Warp drive

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Warp drive is the principal method of faster-than-light propulsion in Star Trek.

Nature

A warp drive uses power from a matter-antimatter reactor system (often called the "warp core") to generate a subspace field around the vessel, allowing it to exceed the normal speed restrictions of general relativity. Any phenomenon which prevents the formation of this field will prevent a ship from using warp propulsion.

The subspace disturbances created by warp drives seem to be highly visible to subspace sensors, making ships travelling at warp speeds much easier to detect than ships cruising at sublight speeds.

Warp drives subject the fabric of space-time to unspecified stresses. Frequent use of warp drives in a particular volume of space can weaken the separation between subspace and normal space, causing "holes" in space-time through which a ship can become lost in subspace.

It will eventually be phased out when the first successful Quantum Slipstream Drive is made.

Speed

Warp drive appears to be capable of propelling a starship at several thousand times the speed of light.

Speed Examples

TNG, "Encounter at Farpoint"
At this time, top speed for the Enterprise-D is about warp 9.3. Warp 9.8 may be possible, but it may also destroy the ship.

TNG, "Where None Have Gone Before"
Maximum warp speed is about 9000c. (Data reports the distance as 2.7 million ly, and Geordi reports a 300+ year travel time.) As of the pilot, maximum warp is about 9.3.

TNG, "The Icarus Factor"
Riker claims that it would take months at high warp to get from the current location of the Enterprise to the Vega-Omicron sector. Assuming the upper limit on distance is 8000 ly (per Star Trek: First Contact) and the lower limit on travel time is two months, the upper limit on speed is 48,000c. Actual speed is probably far lower.

TNG, "Q Who"
Data reports they are 7000 ly from Federation space, and it would take them and 2 years and 7 mos of travel to get there. This indicates that the maximum sustainable speed of the Enterprise-D is about 2700c.

TNG, "Up the Long Ladder"
The trip from the Bringloid system to NB2323 is 0.5 light-years and takes more than 18 hours at warp 5. This means that warp 5 is less than 244c.

TNG, "Bloodlines"
It would take 20 minutes to travel 300 billion km at warp 9; this would put warp 9 at 833c. This estimate is an outlier, being quite low compared to other TNG speed examples.

TNG, "Clues"
0.54 parsecs is about a day's travel at cruising speed. This would indicate a cruising speed of 644c.

TNG, "The Most Toys"
Kivas Fajo's merchant ship, with a maximum speed of warp 3, could have traveled no more than 0.102 light-years in 23 hours. This is about 39c.

VOY, "The Caretaker"
According to Janeway, at "maximum warp", Voyager's 70,000+ ly trip back to the Federation would take 75 years. This is about 1,000c. "Maximum warp" may represent the best speed they could sustain over that distance with their limited resources.

VOY, "The 37's"
According to Tom Paris, warp 9.9 is 4 billion miles per second, which is 21,473c.

VOY, "Unimatrix Zero"
Voyager travels 2 light years in 2 hours when responding to a distress call. This is about 8,766c.

VOY, "Maneuvers"
Harry Kim gives a current speed of 2 billion kilometers per second, about 6,667c.

VOY, "Equinox"
Using an exotic fuel, the USS Equinox supposedly traveled 10,000 ly in about 2 weeks, for a speed of 260,893c. It should be noted, however, that there is no actual evidence that USS Equinox achieved such speeds other than a statement from Captain Ransom, a known liar and murderer.

VOY, "Friendship One"
A 132 light-year side-trip to investigate a planet would require two months round-trip at "maximum warp". This equates to a speed of about 1584c.

VOY, "Critical Care"
When Janeway asks how quickly Paris can get Voyager to an asteroid 3 ly away, Paris replies 2 hours. This is approximately 13,149c. The "How fast can you get us there?" question suggests top speed.

VOY, Mosaic (non-canon novel)
According to the novel, warp 4.2 is over 100c.

TOS, "That Which Survives"
Spock predicts that the Enterprise can travel 990.7 ly in 11.33 hours at warp 8.4, for a speed of 766,503c. This reference is a major outlier compared to most speed references in TNG and after.