Starfleet Jedi

Recently I have seen a several claims of hundreds of gigatons of firepower for Imperial ships based off the concept that they could make orbit in under ten seconds. This comes from one scene where we see one Republic Attack Cruiser take off, then there is a cut to orbit and it takes only a few seconds, assuming no time passed between scenes.

To me this makes quite a large assumption, so I found an instance where no such assumption is needed. In this clip we see Acclamator class ships take off. They float upwards and begin to move forward, then they begin a powered ascent at a roughly 40º angle. We can see the acent and its angel at 24.8 seconds at the top a little to the right of the center, and again at 35.0 seconds and 54.0 seconds we can see their ascent. The ships travel at a fairly steady rate of about their length per second.

Given a 40º incline and a length of 752 meters the ships are gaining altitude at 752 m*sin(40º) ≈ 483.3763 m per second. Give there is not noticeable acceleration over the corse of one second they are exerting a force roughly equal to their weight, 6000000000 kg*9.8 m/s/s = 5.88*10^10 N. So the work expended to raise them 483 meters with negligible acceleration would be 5.88*10^10 N*483 m ≈ 2.8400*10^13 J or 6.79 kt. This is all in a second, so the power is about 2.84*10^13 W.

Taking drag into account adds a bit more to the engine's output, giving a relevant surface area of about 498,609 m^2 (a quarter of the proportional surface area of an ISD relative to length) and a drag coefficient of about 0.65 (half-way between an angled cube and a cone) the power necessary to overcome drag is .5*1.225 kg/m^3*(752 m/s)^3*498609 m^2*.65 ≈ 8.4418*10^13 W.

I did not expect drag to add that much power, so the engines in this instance are operating at 1.13*10^14 W or 27.0 kt/s. Again this is not necessarily a maximum output for the engines, it is just what is shown at this moment. Maintaining this as their constant speed would put them at ISS orbit altitude (370 km) in under half an hour, but as the atmosphere thinned and gravity weakened with altitude they would definitely accelerate significantly at this power level probably making ISS orbit level short order, but in a scale of minutes not 10 seconds.

Great analysis ... any idea what Attack Cruiser scene they are referring to?

It is the Attack Cruiser on which which Obi Wan departs for Utapau in Revenge of the Sith, just after the last time he and Anakin see each other as friends. I say that they base it entirely off that scene because, as far as I can remember, we never see anything else roughly Star Destroyer sized go into orbit throughout all of the movies. There are plenty of fighter to orbit scenes, with cuts, which people use to support the notion of orbit in ≈ten seconds and then apply that to capital ships. But in all of these cases cuts are assumed to take no time at all.

I decided to look at the scene from another approach. The ships are traveling at about 750 m/s during their ascent giving them a kinetic energy of .5*6000000000 kg*(752^2) m ≈ 1.697*10^15 J. As seen between 22.6 seconds and 36.6 seconds with the ship in the middle taking off, the time it takes to start the accent is greater that fifteen seconds, probably between 20 and 30 seconds. This would require an average power output of approximately 6.786*10^13 W using the 25 seconds figure.

Given that the ship is changing speed, relevant shape, and relevant area I do not want to try and calculate the exact power needed to overcome drag. But it will be significantly less as the velocity is a cubed variable and is significantly less over the course of this event.

In any case, even assuming almost as much drag as in the previous example, the power of taking off and getting up to speed would roughly equal the power of the ascent. So the take off period and the climb match up surprisingly well in this event at about 27 kt/s.

That is nothing more than the precarious logic Brian Young uses so abusively on ALL sequences featuring a ship taking off. The mere idea of a real world director cut so completely flies above their head, it is genuinely dumbfounding.
Like, err... light years above. Words fail me.

It's more of the clear double standard that is employed that bothers me. If you want to be literal in your interpretation of what you are seeing, well fine. But don't pull it when you examine another franchise's tech because that would put it on par with your own? I mean, compare the speed issue from Star Trek Into Darkness where the Altprise gets from the edge of Klingon space back to near Earth in what appears to be no more than a matter of minutes... literally.... since Carol Marcus was clearly shown running from sickbay to the bridge to tell Kirk rather than just call on the com. Or apply bigaton numbers to Federation starships when we have clear high accelerations, like the refit Enterprise's run from Earth to Jupiter in under 1.8 hours.

Or a classic case in ST:FC of the E-E coming back to Earth in a jump cut from Picard giving the order to intercept the Borg to when it is shown arriving in time to save the Defiant less than two minutes later.
-Mike

Aaww com'on, being literal on that question is like claiming you can drive from Los Angeles to Dalla in 1h because someone drove you and you closed your eyes for 99% of the trip.