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Effect of Projectile Design on Coil Gun Performance

Jeff Holzgrafe, Nathan Lintz, Nick Eyre, & Jay Patterson Franklin W. Olin College of Engineering December 14, 2012

Abstract

In this study we provide an analysis of the effect of projectile material on the exit velocity of a coil gun: an electromagnetic actuator which uses a pulse of current to accelerate magnetically active projectiles to high velocity. We derive an approximate closed form solution for the exit velocity of the projectile. As a more accurate model, we also derive a non-linear differential equation for projectile position from first principles. We validate these analytical results with both finite element models and experimental results. The analytical calculations tend to predict larger then measured velocities, which is expected given the assumptions made. From our analytical results we show that the exit velocity is proportional to the magnetic susceptibility of the projectile material. We found that projectiles with large cross sectional area produced the highest exit velocities. and hollow projectiles produced lower velocities and length was found to not substantially. Overall, the investigation was successful and useful results were obtained.

1 Introduction experimental results are presented for a number of projectiles and the results are analyzed. A coil gun is a device which uses to accelerate magnetically active projectiles to high velocity. In a coil gun, a current is passed 2 Coil Gun Theory through a , creating a magnetic field which draws a projectile to the center of the The coil gun works by quickly discharging a large coil. If the current is stopped quickly, it contin- amount of energy from a capacitor through a ues out of the barrel at rapid speed. Many coil coil, creating a strong magnetic field through guns involve multiple stages of coils which are the coil. This strong field induces triggered in series for maximum acceleration. in the slug, causing microscopic to align with the field in a lower energy state. Because Coil guns have many useful applications. For the coil is a solenoid of finite length, the pro- example, orbital satellite launch with coil guns duced magnetic field decays in strength axially has been proposed but has of yet been deemed away from the edge of the coil. The aligned impractical due to large stresses on the pay- dipoles feel a proportional to the gradient load. Coil guns have also been proposed as in the magnetic field: replacements for chemical firing weapons for naval purposes, although the similar rail gun is generally preferred. Coil guns are relatively F = µ0∇(M · H) (1) quiet, wear very well and can be used with a Where M is the projectile magnetization and variety of ammunition types. H is the applied field. The goal of this project is to investigate the If the current were sustained indefinitely, af- effect of varying projectile material and geom- ter being accelerated from one side of the coil, etry on coil gun performance. To accomplish the projectile would encounter an opposite gra- this goal, we built a working coil gun prototype dient on the other side which would apply a which served as a test platform for a variety of force back towards the center of the coil. Thus, projectiles. a coil gun with constant current would simply In this paper, we begin by deriving theoret- cause the projectile to oscillate within the coil. ical models for a coil gun. The design of our If the slug reaches the other side of the coil while coil gun is then presented, followed by numer- significant current is still running in the coil, the ical simulations for model validation. Finally, slug will experience a force toward the center

1 of the coil, slowing its motion. This effect is unit vector. Assuming the slug is completely commonly called suckback, and is undesirable within the uniform field and a linear model of for coil gun operation. However, if all of the magnetization with magnetic susceptibility χm, charge is drained from the capacitors quickly, the induced magnetization in the slug will be: before the projectile reaches the other side of the coil, there will be no repelling force and the M = χmH = χmnIxˆ (3) projectile will continue on to exit the barrel. The energy per unit volume of a magnetized material in an applied field is ρe = −µ0M · H. Order of Magnitude Estimation In our case, the applied field and magnetization We can get a rough estimate for the exit velocity are parallel, because the former creates the lat- of the slug by comparing the energy state of the ter, and thus the dot product can be rendered slug outside and inside the coil. Before the coil as multiplication. The potential energy of the fires, the magnetic field on the slug is negligible. slug inside the coil is thus: We will make the assumption that the current in the coil is constant until the slug reaches the E = −µ MH = −µ χ n2I2 (4) center, at which point it drops to zero. When inside 0 0 m the slug is inside the coil, we can apply the This is a lower potential energy state than common ’s law estimation of the applied the slug outside the coil. Assuming that all po- field H and assume the slug is within a constant tential energy is transferred into kinetic energy, magnetic field. This will have a lower potential the exit velocity is: energy state because the induced magnetization M align with the applied field. r 2 v = V µ χ n2I2 (5) Initial Final exit m 0 m Where V is the volume of the slug and m is the mass of the slug. Using reasonable val- ues for our coil gun with a commercial grade −7 iron slug[3], µ0 = 4π × 10 , n = 500, I = 50, −6 χm = 100, m = .03 and V = 3 × 10 (all in SI units) this approximation predicts an exit velocity of about 4m/s. This order of magnitude calculation makes a number of simplifying assumptions which im- pair the accuracy of the model. The assumption Figure 1: The two states of the slug considered that the slug lies completely within a uniform in the order of magnitude estimation. The slug magnetic field in the final state overestimates starts in neglible field and when it reaches the the amount of potential energy loss, and hence final state the field completely cuts off. causes a larger exit velocity prediction. The assumption that the current dies out instantly We define the potential energy state of the when the slug reaches the center of the coil ig- nores the effect of suckback, and causing a larger slug outside the coil to be zero: Eoutside = 0J. The magnitude of the applied field inside the exit velocity prediction. Furthermore, all the po- coil can be approximated by assuming an in- tential energy will not be transferred into kinetic finitely long coil and applying Ampere’s law. energy: much of it will go toward frictional work. The well-known result is This too, will overestimate the exit velocity.

H = nIxˆ (2) A More Complete Model Where n is the turn count per length, I is To improve the model, we will take into account the current through the coil, and xˆ is an axial the effects of non-uniform fields and suck back.

2 To do this we will derive the axial applied field We can now integrate over the angles sub- of a solenoid and use it to calculate the force on tended by the line from p to the coil to find the the slug. total applied field due to all loops:

The Applied of a Solenoid Z θ2 −K nI H(θ , θ ) = sin θ dθ = (cos θ −cos θ ) 1 2 2 2 2 1 In the following analysis, we will use the system θ1 definition presented in Figure 2. Our goal is to (9) find the magnetic field at a test point p which is This can then be converted into a function a distance x from the left face of the coil. The of x: derivation will first be made in terms of θ, the angle formed by the x-axis and a line from p to a nI L − x x H(x) = ( + √ )x ˆ point on the coil, as it proves to be algebraically 2 p(L − x)2 + R2 x2 + R2 easier. Later, we will convert this into a function (10) of x, to create a differential equation of x. x The Force on the Slug Equation 10 can now be used to calculate the magnitude of the force on the slug. We will R consider the slug to be made up of many in- θ1 θ P 2 finitesimally thin disks, sliced axially. We will θ assume that the applied field on these disks is r constant and equal to the field through the axis. We can then calculate the force on each disk and integrate over the disks to find the total L force. The force on a small volume object in an applied field is [4]: Figure 2: The system parameters used in the derivation of the force on the slug. Note that in the figure the value x, the position of point p, is dF = µ0∇(M·H) dV = µ0∇(M·H)A dx (11) a negative value. Where A is the cross sectional area of the The applied field due to one loop of wire slug. For our case, the magnetization and ap- is[1]: plied field are assumed to be parallel to the x-axis. If we also assume a linear model, the I sin θR I sin θ3 force on a slice is: H(θ) = = 2r2 2R Where R is the radius of the loop and r is d 2 dH dF = µ0 (χmH )A dx = µ0χm2H A dx the distance from p to the edge of the loop. dx dx (12) If we consider the coil to be made of many This infinitesimal equation parallels the em- infinitesimal loops, we can use the equivalent pirical formula for the force on a small object in surface K = nI to calculate the an applied field [5]: current through those loops as a function of θ: dH F = V χ µ H (13) dI = Kdx = −KR csc θ2dθ (7) m 0 dx This similarity gives credence to our derived The contribution to the applied field from result. We can now integrate over the slices one of these loops is thus, using equation ??: to get the total force on our slug. If x is the −1 position of the right side of the slug, and l is the dH = K sin θdθ (8) 2 length of the slug the total force is:

3 The RLC circuit shown in Figure 3 has a Z x d 2 Kirchoff’s Law of: F = µ0 (χmH )A dx (14) x−l dx dI 2 2 VR + VC + VL = 0 = IR + VC + L (16) F (x) = µ0Aχx(H(x) − H(x − l) ) (15) dt

This equation for the force on the slug gives This can be rewritten in terms of VC only: a non-linear second order ordinary differential 2 dVC d VC equation. In the Simulation section, we submit RC + VC + LC = 0 (17) this differential equation to numerical solution. dt dt While this model is more accurate than the The characteristic polynomial of this homo- estimation, there are still a number of simpli- geneous second order linear differential equation fying assumptions. The assumption of uniform is: field for a given x-position ignores the radial dependence of the field. The field close to the LCλ2 + RCλ + 1 = 0 (18) wires would be larger than the center field, mean- Which gives eigenvalues of: ing the predicted velocity would be too small. √ This model still assumes frictionless travel of −RC ∓ R2C2 − 4LC λ = (19) the slug, although it would not be difficult to 1,2 2LC include a frictional force in the simulation. The The solution to the equation is thus: linear model of magnetization is also not en- tirely accurate, especially given the large fields V (t) = c eλ1t + c eλ2∗t (20) we produce in the experimental setups: in fact C 1 2 we may be reaching magnetization. Applying the initial conditions I(0) = 0 and This would mean the expect exit velocity is too VC (0) = V0, we can solve for the constants: high. Furthermore, the calculation of the field λ1 assumes a thin solenoid - that is, the wires are c2 = V0/(1 − ) (21) infinitely thin and do not stack on one another. λ2 This makes the expected field larger, and the exit velocity larger. c1 = V0 − c2 (22) The current through the inductor can then RLC Analysis be expressed as: In order to reduce suckback, the RLC system dV I(t) = C ∗ C (23) defined by the capacitor bank and coil should be dt tuned to provide the minimum discharge time. We used this equation to find a reasonable The faster the discharge time, the lower the cur- set of parameters for our RLC system in order rent will be when the slug exits the coil, giving to create a relatively fast discharge time. This it a higher exit velocity. We developed a math- same analysis was also used in our dynamic ematical model of the RLC system in order to model to find the current though the coil as a tune the parameters before creating it. function of time.

Inductor 3 Prototype Design

A prototype coil gun and projectiles were de- signed to allow us to test the effect of projectile Resistor Capacitor material on performance. The design, shown in Figure 4, was manufactured by team members in the Olin College machine shop. The gun’s Figure 3: An RLC Circuit. transparent polycarbonate barrel has an inner

4 diameter of 5⁄8” and is one foot long. The bar- well as their availability. The iron content of rel is mounted on a clamping support structure each of the steel alloys is given in Table 2. The manufactured from black ABS . A36 steel, which is a hot-rolled , has the highest iron content of the three followed by the 1018 and the 4130 on bottom, both cold rolled alloys.

Alloy Iron Content A36 99.0% 1018 98.8% - 99.3% 4130 97.0% - 98.2% Table 2: Iron Composition of Steel Alloys [6]

Figure 4: Coil gun prototype design. Coil Projectiles The coil gun’s coil is made from 20 turns of 14 AWG wire. The coil was designed to have a low Eight different styles of projectile were manu- resistance and so that the capacitor factured for testing. All projectiles are 5⁄8” in would discharge quickly. The parameters for the diameter and slide easily in the plastic barrel. coil are provided in Table 3. As shown, the resis- Iron projectiles, which we predict will shoot the tance of the coil is extremely low at .116 Ω and best, were made in three different lengths (1”, the inductance is also quite low at 4.62×10−3 11⁄2” and 3”) as well as in hollow and solid con- H. figurations. 1” long solid projectiles were also manufactured out of 6061-T6 Aluminum, A36 Length 30 mm Wire Gauge 14 AWG Steel, 1018 Steel and 4130 Steel. Turns 20 In addition to machined projectiles, a pur- Inner Diameter 19 mm chased magnet and a rolled sheet of mu- Outer Diameter 33 mm −3 will be launched. Mu-metal is a very magneti- Average Inductance 4.62×10 H Inductance Standard Deviation 3.74×10−5 H cally active material and is commonly used for Average Resistance 1.16×10−1 Ω electromagnetic shielding. The purchased mag- Resistance Standard Deviation 9.05×10−3 Ω net has a surface field of 7157 Gauss1. The sizes Samples Taken 7 and masses of all projectiles are given in Table Table 3: Coil Parameters 1. Material Style Diameter Length Mass Iron Solid 5⁄8” 1” 30 g Iron Hollow 5⁄8” 1” 18 g Iron Solid 5⁄8” 13⁄4” 51 g Circuit Design & Characterization Iron Solid 5⁄8” 3” 93 g Steel A36 Solid 5⁄8” 1” 36 g The electrical components of our coil gun are Steel 4130 Solid 5⁄8” 1” 36 g shown in Figure 5. We used a power supply to 5 Steel 1018 Solid ⁄8” 1” 36 g charge the capacitors before firing and a large Magnet Solid 1⁄2” 1” 24 g Mu-Metal Rolled 5⁄8” 4” 18 g block of metal with an insulated handle to dis- Aluminum Solid 5⁄8” 1” 12 g charge the capacitors for storage. Note that while there is no resistor in this circuit, the in- Table 1: Projectile Parameters ductor and capacitors provide some resistance. This equivalent series resistance is omitted for It is important to note that the three differ- simplicity here but is utilized in calculations ent were chosen for their iron content as elsewhere. 1K&J Magnetics Product #D8X0DIA

5 Trigger Circuit Coil Gun Circuit an oscilloscope (Figure 6). After 50ms, 87% of the charge had been dissipated; after 100ms, R1 6V Reg 1 kΩ over 98% of the charge was gone. This exper- SCR imental data matched up with our theoretical

R2 calculations quite well. Capacitor Bank Coil 1 kΩ Trigger Note that the values for resistance, induc- tance and obtained via discharge characterization do not match up perfectly with the results from direct measurement. The char- Figure 5: Coil gun electrical system schematic acterization suggests that the values of resis- tance, inductance and capacitance are .13 Ω, The system is triggered by a silicon- 1 × 10−5 H and .2 F, respectively. We suspect controlled rectifier (SCR). The SCR we are using this is because the properties of the elements is triggered by the application of 1.7-5V refer- change somewhat when run at such high cur- enced to the SCR’s anode. So the system would rents. The equivalent series resistance, for ex- be self-contained, we wanted the triggering cir- ample, may be dependent on current. We are cuit to be driven off of the firing capacitors. We not truly sure of the cause of this discrepancy used a 6V voltage regulator which accepts input but the characterization results presented here between 7 and 40V and an additional reflect how the circuit will behave in practice. 1000 Ω voltage divider to produce the desired Thus these are the values we use in simulation. 3V for the trigger. We attached the SCR to the output of the voltage divider and use a linear Measured SPDT switch to control the voltage regulator Theoretical state and fire. By using a switch to connect and 15 disconnect the voltage divider, we eliminated capacitor voltage bleed through the voltage reg- 10 ulator which some other trigger circuits have.

The system’s charge is stored in a bank of Voltage (V) 5 thirty two 18mF capacitors in parallel. The ca- pacitors were characterized with a capacitance meter to determine their actual capacitance and 0 equivalent series resistance (Table 4). During −0.05 0 0.05 0.1 0.15 0.2 characterization, the capacitors were found to Time (s) have capacitance much lower than rated. How- Figure 6: Capacitor Voltage Discharge Curve ever, each of the capacitors has a ±20% toler- ance so this lower capacitance is not unreason- able. Number of Capacitors 32 Experimental Test Setup Rated Unit Capacitance 1.80×10−2 F Rated Capacitor Tolerance ± 20 % To obtain results on coil shooting performance, Average Measured Unit Capacitance 1.53×10−2 F a Vernier system photogates was used to mea- −4 Capacitance Standard Deviation 8.33×10 F sure the time required for the projectile to pass. Unit Capacitance Measurements Taken 10 Average Measured equivalent Resistance 8.35×10−2 Ω The known length of the projectile could then Resistance Standard Deviation 7.11×10−4 Ω be used to calculate the exit velocity. Samples Taken 7 Table 4: Capacitor Parameters 4 Simulation

As the capacitors discharge into the coil, the In order to assist in field visualization, several circuit acts as an RLC circuit. To characterize computer simulations of the system were made. the circuit, we measured its discharge curve with We used two finite element modeling packages to

6 calculate the field induced by the coil with and tween the two models so we are confident in the without the slug. We used a MATLAB model results obtained from FEMM. to numerically integrate equation 15, the force on the projectile.

Finite Element Models First, to visualize the fields surrounding the coil, a simple coil model was made in COMSOL. This model uses the peak discharge current which was measured at 60 A. The resultant fields are shown in Figure 7. As shown, the fields vary, but not significantly, off the axis of the coil. Our MATLAB simulation assumes the on-axis field is constant through the projectile and because of this simulation result, we are confident that this assumption is not throwing off the results Figure 8: Simulated magnetic field around coil significantly. from FEMM

Next, the iron projectile was added to the FEMM model. The addition of the projectile changes the fields significantly, with extremely intense fields concentrated within the projectile (Figure 9).

Figure 7: Simulated magnetic field around coil from COMSOL

Next, a secondary model was created in Fi- nite Element Method Magnetics (FEMM), a free simulation package specifically designed for magnetic systems. FEMM is ideal for the coil gun system because it is scriptable, allowing us Figure 9: Simulated magnetic field around coil to calculate the work done by the coil on the with Iron Projectile Present from FEMM projectile as it moves through the length of the barrel. Using the FEMM model, the force on the To validate our FEMM results, we replicated projectile as it moves through the field gradient the magnetic field plot from COMSOL using was calculated at thirty five points through the FEMM (Figure 8). The numerical value of the field gradient of the coil. These were nu- field is slightly different with the values from merically integrated to derive the work done by FEMM being lower than the COMSOL values the field on the projectile. When combined with by a factor of 4⁄3. However, this is quite close, the actual masses of the projectiles, the barrel within less than an order of magnitude and the exit velocity of each was calculated. Note that qualitative shape of the field is very similar be- this simulation assumes that the current is at

7 its peak for the entire transit of the projectile tail edge of the coil. The velocity data is given in and disregards friction in the barrel. Table 6. Note that the aluminum projectile did The results of this FEMM simulation are not move at all in the barrel, as expected due given in Table 5. Note that two of the chosen to its extremely small magnetic susceptibility. steels were not in FEMM’s material database Material Length Style Average St. Dev. and were substituted with similar steels. “Hot Iron 1” Solid 1.72 0.04 Rolled Low Steel” was used for A36 and Iron 1” Hollow 1.00 0.26 “Cold Drawn ” was used for 4130. Iron 1.75” Solid 1.92 0.05 Furthermore, the Mu-Metal was modeled as a Iron 3” Solid 1.68 0.05 Steel A36 1” Solid 1.49 0.12 solid 1” Long Slug, which differs from the actual Steel 4130 1” Solid 1.23 0.35 geometry of our projectile. Steel 1018 1” Solid 1.24 0.12 Magnet 1” Solid 1.62 0.16 Material Length Style Exit Velocity Mu-Metal 4” Rolled 1.37 0.02 Iron 1” Solid 0.988 m s ⁄ Aluminum 1” Solid 0 0 Steel A36 1” Solid 0.245 m⁄s Steel 4130 1” Solid 0.205 m⁄s Table 6: Velocity Results in m⁄s Steel 1018 1” Solid 0.989 m⁄s Mu-Metal 1” Solid 0.180 m⁄s m Aluminum 1” Solid 0.001 ⁄s A plot of the deviation of the data is shown

Table 5: Velocity Results in m⁄s in Figure 10. For certain materials, the launch velocities were rather inconsistent leading to wider than ideal spreads. We attribute this in- It is interesting to see that according to the consistency to poor surface finishes on some of FEMM simulation, the 1018 steel ended with the machined slugs, causing friction to vary sig- a higher exit velocity than the pure iron, an nificantly depending on the orientation of the unexpected result. Furthermore, the two steels slug in the barrel. for which similar steels were substituted both

performed very poorly with vastly different re- 2.00

sults than the 1018 steel. As expected, because 1.80

aluminum has low magnetization, the forces on ) 1.60 m/ s ( the aluminum projectile were very low and we t y i 1.40

suspect that in experimental testing, it will not o c e l

V 1.20

overcome friction and will remain stationary. h c

Finally, the exit velocity of the mu-metal was u n 1.00 L a surprisingly low given the high magnetization 0.80 of the material. 0.60

Dynamic Model We submitted equation 15 to numerical inte- gration in Matlab, using equation 23 to find Figure 10: Deviation of launch velocity results the current through the coil at each time-step. for different projectiles The results of a simulation with parameters that match our experimental setup are shown in Fig- ure ??. 6 Analysis 5 Experimental Results Comparison of Results Each of the ten projectiles was launched three times out of the coil gun barrel and its velocity An analysis of ideal theoretical calculations, nu- measured by the sensors. For each test, the - merical simulations and experimental results ing edge of the projectile was aligned with the to some interesting conclusions.

8 First of all, we see that the order of mag- 1” long hollow slug reached an exit velocity of nitude theoretical calculation which was per- 1.00 ± 0.26 m⁄s, much lower the 1” long solid formed matches up surprisingly well with the slug which reached 1.72 ± 0.04 m⁄s. In fact, the experimental results. The results from this cal- hollow slug may have been the slowest of all culation were off from the final results by a of the projectiles tested. This much lower exit factor of about 3, quite close considering all of velocity for the hollow projectile helps to corrob- the assumptions that were made. orate our theoretical results: both the order of Furthermore, the FEMM numerically inte- magnitude and detailed calculations show that grated velocity data lines up with the data quite the force is roughly proportional to the cross well and is off by less than a factor of two for sectional area of the slug. Thus a hollow slug the iron slug. For some of the steels, however, would be expected to have a lower exit velocity, the results differ significantly from the FEMM which we see in the experimental data. simulation, a fact which we believe can be at- Subsequently, it is interesting that length of tributed to differences between the simulated iron projectile did not significantly affect the materials and the actual used materials. launch performance of the coil gun. This is be- Our Matlab dynamics model predicts exit cause the larger projectiles obtain higher levels velocities on the order of 4m/s, about twice as of magnetization but also have higher masses fast as our experimental results showed. The dy- and normal forces in the barrel, leading to in- namic model makes several assumptions which creased friction. This suggests that a coil gun would increase the exit velocity. It assumes there of a fixed design may be able to launch a large is no friction or air resistance in this system, that range of projectiles with good results. In fact, in a linear model of magnetization holds true and the order of magnitude approximation the mass that the field is radially uniform and equal in of the slug has no effect on the exit velocity, magnitude to the axial field. The finite element using equation 5: models showed that the radial uniformity ap- proximation was not a terrible, but the actual r 2 p field generally decreases in the radial direction. v = V µ χ n2I2 = 2ρ µ χ n2I2 The Matlab model predicts peak magnetic fields exit m 0 m m 0 m internal to the slug in excess of 3T using the (24) linear model. The saturation magnetization of That is, the exit velocity depends only on most soft is around 1 or 2T. Thus the the density of the object. actual magnetization may be much lower than Next, the data shows that the iron projectiles the linear model predicts. The combination of performed better than their steel counterparts. these three phenomena could explain the dis- This was expected because iron is a stronger crepancy between the dynamic model and the ferromagnetic material than most steels. How- experimental results. ever, there is not a correlation between percent iron content in a steel and the performance of Material Performance the steel, leading us to believe that the solutes of the alloy have a greater affect its magnetic Although the collected launch data for several susceptibility than the iron content. It is also of the materials had high standard deviation, possible that the process by which the steel some definite conclusions can be drawn from the was formed affects its magnetic performance. data. The data suggests that the hot-rolled A36 steel First of all, it is quite clear that solid pro- performed better than its cold-rolled 1018 coun- jectiles perform better than their hollow coun- terpart. However, the data from the 4130 cold- terparts. Although the hollow projectiles have rolled steel is inconclusive. less air resistance, the 1” long iron slugs clearly The both analytical results suggest that the demonstrate that the increased magnetization exit velocity is proportional to the magnetic from the extra material makes a significant dif- susceptibility of the material. This is the most ference. This demonstrates that cross-sectional likely explanation for the area is quite important in projectile design. The Finally, the launch performance of the rolled

9 mu-metal and the permanent mag- 8 Further Work net raises interesting conclusions. In tests, the mu-metal performed about as well as the tested Further work in the topic could be done in a num- steels. However, in its rolled configuration and ber of areas. In order to improve the dynamic with half the mass of the steel projectiles, its model, an expression for the off-axis field of a performance is nonetheless impressive. We pos- finite solenoid could be derived, and further in- tulate that if we had a solid mu-metal projectile, vestigation could be done into non-linear magne- it would have performed better than both the tization models. The experimental setup could iron and steel projectiles. However, mu-metal is be improved by investigating barrel materials a rather rare material and is not commonly pro- and lubricants to reduce friction. Furthermore, duced in forms other than sheets. Furthermore, improved finish on the projectiles would help the performance of the permanent magnet was to reduce the exit velocity variance and reduce disappointing, with its launch velocities strug- friction. Further study could be done to ana- gling to keep up with the solid iron slugs. We lyze a wider class of projectiles. Attributes like suspect this disparity is because of the high mag- projectile shape, a wider range of alloys, types netization of the iron projectiles which, when of permanent magnets and projectile lengths. combined with an intense magnetic field, caused Second, exploration could be done into how dif- the projectiles to reach magnetic saturation, as ferent barrel materials affect performance and predicted by our dynamics model. The magnet possibly into lubrication as a method of decreas- has a lower saturation magnetization of 1.3 T ing barrel friction. Nevertheless, we feel that when compared to the Iron’s 2.3T[3]. Further- even without including some of these additional more, the magnet had a smaller diameter than factors, our results are conclusive and useful. the slugs and this decreased cross-sectional area may have affected the performance. References 7 Conclusion [1] Griffiths, David J. Introduction to Electrody- namics (3rd Edition). Upper Saddle River, In conclusion, we successfully built a coil gun New Jersey: Prentice-Hall, 1999. and tested its performance with a wide variety of projectiles. In the process, we used several meth- [2] Hansen, Barry. Barry’s Designs. ods to predict our gun’s performance including http://coilgun.info, 2012. the development of a custom, remarkably ac- curate mathematical model. Furthermore, con- [3] Miner, Douglas F. and John B. Seastone. clusive results were reached for a number of Handbook of Engineering Materials (1st Edi- different classes of projectiles. It was found that tion). New York: John Wiley & Sons, 1955. solid iron projectiles perform very well in a coil [4] Livingston, James D. Electronic Properties gun and that projectile length is not very im- of Engineering Materials. New York: John portant to launch performance. Furthermore, Wiley & Sons, 1999. permanent magnets perform well in a coil gun but not substantially different from their iron [5] Hummel, Rolf E. Electronic Properties of counterparts. Additionally, steel projectiles can Materials (3rd Edition). New York: Springer- perform well, but not as well as iron slugs. How- Verlag, 2001. ever, steel is a harder and stronger material and may be more useful than iron in real-world [6] MatWeb, Online Materials Information Re- applications. source. http://matweb.com, 2012.

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