*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) = W^{3} |

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 |

- Significant figures in Calculator
- Show calculator point on graph

Joshua Bell, inexorabletash@gmail.com