Paper: Coilgun Conor Shanley Dr. Dann

Shanley 1

ASR Final (March) Paper: Coilgun

Conor Shanley

Dr. Dann

Applied Science Research

April 24th, 2013

I. Abstract

Over the course of this project, a 3-stage coilgun was constructed using copper magnet- wire coils, polyurethane extruded tubing, capacitors, and various circuit components. The capacitors are charged via an external power source, while the relay circuit is powered by an on- Shanley 2 board battery. Rare-earth magnets serve as the projectiles for the coilgun. Input energy is

27.072J (24.4 used), and output energy is 0.1829J, reaching an efficiency of 0.75%, and a maximum projectile speed of 8.467 m/s.

II. Introduction

A coilgun, or gaussian gun, is a linear motor that accelerates a ferromagnetic projectile via the sequential activation of several electromagnetic coils. For this project, coils will be activated in sequence using hall sensors. Four to six stages will be used for the final design. If time permits, a proper frame and grip will be mounted around the basic design, for a customized look and feel. This project was inspired by a prompt on the ASR webpage. From this project, I hope to gain a deeper understanding for the principles of magnetism, circuitry, and craftsmanship. Shanley 3

A coilgun, as the name infers, uses several coils to produce a magnetic field that runs through the coil lengthwise (see figure 1). A ferromagnetic projectile is placed in the coil, such that the field from the coil and the field from the projectile push against one another, accelerating the projectile. If the coil was on continuously, the projectile would only accelerate until it reaches a certain “equilibrium” point, where it would stop. The projectile, when left alone with an active coil, will align itself with the field of the coil. Thus, if the coil were left on continuously, the projectile would stop in the center of the coil.

Figure 1: Magnetic Field of Coil

There are two ways to work around the problem of a decelerating projectile. The first, and more simple way of preventing the coil from decelerating the projectile, is by placing the projectile “past” the coil. If the field of the projectile and the field of the coil are opposing, and the projectile is already past the center of the coil, the coil will simply push the projectile until the magnetic fields are too far to act upon one another. This method is commonly implemented in single-stage coil guns.

If the projectile does not have the desired speed after just one coil, multiple coils can be used in sequence to accelerate the projectile more. Unfortunately, there is no initial projectile Shanley 4 placement that can solve the problem of deceleration (the projectile cannot be placed “past” more than one coil; the coils would not put any force on the projectile and would hence be useless).

Instead of changing the initial projectile placement, coils can be activated in sequence

(“switched,” much like in the DC motor project). As the projectile approaches a coil, the coil turns on, accelerating the projectile. The coil then switches off, before the projectile reaches the middle, allowing the momentum of the projectile to carry it to the next coil, and so on. Each coil is referred to as a “stage,” hence the name, “staged coilgun.” The sequential activation of the coils in the gun can be achieved in several ways. In this project, several attempts at creating a dark-activated switch were made, with little success. Thus, hall chips were used in sequence with transistors and relays to switch the coils on and off. The specific design for the coilgun is discussed in section IV.

III. History

The coilgun is sometimes referred to as the “gauss gun,” a name attributed due to the contributions made by Carl Friedrich Gauss. Gauss is responsible for “formulating mathematical

descriptions of the magnetic effect used by magnetic accelerators” (5). The gauss gun, or

magnetic linear accelerator, works on the principles of conservation of momentum. Ball bearings are magnetized and in contact with a ferromagnetic object. If one bearing is on one side

of the magnetic object, and several bearings are placed in sequence on the other side, then the

ball bearing at the end of the chain is only very weakly attracted to the magnet (because it is

farther away than the others). However, if a ball bearing collides with the other side of the

magnet, its velocity will increase due to acceleration provied by the force of the magnetic pull.

In the collision, the momentum of the initial bearing is conserved, and transferred to the other

side. Since the far bearing is much more weakly acted upon by the magnet, it shoots off much Shanley 5

faster than the initial bearing. Figure 2 shows a primitive magnetic linear accelerator.

Figure 2: Magnetic Linear Accelerator

The invention of the first electromagnetic coilgun (a derivative of the magnetic linear accelerator) is attributed to Kristian Birkeland, a Norwegian scientist known for describing the

Aurora borealis. Birkeland patented the design in 1900, but failed to develop the idea into a plausible weapon design. Thus, the idea was lost for many years. More recently, however, the coilgun has been suggested for use in several different contexts. Coilguns have several recently proposed applications, due to various advantages held over other technologies. For example, because coilguns are capable of accelerating projectiles to such high velocities, they have been considered for delivering payloads into space (3). In terms of weaponizing the coilgun, it has fewer moving parts than a conventional rifle, and is also naturally silent, save the noise from the projectile moving at such high speeds. Ram accelerators, (essentially large versions of the coilgun), also have numerous applications (4).

IV. Design

The mulit-stage coilgun to be constructed in this project is designed to be adjustable, in order to idealize the position of the coils on the barrel, maximizing the projectile speed. Figure 3 shows a 1-foot section of the barrel, with 3 stages on it. This is the final barrel design. Each stage of the coilgun has a 300-turn 24-gauge copper wire coil. Coils are evenly spaced along the barrel. Shanley 6

Figure 3: 1-ft coilgun

A detail view in figure 4 shows the copper wire coil mounted on a “coil mount,” which is adjustable laterally around the main barrel. Each coil consists of 300 turns, which are shown in the drawings (see appendix B) The barrels are made out of ⅛” ID extruded plastic tubing, and the coil mounts out of ⅜” ID extruded plastic tubing.

Figure 4: Detail View of Coil

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NOTE: Refer to Appendix B for exact Part Drawings/Dimensions.

As previously mentioned, attempts were made at creating dark-activated circuits to activate the coils sequentially. IR LEDs were placed across the barrel from IR phototransistors, which were supposed to act like switches, allowing a bank of capacitors to release their charge through the coil when the light to the phototransistor was interrupted. Unfortunately, the circuit produced could not store a charge in the capacitors without it leaking through the transistor and through the coil. Thus, the idea was scrapped in favor of a hall chip circuit. A circuit diagram of one of these failed dark-activated switches is shown in figure 5.

Figure 5: Dark-Activated Coil Circuit (not used)

In figure 4, the leads on either end of the bank of capacitors correspond to either end of the coil-transistor circuit below. Shanley 8

The hall circuit used in the final design uses a hall chip, which sends current through a relay depending on the position of the projectile with respect to the hall chip. Figure 6 shows a circuit diagram of the final circuit used.

Figure 6: Hall Switch Circuit

The default channel on the relay (closed when the relay is OFF) is “floating,” meaning that it is not connected to a voltage source or ground. This allows the capacitors to charge without leaking. The Hall switch in the circuit is extended via hookup wires to in its position above the barrel, shown in figure 7. Since the projectiles are also magnetic, hall switches can be used to activate the coils when the projectile passes them, thereby producing a chain reaction when multiple coils are placed in sequence. Shanley 9

Figure 7: Hall Chip on top of barrel

V. Theory

This section will discuss the theory behind the operation of a coilgun. As mentioned in the introduction, a coilgun works by spiking a current through a coil for a short amount of time, creating a temporary magnetic field that interacts with the magnetic field of a ferromagnetic projectile, accelerating it along the length of the coil. Several calculations were used to determine the overall efficiency of the gun.

Firstly, the magnetic field of the coil can be calculated by the equation B = µnI, where n = N/L.

In this equation, the magnetic field B is equal to µ (the magnetic permeability constant) times I, the current in the coil, times “n.” This number “n” is determined by the number of turns in the coil, N, divided by the length of the coil, L. In general, the field of the coil should be Shanley 10 greater than the field of the projectile, because the coil’s field is variable, while the projectile’s field is constant. The field can be altered most easily by changing the current through it.

However, since the current through the coil in this coilgun setup is generated by a spike, and not a constant power source, the magnetic field in the coil is only present for a short amount of time, and during that duration is constantly changing. Therefore, the field strength was determined arbitrarily (by choosing the design of the capacitor bank), and is somewhat irrelevant to test results.

The current spike generated by the capacitor bank will have several high-voltage capacitors wired in parallel. The capacitors are wired in parallel because this ensures the maximum charge that is held in the circuit. For adding capacitance of capacitors in parallel, we use the equation

Ct = C1 + C2 + C3...

In the final design, three banks of capacitors, each with 15 4700-uF, 16V capacitors were constructed. Thus, the total capacitance was calculated using the equation.

Ct = C1 + C2 + C3... +C15, where C1 = C2 = C3... = C15

Ct = 15(C1)

Ct = 15(4700uF) = 70,500 uF

By finding the capacitance of the capacitors in the circuit, the input energy of the circuit can be calculated:

U = ½CV^(2)

Where C is the capacitance and V is the voltage across the capacitors. Thus, the energy of one stage of the coilgun was calculated.

U = ½CV^(2) Shanley 11

U = ½(0.0705 F)(16 V)^(2) = 9.024 J

Multiplying by 3, the total input energy to the coilgun is calculated.

3*(9.024 J) = 27.072 J

Since the voltage variable is squared in the equation, increasing the input energy is most effectively done by increasing to voltage in the voltage spike. To do this, several 16 V capacitors are used.

To calculate the output energy, the velocity of the projectile as it exits the coilgun must be measured. With a muzzle velocity, and the weight of the projectile, the kinetic energy of the projectile can be measured, via the equation

KE = ½mv^(2)

Finally, the efficiency of the coilgun can be measured by comparing the input to the output energies:

%E = output/input = KE/U x 100%

Based on early prototype tests, the final coilgun was aimed at around 10% efficiency. If this were to be the case, then an estimate for the velocity of the projectile can be calculated, as follows:

If %E = 10%, then KE = U/10

U/10 = (27.072 J)/10 = 2.7072 J = KE

If KE = ½mv^(2), then v = (2KE)^(½)/m, (m = .24oz = 0.00680389 kg) v = (2*2.7072)^(½)/(0.0068 kg) = 342.189 m/s

The actual efficiency of the coilgun was measured after its completion, and is significantly lower than the projected 10%, because of several sources of systematic error. These results, along with any error, will be discussed in section VI. Shanley 12

VI. Results

As previously stated, the original design for the coilgun involved dark-activated switches to activate the coils in each stage of the coilgun. In principle, and IR LED would shine directly onto an IR phototransistor (attached to the rest of the circuit). When the IR light is uninterrupted, the circuit is open, and the capacitors can charge (in theory). However, when a projectile passes through the barrel, it interrupts the light, causing the capacitors to send a current spike through the coils, thereby propelling the projectile. One of these such circuits is shown in figure 8.

Figure 8: Dark Switch

Unfortunately, when put to use, current leaked through the transistor when the capacitors were supposed to be charging. This is most plausibly due to inconsistency of the IR light source.

After weeks of trials, the idea was eventually scrapped in favor of the hall circuit design.

The hall circuit (see section IV) was replicated three times, and constructed on a single breadboard for consistency. Figure 9 shows the completed circuits on the breadboard. Shanley 13

Figure 9: Breadboard config for final coilgun

Each hall chip was soldered to hookup wires, so that they could plug into the breadboard and be positioned correctly over the coils. The coils were constructed using ⅜ in ID extruded tubing, each in 2-inch sections. These sections (“coil mounts”) each had 300 turns of 24-gauge copper wire wrapped around them, and were slid over a 1-ft section of ¼ in ID extruded tubing, which served as the barrel. of the gun. Figure 10 shows one of these coils. Shanley 14

Figure 10: Coil & Coil mount

3 banks of capacitors, each with 15 4700uF, 16V capacitors were constructed for the circuit. All of the capacitors were wired in parallel to maximize capacitance. Figure 12 displays on of these capacitor banks.

Figure 11: Capacitor Bank

Thus, the final coilgun was constructed on a sheet of plywood, shown in figure 13. Shanley 15

Figure 12: Completed Coilgun

To test the efficiency of the coilgun, a photogate was set outside the end of the barrel, as shown in figure 14. The photogate was attached to a LabQuest, which recorded the times of when the photogate was blocked and unblocked. By subtracting one time from the other, the total time that the photogate is blocked by the projectile is given. Therefore, the bullet travelled its own length (1/2 in) in that amount of time. Shanley 16

Figure 13: Photogate setup

The bullet, when fired, passes the hall sensor so quickly that the capacitors don’t have enough time to release all of their charge. As a result, the coilgun can be fired (with considerable consistency) multiple times on a single charge. Therefore, in order to test the efficiency, the coilgun was fired until there was no charge left in the capacitors, and had in fact used all of the input energy. A velocity vs. # of shot fired graph is shown in figure 15. Shanley 17

Figure 14: Velocity of Projectiles vs. Their sequential order (NOTE: all raw data and calculations are found in

appendix C)

The kinetic energy of each of the projectiles was calculated (see section V), and totaled to find the total output energy, shown in figure 15.

Figure 15: Kinetic Energy of Projectiles & Total KE Shanley 18

The coilgun fired 25 times, without a significant depreciation in the speed of the projectile. At this point, use of the gun ceased, and the voltage across each capacitor bank was measured. These voltages were used to calculate the amount of energy left in the coils.

U = ½CV^(2)

V1 = 1.819 V, V2 = 2.634 V, V3 = 8.081 V

Uf = U1 + U2 + U3

Uf = ½(.0705F)(1.819V)^2 + ½(0.0705F)(2.634)^2 + ½(0.0705)(8.081V)

Uf = 2.663 J

2.663 Joules, out of the initial 270.72 Joules put into the capacitors remained present. By subtracting the leftover energy from the initial input energy, the “true” input energy is found (the amount of the input energy that was actually used).

Ui - Uf = Ut

27.072 J - 2.663 J = 24.409 J

Finally, the efficiency of the coilgun was calculated.

%E = KEt/Ut * 100%

%E = (0.182933 J)/(24.409 J) *100% = 0.749% efficiency

VII. Discussion & Conclusion

Aside from the half-time switch from LED circuits to hall switch circuits, the entire process of building and testing the coilgun went very smoothly. The final product is neat and organized, and can accelerate a ferromagnetic projectile with a respectable amount of force.

Throughout the procedure, several sources of error could attribute to the relatively low efficiency of the coilgun. Firstly, and perhaps the greatest unforeseen issue with the coilgun was that the projectile passed the coils too quickly for the capacitors to release their full charge. Shanley 19

While the gun could shoot multiple times per charge, it depreciated the efficiency of the gun due to friction. If, hypothetically, the capacitors could release all of their charge on a single fire, the projectile would move much more quickly and only be in contact with the barrel for one shot.

Instead, each bullet fired was acted on individually by friction from the barrel, losing lots of energy in the process.

In addition to this, the “optimization process” of the coil mounts around the barrel was not as smooth as intended. Moving the coils and hall sensors around the barrel provided inconsistent and marginal changes in the muzzle velocity of the projectile. In this way, the gun was hardly optimizable, as it was intended to be.

In conclusion, aside from the hiccups and unexpected outcomes of the construcution and testing of the coilgun, the project went smoothly and the final product is respectable. Not only does it fire the projectiles at relatively high speeds, it is also capable of firing multiple projectiles on a single charge. That makes this project an overall successful one.

VIII. Acknowledgements

● Dr. Dann, for help constructing circuits and theory of transistors and capacitors

● Mr. Delcarlo, for help in the lab workshop and with heavy machinery

● Chris “Bagels” Atkeson, for all the good vibes

● Brennon Williams, for general advice & suggestions

● Tinyen Shih, for advice and mutual help

Citations:

1. http://www.multiontwerp.nlmyimgwww.arthistoryclub.com/art_history/Coilgun (accessed

January 12) Shanley 20

2. http://www.ndt- ed.org/EducationResources/CommunityCollege/MagParticle/Physics/CoilField.htm (accessed

January 23)

3. http://en.wikipedia.org/wiki/Space_gun (accessed Febuary 3)

4. http://en.wikipedia.org/wiki/Ram_accelerator (accessed Febuary 3)

5. http://en.wikipedia.org/wiki/Coilgun (accessed April 30)

6. http://www.physicsforums.com/showthread.php?t=320389 (accessed April 30)

Appendix A: Bill of Materials

● Extruded Polyurethane Tubing, ⅛” ID, 12 ft

● Extruded Polyurethane Tubing, ¼” ID, 12 ft

● 24-Gage Copper Wire

● ½” X ⅛” Cylindrical Rare Earth Magnets, 26 ct. Shanley 21

● 2K/1.5K/1K resistors

● Double-throw relays

● 2N 3904 NPN Transistors

● SS441 Unipolar Hall Sensors

● 4700uF * 16V Capacitors

● Electrical Tape

● Breadboard & Hookup Wires

● Plywood Sheet (Base)

Appendix B: Coilgun Barrel Drawings/Specs

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Appendix C: Data Shanley 23

Appendix D: January Paper

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Appendix E: February Paper

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