Lecture 1: Review of Static Pitch Stability
To discuss stability of a steady motion, we must rst introduce some terminology to describe the motion.
Suppose we x a reference frame to some point in the aircraft, as shown in Figure 1. We denote by xB
the uni

Lecture 20: Introduction to Aircraft Control: Pitch Stabilization
dc
Figure 1: An airplane with canards.
Consider a wind-tunnel model which is pinned to allow pitch rotation about the center of gravity. Rather
than a conventional horizontal stabilizer wit

Lecture 22: Routh-Hurwitz Stability Analysis
The following discussion follows that of [2]. For more detailed information about Routh-Hurwitz stability
analysis, see [1].
Suppose we have a transfer function
Q(s) =
B (s)
.
A(s)
The transfer function Q(s) mi

Lecture 21: A Brief Introduction to Linear Control
Figure 1, which is taken from [1], represents the general form of a control system. The fundamental
component is the plant itself. The Plant Dynamics block in Figure 1 represents some system whose
behavio

AOE 3134 Stability and Control Topics I Static Stability and Control A. Definition of Static Stability and Application B. Longitudinal Static Stability 1. Estimating Aerodynamic Properties a) Lifting surface properties i) lift curve slope ii) mean aerodyn

Stability and Control Introduction An important concept that must be considered when designing an aircraft, missile , or other type of vehicle, is that of stability and control. The study of stability is related to the flying qualities of the vehicle and

Stability and Control Longitudinal Static Stability We now examine the concept of longitudinal static stability and the contributors to it. As indicated in previous sections, the concept of static stability is concerned with the forces and moments caused

Stability and Control Complete Vehicle Pitch Stability and Control The equations for the complete vehicle lift and pitch-moment were developed previously and are repeated here:
(1)
where
.
Longitudinal Static Stability Parameter The indicator of longitudi

Stability and Control Estimating Aerodynamic Properties A necessary ingredient for determining the aerodynamic properties of an aircraft is to be able to determine the aerodynamic properties of parts of the aircraft. If we look at the expression for the p

Stability and Control Some Characteristics of Lifting Surfaces, and Pitch-Moments The lifting surfaces of a vehicle generally include the wings, the horizontal and vertical tail, and other surfaces such as canards, winglets, etc. What they all have in com

Stability and Control Stick Free Characteristics Hinge Moments Each control surface on an aircraft has a hinge of some sort. By deflecting the control, there is an aerodynamic moment about that hinge. The pilot (or some power augmentation system) must pro

AOE 3134 Stability and Control Important Equations and Relations March 12, 2002 1. Longitudinal Static Stability a. General i. General moment relation between two reference points
ii. Aerodynamic center:
= constant independent of angle-of-attack
b. Lift r

Roll and Yaw Moments and Stability Yaw Moment Equation The yaw moment is the moment about the zbody axis and is positive if it moves the nose of the plane to the right. The big contributor to the yaw moment is the vertical tail. We can write the yaw momen

Maneuvering Flight The feature that maneuvering flight adds to the equations is the pitch rate. Two types of maneuvering flight that we will look at are a symmetric pull up, and a horizontal turn. In either case an added pitch rate is encountered that mus

Lateral Directional Flight Considerations This section discusses the lateral-directional control requirements for various flight conditions including cross-wind landings, asymmetric thrust, turning flight, and others. The controls for longitudinal flight

AOE 3134 Stability and Control Instructor: Frederick H. Lutze Randolph Hall Room 214 Phone: 231-6409 E-mail lutze@aoe.vt.edu Etkin and Reid, Dynamics of Flight, Stability and Control, John Wiley, 1996 Tests Homework Final Total 2.5 1.5 2 6
Text:
Grading:

Aircraft Dynamics
In order to discuss dynamic stability we essentially need to solve the differential
equations of motion. However, before jumping into the full blown problem of aircraft motion, it
is useful to look at some approximations first, starting

Lecture 15: Longitudinal Stability Derivatives
The term stability derivative arises from the linearization of the aerodynamic terms in the nonlinear
dynamic equations. The connection to stability comes from the role these terms play in the stability
of wi

Lecture 18: Longitudinal Dynamics
The small perturbation equations describing the stick-xed longitudinal motion of an airplane are
xL = AL xL + B L uL
where the reduced longitudinal state vector and input vector are
u
w
e
xL =
and
uL =
q ,
T
the reduc

Lecture 17: LTI Systems in State-Space Form
Consider the homogeneous LTI system
x = Ax,
x(t0 ) = x0 .
(1)
The dynamics of an LTI system are invariant under shifts in the initial time. Without loss of generality, we
may assume that t0 = 0 because if t0 wer

Lecture 2: Component Eects on Static Pitch Moment
Reference line
k
j
i
xcg
Lw
z cg
iw
w
Mac w
xac
V
Dw
Figure 1: Longitudinal force and moment due to the wing.
Pitch moment contribution from the wing. Suppose that the aerodynamic characteristics of a
part

Lecture 3: Total Pitch Moment Coecient
Recall that we found
Cmt = H CLt t
V
l
where H = Stct is the horizontal tail volume ratio (with lt representing the signed longitudinal distance
V
S
from the center of gravity to the tail aerodynamic center). By deni

Lecture 5: Longitudinal Maneuvering Flight
Symmetric pull-up. Consider an aircraft in wings-level ight which is executing a steady pull-up, that
is, a pitch-up maneuver at constant pitch rate. As a simple, but representative case, we will consider
the sit

Lecture 6: Directional Stability & Control
With the exception of steady turning ight at constant radius, we have only considered wings level ight.
In this setting, the three lateral-directional velocities (v , p, and r ) are initially zero and they remain

Lecture 4: Longitudinal Control
We next turn our attention to control of longitudinal motion, particularly control of the pitch attitude .
For wings-level, equilibrium ight at constant altitude, is equal to the pitch angle . Thus, by controlling
the pitch

Lecture 8: Lateral-Directional Steady Flight
A complete discussion of lateral-directional equilibrium ight requires some advanced material which we
will cover in coming lectures. There is no great diculty in studying lateral-directional equilibrium ight,

Lecture 7: Roll Stability & Control
For both pitching and yawing motion, the primary eect of the empennage (the horizontal and vertical
tail assembly) is to provide stabilizing moments which tend to keep the nose of the airplane pointing into
the wind. Th

Lecture 13: Small Disturbance Equations of Motion
We are considering a rigid airplane with a coordinate frame xed at the center of gravity such that the
xz -plane is a plane of symmetry. Written in these coordinates, the kinematic equations are
x
cos cos

Lecture 11: Rigid Body Dynamics & Kinematics
yB
yI
xI
xB
zI zB
Xcm
yI
xI
zI
Figure 1: Rigid body reference frames.
Recall that we are considering the dynamics of a rigid body. The rigid body dynamic equations, expressed
in a reference frame xed in the bod

Lecture 12: Linearization
Consider a set of nonlinear, time-invariant ODEs. Recall that any nth order ODE can be re-written as n
rst order ODEs. We may therefore assume, without loss of generality, that the system takes the form
x = f (x, u),
(1)
where f