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ME 380Aircraft Design
Stability and Control, Pt. 2
Energy Maneuverability Diagram
Puts all of the maneuver information in one compact
diagram
Flight velocity, turn rate, turn radius, & load factor
However, requires a diagram for each altitude and
weight
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Stability
In order of importance: Longitudinal stability
Stability about the pitch axis: horizontal stabilizer
Lateral stability
Stability about the roll axis: bi-lateral symmetry, wing design
(dihedral), ailerons, keel effect,
Directional stability
Stability about the yaw
axis: vertical stabilizer
Note on axes:
Trim Point Location
Compare two aircraft below
Cmcg
+
(nose up)
(nose down)
Aircraft 1
Aircraft 2
Airplane 1
Trimmed at point B
Cm=0 for > 0
Cmcg = 0Trim Pt.
Airplane 2
Cannot be trimmed to point B
Cm=0 for < 0
B CA
For stability,
Cm =dCmcg
d< 0
Cmcg = 0 at > 0
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Balance
The moment about the c.g. is the sum of these moments
Mcg =Mc/ 4 L(xc/ 4 xcg ) +Lt(x txcg )
Mcg = 0
Static Margin & CG Travel
By looking at CL and Cm we can define the static
margin
This is a measure of an
aircrafts stability - this
value should be between
0.03 (low) to 0.1 (high);
0.05 is a good value to
aim for
=Cm
CL
=xc/ 4 xcg
c
c.g. travel must bewithin SM limits
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Pitch Stability
From these we can determine the limits for c.g.(forward, XF, and aft, XR) - note that a larger tail
provides a larger range of c.g. travel
Pitching Tendencies in Stall
Low-tail aircraft pitch down in stall; recovery easier
T-tail aircraft pitch up in stall; tail in stalled wake,
recovery more problematic
cruciform T-tail
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Effect of Sweep on Stall Angle
Sweep reduces drag, but also increases stability atthe expense of lower lift
For example,
Effect of Elevator on Pitch Stability
Shifts stability curve up and down
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Phugoid
The phugoid is the traditional pitch behavior of anaircraft responding to a disturbance
Directional Stability
Cn
> 0
Stability reqmts
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Requirements for Direction Control
Adverse Yaw
When an airplane is banked to execute a turning maneuver, the aileronsmay create a yawing moment that opposes the turn (adverse yaw). Therudder must be able to overcome the adverse yaw so that a coordinatedturn can be achieved.
This usually occurs during slow flight (high CL).
Crosswind landings
To maintain alignment with the runway during a crosswind landing the
pilot must fly at a non-zero sideslip angle. The rudder must be powerful
enough to permit the pilot to trim the airplane for specified crosswinds.
Max. crosswind design value typically 15.5 m/s (51 fps).
Asymmetric power condn
When one engine fails on a multi-engine plane, a critical asymmetric
power condition occurs. The rudder must be able to overcome the yawingmoment produced by the asymmetric thrust arrangement.
The farther an engine is away from the centerline, the greater theasymmetric power control requirements are.
Asymmetric power & Stall into Spin
Spin Recovery
The primary control for spin recovery in most airplanes is the
rudder. The rudder must be powerful enough to oppose the spin
rotation.
Rectangular wing
Stall seen inboard; tail
blanked, but aileron control
still available
Swept wing
Stall outboard; tail available
but ailerons may not be
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Dorsal Fin
Addition of dorsal
fin delays tendency
of tail to stall at high
sideslip angles w/
reduced parasite drag
Forces on Aircraft in Roll
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Roll Stability
Cl
< 0
Stability reqmts
Fuselage Contributions
High wings more stable due to stabilizing roll
moment; low wings typically include dihedral to
counteract the destabilizing moment
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Dihedral & Roll Stability
Dihedral angle denoted by
, typically +3-5o
for a lowwing plane, 0 or slightly negative for a high wing
Dihedral Effect
When an airplane is disturbed from wings level attitude it will
begin to sideslip.
During sideslip, an additional velocity component is present -
The leading wing experiences an increased angle of attack, hence
increased lift.
The trailing wing experiences a decreased angle of attack, hence
decreased lift.
This results in a restoring force.
Wing Dihedral: Simplified Explanation
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Lateral Control and Roll Control Power
MROLL = Ly
Cl =L
qSb=
Clcydy
Sb
Cla =dCl
da
=2Clw
Sbcydy
y1
y 2
Common Coupled Dynamics
Spiral divergence (graveyard spiral); occurs
when static directional stability is large
compared to static lateral stability - solved
with addition of dihedral
Directional divergence; sideslip coupled with
yaw
Dutch roll; occurs when dihedral effect is
large compared to directional stability
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Dutch Roll
Commonly seen in low speed flight or with too muchdihedral
Slipstream Rotation
Slipstream rotation
from prop yaws
aircraft; most critical
at high power/low speed
scenarios (landing
and takeoff)
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Wing Rock
All Coefficients
Each coefficient (3 forces, 3 moments) has a
derivative in each direction and each angle, plus a
derivative with each rate (such as d/dt or q)
In general, a handful of these may be important for
any particular aircraft -
usually determined by
software (including
numerical models)
See Phillips (Mechanicsof Flight) or Etkin &
Reid (Dynamics of
Flight) for more details
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SomeStability Derivatives
Longitudinal derivatives (Etkin & Reid, Table 5.1)
Lateral derivatives (Etkin & Reid, Table 5.2)
Blue denotes tail only, wing-body
formula not available
No formula available
No formula available
Control
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Control Surfaces
Control Surface Deflections
CL =dCL
dee
CL =dCL
d+
dCL
dee
= a+ CLee
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Flap Effectiveness
CL =dCL
de=
dCL
dt
dtde
=CLt
How much extra lift is added by a control surface?
Trim AoA
Hinge Moments & Trim
He = Che1
2U2Sc
To size a servo, we need to note the required moment
to move a control surface
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Stick Forces
Flss =Hee
F=elss
He
= GHe
= GChe12U2Sc
Servo motors on control surfaces easily sized oncehinge moments are determined. Use moment
balance (even if modern control system is used).
Can get flap forces from Xfoil
Stick Fixed v. Stick Free
When the elevator is set free, the stability and control
characteristics change.
Typically, when the AoA
is increased, the elevator
floats upwards.
Regardless, the location
of the stick fixed and stick
free neutral points sets an
aft limit to the center ofgravity travel for the plane.
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Fixed vs. Free Static Margin
stick fixed static margin=xNP
c
xcg
c
stick free static margin=xNP
c
xcg
c5% (0.05c) is the general design rule of thumb for static margin
Static margin is a way of measuring the static stabilityof an aircraft
Neutral point is location of c.g. where stability goes to 0 (neither +
nor -)
Neutral point (NP) is usually the aerodynamic center (AC), or
where the lift vector acts
Stick Force or Speed Stability
Negative stick force gradient provides pilot with
speed stability; once trimmed, the velocity will return
to trimmed speed if perturbed
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Control Issues: e.g., Aileron Reversal
As an example of the many control issues one mayencounter, aileron reversal is one commonly seen at
higher speeds
Control: Open & Closed Loop
Example: wing leveling autopilot
Practically all aircraft are closed-loop control
Classic: pilot gets feedback from stick forces and instruments
Modern: digital autopilot corrects/enhances pilot input
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Types of Control Systems
Direct Push-rod
Cable-and-pulley
Indirect
Hydraulic
Fly-by-wire
Fly-by-light
FBW Philosophy
The computer should have final authority on the
commands sent to the control system. The pilots
inputs should be limited by the computer (hard limits
or protections) to prevent exceeding the physical
design limits of the aircraft (e.g., angle of attack, g-
loads, etc.) to protect the integrity and dynamics of
the aircraft.
The pilot should have final authority of the commands
sent to the control system. The computer shouldmonitor the pilots inputs for limits (soft limits) and
warn when they exceed the physical design limits of
the aircraft, but carry out the commands even if that
would endanger the aircraft integrity or flight.
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Handling Qualities
Controls must feel right to pilot Control parameters (gains, damping, etc.) are unique
to each aircraft and thus must be tuned, typically
through wind tunnel and flight tests
Cooper-Harper Scale
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Weather
Typical Storm Wind Patterns
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Landing in Wind Shear
From headwind to tailwind
1. Normal approach
2. Increasing downdraft and
tailwind
3. Airspeed decreases, pitch down
4. Aircraft crashes short of runway
From tailwind to headwind; hard
landing or overshoot
Wind Shear
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Wind Shear
1- & 2-D Gusts
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Boundary Layer Effect