Screencaps below come from a 25fps vidcap of the scene.
The Millennium Falcon is commonly referred to in the canon as the fastest ship of Star Wars, both in hyperspace and at sublight velocities. In The Empire Strikes Back, we are treated to a demonstration of her abilities. The incident occurs during the chase of the Falcon by the Star Destroyer Avenger under Captain Needa. As portrayed in the novelisation, the chase began immediately after the Falcon left the large asteroid occupied by the space slug.
"From that moment, the Imperial ship renewed its pursuit of the freighter with a blinding barrage of fire. Undaunted by the steady rain of asteroids on its massive hull, the Star Destroyer relentlessly followed the smaller ship.
The Millennium Falcon, far more maneuverable than the other ship, darted around the larger asteroids as they came rocketing toward it. The Falcon was succeeding in holding its lead in front of the Avenger, but it was clear that the steadily pursuing ship was not about to abandon the chase." (ch. 10)
The Falcon's course toward the edge of the asteroid field was thus slowed by her evasive maneuvers, allowing the Avenger to maintain pursuit and evidently gain on her. Once the chase is joined in the film, the Falcon is a mere few hundred meters ahead of the Avenger.
Han is not concerned, though, until he discovers once at the edge of the asteroid field that the Falcon's hyperdrive is still non-functional. In even worse trouble than before, the Falcon angles her nose downward while Han begins to concoct a plan. Besides giving us an excellent view of the relative speed between the two vessels, we can also estimate the Falcon's speed for later use.
Assuming that the observation point (i.e. the camera) is stationary, the Falcon's velocity is roughly her own length per six frames. With a Falcon length of approximately 35 meters and a vidcap speed of 25 frames per second, that works out to 35 meters per 0.24 seconds, or 145.83 m/s. (Note: Some disagree in principle with the notion that you can accurately estimate the speed of a vehicle moving in a reasonably-straight line using the method above, believing instead that you need a side- or top-view. However, that concept makes little sense, especially when you have a stationary observation point or a stationary object near the one whose velocity is being measured. For a real-world analog, consider judging a car's speed by seeing how long it takes for the car to pass a point or line on the road.)
With the failure of the rear deflector shield due to fire from the Avenger, Han's plan coalesces. He orders all power to the forward shields and brings the Falcon around in a 3-4 second turn, possibly after having accelerated.
If we assume a stationary observation point (i.e. camera) for the blended panorama above, the turn ends up being a very odd one, over and above the standard "spaceship turning as if an airplane" oddity. For the first ninety degrees or so, the turn is rather leisurely. Then, the ship slows to a crawl and cuts hard over for the last ninety degrees, before accelerating so hard that plasma sprays from her tail (which, for ease of reference, will be referred to as the "afterburner"). Given that Han's entire purpose at this point is to head toward the Avenger at high speed, it seems as if it would make more sense if he'd made the entire turn in the leisurely-but-fast fashion. This is almost sufficient cause to dispense with the assumption of a stationary observation point in this scene. But, note the width of the turn, which is roughly 15.45 Falcon-lengths (or about 540 meters). (Naturally, without knowing the exact position(s) of the camera, we can't correct for range-change, but 540 is a fairly decent estimation.) That is just about right for getting the ship into position relative to the Star Destroyer's bow, from her location toward the ISD's starboard side in the frame above, to the far port in the coming scene. There may indeed be a leftward drift of the observation point, then, as the scene progresses (in addition to the camera's panning to the left) . . . but it shouldn't be too terribly much.
So, it would seem that she decelerated for some odd reason before rapidly accelerating again. With the possibility of a mobile observation point, the following analysis of the turn can only be considered a rough estimate . . . an analysis of possibilities regarding her manueverings in the turning shot. But, perhaps it will still be useful. Also note that this analysis is rough due to the fact that it does not fully involve the forces related to the curvature of her course.
1. In the marked image of the shot above, note the Falcon that I used for measurement (because it appeared to be the most "dead-on" shot from the top). Measuring from her tail in the first frame to her tail in the measured frame, we have a 90 degree turn which occurs in a lateral width of approximately 375 meters. If that is taken as turn radius along a circular course, then the total distance travelled in those fifty frames would be žpiD, or 589 meters. However, that length estimation should actually be considered an overestimate. Note the fact that the Falcon's turn is harder at the beginning 30 frames, then flattens out significantly in the middle. A conservative (i.e. higher-end) eyeball estimate between the 375 and 589 figures would be about 500 meters travelled, for an average speed in the turn of 250 meters/second.
Were we to assume a stationary observation point, the apparent speed of the measured Falcon at the end of that turn is 218.75 meters/second, since (as per the pic below) she traverses her own length in four frames. The right-hand Falcon is the measured one from the linked image above.
Assuming constant deceleration, that would suggest a speed going into the turn of about 281.25 meters/second, with a deceleration rate of 31.25 m/sē. (Note that if the deceleration were not constant, the speed going into the turn at the start of the sequence would have to be lower, so as to maintain the known average speed in the turn.)
Unfortunately, looking at the second half of the turn is more problematic than looking at the first half. The problem with the total turn is that we can only really measure the midpoint speed. Thus, we had to work out the initial velocity going into the turn. Now, for the second half of the turn, we would have to work out the exit velocity of the turn prior to the application of full forward "afterburner" thrust, which is a much more difficult affair given the angles and curvatures involved. (Since the course is curved, we cannot simply pick an arbitrary point for the Falcon to cross.) Simply watching the film makes it pretty clear that the final velocity is non-zero, but "non-zero" is rather inexact. Also note that the afterburner thrust is engaged just before the Falcon points directly at the observation point, which means that the last moments of her 180-degree turn were at full thrust.
That having been said, I'm of the opinion that we can still get a useful value. The last leg of the turn appears to have a solid circular trajectory, unlike the first half. We may therefore use the estimation method previously employed without worrying about the flattened trajectory. And, since we have the initial velocity of 218.75 m/s, we have something useful to start with.
2. As before, we can estimate the lateral width of the turn and use it as a turn radius. Measuring from her tail in the measured frame to her tail in the frame just before the afterburner is lit (a difference of 30 frames (see below)), we get an approximate lateral width of 145.9 meters.
Note, however, that the Falcon has not achieved a full 90 degree turn. Thus, we cannot use the žpiD method to get actual distance travelled, since ž is not correct . . . it would be an overestimate. Eyeballing it, I'd say the Falcon has turned approximately 75-80 degrees. Splitting the difference, that's 77.5/360piD, or 197.4 meters. (Had she completed the turn at this point, the total distance would be 229.2 meters.)
That's 197.4 meters over the course of thirty frames, for an average speed of 164.5 meters/second. Given an initial speed of 218.75 meters/second, this suggests a final speed on the order of 110.25 meters/second. That works out to the far more impressive constant deceleration of 90.4 m/sē.
It should be noted here that had Han simply swung the nose around in a genuine sort of space turn and then activated his engines, the total velocity change from about 281.25 meters/second forward to about 110.25 meters/second backward, achieved over the course of about 80 frames (3.2 seconds), would require an acceleration of about 122 m/sē.
At this point, the Falcon begins her hard acceleration toward the Avenger, leaping toward the pursuing Star Destroyer while flinging bright blue-white plasma from her engines. Now, in spite of the estimated final speed figure of 110.25 meters/second seen above, I am going to estimate her speed at the beginning of the afterburner process as zero, and count as the beginning of her run the frame (seen as the last frame in the marked image of the turn) at which her nose appears to face the observation point roughly dead-on. This, plus the notion that the afterburning involves maximum acceleration, should give us a top-end value for the Millennium Falcon's straight-line acceleration in open space.
Twenty-seven frames after my designated starting point, the Falcon begins passing the observation point, over the course of approximately just under six frames . . . we'll call it five. Thus, we have a speed of 175 m/s.
Since the afterburning has ceased, let's not use 27 frames for the total tally. Instead, we will count only those frames which involve the plasma spraying from her tail, counted from the designated starting frame. We will thus give her a speed of 175 m/s, obtained over the course of 21 frames. From zero, that works out to an acceleration of 208.3 m/sē.
Assuming that the afterburner effect is intended to suggest maximum acceleration (which would seem to be the case, or else we'd expect to hear Han say something to the effect of "uh-oh, something else is broken, time for Plan C"), the Falcon's maximum straight-line acceleration would seem to be a maximum of 208.3 m/sē, or 21.24g.
(Of course, in reality, the figure should be less. If we were to start from the speed of 110.25 m/s used earlier, the acceleration value would only be 77.1 m/sē. It's also worth noting that this figure is somewhat superior, since it would involve the Falcon traversing 119 meters from start point to camera passing . . . the other figure only allows the Falcon to traverse 73, which appears to be rather short. (On the other hand, the deceleration figure of 90.4 m/sē obtained above would make a maximum of 77.1 somewhat nonsensical.) In any event, I will avoid the use of photographic analysis to determine her distance at the start of the afterburner use, so as to maintain the highest-end 208.3 m/sē figure.)
Captain Needa states with surprise that the Falcon is moving into attack position. The scene cuts to an external view, in which we get to see the Falcon's location relative to the Avenger as she flies along the hull and begins her upward climb toward the bridge. The angles and whatnot do not allow us to glean much more speed information at this point, though we do get a clear impression of the Falcon's course in this and the next external shot, after Needa orders shields raised.
One thing these scenes do offer, though, is timing information. From the moment the Falcon becomes visible in the flight along the hull until the last frame that she's visible in the bridge flyby is 183 frames (7.32 seconds), and with the exception of the 2.32-second bridge scene with Needa ordering shields, the Falcon is almost always visible.
We may therefore say with certainty that the Falcon's course was a simple one, up and over the Star Destroyer's side trench and right up toward the bridge on a fairly straight course, illustrated below:
As you can see, this course would not require the Falcon to traverse more than a maximum of about two kilometers, assuming a 1,600-meter-long Star Destroyer. That gives us a rough average speed of 273 meters/second relative to the Avenger. The "relative to the Avenger" is important, though, since that calculation involves treating the Avenger as stationary. This actually is not the case, though, given that the radio drama version of events (told entirely from within the Falcon) includes C-3PO mentioning that the Avenger had cut her speed, which presumably occurred after the Falcon started her turn. We therefore cannot say with certainty who was going how fast at which moment in the flight along the hull and the climb, though it makes sense to presume that the Falcon was still doing at least 175 meters/second. However, the Avenger's speed (and the amount cut) is simply unknown.
We do know, however, what the relative speed of the ships was at the end of the climb, because we get an exquisite view of the Falcon flying over the bridge.
As you can see, it took the Falcon several frames in the above to traverse her own length. How many exactly? Well, I've taken the liberty of placing two marks on a few of the frames. A red dot appears at the highest point of the Falcon in the first frame, on her starboard mandible. A yellow dot appears in the frame after that, at the approximate centerline between the forwardmost parts of her mandibles, and at their highest point. Observe:
Note that the Falcon takes approximately six frames to make up her own length, which at 25 frames per second equates to a Falcon speed of 145.83 meters/second (or 326.2 mph).
Four seconds after the bridge flyover, a bridge officer reports to Captain Needa that the Falcon no longer appears on the scopes, and the audience is not shown what happened until several scenes later. Fortunately, the lesser canon radio drama tells us what happened, from the Falcon's perspective.
(Click one of the icons for the minute-long clip. I've taken the liberty of converting Wayne Poe's 2.52-megabyte .wav file for ease of download. The smaller version does have lesser quality, however.)
Somewhere between 30-32 seconds into the clip, the Falcon presumably flies over the bridge as seen in the film. (A ~0.3 second "whoosh" sound is heard beginning circa 0:32.2, 1.5-2 seconds after the weapons fire stops.) At 0:34.3, Han begins enunciating the K sound of ordering Chewie to "kill the engines", finishing the S at 0:34.9. We hear something that sounds like a powering-down begin to occur circa 0:35.2, and Han orders everything shut down circa 0:36.4. At 0:40.4, Han reports that the landing claw with which they are attached to the Avenger is secure.
We therefore have a minimum of 2.1 and a maximum of 10.4 seconds for the Falcon to achieve deceleration to zero relative to the Avenger, and final lock-on with the claws. In any case, deceleration to near-zero almost certainly occurs within 2.1 - 4.9 seconds.
Assuming the minimum 2.1 second deceleration from a presumed final speed of 145.83m/s (ignoring, for the moment, whether or not the Falcon was continuing to decelerate as she flew over the bridge), this would require a constant deceleration of 68.5 meters/secondē, or just under 7g, occurring over a distance of 151 meters. If the deceleration took 4.9 seconds this figure would reduce to 29.4 m/sē, or just under 3g, occurring over the course of 352 meters.
In one way, the above estimate is more solid than
the 90.4 m/sē deceleration estimate from the second half of the turning-around
scene, due to there being no issues relating to camera movement, uncertainty
regarding the Falcon's course, and so on. On the other hand, we don't know
exactly how long the Falcon took to decelerate, and thus we would be left with a
top-end figure of 68.5 m/sē. However, I believe it would be rather
difficult to make the smaller figure work well in the second half of the
turning-around scene, since it would require a much longer distance and a higher
ending speed than the circular course estimate gave.
The fastest ship in Star Wars has, at sublight speeds, a maximum upper limit value for straight-line acceleration of about 210 m/sē, or about 21.5g. She can reverse her engines for a rearward acceleration of about 90 m/sē, or about 9.2g.
Pretty impressive for a ship described in chapter ten of the TESB novelisation as having ion engines.
However, compared to Star Trek vessels, this is quite poor acceleration indeed. Compare this to, for instance, the refit Enterprise in ST:TMP, which went from Earth to Jupiter in 1.8 hours. The distance from Earth to Jupiter is quite variable over their respective orbits, but I decided to try narrowing it down a bit. According to the excellent space simulation program Celestia, the example date of July 4, 2271 gives us a distance of 4.773 AU from Earth to Jupiter, or over 714,000,000 kilometers (about .66 light-hours). That's an average speed of 110,191,481.5m/s. Assuming a constant acceleration over those 1.8 hours (and thus the lowest possible acceleration value), the ship would have had to reach a final speed of 220,382,963 m/s (0.73512c), assuming a start from zero. That would be, then, a constant acceleration of just over 34,000 m/sē, or over 3,460g. That is 161 times the Falcon's demonstrated plasma-flinging "afterburn" acceleration.
Objections and Rebuttals