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This article describes a new advanced coupled computational fluid dynamics/flight mechanics designed to compute the flight trajectory of the projectile. A first test has been carried out to compute the unsteady aerodynamics associated with free flight of the finned projectile at supersonic speed. Computed positions and orientations of the projectile have been compared with literature results and close agreements have been underlined. Predicted aerodynamic forces and moments are extracted and have been compared.Nomenclature C = Aerodynamics coefficient vector δ = Total angle attack C p = Specific heat mass at constant pressure η = Azimuth angle C v = Specific heat mass at constant volume κ = Thermal conductivity C d, C I , C S = Smargorinsky coefficient λ i = Quaternion component Cor = Coriolis force μ = Dynamic viscosity d ref = Refinement reference distance μ 0 = Reference dynamic viscosity ds = Surface unit μ T = Turbulent viscosity E = Total energy of mass unit ρ = Volume density f = Function vector of flight mechanics σ ij = Viscous tensor g = Gravity acceleration φ = Roll angle G = Projectile gravity center ψ = precession angle H = Projectile kinetic moment τ = Shear stress I 1 = Projectile longitudinal inertia τ ij = Sub-grid shear tress tensor I 2 , I 3 = Projectile transversal inertia θ = elevation angle J = Projectile inertia matrix ω i = Projectile rotation velocity m = Projectile mass t  = Time step     M  = Transfer matrix between two reference Pr = Prandtl number Pr t = Turbulent Prandtl number q j = Energy sub-grid tensor Q = Quaternion S ij = Deformation tensor u i = Velocity component U = State parameter vector v abs = Projectile absolute velocity x,y,z = Projectile position 1 Doctor, Researcher, FTC Department, Thermal Branch, van-thuan.luu@ensma.fr 2 Doctor, CNRS senior scientist, FTC Department, Thermal Branch, frederic.plource@ensma.fr 3 Doctor, DGA ballistics expert, christophe.grignon@dga.defense.gouv.fr 1 Downloaded by CARLETON UNIVERSITY LIBRARY on March 16, 2015 | http://arc.aiaa.org | I. IntroductionIn the framework of ballistics, the computational study of complete projectile behavior during flight is a challenging problem because of the very complex and multi-coupled physics. The computational fluid dynamic remains difficult to address due to the broad turbulence scales used for depiction of unsteady flow behaviors, especially in the wake of the projectile. The flow field structure obviously depends on the flow regime, i.e. subsonic, transonic and supersonic regime providing specific aerodynamic loads on the projectile due to the multiple physical mechanisms involved: shock waves, detachment/reattachment flows, shear-layer and turbulent wakes. Rotation of gyrostabilized projectiles also significantly contributes to the overall flight trajectory. Significant changes in aerodynamic loads on the projectile will change its relative position in time, thereby directly impinging upon aerodynamic performance. A full Computational Fluid Dynamic (CFD) 1 and a 6 DOF flight mechanics (three ...