## Conventional Rockets: Expensive and Inefficient

 Fig. 1: Schematic Diagram of Railgun. (Source: Wikimedia Commons)

When it comes to launch an object into space, most people would think of a giant rocket that they have seen in the news. Conventionally, rockets carry with them chemical fuel such as liquid oxygen that is used to drive it against gravity. The fact that rockets need a large amount of massive, non-reusable fuel makes the launch inefficient and extremely expensive. For instance, the rocket Atlas V costs around \$125 million to launch payloads of which mass is only about 5% compared to the fuel mass. [1,2] Given this limitation of using rockets, scientists and engineers have been trying to search for alternatives to launch objects into space with less cost. In this report, we will have a look at an inexpensive method of "railgun launch," which uses electromagnetic energy instead of heavy chemical fuel to overcome the issue of small payload to lift-off mass ratio. We will see how this railgun method can launch suborbital payloads and will also discuss its limitations that make it unlikely for stable orbit launch.

## Basic Railgun Mechanism

The structure of the railgun is illustrated in Figure 1. The idea is to convert the energy input from the external emf into the kinetic energy of the projectile through electromagnetic mechanism. When the electric current (of magnitude I) travels through the rails and the projectile in the direction shown in the figure, according to Ampere's law, there is magnetic field curling around both rails, pointing upward in the region between the two rails. The Lorentz force law dictates that the projectile experiences the force in the direction orthogonal to the current and the magnetic field and its magnitude is given by the equation

F = 1/2 L' I2

where L' is the inductance per unit length of the rails. [3] Applying the Work-Energy theorem, we can derive the kinetic energy and the velocity of the projectile at the muzzle:

 KE = 1/2 L' I2 l and v = I (L' l/m)1/2

where l is the distance traveled by the projectile inside the railgun. [3] With these equations, we can calculate how much electrical energy input is needed to yield the desired muzzle velocity of the projectile.

Let us say that we want to launch a sounding rocket of which primary purpose is to conduct scientific experiments. [4] Typically, sounding rockets carry with them payloads as heavy as 500 kg to heights between 50 km and 1500 km and stay in space for up to 20 minutes. [5] In the railgun experiment, though, we are talking about payloads of mass around a few kilograms. Consider a projectile of mass 3.9 kg carrying a 1 kg payload. To reach the apogee of 120 km, for example, a muzzle velocity of 2.1 km/s (8.6 MJ) is required. [5] If our launcher has 33% conversion efficiency, we need supply it with 27 MJ of electrical energy for the projectile to reach the desired muzzle velocity.

 Fig. 2: Hypersonic velocity of the projectile generates extreme heat load and large air drag. (Source: Wikimedia Commons)

Simulation results have shown that such suborbital payload launch is feasible given appropriate aerodynamic properties of the projectile as well as its ability to tolerate heating (around 1000 K) from atmospheric friction. [3] In December 2010, real tests of railgun launch were successful in reaching muzzle energy of 32 MJ, which was more than enough to launch the suborbital payloads in our consideration. [5]

We can see from the previous discussion that railgun launch is very efficient. The payload to lift-off mass ratio is around 25%, which is five times more efficient than that of conventional rocket. The launcher itself can also be reused as many times as we want, allowing room for experiment repetitions with low marginal costs. Still, there are several limitations of this "simple" railgun method that prohibit higher altitude launch (see Fig. 2). To launch a payload to a low earth orbit, for instance, it would require large muzzle velocities of order 10 km/s, which in reality is not possible since the friction from atmosphere would melt the payload and the air drag would force this "no-fuel-power" projectile to cease before reaching the orbit height. Some have proposed the idea of multistage railgun launch, but more research and development are still needed for realistic use of railgun to launch stable orbit payloads. [6,7]

© Saranapob Thavapatikom. The author grants permission to copy, distribute and display this work in unaltered form, with attribution to the author, for noncommercial purposes only. All other rights, including commercial rights, are reserved to the author.

## References

[1] "Seim-Annual Launch Report: Second Half of 2009," U.S. Federal Aviation Administration, HQ-10998.INDD, May 2010.

[2] "Atlas V Launch Services User's Guide March 2010," United Launch Alliance, March 2010, pp. 1-5.

[3] J. Behrens et al., "Hypersonic and Electromagnetic Railgun Technology as a Future Alternative for the Launch of Suborbital Payloads," in 16th ESA European Space Agency Symposium on European Rocket and Balloon Programmes and Related Research, 2003 (SP-530) (European Space Agency, 2003), p 185.

[4] G. Seibert, "The History of Sounding Rockets and Their Contribution to European Space Research," European Space Agency, HSR-38, November 2006.

[5] S. Hundertmark, "Applying Railgun Technology to Small Satellite Launch, Proc. 5th Int. Conf. on Recent Advances in Space Technologies, 9 Jun 11, p. 747.

[6] O. Bozic, M. Schneider and D. Porrmann, "Conceptual Design of 'Silver Eagle' - Combined Electromagnetic and Hybrid Rocket System for Suborbital Investigations," in Proc. 61st Int. Astronautical Congress (IAC 2010), Vol. 12, p. 9735 (Curran Associates, 2011).

[7] M. Schneider, O. Bozic and T. Eggers, "Some Aspects Concerning the Design of Multistage Earth Orbit Launchers Using Electromagnetic Acceleration," IEEE Trans. Plasma Science 39, 794 (2011).