MAE 4242 Aircraft Stability and Control
Unit 10 Course Notes
Linearizing the Equations of Motion
To allow us to further analyze the equations of motion, we require that they behave linearly with
respect to their independent variables. One way that this is
MAE 4242 AIRCRAFT STABILITY & CONTROL
Linear Dynamical Systems Theory
(Nelson: 4.2, 6.1, App. C)
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Linear & Nonlinear Systems (1)
Linear/nonlinear characterization of a system is based on the
system excitation (i
MAE 4242 AIRCRAFT STABILITY & CONTROL
Stick-Fixed Lateral-Directional Dynamics
(Nelson: 5.1-5.4)
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Pure Rolling Motion (1)
Pure rolling motion is the simplest case of lateral aircraft
motion
Corresponds to the ca
MAE 4242 AIRCRAFT STABILITY & CONTROL
Aircraft Flight Dynamics Equations of Motion
(Nelson: 3.1-3.2, 3.4-3.5)
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Reference Frames Used in EOM Derivation
Two reference frames are often used in aircraft motion
analy
MAE 4242 AIRCRAFT STABILITY & CONTROL
Stick-Fixed Longitudinal Dynamics
(Nelson: 4.3-4.6)
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Stick-Fixed Aircraft Response
Stick-fixed aircraft response: motion of aircraft with no
control influence (control varia
MAE 4242 AIRCRAFT STABILITY & CONTROL
Aircraft Rotational Kinematics
(Nelson: 3.3)
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Rotational Kinematics of Aircraft
Rotational kinematics concerns with expressing the angular
orientation and angular rates of a
MAE 4242 AIRCRAFT STABILITY & CONTROL
Directional Static Stability
(Nelson: 2.6)
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Directional Static Stability Criterion
Aircraft Yawing Moment
Steady yawing moment of aircraft (N) about its CG is
affected by an
MAE 4242 AIRCRAFT STABILITY & CONTROL
Lateral Control
(Nelson: 2.9)
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Primary Lateral Control
Primary lateral control: ailerons
Alternative: spoilers
Convention:
Positive if produces
positive rolling
moment
( Rig
MAE 4242 AIRCRAFT STABILITY & CONTROL
Lateral Static Stability
(Nelson: 2.8)
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Lateral Static Stability Criterion
Aircraft Rolling Moment
Steady rolling moment of aircraft (L) about its CG is affected
by angle of
MAE 4242 AIRCRAFT STABILITY & CONTROL
Nomenclature and Aerodynamics Review
(Nelson: Ch. 1)
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Conventional Aircraft Main Parts
Aircraft Axis Systems (1)
Right-handed Cartesian
axis systems that are often
used for
MAE 4242 Aircraft Stability and Control
Unit 1 Course Notes
Airfoil and Wing Aerodynamics Review
First, we recall the definition of an airfoil. An airfoil is the two-dimensional cross-section of a
streamlined object designed to minimize the separation of
MAE 4242 Aircraft Stability and Control
Unit 8 Course Notes
Rigid Body Dynamics
In this unit, we will derive the rotational equivalent to Newtons second law. Where F = ma
governs our change in linear velocity, we need an equation that governs our change i
MAE 4242 Aircraft Stability and Control
Unit 11 Course Notes
Linear Algebra Review
A matrix is an array of numbers arranged into m rows and n columns (read m by n or written
mn ), which we can visualize as
where the entries aij are the elements of A for 1
MAE 4242 Aircraft Stability and Control
Unit 12 Course Notes
Longitudinal Dynamic Stability
Consider the linearized system developed to model longitudinal dynamics of an aircraft. It is of
the form
, where the state vector is
. If we assume
stability axes
MAE 4242 Aircraft Stability and Control
Unit 13 Course Notes
Lateral Dynamic Stability
Consider the linearized system developed to model lateral dynamics of an aircraft. It is of the
form
, where the state vector is
. If we assume stability
axes, such tha
MAE 4242 Aircraft Stability and Control
Unit 9 Course Notes
General Equations of Unsteady Motion
Lets put all of our rigid body dynamics and coordinate system kinematics in the perspective of
the body coordinate system defined in the book, and Chapter 4 i
MAE 4242 Aircraft Stability and Control
Unit 6 Course Notes
Lateral Static Stability and Control
Previously, we considered motion in the plane of symmetry including primarily pitch motion.
Now, we add the possibility that the velocity vector for the aircr
MAE 4242 Aircraft Stability and Control
Unit 5 Course Notes
Longitudinal Control
There are two primary methods for longitudinal control of our aircraft (pitch motion).
1) Change in the weight distribution, or
2) Change in lift generation.
Method (1) shift
MAE 4242 Aircraft Stability and Control
Unit 2 Course Notes
Stability Concepts
A dynamic system is a mechanical or kinematic system that can be dependent on time, t. Given a
set of n variables that we can track x1, x2, , xn, and a set of m control inputs
MAE 4242 Aircraft Stability and Control
Unit 7 Course Notes
Rotational Kinematics of Rigid Bodies
This subject, by necessity, is very mathematical because it does not involve forces we typically
associate with motion, i.e. the forces linked to acceleratio
MAE 4242 Aircraft Stability and Control
Unit 3 Course Notes
Open-Loop Pitch Stability
For steady, level flight we require a constant value of lift, equal to the weight of the vehicle. We
know that CL is a function of , so this means that the angle of atta
MAE 4242 Aircraft Stability and Control
Unit 4 Course Notes
Control Overview
A control is a force or moment that we used as an input to a dynamic system. Our dynamic
system (also called the plant) is made up of a series of measurements for how reference v
MAE 4242 AIRCRAFT STABILITY & CONTROL
Directional Control
(Nelson: 2.7)
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Primary Directional Control
Primary directional control: rudder
Rudder deflection
change side force on vertical tail
change yawing moment