Aircraft Control Sizing - Virginia Techmason/Mason_f/SD1Cotting_control.pdf · in the world, an airplane can fly ... Dynamics of Flight, Stability and Control. John ... Aircraft Dynamics

M. Christopher CottingDepartment of Aerospace and Ocean Engineering, VPISU

February 17, 2009

Senior Design Class

Aircraft Control Sizing

AOE Aircraft Design 02/17/09 Cotting 2

“If you are in trouble anywhere in the world, an airplane can fly over and drop flowers, but a helicopter can land and save your life.”

— Igor Sikorsky, 1947


AOE Aircraft Design 02/17/09 Cotting

Outline

Examples of Aircraft Control Surfaces

Balance (Trim and Equilibrium)

Stability (Static vs Dynamic Stability)

Maneuverability

4


Control Effectors

Effect change on an aircraft state, primarily through a moment imparted on an aircraft

May be part of a high lift system (in which case they may also change lift, which is a force...) or a throttle, which changes a force

In controls speak, a desired moment/force is commanded to an aircraft, it is then allocated according to the “B” matrix, and then effectors are commanded to impart that moment/force.

5


Why Aero Controls Engineers are Needed

6

http://www.wpafb.af.mil/shared/media/photodb/photos/070226-F-8560B-001.JPG

Northrop Grumman STAV




Why control effectors are bad

Create drag Add weight Reduce stealth Change the OML... Increase ground testing Can decrease reliability (increase risk) Add complexity

7


“I know it’s unstable, but it won’t trim!!!!!”

The aircraft must be balanced “Trimmed”

Each dynamic mode of aircraft motion must be:• stabalizable (stability) • controllable (maneuverability)

How many independent control effectors must we have?

8


F-18 HARV

9


F-15 ACTIVE

10


Boeing 767

11

J. Roskam. Airplane Design, volume IV. Roskam Aviation and Engineering Corperation, Ottowa, Kansas, 1986.


C-17

12


F-22

13


X-33

14

Body Flaps

Elevons or“Ruddervators”

Rudders

Thrust Vectoring (TVC)

Reaction Control (RCS)

TVC: Ascent roll and pitch (some yaw)Body Flaps : yaw controlElevons: Pitch / rollRudders: ???

RCS: pitch, roll, and yaw (limited on entry only)


X-35

15

X-35B Flight Control Elements

3BSD Doors

LiftFan

Nozzle

Roll Nozzle!

Aux Inlet “Rabbit Ear” Doors

& Louver Mechanism

LiftFan Inlet

& Doors!

Flaperons

3BSD

Twin Rudders

Horizontal

Tails

Leading Edge

Flaps!

Air Data

Probes!

Rate Gyros &

Accelerometers

Pilot

Inceptors!

Speed Brakes!


Equilibrium

16

B. Etkin. Dynamics of Flight, Stability and Control. John Wiley and Sons, New York, NY, second edition, 1982.


Aircraft Trim

“Fat, dumb and happy...”

All the “state dots” or rate of change of the states is zero.

What are the aircraft states?

What are some “trimmed” flight conditions?

17


Aircraft Nomenclature

18

McRuer, Ashkenas, and Graham. Aircraft Dynamics and Automatic Control.Princeton University Press, 1973. p 208


Wind Angles

19

R. C. Nelson. Flight Stability and Automatic Control. McGraw Hill, 2nd edition, 1998. p.21

V =!u2 + v2 + w2

"0.5

! = tan!1!w

u

"! w

u

! = sin!1! v

V

"! v

u

V =uu + vv + ww

V

! =uw ! wu

u2 + w2

" =vV ! vV

V 2 cos "


Aircraft Wing Only

20

ac cg

Mac

V

!

L(a - h)

x ac

Wx cg


Aircraft with Horizontal Stabilizer

21

ac cg

Mac

V

!

L(a - h)

x ac

Wx cg

np

x n

Lh

x h

l h


Static Stability

22

!

Cm

Complete AircraftAircraft w

ithout Tail

Stick Fixed

tail

contr

ibution

A

Trim is point A, where Cm = 0


Neutral Point

Definition:

“The stick-fixed neutral point is the position of the center of gravity for which Cmα =0”

For static stability, the cg must be ahead of the neutral point (this defines “static margin”, or the margin of static stability).

23

E. Torenbeek. Synthesis of Subsonic Airplane Design. Delft University Press, Netherlands, 1981.


Static Margin

24

Typically you want a static margin of at least 5%, and this aids in finding the aft CG limit

Note: This should be used as a guide, but is not accepted as a “criterion”


X - plot

25

Horizontal Tail Area (S h in ft^2)

Fusela

ge S

tation (

ft)

X ac

X cg

Static Margin

Desired Tail Area


Maneuver Stability

Typically for unaugmented aircraft only

26

If I pull back on the control stick, I expect the nose to come up (or load factor to increase)


Stick Fixed Maneuver Point

27

“ The position of the cg when the stick displacement per g is zero.”



Static Lateral Stability

28


Dihedral Effect

29

L +

V

Positive Sideslip


Wing Sweep “Dihedral” Effects

30

Positive Sideslip

Lv < 0

VV


Directional (Weathercock) Stability

31

Vβ

+ N


Longitudinal Design Goals Trim Control power over range of flight

envelope and weight conditions

Static Margin that gives good short period natural frequencies

Short period damping ratio

Phugoid natural frequency and damping ratio

32

T. Takahashi. Some strategies teaching configuration aerodynamics in aeronautical engineering capstone design. In 47th Annual AIAA Aerospace Sciences Meeting and Exhibit, number AIAA2009-1602, Orlando, Fl, January 5 - 8 2009.


Longitudinal

1. Build a plot of Control Power Required For Pitch Trim, as function of altitude, weight and airspeed (must be <100% for feasibility, should be <<50% for typical flight conditions). Adjust the configuration to ensure feasibility.

2. Build a plot of Short Period Frequency as function of altitude, weight and airspeed in context with the gee’s per radian (attitude), per MIL 8785C chart. Adjust configuration so that the indicators are reasonable for the intended mission.

33



Longitudinal Dynamics

34

D. McRuer, I. Ashkenas, and D. Graham. Aircraft Dynamics and Automatic Control. Princeton University Press, Princeton, New Jersey, 1973.


Time to Half / Double

35

C. A. Woolsey, Review of Linear, Time-Invariant Ordinary Differential Equations, accessed 02/17/09,http://www.aoe.vt.edu/~cwoolsey/Courses/AOE3134/Supplemental/LTIODEs.pdf

http://www.aoe.vt.edu/~cwoolsey/Courses/AOE3134/Supplemental/LTIODEs.pdf

http://www.aoe.vt.edu/~cwoolsey/Courses/AOE3134/Supplemental/LTIODEs.pdf


8785C Aircraft Classes

Class I• Small, lightweight aircraft.• Trainers and G/A aircraft

Class II • Medium weight aircraft• Commuter aircraft, heavy attack, reconnaissance

Class III• Heavy weight aircraft• Large commercial aircraft, bomber

Class IV• High maneuverability aircraft• Fighters / iterceptors

36


8785C Flight Categories

Category A• Those nonterminal Flight Phases that require rapid

maneuvering, precision tracking, or precise flight-path control. (Air-to-air combat (CO) )

Category B• Those nonterminal Flight Phases that are normally

accomplished using gradual maneuvers and without precision tracking, although accurate flight-path control may be required. (Climb (CL), Cruise (CR), Loiter (LO) )

Category C• Terminal Flight Phases are normally accomplished using

gradual maneuvers and usually require accurate flight-path control. (Takeoff (TO), Approach (PA),Landing (L) )

37


PIO

38


PIO

39


Aircraft Model

40

Using Stevens and Lewis F-16 model B. Stevens and F. Lewis. Aircraft Control and Simulation. John Wiley and Sons, 1992.

Altitude (h) 10,000 ft

Airspeed (Vt) 360 KEAS 709 ft/sec, (0.65 mach)

α,θ 1 degree

p,q,r 0

γ, φ,β,ψ 0

Flight Condition


F-16 HQ

41

Using Stevens and Lewis F-16 model B. Stevens and F. Lewis. Aircraft Control and Simulation. John Wiley and Sons, 1992.

Case Natural Frequency ωn

Damping Ratio ζ

1 4.63 rad/sec 0.704

2 2.47 rad/sec 0.448

3 4.0 rad/sec 0.2

4 unstable unstable

Short Period Characteristics

Stick Cmds

delevc

Gain1

K2

Gain

K1

F!16 Mdl

x’ = Ax+Bu y = Cx+Du

q

alpha


8785C SP ωn criterion

42

100 101 10210−1

100

101

102

ωn SP

− ra

d/se

c

n/α − g/rad

Category A Short Period Requirements, Natural Frequency

Level 1

Level 2/3

Level 2

Level 3

Level 3

1

23

n

!=

"L

"!

1W

“load factorper radian”


MIL-HDBK-1797 SP ζ criterion.

43

10−1 10010−2

10−1

100

101

ζSP

CAP

= ω

2 n SP /

(n/α

) − g

*rad

Category A Short Period Requirements, Damping Ratio

Level 1

Level 2

Level 3

1

2

3


Case 1

44


Case 2

45


Case 3

46


8785C SP ωn criterion

47

MIL-F-8785C

15

100

10

1.0

0.1

1.0 10 100

NOTE: THE BOUNDARIES FOR VALUES OF

OUTSIDE THE RANGE SHOWN ARE DEFINED

BY STRAIGHT-LINE EXTENSIONS

10.0

3.6

0.085

0.038

n/!

"nSP

~

RAD/SEC

n/! ~ g's/RAD

LEVEL 1

LEVEL 2

LEVELS 2 & 3

LEVEL 1

"nSP2

n/!

FIGURE 2. Short-period frequency requirements - Category B Flight Phases.

MIL-F-8785C

16

100

10

1.0

0.1

1.0 10 100

NOTE: THE BOUNDARIES FOR VALUES OF GREATER

THAN 100 ARE DEFINED BY STRAIGHT-LINE EXTENSIONS.

THE LEVEL 3 BOUNDARY FOR LESS THAN 1.0 IS

ALSO DEFINED BY A STRAIGHT-LINE EXTENSION

10.0

3.6

0.16

0.096

n/!

"nSP

~

RAD/SEC

n/! ~ g's/RAD

LEVEL 1

LEVEL 2

LEVELS 2 & 3LEVEL 1

"nSP2

n/!

n/!

NOTE: FOR CLASS I, II-C, AND IV AIRPLANES,

SHALL ALWAYS BE GREATER THAN 0.6

RADIANS PER SECOND FOR LEVEL 3

n/!

LE

VE

L 2

, C

LA

SS

ES

II-

L,I

II

LE

VE

L 2

, C

LA

SS

ES

I,

II-C

,IV

CL

AS

SE

S I

I-L

,III

CL

AS

SE

S I

,

II-C

, IV

FIGURE 3. Short-period frequency requirements - Category C Flight Phases.


MIL-HDBK-1797 CAP

48

MIL

–S

TD

–1

79

7A

AP

PE

ND

IX A

174


takeoff rotation

49



Control in a Stall

50


Configuration

-0.18 split flap, plain flap

-0.26 single slotted flap

-0.385 double slotted flap

-0.415 single slotted fowler flap

-0.445 double slotted fowler flap

-0.475 trip slotted fowler flap


Phugoid Damping 8785C

52

The long-period oscillations which occur when the airplane seeks a stabilized airspeed following a disturbance shall meet the following requirements: a. Level 1 ----- ζp at least 0.04 b. Level 2 ----- ζp at least 0 c. Level 3 ----- T2 at least 55 seconds


Lateral/Directional Goals

Trim roll and yaw over flight envelope for required cross winds

Lateral/Directional cross coupling: adverse yaw of ailerons should not overpower directional stability

Favorable dutch roll frequencies and damping over flight envelope and weights

53


Lateral - Directional 1. Evaluate ability for Directional Trim as a function of altitude, weight and airspeed (what is the maximum sideslip angle than can be trimmed with 100% control power?). Adjust configuration so that this is reasonable for the intended mission.

2. Plot Dutch Roll Frequency as a function of altitude, weight and airspeed. Verify positive Dutch Roll stability; adjust configuration so that the frequencies are reasonable for the intended mission.

3. Evaluate Dutch Roll Stability Parameter (Cnβdynamic) as a function of turn coordination stability (LCDP) , per Bihrle-Weissman chart7(see Figure 8). Verify that the configuration is not departure prone for maneuvering flight. Adjust configuration to ensure spin departure resistance.

54



Lateral-Directional Dynamics

55


W. H. Mason High Angle-of-Attack Aerodynamics 9-9

3/10/06

-0.015

-0.010

-0.005

0.000

0.005

0.010

-0.015 -0.010 -0.005 0.000 0.005 0.010 0.015

Integrated Bihrle-Weissman Chart

LCDP

Cn! dyn

AU

F

D BE

C

D

With following key: A - Highly departure and spin resistantB - Spin resistant, objectionable roll reversals can induce departure and

post stall gyrationsC - Weak spin tendency, strong roll reversal results in control induced

departureD - Strong departure, roll reversals and spin tendenciesE - Weak spin tendency, moderate departure and roll reversals, affected

by secondary factorsF - Weak departure and spin resistance, no roll reversals, heavily

influenced by secondary factorsU - High directional instability, little data

Figure 9-9. The Bihrle-Weissman chart (Ref. 15)

Bihrle, William, Jr., and Billy Barnhart, “Design Charts and Boundaries for Identifying Departure Resistant Fighter Configurations,” NADC-76154-30, July 1978.

A - Highly departure and spin resistant B - Spin resistant, objectionable roll reversals can

induce departure and post stall gyrations C - Weak spin tendency, strong roll reversal results

in control induced departure D - Strong departure, roll reversals and spin

tendencies E - Weak spin tendency, moderate departure and

roll reversals, affected by secondary factors F - Weak departure and spin resistance, no roll

reversals, heavily influenced by secondary factors

U - High directional instability, little data

Mason, W.H. High Angle of Attack Aerodynamics, downloaded 2006. see: http://www.aoe.vt.edu/~mason/Mason_f/ConfigAeroHiAlphaNotes.pdf


8785C Dutch Roll

57

MIL-F-8785C

3.3 Lateral-directional flying qualities

3.3.1 Lateral-directional mode characteristics

3.3.1.1 Lateral-directional oscillations (Dutch roll). The frequency, !nd

, and damping ratio, "d, of

the lateral-directional oscillations following a yaw disturbance input shall exceed the minimumvalues in table VI. The requirements shall be met in trimmed and in maneuvering flight withcockpit controls fixed and with them free, in oscillations of any magnitude that might beexperienced in operational use. If the oscillation is nonlinear with amplitude, the requirementshall apply to each cycle of the oscillation. In calm air residual oscillations may be tolerated onlyif the amplitude is sufficiently small that the motions are not objectionable and do not impairmission performance. For Category A Flight Phases, angular deviations shall be less than ±3mils.

TABLE VI. Minimum Dutch roll frequency and damping.

Flight Phase Min "d!

nd* Min !

nd

LevelCategory Class Min "

d* rad/sec. rad/sec.

A (CO and GA) IV 0.4 - 1.0

A I, IV 0.19 0.35 1.0

II, III 0.19 0.35 0.4**

1 B All 0.08 0.15 0.4**

C I, II-C,IV 0.08 0.15 1.0

II-L, III 0.08 0.10 0.4**

2 All All 0.02 0.05 0.4**

3 All All 0 0 0.4**

* The governing damping requirement is that yielding the larger value of "d, except that "

dof 0.7 is the maximum required for Class III.

** Class III airplanes may be excepted from the minimum !nd

requirement, subject to

approval by the procuring activity, if the requirements of 3.3.2 through 3.3.2.4.1, 3.3.5and 3.3.9.4 are met.

When !nd2 #/$

d is greater than 20 (rad/sec)2, the minimum "

d!

nd shall be increased

above the "d!

nd minimums listed above by:

Level 1 - %"d!

nd = .014 !

nd2 #/$

d - 20

Level 2 - %"d!

nd = .009 !

nd2 #/$

d - 20

Level 3 - %"d!

nd = .004 !

nd2 #/$

d - 20

with !nd

in rad/sec.

22


8785C Maximum Roll Mode Time Constants

58

MIL-F-8785C

3.3.1.2 Roll mode. The roll-mode time constant, !R, shall be no greater than the appropriatevalue in table VII.

TABLE VII. Maximum roll-mode time constant, seconds.

FlightPhase

CategoryClass Level

1 2 3

A I, IV 1.0 1.4

II,III 1.4 3.0

B All 1.4 3.0 10

C I. II-C, IV 1.0 1.4

II-L, III 1.4 3.0

3.3.1.3 Spiral stability. The combined effects of spiral stability, flight-control-systemcharacteristics and rolling moment change with speed shall be such that following a disturbancein bank of up to 20 degrees, the time for the bank angle to double shall be greater than the valuesin table VIII. This requirement shall be met with the airplane trimmed for wings-level, zero-yaw-rate flight with the cockpit controls free.

TABLE VIII. Spiral stability - minimum time to double amplitude.

Flight PhaseCategory Level 1 Level 2 Level 3

A & C 12 sec 8 sec 4 sec

B 20 sec 8 sec 4 sec

3.3.1.4 Coupled roll-spiral oscillation. For Flight Phases which involve more than gentlemaneuvering, such as CO and GA, the airplane characteristics shall not exhibit a coupled roll-spiral mode in response to the pilot roll control commands. A coupled roll-spiral mode will bepermitted for Category B and C Flight Phases provided the product of frequency and dampingratio exceeds the following requirements:

Level "RS#

nRS

, rad/sec

1 0.5

2 0.3

3 0.15

23


Crosswind Landing

59


L. M. Nicolai. Fundaments of Aircraft Design. METS, Inc, Xenia, OH, 1975.




How to find rudder effectiveness?

62


Cn can come from: crosswind (β) or asymmetric thrust


References

63

D. McRuer, I. Ashkenas, and D. Graham. Aircraft Dynamics and Automatic Control. Princeton University Press, Princeton, New Jersey, 1973.

C. D. Perkins and R. E. Hage. Airplane Performance Stability and Control. John Wiley and Sons, Princeton, New Jersey, 1949.


B. Etkin. Dynamics of Flight, Stability and Control. John Wiley and Sons, New York, NY, second edition, 1982.

J. Roskam. Airplane Flight Dynamics and Automatic Flight Controls. Roskam Aviation and Engineering Corperation, Lawrence, Kansas, 1979.

J. Roskam. Airplane Design, volume IV. Roskam Aviation and Engineering Corperation, Ottowa, Kansas, 1986.

B. Stevens and F. Lewis. Aircraft Control and Simulation. John Wiley and Sons, New York, NY, 1st edition, 1992.

D. P. Raymer. Aircraft Design: A Conceptual Approach. AIAA Education Series, Alexandria, Va., second edition, 1992.

T. Takahashi. Some strategies teaching configuration aerodynamics in aeronautical engineering capstone design. In 47th Annual AIAA Aerospace Sciences Meeting and Exhibit, AIAA2009-1602, Orlando, Fl, January 5 - 8 2009.

Mason, W.H. High Angle of Attack Aerodynamics, downloaded 2009. see: http://www.aoe.vt.edu/~mason/Mason_f/ConfigAeroHiAlphaNotes.pdf

Mason, W.H. Control and Stability in Aircraft Conceptual Design, downloaded 2009. see: http://www.aoe.vt.edu/aoe/faculty/Mason_f/SD1L13.pdf

http://www.aoe.vt.edu/~mason/Mason_f/ConfigAeroHiAlphaNotes.pdf




http://www.aoe.vt.edu/aoe/faculty/Mason_f/SD1L13.pdf





Documents

Aircraft Control Sizing - Virginia Techmason/Mason_f/SD1Cotting_control.pdf · in the world, an airplane can fly ... Dynamics of Flight, Stability and Control. John ... Aircraft Dynamics