It can be shown that the net thrust of a rocket is:

where:

propellant flow (kg/s or lb/s)

the effective exhaust velocity (m/s or ft/s)

The

**math_failure (math_image_error): v_{e}**of a rocket engine is often almost constant in a vacuum, but in practice the effective exhaust velocity of rocket engines goes down when operated within an atmosphere as the atmospheric pressure goes up. In space, the effective exhaust velocity is equal to the actual exhaust velocity. In the atmosphere, the two velocities are close in value.

The Tsiolkovsky rocket equation, or ideal rocket equation, is a mathematical equation that relates the delta v with effective exhaust velocity and the initial and end mass of a rocket.

The equation is named after Konstantin Eduardovich Tsiolkovskii|Konstantin Tsiolkovsky who independently derived it and published it in his 1903 work(К. Э. Циолковский, Исследование мировых пространств реактивными приборами, 1903. It is available online http://epizodsspace.airbase.ru/bibl/dorev-knigi/ciolkovskiy/sm.rar here in a RARed PDF). It considers the principle of a rocket: a device that can apply an acceleration to itself (a thrust) by expelling part of its mass with high speed in the opposite direction, due to the conservation of momentum.

For any such maneuver (or journey involving a number of such maneuvers):

:

where:

: is the initial total mass, including propellant.

: is the final total mass.

: is the effective exhaust velocity. ()

: is delta-v.

Units used for mass or velocity do not matter as long as they are consistent.

The following is a simulation of a rocket.

You can change

1. ratio: The

**initial rocket mass/ final rocket mass**ratio,

2. pratio: propellant mass/ total mass

3. dmdt:

4. T: total acceleation time

5. u:

It will draw it's displacement as a function of time x(t) and velocity as a function of time v(t).

**Press the Alt key and the left mouse button to drag the applet off the browser and onto the desktop.**This work is licensed under a Creative Commons Attribution 2.5 Taiwan License

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