Warp Scales - Notes

Universe :	Prime Timeline
Name :	Warp Scales

Since warp drive was first used by Zefram Cochrane in 2063, two methods of scaling warp speeds have been used. The original "Cochrane Scale" was devised by the great man himself for his first test flight aboard the USS Phoenix. It was a relatively straightforward scale in which the speed of the vessel was proportional to the warp factor cubed. Cochrane's first ship didn't exceed lightspeed by more than a few percent, but the scale was flexible enough to remain in force for over two centuries.

Original Scale

Universe :	Prime Timeline
Name :	Original Scale

The original "Cochrane Scale" was devised by the great man himself for his first test flight aboard the USS Phoenix. It was a relatively straightforward scale which followed the formula

V/c = WF³

Where V = Velocity of the vessel, c = the velocity of light, and WF = the warp factor. This scale has the advantage of simplicity; the velocity in multiples of light speed at any given warp factor is that number cubed, hence : [1]

Warp Factor	Velocity (xc)
1 [1]	1 [1]
2 [1]	8 [1]
3 [1]	27 [1]
4 [1]	64 [1]
5 [1]	125 [1]
6 [1]	216 [1]
7 [1]	343 [1]
8 [1]	512 [1]
9 [1]	729 [1]
10 [1]	1,000 [1]
11 [1]	1,331 [1]
12 [1]	1,728 [1]
13 [1]	2,197 [1]
14 [1]	2,744 [1]

By 2300 many were becoming increasingly dissatisfied with the Cochrane Scale. Although convenient for those using the warp formula, it was of limited use to Engineers and specialists since it took relatively little account of the interstellar conditions at the moment. Thus it took a great deal more engine power to achieve a speed of Warp 5 while within a gravimetric distortion than it did while in relatively "calm" interstellar space. Engineering departments lobbied for years to bring in a new scale, but the bridge crews resisted and Starfleet Headquarters - primarily composed of ex-bridge officers - concurred.

The loss of the USS Wilmington with all hands during an Ion storm in 2309 changed this attitude. It emerged during the inquiry that Captain Lamarr had seriously over stressed the Wilmingtons engines by ordering Warp 7 while within the storm; although the Wilmington was quite capable of maintaining this speed under normal conditions, during an Ion storm it was far too great a load. Although other factors contributed greatly, such as a serious breakdown in communications on the ship, Starfleet was unwilling to chance such a situation again.

TNG Scale

Universe :	Prime Timeline
Name :	TNG Scale

The Terrance-Neltorr Graduated Scale was first suggested in 2298 by two civilian warp field specialists of those names. On the TNG Scale the warp factor is indicative of the subspace stress levels which the vessel must both create and endure, rather than the actual velocity of the vessel itself. The actual speed denoted by any given warp factor would depend upon the precise conditions prevalent at the time. So a Captain using the TNG scale would be able to order Warp 7 while in space, a solar system, or an Ion storm and be assured that he would not be over stressing his engines. The new scale was also tweaked to accommodate a number of technical advances made over the last century and in development at the time. Starfleet conducted a quick assessment of several possible new warp scales between 2310 and 2311 before formally adopting the TNG scale, with the changeover made in 2312.

For ideal conditions, such as are found in interstellar space, the speeds of TNG warp factors are calculated using either of two formulae :

Up to Warp 9 :

V/c = WF^(10/3)

Which is very similar to the Cochrane Scale. Beyond Warp 9 the formula becomes somewhat more complex. [2] It is best approximated by :

V/c = WF^{[<(10/3)+a*(-Ln(10-WF))^n>+f1*((WF-9)^5)+f2*((WF-9)^11)]}

Where a is the subspace field density, n is the electromagnetic flux, and f1 and f2 are the Cochrane refraction and reflection indexes respectively. Under ideal conditions values of a = 0.00264320, n = 2.87926700, f1 = 0.06274120 and f2 = 0.32574600 can be expected within a "normal" area of deep interstellar space. The values for TNG warp speeds under these conditions are shown below, along with travel times across typical distances :

Warp Factor	Equals (xc)	Time to travel
Warp Factor	Equals (xc)	Earth to Moon (400,000 km)	Across Sol System (12 billion km)	To nearby star (5 ly)	Across Sector (20 ly)	Across Federation (8,000 ly)	To Andromeda (2 million ly)
1 [3]	1 [3]	1.3333 Sec [3]	11.1 Hours [3]	5.0 Years [3]	20.0 Years [3]	8,000.0 Years [3]	2,000,000 Years [3]
2 [3]	10 [3]	0.1323 Sec [3]	1.1 Hours [3]	181.1 Days [3]	2.0 Years [3]	793.7 Years [3]	198,425.1 Years [3]
3 [3]	39 [3]	0.0342 Sec [3]	17.1 Minutes [3]	46.9 Days [3]	187.5 Days [3]	205.4 Years [3]	51,360.1 Years [3]
4 [3]	102 [3]	0.0131 Sec [3]	6.6 Minutes [3]	18.0 Days [3]	71.9 Days [3]	78.7 Years [3]	19,686.3 Years [3]
5 [3]	214 [3]	0.0062 Sec [3]	3.1 Minutes [3]	8.5 Days [3]	34.2 Days [3]	37.4 Years [3]	9,356.9 Years [3]
6 [3]	392 [3]	0.0034 Sec [3]	1.7 Minutes [3]	4.6 Days [3]	18.6 Days [3]	20.4 Years [3]	5,095.6 Years [3]
7 [3]	656 [3]	0.0020 Sec [3]	1.0 Minutes [3]	2.8 Days [3]	11.1 Days [3]	12.2 Years [3]	3,048.2 Years [3]
8 [3]	1,024 [3]	0.0013 Sec [3]	39.1 Sec [3]	1.8 Days [3]	7.1 Days [3]	7.8 Years [3]	1,953.1 Years [3]
9 [3]	1,516 [3]	0.0009 Sec [3]	26.4 Sec [3]	1.2 Days [3]	4.8 Days [3]	5.3 Years [3]	1,318.9 Years [3]
9.1	1,573	0.0008 Sec	25.4 Sec	1.2 Days	4.6 Days	5.1 Years	1,271.2 Years
9.2 [3]	1,649 [3]	0.0008 Sec [3]	24.3 Sec [3]	1.1 Days [3]	4.4 Days [3]	4.9 Years [3]	1,212.9 Years [3]
9.3	1,693	0.0008 Sec	23.6 Sec	1.1 Days	4.3 Days	4.7 Years	1,181.6 Years
9.4	1,757	0.0008 Sec	22.8 Sec	1.0 Days	4.2 Days	4.6 Years	1,138.3 Years
9.5	1,828	0.0007 Sec	21.9 Sec	24.0 Hours	4.0 Days	4.4 Years	1,093.9 Years
9.6 [3]	1,909 [3]	0.0007 Sec [3]	21.0 Sec [3]	23.0 Hours [3]	3.8 Days [3]	4.2 Years [3]	1,047.7 Years [3]
9.7	2,044	0.0007 Sec	19.6 Sec	21.4 Hours	3.6 Days	3.9 Years	978.5 Years
9.8	2,304	0.0006 Sec	17.4 Sec	19.0 Hours	3.2 Days	3.5 Years	868.0 Years
9.9 [3]	3,053 [3]	0.0004 Sec [3]	13.1 Sec [3]	14.4 Hours [3]	2.4 Days [3]	2.6 Years [3]	655.1 Years [3]
9.95	4,183	0.0003 Sec	9.6 Sec	10.5 Hours	1.7 Days	1.9 Years	478.1 Years
9.975	5,552	0.0002 Sec	7.2 Sec	7.9 Hours	1.3 Days	1.4 Years	360.2 Years
9.99 [3]	7,912 [3]	0.0002 Sec [3]	5.1 Sec [3]	5.5 Hours [3]	22.2 Hours [3]	1.0 Years [3]	252.8 Years [3]
9.995	10,553	0.0001 Sec	3.8 Sec	4.2 Hours	16.6 Hours	276.7 Days	189.5 Years
9.999	25,567	0.0001 Sec	1.6 Sec	1.7 Hours	6.9 Hours	114.2 Days	78.2 Years
9.9999 [3]	199,516 [3]	0.0000 Sec [3]	0.2 Sec [3]	13.2 Minutes [3]	52.7 Minutes [3]	14.6 Days [3]	10.0 Years [3]
10 [4]	Infinite [4]	An object at warp 10 travels at infinite speed, occupying all points in the universe simultaneously [4]

Although the TNG Scale has proved highly successful in use, recent advances in warp drive have brought its practicality into some question. In 2312 it seemed unlikely that Starships would get beyond Warp 9.9 for a very long time, but modern vessels are capable of Warp 9.97+ [5] speeds and some predict that the next twenty years will see ships which can travel in the Warp 9.999+ region. While there remains no engineering difficulties with these numbers, it is becoming problematic for bridge crews to keep track of a tactical situation while having to use numbers to three significant figures. Although nothing definite has yet emerged, several proposals for new warp scales are currently under consideration by Starfleet.

Warp Highways

Universe :	Prime Timeline
Name :	Warp Highways

Although the above values hold true for ideal conditions, there are occasions when a Starship can travel at speeds significantly higher than normal. For instance, shortly after Zefram Cochrane made his famous warp flight, the SS Valiant was able to reach the edge of the galaxy. [6] In 2286 Captain Kirk was able to reach the centre of the Galaxy from Nimbus III, covering a distance of 22,000 light years in just 6.8 hours at warp 7 - an average of 3,235 light years per hour. [7] These high speeds are allowed by so called "warp highways". Named after an ancient transportation system, these can consist of broad areas encompassing a number of whole star systems, or narrow corridors which can extend for many thousands of light years.

The effect of a warp highway is to change the speed associated with any given warp factor according a multiplier known as Cochranes Value, which is highly variable from region to region. These phenomena are known to exist for a finite period of time; the one between Nimbus III and the Galactic core no longer exists, which is why the USS Voyager is unable to make use of it in her attempts to return from the other side of the galaxy.

Amongst their other properties, highways are notoriously difficult to detect and map - Starfleet has always put considerable effort into locating these regions, carrying out many mapping missions. Voyager has been partially able to overcome this difficulty with the use of advanced Astrometric sensors, which cut five years off their journey time [8] by allowing the vessel to detect regions where the Cochrane Value would be slightly higher from many thousands of light years away.

Since their discovery, the warp highways have been a crucial factor in the expansion of the Federation and other powers. They allow the journey time across known space to be cut from years or even decades down to a matter of days.

Warp Shallows

Universe :	Prime Timeline
Name :	Warp Shallows

Whilst some regions of space have a speed multiplier in the tens of thousands, there are also regions where the value is less than unity. For example, in the region around the Xendi Sabu system warp speeds are reduced by almost one half - a Cochrane Value of 0.55. [9] These regions, which are commonly nicknamed 'Warp Shallows', are generally more common than warp highways and tend to cover a larger area. Warp shallows can be caused by a variety of phenomena - the Hekaras corridor is a region of relatively normal space which passes through a large warp shallow caused by unusually intense tetryon fields. The Briar Patch is a warp shallow caused by the unusual metaphasic radiation common to the region.

Subspace Sandbars

Universe :	Prime Timeline
Name :	Subspace Sandbars [10]

Subspace Sandbars are a phenomenon which prevents a vessel using warp drive at all within a given region [10] - essentially, a region with a Cochrane factor of zero. These regions are, fortunately, very rare.

Colour key

References

#	Series	Season	Source	Comment
1			Star Trek - Starfleet Technical Manual	2:06:20
2			Star Trek The Next Generation Technical Manual	Page 55
3			Star Trek Encyclopedia	third edition Page 558
4	VOY	2	Threshold
5	VOY	1	Caretaker
6	TOS	1	Where No Man Has Gone Before
7			Star Trek V : The Final Frontier
8	VOY	4	Year of Hell, Part 1
9			Speculative	Speculation to explain the low speed quoted by Riker in Bloodlines
10	VOY	5	Bride of Chaotica!

Page views : 112,945

Last updated : 1 Jan 1970

Series :	VOY Season 2
Episode :	Threshold

Series :	VOY Season 1
Episode :	Caretaker

Series :	TOS Season 1
Episode :	Where No Man Has Gone Before

Series :	VOY Season 4
Episode :	Year of Hell, Part 1

Series :	VOY Season 5
Episode :	Bride of Chaotica!

Book :	Star Trek - Starfleet Technical Manual
Comment :	2:06:20

Source :	Speculative
Comment :	Speculation to explain the low speed quoted by Riker in Bloodlines