Rockets are a way of accelerating based on Newton's Third Law of Motion- by throwing propellent away the body of the rocket is thrown in the opposite direction.

However as the propellent is used up, the emptier rocket will accelerate faster, and the acceleration increases. Hence there is a need to be able to calculate the final speed after some or all of the fuel has been burnt, allowing for this fact.

The rocket equation relates the before and after mass of the rocket, the exhaust velocity and the overall change in speed, when the thrust is applied in a straight line.

The equation is:

dV = Ve loge( Mi/Mf)

where:

  • dV is the change in speed of the rocket (Delta-v)
  • Ve is the exhaust velocity
  • Mi is the initial mass
  • Mf is the final mass

The rocket equation neglects any effects of gravity, wind resistance and assumes a constant exhaust velocity relative to the rocket. You'll note that the rocket equation doesn't depend on the rate that the fuel is burned.

Ve is closely related to the specific impulse (Isp). In fact you multiply specific impulse by the sea level acceleration due to gravity to get Ve.

e.g. Ve of a rocket with an Isp of 300 seconds:

  • 300 * 9.81 m/s (In SI units)
  • 300 * 32 ft/s (In 'english' units)

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