Aero Engineering 315

Lesson 37

Longitudinal Static Stability

Lesson 37 Objectives Draw a stability curve (Cm vs for tail and wing

Draw a curve for positive, negative and neutral stability Understand tail and wing contributions to stability

List factors that contribute to longitudinal static stability State criteria for positive long-stat stability Identify trim AoA and velocity Predict changes in stability with changes in tail area,

moment arm, incidence angle, camber, CG, etc. Define neutral point and static margin Know criteria for positive long-stat stability WRT CG and

static margin

Zero Lift Line

V

+Macwing

Lw

Moment Contribution from the Wing

xw

Recall:

Mac,wing < 0 (for + camber)

and

Lw = CL q S = CLwq S

Summing the moments and dividing by qSc:

C = (CLw xw/c ) + CMac,wing

Mcg

Positive slope(+)

Negative (-) Intercept for symmetrical

wing

C (from wing)M

cg

Form of: y = mx + b

Zero Lift Line

Lt

t = - it

Vitt

Moment Contribution from the Tail

CMcg = -

+ it

(CLt St xt )

S c (CLt St xt )

S c

Negative slope (-)

Positive (+) intercept

(depending on it)

C (from tail)M

cgSumming the moments and dividing by qSc:

xt

Lt = CLt q StSymmetric airfoil

St = tail area

Form of: y = mx +b

Contributions to Stability - Summary

Required Tail Contribution

Wing Only Contribution

Result – Wing and Tail

Zero Lift Line

Lt

Vitt

Total Airplane Moment

xt

V

+Macwing

Lw

xw

C = (CLw - CLt ) + CMacw+ CLt itMcg

xt

c St

S

xw

c xt

c St

S

Wing WingTail Tail

CM CM

Effects of configuration changes

C = (CLw - CLt ) + CMacw+ CLt itMcg

xt

c St

S

xw

c xt

c St

S

CM CM

LtxtLw xw

c.g.

•Move CG Aft Less Stable•Larger tail (St) More Stable•Increased camber Decrease CMo•Larger distance to tail More Stable•Tail incidence Shifts CMo

C. G. Effect on Stability

CMcg

a

Center of Gravity moving aft

Bottom Line for stable, trimmed aircraft:Stable if CMTrimmed if sum of moments about CG = 0Trimmed at usable lift if CM0 >0

Longitudinal Stability—Wing Effects

Locating wing a.c. farther forward of c.g. is more destabilizing

To improve stability (lower CM):

↓ (xcg – xac) Shorter moment arm (wing back or c.g. forward)

↓ SW Smaller wing area (hard)

↓ CLWLess efficient wing (do we

really want to?)

wacwcg MwLM CcxCC

,,/

Longitudinal Stability—Tail Effects

Tail aft of cg is stabilizing Canards are destabilizing To improve stability (more negative CM):

C = - + itM cg

(CLt St xt )

S c

(CLt St xt )

S c

o xt Longer moment arm

o St Larger tail

o CLt ARt or eot (tail Oswald factor)

or move tail out of downwash

Longitudinal Stability—Tail Effects

it > 0it = 0

it < 0

Tail incidence angle, it , is the angle betweenChord Line of the tail and Aircraft Zero-Lift-Line

Tail leading edge down is positive

Longitudinal Static Stability - Total Aircraft

Most parameters are fixed once the aircraft is built

C.G. can be moved Cargo location Fuel location Weapons, stores, etc.

it changes the trim angle of attack, e

Variable geometry wings—change cg, CLW and moment arm (xcg-xac)

Conventional Tail - Stabilizing

F-22F-16

Canards - Destabilizing

Su-35

Long-Eze

More Canards - Eurofighter

Neutral Point

The Neutral Point (Xn) represents the c.g. location such that CM = 0. It is the center of pressure for the entire aircraft.

Xcg is the distance from the leading edge of the wing to the CG

Xn is the distance from the leading edge of the wing to the Neutral Point

X cg W

X n

Static Margin: Stability Criteria

Non-dimensional difference between Neutral Point (n.p.) and Center of Gravity (c.g.) where:

cgn xxSM cxxandcxx cgcgnn //

If S.M. > 0 (c.g. ahead of the neutral point) - aircraft is stable

If S.M. = 0 (c.g. at the neutral point)

If S.M. < 0 (c.g. behind the neutral point)

- aircraft is neutrally stable

- aircraft is unstable

- CM

CL

=

Typical Static Margin Values

Transports & Consumer AC: 0.05 to 0.20

Cessna 172Learjet 35Boeing 747

P-51 MustangF-106

F-16A (early)F-16CX-29

Fighters: 0 to 0.05

Fighters - FBW

0.190.130.27

0.050.09

-0.020.01

-0.33

More Stable

More Maneuverable

Much More Maneuverable Stabilized by AFCS

F-117Longitudinal

Stability

NEUTRAL PITCH STABILITY IS EXHIBITED BY THE AIRCRAFT AT SMALL POSITIVE ANGLES OF ATTACK

THE AIRCRAFT BECOMES INCREASINGLY UNSTABLE IN PITCH ABOVE 7° AOA

EXCEEDING 14° AOA CAUSES A VIOLENT AND UNCONTROLLABLE PITCH-UP

7° AOA VORTEX

VORTEX FORMS AT WING ROOT

ABOVE 14° AOA VORTEX

VORTEX SHIFTS OUTBOARD AND WING BEGINS TO STALL AT WING TIPS

STALL PROGRESSES TOWARDS WING ROOT AC cp SHIFTS FORWARD RESULTING IN SIGNIFICANT

NEGATIVE STATIC MARGIN STATICALLY UNSTABLE -- OUT OF CONTROL

Longitudinal Static Stability Summary

Axes, Moments, Velocities – Definitions Static vs. Dynamic Stability Absolute Angle of Attack Moments and Forces Static Longitudinal Stability

Wing Effects Tail Effects

Static Margin

Next Lesson (38)… Prior to class

Review sections 6.1 - 6.4 and long-stat stability handout

Complete all homework problems Read lateral/directional stability handout

In class Discuss lateral/directional (roll/yaw)

static stability

Glider Design Project