Is Warp 1 equal to the speed of light?
When they go to warp 10, how do they keep from getting plastered to the wall during acceleration?
The cochrane is the unit used to measure subspace field stress. Cochranes are also used to measure field distortion generated by other spatial manipulation devices, including tractor beams, deflectors, and synthetic gravity fields. Fields below Warp 1 are measured in millicochranes.
A subspace field of one thousand millicochranes or greater becomes the familiar warp field. Field intensity for each warp factor increases geometrically and is a function of the total of the individual field layer values. Note that the cochrane value for a given warp factor corresponds to the apparent velocity of a spacecraft traveling at that warp factor. For example, a ship traveling at Warp Factor 3 is maintaining a warp field of at least 39 cochranes and is therefore traveling at 39 c, the speed of light. Approximate values for integer warp factors are:
| Warp Factor 1 = | 1 cochrane |
| Warp Factor 2 = | 10 cochranes |
| Warp Factor 3 = | 39 cochranes |
| Warp Factor 4 = | 102 cochranes |
| Warp Factor 5 = | 214 cochranes |
| Warp Factor 6 = | 392 cochranes |
| Warp Factor 7 = | 656 cochranes |
| Warp Factor 8 = | 1024 cochranes |
| Warp Factor 9 = | 1516 cochranes |
The actual values are dependent upon interstellar conditions, e.g., gas density, electric and magnetic fields within the different regions of the Milky Way galaxy, and fluctuations in the subspace domain. Starships routinely travel at multiples of c, but they suffer from energy penalties resulting from quantum drag forces and motive power oscillation inefficiencies.
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The short answer to your second question is that the starship's local velocity does not change in the course of shifting from one warp speed to a higher warp speed, but rather the time dilation effect of the warp field is modulated to produce the swifter transit.
For example, a ship traveling at Warp Factor 3 is maintaining a warp field of at least 39 cochranes and is therefore traveling at 39 times c, the speed of light.