Final Project

by Andy Chu Lab Partners: Alan Buckley and Ares Hernandez

February 20, 2015

Abstract

After an entire semester of Physics 111, we have learned so much about

dierent circuits and endeavor on a journey to make a project that requires

knowledge on circuits and electrodynamics. The gauss gun was a perfect

choice for our nal project because building the gun uses knowledge of

magnetism and circuits concepts from Physics 111. We have seen amazing

designs by the Navy and hobbyists and decided to try to build one so we

can gure out how the gun works.

Part I

Introduction

To make our project, we started by looking up several designs that people havemade in the past. We saw many promising designs and divided the gun intomodules, so we could choose to build only the most reasonable circuit for eachmodule, since dierent designs may have one module better than a module fromanother design. Some projects were really cool, but the cost was sometimesunreasonable. One design we really liked was a gauss gun that cost $1500 intotal. We eventually had to scrap that idea even though we considered spendingthat amount of money because that particular group spent an entire semesteron the gun and we have much less time to complete our project. Once we triedto order our parts, we realized that a lot of parts that yielded a great muzzlevelocity were extremely expensive (capacitors 3900 microfarads were 400 dollarsfor two). Expense was not the only factor to consider, other parts to a week andup to ten days just to ship. We did not want to purchase parts that took too longto be delivered because even though we may have our calculations, some partsmay fry because we overlooked a small detail and then we would be withoutparts to construct our project. After we simplied our circuit, we also went toAl Lasher's and the owner was nice enough to nd us a bunch of equivalentcheaper parts that we could obtain the day of. Our parts that took a longtime to come were the capacitors and the MOSFET. The building process alsoyielded many unforeseen hurdles. For instance, we needed a 50V power supplyand once we got it, we were not able to use single wires from BSC lab because

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there is 2 amps that come out of the power supply and one wire would heat upso quickly and cause safety hazards. To solve this problem, we had to get threewires and twist them around each other. One end of these three twisted wireswould be connected to the power supply and the other end would be connectedto our capacitors. To have a good connection, we had to solder these wires tothe capacitors (these capacitors were part of our capacitor bank). Our gauss gunis divided into the following modules: power supply, capacitor bank, and switchand coil. Originally, we were going to use an SCR (silicon controlled rectier)as part of our switch, but the SCR was slower than a MOSFET and switchingslowly will prevent the magnetic eld from turning o really quickly after theprojectile is past the halfway point of the coil and slow the projectile down, sincemagnetic elds in inductors accelerate projectiles towards the center. Also, theSCR needed an AC signal, so we would have to wait and nd just the righttime to re, which would complicate things even further. We used electrolyticcapacitors, so we wanted an SCR, since it acted also as a diode and preventedback ow of current. It was not until after we calculated impedances that werealized we our circuit behaved more like an RC circuit and not LC circuit.Therefore, it was okay to replace our SCR with a MOSFET, since there wasno back ow of current and our electrolytic capacitors would not be damaged.After constructing our circuit, we did some test shots and some steel projectilesjust did not go too far. Our rst test moved our projectile 1 mm. We madesmaller steel projectiles, since force is acceleration over mass and a smaller masswould allow the projectile to accelerate and yielded better results. After wewere done constructing our gauss gun, we played with making a second stage,but could not get the timing right to yield a projectile that traveled faster thanthe rst stage.

Part II

Ciruit Diagrams

The block diagram shows the dif-ferent modules in our circuit. Our power supply is a 50 V supply we borrowedfrom the advanced lab. The 45V supply is used to charge our capacitor bank. Itcould only charge our capacitors to a maximum of around 44.7V. Our capacitor

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bank is where we store our charge and do not discharge until we are ready tolaunch our projectile. We have a switch that allows us to complete our circuit,which will allow the capacitor to discharge and pour current into our coil. Ourcoil receives the current from the capacitor bank and then a magnetic eld willbe created due to the current through the coil. This magnetic eld will causeour projectile that site halfway into our stage because when we use the analogyof ~B → ~D and ~M → ~P we can see when the projectile is a little bit outsideof the back end of the coil (back is the side opposite the magnetic eld whichis determined by the right hand rule) and the projectile will accelerate towardsthe magnetic eld.

Our circuit diagram for our capacitor bank isshown. We have two capacitors in parallel because we would then have the ca-pacitances added and more charge can be stored in this overall block. We chargethe capacitors with the 45V power supply borrowed from advanced laboratory.Once we are ready to re, we discharge one of the capacitors with a wire.

Our switch and coil allow us to launch ourprojectile. The IRPF450 is a MOSFET with a gate source voltage of 3V. Anyvoltage above 3V will allow the MOSFET to turn on and once it is on, currentwill ow from the drain to the source. We turn on the MOSFET by hitting aswitch on the breadboard. This switch keeps the circuit open, until will press thebutton. Once we press the button, we will have 10V between the 2kΩ and 10kΩ

since voltage division with Vout = VinR2

R1R2= 10kΩ(12V )

2kΩ+10kΩ = 10V .The gauss gun usesthe concept that inductors store energy in magnetic elds whenever there iscurrent through the coils. Current can be provided from capacitors, which not

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only store charge, but can also discharge. Controlling the magnetic elds fromthe inductors is important because objects such as steel will accelerate towardsa magnetic eld. Steel inside an inductor with a magnetic eld will acceleratetowards the center of the steel. Turning o the magnetic eld once the projectiles halfway through the coil will allow the projectile to have maximum accelerationthrough the stage because once the projectile passes the halfway point of the coiland the magnetic eld is still on, the magnetic eld will accelerate the projectileback into the center of the coil, which will end up slowing down our projectile.After we press the switch, the circuit gets completed, and our MOSFET willthen receive a gate source voltage of 10 V. Our MOSFET will then turn on andwe will have current go from the drain to source and current will go throughthe inductor. The inductor will then create a magnetic eld and our projectilewill then accelerate on our stage.

Part III

Theory

Using the analogy of ~B → ~D and ~M → ~P , we can see why the projectile will ac-

celerate towards the magnetic eld. Withright hand rule, we determine the clockwise coil we wrapped and the current,

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our thumb pointed in the direction of positive magnetic eld. We put our pro-jectile on the side opposite our thumb. So we have the case on the left. Oncewe have a magnetic eld in our inductor, the Electric eld analogy shows thatthe Electric eld is stronger in the positive side of the magnetic eld and thenour projectile will acclerate up. Our magnetic eld was shortlived and oncethe projectile passes the halfway point we have the second case (right side ofelectric), but since our magnetic eld is o, our projectile will continue travelingat the same speed with only air resistance to slow it down.

Looking at the oscilloscope, we have our τ = 12ms, so f = 112ms

= 83Hz.Thus, according to our graph, each capacitor should have 1.4Ω impedance. Wehave two capacitors in parallel and the Zcapbank = ( 1

1.4Ω + 11.4Ω ) = 0.7Ω. Our

coil was measured with the LCR to be 0.8Ω = Zcoil. Resistor is 0.1Ω = Zresistor.Mosfet (D-s) is 0.4Ω = Zmosfet. Total impedance of our circuit is Z = (0.7 +0.8 + 0.1 + 0.4)Ω = 2Ω. We initially thought that our circuit would oscillatelike a LC circuit, however after calculating the total impedance of the circuit,we see that the Impedance is so high that the inductance rom the inductor isso negligible that the circuit ends up behaving like a RC circuit. R = τ

C =12ms

5600µF = 2.14Ω.

Part IV

Data

Below is work for the calculation of one of our projectiles. We calculated therest of the data for the other projectiles in the exact same way. Our time wascalculated by nding how tall our gauss gun was from our table (which is theoor). That distance from the stage of our gun to our table is our value for∆y. After we red each projectile, we calculated how far the projectile traveleduntil it hit the table. This value was what we used for ∆x. DNLM means theprojectile did not leave the muzzle. This projectile was a bit too bulky and mostlikely due to friction and not a large enough magnetic eld could not leave themuzzle.

t =√

2∆yg =

√2x.14m9.8 m

s2

= 0.17s = timetofall Vtrial1 = ∆xt = 0.51m

.17s = 3ms

Vtrial2 = ∆xt = 0.55m

.17s = 3.24msVtrial3 = ∆x

t = 0.74m.17s = 4.35m

s

To see how accurate we were in our method of measurement, we used theoscilloscope and measured the discharge voltage of our capacitor. Since the

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voltage drop is the same in all of the components, it is okay for us to chooseto measure the second parallel capacitor (one that is closest to our switch),we connected red to the plus terminal of our capacitor and black to the minusterminal of our capacitor. Our oscilloscope was set to single and clicking on thetrigger menu, we changed the slope to down and the voltage to 3V. We also useda 10 x 1 probe because our oscilloscope can only read 5V/div and we had a 50Vpower supply and needed to see our entire signal. We measured the distanceof our stage and for the slope on the oscilloscope, we used the time for whenthe nonzero slope existed. For speed of our projectile, we divided the distanceof our stage by the time because the time it takes the projectile to leave ourstage is the same amount of time it takes our capacitors to discharge. We knowthis is true because our projectile left our stage and never attracted back intothe coil. This is possible when our projectile is past the halfway point of ourcoil and the magnetic eld is turned o. Below is a picture of our oscilloscopereading of our second capacitor when we red our projectile.

We see that the time is about 12 ms and the length of our stage is 33 mm.This yields speed of 2.75 m/s. Our calculated speed for projectile one is 3 m/s.The error in our method of measurement is about 9 percent.

Part V

Conclusion

Given more time, I would like to increase the muzzle velocity of our gaussgun. We would make larger coils, and work on the timing for our second stage.Time and money are denitely very key in making a project in real world jobs.A lot of our project turned out the way it is because we could only chooseparts that would come in a timely fashion and were reasonably aordable forus undergraduate students.

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Part VI

Acknowledgements

Arielle Little, Eric Hunter, Celeste Carruth, Erik Urban, Michael Cole, BobJacobsen, Donald Orlando, and Al Lasher's Owner.

Part VII

References

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0.2 DeltaV. (2011, January 1). Portable 1.25 kJ Coilgun. . Re-trieved , from http://www.deltaveng.com/gauss-machine-gun/design/

0.3 Electromagnetic Projectile Accelerators. (2010, November 7).. Retrieved April 13, 2014, from http://4hv.org/e107_plugins/forum/forum_viewtop

ic.php?100083.0

0.4 Griths, D. J. (2013). Electric Fields in Matter, Magnetostatics, Magnetic Fields in Matter. Introduction to electrody-namics (Fourth ed., ). Glenview: PEARSON

0.5 Magnet. (n.d.). Retrieved, from http://en.wikipedia.org/wiki/Magnet

0.6 Permeability(electromagnetism). (n.d.). Retrieved, from https://en.wikipedia.org

/wiki/Magnetic_permeability

0.7 Saz43, U. (n.d.). Simulation. . Retrieved , from http://s1226.photobucket.com/user

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0.8 ST_Microelectronics. (n.d.). IRFP450 Datasheet. . Re-trieved,from http://www.datasheetcatalog.com/datasheets_pdf/I/R/F/P/

IRFP450.shtml

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