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.