A Dimensionless Theoretical Framework for Longitudinal Centre-of-Mass Effects on Gliding Performance

A longitudinal shift in the centre of mass (COM) changes the pitching-moment balance of a gliding aircraft. The resulting change in trim can alter the loading of the wing and tail and, in turn, the drag and glide performance. This paper develops a general, dimensionless theoretical framework for that chain of effects without assuming an aircraft-specific numerical dataset. The framework has two levels. First, a reduced-order formulation uses an incremental static-trim relation and a parabolic induced-drag approximation to obtain an explicit dimensionless expression for the drag and glide ratio. Second, a coupled formulation retains airspeed, angle of attack, glide angle, Reynolds number, component aerodynamic coefficients, intrinsic pitching moments, and force-line offsets as parts of a common equilibrium problem. The reduced formulation yields a clear mathematical result: for fixed dynamic pressure, geometry, and the stated parameter conditions, a forward COM displacement can increase the induced-drag contribution associated with the additional trim loading and decrease the reduced-model glide ratio. This result is conditional on the reduced assumptions and is not presented as a universal law for paper aircraft. The coupled formulation shows how the same COM displacement enters a more complete trim problem through the CG location, static margin, tail geometry, tail aerodynamics, and the full pitching-moment equation. No aircraft-specific numerical validation is claimed. A reproducible Python implementation is provided for the dimensionless analysis and for future insertion of validated aerodynamic functions.