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A magnetohydrodynamic (MHD) drive is an engine with no moving parts that creates thrust by accelerating a charged fluid with an electromagnetic field. This is known as the Lorentz force, whose magnitude in newtons on any specific charged particle can be calculated by adding the density of the electric field in volts per meter to the instantaneous velocity of the particle in m/s, multiplying the sum by the density of the magnetic field in teslas, and multiplying that product by the electric charge of the particle in columbs.
When the intensity of the electromagnetic field increases, both the thrust and specific impulse of a magnetohydrodynamic drive also increase. The Lorentz force can be exploited for propulsion in spacecraft, which use charged plasma as the fluid medium, and are therefore called magnetoplasmadynamic (MPD) thrusters. Experimental prototypes have been tested on both Russian and Japanese satellites.
Magnetohydrodynamics in general is the scientific discipline that studies any electrically charged fluids. Explaining and predicting the behavior of electrically charged fluids requires combining the Navier-Stokes equations of fluid dynamics with Maxwell's equations of electromagnetism. This means that two sets of differential equations must be solved simultaneously, meaning the calculations are computationally intensive and frequently require supercomputers.
In the 1990s, Mitsubishi built prototypes for seagoing vessels that used magnetohydrodynamic drives, but these only reached speeds of 15 km/h (9.3 mph), despite predictions of 200 km/h (124.3 mph). Due to the lack of moving parts, magnetohydrodynamic engines can in principle be reliable, economical, efficient, silent, and mechanically elegant. However, because their fuel source is electricity and we still lack a cheap means of creating high power-density fuel cells, ships that use the MHD drive must have a heavy onboard generator that burns diesel. If the cost of hydrogen fuel cells increases drastically in coming years, the MHD drive might prove a viable alternative to the propeller.
In spacecraft, magnetoplasmadynamic thrusters require a fair amount of power -- in the megawatts -- to perform optimally. Today, even the strongest spacecraft power generators only provide a few hundred kilowatts, meaning that MPD thrusters remain primarily a future technology. However, the operating principles of MPD thrusters allow them to possess extremely high specific impulses, more than 20 times the specific impulse of chemical rockets, given sufficient power.