Unsteadiness in Aircraft Design

A Report

On

UNSTEADINESS IN AIRCRAFT DESIGN

By

AVIRAL TALWAR

2011A4PS152U

At

BITS Pilani Dubai Campus

Dubai International Academic City, Dubai

U.A.E

Second Semester, 2013-2014

A Report

On

UNSTEADINESS IN AIRCRAFT DESIGN

BY

AVIRAL TALWAR 2011A4PS152U MECH

Prepared in Partial Fulfillment of the

Project Course: ME F366 Laboratory Project

At

BITS Pilani Dubai Campus


UAE

Second Semester, 2013-2014

I I

BITS Pilani, Dubai Campus


UAE

Course name: Laboratory Project

Course number: ME F366

Duration: 23.02.2014 to 22.05.2014

Date of start: 23.02.2013

Date of submission: 22.05.2014

Title of Report: Unsteadiness in aircraft design

Name / ID Number: Aviral Talwar/ 2011A4PS152U

Discipline of Student: B.E (Hons) Mechanical Engineering

Name of Project Supervisor: Dr. A.M. Surendra kumar

Project Area: Aerodynamics, Fluid Dynamics, Elasticity

Abstract:

The traditional process of aerodynamic design is carried out manually by trial-and-error

method. This process requires a large number of design engineers working alongside a

huge budget. In order to overcome this manual method, the technologically driven

software design using CFD will provide a cost effective optimal design method.

Software products for automatic aerodynamic design are intended to solve the basic

problem of preliminary aerodynamic design: to develop a configuration with as low a

Signature of the Student Signature of Supervisor

Date: Date:

I I I

ACKNOWLEDGEMENTS

Firstly, I would like to express my sincere gratitude to Dr. R.N. Sahah, Director BPD

who has given me an opportunity to understand and apply engineering concepts in real

life problems through the Project.

I am very grateful to Prof. Dr.A.M. Surendra Kumar, Project in-charge, for assisting me

enthusiastically in the entire project. It is only with his guidance that the objectives of the

project have been accomplished.

I V

TABLE OF CONTENTS

TITLE PAGE NO

Abstract...III

Acknowledgements..IV

Chapter1 INTRODUCTION TO THE REPORT..1

1.1 Introduction.1

1.2 Layout of the Report..1

Chapter2 LITERATURE SURVEY2

2.1 Introduction.2

2.2 Literature Survey2

2.3 Diagrams.4

2.4 Inference from literature study.....5

2.5 Scope of present work..5

Chapter3 THEORY.........6

3.1 Introduction.6

3.2 Theory.6

3.2.1 Theory of wake Turbulence..6

3.2.2 Principle of Wake Turbulence..9

3.2.3 Components of Wake Turbulence9

3.3 Advantages of Wake Turbulence..11

3.4 Disadvantages of Wake Turbulence11

3.5 Ways to measure Wake Turbulence11

3.6 Analysis of Wake Turbulence12

Chapter4 DESIGN.13

4.1 Introduction..13

4.2 Wing Design....13

4.2.1 Airfoil...14

4.2.2 Wing Incidence.15

4.2.3 Taper Ratio15

4.2.4 Sweep Angel.16

4.3 Accessories..16

4.3.1 Strake.16

4.3.2 Fence.17

4.3.3 Vortex Generator.17

Chapter5 DESIGN ANALYSIS AND RESULTS...20

5.1 Introduction..20

5.2 Design Analysis and Sample Calculation...20

5.3 Results..24

Chapter6 Conclusion and Inference...25

6.1 Conclusion25

6.2 Inference...25

REFERENCE..26

CHAPTER 1

INTRODUCTION

1.1 INTRODUCTION

In an aircraft there are various types of unsteadiness like various types of turbulences

for eg. Wake Turbulence, Aero-elasticity and Fluid mechanics. The major cause is

Wake Turbulence for unsteadiness in aircraft as it can be very dangerous while the

aircraft is in the air which can cause it to become unsteady and crash. A lot of airplane

crashes have occurred due to Wake Turbulence and it has become a major problem in

todays world. The wingtip vortices and jetwash of an aircraft are the main reasons for

the generation of Wake Turbulence. This report is about the different causes of

unsteadiness in aircraft but mainly focuses on Wake Turbulence. There will be an

extensive study on this topic from the already existing research that has been done by

various people and the study that already exists.

1.2 LAYOUT OF THE REPORT

The first chapter covers the introduction to the topic of unsteadiness in aircraft

and tells that the main focus is on Wake Turbulenece.

The second chapter covers the literature survey. Journals with concepts on

cause of the unsteadiness of aircraft and the already existing study about the

topic.

The third chapter covers the basic theory of wake turbulence and its

disadvantages.

The final chapter provides the conclusion with the overall summary and future

scope.

1

CHAPTER 2

LITERATURE SURVEY

2.1 Introduction

This study tells the various technological and design advancements in the field of Wake

Turbulence in Aircraft over the many years in the aviation industry. The following data

summarizes the various research on this topic.

2.2 Literature Study

- Wake turbulence is a form of turbulence that forms behind an aircraft as it passes

through the air. This turbulence includes a lot of components, some important ones

are namely wingtip vortices and jetwash.

- Jetwash refers simply to the rapidly moving gases expelled from a jet engine; it is

extremely turbulent, but of short duration.

- Wingtip vortices, on the other hand, are much more stable and can remain in the air

for up to three minutes after the passage of an aircraft

- At altitude, vortices sink at a rate of 90 to 150 meters per minute and at about

150 to 270 meters they stabilize below the flight level of the generating aircraft.

Because of this, aircraft operating at a height greater than 600 meters above the

terrain are considered to be at less risk.

- The wake unsteadiness is dominated by a small amplitude displacement of the

cores of the vortex.

2

- . The strength of the wake turbulence is measured and governed by the weight,

speed and wingspan of the generating aircraft.

- The maximum strength occurs when the generating aircraft is heavy, at slow

speed with a clean wing configuration.

- Any perturbation in rotating flow leads to the propagation of dispersive waves,

called inertia waves. These types of waves are equivalent to gravity waves in a

stably stratified medium. The inertia waves that propagate along a vortex are

called Kelvin waves.

- Due to the presence of very sharp velocity gradients within the cores, this

rambling of the vortices leads to the observation of very large amplitude velocity

fluctuations in LDV and also hot wire measurements.

3

2.3 Diagrams -

Fig. 2.1.Sketch of the far-field wake downstream of a wing.

Fig 2.2 Picture from a NASA study on the wingtip vortices which qualitatively illustrates the

wake turbulence.

2.4 Inference from Literature Study

Wake Turbulence in an Aircraft is basically the turbulence that forms behind an aircraft

while it is moving. This turbulence includes a lot of components but the main component

that will be researched and studied upon are the Wingtip Vortices. The height at which

the aircraft travels at is a major factor for this type of turbulence. The strength of the

wake turbulence, the different type of waves due to which this turbulence occurs and

the different type of velocity gradients all will be studied for this project.

.

2.5 Scope of the Present of work

This paper will aim at presenting the current status of our understanding of

unsteadiness in wake vortices by studying all the current research done on this topic

which will be gained by theoretical analysis of model vortex flows and also from the

already existing experimental investigation of representative trailing Wakes that have

already been done by people and this paper will tell about the different kind of

unsteadiness that can occur due to elasticity, turbulences and fluid mechanics. But the

main concentration of the study will be on Wake turbulence and how it can effect the

steadiness of aircrafts and how it is a hazard in real life. This type of unsteadiness is a

such a major hazard in aircraft design has attracted the attention of hundreds of

research groups worldwide.

5

CHAPTER 3

THEORY

3.1 Introduction

This study tells the details of how a wake turbulence is generated in an aircraft, how the

elasticity of the wings on an aircraft can affect the steadiness about an aircraft and how

fluid mechanics helps in the same. It gives detailed information on this type of

unsteadiness in aircrafts.

3.2 Theory

The stability of two vortex pairs is analyzed as a model for the vortex system generated

by an aircraft in flaps-down mode. The co-rotating vortices on the starboard and port

sides tumble about one another as they propagate downward. This results in a time-

periodic basic state for the stability analysis. The dynamics and instability of the trailing

vortices are modeled using thin vortex filaments. Stability equations are derived by

matching the induced velocities from BiotSavart integrals with kinematic equations

obtained by temporal differentiation of the vortex position vectors. The stability

equations are solved analytically as an eigenvalue problem, using Floquet theory, and

numerically as an initial value problem. The instabilities are periodic along the axes of

the vortices with wavelengths that are large compared to the size of the vortex cores.

The results show symmetric instabilities that are linked to the long-wavelength Crow

instability. In addition, new symmetric and antisymmetric instabilities are observed at

shorter wavelengths. These instabilities have growth rates 60100% greater than the

Crow instability. The system of two vortex pairs also exhibits transient growth which can

lead to growth factors of 10 or 15 in one-fifth of the time required for the same growth

due to instability.

6

3.2.1 Generation of Wake turbulence in aircraft

Wake turbulence is hazardous in the region behind an aircraft in

the takeoff or landing phases of flight. During take-off and landing, aircraft operate at

high angle of attack. This flight attitude maximizes the formation of strong vortices. In

the vicinity of an airport there can be multiple aircraft, all operating at low speed and low

height, and this provides extra risk of wake turbulence with reduced height from which

to recover from any upset. At altitude, vortices sink at a rate of 90 to 150 meters per

minute and stabilize about 150 to 270 meters below the flight level of the generating

aircraft. For this reason, aircraft operating greater than 600 meters above the terrain are

considered to be at less risk.

7

Fig. 3.1 Sketch of separated flow field dominated by vertical flow structures

8

3.2.2 Principle of Wake turbulence in aircraft

The unsteady motion of a forebody or delta wing results in a modification of the flow

field in response to the maneuver. The model motion can result in delays of flow

separation and vortex formation at low angles of attack, and changes in vortex location

at higher angles of attack. At high angles of attack, the vortices can undergo a transition

process known as vortex breakdown. When vortex breakdown occurs over a lifting

surface, the aerodynamic loading can change abruptly. More dramatic chances in

loading occur when breakdown reaches the apex of the lifting surface and the flow

becomes fully separated. The nonlinear lift created by the vortex is reduced in the

region aft of vortex breakdown. This leads to changes in both the longitudinal and lateral

aerodynamic forces and moments, and in the stability derivatives.

3.2.3 Components of Wake turbulence

- Wingtip Vortices

- Jetwash

Jetwash refers simply to the rapidly moving gases expelled from a jet engine; it is

extremely turbulent, but of short duration. Wingtip vortices, on the other hand, are much

more stable and can remain in the air for up to three minutes after the passage of an

aircraft.

3.2.3.1 Wingtip Vortices

9

Wingtip vortices occur when a wing is generating lift. Air from below the wing is drawn

around the wingtip into the region above the wing by the lower pressure above the wing,

causing a vortex to trail from each wingtip. Wake turbulence exists in the vortex flow

behind the wing. The strength of wingtip vortices is determined primarily by the weight

and airspeed of the aircraft. Wingtip vortices make up the primary and most dangerous

component of wake turbulence.

Figure 3.2 Shows the trailing vortex of an aircraft.

10

3.3 Advantages of Wake Turbulence

There are no known advantages of wake turbulence.

3.4 Disadvantages of Wake Turbulence

If a light aircraft is immediately preceded by a heavy aircraft, wake turbulence from the

heavy aircraft can roll the light aircraft faster than can be resisted by use of ailerons. At

low altitudes, in particular during takeoff and landing, this can lead to an upset from

which recovery is not possible. Air traffic controllers attempt to ensure an adequate

separation between departing and arriving aircraft, and issue wake turbulence cautions

to pilots.

3.5 Ways to measure Wake Turbulence

Wake turbulence can be measured using several techniques. Currently, ICAO

recognizes 2 methods of measurement, sound tomography, and a high-resolution

technique is Doppler lidar, a solution now commercially available. Techniques

using optics can use the effect of turbulence on refractive index (optical turbulence) to

measure the distortion of light that passes through the turbulent area and indicate the

strength of that turbulence.

11

3.6 Analysis of Wake Turbulence

The wake turbulence in an aircraft is created by the wing vortices and can be a very

dangerous thing for the pilots as it makes the plane unsteady due to which it can lead to

problems in flying. There is no possible way to avoid this but only can be avoided by

going in circle. If wake turbulence occurs then the pilot should be trained to handle it in

an appropriate manner. Therefore, it is a hazard in disguise.

12

CHAPTER 4

DESIGN

4.1 INTRODUCTION

This chapter will be focusing on the Design aspects of Wingtip Vortices, its different

components and the material by which these wings are made. The wing tip vortex is a

very important part in a wing design. The structure and the components that are

associated with its design and structure are very crucial in determining if the wing be

able to put in use or not.

4.2 WING DESIGN

One decision that the designer has to make is the number of wings that he wants to put

in an airplane. It can be classified as-

1. Monoplane (i.e. one wing).

2. Two wings (i.e. biplane).

3. Three wings.

Then comes the location or the placement of the wings which are High wing, Mid wing,

Low wing and Parasol wing. The most beneficial for avoiding wake turbulence is the Mid

Wing segment.

Another important factor in the design of wings is the airfoil. The airfoil section is

responsible for the generation of the optimum pressure distribution on the top and

bottom surfaces of the wing such that the required lift is created with the lowest

13

Aerodynamic cost (i.e. drag and pitching moment).

4.2.1 Airfoil

Any section of the wing cut by a plane parallel to the aircraft xz plane is called an airfoil.

It is usually looks like a positive cambered section that the thicker part is in front of the

airfoil. The most reliable airfoil resources are NACA and Eppler. An airfoil-shaped body

moved through the air will vary the static pressure on the top surface and on the bottom

surface of the airfoil. If the mean camber line in a straight line, the airfoil is referred to as

symmetric airfoil, otherwise it is called cambered airfoil. The camber of airfoil is usually

positive. Wake turbulence is a majorly affected by choosing the right type of foil.

Fig 4.1 A simple diagram of an airfoil.

14

4.2.2 WING INCIDENCE

The wing incidence (iw) is the angle between fuselage center line and the wing chord

line at root. It is sometimes referred to as the wing setting angle. The fuselage center

line lies in the plane of symmetry and is usually defined parallel to the cabin floor. This

angle could be selected to be variable during a flight operation, or be constant

throughout all flight operations. If it is selected to vary during flight, there is no need to

determine wing setting angle for the purpose of the aircraft manufacture. It also reduces

wake turbulence if the correct angle is chosen.

4.2.3 Taper Ratio

Taper ratio () is defined as the ratio between the tip chord (Ct) and the root chord (Cr).

This definition is applied to the wing, as well as the horizontal tail, and the vertical tail.

Root chord and tip chord are illustrated in figure.

= Ct/Cw

The geometric result of taper is a smaller tip chord. In general, the taper ratio varies

between zero and one. The three major platform geometries relating to taper ratio are

rectangular, trapezoidal and delta shape. In general, a rectangular wing platform is

aerodynamically inefficient, while it has a few advantages, such as performance, cost,

ease of manufacture and help reducing wake turbulence.

Fig 4.2 Different type of tapered wings

4.2.4 SWEEP ANGLE

The angle between a constant percentage chord line along the semi-span of the wing

and the lateral axis perpendicular to the fuselage centerline (y-axis) is called leading

edge sweep (LE). The angle between the wing leading edge and the y-axis of the

aircraft is called leading edge sweep (LE). Similarly, the angle between the wing

trailing edge and the longitudinal axis (y-axis) of the aircraft is called trailing edge sweep

(TE). In the same fashion, the angle between the wing quarter chord line and the y-

axis of the aircraft is called quarter chord sweep (C/4). And finally, the angle between

the wing 50 percent chord line and the y-axis of the aircraft is 50 percent chord sweep

(C/2).

4.3 ACCESSORIES

To keep Wake turbulence to the minimum, a number of different accessories are

employed on the wings. These are-

4.3.1 STRAKE

A strake (also known as a leading edge extension) is an aerodynamic surface generally

mounted on the fuselage of an aircraft to fine-tune the airflow and to control the vortex

over the wing. In order to increase lift and improve directional stability and

maneuverability at high angles of attack, highly swept strakes along fuselage fore-body

may be employed to join the wing sections.

16

4.3.2 FENCE

Stall fences are used in swept wings to prevent the boundary layer drifting outboard

toward the wing tips. Boundary layers on swept wings tend to drift because of the

spanwise pressure gradient of a swept wing. Swept wing often have a leading edge

fence of some sort, usually at about 35 percent of the span from fuselage. The cross-

flow creates a side lift on the fence that produces a strong trailing vortex. This vortex is

carried over the top surface of the wing, mixing fresh air into the boundary layer and

sweeping the boundary layer off the wing and into the outside flow. The result is a

reduction in the amount of boundary layer air flowing outboard at the rear of the wing.

This improves the outer panel maximum lift coefficient.

4.3.3 VORTEX GENERATOR

Vortex generators are very small, low aspect ratio wings placed vertically at some local

angle of attack on the wing, fuselage or tail surfaces of aircraft. The span of the vortex

generator is typically selected such that they are just outside the local edge of the

boundary layer. Since they are some types of lifting surfaces, they will produce lift and

therefore tip vortices near the edge of the boundary layer. Then these vortices will mix

with the high energy air to raise the kinetic energy level of the flow inside the boundary

layer. Hence, this process allows the boundary layer to advance further into an adverse

pressure gradient before separating. Vortex generators are employed in many different

sizes and shapes.

Most of todays high subsonic jet transport aircraft have large number of vortex

generators on wings, tails and even nacelles. Even though vortex generators are

beneficial in delaying local wing stall, but they can generate considerable increase in

aircraft drag. The precise number and orientation of vortex generators are often

determined in a series of sequential flight tests. For this reason, they are sometimes

17

referred to as aerodynamic afterthoughts. Vortex generators are usually added to an

aircraft after test has indicated certain flow separations. In Northrop Grumman B-2A

Spirit strategic penetration bomber utilizes small, drop-down spoiler panels ahead of

weapon bay doors to generate vortexes to ensure clean weapon release. It is major

component in reducing the impact Wake Turbulence.

Fig 4.3 Vortex Generator in action in an aircraft wing.

18

CHAPTER 5

DESIGN ANALYSIS AND RESULTS

5.1 INTRODUCTION

In this chapter we will cover the experimental analysis of the Unsteadiness in aircraft

structure due to wake turbulence, we will analyze and calculate the ideal dimensions to

build a General Aviation Aircraft and calculate its lift distribution with the help of

MATLAB m-file.

5.2 DESIGN ANALYSIS AND SAMPLE CALCULATIONS

To make a General Aviation Aircraft we will be taking a model aircraft that has a

monoplane high wing and employs a split flap. Then the lift distribution will be calculated

by creating a MATLAB m-file. The values used will be-

S=Wing Area= 25 m2,

AR =Aspect Ratio= 8

=Sweep Angle= 0.6

iw =Wing Incidence= 2 deg

t =Twist Angle= -1 deg

Airfoil section: NACA 63-209

Altitude= 5000m

Speed=180 knot

20

From the Cl- graph we find that 0=Angle of attack= -1.5 degree

And Cl= The lift curve= 6.3 1/rad

The application of the lifting-line theory is formulated through the following MATLAB m-

file i.e.-

clc

clear

N = 9; % (number of segments - 1)

S = 25; % m^2

AR = 8; % Aspect ratio

lambda = 0.6; % Taper ratio

alpha_twist = -1; % Twist angle (deg)

i_w = 2; % wing setting angle (deg)

a_2d = 6.3; % lift curve slope (1/rad)

alpha_0 = -1.5; % zero-lift angle of attack (deg)

b = sqrt(AR*S); % wing span (m)

MAC = S/b; % Mean Aerodynamic Chord (m)

Croot = (1.5*(1+lambda)*MAC)/(1+lambda+lambda^2); % root chord (m)

theta = pi/(2*N):pi/(2*N):pi/2;

alpha=i_w+alpha_twist:-alpha_twist/(N-1):i_w; % segment's angle of attack;

z = (b/2)*cos(theta);

21

c = Croot * (1 - (1-lambda)*cos(theta)); % Mean Aerodynamics Chord at each segment

mu = c * a_2d / (4 * b);

LHS = mu .* (alpha-alpha_0)/57.3; % Left Hand Side

% Solving N equations to find coefficients A(i):

for i=1:N

for j=1:N

B(i,j) = sin((2*j-1) * theta(i)) * (1 + (mu(i) * (2*j-1)) / sin(theta(i)));

end

end

A=B\transpose(LHS);

for i = 1:N

sum1(i) = 0;

sum2(i) = 0;

for j = 1 : N

sum1(i) = sum1(i) + (2*j-1) * A(j)*sin((2*j-1)*theta(i));

sum2(i) = sum2(i) + A(j)*sin((2*j-1)*theta(i));

end

end

CL = 4*b*sum2 ./ c;

22

CL1=[0 CL(1) CL(2) CL(3) CL(4) CL(5) CL(6) CL(7) CL(8) CL(9)];

y_s=[b/2 z(1) z(2) z(3) z(4) z(5) z(6) z(7) z(8) z(9)];

plot(y_s,CL1,'-o')

grid

title('Lift distribution)

xlabel(Semi-span location (m))

ylabel (Lift coefficient)

CL_wing = pi * AR * A(1)

Fig 5.1 The lift distribution of the wing as an output of the m-file.

23

Note, the distribution in this wing is not elliptical. The total lift coefficient of the wing is

CL = 0.268. The lift that will be generated by this wing is:

5.3 RESULTS

The wing needs some modification (such as increasing wing twist) to produce an

acceptable output. The more Ideal the wing the less wake turbulence will be

experienced by it and more feasible it will be. Hence increasing the usability.

24

CHAPTER 6

CONCLUSION AND INFERENCE

6.1 CONCLUSION

Thus in this study of unsteadiness in aircraft structure we studied that the wake

turbulence in an aircraft that is created by the wing vortices and can be a very

dangerous thing for the pilots as it makes the plane unsteady due to which it can lead to

problems in flying. There is no possible way to avoid this but only can be avoided by

going in circle. If wake turbulence occurs then the pilot should be trained to handle it in

an appropriate manner. We have also calculated lift distribution of a General Aviation

Aircraft using MATLAB and creating a m-file.

.

6.2 INFERENCE

This study mainly focused at studying and understanding of the unsteadiness in wake

vortices by studying all the current research done on this topic that has been gained by

theoretical analysis of model vortex flows and also from the already existing

experimental investigation of representative trailing Wakes that have already been done

by people and this paper tells about the different kind of unsteadiness that can occur

due to elasticity, turbulences and fluid mechanics. But the main concentration of the

study is on Wake turbulence and how it can effect the steadiness of aircrafts and the

reason why it is a hazard in real life. Also we have calculated the lift distribution of a

General Aviation Aircraft by using MATLAB and creating a m-file on it.

25

REFERENCES

[1]^ http://www.faa.gov/training_testing/training/media/wake/04SEC2.PDF.

[2] A. Betz, Verhalten von Wirbelsystemen, Z. Ang. Math. Mech. 12

(1932) 164174.

[3] Barkley, R. Henderson, Three-dimensional oquet stability analysis of

the wake of a circular cylinder, J. Fluid Mech. 322 (1996) 215241.

[4] S.C. Crow, Stability theory for a pair of trailing vortices, AIAA

J. 8 (12) (1970) 21722179.

[5] J.D. Crouch, Instability and transient growth for two trailing vortex

pairs, J. Fluid Mech. 350 (1997) 311330.

[6 ] W.J. Devenport, M.C. Rife, S.I. Liaps, G.J. Follin, The structure and

development of a wing tip vortex, J. Fluid Mech. 312 (1996) 67106

[7] Herbst WB. Future fighter technologies. J Aircr 1980; 17(8):5616.

[8] Orlik-R.uckemann KJ. Aerodynamics ofmanoeu vring aircraft. Can Aeronaut Space J

1992;38(3):10615.

[9] Kalviste J. Aircraft stability characteristics at high angles of attack. AGARD-CP-235,

Paper #29, 1978.

[10] Evans C. An investigation oflarge amplitude wing-rock. Aeronaut J

1984;88(873):517.

[11] Orlik-R.uckemann KJ. Aerodynamic aspects ofaircraf t dynamics at high angles

ofattack. J Aircr 1983;20(9):73752.

[12] Orlik-R.uckemann KJ. Dynamic stability testing ofaircraft needs versus

capabilities. Prog Aerosp Sci 1975;16(4):43147.

[13] Brown CE, Michael Jr. WH. Effect of leading-edge separation on the lift of a delta

wing. J R Aeronaut Sci1954;21:690706.

26

[14] Hummel D, Srinivasan PS. Vortex breakdown effects on the low speed

aerodynamic characteristics of slender delta wings in symmetrical flow. J RA"eronaut

Soc 1967;71:31922.

[15] Wentz WH. Wind tunnel investigations of vortex breakdown on slender sharp-

edged wings. PhD thesis, University Of Kansas, June 1968.

[16] www.wikipidea.org

[17] Wing Design; by Mohammad Sadraey Daniel Webster College.

[18] Tiffany, S. H., and Adams, W. M., Jr., Fitting Aerodynamic Forces in the Laplace

Domain: An Application of a Nonlinear Nongradient Technique to Multilevel Constrained

Optimization, NASA TM 86317, Oct. 1984.

[19] Dunn, H. J., An Analytical Technique for Approximating Unsteady Aerodynamics in

the Time Domain, NASA TP-1738, Nov. 1980.

[20] Karpel, M., Multidisciplinary Optimization of Aeroservoelastic Systems Using

Reduced Size Models, Journal of Aircraft, Vol. 29, No. 5, 1992,pp. 939946.

[21] Poirion, F., Modelisation Temporelle des Syst`emes Aeroservo-elastiques.

Application `a l Etude des Effets des Retards, La Recherche Aerospatiale, Vol. 2,

1995, pp. 103114.

[22]Poirion, F., Multi-Mach Rational Approximation to Generalized Aerodynamic

Forces, Journal of Aircraft, Vol. 33, No. 6, 1996, pp. 11991201.

[23]Winther, B. A., Goggin, P. J., and Dykman, J. R., Reduced-Order Dynamic

Aeroelastic Model Development and Integration with Nonlinear Simulation, Journal of

Aircraft, Vol. 37, No. 5, 2000, pp. 833839.

[24]Cotoi, I., and Botez, R. M., Method of Unsteady Aerodynamic Forces

Approximation for Aeroservoelastic Interactions, Journal of Guidance,Control, and

Dynamics, Vol. 25, No. 5, 2002, pp. 985987.

27

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< 1% match (Internet from 14-Feb-2014) http://ftp.cbi.pku.edu.cn/pub/database/hssp/1mzr.hssp

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< 1% match (Internet from 20-Sep-2013) http://ftp.cbi.pku.edu.cn/pub/database/hssp/1gwn.hssp

11

< 1% match (publications) Bokor, Shaun(Swaffield, JA and Wakelin, RHM). "Correlation of laboratory and installed drainage system solid transport measurements", Brunel University School of Engineering and Design PhD Theses, 2012.

Documents

Unsteadiness in Aircraft Design