With reference to the figure below, we define the following angles. Let B, be the angle that the velocity vector(tangent to the fight path) makes with the x-axis. Thus, we will have tan B=vu/ur. Let a be the ngle of attack of the aircraft relative to velocity vector. As we will see, the angle of attack is relevant, as it determines the lift(and drag) for a given velocity and altitude. The angle of attack, is defined so that the lift generated when a= 0, is equal to zero. In addition, we define the angle ar as the angle that the thrust ector T makes with the zero-lift line. In most cases, this angle will be constant, but in some situations (e. g thrust vectoring in aircraft or rockets)it can be an input, or control, variable. All the angles are positive as thrust lin tero-lift line flight path X-axis The aerodynamic forces, are resolved into a lift component L, orthogonal to the velocity, and a drag compo- nent D, parallel to the velocity. In addition, we will have, the weight of the vehicle, w, and the thrust t, due to the propulsive system. When these forces are referred to the center of mass of the aircraft, we may have an additional pitching moment M. For this aircraft model, we will assume that the control surface guarantees that the pitching moment about the center of mass is always zero Forces on the aircraft For a standard wing-tail configuration aircraft we have the following Lift Most of the aircraft's lift is generated by the wing and horizontal stabilizer. For a given angle of attack a the lift is proportional to the relative wind s dynamic pressure q =(1/2)pu, and to the wings area S, L=louseWith reference to the figure below, we define the following angles. Let β, be the angle that the velocity vector (tangent to the flight path) makes with the x-axis. Thus, we will have tan β = vy/vx. Let α be the angle of attack of the aircraft relative to velocity vector. As we will see, the angle of attack is relevant, as it determines the lift (and drag) for a given velocity and altitude. The angle of attack, is defined so that the lift generated when α = 0, is equal to zero. In addition, we define the angle αT as the angle that the thrust vector T makes with the zero-lift line. In most cases, this angle will be constant, but in some situations (e.g. thrust vectoring in aircraft or rockets) it can be an input, or control, variable. All the angles are positive as shown in the diagram. CM x-axis flight path zero-lift line thrust line T β y x v The aerodynamic forces, are resolved into a lift component L, orthogonal to the velocity, and a drag compo￾nent D, parallel to the velocity. In addition, we will have, the weight of the vehicle, W, and the thrust T, due to the propulsive system. When these forces are referred to the center of mass of the aircraft, we may have an additional pitching moment M. For this aircraft model, we will assume that the control surface guarantees that the pitching moment about the center of mass is always zero. Forces on the Aircraft For a standard wing-tail configuration aircraft we have the following: Lift Most of the aircraft’s lift is generated by the wing and horizontal stabilizer. For a given angle of attack α, the lift is proportional to the relative wind’s dynamic pressure, q = (1/2)ρv2 , and to the wing’s area S, L = 1 2 ρv2SCL. (3) 4