曲速航行的速率通常以曲速層級(warp factor)代之。一般認為曲速1級是真空光速(c);更高的層級下,速率呈指數增加。原始影集的數個劇集曾設定了企業號冒著危險以高曲速層級航行,一度高到曲速14.6級("That Which Survives")。然而,任一曲速層級的實際速度從未在螢幕上顯明地被陳述,以作為經典紀錄。更甚者,各影集中航行時間與星際距離在陳述上,從未嚴格地保持一貫性(甚至是相當鬆散的)。
在了解這是個問題,也想 wanting to remove this plot element, 《下一代》的創造者決定曲速10級應作為最大值。後台的星際奇旅術語建議將曲速尺標重新調整,將舊曲速6級變為新曲速5級,而曲速10級為無限大速度而無法達到。製作人指示船隻可以任意接近曲速10級,但就是無法到達剛好曲速10級。如此則貴族與旅人等生命體則能以相當快的速度航行,又可以迴避限制。舉例而言,據估計,旅人將企業號推進到曲速9.999996級的速度。而第四代影集《航海家號》中的劇集"Threshold"附議了這項設定,其中角色提到曲速10級的速度是不可能達到的,因為那是無限大的速度——但不管如何,隨後他們卻達到了,伴隨了快速地(反向)演化成兩棲類的蠑螈的副作用。(雖然許多影迷、製作人員,甚至是該集的編劇與製作人Brannon Braga普遍忽略該集的事件。)
然而這樣設定仍然無法完整解釋整個影集所出現的場合,因為如此企業號航行速度變得過慢,和電視影集中所提的有時相牴觸,例如That Which Survives這集中,企業號以曲速8.4級航行了11.33小時,而橫越了990.7光年(此段文句為史巴克的台詞)。這樣計算出來的速率超過600,000倍光速;即使是曲速15級,這樣也還超過兩個數量級。
There is also the fact that the Enterprise could quite easily travel to and from the edge of the galaxy at will (Is There in Truth No Beauty and By Any Other Name), a journey which should take years at the typical warp 8, if warp 8 is merely a cube of the warp factor.
This discrepancy between the behavior of warp speeds in the show and the simple formula of the warp factor cubed was picked up by fans in the 1970's and 80's who published books like Star Trek Maps (all published material is considered non-canon, even if it is by Paramount-approved Pocket Books) where the idea of an additional factor, referred to as the Chi factor or the Cochrane factor, was used in the warp calculations. The idea was that since warp drive pulls in space, you get higher speeds in areas where there is high density of mass, and lower speeds in areas of low density. If we take a warp factor and cube it, we take that product and multiply it by the number 1292.7238 (the Chi or Cochrane factor), to get the actual speed that the ship travels at (this is the number that was factored out of the factoids from That Which Survives). The Cochrane factor represents an "average" density of space in the UFP. Other areas of space will have different values for it. This is one way to explain the relationship between stated warp factors and actual calculable speeds as given in the dialogue in the episodes. Although it is not actually canon, it at least explains how the ships behaved as they did, without having to find higher exponents to factor the warp base numbers by, as 星際奇旅藝術指導麥可·奧田(Michael Okuda)did later for TNG (which nobody on the show ended up paying attention to anyway).
新式曲速層級對應的速度表與消耗功率。白色是新式速度;鉻黃色是消耗功率;圖中另標有舊式曲速層級對應的速度表,以藍綠色呈現。在後起的幾部影集,奧田以舊制為基礎設定了一項公式,但做出了幾個重要的改變。For warp 1–9, 若w是曲速層級,s是以公里每秒計量的速率,而c表示光速,則無法解析 (Missing texvc executable; please see math/README to configure.): s(w) = w^{10 \over 3}c . 在曲速9級到曲速10級間的半開放區間,w的指數項快速地增加到無限大。如此,在奧田式尺度中,曲速以漸進線方式趨向曲速10級。這段區間並沒有精確公式,因為在這一段所摘錄到的速率是根據手繪曲線。然而在1995年,寇克瑞恩曲速力學進展獎(Cochrane Award for Advancements in Warp Mechanics)頒給了一位勝出者,其所提的曲速公式為[1]:
Here is a table of the times it would take to cover a number of distances. Since warp 1 is c, the distances for warp 1 (in years) is the light year distance. Earth's solar system is approximately 1.2x1010 km wide, measured as the diameter of the Oort Cloud.
In general, the farther away a Star Trek show is in production date from the publish date of the Star Trek Technical Manual, the more likely a ship would be to travel at the "speed of plot". For example, in the Star Trek: Enterprise pilot episode they give a time and speed to Neptune that accords with the original series' formula, but then they estimate a trip to the Klingon Homeworld at warp 5 as a four-day journey, placing it just one light-year away from Earth—far closer than the nearest stellar system, Alpha Centauri. This plot hole has later been wrapped up by various sources that suggest that there is a spatial rift that allowed the Enterprise to arrive at the Klingon homeworld in such a short length of time, and that it was the Vulcans who provided Enterprise with the whereabouts of this shortcut. It should be noted, however that such a high speed for warp 5 is consistent with the extremely high speed given for warp 8.4 in That Which Survives, which has the speed at over 600,000 times lightspeed (therefore warp 5 would be 161,500 times lightspeed). In those terms, four days travel at warp 5 places the Klingon homeworld at 1,772 light years (or 536 parsecs) away from Earth.
理論與科技
要對曲速推進系統有更深入的討論,通常會參考由里克·史騰巴赫(Rick Sternbach)和麥可·奧田(Michael Okuda)所著的《下一代技術手冊》(Star Trek: The Next Generation Technical Manual)第五章「曲速推進系統」,其中提到幾項主題:
在星際奇旅全部系列中,曲速航行的一項副作用是彈射效應(Slingshot effect)。在星際爭霸戰最初幾個劇集中的"Tomorrow is Yesterday"這集內容中,企業號發生意外而首次發現這項效應,成了利用曲速引擎做時光旅行的方法。雖然實際程式的設定故意保留模糊化,但大體上它涉及了以高曲速向恆星航行(設定於第四部電影《搶救未來》,大概速度超過曲速9.8級),軌跡設定在精確計算的彈射路徑。若成功,則旅行至過去或未來都是被允許的。相同的技術隨後於劇集Assignment Earth中被故意使用,目的是進行歷史研究;其中此技術被命名為「光速脫離級數」(light speed breakaway factor)。而在電影《搶救未來》中又被用上;其中此技術被稱為「時間翹曲」(time warp)。這項技術在《下一代》劇集"Time Squared"中被提及是一種可行的時間旅行方法。
環境影響
在《下一代》第七季劇集"Force of Nature"中,曲速航行對子空間有不利影響,且在一些區域,頻繁使用航線的路徑上可能會造成子空間裂縫。因此在此之後的劇集,超過曲速5級的航行被禁止,然而在影迷社群中有過爭論,討論到這項禁令是只針對受影響區域而設,或者是全區的禁令。如果這是全區的限制,那在之後的劇集與系列影集則被廣泛地忽略,也鮮少提及。然而,曾有這么一例,在《下一代》一集中,皮卡德艦長下令以高於曲速5級的速度航行,而有人提醒他這項禁令。一些影迷臆測已有技術解決方案被發現,並可能用到了聯邦星艦航海家號的曲速引擎上頭。這點由星際奇旅官方網站的圖文庫所證實,其中解釋了航海家號設計上可以高於曲速5級的速度航行而不會造成子空間破壞,比如空間裂縫。元首級星艦企業號-E也配有進階曲速動力引擎,允許相當高的曲速航行而不破壞空間結構。
思想實驗還在理論物理荒蕪的前沿漫步前進,時至今日仍未有允許曲速航行且被主流科學接受的體系被拓展出來。一些物理學家提出一種超光速航行的模型,以洛侖茲流形的架構來陳述;這種架構在廣義相對論中被用以建立時空模型。然而,相反於平常的誤解,這些模型並非愛因斯坦場方程式的解。它們也沒有給出如何實做曲速泡(warp bubble)的提示。These models do however show that while it is indeed impossible to go faster than the speed of light, in principle it might be possible to circumvent the problem by suitably "warping" spacetime itself. 其中最廣為人知的是阿庫別瑞引擎,具有有趣的特質——其用詞上與星艦系列術語一致:「曲速層級」是空間(或者說時空更為恰當)翹曲的量度,而不是實際速度。