Tungsten projectile flies in a tube filled with hydrogen gas and closes a high-voltage circuit. An electric current flowing in tungsten foil raises the temperature and pressure of the gas. The maximum velocity is unknown. The minimum mass (for 1-ton cargo) is 105 tons.
The electrothermal ramjet is as power hungry as the railgun. The cost of generating and controlling the enormous electric power is prohibitive. Rails guiding the projectile are eroded by direct physical contact with the projectile. The electrothermal ramjet belongs to the transverse gas gun family because the hydrogen flow is transverse to the projectile direction.
P. J. Wilbur, C. E. Mitchell, and B. D. Shaw, "The Electrothermal Ramjet," Journal of Spacecraft and Rockets, Vol. 20, November-December 1983, pp. 603-610.
B. D. Shaw, C. E. Mitchell, and P. J. Wilbur, "The Annular Flow, Electrothermal Plug Ramjet," Journal of Propulsion and Power, Vol. 1, November-December 1985, pp. 417-425.
Tungsten rocket is propelled by hydrogen gas heated by electric current. All the hydrogen is carried by the rocket. Two parallel rails provide electric power. The rocket flies between the rails and closes a high-voltage circuit. The specific impulse is about 9 km/s. The maximum velocity is determined by the mass of hydrogen carried by the rocket. The minimum mass is 105 tons. No bibliography.
Power requirements and rail erosion are similar to that of the electrothermal ramjet. Brian Tillotson and Dani Eder proposed this idea and called it electric rail rocket.