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8/2/2019 Lecture 8 Longitudinal Stability
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Lecture 8 Longitudinal stability
Dr Jian Wang
08/03/2010
8/2/2019 Lecture 8 Longitudinal Stability
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Aims To understand the concepts of stability
To know the basic requirements for longitudinaland Lateral Stability
To learn procedures for Longitudinal Stabilityanalysis
To learn procedures for Lateral Stability analysis
To take the students through the exercises ofStability and Control
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What is stability:
Natural stable: The bodyalways stays in equilibrium
Statically stable: If the forces & themoments on the body cause by thedisturbance tend initially to return the bodytowards its equilibrium position
Statically unstable: If the forces& the moments are such that the body
continues to move away from itsequilibrium position after being disturbed
Is this dynamicstable?
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What is stability:--dynamic stability
Dynamic Stability: deals with the time history of the bodys motion afterit initially responds to its static stability
Dynamic Stable Behaviour Dynamic Unstable Behaviour
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What is stability:--Aircraft Motion
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Stability and Control:--What have be done before?
Historical data were used: Volume coefficients: Chapter 8.10.3
Those data come from the statistical data for different types of aircraft
There are no aerodynamics being considered
Stability and Control:--What will we do?
Forces and moments balance: equilibrium Considering of aerodynamic equations
Equilibrium
Characteristics of controlling surfaces
8/2/2019 Lecture 8 Longitudinal Stability
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h0
h
hG
lT
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Stability and Control: A classical airplane has three basic controls: ailerons, elevator,and rudder (tailplane and fin)
Longitudinal Stability
The size, shape & location of the tailplane necessary to provide aspecific degree of longitudinal stability
The range of elevator deflection necessary to control the aircraft
Lateral Stability
The size, shape & location of the fin necessary to provide a specificdegree of directional stability
The size of the ruder & the range of its deflection necessary to controlthe aircraft throughout its speed envelope
The wing dihedral angle
The size & location of the ailerons
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Longitudinal Stability and Control:
Tailplane sizing
i. Evaluate the cruise trim condition
ii. Evaluate the range of elevator angles required forthe chosen value of
iii. Calculate the minimum value of required at eachvalue of h
iv. Rotation in the takeoff
v. Estimate the damping for the short period oscillation
vi. Select that lowest value of consistent with theconditions in parts (iii), (iv) and (v)
T
S
ST
S
ST
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i. Evaluate the cruise trim condition
CMG: pitch moment for C.G.
CM0: pitch moment for aerodynamiccentre (zero lift)
CL: Lift coefficient
h: Position of C.G.
h0: Position of aerodynamic centre zT: Distance that the thrust line lies
belowthe C.G.
Equation we use:
21
11 aa
d
d
a
aCV
c
zChhCCC
TLT
T
ToLMM OG
a: wing and body lift curve slop
a1: tailplane lift curve slope d/d: change of down wash
T: the tailplane setting angle
: elevator deflect angle
: M.A.Cc
qSTCT
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i. Evaluate the cruise trim condition
During cruise, L=W, T=D. Moment aboutC.G. = 0.
Zero elevator angle
d
d
a
C
Fc
l
S
Sa
czChhCC
L
TT
TToLM
T
O
1
1
1
1
d
d
a
a
S
SFFG
factorcorrectaisFF
T11
:1
1
1
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ii.Evaluate the range of elevator angles
required for the chosen value of
Equation we use:
T
T
L
TT
TToLM
d
d
a
C
a
a
Fc
l
S
Sa
c
zChhCC
O
1
1
12
1
2
Use the same range of and CG position, h, employed in part (i)
The landing configuration (flaps down), more negative, higher
Compare the maximum elevator angle required with the maximum
movement available, 67% is the limit.
SST
OM
CL
C
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iii.Calculate the minimum value of
required at each value of h
Equation we use:
is the static margin
S
ST
d
d
a
a
Fc
l
S
Shh
d
d
a
aVhhK TToToN 1
1
11 11
NK
d
d
a
a
Fc
l
hhK
S
S
T
oNT
11
11
Minimum Static Stability: h = minimum
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iv.Rotation in the takeoff
Limited by forward C.G.
Use
the minimum value of h
the previously selected value of ,
the maximum (negative) value of elevator angle
Calculate the required tailplane area
T
21
12
1 aad
d
a
aCV
c
zChh
qS
MghhCC
cS
MkTLT
GTGOGLM
B
O
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iv. Rotation in the takeoffMIk yB the pitch radius of gyration of the aircraft
a specified pitch acceleration
the non-dimensionalised longitudinal position of the aftwheels (analogous to h)
Gz the vertical distance of the aft wheels belowthe engine thrust
line
Gh
211
2
1 aad
d
a
aC
cS
Mk
c
zChh
qS
MghhCC
V
TL
BGTGOGLM
T
O
c
laa
d
d
a
aC
cS
Mk
c
zChh
qS
MghhCC
S
S
TTL
BGTGOGLM
T
O
211
2
1
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v.Estimate the damping for the short
period oscillation
Equation used
cS
MaKa
c
lVCa
k
c
ac
lV
d
d
k
cCa
nTTD
B
TT
B
D
2
2
1
1
1
2
Calculate for the sae range of and CG position, h,
employed in part (i)
Carpet plot the results Ideally great than about 0.5
SST
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vi.Select that lowest value of
consistent with the conditions in
parts (iii), (iv) and (v)
In Figures 9.1 to 9.3, a value of 0.25satisfies all the conditions (except for thecondition on SPO damping, is lessthan 0.5)
S
ST
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-6
-5
-4
-3
-2
-1
Tailplanesettinga
ngletotrim(
degrees)
ST/S
0.10
0.40
0.28
0.16
0.300.25
0.20
0.15
h
Chosen T
Chosen ST/S
Take-off
rotation
Static stability
in cruise
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-20
-18
-16
-14
-12
-10
-8
-6
-4
-2
0
Elevatorangletotr
im(
degrees)
ST/S
0.10
0.40
0.28
0.16
0.300.25
0.15
h
Limit on
Chosen ST/S
Take-off
rotation
T = -3.65 degrees
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0.2
0.3
0.4
0.5
SPOda
mpingratio
ST/S
0.10
0.40
0.28
0.16
0.30
0.25
0.20
0.15
h
Chosen ST/S
= 0.3