The "at least" here is totally optional. He could omit it or relocate it to after "second." He could easily have said "We'd need to apply a delta-v of four km per second." Even if it is not linguistically perfect (my grammar skills ain't the best,) it'll be unambigious. In short, come on, don't blame anyone else for your own goof
Yes but little words like "at: and "by" do have a meaning. I could be wrong in my problem with Geordie's phrasing, but the mistake is mine whatever the outcome.
"If you are starting from 0 KE and a PE of X joules, and you allow the object to free-fall , then yes, the PE will be converted into KE. As it falls through the atmosphere, some of the KE will turn into thermal, even as more and more PE goes into KE. Then it hits the ground, and there is no PE left, and no KE as the object finally stops."
Look the energy has to go somewhere, most of it will be left over for the the impact unless I'm horribly wrong. You claim an apreciable amount of energy will go to thermal waste, fine let's see your calcs.
"Two, your numbers only work if you use a free fall solution. If you are shoving it down faster than the natural transfer rate (9.8m/s^2) then you WILL have to put in extra effort. Your hand exerts effort on the basketball every time you slap on it so it'll bounce higher than it otherwise would (can you tell I'm not very fond of basketball? ) You are adding your own energy into the what the GPE transfer will be. "
Of course its called a low end estimate. The ISD could be going faster, but that only makes a *bigger* impact. So long as the GCS(s) is (are) pushing harder than the ISD you will go down and the minimum amount of total energy will be at least equal to the GPE. Anymore is just "bonus" =)
"However, if you want to accelerate it further, then you will increase the KE at impact. What can do that except for extra work, from your hand? "
lower limit approaches zero (depending on how lightly contact is made) upper limit is without bound (at least until something in your hand or the basketball gives).
The point is no matter how you dice it the basketball hits the ground with at least 1J, some is of course bled out by wind resistance, but any work done by your hand is going to be extra. If you want to say the GCS makes an appreciable *increase* in total energy ... fine by me =)
"Not only are you actively trying to accelerate it towards the ground, BUT you are also fighting the ISD. Let's say you win this little shoving contest, but it is even enough that the ISD barely scrapes the floor at ONE m/s. Then the actual KE figure will be eons from your GPE hopes (1.25E10J of KE impact.) "
That only occurs if the ISD is pushing harder than the GCS(s) at some point in time. Let's say the GCS is pushing at 10^11 N (numbers not correct). Let's say the ISD is pushing back at 9*10^10 N. Now let's say that happens the entire time. The net result is 10^10 N towards the Earth. Which means net you have all the KE derived from GPE and *then* some. There are 3 forces at work here. The GCS(s) pushing down. The ISD (pushing up presumably). Gravity pulling down. If the |Fgcs| >= |Fisd| then you will have at least the amount of energy specified by GPE, possibly *more*.
The only way an ISD can impact at anything close to slow speeds is if |Fgcs| < |Fisd| < |Fgcs + Fg|.
If |Fisd| > = |Fgcs + Fg| then ISD won't even budge.
Where Fisd is the force supplied by the ISD's engine pushing up
Fgcs is the force from the GCS pushing down
Fg is the force of gravity on the ISD
The ISD is actively producing force, and when at full thrust, it is doing 1.125E19W to accelerate (your numbers.) That's more than the GPE can possibly hold it down with. Gravity is on your side, but the more significant thing is the ISD's own resistance. You have to fight that to push it closer to the ground, and force and work will be required.
First off an ISD only does work if it moves up from the gravity well. To see if that happens we need to look at forces.
Yes but by my original numbers the GCS would be hitting with an effective 2.4*10^17N. An ISD can push back with 1.8*10^15N. In other words the ISD would have done jack didly squat. The only reason I figure from GPE is because we don't what mechanism is used to produce the force which pushes this thing down, it might be some treknobabble device which does not require vast amounts of energy (so that when it's turned off the object it had been pushing slows down). But regardless of how the treknobabble works you *always* have a net change equal to GPE if you go from "up" to "down", that energy may go into deforming the impact site, heating air on the way down ... but it goes somewhere.
Any way using more correct numbers (I think) a single GCS will push with about 10^13 N. So about 200 of em could bully an ISD around (until they become cannon fodder) =) In this case even a dozen 10 GCS will only push with 10^14 N, which means that net motion (if the ISD pushes with max engines) is up, and the ISD is also doing work (as its moving out of the gravity well).
"In fact, let's do it REAL far from Earth, where the gravitational potential energy of Earth nears INFINITY. But that isn't going to help you much practically at all. The ISD is still accelerating with 1.125E19W, and you are still trying to drag it another with 3E16W. The victor is clear using something simple like the KE formula"
Sigh look this is a fairly simple problem (I think) you have 3 forces. 1 going up (the ISD), one going down (the GCS) and another going down gravity. The first two can employ all sorts of fun tricks (indeed something screwy has to happen considering the bridge crew stays standing while these suckers accelerate), so that the energy requirement goes down. So looking at magnitudes here there are several possibilities:
1. Fgcs > Fisd - ISD goes down hard, an extremely conservative lower limit is the GPE of the ISD, upper limit is whatever energy the GCS can impart.
2. Fgcs <= Fisd <= Fgcs + Fg - ISD goes down, but not as hard. Lower limit here is 0 joules, upper limit is GPE.
3. Fisd > Fgcs + Fg - ISD goes wherever the hell it wants to. Lower limit is 0, upper limit is also 0 if the ISD does not want to move.
Which means given my earlier incorrect figures we were in case 1. The ISD goes down hard with
at least GPE.
Given the corrected figures we are in case 3.
Given a few hundred GCS pushing the ISD you get back to case 1.
The victor is clear using simple forces and accelerations. I avoid working out force problems with power.
BTW, yes, I've read those numbers, but these days, a single HTL now goes for 8.372E20J. Do the math
Why do SW ships even bother having HTL's? With that type of energy you can make damn powerful railgun (gaus gun ... whatever the hell you like) which would shread your opponents immensly weaker KE sheilds with ease. I mean hell does *anyone* give a damn about fighting economically in SW? I mean seriously supposedly ISD's can fight for several volleys, yet ships (even damaged ones) were getting crunched by a small fraction of that in KE. Not to mention they'd actually be faster in flight than TL (we are talking enough rKE to be going .995 c if the missile is 1000 kg).
Let's pump out orders of magnitude more energy for the hell of it so we can have equivalent firepower of a much less energy intensive KEM.