Aircraft Design With Maneuver and Gust Load Alleviation

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Aircraft Design with Maneuver and Gust Load

Alleviation

Jia Xu

and Ilan Kroo

Stanford University, Stanford, CA, 94305, U.S.A

The effects of maneuver (MLA) and gust load alleviation (GLA) systems on aircraftperformance are evaluated at the conceptual design level. Results suggest that a conven-tional transonic transport aircraft designed with an aggressive aerodynamic MLA systemmay achieve some 3% lower direct operating cost (DOC) and more than 4% reduction infuel consumption relative to a conventional baseline design. The addition of a GLA sys-tem can more than double these savings. Sensitivity studies confirm that the control andactuator requirements for effective maneuver and gust load alleviation are consistent with

the performance parameters of modern aircraft. The active load control design frameworkcan serve as a platform for the assessment of new technologies, configurations, and opera-tional paradigms that may significantly reduce aircraft fuel consumption and environmentalimpact.

I. Nomenclature

c Chord at breakpointsClres Clmax margin Non-dimensional semispan y/(b/2)F Generalized forceFg Gust dynamics alleviation factorf c Final cruise

fm MLA flap deflectionfg GLA flap deflection Wing twist at breakpointsd Wing twist from aerodynamic dampings Wing twist from aerodynamic stiffness Wing taper ratio1/4 Wing quarter chord sweeph Gust gradient length; one half of the gust wavelengthic Initial cruisekd GLA control derivative gainskp GLA control proportional gainsK Wing stiffness matrixlfuse Fuselage lengthland Landing conditionM Wing mass matrixQ Orthonormal eigenvectorsa Allowable tensile strengthsm Aircraft static margina Allowable shear strengtht/c Wing t/c at breakpoints

Ph.D. Candidate, Department of Aeronautics & Astronautics. Student Member AIAAProfessor, Department of Aeronautics & Astronautics. Fellow AIAA

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American Institute of Aeronautics and Astronautics

29th AIAA Applied Aerodynamics Conference27 - 30 June 2011, Honolulu, Hawaii

AIAA 2011-318

Copyright 2011 by Jia Xu. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.
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ts Wing skin gauge at breakpointstw Wing web gauge at breakpointsT0 Sea level thrustto Takeoff conditionUds Design gust velocityUref Reference gust velocityWmlw Maximum landing weightWmtow Maximum takeoff weight

Wmzfw Maximum zero-fuel weightwg Gust velocity in zwa Aircraft perturbation velocity in zzmo Maximum cruise altitude

II. Introduction

Aerodynamic maneuver load alleviation systems use trailing edge deflections to concentrate lift inboardand reduce the wing bending moment. This allows the wing to be made lighter, or longer and thinner at thesame weight. The basic idea behind MLA is illustrated in Figure 1.

Figure 1. The maneuver lift distribution on a conventional (left) and MLA aircraft (right). The extent of loadalleviation is constrained by maximum lift.

MLA is well-understood in the context of wing design. Studies have shown that span increases of 1015%and drag savings of 813% can be achieved with MLA at fixed wing weight. 14 MLA systems have beentested in flight by the NASA Mission Adaptive Wing (MAW) and Active Flexible Wing (AFW) programsand integrated into the flight control systems of the Lockheed L-1011 and Airbus A320/330.57

MLA design becomes more complex in the context of aircraft and mission performance. As MLA relaxesthe structural constraints imposed by maneuver loads, gust loads can become critical.8 The implications aretwofold: 1) gust loads should be considered when evaluating the effectiveness of MLA systems and 2) a gustload alleviation (GLA) system is likely needed to realize full the benefits of MLA.

Similar to a MLA system, a GLA system uses control deflections to minimize the dynamic loads in gustencounters. However, the interdependence between aircraft configuration and gust response complicatesGLA design. Previous studies have separately addressed the different components of the problem: 1) howto find the worst-case gust for a given airplane,913 2) how to design aircraft structure to sustain a givengust,1417 and 3) how to design a GLA control systems for a given airplane and gust.1820 The present work

address the integrated problem of how to design an aircraft with both MLA and GLA control systems.

III. Aircraft Parameterization

We assess the benefits of maneuver and gust load alleviation in the context of aircraft performance. Theaircraft parameters are optimized with the MLA deflections schedule and GLA control gains to minimizedirect operating cost (DOC).

The mission analysis is based on the Program for Aircraft Synthesis Studies (PASS).21 PASS is a firstorder conceptual design too based on semi-empirical and first-order physics-based methods. It can be used to

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rapidly evaluate aircraft performance as functions of configuration and mission parameters. The performancemodels in PASS are smooth and can be used in conjunction with gradient-based optimization to solve large-scale design problems.

We extend the semi-empirical methods in PASS with Weissinger panel methods, finite element methods,structure dynamics solvers and aircraft dynamic simulations to capture the complex aeroservoelastic tradeoffsthat drive the MLA and GLA design problem.

The baseline for all subsequent design studies is a Boeing 737-class aircraft with a 2300nm range anda cruise Mach number of 0.78. The fuselage geometry is fixed while the wing, horizontal tail and engine

parameters are optimization variables:

Figure 2. Mission profile.

xa=

Sref, AR, , 1/4,

xwinglfuse

, ShSref

, Wmtow, Wmzfw

Wmtow, T0

Figure2shows the flight conditions in the mission analysis. The mission-related variablesxminclude theangle of attack at each flight condition, the initial and final cruise altitudes, and the takeoff and landingMach numbers and flap deflections:

xm= [ic, fc , climb, to, land, gust, maneuver, zic, zfc , Mto, Mland, fto, fland]

The optimization is subject to trim, stability and tail maximum lift constraints at each flight condition:

nW=v2SrefCL

2 (For all flight conditions)

1

cmac

dCMacdCL

>0.15 (For all flight conditions)

CLhCLhmax

0.024

We further impose constraints on cruise drag-to-thrust ratios D/Tto allow for operational climb. Similar

thrust margins are imposed ahead of gust encounters to prevent the optimizer from exploiting local trim tominimize gust load:

D

T


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Figure 3. The wing geometry is defined by properties at the breakpoints. Intermediate geometric are linearlyinterpolated. The aerodynamic control points are collocated with the y-locations of the structural constraints.

We compute the lift and stability derivatives using the Weissinger method with compressibility correc-tions. The induced drag is computed by integrating the normal wash in the Trefftz plane. We estimatethe wing parasitic drag using empirical shape factors21 and compressibility drag using the strip-wise Kornequation.22

The wing design is subject to maximum lift constraints at takeoff, climb, cruise, maneuver and landing.Effective high-speed maximum lift prediction is critical for MLA design. Figure1 illustrates that aggressiveinboard load concentration can stall the wing. The spanwise Clmax constraint in maneuver plays thereforea critical role in determining the extent of load alleviation. For purposes of conceptual design we employthe simplified method of critical sections to account for CLmax. This approach makes the conservativeassumption that the wing is at CLmaxif any of its sections is at the local Clmax.

23 The spanwise maximumlift constraint is then:

{Cl(y)}

{Clmax(y) Clres}


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0.06 0.08 0.1 0.12 0.14 0.16

0.8

1

1.2

1.4

1.6

1.8

2

t/c

Clmax

Mach 0.6

Mach 0.7

Mach 0.8

(a) Clean Wing

0.06 0.08 0.1 0.12 0.14 0.16

0.8

1

1.2

1.4

1.6

1.8

2

t/c

Clmax

f=0

f=15

f=30

(b) With flap deflections (Mach 0.78)

Figure 4. Airfoil Clmax variation with t/c. The results are for a section at 30,000 ft, Re=20 million and1/4 = 30

.

IV. Maneuver Load Alleviation

The first step in maneuver load analysis is to define the design maneuver condition(s). One wouldideally consider the entire V-n envelope to determine the limit load conditions. The design framework canaccommodate an arbitrary number of maneuver load conditions. After some experimentation with maneuversat different altitudes and weights, we simplify the problem by choosing a 2.5-g symmetric pull-up at 15,000ft as the representative design maneuver condition. The aircraft is at its maximum cruise speed Vc for themaneuver.

The MLA control arrangement is shown in Figure 5. The design variables are the wing flap deflectionsbetween the wing breakpoints:

xmla= fm

We model flap deflection with incidence change. This simplification allows us to use the simple spanwiseWeissinger method to capture the 3-D aerodynamic effects of MLA control deflection and the tradeoff amongload alleviation, allowable deflections and maximum lift. The effects of flap deflection were modeled as achange in section zero lift angle and pitching moment based on experimental data.25

The range of allowable MLA flap deflection determines how far the lift centroid can be moved inboard.High-speed deflection limits are typically set by hinge moment, control reversal and flow separation con-straints. Experiments have shown that trailing edge deflection of 6 8 can be sustained on typical flapswithout significant penalties.2 These limits are consistent with the deflections in the F-111 MAW experimentsat up to 7.5.2

However, while deflections at high speed incur penalties, having the aircraft perform the same maneuverwithout load alleviation can incur even greater penalties. Moreover, there is no need to perform designmaneuvers at constant altitude or favorable aerodynamic conditions. White1 therefore study MLA control

deflections of up to 30

. In subsequent design studies we limit the MLA flap deflection to 20

:

20 < fmi < 20

We further explore the impact of deflection bounds on performance through a sensitivity study in Sec-tionVI.C.

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Figure 5. The optimizer may control the flap deflections in between breakpoints to tailor the lift distributionin maneuver.

V. Gust Load Alleviation

Part 25 of the Federal Aviation Regulations (FAR) specifies both a continuous and a discrete gust designcriteria.12, 26 Although continuous gust analysis is relevant in fatigue-related structural considerations, this

paper focusses on discrete gust encounters and their effect on aircraft sizing. The discrete gust criteriarequires aircraft to be designed against 1Cosine gusts of varying wavelength at different flight altitudes.A typical family of 1Cosine gusts is shown in Figure 6. The gust amplitude is a function of the aircraftweights, the flight altitude and the gust gradient length h, which is one half of the gust wavelength. Thediscrete gust criteria is summarized below:

wg =Uds

2

1 cos

V

ht

, Uds= UrefFg

h

350

1/6, h: [35, 1500]f t

Uref|Vc =

56 12 h15000

ft/s for 0 h 15000ft

44 18h1500035000

ft/s for 15000 h 50000f t

, Uref|Vd =Uref|Vc

2

Fg = f(Wmzfw, Wmtow, Wmlw, zmo)

For a given aircraft the reference gust velocity Urefdecreases in a piecewise linear fashion with increasingaltitude. The reduction in gust amplitude at higher altitudes reflects the reduced likelihood of severe gustevents. The gust amplitude also scales with the 1/6 power of the gust gradient length h. This is consistentwith the frequency spectrum of severe atmospheric turbulence. The gust load alleviation factor Fg accountsfor dynamic and unsteady effects.

The deterministic 1Cosine gust is inadequate for detailed control design: a combination of LIDAR andoptimum control can anticipate the 1Cosine gust shape and exactly cancel its effects. However, for reactivecontrollers the 1Cosine gust can still impose meaningful performance bounds, especially when non-lineareffects like actuator saturation are taken into consideration.

The aircraft is designed for 1Cosine gust encounters at 10,000 ft and Vc, and at the initial and finalcruise altitudes. At each altitude we consider positive and negative 1Cosine gusts at 12 different gradientlengths, ranging from 35 to 1200 ft. A multi-point design prevents the optimizer from exploiting local trim

at one altitude to excessively minimize gust loads.Gust encounter at 10,000 ft is likely critical because this altitude combines high dynamic pressure withhigh reference gust velocity Uref. Below 10,000 ft speed and dynamic pressure are limited by regulations.Cruise stage gust encounters are also likely critical because of the need to achieve a high span efficiency.

For each gust encounter we integrate the plunge-only, pseudo-steady aircraft equations of motion toobtain the dynamic response:

w=dCL

CLg , dC L=

wg w

v

CL+ fgiCLfi

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0 0.5 1 1.5 2

0

5

10

15

20

25

30

35

40

45

50

1Cosine Gusts

t

ft/s

h = 35

h = 100

h = 200

h = 300

h = 400

h = 600

h = 800

Figure 6. A family of 1Cosine gusts at varying gradient lengths h.

The assumption of pseudo-steady aerodynamics in gust encounters has been shown to be generally con-servative and greatly simplifies the analysis.27 A plunge-only dynamics model is reflective of the fact that

a GLA system would likely have to operate within the confines of an aircraft pitch stability augmentationsystem.

The GLA control law is a proportional-derivative (PD) controller that takes in the gust-induced apparent and and produce flap deflection commands:

fgi = kpi + kdi

The control gains are optimization variables:

xgla = [kp, kd]

We assume knowledge of and in the present, first-order control analysis. More detailed studies ofthe impact of measurement uncertainty and delay would improve the fidelity of the result. The GLA flapdeflection limits are consistent with those of the MLA control surfaces:

20 < fgi< 20

The maximum GLA deflection rate is typical of commercial transports:

dfgidt


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Mu(t) + Cu(t) + Ku(t) = F(t)

Direct integration of the dynamic equations of motion is expensive and prone to numerical error. Weapply modal decomposition to isolate and decouple the low-frequency structural modes that contain most ofthe vibration energy. The generalized displacement u can be transformed into the modal coordinate systemy(t) using the orthonormal set of eigenvectors Q:

u(t)= Qy(t)M= QTMQ= [I] , K= QTKQ=

2

C= QTCQ, F(t) = QTF(t)

The equations of motion is now decoupled into scalar ODEs, which can be integrated by as superpositionsof second-order impulse responses:30

yi(t) + 2iiyi(t) + i2yi(t) = fi(t)

A major drawback of the modal decomposition method is its inability to model non-proportional damping.Aerodynamic damping is non-proportional and significant. We incorporate the aeroelastic damping andstiffness as applied forces:

s 2uib

sine, d uiv

Here ui refers to the spanwise deflection. s comes from the twist-deflection coupling in swept wingswhile d captures the aerodynamic damping. At each time-step we compute the aeroelastic twist usingthe spanwise deflections and rates from the previous time-step. The aeroelastic twist, combined with thecontrol deflections produce the aerodynamic forces used to advance the modal solution. We recover the dy-namic bending and shear stresses from the modal displacement using standard finite element post-processingtechniques.29 The spanwise gust-induced stresses in time become constraints in the optimization:

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Aircraft Design With Maneuver and Gust Load Alleviation