A Simple Framework for the Study of Airplane Trim and Stability

We develop a reformulation of the study of airplane trim and stability intended mainly for teaching purposes. This approach yields a slightly different form of the governing equations with respect to that commonly adopted in the literature and in education programs. Under hypotheses of linear, low subsonic, steady-state aerodynamics in symmetric flight, the constitutive laws for lift and pitching moment are rewritten in a homogeneous form and appropriate characteristic points are introduced: the first is the well known neutral point, while the second is termed the control point. This allows the reduction of the complex system of aerodynamic forces acting on the airplane to an equivalent one consisting in only two applied forces. Basic considerations of trim and stability are easily carried out within this framework by simple, intuitive reasoning upon the resulting force distribution patterns. In order to help the reader to familiarize with this approach, applications to level flight in both the stick-fixed and stick-free settings, as well as to maneuvering flight, are briefly addressed.