Since Zephram Cochrane first used warp drive 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 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 :

V

c

1

1

2

8

3

27

4

64

5

125

6

216

7

343

8

512

9

729

10

1000

11

1331

12

1728

13

2197

14

2744

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 UFED Headquarters - primarily composed of ex-bridge officers - concurred

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. UFED 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 : (1a) 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 :

(1b) V/c = WF((10/3)+(Yx(-ln(10-WF))^x))

Where Y is the subspace field density and x is the electromagnetic flux. Under ideal conditions values of Y = 0.03684678 and x = 0.03684678 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 :

(2) Warp Factor Equals x c

Warp Factor

c

Across Sol System

To Nearby Star

Across sector

Across Federation

(12 billion km)

(5 light years)

(20 light years)

(8000 light years)

1

1

11.1 hr

5 yr

20 yr

8000 yrs

2

10

1.1 hr

181.1 days

2 yrs

793.7 yrs

3

39

17.1 min

46.9 days

187.5 days

205.4 yrs

4

102

6.6 min

18 days

71.9 days

78.7 yrs

5

241

3.1 min

8.5 days

34.2 days

37.4 yrs

6

392

1.7 min

4.6 days

18.6 days

20.4 yrs

7

656

1 min

2.8 days

11.1 days

12.2 yrs

8

1024

39.1 sec

1.8 days

7.1 days

7.8 yrs

9

1516

26.4 sec

1.2 days

4.8 days

5.3 yrs

9.1

1576

25.4 sec

1.2 days

4.6 days

5.1 yrs

9.2

1641

24.4 sec

1.1 days

4.4 days

4.9 yrs

9.3

1714

23.3 sec

1.1 days

4.3 days

4.7 years

9.4

1,797

22.2 sec

1 day

4.1 days

4.5 yrs

9.5

1,896

21.1 sec

23.1 hrs

3.9 days

4.2 yrs

9.6

2,019

19.8 sec

21.7 hrs

3.6 days

4 yrs

9.7

2,187

18.3 sec

20 hrs

3.3 days

3.7 yrs

9.8

2,453

16.3 sec

17.9 hrs

3 days

3.3 yrs

9.9

3,035

13.2 sec

14.4 hrs

2.4 days

2.6 yrs

9.92

3,272

12.2 sec

13.4 hrs

2.2 days

2.4 yrs

9.94

3,623

11 sec

12.1 hrs

2 days

2.2 yrs

9.96

4,228

9.5 sec

10.4 hrs

170 days

1.9 yrs

9.975

5,514

7.8 sec

8.5 hrs

1.4 days

1.6 yrs

9.991

8.384

4.8 sec

5.2 hrs

20.9 days

348.3 yrs

9.995

11.556

3.5 sec

3.8 hrs

15.2 days

252.7 days

10

0

0

0

0

0

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 9.99+ 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 UFED.