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How to Calculate Thrust for an Electric Power System

Imagine the fuel bill for the Space Shuttle. It̵7;s hard enough to fill your car with 16 gallons of ordinary gas, so imagine the cost to fill a 526,000-gallon tank with rocket fuel. And that̵7;s just to ferry a satellite into orbit. Once in orbit, satellites have to jet themselves around with fuel they̵7;ve brought themselves. Space travel is expensive and there̵7;s a constant search for less costly means of propulsion.

The thrust generated by a propulsion system is proportional to the mass of the propellant multiplied by its velocity. That is, a spacecraft sending 50 grams of propellant away at 3 meters per second has the same thrust as another sending 25 grams away at 6 meters per second. That̵7;s the idea behind electric propulsion: Use less mass than traditional propulsion systems, yet expel it more rapidly. And bringing less mass into Earth's orbit means the spacecraft is lighter, so it needs less expensive rocket fuel to the begin with.

Instructions

- 1
  Calculate the charge on the propellant ions. Chemical rockets provide thrust by mixing two compounds that react and release energy. Electric propulsion systems create their thrust by adding energy to charged atoms: Ions. For example, you could have a xenon ion with a charge of +1.
- 2
  Determine the mass of your propellant ion. You can find the atomic mass on a periodic table; round it to the nearest whole number. Xenon, for example, has an atomic mass of 131.29, which rounds to 131 atomic mass units (amu).
- 3
  Define the accelerating voltage of your electric propulsion system. If making calculations for an existing system, you̵7;ll find this in the system specifications. If you̵7;re designing your own system, you̵7;ll have to make a guesstimate and see how it works. For example, you could pick 2,000 volts.
- 4
  Calculate the exit velocity of a single ion. This is the speed at which it exits the spacecraft. The velocity is given by: velocity = sqrt (2 x voltage x charge / mass). For the example:
  
  velocity = sqrt (2 x 1000 volts x 1.6 x 10^-19 coulombs/ (131 amu x 1.66 x 10^-27 kg/amu))
  velocity = 38,000 meters/second
- 5
  Calculate the thrust by multiplying the velocity of a single ion times the mass of all the ions ejected per second. For example, assume your thruster burns 1/10 of a gram of xenon per second, the thrust is then:
  
  thrust = .0001 kg x 38,000 meters/second
  thrust = 3.8 newton

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