Mean and Structural Axes

Even after the advent of panel methods, there remain controversial aspects of the quasi-static aeroelastic problem, related to the choice of axes. Structural distortions must be referred to some set of reference axes. There are essentially two sets of reference axes that will serve. One choice, called structural axes, corresponds to a natural reference for laboratory structural deflection tests or their analytical equivalent. Structural axes are aligned with a central hard section of the airplane, such as the wing interspar structure at the airplane’s centerline.

The second choice, which is the only one that is consistent with the ordinary pitch – plunge equations of airplane motion, are mean axes. Mean axes are a familiar concept in normal mode analysis. They correspond to the midpoint of normal mode oscillations, the point at which all transverse deflections are momentarily zero. While structural influence coefficients may well be measured or calculated in an arbitrarily chosen structural axis system, pitch and plunge motions of the aeroelastic airplane must be calculated in mean axes, to avoid systematic error (Milne, 1964, 1968). A refinement of mean axes is the use of principal axes in which distributed moments of inertia are accounted for in addition to longitudinal mass distributions.

John H. Wykes and R. E. Lawrence used both mean and structural axes in a 1965 study of aerothermoelastic effects on stability and control, but they noted the difficulties involved in relating airplane angle of attack in the two systems. The angle of attack difficulty found by Wykes and Lawrence is resolved in an offline transformation of the results, such as pitch attitude and angle of attack time histories, from mean to structural axes (Rodden and Love, 1984). The transformation is feasible at the end of the dynamics calculations. The Rodden and Love paper, corrected in Dykman and Rodden (2000), also presents transformation equations from mean to structural axes.

The Rodden papers have an interesting proof of the fallacy of using the more convenient structural axes for dynamics studies in place of mean axes, as has been done by investigators unwilling to face angle of attack difficulties. In a simple swept-forward airplane example using structural axes, load factor and pitching acceleration time histories depend on the fixity choice of the axes, an evidently incorrect result. This error is avoided with mean axes. Mean axes are used in the FLEXSTAB program.