Points for a Prepared Pilot

[Mreh K'hal 0]

I realize this isn't really a log, per se, but I was curious about this and how it would relate to traveling around on the Excalibur, and I wanted some sort of reference as it applies to Mreh and his helmsman duties.

Warp Factor	× c	au/s	ly/s
1.0	1	0.002	µ
1.5	4	0.008	µ
2.0	10	0.020	µ
2.5	21	0.042	µ
3.0	39	0.078	µ
3.5	65	0.130	µ
4.0	102	0.204	µ
4.5	150	0.301	µ
5.0	214	0.428	µ
5.5	294	0.589	µ
6.0	392	0.787	µ
6.5	513	1.027	µ
7.0	656	1.315	µ
7.5	826	1.655	µ
8.0	1024	2.052	0.00003
8.5	1253	2.512	0.00004
9.0	1516	3.039	0.00005
9.25	5803	11.630	0.00018
9.50	2.38 × 104	47.600	0.00075
9.75	1.04 × 105	209.044	0.00331
9.90	4.93 × 105	988.542	0.01563
9.99	2.52 × 106	5052.325	0.07989
c	au	ly	pc
299,792,458 m/s 0.002 au/s 3.169 × 10-8 ly/s	149,598,000 km	63,239.6717 au 0.3066 pc	3.26156 ly 206.26 × 103 au

The calculations above come from the canon TNG formula^[1] for determining warp factors and the associated velocities. The formula holds true for warp 9.0 and below. Above that, there is no canon formula for determining the velocity at a specific warp factor, but the theory is that the number increases exponentially, with Warp 10 at ∞

The formula:
Where:
WF = Warp Factor
v is the velocity
c is the speed of light

All "× c" values (through Warp 9.25) have been rounded to the nearest integer for ease of use. After that, the numbers are slightly unwieldy so they have been put in scientific notation.

The addition of the Astronomical Unit per Second data was added for the sake of "visualizing" the speeds, as it is slightly easier to contemplate the distance from Earth to the Sun than trying to deal with meters or the larger unit of light-years. Using that data, for instance, means traveling at Warp 1 (the speed of light) will take around 8 minutes to traverse that distance.

To truly get a sense for the vast amount of space between possible destinations in space, consider this scenario: α Cen C^[2] (commonly referred to as Proxima Centauri or just Proxima) is the closest extra-solar star to Earth.

It lies 4.243 ± 0.002 ly from earth. Travel Times:

Warp 1: 4 Years, 88 Days, 18 Hours, 8 Minutes, 17 Seconds
Warp 2: 153 Days, 18 Hours, 14 minutes, 24 Seconds
Warp 3: 39 Days, 19 Hours, 12 minutes
Warp 4: 15 Days, 6 Hours
Warp 5: 7 Days 6 Hours
Warp 6: 3 Days, 22 Hours, 48 Minutes
Warp 7: 2 Days, 8 Hours, 38 Minutes, 24 Seconds
Warp 8: 1 Day, 12 Hours, 6 Minutes
Warp 9: 1 Day, 0 Hours, 28 Minutes, 48 Seconds

Even at Warp 9, it would still take over a day to get to our nearest neighbor!

In the same vein, Vulcan (said by Gene Roddenberry and others associated with canon Star Trek™ to be located in the star system 40 Eridani A [40 Eri A]^[3]; though not ever officially mentioned in any series, the evidence is sufficient for use here^[4]) is 16.45 ± 0.07 ly from Earth.

The Excalibur's official Standard Cruise Speed is Warp 7.0^[5]. At this speed, it would take 9 Days, 3 Hours, 50 Minutes and 24 Seconds for the Excalibur to travel from Earth to Vulcan!

According to multiple sources, the size of the Federation is 8,000 ly across at it's widest point^[6]. At Warp 7.0, it would take over twelve years to traverse the distance!

There are multiple instances in the history of all series and movies that seem to throw these numbers out the window^[7], one way or the other. Which is helpful, because these time frames are seriously problematic for simulations, so it's nice to know that even canonically there is permission to take liberties where needed. This all does serve to illustrate, even with the miracle of warp drive, how seriously big space is and how difficult it can be to stick to the theory of it for the sake of practicality.

Notes & References

• All the calculations done to determine the warp speeds were done on a TI-85 Graphing Calculator (without which the author of the article would have floundered during math classes). The v & c values were done in meters per second (m/s).
• The calculations for speeds in excess of warp nine (which is something up in the air) are the prior speed's velocity to the 1.05th (v^1.05). It may be a bit low, however I wanted it to generally fit with the observed performace of Voyager at 9.975.

1. Warp Factors @ Memory Alpha
2. Proxima @ Wikipedia
3. 40 Eri A @ Wikipedia
4. Vulcan (planet) @ Memory Alpha
5. Excalibur-C Statistics & Specifications @ STSF Forums
6. United Federation of Planets @ Memory Alpha
7. Warp Speed Anomalies @ DITL

Note: edited to re-activate the css/html

Edited June 29, 2009 by Mreh K'hal