace Career Handbook!

–  Scholarships, design competitions, student conferences!

MAE department will reimburse dues when you join!

i.e., it’s free!"

Goals for Design"

•  Shape of the airplane

determined by its purpose"

•  Handling, performance,

functioning, and comfort"

•  Agility vs sedateness"

•  Control surfaces adequate to

produce needed moments"

•  Center of mass location"

–   too far forward increases

unpowered control-stick forces"

–   too far aft degrades static

stability "

Configuration Driven By The Mission and Flight Envelope"

Inhabited Air Vehicles"

Uninhabited Air Vehicles (UAV)"

Quick Quiz #1

First 5 Minutes of Next Class

!   Briefly describe the differences between one of the

following groups of airplanes:

!  Use Wikipedia to learn about all of these planes

!  Group (A or B or C or D) will be chosen by coin flip

in next class

!  Be sure to bring a pencil and paper to class

Introduction to Flight Dynamics

Airplane Components "

Airplane Rotational Degrees of Freedom"

Airplane Translational

Degrees of Freedom"

Axial Velocity"

Side Velocity"

Normal "

Velocity"

Phases of Flight"

Flight of a

Paper Airplane

Flight of a Paper Airplane


•   Red: Equilibrium flight path"

•   Black: Initial flight path angle = 0"

•   Blue: plus increased initial airspeed"

•   Green: loop"

•   Equations of motion integrated numerically to estimate the flight path "

Flight of a Paper Airplane 


•   Red: Equilibrium

flight path"

•   Black: Initial flight

path angle = 0"

•   Blue: plus

increased initial

airspeed"

•   Green: loop "

Assignment #2

Gliding Flight"

Configuration Aerodynamics"

Math Preliminaries

Notation for Scalars and Vectors "

a= −72 16

⎡

⎣

⎢

⎢

⎢

⎤

⎦

⎥

⎥

⎥

⎡

⎣

⎢

⎢

⎢

⎤

⎦

⎥

⎥

a b c d

⎡

⎣

⎢

⎢

⎢

⎢

⎤

⎦

⎥

⎥

⎥

⎥

•  Ordered set"

•  Column of scalars"

•  Dimension = n x 1"

Matrices and Transpose"

x=

p q r

⎡

⎣

⎢

⎢

⎢

⎤

⎦

⎥

⎥

⎥; A=

a b c

d e f

g h k

l m n

⎡

⎣

⎢

⎢

⎢

⎢

⎢

⎤

⎦

⎥

⎥

⎥

⎥

⎥

AT =

⎡

⎣

⎢

⎢

⎢

⎤

⎦

⎥

⎥

⎥

xT = x⎡⎣ 1 x2 x3 ⎤⎦

•  Dimension = (m x n)"

3× 1 ( ) ( 4 × 3 )

Multiplication "

ax T = ax⎡ 1 ax2 ax3

ax1

ax2

ax3

⎡

⎣

⎢

⎢

⎢

⎤

⎦

⎥

⎥

⎥

•   Operands must be conformable"

distributive"

dim x( )= dim y( )

Addition "

b

⎡

⎣

⎦

⎥ ; z = ⎡ d c

⎣

⎦

⎥

term "

x+ z = a + c

b + d

⎡

⎣

⎦

⎥

Inner Product "

x1

x2

x3

⎡

⎣

⎢

⎢

⎢

⎤

⎦

⎥

⎥

⎥

•  Inner (dot) product of vectors produces a scalar result"

(1× m)(m × 1) = (1× 1)

)

•  Length (or magnitude ) of vector is square root of dot product"

Vector Transformation "

y = Ax =

−9 −6 −3

⎡

⎣

⎢

⎢

⎢

⎢

⎤

⎦

⎥

⎥

⎥

⎥

x1

x2

x3

⎡

⎣

⎢

⎢

⎢

⎤

⎦

⎥

⎥

⎥

•  Matrix-vector product transforms one vector into another "

•  Matrix-matrix product produces a new matrix"

=

2x1+ 4x2 + 6x3

3x1− 5x2 + 7x3

4x1+ x2+ 8x3

−9x1− 6x2− 3x3

⎡

⎣

⎢

⎢

⎢

⎢

⎢

⎢

⎤

⎦

⎥

⎥

⎥

⎥

⎥

⎥

=

y1

y2

y3

y4

⎡

⎣

⎢

⎢

⎢

⎢

⎢

⎤

⎦

⎥

⎥

⎥

⎥

⎥

Derivatives and Integrals

of Vectors"

derivatives and integrals "

dx

dt =

dx1 dt

dx2 dt

dx3 dt

⎡

⎣

⎢

⎢

⎢

⎢

⎢

⎢

⎤

⎦

⎥

⎥

⎥

⎥

⎥

⎥

x

∫ dt =

∫ dt

∫ dt

∫ dt

⎡

⎣

⎢

⎢

⎢

⎢

⎢

⎤

⎦

⎥

⎥

⎥

⎥

⎥

Matrix Inverse"

x y z

⎡

⎣

⎢

⎢

⎢

⎤

⎦

⎥

⎥

⎥

2

=

⎡

⎣

⎢

⎢

⎢

⎤

⎦

⎥

⎥

⎥

x y z

⎡

⎣

⎢

⎢

⎢

⎤

⎦

⎥

⎥

⎥

1

Transformation"

Inverse Transformation"

x y z

⎡

⎣

⎢

⎢

⎢

⎤

⎦

⎥

⎥

⎥

1

⎡

⎣

⎢

⎢

⎢

⎤

⎦

⎥

⎥

⎥

x y z

⎡

⎣

⎢

⎢

⎢

⎤

⎦

⎥

⎥

⎥

2

x2 = Ax1

x1= A−1x2

Matrix Identity and Inverse"

0 0 1

⎡

⎣

⎢

⎢

⎢

⎤

⎦

⎥

⎥

⎥

AA−1 = A−1

A = I

y = Iy

when it multiplies a conformable vector or matrix"

multiplied by its inverse forms

an identity matrix"

AA−1 = cosθ 0 −sinθ

sinθ 0 cosθ

⎡

⎣

⎢

⎢

⎤

⎦

⎥

⎥

cosθ 0 −sinθ

sinθ 0 cosθ

⎡

⎣

⎢

⎢

⎤

⎦

⎥

⎥

−1

= cosθ 0 −sinθ

sinθ 0 cosθ

⎡

⎣

⎢

⎢

⎤

⎦

⎥

⎥

cosθ 0 sinθ

−sinθ 0 cosθ

⎡

⎣

⎢

⎢

⎤

⎦

⎥

⎥

= 1 0 00 1 0

0 0 1

⎡

⎣

⎢

⎢

⎤

⎦

⎥

⎥

Dynamic Systems"

Dynamic Process: Current state depends on

prior state "

x " = dynamic state "

u " = input "

w " = exogenous disturbance"

p " = parameter"

t or k " = time or event index "

Observation Process: Measurement may contain error or be incomplete "

y " = output (error-free)"

z " = measurement"

n " = measurement error "

•   All of these quantities are vectors"

Sensors!

Actuators!

Mathematical Models of Dynamic Systems are Differential Equations"

x(t)  dx(t)

Continuous-time dynamic process:

Vector Ordinary Differential Equation "

Output Transformation "

Measurement with Error "

dim x( )= n × 1( )

dim f( )= n × 1( )

dim u( )= m × 1( )

dim w( )= s × 1( )

dim p( )= l × 1( )

dim y( )= r × 1( )

dim h( )= r × 1( )

dim z( )= r × 1( )

dim n( )= r × 1( )

Next Time:

Point-Mass Dynamics and

Aerodynamic/Thrust Forces

Reading:

Flight Dynamics

for Lecture 1: 1-27 for Lecture 2: 29-34, 38-53, 59-65, 103-107

Virtual Textbook , Parts 1 and 2

Material

Ordinary Differential Equations"

dx(t)

dx(t)

dx(t)

Examples of Airplane Dynamic

System Models"

•  Nonlinear, Time-Varying "

–  Large amplitude motions"

–  Significant change in mass"

•  Nonlinear, Time-Invariant" –  Large amplitude motions" –  Negligible change in mass"

•  Linear, Time-Varying"

–  Small amplitude motions"

–  Perturbations from a dynamic flight path"

•  Linear, Time-Invariant" –  Small amplitude motions" –  Perturbations from an equilibrium flight path"

Simplified Longitudinal Modes of Motion"

Phugoid (Long-Period) Mode"

Short-Period Mode"

•   Note change in time scale"

Simplified Longitudinal Modes of Motion"

Simplified Lateral Modes of Motion"

Dutch-Roll Mode"

Roll and Spiral Modes"

Simplified Lateral Modes of Motion"

Flight Dynamics Book and

Computer Code"

•   All programs are accessible from the Flight Dynamics web

page"

–  http://www.princeton.edu/~stengel/FlightDynamics.html"

•   or directly"

•  Errata for the book are listed there"

•   6-degree-of-freedom nonlinear simulation of a business jet

aircraft (MATLAB)"

–  http://www.princeton.edu/~stengel/FDcodeB.html "

•   Linear system analysis (MATLAB)"

–  http://www.princeton.edu/~stengel/FDcodeC.html "

•   Paper airplane simulation (MATLAB)"

–  http://www.princeton.edu/~stengel/PaperPlane.html "

•   Performance analysis of a business jet aircraft (Excel)"

–  http://www.princeton.edu/~stengel/Example261.xls "

Helpful Resources"

•   Web pages"

–  http://blackboard.princeton.edu/ "

–  http://www.princeton.edu/~stengel/MAE331.html"

– http://www.princeton.edu/~stengel/FlightDynamics.html "

•   Princeton University Engineering Library (paper and on-line)"

–  http://lib-terminal.princeton.edu/ejournals/by_title_zd.asp "

•   NACA/NASA and AIAA pubs"

–  http://ntrs.nasa.gov/search.jsp "

Primary Learning Objectives

!   Introduction to the performance, stability, and control of

fixed-wing aircraft ranging from micro-uninhabited air

vehicles through general aviation, jet transport, and fighter

aircraft to re-entry vehicles.

!   Understanding of aircraft equations of motion,

configuration aerodynamics, and methods for analysis of

linear and nonlinear systems.

!   Appreciation of the historical context within which past

aircraft have been designed and operated, providing a sound

footing for the development of future aircraft.

More Learning Objectives"

!   Detailed evaluation of the linear and nonlinear flight characteristics of a specific aircraft type."

!   Improved skills for presenting ideas, orally and on paper."

!   Improved ability to analyze complex, integrated problems."

!   Demonstrated computing skills, through thorough knowledge and application of MATLAB."

!   Facility in evaluating aircraft kinematics and dynamics, flight envelopes, trim conditions, maximum range, climbing/diving/turning flight, inertial properties, stability-and-control derivatives, longitudinal and lateral-directional transients, transfer functions, state-space models, and frequency response."