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In Star Trek, "warp 1" is the speed of light (c). Up to warp 9, speed varies cubically with the warp#, so warp2 is 8*c, warp3 is 27*c, etc.
Take the warp speed and cube it, and it is traveling at that many times the speed of light. e.g., warp 1 is 1x the speed of light; warp 3 = 27 times the speed of light.
The calculation for Star Trek warp speed is the speed of light times the warp factor squared minus the coefficient of the tangent of the line your are following in space.
The calculation for warp speed in star trek is s(w)=w10/3c. Using that calculation, warp 1 is equivalent to 299792 km per second. Warp 5 is 64155586 km per second, and so on.
Star Trek Warp Factor is equivalent to 1 times C (the speed of light), or about 299792 kilometers per second. These calculations are based on the next generation scale.
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