本論文在於探討如何使一架飛機的飛行軌跡持續繞圈於固定路徑上，並且讓這個路徑成為一個垂直方向的圓圈。在此研究中，是以飛機的運動方程式作為模型加以討論，考慮飛機由平飛的情況下開始上述的飛行動作。一般而言，飛機在作縱向動作時，其運動皆以油門與升降舵一起控制，但於本研究中，將在不改變油門，指憑藉升降舵操作的條件下，探討是否能達到此目的。在這個研究裡，我們將分析不同的升降舵指令對飛行軌跡所造成的影響，並計算在上述的飛行動作中，所需之升降舵變化量、攻角變化量、速度變化量、姿態角變化量，和所承受之向心力。藉由觀察不同初始速度條件下，上述諸量的變化，以及其相互的關連性，我們希望在對這個飛行軌跡動作作深入的了解。

The maneuver of an aircraft into an aerobatic repeated vertical loop motion is analyzed. Computer simulations of the maneuver will be conducted based on the longitudinal equations of motions of an example aircraft. Starting form a steady level flight of some pre-selected initial speed, the simulated maneuver is triggered through the application of an elevator command. The elevator command will be generated by an elevator control law. Through out the maneuver, a constant throttle will be maintained. The synthesis of an appropriate elevator control law to achieve the sought maneuver is the main theme of this research. The trajectories of the aircraft under the synthesized control law and different initial flight speeds will be recorded and analyzed for a full understanding of this automatic aerobatic aircraft motion.

[1] Neil Williams, Aerobatics, Airlife Publications, 1975

[2] Robert C. Nelson, Flight Stability and Automatic control, McGraw-Hill, 1989

[3] 陳正宗，國立成功大學航空太空工程學系飛行動力學上課講義
http://www.iaa.ncku.edu.tw/%7Ejthchan/飛行動力學.htm

[4] Etkin, B. and Reid, L. D., Dynamics of Flight Stability and Control, John Wiley & Sons, Inc.,1996

[5] Stengel, Robert F., Flight Dynamic Princeton University Press, 2004