Computational Analysis of a Spinning Fin-Stabilized Projectile

Abstract

A computational analysis was undertaken to better understand the behavior of a proposed sub-caliber fin-stabilized projectile prior to experimental testing at the request of GX3 Innovations, the projectile designer. The original configuration was found to meet drag requirements and was statically stable. However, the spin rate approached that of the yaw resonance frequency, which is undesirable. The redesigned projectile had predicted equilibrium spin rates that were greater than those typically seen in a fin-stabilized round. As such, transient, moving mesh simulations to determine the pitch damping sum and rollinduced side moment coefficients were completed for input into a dynamic stability analyses. The dynamic stability analyses showed that the round should not experience any coning due to roll-induced side moment and would also remain dynamically stable. Nomenclature= pitching moment coefficient = pitch damping moment coefficient sum, rad -1 = pitching moment coefficient derivative, rad -1 = normal force coefficient derivative, rad -1 C N = normal force coefficient C n = side moment coefficient = = Magnus moment coefficient derivative, rad -1 C X = axial force coefficient = zero-yaw axial force coefficient d = projectile diameter, m I x = projectile axial moment of inertia, kg-m 2 I y = projectile transverse moment of inertia, kg-m 2 k = turbulent kinetic energy, m 2 /s 2 k = reduced frequency m = projectile mass, kg M = Mach number N = number of time steps per cycle * = normalization factor for stability equations, p = projectile spin rate (in non-rolling coordinate frame), radians/sec p eq = equilibrium projectile spin rate, radians/sec q = pitch rate, radians/sec 2 S = projectile cross-sectional area, m 2 S d = dynamic stability factor S g = gyroscopic stability factor t = time, seconds T = time period, seconds V = free stream velocity, m/s X cg = center of gravity location, calibers X CP = center of pressure location, calibers  = angle of attack in non-rolling coordinates, radians (or degrees)  mean = mean angle of attack, radians   = angular amplitude, radians t = time step, seconds  = turbulent dissipation rate, m 2 /s 3  F,S = fast and slow mode damping exponents, m -1  = density, kg/m 3  = angular rate for imposed sinusoidal planar pitching function, radians/sec