Magnetic cannon: The physics of the Gauss rifle

Abstract

The magnetic cannon is a simple device that converts magnetic energy into kinetic energy: when a steel ball with low initial velocity impacts a chain made of a magnet followed by a few other steel balls, the last ball of the chain is ejected at a much larger velocity. The analysis of this spectacular device involves understanding of advanced magnetostatics, energy conversion and collision of solids. In this article, the phenomena at each step of the process are modeled to predict the final kinetic energy of the ejected ball as a function of a few parameters which can all be experimentally measured.

The Gauss pendulum

“…The rotational energy gradually comes into play as the friction force against the rail prompts the ball to roll. -The kinetic energy gained by the trigger ball due to the magnetic force is transferred to the projectile ball by a Nesterenko soliton [2] propagating through the elements of the assembly in a similar way that happens in a Newton's cradle [9]. However, in the latter, the elements of the chain are identical and, in a first approximation, all kinetic energy from the trigger ball is transferred to the projectile.…”

“…More recently, a device using a different method to magnetically accelerate a projectile has drawn attention from the university community and amateur developers. This device is known as the Gauss rifle (the terms "gun" and "cannon" are also used) and employs strong magnets and steel balls [2]. To those who are not familiar with the Gauss rifle we suggest to take a few minutes to watch the educational video made by our group, available on the internet [3].…”

Waves in strongly nonlinear discrete systems

“…Only later this area became an active domain of theoretical and experimental research. During the last few decades multiple papers focused on strongly nonlinear wave dynamics (total number is close to 500), reviews [15,[17][18][19][20][21][22][23][24][25][26], books [2,3,27,28] and even popular articles [29,30] were published.…”

Critical density for the stability of a 2D magnet array

“…5). In the past, the dynamics of close-range (d ≈ 3R) interacting magnets of varying shape has been predicted accurately using the dipole model [9,10,11]. Considering the magnetic momentm and magnetic moment norm m of a single magnet, the vacuum permeability m 0 and the distance between two magnets d, the magnetic energy of magnet (2) placed in the field ← B generated by magnet (1) is:…”

“…Using the results of the previous section, we compute a theoretical total critical density by solving in equation (10) by injecting the values for z and u given by the fits on Figures 8a and b and using a numerical solver. This gives us a theoretical density that takes into account force and torque, for which the results are displayed on Figure 8c.…”