introduction to aircraft performance and static stability

8/7/2019 Introduction to Aircraft Performance and Static Stability

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Introduction to AircraftPerformance and Static Stability

16.885J/ESD.35JAircraft Systems Engineering

Prof. Earll Murman

September 18, 2003


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Todays Topics Specific fuel consumption and Breguet range

equation

Transonic aerodynamic considerations

Aircraft Performance

Aircraft turning Energy analysis

Operating envelope

Deep dive of other performance topics for jet transportaircraft in Lectures 6 and 7

Aircraft longitudinal static stability


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Thrust Specific Fuel Consumption (TSFC) Definition:

Measure of jet engine effectiveness at converting fuel touseable thrust

Includes installation effects such as

bleed air for cabin, electric generator, etc.. Inlet effects can be included (organizational dependent)

Typical numbers are in range of 0.3 to 0.9. Can be up to 1.5 Terminology varies with time units used, and it is not all

consistent. TSFC uses hours c is often used for TSFC Another term used is

TSFC lb of fuel burned(lb of thrust delivered)(hour)

ct

lb of fuel burned

(lb of thrust delivered)(sec)


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16.885J/ESD.35J - Oct 1, 2002

Breguet Range Equation Change in aircraft weight = fuel burned

Solve for dt and multiply by V to get ds

Set L/D, ct, V constant and integrate

dW ctTdt ctTSPC/3600 T thrust

dsVdtV

dW

ctT

V

W

ctT dWW

V

L

ctD dWW

R 3600TSFC

VLD

ln WTOW

empty


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16.885J/ESD.35J - Oct 1, 2002

Insights from Breguet Range EquationR 3600

TSFCV

LD

lnW

TOW

empty

3600TSFC

represents propulsion effects. Lower TSFC is better

V

L

D

represents aerodynamic effect. L/D is aerodynamic efficiency

VLD

aMLD

. a is constant above 36,000 ft. MLD

important

lnW

TOW

emptyrepresents aircraft weight/structures effect on range


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16.885J/ESD.35J - Oct 1, 2002

Optimized L/D - Transport A/CSweet spot is in transonic range.

Lossesdue toshock

waves

Ref: Shevell

M

ax(L/D)

Mach No.1 2 3

10

20

Concorde


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16.885J/ESD.35J - Oct 1, 2002

Transonic Effects on Airfoil Cd, ClCd

Mcr

Mdragdivergence

M8

1.0

M < Mcr8

V8

V8

Region I. II. III.

I.

II.

III. M > Mdragdivergence

8

Mcr < M < Mdragdivergence

8

M


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16.885J/ESD.35J - Oct 1, 2002

Strategies for Mitigating Transonic Effects Wing sweep

Developed by Germans. Discovered after WWII by Boeing

Incorporated in B-52 Area Ruling, aka coke bottling

Developed by Dick Whitcomb at NASA Langley in 1954

Kucheman in Germany and Hayes at North American contributors Incorporated in F-102

Supercritical airfoils Developed by Dick Whitcomb at NASA Langley in 1965

Percey at RAE had some early contributions

Incorporated in modern military and commercial aircraft


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16.885J/ESD.35J - Oct 1, 2002

Basic Sweep Concept Consider Mach Number normal to leading edge

For subsonic freestreams, Mn < M - Lower effective freestream

Mach number delays onset of transonic drag rise. For supersonic freestreams Mn < 1, > - Subsonic leading edge Mn > 1, < - Supersonic leading edge

Extensive analysis available, but this is gist of the concept

sin =1/ M

= Mach angle,the directiondisturbances

travel insupersonic flow

M Mn=Mcos


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16.885J/ESD.35J - Oct 1, 2002

Wing Sweep Considerations M > 1 Subsonic leading edge

Can have rounded subsonic type wing section Thicker section Upper surface suction

More lift and less drag Supersonic leading edge

Need supersonic type wing section

Thin section Sharp leading edge


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16.885J/ESD.35J - Oct 1, 2002

Competing Needs Subsonic Mach number

High Aspect Ratio for low induced drag Supersonic Mach number

Want high sweep for subsonic leading edge

Possible solutions Variable sweep wing - B-1 Double delta - US SST Blended - Concorde Optimize for supersonic - B-58


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Supercritical AirfoilSupercritical

airfoil shapekeeps uppersurface velocityfrom getting too

large.Uses aft camberto generate lift.

Gives nosedown pitchingmoment.

Cp

x/c

Cp, cr

V8


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Todays Performance Topics Turning analysis Critical for high performance military a/c. Applicable to all.

Horizontal, pull-up, pull-down, pull-over, vertical Universal M- turn rate chart , V-n diagram

Energy analysis Critical for high performance military a/c. Applicable to all. Specific energy, specific excess power M-h diagram, min time to climb

Operating envelope Back up charts for fighter aircraft

M- diagram - Doghouse chart Maneuver limits and some example

Extensive notes from Lockheed available. Ask me.


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16.885J/ESD.35J - Oct 1, 2002

Horizontal TurnW = L cos, = bank angleLevel turn, no loss of altitude

Fr= (L2

- W2

)1/2

=W(n2

-1)1/2

Where n L/W = 1/ cos is the loadfactor measured in gs.

But Fr= (W/g)(V2/R)So radius of turn is

R = V2/g(n2-1)1/2

And turn rate = V/R is

= g(n2-1)1/2 / V

Want high load factor, low velocity

Flight pa

th

R

R

L

W

Fr

z

z


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16.885J/ESD.35J - Oct 1, 2002

Pull Up Pull Over Vertical

Fr= (L-W) =W(n-1)

= (W/g)(V2/R)

R = V2/g(n-1)

= g(n-1)/ V

Fr= (L +W) =W(n+1)

= (W/g)(V2/R)

R = V2/g(n+1)

= g(n+1)/ V

Fr= L =Wn

= (W/g)(V2/R)R = V2

/gn

= gn/ V

R

L

W

R

L

W

R

L

W

V i l Pl T R


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Let

Pull Over

K = (n+1)/(n2-1)1/2

Vertical Maneuver

K = n/(n2-1)1/2

Pull Up

K = (n-1)/(n2-1)1/2

For large n, K 1 and for all maneuvers gn/ V

Similarly for turn radius, for large n, R V2/gn.

For large and small R, want large n and small V

Pulloverfrom inverted attitude

Verticalmaneuver

Pull-up from level attitude

0

0.5

1.0

1.5

2.0

2.5

1 2 3 4 5 6 7 8 9

Turn

rate

ratio,K

Load factor, in 'g's

Vertical Plan Turn Rates

Vertical planeturn rateK=

Horizontal planeturn rate


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gn/ V

= gn/aM

so ~ 1/ M

at const h (altitude) & n

Using R V2/gn, V

/R = a

M/R. So ~ M

at const h & R

For high Mach numbers, the turn radius gets large


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16.885J/ESD.35J - Oct 1, 2002

Rmin

and maxUsing V

= (2L/

SCL)1/2 = (2nW/SCL)1/2

R V2/gn becomes R = 2(W/S)/ g

CL

W/S = wing loading, an important performance parameterAnd using n = L/W =

V2

SCL/2W

gn/ V= g

V

CL/2(W/S)

For each airplane, W/S set by range, payload, Vmax.

Then, for a given airplane

Rmin

= 2(W/S)/ gC

L,maxmax

= g V

CL,max /2(W/S)

Higher CL,max gives superior turning performance.

But does n CL,max = V2CL,max/2(W/S) exceed structural limits?


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V-n diagram

V* 2nmax

CL,max

W

S

Highestpossible

Lowestpossible R

Each airplane has a V-n diagram.

Source: Anderson

Stall area

Stall area

Structural damage

Structural damage

q>

qmax

Loadfactorn

V8V*

CL < CLmax

CL < CLmax

Positive limit load factor

Negative limit load factor

0


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Summary on Turning Want large structural load factor n

Want large CL,MAX Want small V

Shortest turn radius, maximum turn rate isCorner Velocity

Question, does the aircraft have the powerto execute these maneuvers?


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Specific Energy and Excess PowerTotal aircraft energy = PE + KE

Etot = mgh + mV2/2

Specific energy = (PE + KE)/WHe = h + V2/2g energy height

Excess Power = (T-D)V

Specific excess power*

= (TV-DV)/W

= dHe/dtPs = dh/dt + V/g dV/dt

Ps may be used to change altitude, or accelerate, or both* Called specific power in Lockheed Martin notes.


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Excess PowerPower Required

PR= DV

= q

S(CD,0 + C2L/ARe)V

= qSCD,0V + qSVC2L/ARe

= SCD,0V3/2 + 2n2W2/SVARe

Parasite powerrequired

Induced powerrequired

Power Available

PA = TV and Thrust is approximatelyconstant with velocity, but varieslinearly with density.

Excess powerdepends uponvelocity, altitudeand load factor

P

ower

Excesspower

V8

PR

PA


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Altitude Effects on Excess PowerPR= DV = (nW/L) DV

= nWV

CD/CL

From L=

SV2

CL/2 = nW, getV

= (2nW/ SCL)1/2

Substitute in PRto get

PR= (2n3W3C2D/ SC3L)1/2

So can scale between sea level 0 andaltitude alt assuming CD,CL const.

Valt = V0(0/alt)1/2, PR,alt = PR,0(0/alt)1/2

Thrust scales with density, so

PA,alt = PA,0(alt/0)


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Summary of Power Characteristics He = specific energy represents state of aircraft. Units are in

feet.

Curves are universal Ps = (T/W-D/W)V= specific excess power

Represents ability of aircraft to change energy state.

Curves depend upon aircraft (thrust and drag) Maybe used to climb and/or accelerate Function of altitude Function of load factor

Military pilots fly with Ps diagrams in the cockpit,Anderson


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A/C Performance SummaryFactor Commercial

TransportMilitary

TransportFighter General Aviation

LiebeckTake-offhobs = 35 hobs = 50 hobs = 50 hobs = 50

LiebeckLandingVapp = 1.3 Vstall Vapp = 1.2 Vstall Vapp = 1.2 Vstall Vapp = 1.3 Vstall

Climb LiebeckLevel Flight Liebeck

Range Breguet Range Radius of action*.Uses refueling

Breguet for prop

Endurance,Loiter

E (hrs) = R (miles)/V(mph), where R = Breguet Range

Turning,Maneuver

Emergency handling Major performance

factor

Emergencyhandling

SupersonicDash

N/A N/A Important N/A

ServiceCeiling

100 fpm climb

Lectures 6 and 7 for commercial and military transport

* Radius of action comprised of outbound leg, on target leg, and return.


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S&C Definitions L - rolling moment Lateral motion/stability

M - pitching moment

Longitudinal

motion/control

N - rolling moment

Directional motion/control

CM

qSc

Moment coefficient:

L'

M

Rudder deflection

Elevator deflection

N


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Aircraft Moments

Aerodynamic center (ac): forces and moments can be completelyspecified by the lift and drag acting through the ac plus a moment aboutthe ac CM,ac is the aircraft pitching moment at L = 0 around any point

Contributions to pitching moment about cg, CM,cg come from

Lift and CM,ac Thrust and drag - will neglect due to small vertical separation from cg Lift on tail

Airplane is trimmed when CM,cg = 0


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Absolute Angle of Attack

Stability and control analysis simplified by usingthe absolute angle of attack which is 0 at CL = 0.

a = + L=0

Lift s

lope =

CL,max

L=0

dC L

d

Lift s

lope =

CL,max

dC L

d

Lift coefficient vs geometric angle of attack, Lift coefficient vs absolute angle of attack,a

CL

a

CL

16 885J/ESD 35J O t 1 2002


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Criteria for Longitudinal Static Stability

CM,0

must be positive

C

M,cga must be negativeImplied that e is within flight range of angle of attackfor the airplane, i.e. aircraft can be trimmed

CM,0

a

CM,cg

e

Slope= dCM,cgda

(Trimmed)

16 885J/ESD 35J O t 1 2002


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Moment Around cg

Mcg

Mac

wb

Lwb

(hc hac

c) ltL

t

Divide by qSc and note that CL ,t L

t

qSt

CM,cg

CM,ac

wb C

L wb(h h

ac) ltSt

cSC

L ,t, or

C

M,cg C

M,acwb C

L wb

(h hac

) VH

C

L ,t, where V

H

ltS

t

cS

16 885J/ESD 35J Oct 1 2002


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CM,cg

CM,ac

wb C

L wb(h h

ac) V

HC

L ,t

CLwb

dCL wb

d a, wb awba, wb

Cl, t att at(wb it )

where is the downwash at the

tail due to the lift on the wing 0

a, wb

CL, t

at

a, wb1

a

t(i

t

0)

At this point, the

convention is dropthe wb on awb

CM,cg

CM,ac

wb a

a(h h

ac) V

H

at

a1

VH

at

it

0

Lift

slope

=

Cl, max

L=0

dC l

d

Cl

stall

16 885J/ESD 35J Oct 1 2002


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Eqs for Longitudinal Static Stability

CM,cg

CM,ac

wb a

a(h h

ac) V

H

at

a1

VH

at

it

0

CM,0 CM,cg

l 0 CM,ac

wb VHat it0

CM,cg

a

a (h hac

) VH

at

a1

CM,acwb < 0, VH> 0, t> 0 it> 0 forCM,0 > 0

Tail must be angled down to generate negative liftto trim airplane

Major effect of cg location (h) and tail parameterVH=

(lS)t/(cs) in determining longitudinal static stability

CM,0

a

CM,cg

e

Slope= dCM,cgda

(Trimmed)

16 885J/ESD 35J - Oct 1 2002


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Neutral Point and Static Margin

The slope of the moment curve will vary with h, the

location of cg. If the slope is zero, the aircraft has neutral longitudinal

static stability.

Let this location be denote by

or

CM,cg

a

a (h hac

) VH

at

a1

hn hac VHat

a 1

For a given airplane, the neutral point is at a fixed location. For longitudinal static stability, the position of the center of

gravity must always be forward of the neutral point.

The larger the static margin, the more stable the airplane

CM,cg

a

a h hn a hn h a static margin

16 885J/ESD 35J - Oct 1 2002


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Longitudinal Static Stability

Aerodynamic centerlocation moves aft forsupersonic flight

cg shifts with fuel burn,stores separation,configuration changes

Balancing is a significant design requirement

Amount of static stability affects handling qualities

Fly-by-wire controls required for statically unstable aircraft

16.885J/ESD.35J - Oct 1, 2002


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Todays References Lockheed Martin Notes on Fighter Performance John Anderson Jr. , Introduction to Flight, McGraw-

Hill, 3rd ed, 1989, Particularly Chapter 6 and 7

Shevell, Richard S., Fundamentals of Flight, PrenticeHall, 2nd Edition, 1989

Bertin, John J. and Smith, Michael L., Aerodynamicsfor Engineers, Prentice Hall, 3rd edition, 1998

Daniel Raymer, Aircraft Design: A ConceptualApproach, AIAA Education Series, 3rd edition, 1999,Particularly Chapter 17

Note: There are extensive cost and weight estimationrelationships in Raymer for military aircraft.

introduction to aircraft performance and static stability

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