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The Aims of the thesis: Develop a method to determine the AC of a FO from measured MPs in experiment, The method is based on a mathematical model describing the motion dynamics of FO in

MAI DUY PHUONG

DEVELOP A METHOD TO DETERMINE THE

AERODYNAMIC CHARACTERISTIC OF FLYING OBJECT

AS A BASIS FOR CALIBRATION ACCORDING TO RECORDED MOTION PARAMETERS

Major: Mechanical engineering

Code: 9.52.01.01

SUMMARY OF DOCTORAL DISSERTATION

Hanoi, 2018

THE STUDY COMPLETED AT ACADEMY OF MILITARY SCIENCE AND TECHNOLOGY – MINISTRY OF NATIONAL DEFENCE

Scientific Advisors:

1 Assoc Prof PhD Pham Vu Uy

2 Prof Ph.D Nguyen Duc Cuong

Reviewer 1: Prof Ph.D Vu Duy Quang

Hanoi University of Science and Technology

Reviewer 2: Assoc Prof PhD Nguyen Minh Xuan

Military Technical Academy

Reviewer 3: Assoc Prof PhD Trinh Hong Anh

Academy of Military Science and Technology

The Thesis is defenced at Doctoral Committee at Academy of Military Science and Technology , date 2018

The dissertation can be found at:

- Library of the Academy of Military Science and Technology

- National Library of Vietnam

INSTRUCTION

The Urgency of the topic: Determining the aerodynamic

characteristics (ACs) of a flying object (FO) is a real necessity A general purpose of many research topics, design and manufacture of

FO Determining the ACs of FO most accurately from the motion parameters (MPs) in experiments applied to the research, design, manufacture of FO, support for improvement , upgrading some types

of FO in equipment is needed

The Aims of the thesis: Develop a method to determine the AC of

a FO from measured MPs in experiment, The method is based on a mathematical model describing the motion dynamics of FO in space

Research content: Establish the relationship between the MP in

space and the AC of the object through the inverse equations Verify the results of the research on a theoretical model and apply research results to determine some ACs for a particular type of FO

Object and scope of the study: The research model is a classical

FO, fixed wing, equipped with dynamic system, aerodynamic coefficients, theoretical ACs, experimental MPs, dynamic parameters and the dynamic equations describes motion of a FO in space

Rerearch Methods: Combining the research methods of

theoretical calculations with experimental studies

Scientific signifiance of the thesis: Applying general knowledge

and ensure rigorously in conceptualization, reasoning, interpretation and building program and algorithm

Practical significance of the thesis: The results of the thesis can

be applied to the topics in our country Meet practical needs in the experimental field, create a tool to support calculations, data process, expand knowledge of specialized software, and use them as a useful

tool, high reliability, low cost, fast and efficient

The thesis consists of Introduction, Conclusion and 4 chapters that are presented in 126 pages and appendix

Chapter 1 OVERVIEW OF DETERMINATION AND

IDENTIFICATION AC OF FO 1.1 Determination of AC in designing, manufacturing and testing of FO

In order to improve the quality of flight control, it is necessary to have a precise method of accurately determining the real ACs of FO

- a mandatory step that can not be ignored with any FO design project

Fig 1.1 A process FO design, manufacture and experiment The research, design, manufacture and experiment of FO can be done in a project and divided into several phases Determining the ACs of FO is carried out throughout the entire process before, during and after manufacture The method of determining the ACs of each type of FO in each stage may vary The above points confirm the significance, the importance of ACs in the research, design, manufacture of FO

1.2 Research situation in abroad

For advanced countries in the world, the process of designing and

manufacturing FO has developed into an industry Theoretical foundations include design, fabrication, testing, including the identification of ACs that have been thoroughly researched However, the study of FO is often in the field of military defence so very little publicity and dissemination as some other science Especially technology, algorithms, solutions and techniques

1.3 Research situation in Vietnam

There have been many researches on design, manufacture of FO However, due to the limited technology infrastructure, the problems

of research, calculation and design are mainly based on the tools and methods of classical calculations We are in the early stages of adopting new tools In general, the research in Vietnam has not shown how to solve problems in the solution and research of the thesis content

1.4 Overview of methods to determine the AC of FO

It is possible to classify the method of calculating the AC in two forms:

- Theoretical calculation methods include analytical methods and numerical methods

- Experimental method: consists of model test in wind tunnel and flight test

1.5 Problems and research solution of the thesis

There are not many scientific researchs, breakthrough solutions, technical solutions and measurement technology, apply modern computational tools in the implementation, establish a calculation base that determines the ACs of FO through MPs measured during work, test, exploitation and use of FOs

Research solution of the thesis:

The experimental MPs reflect the physical elements of the object, the MPs can be measured by modern measuring tools, they are simply as angles, space coordinates This thesis selects the method of using the recorded experimental MPs combined with the mathematical model which is inverse motion equations in space to determine the ACs of FO

In order to implement the above research problems, it is necessary

to construct a system of inverse problem and to have the method of solving that problem and to have the method of dealing with the result of the inverse problem In the field of robotics, automation, many studies have applied the method of solving the inverse problem

to study kinetic or dynamics problems However, up to now, there have been no researches on solving the aerodynamic equations by the inverse method

CONCLUSION OF CHAPTER 1

- This is an important issue that attracts the attention of scientists around the world Especially with our country, this is an important, very new issue and almost not interested in research

- Flight test using advanced measuring tools to measure MPs, incorporating advanced calculation methods, opens new possibilities for determining ACs of FO It enables the expansion and improves the effective of determining the ACs of FO in the testing, using or improvement of aircraft

Chapter 2 THEORY BASIS TO DETERMINE THE AC OF FO

ACCORDING TO FLIGHT TEST RESULT

2.1 Concepts Give some concepts and technical term

2.2 Forward problem Mandatory in design of FO is to solve the

equations of motion in space, that is referred to as forward problem

in the thesis Purpose of the forward problem solving is to determine the moving parameters, from which we can make preliminary assessment and evaluate of design and calculation

Fig 2.3 Forward problem architecture Forward problem can be describled via 12 differential equations (1-12) and 3 transcendental trigonometric equations (13-15) [2]:

1 F Pcos cos X Gsin

cos

sinsincoscos

sin

G Z

a a

k

−

−

++

a a

k

Z Y

P dt

cossincossin

sincos

cossincoscoscoscossin

cos

cos

cossincossinsincossin

sin

cos

coscoscossincos

sin

+

−+

sinsincoscossincossincos

Therein: G - weight of FO [N]; Vk - ground speed [m/s]; S - characteristic area [m2]; ba - characteristic length [m]; α, β, γa - angles of attack, slide and tilt [degree]; Ψ, θ - angles of direction and trajectory tilt [degree]; ψ,  , γ - angles of yaw, pitch, roll [degree];

ωx, ωy, ωz: angle speeds in body coordinates [degree/s]

To solve the forward problem, we need to determine 3 groups of parameters:

- Dynamics parameters: 3 components of aerodynamic force Xa,

Ya, Za in speed coordinates and 3 components of aerodynamic torque

Mx, My, Mz They represent all the ACs of FO in each specific flight condition

- Control parameters: They can be measured under CLDC, CLH,

CL

 control angles, which in turn elevator [degree]; rudder [degree]; aileron [degree] and thrust of engine P [N] The thesis does not study and determine the thrust of engine and considerates as a known value

- Mass charateristics of FO:

m: mass of FO [kg]; Jx, Jy, Jz: inertia momentums of FO [kg.m2] This thesis is concerned with dynamic parameters Which are determined from ACs of FO

Due to ACs determining is taken during the design period, it is usually used calculation or wind tunnel method Thus, the results of

the forward problem and the measurement results in actual flight test always exist errors

2.3 Develop a method to determine the ACs of FO

The forward problem is combined together with other objects and relationships with the experimental groups:

Fig 2.4 The basis of the method to determine ACs

There are two methods of determining ACs as bellow:

Direct comparision method:

Survey theoretical and experimental results by directly comparing the results of the theoretical MPs of the forward problem with the measured MPs from the experiment

The direct method is difficult and complex, the thesis will not follow this method

Indirect comparision method:

Using 6 experimental dynamics parameters as intermediate parameters to determine the ACs of FO These parameters are three components of the aerodynamic forces Xa, Ya, Za, and three aerodynamic torque Mx, My, Mz appear in the equations (2.1)

The thesis is done indirectly method Therefore, it is necessary to solve two problems: the inverse problem and the experimental

statistics problem In addition to the above two problems, a number

of related issues are described in Figure 2.5 and specific contents are presented in the following sections

Fig 2.5 Determination of ACs Indirect method does not limit the state of motion, flexibility, can investigate all cases of motion of FO and has ability to determine all the ACs of FO So indirect method has more advantages than direct method or method of creating basic flight test

The thesis determines ACs by indirect method In order to implement this method, there are two main problems have to be solved: inverse dynamic problem and experimental statistics problem

2.4 Establish the inverse dynamics problem and solving method 2.4.1 The basis of the problem

Fig 2.6 Inverse problem architecture The purpose of the inverse problem is to determine the 6 experimental dynamic parameters, from measured experimental MPs, the mass characteristics and the thrust of FO In the thesis this

is referred to as the reverse dynamic problem or reverse problem The inverse problem allows identify of 15 variables Xa, Ya, Za,

Mx, My, Mz, Vk, θ, Ψ, ωx, ωy, ωz, α, β, γa

The reverse problem plays very important role: It allows

identify angle MPs α, β, γa - these are parameters associated with ACs, these parameters can not be measured during flight, they are only determined through the calculation process Because of the determination of these parameters, so continue to open the direction

of the next study of this thesis

2.4.2 Assumptions

Only consider FOs with classical type, fixed wing, flying in standard atmospheres; Measured data are applied to noise-canceling, smoothing and dividing by suitable time step This data ensures sufficient information and required precision for processing of

movement; The actuator, the steering system is considered the ideal elements, no latency, instant response to the controllers; The thrust of the engine is the known parameter, it dependents on the speed of FO and the height relative to the ground Thrust vector P

coincides with the Ox axis of the body coordinate, the thrust does not produce other torque components; Ignore disturbances, errors of sensor parameters, wind effects, meteorological factors, curvature of the earth

2.4.3 Establish the inverse problem

In experiment, six time-dependent MPs can be measured: 3 coordinate parameters x, y, z and 3 angle parameters ψ, , γ - these are the solution to the forward problem From equations (2.1), It is possible to permute 6 dynamic parameters with 6 MPs, when the input parameters are the experimental MPs and the result is the dynamic parameters Then we will get the inverse problem (2.18) When solving the inverse problem, we need to solve simultaneously the transcendental trigonometric equations (2.2)

tan

12

cos sin

11 cos

sin cos

10

sin cos 9.

sin

8 cos

cos

7

6.

5.

4.

cos cos

sin

cos sin cos sin

sin

3

cos sin

cos

sin sin cos cos

sin

2

sin cos

x

z y

z y

k k

k

z z y x x y z

y y z x z x y

z y y z x

k a

a a a

a a

k a

a a a

a a

k a

z V

y V

x V

J J

J

M

J J

J M

J J

J M

V m Z

Y

P

V m G

Z Y

P

V m G

X P

(2.18)

2.4.4 Building algorithm for solving the inverse problem

For convenience, build into functions and procedures separately

a diff1(); b sol_eqs1();

c diff2(); d sol_eqs2();

e sol_transcen_eqs1()

Fig 2.8 Algorithm for solving the inverse problem

2.5 Develop a method to determine the ACs of FO on the basis of applying the results of the reverse problem

Purpose: From the experimental dynamic parameters determined

by the inverse problem, together with the control, develop a method

to determine the ACs of FO

z z CLDC z

z z

z

a a

y y CLH y

y

y

a a

x x CLH x

CL x x

x

CLH z

z

a

a z y CLDC y

y y

a

x x

a

b S V V

b m m

m

m

M

b S V V

b m m

m

M

b S V V

b m m

m m

M

S V C

C

Z

S V V

b C C

C

C

Y

S V C

C

X

z CLDC

y CLH

x CLH

CL CLH

z CLDC

.2

.2

.2

2

2

.2

2 0

2

2 2

2 0

2 2 0

2.5.2 Building method for determining the ACs of FO

There are two method can be applied to solve this problem:

- Reduce variable: so that the number of remain variables equals the number of equations This method is simple, but only a few simple ACs can be determined, and the test flight required to follow the basic flight test

- Increase the number of equations: Each equation is expanded into a first-order equations The solvable condition is that the variables (or ACs) must be constant in the equations, the number of equations being at least equal to the number of variables Each equation is a set of experimental data This is an experimental statistics method The dissertation follows this method

Experimental system of equations:

X

2

2 2

2

i Mj

i i

a zi y CLDCi y

j j y y

V

b C C

C C

i Mj

i CLHi z

j j

.

i a i i

a xi x CLHi x CLi x j x

V

b m m

m m

i a i i

a yi y CLHi y

j y

V

b m m

.

i a i i

a zi z CLDCi z

j z z

V

b m m

m m