# Optimisation of Energy Transfer in Reluctance Coil Guns: Application to Soccer Ball Launchers
## 1 Introduction  
Propelling projectiles with a controlled speed and trajectory is a technological challenge having lots of applications ranging from kicking soccer balls to launching rockets or satellites, including testing military ammunitions. In this introduction, we focus on propulsion techniques having strong accelerations, so that an important speed can be obtained in a short distance. Common propulsion techniques of this type are among the following ones:  
* **Chemical propulsion**: mainly used for propelling weapons or rockets; chemical propulsion uses the product of a chemical explosive or expanding reaction to push out a projectile [1]. The benefit of this propulsion is to have a high density of energy stored in a small size as achemical product leading to strong accelerations, without the need of being connected to a power supply. Its drawback is that the propulsion is a single shot one due to the chemical reaction.
* **Mechanical propulsion**: there are many types of mechanical propulsion systems. Among the solutions allowing a strong acceleration of the payload are the inertial launchers. They are mostly using an energy storage in heavy high speed rotating mechanical parts such as iron cylinders. These parts are accelerated slowly by a standard motor and part of the stored energy is transferred in a very short amount of type to a projectile by friction. These systems are very simple but their size is much more important than the size of chemical or electromagnetic launchers for a given propelling strength. An example is presented later in this paper.
* **Rail Gun propulsion**: a rail gun is composed of a pair of conductive parallel rails connected to a direct current (DC) power supply. The electrical circuit is a closed sliding conductor where a payload is placed. Once current flows through the rails, a Lorentz force is created, accelerating the payload to launch it. This propulsion technique is very efficient, and output speed can be higher than using a conventional chemical propulsion as shown in [1], for a launching structure having the same overall size. Compared with chemical propulsion, this solution can be far less expensive than chemical propulsion for launching limited size payloads such as small satellites [2]. However, the presence of a mechanical contact between the rails and the payload propeller can lead to several issues reducing the energy transfer, such as friction losses [3] and plasma phenomena at very high speeds [2; 4].
* **Coil Gun propulsion**: a coil gun is an electromagnetic launcher (EML) converting electricity into kinetic energy using coils [5; 6]. There are two types of coil guns. The first one is based on induction to accelerate a conductive non-magnetic projectile using eddy currents induced in a conductive/non-magnetic moving rod inside a magnetic field created by a fixed coil [7]. This solution has an important drawback due to magnetic losses leading to heat generation and controllability loss. The second one is based on accelerating a magnetic projectile by minimizing the reluctance between the projectile and a magnetic field generated by a current flowing through a fixed coil [8]. This type of coil gun, also named reluctance accelerator is simpler to drive than induction coil guns and is very compact.