Star Destroyer Fast Deceleration in TESB

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Star Destroyer Fast Deceleration in TESB

Post by 2046 » Mon Feb 12, 2007 7:24 am

Hot damn.

This page on the Falcon's acceleration abilities points to the Falcon having acceleration measured in the tens of g.

However, I think I've found something that totally breaks that wide open.

This new part of the weapon range page shows that the two-second shot of the ISDs "comin' right at us" shows that they close by about 60 kilometers in those two seconds, for an average velocity of 30km/sec . . . which sure seems hella-fast for them, but whatever. It was weird enough for me to point out on the page when I was making it.

I was then working on my Imperial power generation page, wherein at one point I needed an estimate of Star Destroyer acceleration ability in open space. My other example was totally ballparked, so I decided to see what I got by taking the 30km/sec, counting how many seconds it took for the pair of ISDs and the Falcon/Avenger pair to get close for the dive scene, and then see how fast the pairs were going relative to each other. This would, theoretically, give me a deceleration rate for the ISDs.

After the out-the-window shot from the Falcon cuts to an interior view, it's about ten seconds until the scene when the two Star Destroyers are visible as the Falcon dives away, with Avenger right behind. The vessels at that point are moving at a relative velocity of perhaps a hundred meters per second, or effectively zero compared to the earlier relative velocity of both pairs.

There is no way to know how much forward velocity any of the parties shed on their way to close encounter (and, in the case of at least two of the ISDs, a minor collision). At maximum, one or the other pair of ships dropped from 30km/sec to near-zero. Alternately, both were at about 15km/sec and came to nearly a relative stop. This range would imply an ISD deceleration of between 1500m/s² and 3000m/s².

That said, a vessel at 15km/sec stopping in ten seconds with a deceleration of 1500m/s² would require a distance of 75 kilometers, which happens to be in good agreement with the vessel distance at the end of the scene of the Star Destroyers out the Falcon's window. A vessel at 30km/sec stopping in 10 seconds with a deceleration of 3000m/s² would require 150 kilometers, meaning the vessels would still be moving quickly as they passed. Thus for one of the pairs to be moving at 30km/sec with the other more or less stationary would require that the decelerating pair decelerate at some 6000m/s².

So the maximum value here is 6000m/s², or 611g. The low end is 153g.

Obviously, that's a helluva lot more than the 210m/s² (21.5g) I found for the Falcon previously.

Reviewing the script and novelization doesn't seem to suggest that there is more time that we don't see, so the ten second value seems solid. And the ships were definitely moving at a relative average velocity of 30km/sec in those two seconds. Even assuming that they were already decelerating (thereby giving us 12 seconds) doesn't really change the final value. (You can try it yourself with the cheat-sheet calculator here.

The way I see it, applying the Falcon acceleration from that scene as a maximum was wrong in one or more of the following ways:

1. Despite the afterburner, the Falcon was not, in fact, accelerating to maximum ability.

2. The Falcon is not the most "accelerative" ship at sublight (implied by the novelization description of the "coming right at us" scene's text)

3. The ISD in the afterburner scene decelerated/reversed, driving up the Falcon's true acceleration.

4. The camera was not even close to stationary, which is required for most of the Falcon calcs.

Or:

5. There's something wrong with my analysis of the "comin' right at us" scene.

#1 seems invalid on an instinctual level. It doesn't make sense in light of the rest of the films.

Personally, I don't think #2 is valid. Han insists that Lando take the Falcon to Endor because she's the fastest . . . this would not logically have squat to do with hyperspace speed because the whole fleet was supposed to arrive at the same time in hyperspace. To be sure, the Falcon kept getting caught by Star Destroyers in the films, but in most cases this is readily explained by ISDs getting a head start as the Falcon achieves orbit while a Star Destroyer is already at orbital speed.

#3 and #4 are entirely possible, though there's no real indication of #3.

And really, I don't see how #5 is possible.

But, I wanted other opinions. Thoughts?

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Post by 2046 » Mon Feb 12, 2007 7:55 am

Oh yeah . . . I forgot to mention that the results are probably rather different if the Star Destroyer is smaller (as per the old scaling debates from STrek-v-SWars).

I don't recall the conclusions, but I remember a 700 meter ISD being bandied about. 55% of that length (a rough approximation of its width) is 385 meters, which per Method One on the weapons range page would give us 58.8 kilometers distance at the start of the two-second scene, and 32.7km range at the end. That's a difference of 26.1 kilometers, or 13km/sec relative speed. But even the lowest end deceleration rate of 650m/s² is still impressive, giving us 66g. That has the benefit of being closer to the value I obtained for the Falcon, though still much greater.

However, I don't remember the 700m ISD being a bulletproof value.

Damn, I wish I was done with my scaling project!

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Post by Jedi Master Spock » Mon Feb 12, 2007 8:44 am

Interesting. A much closer match for the ANH fighter accelerations if we take it this way, which really do cook out around 300g.

There are two general criticisms of these figures that I can come up with right now, and a few nitpicky comments.

First, are the perennial problems relating to ISD scalings. Your distances are using the Imperial Star Destroyer as a measuring brick, which - as we've known - have some known issues. Scaling the ISD up or down scales the acceleration up or down equivalently, meaning that if you have an ISD that's only, say, 500m wide, your acceleration drops to 86g.

Second, the possibility that the cut involves more time. You've talked about this, but it's hard to completely dismiss the possibility.

Nitpicky point #1:
OK, let's say you've got the timing and the distance right.
EDIT: Ignore the following greyed text unless you're looking for an example of how to make a careless mistake. - JMS
If we assume that the ISDs do not, in fact, stop "slamming on the brakes" from whenever they start braking to when they're near collision (that is what happens, right? It's too early in the morning for me to remember this sort detail...), then we actually have a pretty precise figure, assuming time and distance to be correct.

The fact that the figures work neatly for assuming that they both do so at ~75 km actually requires that they do so at an average of 75 km, giving both a maximum deceleration of 1.5 km/s^2 to within your MOE for measuring time and distance. See, if one ISD is decelerating sharply while the other maintains vector, they run into each other much more quickly unless one decelerates really quickly and then eases off on the brakes.


Given an almost-collision, that doesn't seem like a reasonable assumption - if anything, the acceleration curve should sharply increase closely in based on the psychology of realizing you're on a collision course. Then, the fact that they didn't simply vector off to the side while trying to match the Falcon's "forward" (for them) vector means that the Imperials are engaged in rather tactically questionable maneuvers in the first place. Perhaps the Imperials are accustomed to trying to reduce tactical problems for capital ships to a single dimension of motion.

What all of this means is that all the "higher figures" you're introducing are based on highly counter-intuitive assumptions of Imperial behavior and can be safely discarded. Actually, since those models require variable acceleration, they also can't be derived using equations relying on constant acceleration.

All told, 153g - or a somewhat smaller figure based on a smaller ISD - is not out of the ballpark for SW acceleration figures. It's higher than the other TESB ones, but not too unusual IMO.

Nitpicky point #2:
You don't express the distance between the chasing ISD (Avenger) and Falcon at the time that Han sights the others. Since you actually have a situation that can give you a truly remarkably precise maximum "reverse" direction acceleration for the ISDs given a little time, it's actually worth accounting for the "visual" ranges on the order of a few km, since they do have an impact at this order of precision.

Nitpicky point #3:
Problem #3 with the "they're coming right at us" scene seems pretty likely. Fortunately, you now know the maximum reverse acceleration of an ISD, so you can run figures taking it into account.
Last edited by Jedi Master Spock on Mon Feb 12, 2007 11:14 am, edited 1 time in total.

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Post by AnonymousRedShirtEnsign » Mon Feb 12, 2007 9:10 am

I don't see any major problems with the low 100's of gs of acceleration for an ISD.

I don't think the Falcon has better acceleration than an ISD, or at least not during ANH and TESB, it could have been upgraded when it rendezvoused with the Rebel fleet at the end of TESB, or near Sullust in RotJ. Even if it wasn't upgraded, it is just the fastest of the Rebel ships, which ought to be inferior to the Imperial ships of the line.

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Post by Jedi Master Spock » Mon Feb 12, 2007 11:05 am

OK, something that I didn't pay close attention occurred to me now that I've finished waking up, had my breakfast, and gotten some work done for RL concerns.

I let myself slip up pretty badly in reviewing the figures. I'd delete the above commentary entirely, but I may as well leave it up as proof that I make mistakes. I should have realized I was slipping up when I suggested it mattered which ship was accelerating, but I knew the factor of four was incorrect.

Properly, it's 6 kps^2 for one ship stopping in 75 km from 30 kps, and 3 kps^2 for one ship stopping in 37.5 km from 15 kps (the two meet in the "middle" when we distribute the acceleration vector).

OK, now... to correct "Nitpick #1" above:

The fact that the stopping distance is neatly 75 km in 10 seconds for a 1.5 kps^2 ship is a problem with a factor of 2 that separates it from this description. In other words, for this to fit, the Avenger has to be 75 km behind the Falcon, when we're pretty sure it's on their tail.

The problem is that with an initial relative velocity of 30 kps at 75 km, you're going to simply close much too fast. Whether you have one ship decelerating at 3 kps^2 or 2 ships decelerating at 1.5 kps^2, you end up with an intercept around five seconds.

I already explained why the Imperial ships shouldn't stop braking once they do; that said, we have a serious problem with that initial velocity. It's a problem that works out neatly if there was a factor of 2 error in measuring the initial velocity, so I'd check over those next.

Otherwise, we're either back to a VFX bugaboo or the assumption of mass insanity.

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Post by Jedi Master Spock » Mon Feb 12, 2007 12:10 pm

And now after more real life and another revisit, you get to see how I can change my mind three times before lunch when I get rolling. Before, I pointed out that the neatly-fitting figures were off by a factor of two. In this post, I explore the margins of error and the possibility of assuming errors of the most probable combination in order to produce tactically semilogical behavior from the ISDs. (They're still acting dumb, but dumb in a logical "We're not thinking in three dimensions" way).

If we fiddle around a lot with the numbers to try and get this to edge barely within MOEs, we can get a decent feel for the above. FYI, this is a scaling-independent issue, so it doesn't go away if we rescale the ISD, although that's clearly relevant.

We can fiddle it some by picking the optimum braking time.

We can get within a half second of the stated time (i.e., close to acceptable MOE with the figures as stated for time) with 20 kps and 1.9 kps^2 relative acceleration or so...

We're dealing with pixels. When I stare at the pixels on the page and count them, I see a 19 +/-1 px and 11 +/- 1 px ISD where G2K has measured a 18 and 10 px ISD.

Sounds OK; the most I can shift from the 18:10 ratio stated by G2K is, according to my measurements, is to a 18:12 ratio, which gives me a distance ratio of 1.5:1, which gives me a delta-x of 37.5 km.

If I start braking immediately, initial velocity is then ~20.7 kps with 1.9 kps^2 relative acceleration, and the ISDs meet up at t=10.9 seconds.

This would be pushing the MOEs in all cases, but we could make the rough assumption that the ISD behind the Falcon actually starts dropping behind a little earlier than this to try and get it to fit.

So I guess if we don't mind the improbable correlation of errors - pixel rounding or blurriness can be a real pain in the tail for small objects - we can conclude a ~1.9 kps^2 relative acceleration by fitting to the most likely (practically only possible) family of combinations of errors, which would be 97-194 g depending on whether or not both ISDs decelerate (and when the one behind the Falcon starts); at least one should start fairly close to the beginning of this clip if not slightly before.

(I'd call both decelerating the most logical conclusion, given the Falcon's behavior in all this, but it's not necessary.)

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Post by 2046 » Mon Feb 12, 2007 12:50 pm

Re: Nitpicky point #1

Well, it was too late at night for me to realize that the 1500m/s² thing I mentioned doesn't work because 75km can't be right . . . if both pairs are at equal speed, they have to decelerate to near-zero in about 37.5 kilometers.

EDIT: Ah, you caught that, too. We both work better when it's not late evidently.

Re: Nitpicky point #2

The distance between the Avenger and Falcon is so small as to be virtually nil for our purposes. At the time of the dive the Falcon had pulled out ahead slightly, but was still maybe a kilometer away, tops. Just before the pair of ISDs was spotted they were maybe a hundred meters out from the Avenger's bow.

Re: Nitpicky point #3

That'll be fun. Blech.

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Post by SailorSaturn13 » Mon Feb 12, 2007 6:39 pm

There is indeed evidence for greater MF acceleration.

In ANH , while escaping the DS1, MF fires afterburners, and 10 sec after that the DS1 is nearly fully visible from "Falcon"'s position, so I'd guess it is 80 km or so.
I'd guess "MF" can accelerate at 1-2 km/s^2 when FLYING STRAIGHT, but when it turns, only a fraction of this can be used. Indeed, the leverage moment of it's engines is small in vertical axis, and to increase it Falcon should only fire the engines on one side, and only outermost parts. (In ANH MF turned (which took additional 5-6 secs) and THEN accelerated).

So yes, an acceleration at 100-200 g is there.

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Post by AnonymousRedShirtEnsign » Mon Feb 12, 2007 7:43 pm

After the trench run in ANH, they (MF, 2 X-wings, & a Y-wing) get to around a few hundred km (I'd guess 300km just by eye-balling it) in 7 seconds. Assuming it's in real time that is a constant acceleration of ~6.1 km/s^2 or 625 gs.

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