Note: This page uses HTML5 Canvas, JavaScript, and some advanced CSS2 properties for the layout of equations.
| Berry-Shields Equation | v(W) = W((10/3)+u(W−9)∙A∙(−loge(10−W))n |
| Basic Equation | v(W) = W(10/3) ) + (10 − W)(-11/3) |
| TOS Equation | v(W) = W3 |
| Chart Data Points | see chart below |
| Warp Factor (W) | Velocity (c) | Time to Travel | ||||
| 1 AU | 1 LY | 1 Sector (20LY) | Across Galaxy (100,000LY) | LY | ||
The equation used in the calculator is the Berry-Shields equation, named after the contributors who discovered and refined it (Dominic Berry and Martin Shields). The equation is:
v(W) = W((10/3)+u(W−9)∙A∙(−loge(10−W))n
Where:
u(x) =
{
0; x ≤ 0
e−1/bx2; x > 0
A = 0.03658749373
n = 1.7952294708
And b is an indeterminate constant (1000 is used in the converter) which governs the exact shape of the warp function curve at W=9.
Conversion of velocity to Warp Factor is done by successive approximation to some arbitrary number of iterations and accuracy. On slower machines this may take some time.
| Warp Factor | Velocity (c) | Source | Comment |
|---|---|---|---|
| 1 | 1 | TM | Speed of Light |
| 2 | 10 | TM | |
| 3 | 39 | TM | |
| 4 | 102 | TM | |
| 5 | 214 | TM | Federation speed limit in the year 2370 |
| 6 | 392 | TM | |
| 7 | 656 | TM | |
| 8 | 1024 | TM | |
| 9 | 1516 | TM | Defiant's maximum speed ("The Sound of Her Voice" [DS9]) |
| 9.2 | 1649 | Encyclopedia | |
| 9.6 | 1909 | Encyclopedia | |
| 9.9 | 3053 | Encyclopedia | Enterprise-D maximum speed. |
| 9.975 | ? | "Caretaker" [VOY] | Voyager "cruise velocity" |
| 9.99 | 7912 | Encyclopedia | |
| 9.9997 | ~198696 | TM | (derived) Subspace radio speed |
| 9.9999 | 199516 | Encyclopedia | Maximum boosted subspace radio speed |
Joshua Bell, inexorabletash@gmail.com