A low voltage “railgun” Stanley O. Starr and Robert C. Youngquist NASA, Mailstop NE-L5, KSC Applied Physics Lab, Kennedy Space Center, Florida 32899 Robert B. Cox QinetiQ North America, Mailstop ESC-55, Kennedy Space Center, Florida 32899 (Received 18 March 2012; accepted 2 October 2012) Due to recent advances in solid-state switches and ultra-capacitors, it is now possible to construct a “railgun” that can operate at voltages below 20 V. Railguns typically operate above a thousand volts, generating huge currents for a few milliseconds to provide thousands of g’s of acceleration to a small projectile. The low voltage railgun described herein operates for much longer time periods (tenths of seconds to seconds), has far smaller acceleration and speed, but can potentially propel a much larger object. The impetus for this development is to lay the groundwork for a possible ground-based supersonic launch track, but the resulting system may also have applications as a simple linear motor. The system would also be a useful teaching tool, requiring concepts from electrodynamics, mechanics, and electronics for its understanding, and is relatively straightforward to construct. VC 2013 American Association of Physics Teachers. [http://dx.doi.org/10.1119/1.4760659]
I. INTRODUCTION of a low-voltage, long time-constant rail motor has been built and operated and is described in this paper. Such a device Railguns have been studied and developed primarily as both demonstrates that rail motor launch assist may be possi- high-speed ballistic launchers for a variety of applications 1–4 ble and provides an interesting new motor that could be ranging from military weapons to space launchers. Typi- constructed as an upper-level class project. cally, a high voltage capacitor bank is rapidly discharged (a This paper begins by developing rail motor theory and is few milliseconds) down a rail, across a sliding armature, and followed by a description of the tabletop motor we have con- then up a return rail. The resulting current surge generates a structed. Special attention is given to the power supply large magnetic field and huge Lorentz forces across the ar- design, as this is the new enabling entity that allows the rail mature, accelerating it at thousands of g’s to speeds as high 1 motor to operate. Experimental results are then presented, as 5.9 km/s. Recent demonstrations are impressive: a 2010 followed by a section on safety issues. Navy railgun test implies a projectile range of 110 miles,2 inevitably leading to student interest in the operation and II. RAILGUN THEORY performance of these advanced linear motors.5 Our interest at the Kennedy Space Center is not in the use It is surprisingly difficult to find a clearly stated set of of these devices as projectile launchers, but in the possibility equations describing a railgun or rail motor in the literature. that they can be used to construct a launch assist track. Many of the publications present an incomplete model with NASA studies have argued that future generation launch sys- reference to prior railgun papers. Following the resulting tems, composed of an air breathing hypersonic vehicle citation trail back in time usually yields a text on inductive launched off of a high speed rail, as depicted in Fig. 1, could forces, the most common of which is a 1932 translation of an substantially reduce the cost of placing payloads into earth obscure German book on switchgear design.10 Other publica- orbit.6–9 Significant advantages in airframe weight, engine tions develop numerical models, bypassing the need for a type, and engine scale could be realized if this vehicle were lumped parameter model, but like the switchgear reference, launched from a ground based track at supersonic speeds provide limited physical insight. Yet, developing railgun (above Mach 1.2). Yet to date, most studies and prototype equations is not difficult, especially for the low voltage case launch assist systems have proposed using linear synchro- where high frequency phenomena such as skin effects can be nous motors7 or linear induction motors,9 neither of which ignored. In this section such a model is developed by follow- appear to have been demonstrated at speeds above Mach 1 ing, and refining, a problem proposed by Lorrain and and which would be expensive to construct and operate. Corson.11 Given its relative simplicity and exceptional speed, this Figure 2 shows a schematic of a rail motor, where the rail/ raises the question, “can railgun technology be used to sled assembly is stacked three levels high. We choose this launch a hypersonic air breathing vehicle?” looped approach in order to increase the magnetic induction Operating a railgun at relatively low acceleration (2 to 3 and thus increase the force on the sled, understanding that g’s) does not change the fundamental physics—current still such an approach adds complexity and increases the back flows through a closed circuit with a movable sliding emf, thereby reducing the maximum achievable velocity. It armature—however, the time scale differs by orders of mag- is assumed that the sleds are attached to each other and move nitude. So the name “railgun” is a misnomer in our applica- as a single entity. Such designs are reviewed in the tion and we will instead use the name rail motor below. literature.12 Also, the components needed to construct a rail motor are Fundamentally, the force on the sleds is the result of the different from those used in a railgun, yet, fortuitously, the interaction of the current traveling through the sleds with the necessary items for the development of such a device have magnetic field generated by the current traveling around the recently become available. In fact, a tabletop demonstration rails. However, calculating this force directly is difficult
38 Am. J. Phys. 81 (1), January 2013 http://aapt.org/ajp VC 2013 American Association of Physics Teachers 38 where prime is used to indicate a time derivative. Using this result, the power delivered to the rail motor can be written as
P ¼ RI2 þ L0I2 þ LI0I: (2)
Next, consider the power, or change in energy in time, seen in each element of the rail motor, including the total re- sistance, the friction between the sleds and the rails, the motion of the sleds, and the rail-motor inductance. Because the power delivered to the rail motor must equal the total power appearing in the rail motor components, we find a sec- ond expression for the power, namely 1 1 P ¼ RI2 þ F x0 þ ðLI2Þ0 þ ðmx02Þ0; (3) f 2 2
Fig. 1. This futuristic image shows an air-breathing vehicle carrying an or- where Ff is the total frictional force between the sleds and bital insertion vehicle having just taken off from the Kennedy Space Center. rails, and where xðtÞ, x0ðtÞ, and m are the position, velocity, Such a vehicle requires a high initial velocity to ignite its engines and a rail- and mass of the sled(s), respectively. Equating and simplify- gun or rail motor extended linear track is proposed to provide this. ing these two expressions for power yields the important result since the magnetic field is a complex function of position 1 within the sled. Instead, the rail-motor theory is developed L0I2 ¼ F x0 þ mx00x0 ¼ Fx0; (4) through a lumped parameter approach by “investigating the 2 f magnetic and mechanical energies involved.”11 where FðtÞ is the total force generated by the rail motor. This We start by assuming that when the MOSFET switches 10 are closed, a voltage VðtÞ is connected to the rail motor sup- is a standard result in the literature yielding the mechanical plying a current IðtÞ, both of which are functions of time. power needed to open or close an inductive switch, but The power PðtÞ delivered to the rail motor by the capacitor which is also applicable to the railgun/rail motor. bank is given by the product VðtÞIðtÞ. Then, modeling the Recall that the inductance of a coil is proportional to its rail motor electrically as a resistor RðtÞ in series with an in- area, which, for the railgun, means that the inductance is lin- ductor LðtÞ (capacitance effects are minimal), the voltage early dependent on the position of the sleds. Mathematically, applied must equal the voltage drop across these two compo- LðtÞ¼L0 þ LgxðtÞ, where L0 is the inductance of the rail nents. From Ohm’s law, the voltage drop across a resistor is when the sled is at its starting position (at xðt ¼ 0Þ¼0), and given by IðtÞRðtÞ. From the Faraday induction law, the volt- Lg is the (constant) variation in inductance with sled posi- age drop across an inductor is given by the time derivative of tion. The assumption that Lg is a constant could be used as a the flux within that inductor. Recall that inductance is definition of a railgun or rail motor, indicating an inductive defined such that the flux is given by the product LðtÞIðtÞ. “switch” where the armature is constrained to move in one Adding these voltage drops yields dimension and sees an identical geometry (i.e., the rails) regardless of its position. Inserting this expression for induct- 0 ance into Eq. (4) yields the commonly cited force law for a V ¼ RI þðLIÞ ; (1) railgun1,12
Fig. 2. This is a railgun schematic showing a triple sled/rail configuration. When the metal oxide semiconductor field effect transistor (MOSFET) switches are closed, charge flows from the capacitor bank, around the loop formed by the sleds and rails. The threshold voltage suppressor (TVS) and diode direct the current when the MOSFET switches reopen.
39 Am. J. Phys., Vol. 81, No. 1, January 2013 Starr, Youngquist, and Cox 39 1 F ¼ L I2 ¼ F þ mx00: (5) 2 g f This result is elegant in its simplicity, yet captures the essential physics. The force on the sled varies with the cur- rent and with the magnetic induction (the Lorentz force law), and the magnetic induction also varies with the current (Biot-Savart law), hence the force is proportional to the cur- rent squared. The inductance gradient then conveniently cap- tures all other dependencies as a measurable lumped parameter. Equation (5) connects the current IðtÞ to the sled position xðtÞ, but a second differential equation is needed to complete the model and this is obtained by inserting the rail motor in- ductance expression into Eq. (1), yielding
0 0 V ¼ðR þ Lgx ÞI þðL0 þ LgxÞI : (6) Fig. 3. The rail motor power supply shown above consists of a 2000-F, 16.2 -V capacitor bank, a flyback diode bank (lower left), and a MOSFET The resistance has been written as a function of time to switch bank with protective transient voltage suppressors and MOSFET driver circuit. This power supply can be operated in pulsed or continuous account for increasing resistance in the rails as the sled’s mode. It has a total equivalent series resistance of less than 2 mX and can position increases, so RðtÞ can be calculated. Also, the volt- supply over 4000 A. age function can be measured or, assuming a capacitive volt- age source, appropriately modeled. The result is that Eqs. (5) and (6) form a nonlinear, coupled pair of differential equa- the capacitor bank voltage versus time during charging with tions with unknown functions of position and current that a known current. The 4 6 bank showed 1600 F of capaci- model the railgun or rail motor. Additional forces that might tance at 2.6 V, rising to 2000 F at 10.5 V and to 2400 F at arise with a larger-scale motor, such as air resistance and lift, 15 V, but then dropping back to 2000 F at 14 V after a few are beyond the scope of this paper. days. Also, the equivalent resistances of these capacitor banks are typically higher than listed above due to the added III. THE LOW VOLTAGE RAIL MOTOR resistance of the interconnections. The total equivalent series resistance of the 4 6 bank configuration including all The time scale for a typical railgun is milliseconds, dic- connections and electrical components was less than 2 mX. tated by the time that the projectile is inside the gun and lim- In addition to ultra-capacitors, the other new component ited by the time scale of the pulsed power supply. The power that makes the low-voltage rail motor feasible is the avail- supply should accelerate the projectile through the entire ability of very low impedance MOSFET switches. Devices length of the gun, but it can be expensive to construct a ca- such as the IXTN600N04T2 power MOSFET from IXYS pacitor bank of sufficient size; one researcher13 sequentially have been available only since the summer of 2010 and are fired smaller capacitor banks to extend the power supply capable of switching up to 600 amps at 40 V with an internal time scale. This problem is compounded with the linear impedance of only 1.05 mX (these parameters are dependent motor where the time scale is a thousand times longer. on internal heating). We used 10 of these in parallel to Instead of 0.1 to 1.0 F capacitors in a typical railgun, we increase the current capability and decrease the resistance need a capacitor bank with more than 1000 F. This might ten-fold. Figure 3 shows the MOSFET module in the upper seem impossible, but the high voltages used in a railgun are left with the copper bus-bars. The MOSFET bank was driven not needed in the rail motor so there is a path forward. using a standard function generator to produce precise Within the last few years, ultra-capacitors have appeared pulses, which were buffered using a MOSFET driver circuit in the marketplace14 with enormous capacitances, but limited based on IXYS part number IXDD604PI. This circuit is to low voltage. For the rail motor, we chose to construct the located on the small board shown in the upper left corner of power supply with these new components, using 24 of the Fig. 3. Maxwell Technology 3000 F capacitors, part number Switched power supplies used to drive inductive loads, BCAP3000P. These capacitors can be charged to 2.7 V each, such as the rail motor, require flyback diodes, shown in Fig. have a maximum series resistance of 0.29 mX, and can be 2 and in the lower left of Fig. 3. The purpose of these diodes stacked using an active balancing module available from is to redirect the current flowing through the rail motor back Maxwell Technology. We configured these 24 capacitors in to the rail when the MOSFET switches open. Without these two arrangements, either as three banks of 8 to provide a diodes, the current would flow to the open MOSFETs, caus- maximum voltage of 21.6 V, a total capacitance of about ing their drain voltage to rise beyond the MOSFET break- 1125 F, and a minimum equivalent resistance of about down voltage, resulting in damage. However, this is not the 0.8 mX, or as four banks of 6 (see Fig. 3) to provide a maxi- only inductively coupled current in the power supply. There mum voltage of 16.2 V, a total capacitance of 2000 F, and a is inductance in the capacitor bank such that they continue to minimum equivalent resistance of about 0.44 mX. The sec- supply current even after the MOSFETs have opened and the ond choice was usually preferable, with the drop in resist- flyback diodes cannot redirect this current. In order to protect ance making up for the loss of voltage, though some of our the MOSFETs from this source of over-voltages, a 15-kW, better performing rail runs were made with the first arrange- 24 -V transient voltage suppressor was placed across each ment. The actual capacitance achieved in these banks was MOSFET, Littelfuse part number 15KPA24CA. These devi- voltage and time dependent, being measured by monitoring ces do not conduct below 24 V, but when the MOSFETs
40 Am. J. Phys., Vol. 81, No. 1, January 2013 Starr, Youngquist, and Cox 40 open and the voltage starts to rise they switch rapidly (pico- seconds) into a conducting state, redirecting the current around the MOSFETs. Without these protections, the MOSFET bank can fail destructively as is described in the safety section below. The power supply described above was used to drive the tabletop rail motor shown in Fig. 4. This motor consists of three layers of extruded aluminum bar (1/2 in. by 3/4 in. by about 1.1 m) bolted to each other and to a plastic sheet every 4 in. with plastic sleeves around the bolts and plastic shims between the bars. Three sleds are placed into the 3 in. gap between the rails and heavy gage electrical wire is used to close the “coil” formed by the rails and the sleds as shown in Fig. 4. Also, not shown in Fig. 4, a 3-in. diameter, 1/4-in. thick rare-earth magnet was installed in the plastic below the Fig. 5. Some of the various sleds tried in the rail motor. starting location of the sleds. This was done to provide a kick-start to the sleds and minimize welding of the sleds to the rails. inductance gradient and hence the force, but also increases One of the most critical and least understood aspects of the sled weight, friction, system complexity, and back emf. the development of this motor is sled design. A proper sled For the track configuration shown in Fig. 4, we measured the has the conflicting requirements that it must press firmly and kinetic friction to be 13 N by slowly pulling the sleds down uniformly against the rails to maximize conduction and mini- the track with a load cell. The total mass of the sleds shown mize welding, while at the same time it must experience in Fig. 4 is 0.32 kg and the total resistance of the rail motor minimal friction with the track so it can accelerate. Figure 5 (excluding the power supply) was about 2 mX. shows four of the sled designs we tried. All are spring loaded During one typical successful test, the 3 8 capacitor and provide low electrical resistance, but only the “X” bank was charged to 16.932 V and the MOSFETs were design in the lower middle worked well. It is composed of closed for 0.1 s sending current through the rail motor. The spring loaded aluminum bars with four aluminum feet three sleds accelerated (as determined from video frames) at attached with axles, allowing the sled contact to conform to about 120 m/s2 (about 12 g’s), moving about 24 in. down the the rails as it moves down the track. The other three designs track during this tenth of a second and reaching a peak exhibited significant welding along their upper or lower con- velocity of about 12 m/s. This corresponds to about 38 N of tact surfaces. We tried copper, brass, nickel, and silver con- acceleration force. tacts instead of aluminum with no clear advantage to any of In order to establish the full current, the power supply them. We also tried conductive oil and conductive grease must overcome the system inductance [Eq. (6) with xð0Þ¼0 0 (silver impregnated) as a lubricant between the sleds and the and x ð0Þ¼0], requiring about L0=R seconds, where L0 is rails, with minimal improvement in operation. about 1 lH and R is about 4 mX, i.e., 0.25 ms. After this short Railguns with a single rail loop have an inductance gradi- interval, current is flowing through the rail motor and the 15 0 ent of about 0.5 lH/m, but coil inductance scales as the sleds accelerate. Now, consider the RðtÞþLgx ðtÞ factor in number of loops squared. Using an LCR meter, we measured Eq. (6). As this term grows the current drops, so it is impor- the rail motor shown in Fig. 4 to have an inductance gradient tant in determining the force. The resistance increases by of 5.2 lH/m, which is reasonable given the three levels in 0.4 mX due to the additional 24 in. the current must travel this track. Increasing the number of layers increases the down the six aluminum rails and the inductance gradient- velocity product reaching 0.06 mX. These two terms reach a value of 0.46 mX, which is small compared to the 4 -mX sys- tem resistance so we can safely assume that the current is constant during this test. This current can be found from the drop in the capacitor bank voltage caused by the test, 0.301 V, and the capacitor bank’s capacitance, 1300 F. Multi- plying these yields a total charge of 390 coulombs that flowed during the 0.1 s event, yielding a current of 3900 A. This current and inductance gradient can be used in Eq. (5) to estimate a force on the sled of 40 N, very close to the observed 38 N, but inconsistent with the measured force of friction. We should have seen an acceleration corresponding to 27 N, the generated force minus friction, but this was not the case. We can only assume that somehow friction is reduced under high current operation since there is no other significant mechanism that could have resulted in accelera- tion this much higher than what has been predicted. There are areas where further work is needed. Foremost Fig. 4. The rail motor consists of three layers of extruded aluminum bar would be developing a better sled design that minimizes rail bolted together every four inches with insulators. The sleds were constructed from aluminum and were designed to conform to the rails with a spring friction and welding but offers high conductivity. Also, loaded “X” design and axle mounted feet. Heavy gauge electrical wire was based on the rail motor’s projected use, the motor design used to close the “coil” formed by the rails and the sleds as shown. requires optimization rules for the number of layers used in
41 Am. J. Phys., Vol. 81, No. 1, January 2013 Starr, Youngquist, and Cox 41 the motor, the capacitor bank configuration, the length of the track, etc. The acceleration profile requires smoothing; sim- ply closing the MOSFETs causes an acceleration spike fol- lowed by a decreasing acceleration, which will require a more controllable power supply. In order to scale this tech- nology to very long tracks, we believe that to minimize rail resistance, a launch assist system must be segmented. In other words, the complete system would be composed of many smaller linear motors with individual capacitor banks, through which the sled/vehicle would move at different velocities. This presents other design challenges, especially in the interfacing between the segments. Nevertheless, this vision for a launch assist system is simpler, less expensive, and more feasible than those based on other linear motor approaches. One might even suggest using solar cells to charge the low voltage capacitor banks, making this a “green” launch system.
IV. SAFETY ISSUES There are several safety concerns that should be consid- ered before constructing or operating one of these rail motors. First, as mentioned above, the MOSFET bank must Fig. 7. On several occasions the sled accelerated down the rails accompanied be protected from inductive voltage surges, but it also must by a shower of sparks, resulting in damage to both the sled and the rails. be protected from allowing the gate voltage to stray away from ground (closed) or rail (open). If the gate voltage drifts should be taken before operating this power supply at high into a range where the MOSFETs are partially switched they current for longer time periods. can be damaged. Figure 6 shows the results when the MOS- Finally, many of our test firings went smoothly with no FETs fail and allow the energy stored in the capacitor bank damage, but many did not. Figure 7 shows one of the more to discharge through them. Note that this is not an explosive damaging test runs imaged with a high-speed camera as the event—the capacitor bank takes several seconds to dis- sleds traveled down the track. It is not clear to us why some charge—but an intense thermal breakdown of the semicon- runs were uneventful and then another was so damaging, ductors. Care must be taken in the power supply construction leading to pitting and deposition of aluminum on both the and operation to follow proper grounding and voltage protec- rails and the sleds. We highly recommend that eye protection tion practices. be worn during operation of the rail motor. The capacitor bank should be treated with a respect similar to that given to working on a car battery. Fully charged, the V. CONCLUSIONS 24 capacitors can store 130 kJ (36 W-h) of energy, which is about ten times less than a car battery, but the available Recent advances in ultra-capacitors and very low imped- power can be 5–10 times higher—the total energy stored can ance, high-current MOSFETs have made it possible to con- be delivered in about 10 s. Just as a screwdriver can be struct and demonstrate a low-voltage rail motor based on the welded to car battery terminals, it can be welded to the ca- railgun concept. NASA is interested in the possibility of pacitor bank terminals. Rings, keys, and metallic tools using a scaled-up version of this linear motor to launch air- should be kept away from energized metal, which includes breathing vehicles at speeds above Mach 1 as a first stage of the rails and sled. a potential space launch system. Significant work is needed We rarely operated the power supply at high current for to develop a launch assist system with force control and seg- more than 0.1 s due to the short length of our track. There are mented design to provide near constant acceleration over a thermal limitations in the electronics, and care and analysis distance of a mile or more. The small-scale motor described in this paper is a start in this direction. This motor could be a challenging upper-level student project demonstrating elec- tromagnetic principles and would also provide a test bed for better sled design and controlled current operation. In addition, the power supply described in this paper is capable of generating low-voltage, high-current pulses that can be used to demonstrate other inductive and electromagnetic phenomena.
ACKNOWLEDGMENTS We would like to thank Curtis Ihlefeld, Stephen Simmons, and Ariel Pavlick for helpful discussions on the power sup- Fig. 6. The MOSFET bank can fail destructively if proper precautions are ply design as well as Nicole Dufour and Mark Nurge for not taken, causing all of the energy stored in the capacitor bank to drain technical assistance. We would also like to acknowledge the through them. excellent comments made by the reviewers. This work was
42 Am. J. Phys., Vol. 81, No. 1, January 2013 Starr, Youngquist, and Cox 42 supported in part by the NASA Innovative Partnerships 8J. C. Mankins, W. J. D.Escher, J. Howell, and J. R. Olds, “Combined air- Program. beathing/rocket powered highly reusable space transport flight profiles: A progress report,” in AIAA 7th International Spaceplanes and Hypersonic Systems and Technology Conference, Norfolk, Virgina, 1996, pp. 26–37. 1S. C. Rashleigh and R. A. Marshall, “Electromagnetic acceleration of 9K. J. Kloesel, J. B. Pickrel, E. L. Sayles, M. Wright, D. Marriott, L. Hol- macroparticles to high velocities,” J. Appl. Phys. 49(4), 2540–2542 land, and S. Kuznetsov, “First Stage of a Highly Reliable Reusable Launch (1978). System,” in AIAA Space 2009 Conference and Exposition, Pasadena, 2G. Fein, “Navy sets new world record with Electromagnetic Railgun demon- California, 2009, pp. 1–14. stration,” Office of Naval Research story number NNS101210–19, December 10I. F. Kesselring, The Elements of Switchgear Design (Sir Isaac Pitman and 10, 2010
43 Am. J. Phys., Vol. 81, No. 1, January 2013 Starr, Youngquist, and Cox 43