Lateral-Directional Flying Qualities Criteria!

Robert Stengel, Aircraft Flight Dynamics!MAE 331, 2016

Copyright 2016 by Robert Stengel. All rights reserved. For educational use only.http://www.princeton.edu/~stengel/MAE331.html

http://www.princeton.edu/~stengel/FlightDynamics.html

•! Lateral Control Divergence Parameter (LCDP)

•! !"/!d and "/#•! Eigenvectors•! Pilot-Vehicle Interactions•! Pilot-Induced Oscillations•! Optimal Control Pilot Model

Learning Objectives

1

Design for Satisfactory Flying Qualities•! Satisfy procurement requirement (e.g., Mil

Standard)•! Satisfy test pilots (e.g., Cooper-Harper ratings)•! Avoid pilot-induced oscillations (PIO)•! Minimize time-delay effects•! Time- and frequency-domain criteria

2

Lateral-Directional Criteria!

3

Early Lateral-Directional Flying Qualities Criteria

O Hara, via Etkin4

!"

! d

#$%

&'(

2

! d

!" ! d : Numerator frequency to Dutch roll Natural Frequency

in #" s( ) #$A s( ) transfer function (more later)% d : Dutch roll damping frequency

Early Lateral-Directional Flying Qualities Criteria

Ashkenas, via Etkin5

1T1 2

T1 2 = 0.693 /! d" nd: Time to one-half amplitude, Dutch roll oscillation

# v =VN # $ : Ratio of roll to sideslip angle in Dutch roll oscillation

! v , deg/(ft/s)

Lateral-Directional Flying Qualities Parameters

•!Lateral Control Divergence Parameter, LCDP•!!!""//!! Effect•! ""//## Effect

6

Lateral Control Divergence Parameter (LCDP)

•!Aileron deflection produces yawing as well as rolling moment–! Favorable yaw aids the turn command–! Adverse yaw opposes it

•!Equilibrium response to constant aileron input

!"!#A

=N$ + Nr

Y$VN

%&'

()* L#A + L$ + Lr

Y$VN

%&'

()* N#A

gVN

L$Nr + LrN$( )•!Large-enough N$$A effect can reverse the sign of the response–! Can occur at high angle of attack –! Can cause departure from controlled flight” 7

Lateral Control Divergence Parameter (LCDP)

•!Large-enough N$$A effect can reverse the sign of the response–! Can occur at high angle of attack –! Can cause departure from controlled flight

•!Lateral Control Divergence Parameter provides simplified criterion

LCDP ! Cn"#Cn$A

Cl$A

Cl"

N!( )L"A # L!( )N"A

L"A

= N! #N"A

L"A

L!

8

!!""/!!d Effect

Aileron-to-roll-angle transfer function

!"(s)!#A(s)

=k" s2 +2$"%"s+%"

2( )s&'S( ) s&'R( ) s2 +2$DR%nDR

s+%nDR2( )

!! !!"" is the natural frequency of the complex zeros!! !!d = !!nDR is the natural frequency of the Dutch roll mode

•!Conditional instability may occur with closed-loop control of roll angle, even with a perfect pilot

9

!!""//!! Effect is Important in Roll Angle Control

•!As feedback gain increases, Dutch roll roots go to numerator zeros •! Zeros over poles: conditional instability results•!Poles over zeros: no instability

!"(s)!#A(s)

=k" s2 +2$"%"s+%"

2( )s&'S( ) s&'R( ) s2 +2$DR%nDR

s+%nDR2( )

10

""//## Effect

•!""//## measures the degree of rolling response in the Dutch roll mode–! Large ""//##: Dutch roll is primarily a rolling motion–! Small ""//##: Dutch roll is primarily a yawing motion

•!Eigenvectors, ei, indicate the degree of participation of the state component in the ith mode of motion

det sI! F( ) = s ! "1( ) s ! "2( )... s ! "n( )"iI! F( )ei = 0

11

EigenvectorsEigenvectors, ei, are solutions to the equation

!iI" F( )ei = 0, i = 1,nor

!iei = Fei , i = 1,n

For each eigenvalue, the corresponding eigenvector can be found (within an arbitrary constant) from

Adj !iI" F( ) = a1ei a2ei … anei( ), i = 1,n

MATLABV,D( ) = eig F( )

V: Modal Matrix (i.e., Matrix of Normalized Eigenvectors)D: Diagonal Matrix of Corresponding Eigenvalues 12

""//## EffectWith %%i chosen as a complex root of the Dutch

roll mode, the corresponding eigenvector is

eDR+ =

ere!epe"

#

$

%%%%%

&

'

(((((DR+

=

) + j*( )r) + j*( )!) + j*( )p) + j*( )"

#

$

%%%%%%

&

'

((((((DR+

=

AR ej"( )rAR e j"( )!AR ej"( )pAR e j"( )"

#

$

%%%%%%%

&

'

(((((((DR+

""//## is the magnitude of the ratio of the "" and ## eigenvectors

!" =

AR( )!AR( )"

= VNg

#$%

&'(

) DR* nDR+Y"

VN+L"

Lr

#$%

&'(

2

+ * nDR1+) DR

2( ),

-..

/

011

12

13

""//## Effect for the Business Jet Example

eDR+ =

ere!

ep

e"

#

$

%%%%%%%

&

'

(((((((DR+

=

0.5250.4160.6030.433

#

$

%%%%

&

'

((((DR+

!" = 1.04

Roll/Sideslip Angle ratio in the Dutch roll mode

14

Criteria for Lateral-Directional Modes (MIL-F-8785C)

Maximum Roll-Mode Time Constant

15

Criteria for Lateral-Directional Modes (MIL-F-8785C)

Minimum Spiral-Mode Time to Double

16

Minimum Dutch Roll Natural Frequency and Damping (MIL-F-8785C)

17

Pilot-Vehicle Interactions!

18

YF-16 Test Flight Zero•! High-speed taxi test; no flight intended•! Pilot-induced oscillations from overly

sensitive roll control•! Pilot elected to go around rather than eject

19

Pilot-Induced Roll Oscillation

!"(s)!#A(s) pilot in loop

=Kp /Tp

s +1 /Tp

$

%&

'

()

k" s2 + 2*"+"s ++"2( )

s , -S( ) s , -R( ) s2 + 2*DR+nDRs ++nDR

2( ).

/00

1

233

Aileron-to-Roll Angle Root Locus Pilot-Aircraft Nichols Chart

Pilot Transfer Function Aircraft Transfer FunctionYF-16

20

Optimal Control Pilot Model

21

Aircraft Model

Pilot Model

DelayState EstimationControl

NeuromuscularLag

Disturbances

ObservationError

Observation

PilotInput

Display

Kleinman, Baron, Levison, 1970

Inverse Problem of

Lateral Control•! Given a flight path, what

is the control history that generates it?

–! Adapted Optimal Control Pilot Model generates necessary piloting actions

•! Aileron-rudder interconnect (ARI) simplifies pilot input

Grumman F-14 Tomcat

Yaw Angle DesiredRoll Angle

Lateral-Stick Command

Angle of attack (&&) = 10 deg; ARI off

&& = 30 deg; ARI off

&& = 30 deg; ARI on

Stengel, Broussard, 1978 22

Next Time:!Maneuvering at High Angle and

Angular Rate!

23

Learning ObjectivesHigh angle of attack and angular rates

Asymmetric flightNonlinear aerodynamics

Inertial couplingSpins and tumbling

Supplemental Material

24

Criteria for Oscillations and Excursions (MIL-F-8785C)

25

Criteria for Oscillations and Excursions (MIL-F-8785C)

26