A New Analytical Approach to Flight Equations

The six-degree equations of flight in their classic form do not provide a proper physical perception due to a number of interferences. Nor do they render visible the important role of attack angles. In this study, attempts have been made to develop a complete set of 3D acceleration equations from the equations of normal and tangential acceleration αN=vωv, αt=v ̇. For this purpose, a coordinate set stuck to the velocity vector is introduced such that the angles of attack act as a bridge between the coordinate introduced and that of the body. Thus, αNy=vωz and αNz=vωvy, are obtained, where ωvz and ωvy are the components of angular velocity vector given in terms of attack angles and p, q, r (the angular velocity of body in the body coordinate). It is also known that momentum equations are written in terms of p, q, r. Thus, the angles of attack play the role of a bridge between the force equations (now written in velocity coordinate) and the momentum equations (already written in the body coordinate). For symmetric missiles without roll, these equations become simpler and nearly linear. The undesired and nonlinear effects also become easier to analyze. The dynamic behavior among the momentum, the rotation of the body and the rotation of the velocity vector become completely visible. Thus, the aerodynamic coefficients appear directly in the dynamic equations. It follows that this new approach should help not only the auto pilot designer but also the aerodynamic body designer.