VISION BASED SENSOR AND NAVIGATION SYSTEM FOR ...
Prediction of Icing Effects on the Coupled Dynamic Response of Light Airplanes Amanda Lampton Advisor: Dr. John Valasek Texas A&M University AIAA Atmospheric Flight Mechanics Conference and Exhibit Hilton Head, SC August 21, 2007 Lampton
1
Aerospace Engineering
Outline • Concerns Regarding Aircraft Ice Accretions • How This is Different from Previous Research h h
Rudimentary, first-cut analysis Based on limited data
• Develop Aircraft Model and Test Methodology h h
Validate and verify the model Several numerical examples 4 System identification type maneuver “fully iced” 4 Uneven ice distribution
• Conclusions and Recommendations
Lampton
2
Aerospace Engineering
Problem and Significance • Inclement weather h
Average of 19.6% of environment related reported general aviation (GA) accidents from 1998 to 2000
• Icing conditions h h h h h
2.9% in 1997 2.4% in 1998 3.6% in 1999 2.7% in 2000 44.55% of these resulted in fatalities Lampton
3
Aerospace Engineering
Type of Ice Accretions • Rime, glaze, and mixed ice • Dependent on: h h h h h h
Aircraft Configuration Airspeed Exposure time Atmospheric air temperature Liquid water content Median volumetric diameter
Lampton
4
Aerospace Engineering
Separation Bubble
Schematic of Upper Surface Separation Bubble Aft of Leading-Edge Ice Accretion
Lampton
5
Aerospace Engineering
Basic Effects of Ice Accretion on Aircraft • Possible separation bubble aft of ice ridge • Reduced longitudinal stability h
↓CL, ↑ CD, ↓CLα, ↓Cmα
• Reduced lateral/directional stability • Reduced aileron and rudder effectiveness • Possible hingemoment reversal
Lampton
6
Aerospace Engineering
Considerations • Prediction and Analysis h h h
Wind tunnel testing with icing Flight testing with icing Sophisticated numerical analysis codes
• Limitations h h h
All of these techniques are costly Require full scale vehicles or wind tunnel models Require detailed data Lampton
7
Aerospace Engineering
Previous Research • Bragg et. al, (1996-2004) h h h h h
Wing and airfoil Wind tunnel data Flight data Parametric models CFD code
C( A )
h
iced
A
Static effects on performance only
• Sharma et. al, (2004) h
= (1 + ηice kC )C( A ) '
Pitch angle hold autopilot Envelope protection
• Broeren et. al, (2003, 2004) h
Inter-cycle ice accretions
• Lee et. al, (1999, 2000) h
Simulated ice on airfoils
Lampton
8
Aerospace Engineering
Objectives of This Work • Develop a tool for studying and predicting icing effects on: h h h
• • • • •
Stability & control Performance Accident investigation
Use only relatively simple, easy to obtain data Inexpensive Leverage existing data/results as much as possible Extensible to similar configurations Accurate within limitations of data and results used
Lampton
9
Aerospace Engineering
Scope • Complete configuration • USAF Data Compendium (DATCOM) methods • Propulsion model h h
• • • • •
Altitude and power effects Table lookup
Linear time invariant (LTI) state-space model Simulated in MatLab 7.0 Longitudinal dynamics only Climb performance only Lateral/directional dynamics only
Lampton
10
Aerospace Engineering
Coupled Aircraft Model – Longitudinal u& = − g cos Θ1θ + ( X Tu + X u )u + X αα + X q q + X δ e δ e + X δT δ T + X α&α& w& = ( − g sin Θ1 cos Φ1θ − g cos Θ1 sin Φ1φ + Z u u + Zαα + Z q q + U1q + Zδ e δ e + ZδT δ T + Zα&α& ) / U1 U1 q& = ( M Tu + M u )u + ( M Tα + M α )α + M q q + M δ e δ e + M δT δ T + M α&α&
α& =
θ& = − q cos Φ1 − r sin Φ1
h
Steady, level, 1-g trimmed flight in the stability axis
h
P1 = Q1 = R1 = V1 = W1 = Φ1 = 0
Lampton
11
Aerospace Engineering
Coupled Aircraft Model – Lateral/Directional β& = (Yp p + gφ cos Θ1 cos Φ1 + gθ sin Θ1 sin Φ1 + Yβ β + (Yr − U 1 ) r + Yδ δ A + Yδ δ R ) / U 1 A
p& = Lβ β + LP p + Lr r + Lδ δ A + Lδ δ R + A
R
I xz I xx
r& = N β β + N P p + N r r + N δ δ A + N δ δ R + A
R
r& I xz I zz
p&
φ& = p + r cos Φ 1 tan Θ1 + q sin Φ 1 tan Θ1 ψ& = r cos Φ 1 sec Θ1 + q sin Φ 1 sec Θ1 h
Steady, level, 1-g trimmed flight in the stability axis
h
P1 = Q1 = R1 = V1 = W1 = Φ1 = 0
Lampton
12
Aerospace Engineering
R
System Modeling Method • State-space representation h
Linear time invariant system (LTI)
& 4 JX
= AX + BU Y = CX + DU
h
4
X = [u α
4
U = [δ e δ T
q θ
T
Φ (h ) = e
X k +1 = Φ X k + ΓU k
Ah
⎛h ⎞ Aτ ⎜ Γ = ∫ e dτ ⎟ B ⎜ ⎟ ⎝0 ⎠
Yk = CX k + DU k Lampton
T
δa δr ]
Discrete model 4
p r φ ψ]
β
13
Aerospace Engineering
Validation • Use available data for a Cessna 208B Super Cargomaster • Check stability and controllability • Simulation of discrete model • Check governing physics using a ramp input aileron deflection Lampton
14
Aerospace Engineering
Validation Analysis – Longitudinal Modal Composition
Modal Coordinates
λ1,2 = −1.49 ± 2.54 j
X = Mξ
ωsp = 2.94 rad/sec
ξ& = M −1 AMξ + M −1BU Y = CMξ + DU
ζ sp = 0.51 λ 3,4 = −0.013 ± 0.19 j ω p = 0.20 rad/sec
Short period mode primarily angle-of-attack, some pitch rate
ζ p = 0.065
Controllability C = [B
AB
AAB
AAAB ]
Phugoid mode pitch attitude angle, some angle-of-attack and pitch rate
rank (C) = 5 ; controllable
Lampton
15
Aerospace Engineering
Validation Analysis – Lateral/Directional
Modal Composition
Modal Coordinates
λ1,2 = −1.49 ± 2.54 j
X = Mξ
ωd = 1.76 rad/sec
ξ& = M −1 AMξ + M −1BU Y = CMξ + DU
ζ d = 0.21 λ3 = −4.84
τ r = 0.21sec
Dutch roll primarily yaw rate, some roll attitude angle
λ 4 = −0.016
τ s = 63.68sec
Roll mode sideslip angle, some roll rate
Controllability C = [B
AB
AAB
AAAB
AAAAB ]
Spiral mode Roll attitude angle, yaw rate
rank (C) = 5 ; controllable
Lampton
16
Aerospace Engineering
Verification • Ensure particular aircraft is correctly modeled • Compare simulation to flight test data • Simulation maneuver dictated by flight test data maneuver ensemble h h
Elevator doublet Aileron singlet 4Both show good matching
Lampton
17
Aerospace Engineering
Numerical Examples • Conducted ~80 simulations • 3 cases considered: h h
Parameter Identification – Fully Iced Uneven Asymmetric Icing 4Cruise 4Right wing half fully iced
h
Uneven Asymmetric Icing 4Climb 4Right wing half fully iced
Lampton
18
Aerospace Engineering
Icing Factors Applied derivative
-ΔCL0
-ΔCLα-ΔCD1
-ΔCLq
-ΔCLδe
ΔCm0
ΔCmα
ΔCmq
ΔCmδe
fice (%)
-20.0
-8.0
-10.0
-10.0
-10.0
-8.0
-20.0
-6.111
derivative
ΔCYβ
ΔCYδr
ΔClβ
ΔClp
ΔClδa
ΔClδr
ΔCnβ
ΔCnr
ΔCnδa
fice (%)
-20.0
-8.0
-10.0
-10.0
-10.0
-8.0
-20.0
-6.111
-8.330
*Based on data from the DeHavilland Twin Otter from AIAA 2000-0360
Mα
Lampton
=
qSc * (1 − 0.20 * f ice ) * Cm
α
I zz
iced
19
Aerospace Engineering
Fully Iced System Identification Style Maneuver Longitudinal Responses
Flight Condition: Altitude – 15000. ft Airpeed – 113 kts Dynamic Pressure – 30.6 lbs/ft2 (same for all responses)
Lampton
20
Aerospace Engineering
Fully Iced System Identification Style Maneuver Lateral/Directional Responses
Lampton
21
Aerospace Engineering
Asymmetric Icing Climb Performance Longitudinal Responses
Lampton
22
Aerospace Engineering
Asymmetric Icing Climb Performance Lateral/Directional Responses
Lampton
23
Aerospace Engineering
Conclusions •
Modeling and simulation methodology appears to be a promising tool for the scope of this research
•
Evenly distributed ice cause aircraft to become less stable h
•
Remains inherently stable
Uneven ice accretion resulted in ice induced moments apparent within 50 seconds h
Cruise case 4 300 count drag increase 4 Time-to-Double=20 sec
h
Climb case 4 400 count drag increase 4 Time-to-Double=20 sec
Lampton
24
Aerospace Engineering
Recommendations for Future Research • Simple, time dependent icing severity • Improve simulation fidelity h h
Continue aircraft model refinement Vortex lattice method code 4 Model horn and surface roughness 4 Extract stability derivative increments
h
Compile a more complete ensemble of test cases 4 Wide variety of altitudes 4 Compare to maneuvers already analyzed
h
Vary simulation ice accretion severity
Lampton
25
Aerospace Engineering
Questions?
Lampton
26
Aerospace Engineering
1
Aerospace Engineering
Outline • Concerns Regarding Aircraft Ice Accretions • How This is Different from Previous Research h h
Rudimentary, first-cut analysis Based on limited data
• Develop Aircraft Model and Test Methodology h h
Validate and verify the model Several numerical examples 4 System identification type maneuver “fully iced” 4 Uneven ice distribution
• Conclusions and Recommendations
Lampton
2
Aerospace Engineering
Problem and Significance • Inclement weather h
Average of 19.6% of environment related reported general aviation (GA) accidents from 1998 to 2000
• Icing conditions h h h h h
2.9% in 1997 2.4% in 1998 3.6% in 1999 2.7% in 2000 44.55% of these resulted in fatalities Lampton
3
Aerospace Engineering
Type of Ice Accretions • Rime, glaze, and mixed ice • Dependent on: h h h h h h
Aircraft Configuration Airspeed Exposure time Atmospheric air temperature Liquid water content Median volumetric diameter
Lampton
4
Aerospace Engineering
Separation Bubble
Schematic of Upper Surface Separation Bubble Aft of Leading-Edge Ice Accretion
Lampton
5
Aerospace Engineering
Basic Effects of Ice Accretion on Aircraft • Possible separation bubble aft of ice ridge • Reduced longitudinal stability h
↓CL, ↑ CD, ↓CLα, ↓Cmα
• Reduced lateral/directional stability • Reduced aileron and rudder effectiveness • Possible hingemoment reversal
Lampton
6
Aerospace Engineering
Considerations • Prediction and Analysis h h h
Wind tunnel testing with icing Flight testing with icing Sophisticated numerical analysis codes
• Limitations h h h
All of these techniques are costly Require full scale vehicles or wind tunnel models Require detailed data Lampton
7
Aerospace Engineering
Previous Research • Bragg et. al, (1996-2004) h h h h h
Wing and airfoil Wind tunnel data Flight data Parametric models CFD code
C( A )
h
iced
A
Static effects on performance only
• Sharma et. al, (2004) h
= (1 + ηice kC )C( A ) '
Pitch angle hold autopilot Envelope protection
• Broeren et. al, (2003, 2004) h
Inter-cycle ice accretions
• Lee et. al, (1999, 2000) h
Simulated ice on airfoils
Lampton
8
Aerospace Engineering
Objectives of This Work • Develop a tool for studying and predicting icing effects on: h h h
• • • • •
Stability & control Performance Accident investigation
Use only relatively simple, easy to obtain data Inexpensive Leverage existing data/results as much as possible Extensible to similar configurations Accurate within limitations of data and results used
Lampton
9
Aerospace Engineering
Scope • Complete configuration • USAF Data Compendium (DATCOM) methods • Propulsion model h h
• • • • •
Altitude and power effects Table lookup
Linear time invariant (LTI) state-space model Simulated in MatLab 7.0 Longitudinal dynamics only Climb performance only Lateral/directional dynamics only
Lampton
10
Aerospace Engineering
Coupled Aircraft Model – Longitudinal u& = − g cos Θ1θ + ( X Tu + X u )u + X αα + X q q + X δ e δ e + X δT δ T + X α&α& w& = ( − g sin Θ1 cos Φ1θ − g cos Θ1 sin Φ1φ + Z u u + Zαα + Z q q + U1q + Zδ e δ e + ZδT δ T + Zα&α& ) / U1 U1 q& = ( M Tu + M u )u + ( M Tα + M α )α + M q q + M δ e δ e + M δT δ T + M α&α&
α& =
θ& = − q cos Φ1 − r sin Φ1
h
Steady, level, 1-g trimmed flight in the stability axis
h
P1 = Q1 = R1 = V1 = W1 = Φ1 = 0
Lampton
11
Aerospace Engineering
Coupled Aircraft Model – Lateral/Directional β& = (Yp p + gφ cos Θ1 cos Φ1 + gθ sin Θ1 sin Φ1 + Yβ β + (Yr − U 1 ) r + Yδ δ A + Yδ δ R ) / U 1 A
p& = Lβ β + LP p + Lr r + Lδ δ A + Lδ δ R + A
R
I xz I xx
r& = N β β + N P p + N r r + N δ δ A + N δ δ R + A
R
r& I xz I zz
p&
φ& = p + r cos Φ 1 tan Θ1 + q sin Φ 1 tan Θ1 ψ& = r cos Φ 1 sec Θ1 + q sin Φ 1 sec Θ1 h
Steady, level, 1-g trimmed flight in the stability axis
h
P1 = Q1 = R1 = V1 = W1 = Φ1 = 0
Lampton
12
Aerospace Engineering
R
System Modeling Method • State-space representation h
Linear time invariant system (LTI)
& 4 JX
= AX + BU Y = CX + DU
h
4
X = [u α
4
U = [δ e δ T
q θ
T
Φ (h ) = e
X k +1 = Φ X k + ΓU k
Ah
⎛h ⎞ Aτ ⎜ Γ = ∫ e dτ ⎟ B ⎜ ⎟ ⎝0 ⎠
Yk = CX k + DU k Lampton
T
δa δr ]
Discrete model 4
p r φ ψ]
β
13
Aerospace Engineering
Validation • Use available data for a Cessna 208B Super Cargomaster • Check stability and controllability • Simulation of discrete model • Check governing physics using a ramp input aileron deflection Lampton
14
Aerospace Engineering
Validation Analysis – Longitudinal Modal Composition
Modal Coordinates
λ1,2 = −1.49 ± 2.54 j
X = Mξ
ωsp = 2.94 rad/sec
ξ& = M −1 AMξ + M −1BU Y = CMξ + DU
ζ sp = 0.51 λ 3,4 = −0.013 ± 0.19 j ω p = 0.20 rad/sec
Short period mode primarily angle-of-attack, some pitch rate
ζ p = 0.065
Controllability C = [B
AB
AAB
AAAB ]
Phugoid mode pitch attitude angle, some angle-of-attack and pitch rate
rank (C) = 5 ; controllable
Lampton
15
Aerospace Engineering
Validation Analysis – Lateral/Directional
Modal Composition
Modal Coordinates
λ1,2 = −1.49 ± 2.54 j
X = Mξ
ωd = 1.76 rad/sec
ξ& = M −1 AMξ + M −1BU Y = CMξ + DU
ζ d = 0.21 λ3 = −4.84
τ r = 0.21sec
Dutch roll primarily yaw rate, some roll attitude angle
λ 4 = −0.016
τ s = 63.68sec
Roll mode sideslip angle, some roll rate
Controllability C = [B
AB
AAB
AAAB
AAAAB ]
Spiral mode Roll attitude angle, yaw rate
rank (C) = 5 ; controllable
Lampton
16
Aerospace Engineering
Verification • Ensure particular aircraft is correctly modeled • Compare simulation to flight test data • Simulation maneuver dictated by flight test data maneuver ensemble h h
Elevator doublet Aileron singlet 4Both show good matching
Lampton
17
Aerospace Engineering
Numerical Examples • Conducted ~80 simulations • 3 cases considered: h h
Parameter Identification – Fully Iced Uneven Asymmetric Icing 4Cruise 4Right wing half fully iced
h
Uneven Asymmetric Icing 4Climb 4Right wing half fully iced
Lampton
18
Aerospace Engineering
Icing Factors Applied derivative
-ΔCL0
-ΔCLα-ΔCD1
-ΔCLq
-ΔCLδe
ΔCm0
ΔCmα
ΔCmq
ΔCmδe
fice (%)
-20.0
-8.0
-10.0
-10.0
-10.0
-8.0
-20.0
-6.111
derivative
ΔCYβ
ΔCYδr
ΔClβ
ΔClp
ΔClδa
ΔClδr
ΔCnβ
ΔCnr
ΔCnδa
fice (%)
-20.0
-8.0
-10.0
-10.0
-10.0
-8.0
-20.0
-6.111
-8.330
*Based on data from the DeHavilland Twin Otter from AIAA 2000-0360
Mα
Lampton
=
qSc * (1 − 0.20 * f ice ) * Cm
α
I zz
iced
19
Aerospace Engineering
Fully Iced System Identification Style Maneuver Longitudinal Responses
Flight Condition: Altitude – 15000. ft Airpeed – 113 kts Dynamic Pressure – 30.6 lbs/ft2 (same for all responses)
Lampton
20
Aerospace Engineering
Fully Iced System Identification Style Maneuver Lateral/Directional Responses
Lampton
21
Aerospace Engineering
Asymmetric Icing Climb Performance Longitudinal Responses
Lampton
22
Aerospace Engineering
Asymmetric Icing Climb Performance Lateral/Directional Responses
Lampton
23
Aerospace Engineering
Conclusions •
Modeling and simulation methodology appears to be a promising tool for the scope of this research
•
Evenly distributed ice cause aircraft to become less stable h
•
Remains inherently stable
Uneven ice accretion resulted in ice induced moments apparent within 50 seconds h
Cruise case 4 300 count drag increase 4 Time-to-Double=20 sec
h
Climb case 4 400 count drag increase 4 Time-to-Double=20 sec
Lampton
24
Aerospace Engineering
Recommendations for Future Research • Simple, time dependent icing severity • Improve simulation fidelity h h
Continue aircraft model refinement Vortex lattice method code 4 Model horn and surface roughness 4 Extract stability derivative increments
h
Compile a more complete ensemble of test cases 4 Wide variety of altitudes 4 Compare to maneuvers already analyzed
h
Vary simulation ice accretion severity
Lampton
25
Aerospace Engineering
Questions?
Lampton
26
Aerospace Engineering
