Star Trek: Sub-Light Accelerations and travel times

[Lucky]

The purpose of this thread is to list non-warp travel times and accelerations, but i can only think of two examples.

SHELBY: Captain, the Borg have entered Sector zero zero one. 


(A little later, Riker and Worf enter) 


SHELBY: The Borg have dropped out of warp, sir. Jupiter outpost nine two reported visual contact at twelve hundred hours, thirteen minutes. 


RIKER: Planetary defences?


SHELBY: Responding. No reports on effectiveness but I can't believe that against the Borg 


RIKER: Ensign Crusher, at their current speed, when will they reach Earth? 


WESLEY: Twenty seven minutes. 


RIKER: The soonest we could intercept?


WESLEY: Forty two minutes, sir.


RIKER: Riker to Data.

The distance between jupiter and Earth is about 628734036 km to 928081020 km

One light Second = 299792.458 km

Borg Sub-light speed
Low End
628734036/27=23286445.7778
23286445.7778/60=388107.42963
388107.42963/299792.458=1.29458703604

High End
928081020/27=34373371.1111
34373371.1111/60=572889.518518
572889.518518/299792.458=1.91095373893

Low End: 1.29458703604c

High End: 1.91095373893c

LAFORGE: Plasma injectors are on-line. Everything's looking good. I think we're ready.


RIKER: They should be out there right now. We better break the warp barrier in the next five minutes if we're going to get their attention.


LAFORGE: Main cells are charged and ready.


RIKER: Let's do it.


COCHRANE: Engage.


LAFORGE: Warp field is looking good. Structural integrity is holding.


RIKER: Speed, twenty thousand kilometres per second.


COCHRANE: Sweet Jesus!


(Cochrane has spotted the Enterprise in orbit)


RIKER: Relax, Doctor. I'm sure they're just here to give us a send-off.

+++++

RIKER: Thirty seconds to warp threshold. ...Approaching light-speed.


COCHRANE: We're at critical velocity.

1 Light Second = 299792.458 km

1 Minute = 60 Seconds

Starting Velocity: 20,000 km per second

Ending Velocity: 299792.458 km per second

Time Spent Accelerating: A maximum of 5 minutes

The Phoenix's Average Rate of Acceleration
299792.458-20000=279792.458
279792.458/300=932.641526667

Average Rate of Acceleration: 932.641526667 kilometers per second

Note:
The heavily damaged Enterprise-E seems to have been able to easily keep up with or possibly out accelerate the Phoenix.

[359]

A while back I created a rather short list of seven derived impulse speeds. None of them use acceleration as the duration would be unknown.

From that thread, including a duplicate of "Best of Both Worlds", we get:

DS9: "Blaze of Glory": 248c to 8.27c

Star Trek: The Motion Picture: 0.3c to 0.5c

VOY: "Dragon's Teeth": 1.3c to 1.4c

VOY: "Timeless": 0.17c

TNG: "The Best of Both Worlds Part II": 2.9c

TNG: "Chain of Command Part II": 0.7c

VOY: "Fair Haven" <0.67c

DS9: "Blaze of Glory":

Sisko: "We both do. They're getting closer. One AU away. Point nine AU. You said you wanted to be blown to bits by the Jem'Hadar? Well, it looks like you're going to get your wish." (time: 00:22:16)
...
Sisko: "I don't think so. Point seven AU." (time: 00:23:34)
...
Sisko: "Half an AU and closing. If you do have a plan, I guarantee I'll learn to love it."
...
Sisko: "You mean shut down the engines? They'd be on us in a second."

1 AU ≈ 149,597,870,691 m

The Jem'Hadar ship is said to close from 0.5 AU in one second if the runabout stops, so 74,797,935,350 m/s or 249.5023 c for the speed of the warships.
149597870691/2 ≈ 74798935350 m

The warship was stated to be closing on the runabout at a rate of 0.2 AU every 78 seconds for a difference in speed of 383,584,283.8 m/s. So the speed of the runabout is the speed of the Jem'Hadar minus the closing speed, or 74,415,351,070 m/s or 248 c for the speed of the runabout.
(0.2*149597870691)/78 = 383584283.8 m/s

74798935350-383584283.8 ≈ 74415351070

Now "in a second" is a vague expression, so 248c is the maximum speed. The minimum would be more around 8.27c, if the time to intercept the stopped runabout were 1 minute which is not quite "in a second".


Star Trek: The Motion Picture:

Kirk: "Captain's log, stardate 7412.6. one point eight hours from launch. In order to intercept the intruder at the earliest possible time, we must now risk engaging warp drive while still within the solar system."

This is as we see them pass Jupiter. The distance to Jupiter from Earth varies between 588 million km and 968 million km.


VOY: "Dragon's Teeth":

Seven: "There's a planet eight million kilometres ahead, uninhabited but the atmosphere is charged with radiogenic particles."

Voyager was under attack at the time by one and later three ships, the minimum time is 20 seconds (real screen time), given the rate they were stated to be loosing shields the transit time should not be more than one minute.


VOY: "Timeless":

Paris: "I'm reading a planet nine million kilometres ahead. It's class L."
...
EMH: "I have it. Her cybernetic systems were terminated on Stardate 52164.3. Borg time index: 9.43852. You're encoding the transmitter for time index 9.40? That's less than four minutes before Voyager was destroyed! Cutting it a little close, aren't we?"

Seven receives transmission:00:34:22
Voyager seen to arrive at planet: 00:34:54
Voyager impacts surface and bounces off (presumably time of death): 00:36:10

We know that seven recieved the transmission 4 minutes before the point of impact, and they arrive at the planet at least 88 seconds before impact (the descent may not be real-time). So the travel time is 172 seconds.
35:50-34:22 = 1:28
4:00-1:28 = 2:22
1:28 = 88 seconds
2:22 = 172 seconds

We also know the travel distance is 9 billion meters, so the speed is 52,325,581 m/s or 0.1745c.
9000000000/172 ≈ 52325581


TNG: "The Best of Both Worlds Part II":

Riker: Slow to impulse. Time to intercept?
Wesley: Twenty-three minutes, fourteen seconds, sir.

When Wesley says this they have just passed Saturn, the Enterprise reaches the Borg cube over earth.

The minimum distance from Saturn to Earth is 8 au or 1,196,782,966,000 m, this gives a speed of 858,524,365 m/s or 2.8637c
1196782966000/1394 = 858524365


TNG: "Chain of Command Part II":

Jellico: "Then you must've done Titan's Turn."
LaForge: "Oh, yeah. You set a course directly for Titan, hold it until you're just brushing the atmosphere, throw the helm hard over and whip around the moon at point seven c."
Jellico: And pray like hell nobody saw you."

The gravitational effect of a moon or even a planet are not enough to noticeably effect you speed on the scale of 0.7c, so the shuttle must have reached that speed under its own power.


VOY: "Fair Haven":

Seven: "I believe it was formed by the collision of two neutron stars. The wavefront is travelling at a velocity of two hundred thousand kilometres per second, and it extends for three point six light years."
...
Torres: "We're already feeling its effects. The neutron radiation is disrupting plasma flow. We can't jump to warp."
Paris: "Impulse power won't be enough to outrun that thing."

This implies that it is on the order of what impulse can do, but it is definitely to fast for impulse.

[Lucky]

COMPUTER: Warp core breach in thirty seconds. 


TORRES: Where are we going? 


PARIS: A J Class nebula filled with ionised gas. Should contain the explosion. 


TORRES: I can't get the ejection subroutines online. 


COMPUTER: Warp core breach in twenty seconds. 


PARIS: So, what's your answer? 


TORRES: My answer? 


PARIS: Will you marry me? 


COMPUTER: Warp core breach in fifteen seconds. 


TORRES: You're proposing now? 


PARIS: It's as good a time as any. 


TORRES: Subroutines back online.


COMPUTER: Warp core breach in ten seconds, nine, eight. 


TORRES: Clear!


COMPUTER: Four. 


TORRES: Go!


COMPUTER: Three.


[Mess hall]


(Assan zips through the finish line) 


JANEWAY: Damn. 


O'ZAAL: I'm sorry your team didn't win, Captain. 


JANEWAY: Janeway to the Bridge. Report. 


TUVOK: That was a shock wave from an antimatter explosion approximately one point two million kilometres from here. 


JANEWAY: Excuse me.


[Delta Flyer]


PARIS: B’Elanna. 


TORRES: Guess we lost. 


PARIS: That depends. 


TORRES: On what?


PARIS: On how you answer my question. 


TORRES: I thought you only asked it because you thought we were about to explode. 


PARIS: Well, we’re still alive and I’m still asking. 


TORRES: How come you never asked me before? 


PARIS: How come you’re still avoiding the question? 


TORRES: I’m thinking. 


PARIS: Think faster.


TORRES: Why? You going to withdraw the question? 


PARIS: No, but I might start to beg. Could get embarrassing.

One light Second = 299792.458 km

Low End
1.2 million= 1200000
1200000/3=400000
400000/299792.458= 1.33425638079

High End
1.2 million= 1200000
1200000/2=600000
600000/299792.458=2.00138457119

Low End: 1.33425638079c

High End: 2.00138457119c

[359]

"Abqneth-bifaebus!"
A thread returns from the dead...


I was watching TNG: "Booby Trap" when I noticed this useful exchange near the end of the episode:

LaForge: "Everything we've tried to do has been based on overpowering the trap. More energy, faster adjustments. But that's exactly what we can't do because that's what we're supposed to do. That's the booby trap. The answer lies in our own computer, the mind. The best piece of engineering we'll ever need."
Picard: "But didn't your researches indicate a thousand adjustments per second would be required?"
LaForge: "Not if we shut everything off. One blast of everything we've got left for a microsecond to beat the inertia and then we shut it all down, except minimal life support and two thrusters. No impulse engines. No computer."

...

Picard: "Thank you, Number One. Firing impulse engines."
Data: "Impulse engines are down."
LaForge: "Shutting down all systems."
Data: "Velocity is one hundred thirty five meters per second."
Worf: "We will be entering the debris field in eight seconds."

So if we take what LaForge said literally we have the ship accelerating to 135 m/s, at maximum output, in 1*10^-6 seconds, or 135,000,000 m/s^2 (13.8 million g's and c in 2.2 seconds). And at the other end of the spectrum of assuming equivalent thrust across the 0.8 second visible flare from the impulse engines gives an absolute minimum of 168.8 m/s^2 (17.2 g's).

Now what is more likely is that the impulse engines were powering on, giving off a short burst, and then powering back down. If that were the case and we are looking at say... a millisecond thrust duration (not as insanely quick as LaForge's statement, but along similar lines), then the acceleration would be 13,800 g's.

So here we have an example clearly showing an impulse engine output on the order of ten thousand if not ten million g's for basic linear acceleration. Additionally there is no chance of a subspace field assist to acceleration as one of the effects of the booby trap was to prevent the formation of subspace fields.

LaForge: "So it kept us from forming a subspace field for the warp drive?"
Computer: "That is correct."

[2046]

I think this is one of the most important threads on the forum. It just hasn't gotten the attention it deserves, including from me. I'll work on that ASAP.

[359]

This one's had it coming for a long time. In TNG: "Peak Performance" we see the Enterprise engage in what is known as the Kumeh Maneuver. In which the ship zips around from behind a planet and slows to draw out its opponent, in this case the Hathaway.

The Enterprise part-way through its maneuver, it started off screen behind the planet and slows in front of the planet some 3 seconds later. Apparently this is a well known tactic as discussed by Riker and LaForge:

LaForge: "Kumeh manoeuvre? Why would they start out with such a recognisable ploy?"
Riker: "He's teasing. He wants us to reveal our tactics on his terms. Mister Worf?"

Looking at the event frame-by-frame the Enterprise appears to cover an orbit of 1/3 of the planet at an altitude about 1/5 the planetary diameter. If we assume a planet slightly smaller than Earth with a diameter of 10,000 km, then the Enterprise would have covered a distance of about 14,600 km in around 3 seconds before slowing. This is an average speed of around 4,890 km/s. Now after that the ship slows greatly as it approaches the Hathaway. This happens in about half a seconds, so the approximate acceleration involved is slightly less than 9,770 km/s^2 or 997,000 g's.

Now this is a rather high value, and it is possible that there was a greater time of acceleration, so let's assume the case of least possible acceleration. Say the Enterprise was already at full speed and had the whole 3.5 seconds to slow down (again ignoring the acceleration involved in making the orbital turn). In this case their velocity would be represented by the formula -at+3.5a so that they start at some velocity and end at zero 3.5 seconds later assuming some constant acceleration a. They must still cover some 14,600 km, so the integral from 0 to 3.5 of (-at+3.5a) dt = 14600, so the acceleration a = 2,400 km/s^2. So the absolute minimum acceleration in this event is 245,000 g's.

This is still a rather high end acceleration, but is the minimum possible to achieve close to what is seen to occur on screen.

[Mike DiCenso]

Don't just look at impulse power accelerations. There are also many instances of the ships moving around on thrusters as well. For example there is the refit Constitution-class Enterprise in Star Trek: The Motion Picture when it is leaving the drydock and later using thrusters only to maneuver inside V'Ger. Although no specific numbers are given by anyone as to what velocity the ship is supposed to achieve, ST:TMP's visual FX shows it well enough that we might be able to get reasonable figures from it:


* First the visuals for drydock

* Next the dialog:

UHURA: Dock control reports ready, sir.

SULU: Helm ready, sir.

ILIA: Orbital departure on plot, sir.

UHURA: Yard command signalling clear, sir.

KIRK: Maneuvering thrusters, Mister Sulu.

SULU: Maneuvering thrusters, sir.

KIRK: Hold station.

SULU: Thrusters at station keeping.

KIRK: Thrusters ahead, Mister Sulu. ...Take us out.

* Finally working out the numbers: The thrusters being on station keeping is not important for the purposes of this calculation except that it establishes that the ship is using only thrusters and is being held at zero relative acceleration to the drydock. When Kirk finally orders "Thrusters ahead in the video at 1:04 the scene cuts immediately to the ship which starts obvious motion at 1:07 and clears the approximately 320 meter drydock at 1:49, or 42 seconds. Thus the average acceleration is 7.61 meters/sec. Some confounding variables are whether the ship is firing the thrusters continually to accelerate or are in start-stop firing mode. I'm assuming continual thruster output the whole scene, and the ship was continually accelerating so that by the time of a brief interval showing the interior and a cut back to the exterior at 2:08 the drydock and attendant facilities are no longer in view behind the ship. But with the jump cut scenes we don't know if a few seconds passed as on screen or if an hour or more went by. Though it cannot be more than an hour as Kirk notes in his log entry later that 1.8 hours had passed since launch, and time was of the essence here.
-Mike

[Lucky]

RIKER: Fleming on long range sensors, approximately zero point three light years away.

><><><><

PICARD: Mister Data, what's your analysis? 

DATA: The event is approximately zero point one light years in diameter, and it is emitting extremely high levels of tetryon radiation. It appears to be what Rabal and Serova predicted, a subspace rift. 

LAFORGE: She was right. 

PICARD: Can you get a fix on the Fleming? Is she still in one piece? 

DATA: Scanning. The Fleming is near its previous coordinates. It appears to be intact, but it is now within the rift.

><><><><

PICARD: What about the Fleming? How long can they survive in there? 

DATA: The waves are even more intense within the rift. I estimate her shields will fail in approximately twelve hours. 

RIKER: Can we risk going in there to get them out? 

LAFORGE: Not at warp, Commander. According to these readings, the rift is in a state of accelerating instability which would make it extremely sensitive to warp field energy. If we go in at warp, we might make it expand even further. 

RIKER: I don't think we have a choice. It would take weeks to reach them at impulse.

.3c distance in week

1 light second = 299792.458

.3 lightyears = 2,838,200,000,000 km

1 week = 7 days

1 day = roughly 24 hours

1 hour = 60 minutes

1 minute = 60 seconds

1 week = 604,800 seconds

2,838,200,000,000/604,800=4692791.01 km per second

4692791.01/299792.458=15.6584659

Impulse equals = 15.6584659c
(Possible Time Dilation not calculated)
(Given this is a rescue mission, I'm not sure why time dilation would be calculated)

[Lucky]

LAFORGE: Plasma injectors are on-line. Everything's looking good. I think we're ready.

RIKER: They should be out there right now. We better break the warp barrier in the next five minutes if we're going to get their attention.

LAFORGE: Main cells are charged and ready.

RIKER: Let's do it.

COCHRANE: Engage.

LAFORGE: Warp field is looking good. Structural integrity is holding.

RIKER: Speed, twenty thousand kilometres per second.

COCHRANE: Sweet Jesus!

(Cochrane has spotted the Enterprise in orbit)

RIKER: Relax, Doctor. I'm sure they're just here to give us a send-off.

><><><><><

RIKER: Thirty seconds to warp threshold. ...Approaching light-speed.
COCHRANE: We're at critical velocity.

Starting Velocity = 20,000 km per second

Ending Velocity = 299792.458

Time For Acceleration = 5 minutes

Average Acceleration = 932.6415 km per second