Dec 302017

A complete explaination of Star Trek’s warp systems. | |||
---|---|---|---|

File Name | File Size | Zip Size | Zip Type |

WARPTE.TXT | 15360 | 5714 | deflated |

# Download File WARPTE.ZIP Here

## Contents of the WARPTE.TXT file

Warp numbers do not directly refer to speed, but to power. Warp 1 is the

power level required to enter the warp continuum, and is known as Threshold

power. Warp 2 is twice that power level, etc. Fractional warp is simply

less than Threshold power while the ship, though traveling via warp field

effect, is still "in" the Einstein space-time continuum at sub-light speed.

The formula relating the Warp number W to velocity in terms of C is not

the ridiculous V = W^3. In Trek Classic's very first episode the Enterprise

was seen at the edge of our galaxy. Even assuming this to be the near edge

reached by going perpendicular to the galactic plane, it is still at least

1500 light years from Earth. At a cruising speed of Warp 6 = 216 C, the

ship would have spent at least 7 years getting out there, then 7 more back.

Instead of V = W^3, velocity is defined by the sum of an infinite series

known as the 3rd-order Cochrane function, which is applicable to Tertiary

warp effect fields such as are utilized by major Federation vessels from the

Tritium class onward. The first term of this series is the familiar W^3, the

second term is the integral of the first term, W^4/4, the third is the

integral of the second, W^5/20, and so on, ad infinitum. Each term is the

integral of the preceding term. Thus the common mistake so often made is to

quote only the first term of the series as if it were the entire function.

The behavior of this series is such that the terms rise in value at

first, then become increasingly smaller so as to converge on a definite

value. This may be calculated by the equivalent formula:

V = 6 * { e^W - [ (W^2)/2 + W + 1] }

where V = velocity, W = Warp factor, and e = base for natural logs 2.71828..

When calculated in this manner, this function gives the following values:

Generated Uncorrected

Power Warp Speeds

1 1.31

2 14.33

3 69.51

4 249.59

5 779.48

6 2270.57

7 6384.80

8 17639.75

9 48315.50

10 131792.79

11 358809.85

12 976018.75

13 2653889.35

14 7214947.68

15 19613332.78

For starship designers, these numbers seemed too good to be true, and

indeed they were. From the earliest days of starship operations, warp

engines had always registered a small power loss as they were fed more than

Warp 1 power. Defined as the difference between Generated Power and

Delivered Power, this drain was ascribed to the faintly conceived notion of

"continuum drag". It was Delivered Power that determined actual velocity

according to the 3rd-order Cochrane function. As the phenomena was still too

poorly understood for mathematical description, progressive increases in

power generation capability had to be matched empirically with increases in

Delivered Power via actual flight testing, and the term Warp Factor continued

to refer to Generated Power.

The Dilithium breakthru made it possible to generate unprecedented

multiples of threshold power, and led to the Federation's investment in the

Constitution class vessels. Able to safely generate and sustain Warp 8

power, these ships found the drag/drain worsening rapidly at the higher

levels.

It was the USS Enterprise, under Christopher Pike, that first challenged

the "Warp Barrier". After three month's total overhaul at the Terran Orbital

Shipyards personally supervised at every stage by Montgomery Scott, the ship

went on speed runs pushing her anti-matter reactors as high as Warp 13 for a

few seconds at a time. The resulting measurements at last permitted Scott to

define the continuum drag equation:

tan(A)

CDF = G - ------------------------------------ + 10

(G-S) + (tan^2(A)+((G-S)^2)-1)^(1/2)

and thus

D = G - CDF

where D = Delivered Power; G = Generated Power; CDF = Continuum Drag

Factor; A = 5.1050881 radians; and S = 9.8658770244 (Scott's constant). The

corrected table of Warp speeds is therefore:

Generated Delivered Warp Speed

Power Power x C

1 1.00000 1.31

2 1.98354 13.91

3 2.96260 65.98

4 3.93509 230.94

5 4.89755 696.42

6 5.84370 1926.80

7 6.76140 4999.38

8 7.62571 12075.26

9 8.38615 26048.20

10 8.96633 46707.91

11 9.33067 67348.90

12 9.53548 82717.85

13 9.65322 93087.64

14 9.72615 100151.85

15 9.77477 105155.01

Old Warp New Warp

A graph of Scott's equation plotting Generated Power as X against

Delivered Power as Y, shows that at threshold power (Scott's equation and the

3rd-order Cochrane's function are not applicable below this point) X = Y = 1,

and the graph line proceeds at an almost 45 degree angle assuming equal

scales.

But as Generated Power exceeds 8 times threshold level, Delivered Power

deviates ever more significantly and the graph curves sharply to the right.

The curve is half of a hyperbola, rotated by angle A, with the significant

asymptote line represented by the equation Y = 10, so that while the

Generated Power may go arbitrarily high, the Delivered Power will only

approach ever more closely but never equal 10. The speed value for Warp 10

from the uncorrected chart, 131792.39 times the speed of light, is the

theoretical limit of the Tertiary warp effect, and can only be approached,

never equaled or exceeded.

By the time of ST:TNG, it had become standard practice to quote Warp

factors in terms of Delivered, rather than Generated, power. This explains

the apparent discrepancy between the eras. Overall Generated Power

capabilities are still crucial to military vessels, as even a few dozen extra

C's may mean the difference between success and failure when outrunning or

catching an opponent.

Just as the 3rd-order Cochrane function is known as Tertiary Warp, the

1st and 2nd orders represent Primary, and Secondary Warp. Primary Warp is

the function consisting of the sum of the infinite series begining with X

plus (X^2)/2 plus (X^3)/6 etc. As with the 3rd-order series, it may be

calculated with the equivalent formula (e^W)-1. This was the first type of

warp drive system developed, and it is still in use on later vessels as the

Impulse Drive system.

When Secondary Warp drive systems were developed, governed by the

2nd-order Cochrane function consisting of the sum of the infinite series

begining with X^2 + (X^3)/3 +(X^4)/12 etc., equivalent formula:

2*((e^W)-(W+1)), it was learned that they, and all higher order warp fields,

were dangerously unstable at low fractions of threshold power. This forced

the retention of some form of Primary warp drive, though it need not handle

enough power to go superluminal.

These first three orders of warp field phenomena correspond to the first

three "generations" of warp drive technology in the "Spaceflight Chronology".

Logically, a "Fourth generation" designation should have waited for the

developement of Quarternary warp, the sum of X^4 + (X^5)/5 + (X^6)/30 etc.,

equivalent formula 24*((e^W)-((W^3)/6 + (W^2)/12 + W + 1)), but the impact of

Dilithium on power generation, and thus overall performance, was so great

that the "Fourth generation" label took hold for the Constitution class. All

orders of warp field phenomena remain subject to the Warp 10 limit on

Delivered Power, but higher order warps produce greater velocity for the same

Delivered Power than lower orders.

The term "Fifth generation" is usually applied to the abortive attempt to

harness "Trans-Warp", a misbegotten application of the Interphase phenomena

first observed by the Enterprise NCC-1701 during the "Tholian Web" incident.

The abandonment of this dangerous system was made doubly disappointing by the

continued failure of Federation science to perfect a workable Quartenary warp

drive. The seemingly insurmountable difficulties encountered in the early

attempts at Quarternary drive design were the prime reason for the costly

"Trans-Warp" interlude.

However, in the intervening decades advanced theoretical studies have led

to vastly simpler, more reliable Tertiary drives which can be pushed far

closer to the Warp 10 limit of Delivered Power than the original design

multi-stage units. These single stage "integrated" units were first used in

ship's of the NCC-1701-C's class, and marked the arrival of warp technology's

"Sixth generation". A highly refined and advanced version of this type of

drive serves as the main propulsion for "Galaxy" class starships such as

Enterprise NCC-1701-D.

As the early efforts at Quarternary warp floundered on the complexities

of a four level multi-stage approach, the success of the single stage

"integrated" approach for Tertiary warp has scientists of ST:TNG's era once

more confident of eventual success, and aggressively paced research programs

are again under way in the race for the Quartenary drive.

Montgomery Scott correctly predicted the crippling deficientcies of the

Trans-Warp system, but was unable to dissuade StarFleet from investing in it.

Rightly convinced that Quartenary warp would have to await improvements in

warp theory permitting "integrated" designs, he attempted to convince

StarFleet to allow him to challenge the Warp 10 Barrier itself. The

mathematically inclined are invited to contemplate the significance of the

other half of the hyperbola, which most Federation scientists dismiss as a

mere geometric curiousity. Of course, scientists once thought that C itself

represented an impassable barrier. As Spock would say, "There are always

possibilities". Alas, Scott was never able to secure StarFleet backing for

his proposal, and only a handful of ST:TNG era technical persons who've

studied his original notes even know what he had in mind.

An interesting aspect of the 3rd-order Cochrane function is that Warp 1

is not C but 1.31xC. Taking the reciprocal of this number, 0.763, gives what

is known as threshold velocity. Under fractional warp power, a starship

"accelerates" as the power is steadily increased. At Warp .99999 etc., the

ship is traveling at 0.763xC. Transition occurs, an explosive event

accompanied by the hauntingly beautiful phenomena known as the Chromatic

Detonation, the optical analog of a sonic boom. In the next micro-instant,

the ship is on "the other side", traveling through the warp continuum at

1.31xC. The ship is never observed at speeds 0.763 < V < 1.31 under normal

conditions.

It should be noted however, that the boundary layer of the warp field

effect creates an envelope of 4 dimensional Einsteinian space-time within in

which the ship travels. Therefore, all the familiar physical laws of the

"ordinary" continuum still apply within the envelope. From the outside, it

appears as though a space-time anomaly were manifested sequentially along a

linear path. Fleeting, multiple images of the vessel in the center of the

anomaly are created at widely spaced intervals which grow more distant at

higher warp factors. Light coming from within the envelope gathers at the

boundary layer until it reaches optical crossover threshold, at which point

it "pulses" through, thus re-entering normal space-time to project the image

of the ship. This effect was nicely filmed for the climactic scene in

ST:TSFS when we see the Enterprise fleeing the detonation of the Genesis

Device.

External light enters the envelope via complex optical interaction with

the warp field boundary layer. The micro-instant lost for photons in front

of the ship's path to cross the boundary layer causes them to appear to

originate from directions shifted away from the line of motion in favor of

apparent origins perpendicular to the direction of travel. While an optical

blind spot exists directly behind the ship along the direction of motion, due

to the superluminal velocity involved, the tear-drop shape of the overall

warp field minimizes the area so blanked out to a vanishingly small region.

The overall effect is curiously symmetrical to that observed by vessels

approaching light speed in normal space-time. Such a vessel would see its

3-dimensional field of view collapsed into twin circles of light in front of

and behind the ship, with a band of darkness around its mid-section. A

vessel in the warp field traveling at superluminal velocities experiences a

tunnel-like effect in which the dark region consists of circles in front of

and behind the vessel, and its view of the universe is projected onto a

cylindrical tube which the ship appears to travel through.

Of course, the ship's computers correct for this effect to present an

intuitively "normal" view upon the bridge and other viewscreens. Windows

facing port or starboard reveal a relatively normal view without

sophisticated correction, others have internal holographic layers which serve

as the functional equivalents of corrective lenses to keep the view at least

intelligible, if not exactly accurate.

-Leon Myerson; 72157,3432; 3/18/88

power level required to enter the warp continuum, and is known as Threshold

power. Warp 2 is twice that power level, etc. Fractional warp is simply

less than Threshold power while the ship, though traveling via warp field

effect, is still "in" the Einstein space-time continuum at sub-light speed.

The formula relating the Warp number W to velocity in terms of C is not

the ridiculous V = W^3. In Trek Classic's very first episode the Enterprise

was seen at the edge of our galaxy. Even assuming this to be the near edge

reached by going perpendicular to the galactic plane, it is still at least

1500 light years from Earth. At a cruising speed of Warp 6 = 216 C, the

ship would have spent at least 7 years getting out there, then 7 more back.

Instead of V = W^3, velocity is defined by the sum of an infinite series

known as the 3rd-order Cochrane function, which is applicable to Tertiary

warp effect fields such as are utilized by major Federation vessels from the

Tritium class onward. The first term of this series is the familiar W^3, the

second term is the integral of the first term, W^4/4, the third is the

integral of the second, W^5/20, and so on, ad infinitum. Each term is the

integral of the preceding term. Thus the common mistake so often made is to

quote only the first term of the series as if it were the entire function.

The behavior of this series is such that the terms rise in value at

first, then become increasingly smaller so as to converge on a definite

value. This may be calculated by the equivalent formula:

V = 6 * { e^W - [ (W^2)/2 + W + 1] }

where V = velocity, W = Warp factor, and e = base for natural logs 2.71828..

When calculated in this manner, this function gives the following values:

Generated Uncorrected

Power Warp Speeds

1 1.31

2 14.33

3 69.51

4 249.59

5 779.48

6 2270.57

7 6384.80

8 17639.75

9 48315.50

10 131792.79

11 358809.85

12 976018.75

13 2653889.35

14 7214947.68

15 19613332.78

For starship designers, these numbers seemed too good to be true, and

indeed they were. From the earliest days of starship operations, warp

engines had always registered a small power loss as they were fed more than

Warp 1 power. Defined as the difference between Generated Power and

Delivered Power, this drain was ascribed to the faintly conceived notion of

"continuum drag". It was Delivered Power that determined actual velocity

according to the 3rd-order Cochrane function. As the phenomena was still too

poorly understood for mathematical description, progressive increases in

power generation capability had to be matched empirically with increases in

Delivered Power via actual flight testing, and the term Warp Factor continued

to refer to Generated Power.

The Dilithium breakthru made it possible to generate unprecedented

multiples of threshold power, and led to the Federation's investment in the

Constitution class vessels. Able to safely generate and sustain Warp 8

power, these ships found the drag/drain worsening rapidly at the higher

levels.

It was the USS Enterprise, under Christopher Pike, that first challenged

the "Warp Barrier". After three month's total overhaul at the Terran Orbital

Shipyards personally supervised at every stage by Montgomery Scott, the ship

went on speed runs pushing her anti-matter reactors as high as Warp 13 for a

few seconds at a time. The resulting measurements at last permitted Scott to

define the continuum drag equation:

tan(A)

CDF = G - ------------------------------------ + 10

(G-S) + (tan^2(A)+((G-S)^2)-1)^(1/2)

and thus

D = G - CDF

where D = Delivered Power; G = Generated Power; CDF = Continuum Drag

Factor; A = 5.1050881 radians; and S = 9.8658770244 (Scott's constant). The

corrected table of Warp speeds is therefore:

Generated Delivered Warp Speed

Power Power x C

1 1.00000 1.31

2 1.98354 13.91

3 2.96260 65.98

4 3.93509 230.94

5 4.89755 696.42

6 5.84370 1926.80

7 6.76140 4999.38

8 7.62571 12075.26

9 8.38615 26048.20

10 8.96633 46707.91

11 9.33067 67348.90

12 9.53548 82717.85

13 9.65322 93087.64

14 9.72615 100151.85

15 9.77477 105155.01

Old Warp New Warp

A graph of Scott's equation plotting Generated Power as X against

Delivered Power as Y, shows that at threshold power (Scott's equation and the

3rd-order Cochrane's function are not applicable below this point) X = Y = 1,

and the graph line proceeds at an almost 45 degree angle assuming equal

scales.

But as Generated Power exceeds 8 times threshold level, Delivered Power

deviates ever more significantly and the graph curves sharply to the right.

The curve is half of a hyperbola, rotated by angle A, with the significant

asymptote line represented by the equation Y = 10, so that while the

Generated Power may go arbitrarily high, the Delivered Power will only

approach ever more closely but never equal 10. The speed value for Warp 10

from the uncorrected chart, 131792.39 times the speed of light, is the

theoretical limit of the Tertiary warp effect, and can only be approached,

never equaled or exceeded.

By the time of ST:TNG, it had become standard practice to quote Warp

factors in terms of Delivered, rather than Generated, power. This explains

the apparent discrepancy between the eras. Overall Generated Power

capabilities are still crucial to military vessels, as even a few dozen extra

C's may mean the difference between success and failure when outrunning or

catching an opponent.

Just as the 3rd-order Cochrane function is known as Tertiary Warp, the

1st and 2nd orders represent Primary, and Secondary Warp. Primary Warp is

the function consisting of the sum of the infinite series begining with X

plus (X^2)/2 plus (X^3)/6 etc. As with the 3rd-order series, it may be

calculated with the equivalent formula (e^W)-1. This was the first type of

warp drive system developed, and it is still in use on later vessels as the

Impulse Drive system.

When Secondary Warp drive systems were developed, governed by the

2nd-order Cochrane function consisting of the sum of the infinite series

begining with X^2 + (X^3)/3 +(X^4)/12 etc., equivalent formula:

2*((e^W)-(W+1)), it was learned that they, and all higher order warp fields,

were dangerously unstable at low fractions of threshold power. This forced

the retention of some form of Primary warp drive, though it need not handle

enough power to go superluminal.

These first three orders of warp field phenomena correspond to the first

three "generations" of warp drive technology in the "Spaceflight Chronology".

Logically, a "Fourth generation" designation should have waited for the

developement of Quarternary warp, the sum of X^4 + (X^5)/5 + (X^6)/30 etc.,

equivalent formula 24*((e^W)-((W^3)/6 + (W^2)/12 + W + 1)), but the impact of

Dilithium on power generation, and thus overall performance, was so great

that the "Fourth generation" label took hold for the Constitution class. All

orders of warp field phenomena remain subject to the Warp 10 limit on

Delivered Power, but higher order warps produce greater velocity for the same

Delivered Power than lower orders.

The term "Fifth generation" is usually applied to the abortive attempt to

harness "Trans-Warp", a misbegotten application of the Interphase phenomena

first observed by the Enterprise NCC-1701 during the "Tholian Web" incident.

The abandonment of this dangerous system was made doubly disappointing by the

continued failure of Federation science to perfect a workable Quartenary warp

drive. The seemingly insurmountable difficulties encountered in the early

attempts at Quarternary drive design were the prime reason for the costly

"Trans-Warp" interlude.

However, in the intervening decades advanced theoretical studies have led

to vastly simpler, more reliable Tertiary drives which can be pushed far

closer to the Warp 10 limit of Delivered Power than the original design

multi-stage units. These single stage "integrated" units were first used in

ship's of the NCC-1701-C's class, and marked the arrival of warp technology's

"Sixth generation". A highly refined and advanced version of this type of

drive serves as the main propulsion for "Galaxy" class starships such as

Enterprise NCC-1701-D.

As the early efforts at Quarternary warp floundered on the complexities

of a four level multi-stage approach, the success of the single stage

"integrated" approach for Tertiary warp has scientists of ST:TNG's era once

more confident of eventual success, and aggressively paced research programs

are again under way in the race for the Quartenary drive.

Montgomery Scott correctly predicted the crippling deficientcies of the

Trans-Warp system, but was unable to dissuade StarFleet from investing in it.

Rightly convinced that Quartenary warp would have to await improvements in

warp theory permitting "integrated" designs, he attempted to convince

StarFleet to allow him to challenge the Warp 10 Barrier itself. The

mathematically inclined are invited to contemplate the significance of the

other half of the hyperbola, which most Federation scientists dismiss as a

mere geometric curiousity. Of course, scientists once thought that C itself

represented an impassable barrier. As Spock would say, "There are always

possibilities". Alas, Scott was never able to secure StarFleet backing for

his proposal, and only a handful of ST:TNG era technical persons who've

studied his original notes even know what he had in mind.

An interesting aspect of the 3rd-order Cochrane function is that Warp 1

is not C but 1.31xC. Taking the reciprocal of this number, 0.763, gives what

is known as threshold velocity. Under fractional warp power, a starship

"accelerates" as the power is steadily increased. At Warp .99999 etc., the

ship is traveling at 0.763xC. Transition occurs, an explosive event

accompanied by the hauntingly beautiful phenomena known as the Chromatic

Detonation, the optical analog of a sonic boom. In the next micro-instant,

the ship is on "the other side", traveling through the warp continuum at

1.31xC. The ship is never observed at speeds 0.763 < V < 1.31 under normal

conditions.

It should be noted however, that the boundary layer of the warp field

effect creates an envelope of 4 dimensional Einsteinian space-time within in

which the ship travels. Therefore, all the familiar physical laws of the

"ordinary" continuum still apply within the envelope. From the outside, it

appears as though a space-time anomaly were manifested sequentially along a

linear path. Fleeting, multiple images of the vessel in the center of the

anomaly are created at widely spaced intervals which grow more distant at

higher warp factors. Light coming from within the envelope gathers at the

boundary layer until it reaches optical crossover threshold, at which point

it "pulses" through, thus re-entering normal space-time to project the image

of the ship. This effect was nicely filmed for the climactic scene in

ST:TSFS when we see the Enterprise fleeing the detonation of the Genesis

Device.

External light enters the envelope via complex optical interaction with

the warp field boundary layer. The micro-instant lost for photons in front

of the ship's path to cross the boundary layer causes them to appear to

originate from directions shifted away from the line of motion in favor of

apparent origins perpendicular to the direction of travel. While an optical

blind spot exists directly behind the ship along the direction of motion, due

to the superluminal velocity involved, the tear-drop shape of the overall

warp field minimizes the area so blanked out to a vanishingly small region.

The overall effect is curiously symmetrical to that observed by vessels

approaching light speed in normal space-time. Such a vessel would see its

3-dimensional field of view collapsed into twin circles of light in front of

and behind the ship, with a band of darkness around its mid-section. A

vessel in the warp field traveling at superluminal velocities experiences a

tunnel-like effect in which the dark region consists of circles in front of

and behind the vessel, and its view of the universe is projected onto a

cylindrical tube which the ship appears to travel through.

Of course, the ship's computers correct for this effect to present an

intuitively "normal" view upon the bridge and other viewscreens. Windows

facing port or starboard reveal a relatively normal view without

sophisticated correction, others have internal holographic layers which serve

as the functional equivalents of corrective lenses to keep the view at least

intelligible, if not exactly accurate.

-Leon Myerson; 72157,3432; 3/18/88

December 30, 2017
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