AE 430 - Stability and Control of
Aerospace Vehicles
Longitudinal Control
Primary Aerodynamic Controls
(+)
(+)
δp
1
Primary Aerodynamic Controls
A simple basic control system as
operated by a pilot
2
Longitudinal Control
z
z
z
through pilot’s change of thrust (propulsion), and/or
through change of configurations using aerodynamic
control surfaces
Main aerodynamic surfaces for longitudinal control:
–
on Tail:
–
on Wing:
z
z
z
z
elevator
slats (leading-edge)
flaps (trailing-edge)
spoilers
Control through Pilot
z
To rotate any of the aerodynamic control surface, it
is necessary to apply a force to it to overcome the
aerodynamic pressures that resist the motion. This
force may be supplied by a human pilot through
different ways:
–
–
–
–
–
Mechanical Linkage Control
Power Assisted Control: pilot’s control is connected to the
control surface and the control lever
Power Operated Control: pilot’s control is connected to the
control lever ONLY
Fly-by-wire: wire carries electrical signals from the pilot’s
control to replace mechanical linkage
Fly-by-optical
3
Longitudinal Control
Factors affecting the design of a control surface are:
1) Control Effectiveness
2) Hinge moments
3) Aerodynamic and mass balancing
1) Control Effectiveness
z
z
Is a measure of how effective the control
deflection is in producing the desired control
moment
Function of the size of the elevator and tail
volume ratio
4
Longitudinal Control
2) Hinge Moment
z
The aerodynamic moment that must be
overcome to rotate the control surface
3) Aerodynamic and Mass balancing
z
To have the control stick force within an
acceptable range
Elevator Effectiveness
How to Change
Airplane Trim
Angle of Attack
Deflecting the elevator:
Change in Lift
∆CL = CLδ δ e
e
Change in Pitching Moment
dCL Elevator Effect. Deriv.
dδ e
dCm Elevator
∆Cm = Cmδ δ e Cmδ =
power
e
e
d δ e control
CLδ =
e
In the case of linear lift and moment, we further have:
Cm = Cm0 + Cmα α + Cmδ δ e
e
CL = CLα α + CLδ δ e
e
5
Cm-α ; δetrim-α
(+)
Cm – α
and
CL - α
6
CLδ =
How to find
∆L = ∆Lt
e
St
S dCLt
∆CLt = η t
δe
S
S dδ e
CLδ = η
St dCLt
S
= η t CLα t τ
S dδ e
S
∆Cm = −ηVH ∆CLt = −ηVH
Cmδ = −ηVH
e
Cmδ =
e
dCm
dδ e
Elevator effectiveness
∆CL = η
e
dCL
dδ e
dCLt
dδ e
dCLt
dδ e
dCLt
dδ e
=
dCLt dα t
= CLα t τ
dα t d δ e
δe
= −ηVH CLα t τ
Elevator Effectiveness
Tail Lift Coefficient vs
Tail Angle of Attack
Tail Lift Coefficient vs
Elevator Deflection
7
Calculating Elevator Effectiveness
z
–
z
dδ e
This is the slope of the graph
From this we get
CLδ =
e
z
dCLt
The elevator effectiveness
St dCLt
η
S dδ e
Elevator control powerCmδ
∆Cmtrim = Cmδ δ e trim
e
= −VH η
dCLt
dδ e
= −ηVH CLα t τ
e
z
Flap effectiveness parameter
τ =−
Cmδ e
VH η CLα
t
Elevator Angle to Trim
Cm = Cm0 + Cmα α + Cmδ δ e = 0
e
δ trim = −
Cm0 + Cmα α trim
Cmδ
CLtrim = CLα α trim + CLδ δ trim
e
α trim =
(+) (+)
e
CLtrim − CLδ δ trim
δ trim = −
(-)
(+)
Cm0 CLα + Cmα CLtrim
Cmδ CLα − Cmα CLδ
e
e
(-)
CLα
(+)
(-)
e
(+)
usually
(-)
8
Some conclusions
z
z
with elevator angle to trim, the
slope of lift coefficient is
slower, less sensitive to
change of α, because
configuration change due to δe
with elevator angle to trim, a
zero angle of attack α = 0 still (+)
generates a lift, due to δe
( −)
CLtrim = CLα α trim + CLδ δ trim = ( CLα −
e
(+)
Cmα CLδ
Cmδ
( −)
e
e
(+)
(-)
)α trim −
Cm0 CLδ
Cmδ
CLα ′ < CLα
e
e
VH set from the static longitudinal stability requirements
9
Variation of δeTRIM with CLTRIM
z
z
for a zero lift, there must
have a positive deflection
of δe for a given CG
(forward) position,
increasing lift requires less
δe deflection
for a given trimmed lift, the
more CG forward (larger
static margin), the less
elevator angle deflection δe
requires
XCG=XNP
(+) (+)
(-)
XCG<XNP
det = Cmδ CLα − Cmα CLδ
(−)
e
( −) ( + )
e
( −) ( +)
Variation of δeTRIM with the speed
z
z
for a given CG (forward)
position, increase trim
speed requires more
elevator angle deflection
for a given trim speed, the
more CG forward (larger
static margin), the less
elevator angle deflection
requires
No compressibility effects,
no propulsive effects
CLtrim =
XCG=XNP
Trim speed
W
1
2
ρ0VE2 S
VE = V ρ
ρ0
10
Flight Measurement of XNP
Cmα
d δ trim
=−
dCLtrim
Cmδ CLα − Cmα CLδ
e
xcg = xNP
d δ trim
=0
dCLtrim
⇒ Cmα = 0 ⇒
e
xNP
c
dCLtrim
− Cm0 CLα det
xcg
c
CLtrim
Elevator deflection to trim
Landing & take-off
Higher speed
11
Elevator Hinge Moment
Only the shaded portion of the lift distribution in these figures acts
on the control surface and contributes to the hinge moment.
Elevator Hinge Moment
z
The aerodynamic forces on any control surface
produce a moment about the hinge. The coefficient
of elevator hinge moment:
12
Elevator, Tab and Their Hinge
He
ce
∫ x∆Ldx = H e
0
Elevator Hinge Moment
z
In practice, it is often satisfactory to assume Che is a
linear function of surface (wing or tail) angle of attack
αt, angle of elevator δe, and angle of tab δt :
Che = Ch0 + Chα t α t + Chδ e δ e + Chδ t δ t
Chα t =
Ch0
dCh
dα t
Chδ e =
dCh
dδ e
Chδ t =
dCh
dδ t
Residual moment
13
Elevator Free (Control stick released)
Stick-fixed condition is an ideal
approximation. The opposite extreme
is also of interest: stick-free
Coeff. of elevator “free” moment
condition:
Che = Chα t α t + Chδ e δ e = 0
δ efree = −
Usually
Chα t
Chδ e
assuming, Ch0 = δ t = 0
αt
Chα t < 0; Chδ e < 0
The elevator will float upward as the angle of attach is increased
Ch
Lift coefficient
CLt = CLα t α t + CLδ δ efree = CLα t α t − α t CLδ α t
for the tail
e
e
Chδ e
“elevator free”
Elevator Free (Control stick released)
⎛ Ch CLδ
e
CLt = CLα t α t + CLδ δ efree = CLα t α t ⎜ 1 − α t
e
⎜ Ch C L
δe
αt
⎝
⎛ Ch CLδ
e
CL′α t = CLα t ⎜1 − α t
⎜ Ch CL
δe
αt
⎝
⎞
⎟ = CLα f
t
⎟
⎠
⎞
⎟ = CL′α α t
t
⎟
⎠
Coeff. hinge ratio
Cm′ 0 = Cm0 w + Cm0 f + VH η CL′α t ( ε 0 + iw − it )
⎡ xcg xac ⎤
Cm′ α = CLα ⎢
−
⎥ + Cmα f − VH η CL′α t
w
c ⎦
⎣ c
dε ⎞
⎛
⎜ 1 − dα ⎟
⎝
⎠
(depend on f )
14
Elevator Free (Control stick released)
⎡ xcg xac ⎤
Cm′ α = CLα ⎢
−
⎥ + Cmα f − VH η CL′α t
w
c ⎦
⎣ c
For the static longitudinal stability
Cmα
′
xNP
x
= ac −
c
c
CLα
f
w
+ VH η
dε ⎞
⎛
⎜ 1 − dα ⎟
⎝
⎠
Cm′ α = 0
CL′α t ⎛
dε ⎞
1−
⎜
CLα ⎝ dα ⎟⎠
w
CL
′
xNP xNP
−
= (1 − f ) VH η α t
c
c
CLα w
dε ⎞
⎛
⎜ 1 − dα ⎟
⎝
⎠
Static Margin: distance between the neutral
point and the actual center of gravity
position
z
Stick fixed static margin
xNP xcg
−
c
c
z
Stick free static margin
xcg
′
xNP
−
c
c
Desirable to have the stick fixed static margin within
5% of the mean-chord
Stick fixed or stick free static neutral points represent an aft limit
on the center of gravity travel for the airplane
15
Flsδ s − H eδ e = 0
F = He
Stick force
1
F = fn ( H e ) = GChe ρV 2 Se ce
2
(+)
F
δe
= H eG
ls δ s
G=
δe
δ s ls
Gearing ratio: measure of
the mechanical advantage
provided by the control
ls δ s
(-)
H e (+)
The work of displacing the control stick is equal to the work in
moving the control surface to the desired deflection angle
Trim Tab
16
Stick Force Gradients
z
Typical variation in control force as function of vehicle velocity
for stable configuration.
Stick
force
Stick
force
Negative
stick force
gradient
push
A
xcg
B
pull
For airplane speed stability:
dF
<0
dV
Stick Force Gradients
z
z
For a given static margin (or c.g. position) the
control force gradient decreases with
increasing flight velocity; and
At a given trim velocity, the gradient
decreases as the c.g. is moved toward the
control-free neutral point.
17
Aerodynamic and mass balance
18