Projectile

About: Projectile is a research topic. Over the lifetime, 13047 publications have been published within this topic receiving 115563 citations.

The motion of an arbitrarily rotating spherical projectile and its application to ball games

Abstract: In this paper the differential equations which govern the motion of a spherical projectile rotating about an arbitrary axis in the presence of an arbitrary ‘wind’ are developed. Three forces are assumed to act on the projectile: (i) gravity, (ii) a drag force proportional to the square of the projectile’s velocity and in the opposite direction to this velocity and (iii) a lift or ‘Magnus’ force also assumed to be proportional to the square of the projectile’s velocity and in a direction perpendicular to both this velocity and the angular velocity vector of the projectile. The problem has been coded in Matlab and some illustrative model trajectories are presented for ‘ball-games’, specifically golf and cricket, although the equations could equally well be applied to other ball-games such as tennis, soccer or baseball. Spin about an arbitrary axis allows for the treatment of situations where, for example, the spin has a component about the direction of travel. In the case of a cricket ball the subtle behaviour of so-called ‘drift’, particularly ‘late drift’, and also ‘dip’, which may be produced by a slow bowler’s off or leg-spin, are investigated. It is found that the trajectories obtained are broadly in accord with those observed in practice. We envisage that this paper may be useful in two ways: (i) for its inherent scientific value as, to the best of our knowledge, the fundamental equations derived here have not appeared in the literature and (ii) in cultivating student interest in the numerical solution of differential equations, since so many of them actively participate in ball-games, and they will be able to compare their own practical experience with the overall trends indicated by the numerical results. As the paper presents equations which can be further extended, it may be of interest to research workers. However, since only the most basic principles of fundamental mechanics are employed, it should be well within the grasp of first year university students in physics and engineering and, with the guidance of teachers, good final year secondary school students. The trajectory results included may be useful to sporting personnel with no formal training in physics.

Three-dimensional numerical simulation of the Kalthoff experiment

Abstract: We use the finite element code DYNA3D to analyze large thermomechanical deformations of a prenotched plate impacted on the notched side by a cylindrical projectile moving parallel to the axis of the notch. Both the projectile and the plate are assumed to be made of the same thermally softening but strain and strain-rate hardening material. It is found that the maximum speed imparted to points of the plate on the impact surface equals nearly 90% of the projectile speed, and the rise time depends upon the quasistatic yield stress of the material. Whereas deformations on the midsurface of the plate closely resemble a plane strain state of deformation, those on the traction free front and back surfaces are quite different. Thus measurements made on these surfaces may not describe well the deformations occurring in the interior of the plate.

Non-lethal cartridge with spin-stabilized projectile

Abstract: The invention is a non lethal weapon cartridge comprising a projectile and means for propelling the projectile through a weapon barrel. A munition of this type can be employed by soldiers during operations-other-than-war, such as riot control during humanitarian missions, or by law enforcement personnel when a lethal response is not warranted. The projectile comprises a full-bore projectile body fitted with a compliant nose. The projectile is designed to be spin-stabilized such that it will fly, and impact, nose first, while describing a ballistic trajectory. The projectile is intended to be launched from a rifled weapon tube. The rifling imparts the spin necessary to achieve dynamic stability. The propulsion system utilizes a modern smokeless propellant in combination with a high-low technique to produce consistent interior ballistics.