【飞行动力学】

1、【飛行動力學】AIRCRAFT DYNAMICS成功大學航空太空工程學系Text book【Flight Stability and Automatic Control】 - NelsonReferences【Aircraft Dynamics and Automatic Control】 - McRuler & Ashkenas【Stability and Control of Airplanes and Helicopter】 - Seckel【Aerodynamics, Aeronautics and Flight Mechanics】 - McCormick【Automatic

2、 Flight Control Systems】 - Donald McLeanFlight Mechanics Course Content2A. Review of dynamics- Derive the basic governing equationof motion (EOM) of an aircraft- Decouple the EOM into a longitudinalmotion and a lateral motionB. Longitudinal motion analysis B.1 Static Longitudinal analysis and elevat

3、or angles for Level flight B.2 Dynamic Longitudinal analysis equations of motionAerodynamic derivatives dynamic analysisthe longitudinal dynamic (I) - Simplified longitudinal motions the longitudinal dynamic (II) - Complete longitudinal analysistC. Lateral motion analysis C.1 Linearization of the la

4、teral EOM C.2 Static lateral analysis C.3 Lateral-directional aerodynamic Derivatives lateral derivatives C.4 Dynamic lateral analysis eristics of lateral dynamics Appendix: Taylor series expansion of analytic function 13【課前預習】 - 請於下週上課前預習下列項目1. 基本動力學(I)，有關牛頓運動定律的問題。2. 基本動力學(II)，有關靜態穩定/不穩定以及動態穩定/不穩定

5、等的定義。3. 基本向量數學(I)，有關一個旋轉座標中之向量的微分問題，如：假設為定義於座標之向量，而且座標之旋轉速度為，則對於慣性座標之微分定義為。4. 基本向量數學(II)，有關向量外積的定義，如： 若及，則可寫為，因此。5. 基本工程數學，如常係數微分方程式之求解、線性函數之拉普拉斯轉換、等。6. 基本空氣動力學，尤其是有關翼面在流場中所受的力與力矩之關係，譬如:a.升力與力矩與流場之速度、攻角，以及翼面積、形狀，等的關係。b. Aspect ratio、Downwash angle、Aerodynamic center等名辭為何義？7. 基本自動控制學理論，如：a.所謂線性系統、轉移函

6、數、極點、零點、等之定義為何？b.何謂根軌跡設計法？ 何謂一個系統之穩定邊限？A. Review of DynamicsDefine a coordinate system - Fixed in body: Axis fixed in body, right handed. Basic governing equations: The coordinate system thus defined is rotating at a speed , hence is a non-inertial frame. For any vector defined therein, its time der

7、ivative with respect to the inertial frame will be: . The inertial force, , is derived as follows: 1. The acceleration of the aircraft is given by 2. We can write ; hence, . 3. As a result, the inertial force of the motion can be written as follows:. Collectively, we haveThe inertial moment, , is de

8、rived next.1. The inertial moment of an aircraft can be obtained by differentiating its angular momentum with respect to time.2. The angular momentum of an aircraft is found by integrating, over the body, the infinitesimal angular momentum of the mass element spread over the aircraft. For the mass e

9、lement shown in the figure on next page, its angular momentum will be as follows:Note that is the position vector of , and is the linear velocity, of , due to rotation . The value of can be computed as： 3. Substitute this into , and we have: 4. The above vector cross product can be expanded into as

10、follows: 5. The angular momentum of the whole aircraft is found by integrating over the entire aircraft body, or: . 6. Expand into , this implies that:- Note that and are independent of position, hence are moved out of the integration. 7. We can recognize the following moments of inertia terms: and

11、the following product of inertia terms: 8. In general, the origin of the coordinates is at the center of mass and the aircraft is symmetrical right and left. Then, ; hence, . 9. We can now compute the inertia moment ： a. - is a vector in a non-inertial frame. b. c. 10. Then, the following expression

12、s of the inertial moment result:. whereGoverning equations of motion of an aircraft.1. and . 2. and can be expanded into the following forms: and .3. As a result, the following 6 equations of motion are obtained: and4. A computable equation of motion will require expansion of and in terms of the sys

13、tem variables, , and their derivatives. This portion of work will constitute most part of this course.Decoupling of the governing equation of motion 1. Approximations on and of aircraft motion: a. The following conditions are mostly true for aircraft in general: b. As a result, some second order ter

14、ms of the equation become negligible, and the following approximations on and can be made: and is preserved in and is preserved in because they do not affect decoupling. We may also let to include , but it is often small c. Approximated in this way, the 6 inertial terms can be separated into two unc

15、oupled group of equations; each group of equations define a specific class of motion, termed the longitudinal motion and the lateral motion, respectively: Longitudinal motion equations Lateral motion equations 2. The uncouple phenomenon also apply to the components of and . Therefore, the subsequent discussions on aircraft motion will be done in two separate pa