A vehicle's in-flight behavior can be represented by the Newton-Euler equations of motion: usually, such a model has a nonlinear and continuous description based on ordinary differential equations. The model structure can be altered using analytic transformations-such as transformation into a quasi-LPV structure-and, when the model is supposed to reflect an existing physical system, some of its parameters might be uncertain. This paper's objective is twofold: firstly, to investigate if a quasi-LPV model does accurately replicate the physical behavior of a large-caliber spin-stabilized projectile in free flight; and secondly, to verify if the available embedded sensors data could be used to determine non-identifiability of uncertain model parameters. In order to investigate these prospects, a permutation-based global sensitivity analysis is employed. The proposed study has highlighted the non-identifiable parameters of the model, either during the whole flight or some periods of it. These results can help to enhance the preparation of free flight experiments at the open-range test site of the French-German Research Institute of Saint Louis. Nomenclature M = Mach number V = airspeed, m s −1 α, β, α t = angle of attack, angle of sideslip, total angle of attack, deg C X , C N α , C y pα = axial force, normal force slope, and Magnus force slope coefficients C lp , C mα , C mq , C npα = roll damping, pitch moment slope, pitch damping and Magnus moment slope coefficients