Here, CL, is the non-dimensional lift coefficient, which is a function of the shape, and the angle of attack a. The variation of Cl with the angle of attack is linear, up to a maximum value Clma, of the order of 1.5-2.0. Thus, we have where a= aCL/aa. For an idealized fat plate wing, a= 2T rad, and more generally for finite wings a=5 rad- to a=6 rad-I. Note that for a=0, CL=0, which implies that we are assuming that a=0 corresponds to the zero-lift line. Pitching Moment The lift force, L, is the result of integrating a distributed force over the surface of the wing. This distributed force is equivalent to L, acting through a particular point called the center of pressure(CP). For this model, re will assume that through proper control of the flaps and tail, the pitching moment about the center of mass is zero. Moreover, we shall assume that any attitude changes commanded by the control system are instantaneous The drag force can als exPress ed as a function of a non-dimensional drag coefficient, CD (5) The drag coefficient in general has a complicated dependence on a and Cl. But commonly it is assumed to have two components, one which is independent of the lift, and one which increases quadratically with the Cp=Cpo +KCi Typical values for CDo for the whole aircraft, are of the order of 0.003 to 0.02. An important ratio used to determine the aircraft's performance is L/D= CL/CD, which is typically of the order of 10-20 for most subsonic aircraft, and up to 60 for some sailplanes Thrust The thrust generated by the engine is a force directed at an angle ar measured with respect to the zero-lift line. In general, both the magnitude of T, and its direction ar, are inputs to the model. Weight Typically we will simple have W=mg and it will be directed along the negative y-axis. Note, however, that we are interested in spacecraft in orbit, the weight might be directed to a fixed point, e. g. the earth center and may be a function of the height.Here, CL, is the non-dimensional lift coefficient, which is a function of the shape, and the angle of attack α. The variation of CL with the angle of attack is linear, up to a maximum value CLmax , of the order of 1.5 − 2.0. Thus, we have CL = aα , (4) where a = ∂CL/∂α. For an idealized flat plate wing, a = 2π rad−1 , and more generally for finite wings a = 5 rad−1 to a = 6 rad−1 . Note that for α = 0, CL = 0, which implies that we are assuming that α = 0 corresponds to the zero-lift line. Pitching Moment The lift force, L, is the result of integrating a distributed force over the surface of the wing. This distributed force is equivalent to L, acting through a particular point called the center of pressure (CP). For this model, we will assume that through proper control of the flaps and tail, the pitching moment about the center of mass is zero. Moreover, we shall assume that any attitude changes commanded by the control system are instantaneous. Drag The drag force can also be expressed as a function of a non-dimensional drag coefficient, CD, as D = 1 2 ρv2 S CD. (5) The drag coefficient in general has a complicated dependence on α and CL. But commonly it is assumed to have two components, one which is independent of the lift, and one which increases quadratically with the lift, CD = CD0 + KC2 L . (6) Typical values for CD0 for the whole aircraft, are of the order of 0.003 to 0.02. An important ratio used to determine the aircraft’s performance is L/D = CL/CD, which is typically of the order of 10 − 20 for most subsonic aircraft, and up to 60 for some sailplanes. Thrust The thrust generated by the engine is a force directed at an angle αT measured with respect to the zero-lift line. In general, both the magnitude of T , and its direction αT , are inputs to the model. Weight Typically we will simple have W = mg and it will be directed along the negative y-axis. Note, however, that we are interested in spacecraft in orbit, the weight might be directed to a fixed point, e.g. the earth center, and may be a function of the height. 5