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Warp drive
In the 24th century, traveling many times the speed of light is business as usual. Using controlled annihilation of matter and antimatter, fine tuned by dilithium crystals, Federation ships travel vast distances on a scale of warp factors from warp 1 (1078 million kilometers per hour) to warp 9.9 (8.53 trillion kilometers per hour). Warp factor 10 is the physical limit of the current scale of warp technology, being an infinite speed requiring an infinite amount of energy. Indeed, warp factor 10 is actually meaningless, as any ship at this speed would occupy all points in the universe simultaneously.
Two major components of a typical warp drive are usually located in pairs of elongated sections, called nacelles, placed towards the back of the ship. These nacelles, using plasma and various future technologies create terrific electromagnetic fields which bend or distort the fabric of space, actually changing the physical characteristics of the surrounding space. This distorting or 'warping', from which the name is derived, allows the nacelles to push outwards on space itself, or the 'ether', and propel the ship forward, backward, sideways, up, down, left, right, or in combinations of these directions.
There are times when a static warp bubble or subspace shell is needed. In these cases a "warp bubble" is created. Such a bubble can lower the inertial mass of a ship or starbase, allowing it to be moved with less energy from engines or thrusters than required in "normal" space. Deep Space Nine was moved to the mouth of the Bajoran wormhole in this fashion in 2369 ("Emissary, Part One" [DS9]).
The USS Enterprise-D had a cruising speed of warp 6, or approximately 392 times the speed of light; however, scientific research found that the warp technology employed by the Federation was damaging the fabric of space, and a new cruising speed of warp 5, or 214 times the speed of light, was established (unless the situation was an emergency, and the commanding officer of the ship could use whichever speed he or she deemed fit) until such time as the Federation could find a way to travel faster without damaging the fabric of space ("Force of Nature" [TNG]).
In order to get a rough approximation of how fast a starship is traveling, a simple equation can be used.
From 2067 to approximately 2299: The warp factor being used, cubed, multiplied by the speed of light (for example, warp factor 33=27 x 1078 million kilometers per hour).
From 2300 to present: The warp factor being used, to the fourth power, multiplied by the speed of light (For example, warp factor 34=81 X 1078 million kilometers per hour).

USS Enterprise Enters Warp

Warp Field Dynamics
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Posted: 2003.02.20
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