Coilgun design and evaluation without capacitor

2.1. Theory and implementation

We will use the basic equations of classical mechanics in a different way and get theoretical values from experimental results. We assume that all the magnetic energy stored in the coil is converted into kinetic energy:

In this equation, the velocity and mass of the projectile are $v$ and $m$, respectively, the inductance of the coil $L$, the current passing through the coil is $I$. The product of $v\left(t\right)i\left(t\right)$ is the power consumed in the coil. Fig. 4 shows the empty shot voltage change made in the single-coil model. The positive and negative peaks shown in the graphic on the left are found by using Lenz’s law and are the result of a quick switching of Mosfets. The enlarged version of the positive peak is on the right graph. Using this chart, we can calculate the inductance of the coil. Normally, it is necessary to perform the ac analysis of the circuit given in Fig. 3, which can be found in any general physics book; we will only use the result here:

where, $\tau$ is the time consumed to increase the voltage applied to the coil by 0.632 when the Mosfet is triggered. This time is equal to the time constant of the $LR$ circuit. The value of $L$ was measured as 43.5 µH from the graph and was calculated as 22.0 µH. The internal resistance of the coil is 168 mΩ. Measurements were made with Picoscope 3406B USB oscilloscope, Keithley, and Fluke multimeter devices.

Fig. 4Empty shot voltage variation in the single coil model [Original]

Fig. 5 shows the projectile shot voltage change in the single-coil model. The graphic on the left shows a sharp rise in the positive peak, and there is a loss of symmetry in the negative peak. The reason for the corruption in the negative peak may be due to the projectile length being longer than the coil length because the inductance of the coil changes with the motion of the projectile. The lengths of the coil and projectile are 14 mm, 25 mm, respectively. The enlarged version of the positive peak is on the right graph.

Fig. 5Projectile shot voltage variation in single coil model [Original]

The inductance of the coil could not be calculated using this chart. While the projectile was stationary in the middle of the coil, its inductance was measured 21.3 µH. In Figs. 4 and 5, the voltage values of the plateau between the two peaks are almost the same, and the duration can be shortened and extended as required by the software. This is independent of the supply voltage. This feature is not available for coil guns with charge-and-discharge capacitors. The output velocity of the projectile can be calculated from Eq. (1). When the maximum inductance of the coil is 22.0 µH and the maximum current passing through the coil is 14.83 A, this speed is 106.8 cm/s (12 V variable power supply can be increased up to 40 V). The kinetic energy of the projectile changes with the position [8]:

3.1. The ejection coil

Two different prototype gun models with two and four coils were made by using the semi-experimental single-coil gun model, as shown in Figs. 6 and 7. In Fig. 6, the tube passing through the center of the coils has no magnetic property and is an insulator. The paper tube was then hardened. The diameter of the tube should be slightly larger than the diameter of the projectile to be used. The number of coils to be wound on the tube will affect the launch speed. In the thumbnail in Fig. 7, there are four coils wrapped on the tube. Winding number, thickness, and length of the coils are the parameters affecting the launch speed. The most important thing is timing pulses that take into account the distance between the coils [6, 9]. In this study, the turn number of coils is 85, the length 14 mm, the thickness 6.55 mm, and the wire diameter 1 mm². These are average values and are not critical.

3.2. Arduino and power Mosfets

A microcontroller was used to control the current passing through the coils that created the magnetic force to accelerate the projectile. A commercial product, Arduino Nano, is a development board that uses an ATmega328P microcontroller [10]. It was used in this study because of its 12 MHz clock speed and small size. The timing pulses of the Mosfets, which limit the current passing through the coils, are produced by this microcontroller. Switching times of Mosfets should be around nanoseconds. Fig. 8 displays the circuit diagram of the four-coil gun. If the diodes D1 ... D4 shown in the scheme are not used, the outputs of the Mosfets can be burned.

Fig. 6Two-coil gun and test projectile (ratchet screwdriver, the thumbnail) [Original]

Fig. 7Four-coil gun with coils (the thumbnail, back side) [Original]

3.3. Velocity measurements

Fig. 9 shows the moment of the projectile exiting from the barrel after firing in the two-coil gun. Various methods are available to measure this speed. The parabolic method using the time-independent orbital equation, the light-sensitive fence gate method that measures flight time, and the ballistic pendulum method using momentum conservation is the most commonly used speed measurement method [11]. Free video analysis and modeling tool Tracker program based on open source physics (OSP) Java framework was used to measure this speed. It is designed for use in physics education and can combine captured videos with computer modeling [12]. A mobile phone’s camera (1080p @ 30fps) was used to find the speed of the projectile. The videos taken were transferred to the computer where the Tracker program was installed, and the speed of the projectile was measured using the recommended instructions for speed measurements. Fig. 10 displays the results of the data analysis produced by the Tracker program. The data are given in the cgs unit system. The position and speed equation of the projectile was found with the “auto-fit” option:

In the last equation, we excluded the initial velocity of the projectile on the grounds that it was not linear. There is a break here by gravity, and its value is –972.727 cm/s². The result is that the slope of the velocity equation is expected to be negative; the projectile hitting the ground continues on its path horizontally.

Fig. 8Four-coil gun circuit schema [Original]

Fig. 9The moment the projectile leaves the barrel, black shade [Original]

Fig. 10Data analysis results [Original]

3.4. FEMM analysis

FEMM is an analysis program written in Lua language. Lua uses a measurement taken in a simulation step as a parameter in the next step. It is easy to examine the pulling force created by the current passing through a coil by FEMM analysis [13, 14]. After creating a physical model of the work to be done, the program tries to reach the solution by numerically integrating the dynamic equations of the projectile [8, 9]. The FEMM analysis results of the physical model for a single-coil are shown in Fig. 11. According to the results, the inductance of the coil is 52.71 µH, and its internal resistance is 84 mΩ. Fig. 12 is the magnetic force change that acts when the projectile is drawn by the coil. In the middle of the coil, the force is maximum, and at this point, the Mosfet must interrupt the current otherwise, the projectile will be locked. The codes required to simulate the change of force on the projectile were written in Python language. In order to work Python language with the FEMM analysis package, pyfemm 0.1.1 module must be imported. For linear problems, the magnetic field co-energy is numerically the same as the magnetic energy in a coil, and its simulated value is 0.0024331 J. We calculated the speed of the projectile from this result. This value should be compatible with the value given by the Tracker program. If we take the derivative of the position with respect to time, we find the speed of the projectile. The kinetic energy of the projectile can be calculated from this speed value:

We divided the $K_{tracker}$ kinetic energy into four because the two-coil gun has four semi-coils due to symmetry. The magnetic force is directly proportional to the field lines passing through the projectile, and in simulation, the left half of the projectile is outside due to symmetry. If we multiply the magnetic field energy value given by the simulation by four, we will find the speed value given by the Tracker program.

Fig. 11FEMM analysis results [Original]

Fig. 12Force change on the projectile [Original]