Warp Scales

Warp Scales ______________________________________________________________________________________________ Since warp drive was first used by Zephram 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. Cochranes 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. 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.
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.
The original "Cochrane Scale" was devised by the great man himself for his first test flight aboard the USS Phoenix. It was a 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.

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. 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 :

		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	1	1.3333 Sec	11.1 Hours	5.0 Years	20.0 Years	8,000.0 Years	2,000,000 Years
2	10	0.1323 Sec	1.1 Hours	181.1 Days	2.0 Years	793.7 Years	198,425.1 Years
3	39	0.0342 Sec	17.1 Minutes	46.9 Days	187.5 Days	205.4 Years	51,360.1 Years
4	102	0.0131 Sec	6.6 Minutes	18.0 Days	71.9 Days	78.7 Years	19,686.3 Years
5	214	0.0062 Sec	3.1 Minutes	8.5 Days	34.2 Days	37.4 Years	9,356.9 Years
6	392	0.0034 Sec	1.7 Minutes	4.6 Days	18.6 Days	20.4 Years	5,095.6 Years
7	656	0.0020 Sec	1.0 Minutes	2.8 Days	11.1 Days	12.2 Years	3,048.2 Years
8	1,024	0.0013 Sec	39.1 Sec	1.8 Days	7.1 Days	7.8 Years	1,953.1 Years
9	1,516	0.0009 Sec	26.4 Sec	1.2 Days	4.8 Days	5.3 Years	1,318.9 Years
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	1,649	0.0008 Sec	24.3 Sec	1.1 Days	4.4 Days	4.9 Years	1,212.9 Years
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	1,909	0.0007 Sec	21.0 Sec	23.0 Hours	3.8 Days	4.2 Years	1,047.7 Years
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	3,053 65	0.0004 Sec	13.1 Sec	14.4 Hours	2.4 Days	2.6 Years	655.1 Years
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	7,912	0.0002 Sec	5.1 Sec	5.5 Hours	22.2 Hours	1.0 Years	252.8 Years
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	199,516	0.0000 Sec	0.2 Sec	13.2 Minutes	52.7 Minutes	14.6 Days	10.0 Years
10	Infinite	An object at warp 10 travels at infinite speed, occupying all points in the universe simultaneously

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+ 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.

Power Usage

Although the above values hold true for ideal conditions, there are regions of space where a Starship can travel at speeds significantly higher than normal. These regions have been nicknamed "warp highways" after an ancient each transportation system. They 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. Shortly after Zephram Cochrane made his first warp flight the SS Valiant was able to use a warp highway, reaching the edge of the galaxy, a distance of some several thousand light years which otherwise would have taken the vessel many years to accomplish at modest warp factors. The most dramatic example of a warp highway is the one which existed between Nimbus III and the galactic core. In 2287 the Enterprise-A travelled this highway at Warp 7, covering the 22,000 light year distance to the core in just 6.8 hours - an average of 3,235 light years per hour. 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 allowed the vessel to detect regions where the Cochrane Value would be slightly higher from many thousands of light years away, enabling the crew to cut five years off their journey time. 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.

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