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The Tsiolkovsky rocket equation, classical rocket equation, or ideal rocket equation is a mathematical equation that describes the motion of vehicles that follow the basic principle of a rocket: a device that can apply acceleration to itself using thrust by expelling part of its mass with high velocity can thereby move due to the conservation of momentum.

${\displaystyle \Delta v=v_{\text{e}}\ln {\frac {m_{0}}{m_{f}}}=I_{\text{sp}}g_{0}\ln {\frac {m_{0}}{m_{f}}}}$

where:

${\displaystyle \Delta v\ }$ is delta-v – the maximum change of velocity of the vehicle (with no external forces acting).

${\displaystyle m_{0}}$ is the initial total mass, including propellant, also known as wet mass.

${\displaystyle m_{f}}$ is the final total mass without propellant, also known as dry mass.

${\displaystyle v_{\text{e}}=I_{\text{sp}}g_{0}}$ is the effective exhaust velocity, where:

${\displaystyle I_{\text{sp}}}$ is the specific impulse in dimension of time.

${\displaystyle g_{0}}$ is standard gravity.

${\displaystyle \ln }$ is the natural logarithm function.

A rolleron is a type of aileron used for rockets, placed at the trailing end of each fin, and used for passive stabilization against rotation. Inherent to the rolleron is a metal wheel with notches along the circumference. On one side, the notches protrude into the airflow. During flight, this will spin the wheels up to a substantial speed. The wheels then act as gyroscopes. Any tendency of the rocket to rotate around its major axis will be counteracted by the rollerons: the gyroscopic precession acts to move the rolleron in the opposite direction to the rotation.

Rollerons were first used in the AIM-9 Sidewinder missile.

The Lockheed Martin X-33 was an uncrewed, sub-scale technology demonstrator suborbital spaceplane developed in the 1990s under the U.S. government–funded Space Launch Initiative program. The X-33 was a technology demonstrator for the VentureStar orbital spaceplane, which was planned to be a next-generation, commercially operated reusable launch vehicle. The X-33 would flight-test a range of technologies that NASA believed it needed for single-stage-to-orbit reusable launch vehicles (SSTO RLVs), such as metallic thermal protection systems, composite cryogenic fuel tanks for liquid hydrogen, the aerospike engine, autonomous (uncrewed) flight control, rapid flight turn-around times through streamlined operations, and its lifting body aerodynamics.

Failures of its 21-meter wingspan and multi-lobed, composite-material fuel tank during pressure testing ultimately led to the withdrawal of federal support for the program in early 2001. Lockheed Martin has conducted unrelated testing, and has had a single success after a string of failures as recently as 2009 using a 2-meter scale model.