Linearized Motion of a Fin-Stabilized Projectile Subjected to a Lateral Impulse

Abstract

An existing analytical theory for modeling the free-e ight motion of nonspinning, statically stable projectiles is extended to include the effect of a simple lateral impulse applied during e ight. The extended theory is based on the incorporation of generalized lateral translational and angular disturbances into the familiar equations of projectile free-e ight motion. The applied disturbances are then modeled using specie ed mathematical forms, and the modie ed equations are solved to obtain the angular and translational motion of the projectile over the trajectory. The various components of the translational motion of the projectile are extracted and characterized. An idealized application is presented for a large-caliber e nned projectile, representative of the class of 120-mmlong rod e nned projectiles e red from current tracked vehicle weapon systems, subjected to a single lateral control impulse in e ight. The closed-form analytical solutions are compared against results obtained using a numerical trajectory simulation code that incorporates generalized guidance and control commands. Nomenclature A = reference area, od 2 =4, m 2 CL® = derivative of aerodynamic lift force coefe cient with respect to angle of attack CM® = derivative of aerodynamic pitching moment coefe cient with respect to angle of attack