# Coil gun

Basic coil gun showing all the components (Barrell, projectile, switch, capacitor and safety bleeding resistor)

Also abbreviated CG.

A device that accelerates a ferromagnetic projectile using a coil of wire and a pulsed power source, usually capacitors. A large current is put through the coil, creating a magnetic field and attracting the ferromagnetic projectile. When the projectile passes through the coil, the current is switched off and the magnetic field disappears, allowing the projectile to keep going.

The principle of operation is simple: Once a voltage is applied to a coil (most of times it is a multi layered solenoid), the current ramps up and a magnetic field establishes in a V/L fashion. Once this magnetic field is established the armature (the projectile) made up of ferromagnetic material magnetizes and experiences a force towards the center of the solenoid. The force is attractive on both ends so it means that once the armature has reached the centerpoint, it will experience a braking force (known as suck-back). It is to be noted that the center point can be a center region depending on the coil and projectile length. With long coils, there will be a period where no force is exerted on the projectile. This is one of the major problems of coilguns since the current cannot be halted instantaneously, so the pulsetimes must be planned or switching system employed. There are many types of designs each with his advantages and drawbacks. If the current is collapsed correctly the projectile will hold a resultant velocity and will exit the coil with his kinetic energy resulted from the balance between acceleration and braking.

From a more theoretic point of view the magnetic system tends to maximize the coupling between the projectile and the coil (tends to maximize inductance) at a given current level and the maximum inductance point is the center of the coil. Hence the projectile is attracted into the center.

## Designs

### Basic

The simplest design is a coil of several turns and several layers around a tube with a cut piece of nail or other ferromagnetic projectile just entering the coil. The leads of the coil are touched to a charged capacitor of several joule of energy. The projectile is pulled into the coil and continues out the other end.

Old ballpoint pens make convenient barrels for first coilguns, but are not ideal. Sewing machine bobbins are a great choice since sewing machines can be used to wind the coil.

### Improvements

There are several aspects to improve apon a quick and simple coil.

It probably

• has high switching losses. The resistance of the coil leads just touching the cap is likely to be higher than the resistance of the coil.
• hasn't got the best turns number.
• has too thick a barrel. The gap between the coil and the armature should be as thin as possible.
• suckback. A reduction in speed after passing the coil's midpoint, due to a remaining magnetic field. This can be avoided with timing changes.
• back EMF. Any energy that isn't put into waste heat or the armature will come back to the capacitor. Unfortunately, it will come back with the opposite voltage, which many capacitors don't like.
• eddy currents. The sudden surge in magnetic field induces currents in any conducting parts of the coilgun. This wastes power. Eddy currents in the projectile are doubly bad since they also repel the projectile.

### Multistage Designs

More powerful coilguns can be made by simply using bigger caps to brutishly dump more energy into the coil. This can only be taken so far and, besides, it isn't efficient. Using bigger caps does not explicitly mean the effiency has change either way. The launching of larger loads naturally increases the required amount of energy. Example: 500 joule of caps in a single stage to launch a 10 gram steel load is excessive just as it would be to use 5 000 joule to launch a 100 gram load. However, this same big 5 000 joule of caps in a single stage to launch a 1 000 gram steel load is not necessarily inefficient.

A better approach is a multistage design. This is using a number of smaller coils with possibly smaller energy banks energized in succession to accelerate the projectile, rather than a single large pulse with a big coil.

To break free from fear perpetuity of when to fire succeeding stages, simply tune the first stage as it it were the only stage in the system then repeat for each stage thereafter. Add another stage to the this tuned first stage. All which needs to be done now is to tune the second stage. As long as the second stage is at a distance from the first, no degree of good and bad tuning of second stage will affect the performance of the first stage. Because each succeeding stage does not affect the performance of a precusor stage, this same approach may be continually applied for remaining stages. As stage numbers increase, the actual coils will require proper tuning of correct wire gauge, length, and layers along with energy selection per stage. This is a pure concern and discipline of an individual stage and not the rumored "abandon ye all hope" hurdle of a multistage design because as stated above once the preceding stages are tuned they are not affected by the addition of untuned stages.

## Parts

### Capacitors

See Capacitor

Capacitors from camera flashes are an excellent choice for their easy availability and 250 volt + rating. See Photoflash Capacitor. Capacitors from computer power supplies have also been used. Although they can store a large amount of energy, supercaps are not suitable because of their ESR and the fact that pulse discharges wreck them.

A good coilgun capacitor has low ESR. Low ESL can also be nice but as long as it is much less than the coil inductance it should be worried about. See ESR and ESL on the capacitor page.

The amount of energy a capacitor needs to be able to hold depends on what you want the coilgun to do. A single 12J capacitor is adequate for a simple demo coilgun.

You could get an idea of how much energy to use from the efficiency and ballistics calculations. Otherwise you could just take something less than 100J and continue building.

### Switching

Switching can sometimes be done with a simple mechanical switch for low power, but this usually wastes energy.

SCRs are the more commonly used naturally commutated switches. The natural commutation may be "forced" but by elaborate and wastefull means. SCRs possess a high power to size ratio as a result of a standard surge-to-average current ratio of 10:1. The only drawback of these devices is the impossibility of being turned off except when the voltage difference measured at the terminals is lower (usually negative) than the forward voltage of the SCR.

IGBTs are forced commutated switches allowing coil current to be turned-off as well as turned-on. Controlled switching allows for more control. The presence of an IGBT does not mean an automatic increase in performance. The combined integration of inductance, projectile geometry, and storage energy still must be finely tuned along with this newly added variable of proper turn on/off timing. IGBTs possess a low power to size ratio as a result of an standard surge-to-average current ratio of 3:1. Their cost is higher than SCRs though.

### Projectiles (or Armatures)

The projectile should be ferromagnetic, ie. strongly attracted to a magnet, like iron or steel. (Other than that it's not entirely clear what properties of materials make for a good projectile, but a high saturation magnetization seems to be the most important and with permeability playing a less signigicant role. Many models, simulations and techniques confirmed the importance of a high saturation magnetizazion. In addition simulations have shown supermalloy might be the optimum material to use for a projectile, but nobody on 4HV has managed to get hold of a sample... (anyone?). Permalloy seems good, but strangely, mu metal doesn't seem to perform in simulations. Taking into account both cost and repairability steel seems the best compromise)

The projectile should fit as snugly into the barrel as possible and ideally be about as long as the coil.

The projectile should not support eddy currents- particularly circumferential eddy currents. (This can be achieved by making the projectile out of a laminated material, or not quite as effectively, by slotting the edge of the projectile lengthwise.)

### Barrels

Barrels are usually a thin straight tube of plastic. There are a few performance gains you can get from using properly designed barrels. The most prominent being a "reduction" of eddy currents. To avoid eddy currents you should use a non-metal barrel. Also, thinly walled barrels help the magnetic field "grab on" to the projectile. Generally speaking, plastic barrels can be one of the easiest choices to enhance performance gains.

Metal barrels can be used, but they should be slotted or laminated. If the barrel is ferromagnetic then some magnetic flux will pass through the barrel rather than the projectile which represents a loss of efficiency, but can be better than an air gap. Thin metal barrels are very important to prevent shielding effects.

### Coils and Coilforms

(See also Inductor) The coils are in general wound using enameled copper wire with sizes ranging from AWG28 and AWG14. Coilforms are used to keep the coils straight and hold them in place (and eventually host various type of sensors). They can be made from plastics and must assure good mechanical and thermal properties for coils.

### External Iron

The main idea behind external iron is to try to reduce the reluctance around the loop, so that a higher flux can be concentrated on the projectile. End iron should have holes only slightly bigger than the projectile, and there should be external iron surrounding the entire coil and butting up to the end iron as closely as possible to reduce the total air gap in the magnetic circuit.

The role of external iron can be better thought of in terms of ΔL. If there is no external iron, the projectile can at the absolute theoretical maximum only halve the airgap in any loop inside and around the coil. On the other hand, if there is external iron, the airgap in the loop can be reduced by a huge factor from the total amount of air inside the coil to the very small gap between the projectile and the external iron.

Using external iron is a balance between this improvement in ΔL and the extra source of eddy currents. Thus external iron needs to be as ferromagnetic as possible while having the lowest conductance. External iron may need to be laminated or slotted to prevent eddy currents. Also it must be assured it doesn't saturate, so it may be a waste of time and efforts when the energy per stage is higher than a couple of hundred joule

There are many ways to provide external iron. One is to put washers on each end of the coil and then push the whole thing into a piece of iron pipe. Eddy currents can be a major issue with this method so remember to cut slots in the metal - at least one along the length of the pipe and one from the centre of each washer to the outside.

A simple method that can be effective is to simply wrap the coil in old video tape. Some people have also experimented with using powdered or filed iron, held in place with glue.

External iron should thick enough to provide a good 'flow' path for the magnetic flux. Large overlaps with the projectile seem to be needed, so a longer projectile is optimum when end iron is present.

Experimental results have been a bit mixed however.

## Potential Issues

### Coil Resistance

The vast majority of the energy is lost as heat, rather than going into the projectile.

The main offender is the resistance of the coils. Power dissipated is a square law on current, so the very high currents used in coil guns means that very large amounts of power are lost there. Using lower currents reduces losses, but reduces accelerations and hence demands an impractically long multistage coilgun.

Ideally coils should be superconducting, but no amateur to date (because I actually asked every person on earth(4hv is considered earth)) has attempted this. Madgyver, however, has experimented with cooling coils with liquid nitrogen before firing. (See 4HV thread) Research suggests that ~50% efficiency should be achieveable with superconducting coils.

### Eddy Currents

The sudden magnetic pulse from the coil not only pulls the projectile but induces currents in any conducting parts of the coilgun. This wastes power as heat. Eddy currents are typically produced in any external iron, the barrel, if metal, and the projectile. Eddy currents in the projectile also produce a Lenz reaction (See Lenz's Law) which repels the projectile. See Eddy current.

### Energy in the Magnetic field of the coil

The energy in the magnetic field does not dissipate, it returns to the capacitor when the EMF is removed and the current is decreasing. Unfortunately it does this in the reverse direction (via a 'ringing' mechanism), which can seriously damage polarised capacitors (such as electrolytics).

In the circuit it appears as if the magnetic field keeps the current in the coil flowing after the capacitor has discharged, so that it keeps "discharging" and builds up a negative voltage. This is similar to an LC oscillator.

#### Quenching

The capacitor can be protected using a diode in antiparallel, stopping it from developing much reverse voltage. Now the back current loops around through the coil and diode circuit until it dissipates by any resistance.

Often a resistor is put in series with the diode to help the back current die away more quickly. This can also help with the issue of suckback. Unfortunately the resistance of this resistor is limited by the switch voltage since the higher the resistor, the higher the voltage spike of the switch. The degree of which will not be definetively known until physical effort is take to measure actual results.

#### Halfbridge Circuit

Quenching the back current can improve efficiency but only so far, since it in itself wastes energy. Instead of channeling the back current to a resistor, the halfbridge circuit channels it with the right polarity to a capacitor. This can increase the efficiency per stage up to 10% and higher depending on the coil resistance. The main drawback of this technique is doubled power component count and special types of drivers for the switches. Some members of 4HV managed to build a similar device with lots of efforts put in and good results.

### Back EMF

Back EMF is caused by the motion of the projectile in the magnetic field- the projectile becomes magnetised and since it is moving through the coil induces a back EMF that opposes some of the voltage on the coil, reducing current in the coil and hence lowering acceleration.

The back EMF does not directly lose power. Indeed, by reducing the current in the coil it reduces I2R losses there. However it does considerably reduce performance.

### Suckback

The magnetic field of the coil pulls the projectile into its centre. When the projectile has passed the centre of the coil, if the magnetic field hasn't been completely switched off, it is now working against the magnetic field. This is called suckback.

The projectile slows down and its kinetic energy is returned to the coil in the form of current. So suckback does not directly waste energy (although the current indirectly induces resistance losses in the coil); some of the energy is recoverable by a halfbridge system. It does reduce the amount of energy in the projectile.

To avoid suckback, there should be minimal current in the coil once the projectile has passed the centre. This can be achieved either just by good timing, by switching or by quenching.

### Projectile saturation

1. When the armature is far from saturation, the force is roughly proportional to the square of the coil current.
2. When the core is strongly saturated, the force is nearly linearly proportional to coil current.

#### Limits imposed by projectile saturation

In short, even when the armature is saturated, force still increases with coil current, albeit at a slower rate. Where the diminishing returns come in is with the losses. When the armature is not saturated, force and coil loss follows roughly the same I2 law. When the core is saturated, armature force goes as I and loss still as I2...so as you increase coil current beyond a certain point, efficiency degrades when energy losses outstrip energy transfer to the armature. This is why multistage launchers are always advantageous....

#### Intuitive view of saturation

Iron contains a large number of small magnetized areas with random orientation so the sum of magnetization is zero. When the iron is placed in a magnetic field the small areas start to align themselves with the magnetic field.

The stronger the field the more areas align and the stronger a magnet the iron becomes. So the force rises with the square of the current because the field gets stronger and the iron becomes a better magnet.

When all available areas are aligned the iron is said to be saturated and can't become a better magnet. The force then continues to rise linearly.

## Design Principles and Concepts

### Fundamentals

It's the magnetic field (B field) that propels the projectile and a stronger B field generally means more force. The B field depends on the effective current in the coil, or the actual current flowing into and out of the coil multiplied by the number of turns in the coil.

As more turns are added to the coil, the strength of the B field for a given current is increased, however the maximum current in the coil is decreased due to the extra resistance of the wire and inductance in the coil. The resistance does nothing to pull the projectile and should be avoided. (See the other sections of this page for more details on finding the optimum number of turns.)

### ΔL

A good coilgun has a large change in inductance (ΔL) when the projectile enters the coil. In other words, there's a sudden increase in flux when the projectile is pulled inside.

In fuzzy anthropomorphic terms, the coil wants to complete a good, low-reluctance magnetic circuit through the middle and out around the outside. The more that the projectile would help it achieve this, the more eager the coil will be to pull it in.

In crisper theoretical terms, low-reluctance represents a minimal energy for the coil. The projectile is pulled into the coil to achieve this low energy stage and the energy is transferred to the projectile. The greater the drop in energy, the more energy the projectile gets.

Good ΔL can be achieved using external iron.

Measuring inductance with and without projectile tells you how good the magnetic properties of your coilgun are at low power and frequency. It doesn't, however, show if your coilgun has problems with eddy currents, saturation or other problems that only appear in real tests.

### Timing

If the pulse is too long then the projectile will have suckback. If the pulse is too short the projectile won't have moved through the magnetic field for long enough to pick up much energy.

The length of the pulse is defined by the inductance of the coil, the capacitance, the resistance in the circuit as well as the complex interactions between the projectile and the coil.

The time in which it takes the projectile to reach the middle of the coil depends on the mass of the projectile, the power of the coilgun and the initial position of the projectile.

The issue of timing becomes even more involved with multistage coilguns, since there is the added question of when to fire each stage.

To break free from fear perpetuity of when to fire succeeding stages, simply tune the first stage as it it were the only stage in the system then repeat for each stage thereafter. Add another stage to the this tuned first stage. All which needs to be done now is to tune the second stage. As long as the second stage is at a distance from the first, no degree of good and bad tuning of second stage will affect the performance of the first stage. Because each succeeding stage does not affect the performance of the preceding stage, this same approach may be continually applied for remaining stages. As stage numbers increase, the actual coils will require proper tuning of correct wire gauge, length, and layers along with energy selection per stage. This is a pure concern and discipline of an individual stage and not the rumored "abandon ye all hope" hurdle of a multistage design because as stated above once the preceding stages are tuned they are not affected by the addition of untuned stages.

## Modelling

### LC Model

This is the simplest useful model. It describes the capacitor and coil system as an LC Oscillator. The capacitor discharging into a coil is a quarter of a complete LC cycle.

The LC model does not say anything about the projectile because in fact it assumes there is no projectile. Instead it can give simple estimates of discharge times and currents.

### LCR Model

The LCR model goes one step further than the LC model and takes into account any resistance from the wires and the capacitors ESR.

There are some Java simulators for LCR circuits on the web. Try Barry's RLC Simulator or the Circuit Simulator.

### Simple magnetization models

Considering the projectile simply a dipole with mass with a magnetization following simple laws interacting with a magnetic field can be helpful to model coilguns but the results cannot be very precise (20% error), however it is useful for learning of coilgun dynamics

### Finite Element Analysis

Using FEA software, such as FEMM, you can build a model of your coilgun and see its electromagnetic properties.

This can help with understanding how the parts of the coilgun affect the magnetic field and how it interacts with the projectile. They aren't usually made for coilgun design and don't say anything about how the motion of the projectile and the coilgun circuitry affect each other. Fortunately many of these FEA programs include scripting and can be used to model coilguns. Some members of 4hv have managed to run some simulations and compare with the reality obtaining small errors (<5%)

Bill's models take into account the interaction between the coil and projectile and attempt to work out its path.

See Bill Slade's Page for full details.

## Calculation and Measurement

### Discharge Time

Using the LC or LCR model, this can be taken as the quarter of a period.

For the LC model this is $\frac {\pi \sqrt{LC}}{2}$.

### Peak Current

With the LC model, an upper estimate can be taken as $V.\sqrt{\frac{C}{L}}$

### Velocity

The velocity of the projectile can be calculated by taking measurements of the landing position, using a ballistic pendulum or a photogate speed-trap.

#### Ballistics Measurements

This method requires the least investment in equipment.

It involves taking measurements of the initial and final positions of the projectile and using these to calculate its velocity (see ballistics). There is no need to measure any times as long as you take the right measurements of space.

The two simplest situations to do measurements and calculations for are firing the coilgun perfectly horizontally and firing it at 45 degrees on a horizontal surface.

A very low power coilgun can also be fired vertically and the highest point reached by the projectile measured but this unlikely to be accurate.

If the projectile isn't fast enough to leave any dent marks in things, it can sometimes help to dust it with chalk or something. Having some sort of mark to refer to makes measurements much more accurate.

Note that if the projectile is spinning significantly in flight, then this will represent some energy in the projectile not accounted for by the velocity measurements.

#### Acoustic Measurements

One of the easiest ways to measure velocity is with a microphone and your sound card. Use a waveform editing program (e.g. http://audacity.sourceforge.net) to obtain the exact time between launch and impact. Put a soundboard as a target two or three meters away, and measure the distance carefully. Level your barrel before shooting, but the amount of vertical drop is of no consequence in this test; we only want the horizontal component of velocity.

Be sure to account for the speed of sound in air (~343m/s) -- it will make a big difference. This will be easiest if your microphone is either on the coilgun or on the target, since then you'll only have to make one correction. If you put the microphone on the coilgun, the corrected time will be t0 - s / (343m / s) where t0 is time measured on the computer, and s the distance between coilgun and target. Alternatively, if you place the microphone the same distance from the gun and the target then you do not need to correct for the speed of sound since the time delays are the same.

#### Ballistic Pendulum

If the projectile is fired at a pendulum and becomes trapped/embedded in it, the pendulum will swing upwards. We can use conservation of both energy and momentum to estimate the speed of the projectile. The momentum of the projectile and pendulum immediately after the collision will be the same as the momentum of the projectile. The speed of the pendulum can be estimated from seeing how high it swings, its potential energy due to the difference in height from the top tot he bottom of the swing is the same as its kinetic energy at the bottom of the swing.

For an example of how to make a computerised ballistic pendulum, see Smart Ballistic Pendulum.

#### Photogate Speed-trap

An object passing through a photogate breaks a light-beam, triggering an electronic circuit. If two photogates are set at a fixed distance apart and an object passes one and then the other, the average speed of the object can be calculated by measuring the time taken. See PIC speed trap.

#### Mixed "Acoustic" and Photogate Speed-trap

A combination of a pair of photodiodes (or phototransistors) and a PC soundcard can also be used as a speed trap. As in the "Acoustic Measurements" section above you use the sound card as the data logging system. The actual detection of the projectile is done optically instead of acoustically. A pair of detectors is positioned such that the shadow of the projectile passes over them. For many soundcards the MIC can provide the voltage needed for the photodetectors. If the detectors are placed one inch apart then a typical soundcard can measure velocities in the few feet per second to several hundred feet per second range. For more information see [1] or [2]

### Efficiency

Efficiency is usually calculated as the amount of energy the projectile gains divided by the amount of energy initially stored in the capacitor.

Efficiencies for coilguns are currently very low. First coilguns are often below 1% efficient. Coilguns above this are fairly good.

The energy in the capacitor is calculated as $E = \frac {V^2 C}{2}$.

There are a number of ways to calculate the energy of the projectile. The most common is to measure its velocity and use $E_K = \frac{m v^2}{2}$

Another way is to use a ballistic pendulum.

### Optimum Coil Shape

Best Coil for a given Capacitor Size

• Pulse width

The best coil for a given capacitor size is the one where when the capacitor is discharged and accelerates a load, the pulse width is approximately equal to what you wanted it to be and the magnetic force exerted on the load is approximately equal to what you wanted it to be. A coil might have the correct pulse length as desired but yet not exert sufficient force on the load due to a low inductance value, 1 layer and 5 windings for example. As for pulse width, say the force on the projectile exerted is satisfied, but the pulse width is longer than desired, so long that the projectile is slowed down or oscillates. Proper force alone without proper pulse width would then be meaningless.

• Pulse Shape

The best coil for a given capacitor size is the one where when the capacitor is discharged and accelerates a load, the pulse shape is approximately equal to what you wanted it to be. For a forced commutation system (on/off) controlling a constant current source (excess capacitance) the waveform should be as horizontal as possible or as designed. If the waveform significantly drops as it approaches the end of the pulse width, then the coil needs to be altered or the capacitor size (Farads) need to be increased, which negates the whole "Given capacitor size" idea.

The best coil for a given capacitor size is the one where when the capacitor is discharged and accelerates a constant load, the dynamic pulse width and pulse shape requirements are satisfied. A coil may actually produce the correct pulse width and shape for an unloaded (dry fire) discharge. However, the coil's inductance does dynamically change when in close proximaty to a metallic object, thereby affecting pulse width and shape, and consequently demoting the coil from the rank of best. Another example of load constraint is to have the best coil for a 5 gram slug during experimentation but not have the best coil for a finally decided same 5 gram mass slug but with a different diameter, length, or metallic property.

## Safety

Switching systems sometimes do unexpected things, the capacitor is probably charged even when the charger is off and coilguns have been known to fire backwards so always stand to the side of any coilgun with projectile in the barrel.

The capacitors used in coilguns contain a potentially lethal amount of energy. Use bleeder resistors and hard-wired voltage indicators and be aware that the charge will stay in the cap even when the charger is switched off. See Electrical safety.

Making an attempt to first learn basic electronics and then build an experience base will not only go a long way but will also empower this same builder to solve multitudes of problems in short order which would otherwise appear to be difficult to overcome for the low effort attempted builder whom always ask first without even considering to try for oneself.