This study investigates the throw of slender elastic projectiles. By integrating experimental data, numerical simulations, and theoretical analyses, we explore the acceleration and ejection dynamics of these projectiles. We considered various conditions, including the amplitude and frequency of the thrower, as well as the geometrical and mechanical properties of the projectile and its mass distribution. Conversely to homogeneous projectiles, weighted projectiles with a mass at the leading edge exhibit strong lateral deformations that substantially influence their dynamics. This results in an increase in kinetic energy compared to rigid objects. This superpropulsion effect is maximum at a particular value of a dimensionless factor, namely, the ratio between the Euler's critical load of the beam and the acceleration force imposed by the thrower. For heavily weighted projectiles with a mass ratio of 2 between the leading and trailing edges, this maximum corresponds to a 160% increase of kinetic energy. Our results contribute to a deeper understanding of the mechanical behaviors influencing elastic energy transfer in slender structures, with potential applications in sports and robotics.

We study by numerical simulation the impact of a one-dimensional composite projectile, composed of two superposed homogeneous parts, on an infinitely rigid and massive wall. The coefficient of restitution and the contact time are systematically measured as functions of the contrasts of mass and stiffness between the two parts. For purely elastic parts, these quantities show complex trends associated with different dynamics of the deformation waves propagating inside the projectile. A significant portion of the initial kinetic energy can be trapped in the deformation modes: the coefficient of restitution is lowest, about 0.2, when there is a strong stiffness contrast between the two parts and the stiff and soft parts are at the leading and trailing edges of the projectile respectively. In this case, we highlight the presence of multiple bounces, whose number increases as the proportion of the soft part increases. Finally, viscoelastic parts can be implemented in the same numerical framework to successfully recover the results obtained in real composite projectile impact experiments [D'Angelo et al., Phys. Rev. E 103, 053005 (2021)2470-004510.1103/PhysRevE.103.053005].

Muscles and tendons, actuators in robotics, and various sports implements are examples that exploit elasticity to accelerate objects. Tuning the mechanical properties of elastic elements connecting objects can greatly enhance the transfer of mechanical energy between the objects. Here, we study experimentally the throw of rigid projectiles by an actuator, which has a soft elastic element added to the distal end. We vary the thickness of the elastic layer and suggest a simple mass-spring chain model to find the properties of the elastic layer, which will maximize the energy transfer from the actuator to the projectile. The insertion of a soft layer, impedance matched to the ejection frequency of the projectile mass, can increase the throwing efficiency by over 400%. Finally, we identify that very thick and very soft compliant layers could potentially lead to high efficiency and flexibility simultaneously.