Flight Stability of an Asymmetric Projectile with Activating Canards

Driven by the creation of new smart projectile concepts with maneuver capability, projectile configurations with large aerodynamic asymmetries are becoming more common. Standard linear stability theory for projectiles assumes the projectile is symmetric, both from aerodynamic and mass properties perspectives. The work reported here extends standard projectile linear theory to account for aerodynamic asymmetries caused by actuating canards. Differences between standard linear and extended linear theories reported here are highlighted. To validate the theory, time simulation of the extended linear theory and a fully nonlinear trajectory simulation are made for a representative scenario, with excellent agreement noted. The extended linear-projectile theory offers a tool to address flight stability of projectiles with aerodynamic configuration asymmetries. Nomenclature Ci = projectile aerodynamic coefficients Cic = projectile aerodynamic coefficients due to a canard D = projectile characteristic length (diameter), ft f, , = Euler roll, pitch, and yaw angles of projectile g = gravitational constant, ft s2 In, Jn,Kn = unit vectors for a coordinate system designated by n IX, IT = mass moments of inertia, slug ft2 m = projectile mass, slug p, q, r = angular velocity components vector of projectile, s1 r = atmosphere density, slug ft3 S, S = complex and conjugate projectile yaw rates SLCg = station-line center of gravity, ft SLCOP = station-line center of pressure, ft SLCOPC = station-line center of pressure of canard, ft SLMAG = station-line center of Magnus, ft u, v, w = mass center velocity components in the body reference frame, ft s1 jV A=Ij V = projectile center-of-mass velocity, ft s1 xc, yc = displacement of canard center of pressure relative to mass center, ft = canard deflection angle with respect to projectile axi