Mae 331 Lecture 1
-
Upload
peaceout99 -
Category
Documents
-
view
41 -
download
1
description
Transcript of Mae 331 Lecture 1
![Page 1: Mae 331 Lecture 1](https://reader033.fdocuments.us/reader033/viewer/2022052213/5460cf31b1af9f09598b5602/html5/thumbnails/1.jpg)
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.html�– 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�
![Page 2: Mae 331 Lecture 1](https://reader033.fdocuments.us/reader033/viewer/2022052213/5460cf31b1af9f09598b5602/html5/thumbnails/2.jpg)
Text and References�
• Principal textbook: �– Flight Dynamics, RFS, Princeton
University Press, 2004 �– Used throughout��
• Supplemental references �– Airplane Stability and Control,
Abzug and Larrabee, Cambridge University Press, 2002 �
– Virtual textbook, 2012 �
Stability and Control Case Studies"
Ercoupe" Electra"
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 �
• Document the physical characteristics and 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. !
![Page 3: Mae 331 Lecture 1](https://reader033.fdocuments.us/reader033/viewer/2022052213/5460cf31b1af9f09598b5602/html5/thumbnails/3.jpg)
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�• Silence all cellphones and computer alarms�• If you must make a call or send a message,
you may leave the room to do so �• No checking or sending text, tweets, etc. �
– No social networking �– No surfing �
• Pencil and paper for note-taking �
• 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!"
![Page 4: Mae 331 Lecture 1](https://reader033.fdocuments.us/reader033/viewer/2022052213/5460cf31b1af9f09598b5602/html5/thumbnails/4.jpg)
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)"
![Page 5: Mae 331 Lecture 1](https://reader033.fdocuments.us/reader033/viewer/2022052213/5460cf31b1af9f09598b5602/html5/thumbnails/5.jpg)
Quick Quiz #1 �First 5 Minutes of Next Class �
! Briefly describe the differences between one of the following groups of airplanes:�A. Boeing B-17 vs. Northrop YB-49 vs. North American B-1 �B. Piper Cub vs. Beechcraft Bonanza vs. Cirrus SR20 �C. Douglas DC-3 vs. Boeing 707 vs. Airbus A320 �D. Lockheed P-38 vs. North American F-86 vs. Lockheed F-35 �
! 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"
![Page 6: Mae 331 Lecture 1](https://reader033.fdocuments.us/reader033/viewer/2022052213/5460cf31b1af9f09598b5602/html5/thumbnails/6.jpg)
Airplane Translational Degrees of Freedom"
Axial Velocity"
Side Velocity"
Normal "Velocity"
Phases of Flight"
Flight of a Paper Airplane �
Flight of a Paper Airplane Example 1.3-1, Flight Dynamics"
• 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"
![Page 7: Mae 331 Lecture 1](https://reader033.fdocuments.us/reader033/viewer/2022052213/5460cf31b1af9f09598b5602/html5/thumbnails/7.jpg)
Flight of a Paper Airplane Example 1.3-1, Flight Dynamics"
• Red: Equilibrium flight path"
• Black: Initial flight path angle = 0"
• Blue: plus increased initial airspeed"
• Green: loop"
Assignment #2 �
• Compute the trajectory of a balsa glider �
Gliding Flight"Configuration Aerodynamics"
![Page 8: Mae 331 Lecture 1](https://reader033.fdocuments.us/reader033/viewer/2022052213/5460cf31b1af9f09598b5602/html5/thumbnails/8.jpg)
Math Preliminaries�
Notation for Scalars and Vectors "• Scalar: usually lower case: a, b, c, …, x, y, z "
a =2−716
⎡
⎣
⎢⎢⎢
⎤
⎦
⎥⎥⎥; x =
x1x2x3
⎡
⎣
⎢⎢⎢
⎤
⎦
⎥⎥⎥; y =
abcd
⎡
⎣
⎢⎢⎢⎢
⎤
⎦
⎥⎥⎥⎥
• Vector: usually bold or with underbar: x or x"• Ordered set"• Column of scalars"• Dimension = n x 1"
a = 12; b = 7; c = a + b = 19; x = a + b2 = 12 + 49 = 61
Matrices and Transpose"
x =pqr
⎡
⎣
⎢⎢⎢
⎤
⎦
⎥⎥⎥; A =
a b cd e fg h kl m n
⎡
⎣
⎢⎢⎢⎢⎢
⎤
⎦
⎥⎥⎥⎥⎥
AT =a d g lb e h mc f k n
⎡
⎣
⎢⎢⎢
⎤
⎦
⎥⎥⎥
xT = x1 x2 x3⎡⎣
⎤⎦
• Matrix: usually bold capital or capital: F or F"• Dimension = (m x n)"
• Transpose: interchange rows and columns"3×1( ) 4 × 3( )
Multiplication "
axT = ax1 ax2 ax3⎡⎣
⎤⎦
ax = xa =ax1ax2ax3
⎡
⎣
⎢⎢⎢
⎤
⎦
⎥⎥⎥
• Operands must be conformable"• Multiplication of vector by scalar is associative, commutative, and
distributive"
• Could we add ?"x + a( ) • Only if" dim x( ) = 1×1( )
a x + y( ) = x + y( )a = ax + ay( )dim x( ) = dim y( )
![Page 9: Mae 331 Lecture 1](https://reader033.fdocuments.us/reader033/viewer/2022052213/5460cf31b1af9f09598b5602/html5/thumbnails/9.jpg)
Addition "
x = ab
⎡
⎣⎢
⎤
⎦⎥ ; z = c
d⎡
⎣⎢
⎤
⎦⎥
• Conformable vectors and matrices are added term by term "
x + z = a + cb + d
⎡
⎣⎢
⎤
⎦⎥
Inner Product "
xTx = x • x = x1 x2 x3⎡⎣
⎤⎦
x1x2x3
⎡
⎣
⎢⎢⎢
⎤
⎦
⎥⎥⎥
• Inner (dot) product of vectors produces a scalar result"
(1× m)(m ×1) = (1×1)
= (x12 + x2
2 + x32 )
• Length (or magnitude) of vector is square root of dot product"
= (x12 + x2
2 + x32 )1/2
Vector Transformation "
y = Ax =
2 4 63 −5 74 1 8−9 −6 −3
⎡
⎣
⎢⎢⎢⎢
⎤
⎦
⎥⎥⎥⎥
x1x2x3
⎡
⎣
⎢⎢⎢
⎤
⎦
⎥⎥⎥
(n ×1) = (n × m)(m ×1)
• 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( )
⎡
⎣
⎢⎢⎢⎢⎢⎢
⎤
⎦
⎥⎥⎥⎥⎥⎥
=
y1y2y3y4
⎡
⎣
⎢⎢⎢⎢⎢
⎤
⎦
⎥⎥⎥⎥⎥
Derivatives and Integrals of Vectors"
• Derivatives and integrals of vectors are vectors of derivatives and integrals"
dxdt
=
dx1dt
dx2dt
dx3dt
⎡
⎣
⎢⎢⎢⎢⎢⎢
⎤
⎦
⎥⎥⎥⎥⎥⎥
x∫ dt =
x1∫ dt
x2∫ dt
x3∫ dt
⎡
⎣
⎢⎢⎢⎢⎢
⎤
⎦
⎥⎥⎥⎥⎥
![Page 10: Mae 331 Lecture 1](https://reader033.fdocuments.us/reader033/viewer/2022052213/5460cf31b1af9f09598b5602/html5/thumbnails/10.jpg)
Matrix Inverse"
xyz
⎡
⎣
⎢⎢⎢
⎤
⎦
⎥⎥⎥2
=cosθ 0 − sinθ0 1 0sinθ 0 cosθ
⎡
⎣
⎢⎢⎢
⎤
⎦
⎥⎥⎥
xyz
⎡
⎣
⎢⎢⎢
⎤
⎦
⎥⎥⎥1
Transformation"
Inverse Transformation"
xyz
⎡
⎣
⎢⎢⎢
⎤
⎦
⎥⎥⎥1
=cosθ 0 sinθ0 1 0
− sinθ 0 cosθ
⎡
⎣
⎢⎢⎢
⎤
⎦
⎥⎥⎥
xyz
⎡
⎣
⎢⎢⎢
⎤
⎦
⎥⎥⎥2
x2 = Ax1
x1 = A−1x2
Matrix Identity and Inverse"
I3 =1 0 00 1 00 0 1
⎡
⎣
⎢⎢⎢
⎤
⎦
⎥⎥⎥
AA−1 = A−1A = I
y = Iy• Identity matrix: no change
when it multiplies a conformable vector or matrix"
• A non-singular square matrix multiplied by its inverse forms an identity matrix"
AA−1 =cosθ 0 − sinθ0 1 0sinθ 0 cosθ
⎡
⎣
⎢⎢⎢
⎤
⎦
⎥⎥⎥
cosθ 0 − sinθ0 1 0sinθ 0 cosθ
⎡
⎣
⎢⎢⎢
⎤
⎦
⎥⎥⎥
−1
=cosθ 0 − sinθ0 1 0sinθ 0 cosθ
⎡
⎣
⎢⎢⎢
⎤
⎦
⎥⎥⎥
cosθ 0 sinθ0 1 0
− sinθ 0 cosθ
⎡
⎣
⎢⎢⎢
⎤
⎦
⎥⎥⎥
=1 0 00 1 00 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)
dt= f[x(t),u(t),w(t),p(t),t]
�
y(t) = h[x(t),u(t)]
z(t) = y(t) + n(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( )
![Page 11: Mae 331 Lecture 1](https://reader033.fdocuments.us/reader033/viewer/2022052213/5460cf31b1af9f09598b5602/html5/thumbnails/11.jpg)
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 �
Supplemental Material
Ordinary Differential Equations"
dx(t)dt
= f x(t),u(t),w(t)[ ]
dx(t)dt
= f x(t),u(t),w(t),p(t),t[ ] dx(t)dt
= F(t)x(t) +G(t)u(t) + L(t)w(t)
dx(t)dt
= Fx(t) +Gu(t) + Lw(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"
![Page 12: Mae 331 Lecture 1](https://reader033.fdocuments.us/reader033/viewer/2022052213/5460cf31b1af9f09598b5602/html5/thumbnails/12.jpg)
Simplified Longitudinal Modes of Motion"Phugoid (Long-Period) Mode"
Airspeed! Flight Path Angle!
Pitch Rate! Angle of Attack!
Short-Period Mode"
Airspeed! Flight Path Angle!
Pitch Rate! Angle of Attack!
• Note change in time scale"
Simplified Longitudinal Modes of Motion"
Simplified Lateral Modes of Motion"Dutch-Roll Mode"
Yaw Rate! Sideslip Angle!
Roll and Spiral Modes"
Roll Rate! Roll Angle!
Simplified Lateral Modes of Motion"
![Page 13: Mae 331 Lecture 1](https://reader033.fdocuments.us/reader033/viewer/2022052213/5460cf31b1af9f09598b5602/html5/thumbnails/13.jpg)
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."