So, as part of my possibly-continuing "Geometry on Drugs" series, here is a prequel to my post on spherical geometry, which was more of a "hey, this is useful" post in which much there's a whole lot you're expected to take on faith. It was really more intended for the hardcore engineering type who needs to see that use case up front.
This version is going back to first principles, where we do the axiom wanking and you (hopefully) get a sense of why things turn out the way they do.
Also, this is the practice run before I launch into the Essence of Hyperbolic Geometry, so, … Onward …
The Geometry Axiom Everybody Hates
Start with this diagram and the inevitable question that comes up:
Start with a line ℓ and a point A not on it. How do you put a line through A that doesn't intersect ℓ?
(In other news, I am now convinced that the Unicode committee contained at least one disgruntled geometry teacher. How else to explain why there's this isolated script ℓ code point?)
We can drop a perpendicular from A meeting ℓ at some point X, and then it's obvious that the line you want (dotted) is the one perpendicular to XA. If you tilt it even slightly away from 90°, then it simply must intersect ℓ somewhere.
Proof by diagram. We're allowed to do that, right? ( Read more...Collapse )
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a.k.a., Space 11: How to do Interstellar Navigation
Various antecedents you may want to have peered at first:
Today's post is about Hyperbolic Geometry, wherein you learn what those "Warning, Evil, Don't Look" columns are about.
It's now safe to look; well okay, no it isn't, but too late! AHAHAHAHAHAHAHA.
Hyperbolic geometry is basically Geometry On Drugs and we know that's never going lead anywhere good.
To be fair, Spherical Geometry is arguably also on drugs, but at least it's easier to explain in that, having had lots of experience with basketballs and whatnot, you already know what a sphere is. Having a concrete place for the "points" to live, I can then tell you
- what "lines" are (great circles, or planes slicing the sphere through the origin / center of the sphere),
- how to measure "distance" along a "line" segment (measure angle between endpoints from the center of the sphere),
- how to measure "angles" between "lines" (the planes will intersect; there's an angle there; done), and
- what "circles" are (they're um, circles, … or, if you like, planes that don't necessarily go through the origin, or cones coming out of the origin; whatever works for you),
and then you're basically good to go, ready to do all of the geometry/trigonometry you could ever want, once you've heeded my warnings that Certain Things Will Be Different (no such thing as "parallel", triangles add up to 180 plus area instead of just 180, do not feed them after midnight, etc…).
Unfortunately, the place where we're Doing Geometry today is this inside-out Hyperboloid Sheet Thing with a fucked up metric, … and if you've actually seen one of those in real life, I will be very surprised, especially since it's not something that can exist in ordinary 3D space. Oddly enough, it will end up relating to something you do have day-to-day experience with, namely (cue reverb and James Earl Jones voice)… Your Future,… but I'm not sure how much help that's going be in visualizing it.
( bring on the drugs...Collapse )
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So,... picking up where we left off, I, the intrepid hero, am sailing off to your right into the sunset, with my incredibly reliable gerbil keeping time for me. You, the diligent historian, will eventually reconstruct everything I'm seeing from all of the reports you'll get — from the cloud of NSA bugs that I'm flying through — into a big, happy space-time diagram in which:
- My time axis, everything that is happening "Here" according to me, is — as everyone would reasonably expect because I'm moving — slanted away to the right from your own natural, obvious, and vertical notion of "Here",
- My space axis, everything that is happening "Now" in my direction of motion, according to me, is, — as nobody expected prior to 1905, — slanted up from your own natural, obvious, and horizontal notion of "Now" and by the same angle,
that second item being what makes all the difference, ruins Galactic Empire stories, and happens to be the only thing you really have to remember about Relativity because it's enough to derive all of the other wacky effects you hear about.
Here's how: ( Read more...Collapse )
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So, wow, it's been 15 years. And yours truly is Not Actually Illegal in the Russian Federation (at least, not so far as I know and not yet
But I'm still joining the Exodus to Dreamwidth
because, well, fuck every last bit of that noise (also, fuck the ads, and maybe also fuck brad, while I'm at it...).
In other news, I learned enough of the API to fix the cross references in my journal to all point to Dreamwidth so that you can painlessly follow my various n-part series
which might possibly be continuing; we'll see. (I may be sufficiently annoyed to change all of cross references on the LJ side as well, whee...)
Now I just need to turn off commenting on the LJ side (just c'mon over
— or if you don't want to do the wholesale move, just create an account and claim your LJ OpenID
(note that some of you who've already moved here still need to do that...)This entry was originally posted at http://wrog.dreamwidth.org/61213.html. Please comment there using OpenID.
(Still waffling on whether this should be Space Travel part 8 or Relativity part 1; we'll see...
If you want to go back to part 1, that's here though none of the prior material really matters for this one.)
It's weird to me how everybody knows there's a problem.
How, if you are, say, Issac Asimov or George Lucas or Gene Roddenberry trying to write your Galactic Empire/Federation/Whatever story, you've got to do some kind of handwave about Relativity. We know this because we were taught at some early age that trying to go faster than lightspeed is Somehow Bad, even if nobody ever explains the details.
It's particularly annoying to me because many of the details actually could be explained without going beyond 6th grade math. If you get how right triangles work, that's pretty much all you really need for Special Relativity, except nobody seems to bother trying.
I suppose part of the problem here is the mystique of General Relativity. True story:
Arthur Eddington is at a meeting of Royal Society in 1919 where Sir J.J. Thomson (President) concludes a talk saying nobody's ever really stated in clear language what Relativity is about. The meeting disperses, Ludwig Silberstein (the author of one of the early books on relativity) comes up to Eddington and essentially says, "So you must one of three people in the world who actually get this stuff." Eddington demurs, but Silberstein pushes further, "C'mon, don't be modest," at which point Eddington replies, "Actually, I'm trying to think who #3 is..."
Then again, given the sheer number of people I've encountered who have Misner, Thorne, and Wheeler's Gravitation sitting on their bookshelves, that's clearly not the case anymore.
But if even Albert Fucking Einstein had to take five years off to get up to speed on Differential Geometry — which to some extent is just the Partial Differentiation Chain Rule on Steroids and working through all of the various consequences, but if you didn't get past high school calculus, even that much is going to be a bit hard to take — what hope is there for the rest of us ordinary mortals?
But it so happens that, for Special Relativity, you don't need differential geometry. So let's get started:
Why is the speed of light constant?
How did they even get this idea that the speed of light is always the same? That's the part They never explain. They figure there's no way anybody's going to get that without having the full-ass physics course, so they don't bother trying.
The short answer is that they've done the experiments and that's the way it actually is. Since that's unsatisfying, I'm going to try giving you the half-assed physics course instead:
( Read more...Collapse )
(... The curse of being a math geek living in a state where they have caucuses instead of primaries (not to mention having spent some time observing party rules committees) is I end up thinking about this stuff...)
So here's a fun issue with caucuses:
First, a quick review of the basic rule for awarding delegates at caucuses.
Your precinct is allocated some number of delegates, D
, to elect. Some number of people attend your caucus and each declares a preference for a particular candidate. Twenty minutes later, once the blood has been mopped off of the floor, the battle lines have hardened, and everyone who might have been inclined to change his/her mind has been talked to death, you then compute for each candidate the following number
(# of votes for that candidate)
————————————— × D
I'll note first of all that every attendee will in fact be included here, because if you don't ever actually declare a preference, that's treated as equivalent to declaring a preference for "Uncommitted," this extra fake candidate that's always added to the mix. So it's guaranteed that all of these "delegate-share" numbers will indeed add up to D
The next step is to split each delegate-share into a whole number plus a fractional part. For each candidate, the whole number gets awarded directly, and, if those numbers by themselves don't sum to all of the available delegates, you then rank the fractional parts and distribute any remaining delegates, one each, to the highest candidates in that fractional ranking.
(...And yes, for those of you who know about this, I'm skipping the 15% threshold rule, which some states apply at the precinct level. Thankfully, in Washington, we got rid of that 8 years ago, since it's a complete waste of time at the precinct level [also has any number of bad effects, but that's a whole 'nother discussion].)
So first, I'll present Survival Trick Number One, so that you can survive in a chaotic caucus environment without having to do long division in your head. It goes like this: we rewrite the formula above as follows:
(# of votes for that candidate)
i.e., just divide numerator and denominator by D
, which works because multiplication is commutative (...except that the DNC stupidly ruins the commutativity by including a 3-decimal rounding rule in the process, but, as it happens, this doesn't affect things very often at the precinct level, and in any case this still works fine as a rule of thumb so that you can wrap your head around what's going on...)
Bottom line is there's a certain magic number of votes ((# attendees)/D
) that you need to get a "whole delgate".
Meaning you can take your caucus, divide it up into blocs of that many people who are all voting for the same candidate. For each such bloc, that candidate gets a "whole delegate", and then whatever votes you have left over, you rank those, and the candidates that are highest on that ranking get the remaining delegates. The advantage of doing things this way is that you're just counting votes without having to do any long division in your head.
You're in a precinct that's been allocated two delegates.
Twenty people show up.
14 are Kerry supporters.
6 are Dean supporters.
If you follow the worksheet, then it's (14/20)*2 = 1.4 vs. (6/20)*2 = 0.6.
Kerry gets 1 whole delegate and then, because 0.6 beats 0.4, Dean gets the other one.
Or you can do it my way, seeing that (20 attendees)/(2 delegates) = 10 votes needed to get a whole delegate. Thus, Kerry's 14 votes produce one whole delegate (10 votes) with 4 left over that then lose to Dean's 6 leftovers, and so Dean gets the other delegate out of the "fractional ranking", never mind that we're not having to rank fractions any more.
Now for the problem.
It turns out that the number of votes that you need to get a whole delegate is NOT the same as the number of votes you need to win a delegate out of the fractional ranking.
In fact, if your candidate is getting awarded any whole delegates at all, there's a fair argument that some of your votes are being wasted.
What do I mean by this?
Back to our example: Thus far, it's 14 to 6 with each candidate ending up with one delegate. But then the Kerry folks wonder if they can do better. And it turns out, they can!
After a brief strategy session, 7 of the Kerry voters change their preference to Uncommitted. Which now means the totals are 7 Kerry, 7 Uncommitted, and 6 Dean. Since you need 10 to get a whole delegate, there are now zero
whole delegates, the fractional ranking then has to award two and they go to Kerry and Uncommitted.
Except,... since the "Uncommitted" folks are really all Kerry supporters, it's a good bet that "Uncommitted" delegate will be signing in for Kerry at the next caucus level.
Which means Kerry has just effectively cleaned up and claimed both delegates.
WTFF? How did that happen?
On the other hand, he did
have more than 2/3 of the vote in that precinct, so there's some argument that this isn't actually a totally unfair outcome and perhaps the real question is why should the Kerry supporters have to jump through this extra hoop to get the delegates that are rightfully theirs?
The problem is that, while the number of votes you need to get a whole delegate is
the number you need to guarantee one out of the fractional ranking is actually
which, in our example is 20/3 = 6+2/3.
... or, more precisely, if your candidate has at least (# attendees)
and there is at least one candidate with strictly more than (# attendees)
(even if it's only the slightest ε more), then you are guaranteed a delegate out of the fractional ranking (since in that case there cannot be more than D
groups with (# attendees)
votes, and you're one of them, so you win)
Dean with 6 votes isn't quite there, and that makes all the difference in the world.
Meanwhile back in the first scenario, where the Kerry supporters are spending 10 votes to get a "whole delegate", this can now be seen as a ripoff, spending 10 when they only needed to spend 6+2/3, thus wasting 3+1/3 of their votes, which costs them a delegate.
More generally, (# attendees)
be less than (# attendees)
and, if you're in a close race, chances are you're going to care about that difference.
And apparently, they've even thought about this in Iowa, or, rather, it's the only way I can account for Iowa's version of the threshold rule which not only makes things way more complicated, but also introduces the nastier features of thresholds into the lower-delegate caucuses where they weren't originally a problem.
My fix, which will most likely never be adopted, is much simpler:
Instead of multiplying by D
, multiply by (D
That is, for each candidate you instead compute
(# of votes for that candidate)
————————————— × (D+1)
(# total number of voters)
and then proceed as before, awarding the whole numbers, and again if the total number of delegates awarded in this way is different from D
, use the ranking of the fractions to fix it. The only difference now is the (remote) possibility that there will be too many
+1) delegates awarded via the whole numbers, in which case, instead of giving out delegates to whoever is at the top of the ranking, we're taking a delegate away
from whoever is at the bottom (except that if all of the whole numbers are indeed adding up to (D
+1), that means all of the fractional parts will necessarily be zero, so we don't even have to look at any ranking; you just pick somebody at random to lose one).
So in our example, for Kerry the magic number is 14*3/20 = 42/20 = 2.1 and for Dean it's 6*3/20 = 18/20 = 0.9, Kerry gets 2 and we are done
; we don't even need to consult the fractional ranking at all.
Or, calculating things my preferred way, you need 20/3 = 6+2/3 votes to get a whole delegate, Kerry has 2 such blocs, Dean doesn't have any, and again we're done. At which point it should be blindingly obvious that there's absolutely no advantage
to be had by splitting your voters up over multiple fake candidates; you'll get the same result either way.
Which is the way caucus rules should be (i.e., they just give you an answer and no amount of gameplaying changes it).
But, even though they're never going to adopt this rule, you can still use it, the point of it being that if you're ever in a situation where the Multiply By (D+1
) rule is giving you a different answer than the actual Multiply By D
rule, that's where you have to watch out.
This effect is most pronounced in the 2 delegate caucuses but it can show up in higher-delegate caucuses as well.Example 2
4 delegate caucus
20 people show up
17 for Kerry
3 for LaRouche
So now it takes 20/4 = 5 votes to get a whole delegate. Thus, Kerry supporters can spend 15 to get 3 of the 4 delegates. Unfortunately, that means they only have 2 votes left over, which lose to LaRouche's 3 in the fractional ranking and so we get one LaRouche delegate.
What does the Multiply By (D
+1) rule say? In this case (D
+1)=5, meaning you only need 20/5 = 4 votes to get a delegate out of the fractional ranking, and, with 17 votes, Kerry supporters can produce four such blocs which will all beat LaRouche's 3 votes.
... the only problem being that those blocs need to be for four different candidates. But this is actually doable:
5 for Kerry
4 for Uncommitted (actually Kerry)
4 for Sharpton (actually Kerry)
4 for Kucinich (actually Kerry)
3 for LaRouche
Now Kerry only gets 1 whole delegate while the fractional ranking awards the rest to Uncommitted, Sharpton, and Kucinich, who all change their votes to Kerry at the next caucus, and thus Kerry cleans up all four delegates.
William has learned about Rock, Paper, Scissors. In honor of that, a puzzle:
Same game: Rock breaks Scissors, Paper covers Rock, Scissors cut Paper. So far so good. Now we add a couple twists:
- I do research and find myself a Better Rock, a chunk of pure New England granite that rules, absolutely crushes all lesser Rocks. Even though it still loses to Paper I'm happy with it.
- Meanwhile you've been doing your own research; being of a technological bent you know there are better ways to do Scissors; carbon steel with a diamond edge; not only cuts Paper but completely destroys other Scissors as well. Granted, even a diamond edge is no match for an any actual Rock, let alone mine, but you still win against everything else, so you're happy.
So... my Rock beats your Rock, your Scissors beat my Scissors, and Paper vs. Paper is the only draw possibility left.
What's my strategy? What's your strategy?
And how does this change if I go out and get really good, battle-ready Paper as well, e.g., some of that Tyvek stuff that they use to insulate houses; something that will entirely shred
your Paper, even if your high-tech Scissors will still make short work of it. Meaning that not only is there no longer any possibility of a draw, but out of the 9 possible scenarios, I'm winning in five of them.
(This is Part 7. There are previous installments; this one is a digression from something I said in Part 6, though you can also start from the beginning at Part 1)
In Part 6, I said:
The theoretical absolute best we can do with rockets is if we can get the exhaust velocity up to the speed of light. This means our exhaust will be pure radiation, that we are somehow powering a huge-ass laser with 100% efficiency, since that's the only way we get all of the exhaust going the same direction. And, boy howdy, do you not want to be following along directly behind,…
Which leads rather directly to this:
The best possible rocket engine and the best possible directed energy weapon are exactly the same thing.
Remember this the next time you're watching Star Wars, Babylon 5, Battlestar Galactica, etc. All of those little fighter ships where the engine is distinct from the guns? Those scenes where they're accelerating forward, closing with the enemy, firing forward with everything they've got?
Wrong. Wrong. Wrong. No military contractor worth its salt is going to waste resources mounting a second gun on a ship when there's already this totally effective and somewhat expensive first gun.
Conversely, if you've got a phaser/laser/gamma-ray-laser that can do real damage from a distance, then most likely that is your engine. If you're in a universe where rockets are your only form of propulsion, you are definitely not going to be wasting resources on a 2nd engine. It's going to be correspondingly expensive to fire, too. Nor will you get off that many shots before you're hurtling away.
What you need to do is arrange to be headed towards your target with as much velocity as you can manage. Then, when you're really close, you flip around and shove the throttle to maximum. It'll look exactly like you're landing on your target (modulo the small matter that you'll want to not be too predictable about it, see below). Best if, once you've killed all of your relative velocity, you can whip out some (really strong) tethers to attach yourself with before continuing to fire, so that you can be expending as much energy as possible on your target vs. propelling yourself away.
Of course, if you actually can get that close you're probably still better off with a burrowing torpedo that can blow up your target from the inside.
In fact, I'm rather having trouble shaking the conclusion that directed energy weapons aren't at least as stupid as rockets. On the other hand, if you're stuck in a universe where rockets are all you have, then so be it. Swords, planted bombs, and bioweapons are all very nice if you can get close enough to use them, but sometimes you just can't.
Also, to be sure, planet and asteroid-based gamma-ray-laser cannons will be a different story. They'll have room for arbitrarily huge reserves of antimatter compared with what you'll have available in your fighter ship, and the momentum consequences of firing off huge blasts will be negligible for them.
Suffice it to say, you'll want to stay well out of range of those. Except for the small problems that,
- being lasers, they'll have lots and lots of range, and
- the moment you stop firing your own engine for any length of time, your trajectory becomes immediately predictable; figure by the time we have practical antimatter distilleries, we'll have the software for this worked out just fine, too
- given the stupidity of rockets, you won't be able to be constantly firing your engine for any length of time before running out of fuel
So, good luck with that.
Granted, if I were going up against an entire planet, I'd probably want to arrange for a dinosaur-killing asteroid to do the dirty work for me. Hide an armada behind it to take out anyone who tries to come near to divert it.
Which then means that any sensible planet is going to have an entire inventory of asteroids of various sizes lined up at its Lagrange points to be able to deal with any such threat, at which point I'd then concentrate my efforts on subverting the folks in charge of the asteroid inventory.
Or maybe just taking a trip down to the planet itself, sneaking in, and detonating the huge antimatter reserve where the phaser cannon is located.
Of course, if everybody has sufficient resources to be distilling out the insane quantities of antimatter needed to be fighting these battles, I'd have to wonder what the hell they're fighting over. Not that this would be the first time in human history where a war got started for completely stupid reasons (cf. WWI)
And round and round we go.
(and there's a Part 8 now, where we move on to Something Completely Different)
(This is Part 6. There are previous installments, though if you only made it as far as Part 3: Rockets Are Stupid, that's good enough for this one.)
Rockets are Even More Stupid Than You Thought
Meanwhile, back on the launch pad, staring at the 2500 tons of Saturn V that I've just told you how to make smaller, we can ponder what's going to be possible once our technology gets Really Good.
The theoretical absolute best we can do with rockets is if we can get the exhaust velocity up to the speed of light. This means our exhaust will be pure radiation, that we are somehow powering a huge-ass laser with 100% efficiency, since that's the only way we get all of the exhaust going the same direction.
And, boy howdy, do you not want to be following along directly behind,…
… which inspires an observation about fighting space battles, which I'm going to defer to Part 7.
Anyway, this Best Possible Rocket brings the fuel cost for getting your Winnebago-sized Command Module to the moon and back again down to a mere 327 grams.
The catch is that half of that 327 grams will need to be antimatter. This also assumes you've solved the problem of storing it in a reasonable way — and if so, the Fusion Power People would really like to hear from you; and no, they won't necessarily be obsolete, because antimatter is merely a storage medium; you still have to extract the energy from somewhere. It should be noted that the amount of energy needed to make that amount of antimatter — and what you get back when you let it recombine — is roughly that of an 8 megaton bomb.
So, if you're imagining this to be the family car, where you can just hop in and fly to the moon for a week when the kids are off school, guess again. Unless you like the idea of each of your neighbors having an 8 megaton bomb in the garage and DUI being about much more than just the occasional lamp post or pedestrian. Hell, let's just have every auto repair garage, bus station, and airport be a terrorist candy shop, where the stakes in question are not just single office buildings but whole continents and planetary habitability.
Suffice it to say, there's a whole range of social and political problems we're going to need to have completely solved before we get to any kind of ubiquitous space travel regime.
Never mind that said problems will have bitten us in the ass long before we have practical antimatter distilleries. No matter how many countries we can get to sign the nuclear non-proliferation treaty, if you're Joe Sixpack sitting at L1 with a 6 ton rock and the right software, that's an 8 megaton bomb you can drop anywhere on earth, no nuclear tech needed.
To The Stars?
And all of that insane energy expense is just to get to the fucking moon. You want to go to the stars?
Using this theoretically perfect rocket which will never actually exist, accelerating at one g (earth gravity) for a day costs you 0.3% of your ship. That may not sound like a lot but you'll need to keep that up continuously for a year to get to 3/4 the speed of light. At which point 2/3 of your ship is now gone (which means at least 1/3 of it was antimatter to start with).
That may be good enough to reach Alpha Centauri, but to get anywhere real, you need to keep this up. Four more years (proper time) of accelerating at 1g — meaning you'll have to spend 242/243 of your original ship; picture launching one third of a Saturn V half-filled with antimatter — puts you 75 light-years out from earth, with finally enough time dilation (100 to 1) so that you can coast across some reasonable fraction of the galaxy (thousands of light-years) in a single lifetime.
Confined to a Winnebago.
And you thought space exploration was going to be fun and exciting.
Also, you better hope you picked a good destination, because, unless you happen to have a perfectly placed neutron star or black hole in your path — at which point you will then also be needing enough shielding to cope with all of the crap likely to be in the vicinity of any such object, because going at any significant fraction of light-speed means you'll need to get really, really close to make any kind of tight turn (also, good luck with the tides) — course changes will be essentially impossible once you get going fast enough.
Nor will you be able to stop anywhere along the way or even slow down at the end of the trip, unless you've arranged to be able to spend another 242/243 of your ship and allowed for another 5 years (proper time) to do it. Meaning we're now launching something 73 times the size of the Saturn V, half-filled with antimatter, and stuck in the Winnebago for a minimum of ten years, in order to be able to do any kind of interstellar travel beyond 150 light-years.
Rockets just suck.
Why I Shouldn't be Allowed to Write for SF Television
This, by the way, is something else that Star Trek and similar shows get wrong.
((Update: It seems I've done Roddenbury an injustice; he apparently did make a pronouncement about impulse engines early on. So you'll have to read this as, "What Star Trek would have been like if impulse engines were rockets." In any case, it doesn't let any of the other shows off the hook: BSG, I'm lookin' at you.))
It's not that I'm going to fault them for postulating the existence of something like Warp Drive, which you just need if you're going to do Galactic Empire stories. Nor am I going to fault them for not dealing with Relativity properly, because the sad fact is that most SF authors only understand Newtonian Universes anyway, and I'd just as soon they stay in their comfort zone and tell stories that make sense on their own terms, rather than attempt to include Relativity and make an utter, complete hash of it. The other fun thing is that if you try to have Warp Drive and Relativity in the same story, then that generally means you have a time travel story even if you don't realize it, at which point JWZ's Law probably applies.
Star Trek — along with everybody else—actually screws up is with the impulse engines, whether they're called that or "thrusters" or "reaction engines" as on some other shows, they are clearly intended to be rockets of some sort. And then they get used in every episode as a completely routine means of puttering around a planetary system.
To which I say, "Wrong." Firing a rocket is cannibalizing your spacecraft; it uses exponential amounts of fuel; you never want to do it if you have any alternative available. Rockets are the propulsion method of last resort.
Meaning if you actually had anything at all like Warp Drive, you would contrive a way to use it for everything you possibly could. You'd use it in-system, you'd install it on the shuttlecraft, you'd use it in the space dock, you'd use it for going to the grocery store. You would use it everywhere that you didn't have some other reasonable alternative (like space elevators, solar sails, tethers, whatever).
WHY? BECAUSE THAT IS HOW MUCH ROCKETS SUCK.
The only proper scene in which the impulse engines would even be brought up would be something like the Battle Aftermath Scene. In which the ship has been wrecked by Commodore Decker's planet killer or some such. They've barely eked out a victory, but half the crew is dead. Bodies are scattered everywhere. Shit is on fire. You can hardly see through the smoke. Sulu and Chekov have big nasty burns. Kirk has his shirt ripped off and is bleeding in a dozen places. McCoy and Chapel are buzzing around doing triage. Warp drive is trashed. Dilithium crystals are hopelessly fused, etc.
And now it transpires that they're spinning out of control into a planet or something.
At which point we have a dramatic pause and musical cue as Kirk calls down to Engineering.
"Scotty," he says, "Ready the impulse engines."
Some of the younger bridge crew startle at this. It comes up in the training sessions but you never imagine that you'll hear it for real. Because if you do, it usually means you're about to die.
And then we have the long anguished close-up on Scotty. He looks around at the debris in the engine room and realizes the captain is probably making the right call. And finally...
His children are about to be murdered and there's nothing he can do about it. He motions two of his surviving lieutenants over and together they remove the cover and break the seal on the impulse controls. There's a huge lever there that takes three men to move.
Back on the bridge, Kirk flicks a switch on his armrest, "All hands! Jettison Stations! Level Three Emergency! Unnecessary mass into the tubes! Repeat! Level Three Jettison Emergency! Unnecessary mass into the tubes!"
Cut to scenes around the ship of surviving crew members, rummaging through every room, grabbing everything not nailed down — wreckage, equipment, random belongings — and stuffing it all into chutes specifically designed for this purpose.
"Sulu, what's our time factor?"
"We need 5000 ΔV in the next 30 minutes or we're dead."
"Impulse engines ready, Captain. You'll have 195 seconds of burn time."
"Thank you, Scotty. We'll make it count. Spock, how's our mass situation?"
"Down 23% We need to lose another 5. Another 10 minutes, 42 seconds if we can keep the jettison rate up."
"That's cutting it too close." Flick. "All hands! Level TWO Jettison Emergency! Repeat! Level TWO!" Cut to more scenes around the ship. Now they're gathering the dead bodies and stuffing them into the tubes. Cut to exterior view of the ship with expanding cloud of debris and bodies and crap.
… and so on.
Really. Rockets just suck.
Up next, Part 7: Space Battles