# Introduction

This page documents my first attempt at building a single stage coilgun. The coilgun is capable of firing a small ferromagnetic projectile at high speeds. A coilgun is a type of a linear electromagnetic accelerator. It fires ferromagnetic projectiles using one or more electromagnetic coils.

I have tried to include some supplementary information regarding the fundamentals of a simple single stage coilgun and how to go about building one. There are however many more resources out there with far more detailed technical explanations regarding coilgun design but hopefully this humble first attempt at building a coilgun proves to be a useful and/or interesting starting point.

This project involves knowledge of RLC circuits, electromagnetic physics, high voltage/energy electrical components. It is not a project recommended for novices or the inexperienced – the energy and voltages involved are LETHAL!

# Coilgun Fundamentals

A coilgun circuit comprises three main components: a large capacitor bank, a high current switch, and a coil of wire (or solenoid) from which the projectile is lunched. The capacitor bank is charged to some desired voltage and then then discharged into the coil via the high current switch. A simplified circuit diagram is shown below.

A projectile made from a ferromagnetic material is used, it can consist of a simple material such as iron or steel through to more exotic ferromagnetic metal alloys and ceramics. A ferromagnetic material is one that has a high susceptibility to magnetisation and that can become magnetised after the applied magnetic field is removed. The ferromagnetic projectile is placed within the coil or coil barrel at a specific distance from the centre of the coil.

The capacitor bank usually comprises of many smaller capacitors connected into parallel and series combinations to obtain the desired voltage and capacitance values for the bank. This is mainly due to the excessive costs of large singular pulse capacitors with the desired ratings. The capacitor bank is charged from a DC current source via a charging circuit. The charging circuit is then isolated from the capacitor bank before the bank is discharged through the coil via a high current switch.

The high current switch is usually a high power semiconductor switch known as an SCR (Silicon Controlled Rectifier) or thyristor.

Ideally if you can buy low ESR pulse caps to build a capacitor bank then you can tune the coilgun circuit to be close to critically-damped when fired. This will utilise most of the capacitor’s stored energy in the coils magnetic field to propel the projectile to high speeds.

However, if like me for my first coilgun attempt you do not purchase expensive low ESR pulse capacitors and instead utilise a box of new-old-stock capacitors, then the capacitor bank may exhibit a relatively large ESR that introduces excessive unwanted damping to the coilgun circuit. If this coilgun circuit was tuned to be critically-damped, the discharge time may be too long and the peek current may be too low to result in an effective coilgun design. However, we can work around this problem by tuning the coilgun circuit to be significantly under-damped. As a result of this a smaller amount of the total capacitor energy will be used during each firing and the inductance of the coil will be smaller but we will regain a short pulse duration and maintain a higher peek pulse current required to propel the projectile to high speeds. A bit of experimentation may be required to obtain optimum performance for these capacitors.

A trigger or pulse generator circuit is needed to activate the thyristor switch. Sending a low voltage current signal to the thyristor’s gate will allow current to flow from its anode through to its cathode; i.e. current flows from the capacitor bank, through the thyristor and then through to the coil.

A pulse discharge with a desired time period can only be achieved using a thyristor if the current through the thyristor falls below its minimum holding current for a duration greater than or equal to its maximum turn-off time. This is an important feature of thyristors, it cannot be arbitrarily switched on and off like a traditional mechanical switch.

For an under-damped coilgun circuit, a desired pulse duration can be achieved by tuning the RLC characteristics of the coilgun circuit such that it exhibits the desired time period for its positive resonant half cycle of a few milliseconds and choosing a thyristor with suitably fast switching characteristics. It is important to have a short pulse discharge to maximise the peek current and hence peek power in the coil to produce the largest field strength possible. The position and mass of the projectile can be tuned inline with the pulse duration such that as the projectile passes the centre of the coil, the coils field strength will have diminished below some minimum value to minimise the effect of it being pulled back toward the coil’s centre that would reduce the projectiles ultimate velocity.

For pulsed or switched circuits using inductors we encounter a problem known as inductive kick-back. Coils/solenoids are inductors which at to oppose a change in current. If a coil is energised by passing current through it and the current is suddenly interrupted, the magnetic field of the coil collapses causing a large negative potential voltage across its terminals. This reverse high voltage pulse can be orders of magnitude higher than the original applied voltage and can easily damage other circuit components, in particular, the polarised capacitor bank which can be damaged from both the reverse voltage and from dielectric punch-through when subjected to a high voltage transient above its rated maximum voltage. The solution is to install a large power diode and resistor bleeder circuit in anti-parallel with the solenoid to bleed this inductive kick-back pulse away safely; this is commonly known as a clamping or free-wheeling diode.

The circuit diagram below shows the configuration of components of the coilgun I am building.

A really useful tool for simulating the RLC transient repose is Barry’s RLC circuit simulation (Java required). This tool enables you to enter your coil inductance, coil resistance, capacitor bank capacitance, and capacitor bank voltage to simulate the transient response of the circuit. It is useful when finding out what trigger pulse is required when operating the thyristor, the time period should be between the time it takes for the current to hit it’s first maximum peak and the time taken for the current to drop below the thyristor’s minimum holding current.

Here is a print screen from Barry’s RLC circuit simulator of a transient response I used during the design of my coilgun:

# Useful Equations

At some point during the design of a coilgun you will require the use of some equations, here are a selection of the most useful ones.

## Parallel Capacitance

The total equivalent capacitance for capacitors in a parallel network is simply the sum of the individual capacitances:

$$ C_{parallel}=C_1+C_2+C_3+\ldots $$

## Series Capacitance

The total equivalent capacitance for capacitors in a series network is simply the reciprocal of the sum of the reciprocals of the individual capacitances:

$$ C_{parallel}=\frac{1}{{\frac{1}{C_1}}+{\frac{1}{C_2}}+{\frac{1}{C_3}}+\ldots} $$

## Capacitor Energy

The energy in Joules, \( E(t) \), stored in a capacitor at time, \( t \), in seconds is defined as:

$$ E(t)=\frac{C{V(t)}^{2}}{2} $$

Where \( C \) is the capacitance in coulombs and \( V(t) \) is the voltage in volts at time \( t \).

## Capacitor Charge

The charge in coulombs, \( Q(t) \), stored in a capacitor at time, \( t \), in seconds is defined as:

$$ Q(t)=CV(t) $$

Where \( C \) is the capacitance in coulombs and \( V(t) \) is the voltage in volts at time \( t \).

## Capacitor Voltage & Current During Charging

The voltage in volts, \( V(t) \), during charging of a capacitor at time, \( t \), in seconds is defined as:

$$ V(t)=V_0 \left( 1 – \operatorname{e}^{\frac{-t}{RC}} \right) $$

The current in amperes, \( I(t) \), during charging of a capacitor at time, \( t \), in seconds is defined as:

$$ I(t)=\frac{V_0}{R} \operatorname{e}^{\frac{-t}{RC}} $$

Where, in both cases, \( V_0 \) is the initial capacitor voltage in volts at \( t=0 \), \( R \) is the resistance in Ohms and \( C \) is the capacitance in coulombs.

## Capacitor Voltage & Current During Discharging

The voltage in volts, \( V(t) \), during discharging of a capacitor at time, \( t \), in seconds is defined as:

$$ V(t)=V_0 \operatorname{e}^{\frac{-t}{RC}} $$

The current in amperes, I(t), during discharging of a capacitor at time, t, in seconds is defined as:

$$ I(t)=\frac{V_0}{R} \operatorname{e}^{\frac{-t}{RC}} $$

Where, in both cases, \( V_0 \) is the initial capacitor voltage in volts at \( t=0 \), \( R \) is the resistance in Ohms and \( C \) is the capacitance in coulombs.

## Coil Inductance

The inductance, L in Henrys of a single layer coil is defined as:

$$ L= \mu_0 \mu_r \frac{N^{2}A}{l} $$

Where \( μ_0 \), in H/m is the magnetic constant (or vacuum magnetic permeability), \( μ_r \) is the relative magnetic permeability of the core material (unitless), \( N \) is the number of turns, \( A \) is the cross sectional area in m^{2} of the solenoid core and \( l \) is the length of the solenoid in meters. Note that the magnetic permeability, \( μ \) in H/m of a material is sometimes used in this equation and is defined as: \( \mu=\mu_0\mu_r \).

For multilayered coils you can use one of the many optimised versions of Wheeler’s continuous formula for wire wound coil inductance. Be careful of the many online calculators that do not inform you what equations they use – many use Wheeler’s long coil formula which requires the coil length to be much greater than the coil diameter (at least an order of magnitude larger) and hence may not provide a suitably accurate value for your coil inductance.

The following calculators by electronbunker.ca are very useful and are well documented:

## Coil Flux Density

The magnetic flux density, \( B \) in Telsa, of an energised coil is defined as:

$$ B=\mu_0 \mu_r \frac{NI}{l} $$

Where \( μ_0 \), in H/m is the magnetic constant (or vacuum magnetic permeability), \( μ_r \) is the relative magnetic permeability of the core material (unitless), \( N \) is the number of turns, \( I \) is the current through the coil in amperes and \( l \) is the length of the solenoid in meters.

## Magnetic Field Energy

The magnetic field energy, \( E_{field} \) in Joules, stored in an energised coil’s field is defined as:

$$ E_{field} = \frac{LI^{2}}{2} $$

Where \( L \) is the coil inductance in Henrys and \( I \) is the current through the coil in amperes.

Substituting the equation of coil inductance and the rearranged equation for coil flux density we obtain:

$$ E_{field} = \frac{\mu_0 \mu_r N^{2} I^{2} A}{2 l} = \frac{B^{2} A l}{2 \mu_0 \mu_r} $$

## Force on a Ferromagnetic Core

The approximate force, \( F \) in newtons, on ferromagnetic core (projectile) positioned outside of the coil at one end is:

$$ F = \frac{{B_0}^{2} A}{2 \mu_0}(\mu_{r_{air}} – \mu_{r_{core}}) $$

Where:

$$ B_0 = \frac{\mu_0 N I}{l} $$

Where \( B_0 \) is the vacuum magnetic flux density of the solenoid in Tesla, \( A \) is the current through the coil in amperes, \( μ_0 \) is the magnetic constant (or vacuum magnetic permeability) in H/m, \( μ_{r_{air}} \) is the relative magnetic permeability of air (unitless), \( μ_{r_{core}} \) is the relative magnetic permeability of the core material (unitless), \( N \) is the number of turns, \( I \) is the current through the coil in amperes and \( l \) is the length of the solenoid in meters.

# Building the coil gun

The first thing I did was look at what things restricted my design. Capacitor values are somewhat fixed in terms of voltage and capacitance. The other components in the circuit like the inductor and thyristor can be built/selected based on the capacitor bank. I utilised a box of 16 new-old-stock capacitors manufactured by BC Components, each with a rating of 200VDC and 2200µF. This seemed like a good opportunity for a first capacitor bank attempt. I decided to arranged two sets of eight capacitors in parallel, with each set connected in series giving me a combined bank rating of 400VDC at 8800µF, with a total energy storage of 704J.

I attempted to manually calculate their DC ESR by charging them to about 30v and then timing the discharge through a known resistive load. Using the discharge of a capacitor equation stated previously, I calculated an average DC ESR of approximately 50mΩ. In the bank configuration described above this results in the capacitor bank having a total DC ESR of 12.6mΩ.

I laid out the capacitors into two sets of eight capacitors in parallel, with each set connected in series. I stripped some lengths of 2.5mm2 single core copper mains wire and straightened them out. I then soldered each capacitor terminal to these copper wires until they were all connected together.

I then made a switching terminal where the charging switch and firing switch would be located. I designed a net and cut it out on a sheet of ridged polystyrene sheet. I then used a strip heater to bend the net at the marked fold lines to form the terminal box. I then cut the holes where the switches were to be inserted. I also screwed a set of choc-block connectors to the top of the terminal where the capacitor bank was connected to the charging circuitry.

I decided that I would separate the charging of each side of the capacitor bank so that I could first charge one set of eight capacitors at 200V and then the other side. This was because I preferred the option of using a lower 200V voltage power supply to charge the capacitor bank. I built a custom DC-DC variable output HV boost charger circuit specifically for this, see the project here.

For this I needed a two gang three pole rotary switch however the only cheap version I could get hold of was a four gang three pole rotary switch. I ensured it was a break before make type and rated for 250VDC. I wired the switch up so that a DC input supply could be switched off, set to charge the left bank or set to charge the right bank. Basically, in position-one the switch would not charge the bank at all, position-two it would charge the left bank of capacitors and in the third-position it would charge the right bank.

This switch comprises of four inner terminals and twelve outer terminals. Each inner terminal is associated with three consecutive outer terminals. The switch has three positions, each switch position connects all inner terminals to one of their three associated outer terminals. The inner terminals are labelled A, B, C and D. The outer terminals are labelled 1 to 12. So terminal A is associated with outer terminals 1,2 and 3 and the continuity between A and one of the other three terminals depends on the position of the switch.

There are two choc-block terminals screwed to the top of the switching terminal. The DC input choc-block has two inputs for positive and negative from the charging circuit and then connect to the four gang three pole switch. The other choc-block terminal has three inputs that are wired from the four gang three pole switch and also connects to the capacitor bank with a mid-point connection. The thyristor anode and coil ground point is also connected to this three terminal choc-block. The switch configuration is illustrated in the following diagram.

I needed to start mounting the components onto a solid base, so I cut a base board from plywood, which was later finished with a few coats of polyurethane varnish to help with insulation of the mounted components. The capacitor bank and switching terminal were connected together and placed on the board and screwed into place. I used four small wood screws to screw the switching terminal to the base. For the capacitor bank I cut large washers from a sheet of ridged polystyrene and screwed long screws directly to the base board clamping the capacitors down with the large washers.

The next thing to mount was the thyristor, this was a great new old stock find on eBay that only cost £35. It is probably over rated for my coilgun but I decided I could always use it for bigger projects later on. It is a Westcode P300KH08EJ0 with the following specifications: 300A (average current), 550A (RMS current), 10,450A (surge current), 800V (average voltage), 25µs (turn-off time), 300mA (gate current). A full data sheet is available here. There were four corner mounting holes in the base of the thyristor so I simply screwed it down to the base board with wood screws and washers. The base of the thyristor is also the anode and the positive wire from the capacitor bank is connected to the base here as well using a crimped O-lug. The cathode of the thyristor (the very thick red wire coming out of the top of the component) was bolted to a metal ‘L’ bracket which was also screwed to the base board.

The all important coil was now needed. The coil needed to be wound on a tube called a coil form. I have seen many different coil forms on the internet ranging from glass, brass and plastic. Metallic coil forms are not advised as eddie currents are created when the coil is energised that oppose the magnetic field that created them, reducing the coils efficiency. Glass has a tendency to shatter under coil compression when energised in a coilgun setting so I decided against this too. I believe that a plastic coil form is a great option and they are easy to obtain and machine.

My coil form has an ID of 10mm and an OD of 15mm and is made from clear polystyrene. PMMA (Acrylic) would also be a viable option. The tube had grooves machined at each end that allowed me to include some metal end guides in the form of large steel E-clips. The grooves had a width of 1.5mm and a diameter of 12mm so 12mm E-clips were used. This gave me a coil length between these end guides of 116mm. Metal end guides may also help to concentrate the magnetic field strength of the coil when energised but am not sure about the effectiveness of using these E-clips for that purpose. I secured them in place using epoxy resin.

I have used 2.5mm^{2} single core copper mains wire with a PVC sheath rated for 600VAC for the windings – in retrospect not the best choice as the thickness of the insulation resulted in a lower than possible winding density; enamelled copper wire would have been a much better choice but I didn’t want to splurge on a whole reel for my first attempt. It is important to work out the length of wire required before purchasing a reel or cutting a length of wire from a reel – it’s not fun getting 90% of the way through winding a coil to find you miscalculated the amount of wire needed.

The coil was made up of four layers, each layer consisting of 33 turns, resulting in a total of 132 turns. Final coil OD was 41mm. The windings were wound tightly and secured by firmly wrapping the outer windings with electrical insulation tape.

To obtain a value for the coil inductance I used a few different methods:

- Using the equation for single layer coil inductance, this gives this coil an approximate inductance value of 85.5µH.
- Measured values using the Peak Atlas LCR meter: 64.3µH @ 200KHz, DC resistance: 200mΩ.
- Measured values with a 40mm ferrite projectile positioned at the coil centre using the Peak Atlas LCR meter: 120.4µH @ 200KHz, DC resistance: 100mΩ.
- Using the electronbunker online calculator for multi-layered coil inductance gave a value of: 75.85µH

From these values I used an average ‘guesstimate’ value of 100µH for the coil inductance in the RLC simulator.

To mount the coil I cut two v-blocks from some wood and screwed them to the base board, the coil was attached to the v-blocks using cable ties. This should allow a quick and easy way to exchange the coil with different ones in the future. It may be necessary to secure the coil even more rigidly using clamping straps and stop blocks but that can come later after some initial testing. Note that the photos only show the temporary fixing of the solenoid using insulation tape.

A choc-block was screwed to the base board next to the coil and its wires were connected to it along with the wires from the thyristor cathode and negative wire from the capacitor bank.

The flywheel diode and its bleed resistor was to be added next. I wasn’t sure what the peek reverse emf surge current would be during a firing so I made an educated guess, hopefully over compensating, and chose to solder three P600J rectifier diodes rated at a total of 1200A surge current together in parallel. For the bleed resistor I managed to fish a power resistor rated 2.2Ω at 26W from my parts bin. The paralleled diode network was soldered in series with the bleed resistor. I then mounted these to a ridged polystyrene sheet which was also screwed down to the base board. This circuit was then wired in parallel with the coil via the same choc-block terminal that connected the coil to the main circuit.

The last part to add to the coilgun was the trigger pulse generator circuit which operates the thyristor gate. This circuit activates the thyristor gate for a specific set amount of time. I have used a variable timer circuit kit based on a 555 timer chip purchased from Maplin Electronics (Vellman PMK111). See below for the circuit diagram of the kit provided in their kit.

The circuit had to be slightly modified to do what I needed. I wanted the pulsed signal to go to the thyristor and not operate the supplied relay (labelled “RY1” on the PCB silkscreen and in the circuit diagram), so I didn’t populate the relay and just used the relay coil drive output by adding two wires connected to “CO2” and “CO1” marked on the PCB silkscreen which then go to the thyristor gate and thyristor cathode respectively. I also included in each of these connections a 1N4148 signal diode to attempt to protect the circuit from reverse polarity transients. The second modification was to adjust the minimum output pulse duration of the circuit. It was originally 0.5 seconds, I needed about a 1.5ms pulse. So to change this I needed to change a capacitor value of the pulse generator circuit. I replaced “C3” in the circuit diagram above with a 0.1µF capacitor. This changed the RC characteristics of the 555 circuit and with a bit of tweaking of the variable potentiometers I managed to get an output pulse with a duration of about 1.5ms. The circuit is operated by a 9V battery (PP3) which has a series push button switch added in series with this circuits input power and is located on the main coilgun switch terminal (this acts as the firing button). The circuit board was screwed to the base board.

For the ferromagnetic projectiles, I used lengths of ferrite rod which were obtained from some old FM radio coil antennas. They can be easily purchased online and are usually listed as 10mm ferrite antenna rods, ranging in lengths up to about 200mm. The rods I salvaged had a diameter just shy of the 10mm ID of the coil form tube and needed a little smoothing down with some emery paper! Different lengths will be experimented with, but I started off with a length of about 40mm.

Everything was complete so some low powered tests were carried out to test the device before a full power test was successfully undertaken. I will be looking into tuning the circuit and making some tweaks here and there to try and improve the coilgun in due course, perhaps use what I’ve learnt to make a second version…

BooGreat work but once an scr is triggered it’s on, plain and simple, why a timing circuit for trigger that has only 2 states of function ?

GardenBallisticsPost authorThat is true for over-damped and critically damped LCR circuits or where the thyristor is always positively biased. However, in this case the LCR circuit was purposely designed to be under-damped to maximise the peak current through the coil and reduce the pulsed discharge duration. This means that after a short incomplete discharge time the voltage across the coil and hence thyristor drops and inverts (thyristor becomes negatively biased). Current, with an phase lag of about 90°, through the thyristor also drops towards zero and below the SCR’s cut-off threshold (i.e. turns off). The duration of the SCR trigger signal is set to be less than this inversion period to ensure that the thyristor does not receive a gate current signal after this initial pulse discharge and then continue to conduct on the next positive resonant cycle; hence the requirement for a timing circuit to produce a trigger pulse with a specific duration. The reversed polarity can potentially damage the the polarised capacitor bank which is why a large clamping freewheel diode is used to shunt the resonant negative voltage across the capacitor bank.