Ball motion in a ball-obturated tubular projectile

Abstract

When a ball with a concentric hole through it is suspended within a spinning tubular projectile the ball will rotate in such a way that its hole is aligned with the axis of spin of the projectile. The ball thus serves as an automatic obturator—plugging the projectile while the two bodies are within the gun barrel and rotating to open the tubular passage following exit from the muzzle. The motion of the ball is gyrodynamic in nature and highly dependent upon the external moments on the ball that arise because of its motion relative to the spinning projectile. This report presents the results of an analytical and experimental study to provide an understanding of such motions in as complete a sense as is possible. The general equations of motion are formulated together with appropriate mathematical expressions for the external moments. These moments have their origins in the forces acting on the ball (gravity and aerodynamic forces are considered) which, in the presence of relative motion between the ball and the projectile, lead to sliding friction torques. Torques due to fluid shear are also considered but these are found to be relatively insignificant. Exact solutions are obtained using standard numerical techniques. In addition, a linear form is developed and these solutions lead to useful approximations that are valid over a broad range of operating conditions. Experiments are described in which the general validity of the theoretical models (exact and linear) is demonstrated for cases in which there is little or no aerodynamic load. The experiments, together with the linear approximation, lead to a semi -empirical method for determining the effective coefficient of sliding friction for such systems. A model is proposed to account for aerodynamic loading and sensitivity studies are conducted to determint the nature and scope of the influence of various design parameters upon systme performance. The linear approximation is proposed as a useful design guide when applied with due awareness of its limitations. In addition, a design criterion is presented by means of which it is possible to avoid designs that lead to operation in a "hovering" region. Such operation leads to prolonged delays in ball opening time. Application of the design criterion leads to ball/projectile designs that are optimum from the point of view of minimum ball opening time.