現今大型航空器的使用及生產已趨於成熟，所以翼尖渦流的影響也越來越受到重視，但在現今的法規中，僅用較為寬鬆的法規來制定飛行器之間的安全飛行距離。本研究最主要的目的，是藉由所新定義的WV參數來找出最佳的閃避軌跡，以訂出更為嚴謹的安全飛行間距。
    第一步我們使用MATLAB來建立不同大小的翼尖渦流，並且從參考文獻中選擇二架不同大小的飛行器做為受影響的飛行器，使用剛體運動方程式建立飛行模型，並用四階的Runge-Kutta解法來解飛行力學方程式，以求得飛行器受到翼尖渦流後應有的飛行姿態及飛行軌跡。
    其次，我們所建立一新的WV參數，其中分別為第一項，風場對於垂直運動的危害程度，第二項為風場對於水平運動的危害程度，第三項為風場對於旋轉運動的影響。在之前所計算出的飛行姿態及飛行軌跡，將其轉變為WV參數，這可以將翼尖渦流對於飛行器的影響做參數化的研究。
    最後，為了要求出飛行器在翼尖渦流中的最佳逃離飛行軌跡，我們使用最佳化的方法來求解，我們所選用的方法為基因演算法(GA)。在本論文中所採用的基因演算法是實數型基因演算法，理由是實數型的基因演算法的計算效率較高，且對系統的環境要求較不嚴苛。本文中所訂定的目標函數有二：其一是WV參數值，其二是三個方位角大小限制，分別針對飛行安全與同時考慮飛安和飛行品質二者。用上述的兩種方法求兩個目標函數的最小值即為最佳飛行軌跡。
    本研究中此方式所找出之最佳飛行軌跡，能逹到飛行安全及飛行舒適的二項要求，並且能有效的減少飛行間距，使得越來越繁忙的空中交通得到舒緩。

In modern airline’s operation, the larger aircraft’s procreation and usage is a common practice. So the influence of wake vortices is more important upon flight safety. But the rules of flight separation distance are legislating somewhat outdated. In our study, the principal purpose is use the newly created WV-factor to find the optimum flight trajectory, so that the separation distance between two flights could be greatly reduced.
    First, we use the MATLAB tool to create three kinds of wake vortices, and two aircrafts (major transport and business jet) are chosen to regard as the aircraft that encounter the wake vortices. And the classical rigid body, mass/mass distribution fixed flight dynamics equations are solved by standard 4th order Runge-Kutta method. It can found the flight path and flight posture when the aircrafts encounter the wake vortices.
    Secondly, we are inventing a new factor, the WV-factor. In this factor, it has three parts. First part is the harm of vertical direction of the wake vortices, second part is the harm of horizontal direction of the wake vortices, and third part is the harm of rotation motion of the wake vortices. Thus we could implement this new factor to fully investigate the effects of the flight path and flight posture when aircraft encounter wake vortices.
    Finally, in order to achieve an optimum flight trajectory of wake vortex, a steering tool has been employed, namely, the genetic algorithm. In our work the real-value GA approach is chosen due to its computation efficiency and the similarity to the natural world. Our GA process is implemented as follow: both WV-factor and Euler angle values are assigned as the objective functions. The optimum flight trajectory thus computed is conforming to flight safety and flight comfort. It is believed that the concepts and procedures developed will be effective to reduce flight separation distance, and increase the airline’s operation efficiency.

Contents

Chapter                                                Page
中文簡介	I
ABSTRACT:	II
FIGURE OF CONTENTS	IV
TABLE OF CONTENTS	VI
1.	INTRODUCTION	1
2.	MODELING	6
2.1.	WAKE VORTEX MODELING	6
2.2.	FLIGHT SIMULATION	8
Coordinate System	8
Moment equation	10
2.3.	WV-FACTOR	13
2.4.	GENETIC ALGORITHM [17][18][19]	15
Elitism	17
Crossover	18
Mutation	18
3.	RESULTS AND DISCUSSION	19
3.1.	INITIAL FLIGHT CONDITIONS	19
3.2.	CALCULATE TRIM CONDITIONS	20
3.3.	CALCULATE WV-FACTOR WITHOUT G.A.	20
3.4.	AVOIDANCE STRATEGY	25
3.5.	CALCULATE OPTIMUM FLIGHT TRAJECTORY	26
4.	CONCLUSION	32
REFERENCES	34
APPENDIX I	37
APPENDIX II	47
APPENDIX III	57
APPENDIX IV	61

 Figure of Contents

Figure                                                 Page
FIG. 2.1 VORTEX FLOW TAKEN FROM HTTP://LAVA.LARC.NASA.GOV/IMAGES/SMALL/EL-1996-00130.JPEG	7
FIG. 2.2 IT WAS SHOW THE THREE KINDS OF WAKE VORTEX	8
FIG. 2.3 EARTH-FIXED COORDINATE SYSTEM	9
FIG. 2.4 BODY AXES COORDINATE SYSTEM	9
FIG. 2.5 WIND AXES COORDINATE SYSTEM HTTP://HISTORY.NASA.GOV/SP-367/F166.HTM	10
FIG. 2.6 PROCESS OF GENETIC ALGORITHM	17
FIG. 3.1 IT IS SHOWN TREE DIFFERENT WAKE VORTICES THAT WE USED IN THIS PART.	21
FIG. 3.2 (A) THE POSITION OF 19-PERSON BUSINESS JET ENCOUNTER WAKE VORTEX AT THE ORIGIN. (B) THE POSITION OF 19-PERSON BUSINESS JET ENCOUNTER WAKE VORTEX AT THE RIGHT. (C) THE POSITION OF 19-PERSON BUSINESS JET ENCOUNTER WAKE VORTEX AT THE LEFT.	23
FIG. 3.3 THE WV-FACTOR OF  =2500 FT/SEC2 AND K=5 FT-2	24
FIG. 3.4 THE WV-FACTOR OF  =4000 FT/SEC2 AND K=40 FT-2	25
FIG. 3.5 IT IS SHOWING US THE TANGENTIAL VELOCITY OF DIFFERENT SEPARATION DISTANCE OF WAKE VORTEX THAT  =1500 FT2/M.	26
FIG. 3.6 THE 3-D FLIGHT PATH OF BOEING 747-100 ENCOUNTER WAKE VORTEX  =1500FT2/SEC AT (0,0)	28
FIG. 3.7 THE 3-D FLIGHT PATH OF BOEING 747-100 ENCOUNTER WAKE VORTEX  =2500FT2/SEC AT (0,0)	28
FIG. 3.8 THE 3-D FLIGHT PATH OF BOEING 747-100 ENCOUNTER WAKE VORTEX  =1500FT2/SEC AT(-16.4,0)	29
FIG. 3.9 THE 3-D FLIGHT PATH OF BOEING 747-100 ENCOUNTER WAKE VORTEX  =2500FT2/SEC AT (-16.4)	29
FIG. 3.10 THE 3-D FLIGHT PATH OF 19-PERSONE BUSINESS JET ENCOUNTER WAKE VORTEX  =1500FT2/SEC AT (0,0)	29
FIG. 3.11 THE 3-D FLIGHT PATH OF 19-PERSONE BUSINESS JET ENCOUNTER WAKE VORTEX  =2500FT2/SEC AT (0,0)	30
FIG. 3.12 THE 3-D FLIGHT PATH OF 19-PERSONE BUSINESS JET ENCOUNTER WAKE VORTEX  =4000FT2/SEC AT (0,0)	30
FIG. 3.13 THE 3-D FLIGHT PATH OF 19-PERSONE BUSINESS JET ENCOUNTER WAKE VORTEX  =1500FT2/SEC AT (-16.4,0)	30
FIG. 3.14 THE 3-D FLIGHT PATH OF 19-PERSONE BUSINESS JET ENCOUNTER WAKE VORTEX  =2500FT2/SEC AT (-16.4,0)	31
FIG. 3.15 THE 3-D FLIGHT PATH OF 19-PERSONE BUSINESS JET ENCOUNTER WAKE VORTEX  =4000FT2/SEC AT (-16.4,0)	31

Table of Contents

Table                                                  Page
TABLE 1.1 KIND OF AIRCRAFT	3
TABLE 1.2 FAA FOR HORIZONTAL SEPARATION REQUIREMENTS (UNIT: MILES)	3
TABLE 1.3 ICAO FOR HORIZONTAL SEPARATION REQUIREMENTS (UNIT: MILES)	4
TABLE 3.1 THE MAXIMUM WV-FACTOR OF DIFFERENT LOCATION THAT AIRCRAFT ENCOUNTER WAKE VORTICES	21
TABLE 3.2 THE MAXIMUM WV-FACTOR OF DIFFERENT WAKE VORTEX	23
TABLE 3.3 THE DISTANCE OF BEHIND AIRCRAFT ENCOUNTER WAKE VORTEX FROM LEAD AIRCRAFT.	27

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