Flight Dynamics Engineering Simulator - An Overview

Development of A Flight Dynamics Engineering Simulator (FDES) at Universiti Teknologi Malaysia: An Overview Shuhaimi Mansor Assoc. Prof. Head of Aeronautical Engineering Laboratory, PhD, PEng MIEM [email protected] Kannan Perumal Postgraduate Research Student, Airline Pilot [email protected] Department of Aeronautical Engineering, Universiti Technologi Malaysia, 81310 Skudai, Johor, MALAYSIA

Abstract This paper provides a brief history of the development of a PC-based flight dynamics engineering simulator facility in Department of Aeronautical Engineering, Universiti Teknologi Malaysia (UTMFDES). The FDES is a simple, easy to use, flexible and user friendly aircraft simulation through the implementation of the classical longitudinal and lateral aircraft equations of motion. FDES allows students to rapidly assess aircraft stability and control parameters and able to give visual representation of the effect of changing the stability derivatives. Currently it is utilized in the flight dynamics and control class for demonstration, research and understanding the basic concepts of flight dynamics, and flying and handling qualities. It has been an effective and efficient teaching and learning tools of basic principles of aircraft dynamics and flight control systems evaluations in a relatively short time. Keywords : Flight Dynamics, Simulation, flying and handling qualities, flight control

1.0 Introduction Flight simulator is a device that is used to simulate the behaviour of an aircraft in flight on the ground. The essence of it is in creating an illusion of reality of an aircraft in flight on ground by which expensive flying time and costs are saved. In has been widely used in the aerospace and aviation industries for commercial and military pilot training, test pilot and flight research activities. PC-based Flight Dynamics Engineering Simulator (FDES) project in UTM started in mid 1995. The motivation for this project was the need to enhance the teaching and the learning process of one of the core and most important subject in aeronautical engineering – Flight Dynamics and Control in a better way. At that point of time the advances in the computer technology and the low cost programming softwares that were readily available in the market encouraged for a simple Head-Up-Display (HUD) simulation. It was also foreseen that such a simple simulator can be used and will help aeronautical engineering students in UTM in understanding the flight dynamics and control system design easily help to make the teaching process more interactive. Few aircraft models were made available with a good numerical and mathematical model using the aircraft equations of motion built in it to represent the behaviour of these particular aircrafts. Students were able to fly any of these aircraft types and appreciate the flying and handling qualities of the aircraft. The project was developed, built, added to and improved upon through five years as a final year undergraduate project. Although the accuracy of the flight simulation was not perfect, but it was un-doubly was a very user friendly and the response was found to be quite realistic. Figure 1 shows the important elements in the development of FDES.

Flight Control System Keyboard Input Equation of Motion

Computer Graphics Output

Joystick Input Aerodynamic Database

Variable Stability Aircraft

Figure 1. Elements of UTM-FDES 2.0 Flight Simulation As its name implies, the objective of flight simulation is to reproduce on the ground the behaviour of an aircraft in flight. The practical value of flight simulation is obvious with the extensive use of the technique in aerospace research and development and by the fact that many flight simulators are in use throughout the world, for training and maintaining the skills of civilian and military aircrew. In research, flight simulators allow designers to explore the implication of different design options without having to incur the expense and delay arising from building and testing a range of prototypes. Flight simulation has provided a means of evaluating the likely behaviour and consequences arising from abnormal operating configurations. Solutions to handling problems associated with deep stall, clear air turbulence and wind shear, have all been worked through with the aid of simulators. The basic structure of flight simulation comprises three parts. These are, a model of the system to be simulated, a device through which the model is implemented and an applications regime in which the first two elements are combined with a technique of usage to satisfy a particular objective. The most usual form of linguistic model encountered in simulation is the mathematical description of the behaviour of a system in terms of a number of equations. A mathematical representation of an aircraft and its dynamic response forms the basic model used with the contemporary flight simulators. [1] For a vehicle flying in the air, the mathematical model is primarily the relationship between the air reactions and the motion of the aircraft relative to the air. Thus, this can be called aerodynamic model. Other external forces and moments arise from engine thrust, the flight controls or external (atmospheric) input such as gust and disturbances. Definitions of all these forces and moments components are the key realistic description of an aircraft’s flight characteristics. Figure 2 shows the detail elements of aircraft mathematical model.

Performance

Dynamics

Engine

Atmosphere

Turbulence

Environment

Ground effect Wings (rotor)

Aerodynamics

Mathematical Model

Aircraft response

Pilot

Tail Undercarriage

Control system

Figure 2. Elements of aircraft mathematical model

3.0 Project Development The initial development of the first prototype for the flight simulator in the Faculty of Mechanical Engineering, UTM started in mid 1995. The flight simulator was developed and enhanced through five final year students as part of their final year project. Many improvements and new features have been introduced in each project. The project development was systematically monitored and supervised in order to ensure the success of the project. Phase I The project was first started by simulating a simple Head-Up-Display (HUD) displaying a ‘gull’ shape aircraft symbol incorporating the basic speed, altitude and heading information. HUD is a projection that allows the pilot to take information from the instruments without taking eye-off from the outside scene. This technology is widely used in the fighter aircraft. The first part of it was to integrate the hardware (a contacless joystick) with the software (Turbo Pascal 7 programming). Simple longitudinal equations of motion were used to represent the dynamics of the aircraft. Then, a simple mathematical model for actuator dynamics and control law was included [2]. Phase II The main concentration of this phase was to improve the aircraft equation of motion by improving the aerodynamic modelling and adding different aircraft type. There are six aircraft models in the program database to be simulated. This function will allow student to experience the flying and handling qualities of different type of aircraft, such as A4D Skyhawk, F104-A, NAVION, Convair 880, Boeing 747 and Jetstar. There are six types of aircraft available in the program database. The main purpose of this type of simulation is to allow the user to feel the flying and handling of different kind of aircraft [3]. The simulation is done using the stability and aerodynamic variable of the aircraft itself [7]. From there, student will be able to understand how the stability derivatives of the aircraft affect the flying and handling qualities of an aircraft. Thus, it is an inherent flying of the aircraft.

The computer codes were made to a modular-type for the ease of management and to be more effective. Capability to use the keyboard as the inceptor to fly the aircraft was also added. Graphics output of the program has been reviewed and improved where the program will run and display HUD graphics with almost the same speed no matter what is the CPU clock speed. Improvement on the HUD display itself was made to a more standard form of HUD symbolic (Figure 3).

30

60

90 60

IAS 300

5000 ALT

Figure 3: Dynamics Demonstration Head-Up-Display Phase III The contactless joystick input was replaced to a normal game joystick. This made the program more users friendly. Real time simulation was attempted by having a reference to CPU clock speed. A Head-Down-Display (HDD) was designed, and meshed with the previous Head-Up-Display (HUD) to create a realistic flight simulator (Figure 4). Several other indicators such as gyroscope and roll and pitch angle were added. Rudder input was added to give more realistic response to lateral motions. Variable stability aircraft model was included to allow user to modify the existing aircraft parameters. The flight dynamics control system was designed to augment the aircraft response, this include the simple pitch rate feedback and PI controller pitch rate error as well as roll rate damper. The second function is the simulation using user-defined variable stability (Figure 5). This is where the users can fly the aircraft created by their own. The meaning of created here does not mean a real aircraft is created, it means the aircraft coefficients and certain dimensions about the aircraft. There are 20 stability coefficients can be inserted by the user in the interface. Another purpose for this type of simulation is that, the user could know what would be the outcome towards the aircraft flying qualities if one of the coefficients is modified. This function is only recommended for advanced user who is expected to have understood the aircraft variable stability well. The derivatives for longitudinal and lateral are editable and this will result the change of aircraft motion. With this, student can see the effect of aircraft motion when any of the derivatives is changed [4].

Figure 4. Main simulation screen

Figure 5: Variable stability aircraft menu (right menu).

Phase IV A new source code for the joystick input was developed in Pascal to give a better control in setting the environment for the joystick hardware interface. The real time simulation was further improved so the program will run at a constant speed regardless of the CPU speed and also the intensity of the graphics [5]. As the flight simulator was aimed to be a teaching and learning tool, modification was done to the program to provide better guidance to guide the student on the handling of the program. At this stage the simulator was complete with four degrees of freedom using linearized aircraft equation of motion. At this stage it allowed the study on the short period and the phugoid motion with the integral controller,

proportional controller and rate control was to be conducted. The third function is the simulation using flight control system. Student can choose from the menu for the desired flight control system that to be applied on the aircraft. At the same time, student may also alter the stability of the aircraft by inserting suitable values for the control gain, damping ratio and natural frequency. There are six flight control systems where student can choose to evaluate. They are: a) b) c) d) e) f)

Simple pitch rate damper. Pitch rate damper using PI controller. Roll angle control system. Roll rate damper control system. Yaw damper control system. Spiral stabilization.

At this stage a complete FDES main program flow chart has been developed shows in Figure 6.

BEGIN

Display type menu

Main Menu

Inceptor Choice

1 = A4D

2 = F104-A

Choice = 1 Joystick

Choice = 2 Keyboard

3 = NAVION Main Menu 4 = Convair 880 5 = Boeing 747

Aircraft Database

Variable Stability Aircraft

Flight Control System

6 = Jetstar HDD Menu

No Indicator

ASI+Altimeter+Turn indicator+Heading

ASI + Altimeter

Real Time Simulation

Start Simulation

All Indicator

Press 1 Press 2

Press Esc Choice = 5

Choice = 6 Choice = 3

Press 3

Choice = 4

Simulation Center

Choice = 2 Choice = 1

Choice = 7

END

Figure 6: Earlier FDES main program flow chart

Help

Phase V Although Turbo Pascal 7.0 is a powerful, integrated applications development software package that includes a compiler, editor and library manager, however since it was interfaced in the DOS mode, there was some limitation in the program handling. This was rectified by reprogramming the simulation using Visual Basic. Previous version of Flight Dynamics Engineering Simulator was programmed using Turbo Pascal language, and the program is in the DOS environment. Thus, there are certain limitations and difficulties when running a program in DOS compared to the windows environment. Therefore, it is the time now for our Flight Dynamics Engineering Simulator to move towards the windows environment, which believed will be more user friendly and easier handling. For that purpose, Visual Basic has been chosen as the programming language to develop the new version of FDES. Although there are other more powerful software to develop windows program, such as C++, Visual C++, Java, Delphi and etc, but Visual Basic has provided enough tools to develop the FDES. Some inaccuracies in the equations of motion, numerical solution, input and output were also corrected. For example, in the previous programs, the simulation of the roll motion is found to be stable but the steady state oscillating periodically with ±25 deg/sec was not giving the desired output. The equations of motion was reviewed and improved to include more detailed derivatives to obtain a better solution. The initial Euler solution was replaced to be more accurate using the Rungga-Kutta numerical solutions. Beside that the graphics was further enhanced to look more realistic with actual aircraft. The symbology, colouring and finer details of the presentation were emphasized. To verify the accuracy of the simulation, a comparison between simulation results and theory using MATLAB was carried out. Finally a more user friendly graphic User Interface (GUI) was created for the aircraft selection and input and output of various parameters. In the previous program, Euler’s Method is used to solve the aircraft mathematical model. Testing was done to compare the output values obtained from the program with the theory values. The theory values were obtained from calculation using MATLAB (Figure 7 and 8). q vs t 120

Solid line – Simulator Dashed line – MATLAB

100

q (deg/s ec )

80

60

40

20

0

-20

0

2

4

6

8

10

12

14

16

18

20

Tim e (s ec )

Figure 7: Pitch rate response for A4-D Skyhawk using Euler’s Method, time step 0.04s.

Solid line – Simulator Dashed line – MATLAB

Figure 8: Comparison of roll rate output using (a) 0.1s, (b) 0.04s and (c) 0.01s time step for Euler’s Method

4.0 Aircraft Equations of Motion and Numerical Solution The equations of motion used in the FDES are a set of linearized equation derived using the small perturbation theory. In applying the small perturbation theory, it is assumed that the motions of the aircraft consist of small deviations about a steady flight condition. Although this theory cannot be applied to problems in large amplitude of motion, it yields sufficient accuracy for practical engineering purposes. The simplicity the equations of motion can be separated into two groups Longitudinal motion and lateral motion with appropriate assumptions in the form of state space equation without coupling between the both longitudinal and lateral derivatives [7]. Longitudinal motion: ⎡Δu& ⎤ ⎡ X u ⎢Δw& ⎥ ⎢ ⎢ ⎥ = ⎢ Zu ⎢Δq& ⎥ ⎢ 0 ⎢ ⎥ ⎢ ⎢⎣Δθ& ⎥⎦ ⎣ 0

Xw Zw Mw

0 u0 Mq

0

1

− g ⎤ ⎡Δu ⎤ ⎡ X δe ⎤ 0 ⎥⎥ ⎢⎢Δw⎥⎥ ⎢⎢ Z δe ⎥⎥ + [Δδ e ] 0 ⎥ ⎢Δq ⎥ ⎢ M δe ⎥ ⎥⎢ ⎥ ⎢ ⎥ 0 ⎦ ⎣Δθ ⎦ ⎣ 0 ⎦

(2.1)

Lateral motion: ⎡Y ⎡Δβ& ⎤ ⎢ β ⎢ ⎥ ⎢ u0 ⎢Δp& ⎥ = ⎢ L ⎢Δr& ⎥ ⎢ β ⎢ ⎥ ⎢N β ⎢⎣Δφ& ⎥⎦ ⎢ ⎣ 0

Yp u0 Lp Np 1

⎛ Y − ⎜⎜1 − r ⎝ u0 Lr Nr 0

⎞ ⎟⎟ ⎠

g cos θ 0 ⎤ ⎡ 0 ⎥ ⎡Δβ ⎤ u 0 ⎥ ⎢ ⎥ ⎢⎢ Δp L 0 ⎥ ⎢ ⎥ + ⎢ δa ⎢ ⎥ Δ r N ⎥ 0 ⎥ ⎢ ⎥ ⎢ δa ⎢ 0 Δφ 0 ⎥⎦ ⎣ ⎦ ⎢⎣

Yδr ⎤ u0 ⎥ ⎥ ⎡Δδ ⎤ Lδr ⎥ ⎢ a ⎥ Δδ N δr ⎥ ⎣ r ⎦ ⎥ 0 ⎥⎦

(2.2)

Numerical method was used to perform the task of integrating the first order differential equation and produce the desired output. There are several numerical analysis methods that can be used such as Euler’s, Runge-Kutta, Milne’s, Hamming’s [6]. All these methods are varying in accuracy, complexity and error produced, depends on the requirement of the user. Initially the Euler’s numerical method was used. The general equation given by Euler’s Method is: y1 = y 0 + hf 0

(2.3)

where h is the constant step size, or the integral of time, dt used in the simulation. Longitudinal motion:

u = u 0 + ( X u u 0 + X w w0 − gθ 0 ) ⋅ dt

(2.4) (2.5) (2.6) (2.7)

w = w0 + (Z u u 0 + Z w w0 + u 0 q 0 + Z δeδe ) ⋅ dt

(

)

q = q 0 + M w w0 + M q q0 + M δeδe ⋅ dt

θ = θ 0 + q0 ⋅ dt

Lateral motion:

β = β 0 + [(Yβ / u 0 )β 0 + (Y p / u 0 ) p0 − (1 − (Yr / u 0 ) )r0 + (g cos θ 0 / u 0 )φ0 + (Yδr δr / u 0 )]⋅ dt

(

)

(2.8) (2.9) (2.10) (2.11) (2.12)

p = p0 + Lβ β 0 + L p p 0 + Lr r0 + Lδa δa + Lδr δr ⋅ dt

(

)

r = r0 + N β β 0 + N p p 0 + N r r0 + N δa δa + N δr δr ⋅ dt

φ = φ 0 + p 0 ⋅ dt ψ = ψ 0 + r0 ⋅ dt

Euler’s method was later replaced by the use 5-stage 4th order Explicit Runge-KuttaMason Method to obtain better accuracy with a times step of 0.1s. The 5-stage 4th order Explicit Runge-Kutta-Mason Method employs the recurrence formula of the form: yn +1 = yn + h

or

5

∑

i =1

bi k i

y n +1 = y n + hb1 k1 + hb2 k 2 + hb3 k 3 + hb4 k 4 + hb5 k 5

(2.13)

where 5 k i = f ⎛⎜ t n + ci h, y n + h ∑ aij k j ⎞⎟ j =1 ⎠ ⎝ 1 a 21 = 3 1 1 a31 = , a 32 = 6 6 1 a 41 = , a 42 = 0 , 8 1 a51 = , a 52 = 0 , 2 1 b1 = , b2 = 0 , 6 1 c1 = 0 , c2 = , 3 h = time step

(2.14)

a 43 =

3 8

a53 = −

3 2

b3 = 0 , c3 =

1 , 3

,

a54 = 2

2 3 1 c4 = 2

b4 =

1 6

,

b5 =

,

c5 = 1

Since the mathematical model for each variable is too complex to be displayed here, only the formulation for forward speed, u is shown. k u ,1 = X u ⋅ u 0 + X w ⋅ wo − g ⋅ θ o

k u , 2 = X u ⋅ (u 0 + h ⋅ a 21 ⋅ k u ,1 ) + X w ⋅ (wo + h ⋅ a 21 ⋅ k w,1 ) − g ⋅ (θ o + h ⋅ a 21 ⋅ kθ ,1 )

k u ,3 = X u ⋅ (u 0 + h ⋅ a31 ⋅ k u ,1 + h ⋅ a32 ⋅ k u , 2 ) + X w ⋅ (wo + h ⋅ a31 ⋅ k u ,1 + h ⋅ a32 ⋅ k w, 2 ) − g ⋅ (θ o + h ⋅ a31 ⋅ kθ ,1 + h ⋅ a32 ⋅ kθ , 2 )

k u , 4 = X u ⋅ (u 0 + h ⋅ a 41 ⋅ k u ,1 + h ⋅ a 43 ⋅ k u ,3 ) + X w ⋅ (wo + h ⋅ a 41 ⋅ k u ,1 + h ⋅ a 43 ⋅ k w,3 )

− g ⋅ (θ o + h ⋅ a 41 ⋅ kθ ,1 + h ⋅ a 43 ⋅ kθ ,3 )

k u ,5 = X u ⋅ (u 0 + h ⋅ a51 ⋅ k u ,1 + h ⋅ a53 ⋅ k u ,3 + h ⋅ a54 ⋅ k u , 4 )

+ X w ⋅ (wo + h ⋅ a 51 ⋅ k u ,1 + h ⋅ a53 ⋅ k w,3 + h ⋅ a54 ⋅ k w, 4 )

− g ⋅ (θ o + h ⋅ a51 ⋅ kθ ,1 + h ⋅ a53 ⋅ kθ ,3 + h ⋅ a54 ⋅ kθ , 4 ) u = u o + hb1k u ,1 + hb2 k u , 2 + hb3 k u ,3 + hb4 k u , 4 + hb5 k u ,.5

Other variables are: w = wo + hb1k w,1 + hb2 k w, 2 + hb3 k w,3 + hb4 k w, 4 + hb5 k w,.5

q = q o + hb1 k q ,1 + hb2 k q , 2 + hb3 k q,3 + hb4 k q , 4 + hb5 k q ,.5

θ = θ o + hb1 kθ ,1 + hb2 kθ , 2 + hb3 kθ ,3 + hb4 kθ , 4 + hb5 kθ ,.5 β = β o + hb1k β ,1 + hb2 k β , 2 + hb3 k β ,3 + hb4 k β , 4 + hb5 k β ,.5 p = p o + hb1k p ,1 + hb2 k p , 2 + hb3 k p ,3 + hb4 k p , 4 + hb5 k p ,.5

φ = φo + hb1kφ ,1 + hb2 kφ , 2 + hb3 kφ ,3 + hb4 kφ , 4 + hb5 kφ ,.5 r = ro + hb1 k r ,1 + hb2 k r , 2 + hb3 k r ,3 + hb4 k r , 4 + hb5 k r ,.5

ψ = ψ o + hb1kψ ,1 + hb2 kψ , 2 + hb3 kψ ,3 + hb4 kψ , 4 + hb5 kψ ,.5

(vertical speed) (pitch rate) (pitch angle) (side-slip angle) (roll rate) (roll angle) (yaw rate) (yaw angle)

5.0 Accuracy of Simulation and Time Step The execution times and accuracies are the two main important factors in the flight simulator. They directly affects the performance FDES. For higher accuracy (real time), smaller time step should be used, however this reduces the execution time. As such a good compromise between both is required. Time step of 0.1s using the Rungga-Kutta method was found to give better accuracy the 0.04s using the Euler method. Figure 10 and 11 show the effect of numerical solutions and time steps on simulation results.

Solid line – Simulator Dashed line – MATLAB

Figure 10: Comparison of roll rate between Runga-Kutta 4th and 5th order for time step 0.04s and input 00.2618 rad

p vs t (RK 5, tim e step 0.1s)

p vs t (RK 5, tim e step 0.2s)

4

4

3

3

2

2

1

1

0

0

2

4

6

0

0

2

p vs t (RK 5, tim e step 0.3s) 4

3

3

2

2

1

1

0

2

4

6

p vs t (RK 5, tim e step 0.5s)

4

0

4

6

0

0

2

4

6

8

10

Figure 11: Comparison of roll rate response using Runge-Kutta 5th order for various time step and input 00.2618 rad.

As a conclusion for the discussion on the execution times and accuracies, if high accuracy is desired in the simulation, smaller time step should be used. But, this will require more execution time because the smaller the time step is used, the more time required to perform the same load of calculation. To obtain the real time simulation, higher time step is required in order to control the total program execution time. The conflict between the time step used and the accuracy of the simulation require some trade-off for optimum simulation result. Table 5.1 and 5.2 summarized the execution time for different numerical method and time step.

\ Table 5.1: Comparison of execution time for different numerical method and time step to obtain 100s simulation time. Time Step, ts (second in simulation time)

Number of loop count for 100s simulation time. (100/ts)

0.04

Execution time for 100s simulation time, t100 (second in real time)

Euler

RK5

2500

7.91

5.17

0.1

1000

-

3.40

0.2

500

-

1.65

0.3

333

-

1.05

Table 5.2: Comparison of one loop execution time for different numerical method and time step Time Step, ts (second in simulation time)

Execution time for one loop [ t100 / number of loop ] (second in real time)

Euler

RK5

0.04

0.003164

0.002068

0.1

-

0.0034

0.2

-

0.0033

0.3

-

0.003153

6.0 Current Status To extend flight simulator’s function further as an engineering analysis tool, user is able to record the output of the simulation so that the response of the stability and control which relates to the flying handling qualities of different aircraft can be analysed. This is achieved by preparing a data recording function during the simulation. START

Advanced Variable Editing (frmVarAdv)

Splash Screen (frmSplash)

View Calculated Variable (frmVarView)

Main Menu (frmMain)

Calculate IAS & Mach (frmVarMach)

END

Type of FCS 1. Pitch Rate Feedback (Simple) 2. Pitch Rate Feedback (P+I Controller) 3. Roll Angle Control 4. Roll Rate Damper 5. Yaw Damper 6. Spiral Mode Stabilization

Select Simulation Type

User-Defined Variables (frmVar)

Selected Aircraft (frmActype)

Flight Control System (frmFcs) Analysis Tool (frmAnalysis)

Main Simulation Screen (frmHUD)

Option 1. Set input value 2. Preset Input 3. HUD Mode

Sim Option (frmOption)

Keys Help (frmHelp1)

Figure 9: Improved FDES main program flow chart

The user interface played an important role for the user to interact with the flight simulator program. The important criteria is that it has to be easy to use and user friendly. Thus, as a learning tool, the simulator has to have a good guidance for the user on the program handling. The new user interface is developed using Visual Basic Programming, which allows program handling in windows environment. With the windows environment, the FDES becomes more user-friendly. Figure 13 to 16 show the current status and the capability of the FDES program which show the important feature such as type of simulation, selection of aircraft and head-up display.

Figure 13 FDES program shows option to select type of simulation and fly with different types of aircraft, and option to save simulation data for analysis.

Figure 14 Calculation of natural frequency, damping ratio and time constant as a function of aerodynamic stability and control derivatives.

Figure 15 Selection of flight control system design.

Figure 16 Latest cockpit and HUD display

7.0 Future Development The suggestions for the future development of FDES are as follows: a) Engineering accuracy: Since the aircraft model of FDES is derived using Small Perturbation Theory, the simulator is only accurate for low or small amplitude of flying performance, that is less than 15 degrees. At the same time, the simulation is done at steady and level flight, where the initial speed is defined as well as the altitude is defined as sea level. b) Addition of non-linear full six degree of freedom (6 DOF) simulation for higher amplitude of motion. For this, non-linear equations of motion need to be developed. At the same time, inclusion of thrust and atmospheric effects. c) The interface and analysis for flight control system need to be improved to a more user friendly one. If possible, include automatic flight control system in the future FDES. With automatic FCS, user can perform more analysis on the dynamics of aircraft. d) Improve the graphics further to represent the actual aircraft display. e) Further improvement on the real time simulation. 8.0 Conclusion It was concluded that PC-based flight simulation can be a valuable tool for illustrating flight dynamics to aeronautical students and can be challenging, interesting and fun. The synergistic learning potential has improved due to more of hands-on experience with FDES and the ease of use has made the course easier to teach, complementing the classical and modern classroom theories. This simple

FDES also serves as a motivation and a starting point for the UTM ambition of a full-scale flight simulator to serve as an engineering, research and instructional tool. References [1]

Rolfe

J

M, Staples

K J, “Flight Simulation”, Cambridge: Cambridge

University Press, 1986. [2]

Perumal K, “Computer Graphic Display of Aircraft Head Up Display (HUD)”, Universiti Teknologi Malaysia: Thesis B. Eng. Mech.(Aero), 1996.

[3]

Yaacob A F, “Aerodynamic Database for Flight Simulator”,

Universiti

Teknologi Malaysia: Thesis B. Eng. Mech. (Aero), 1997. [4]

Ling J W C, “PC-Based Flight Dynamics Engineering Simulato”, Universiti Teknologi Malaysia: Thesis B. Eng. Mech. (Aero), 1998.

[5]

Srinivas B K, “Flight Control System Design Using PC-Based Flight Simulator”, Universiti Teknologi Malaysia: Thesis B. Eng. Mech. (Aero), 1999.

[6]

Ahmad A, “Development of Nonlinear Flight Dynamic Simulation”, Universiti Teknologi Malaysia: Thesis B. Eng. Mech. (Aero), 1999.

[7]

Nelson, R. C. “Flight Stability and Automatic Control”, 2nd Edition. Singapore: McGraw-Hill Book Co., 1998.

[8]

Chua Y Ch, “Application and Modification of Flight Simulator Software”, Universiti Teknologi Malaysia: Thesis B. Eng. Mech. (Aero), 2001.

LIST OF SYMBOLS AND ABBREVIATIONS

x, y, z p, q, r

φ, θ, ψ δe δa δr Utot u,v,w g Xu Xw Yβ Yp Yr Yδr Zu Zw Zδε Lβ Lp Lr Lδa Lδr Mw Mq Mδe Nβ Np Nr Nδa Nδr Ix Iy Iz Ixy Iyz Ixz HUD FAA ALT IAS

-

Rolling, Pitching and Yawing axis. Angular rate of x, y and z axis directions. Roll (bank), Pitch and Yaw (azimuth) angles. Control surface angles (elevator, aileron and rudder). Initial flight airspeed. Airspeed about x, y, z axis. Acceleration due to gravity. Dimensional force derivatives of x-axis due to change in u and w velocities. Dimensional force derivatives of y-axis due to change in β, p, q and δr Dimensional force derivatives of z-axis due to change in u, w and δe Dimensional moment derivatives of x-axis due to change in β, p, r, δa and δr Dimensional moment derivatives of y-axis due to change in w, q and δe Dimensional moment derivatives of z-axis due to change in β, p, r, δa and δr Moment of inertia about x, y and z axis. Product of inertia about xy, yz and xz axis. Head-Up Display Federal Aviation Administration Altitute Indicated Airspeed