I'm removing this until someone cares to fix it:

• In Forbidden Planet, the crew of the spaceship is attacked by a monster and blast it with an impressive looking nuclear powered particle cannon. They then go on to mention that no living being should have survived the hit. The problem is, they give the output of the cannon as "three billion electron volts", presumably per particle, which is an utterly frightening amount. An electron volt is the energy carried by an electron that's been accelerated across a charge differential of one volt. So a three billion volt difference across which the particles are accelerated (or a roughly 1.2 million volt difference, if the cannon throws protons or neutrons) is enormous; the largest differential routinely created artificially is on the order of 100,000 volts, and that with equipment the size of a large building. It seems likely that the real issue here is that "electron volt" is a very different kind of unit from "volt", making this Unit Confusion of a sort: while electron volts are indeed a unit of energy — which volts are not — an electron volt is the sort of unit one would use on a subatomic scale, and not just some sort of energy-equivalent to similar numbers of volts.

—

"the largest differential routinely created artificially is on the order of 100,000 volts, and that with equipment the size of a large building"

100 kV is within the range of a perfectly ordinary x-ray machine - even one small enough to be portable. By comparison, even a regular old CRT screen can have a > 20 kV electron gun driving it. In radiotherapy, electrons with energies of several MeV are routinely used, and proton therapy uses particles with energies of several hundred MeV and above.

TL;DR: Three billion electron volts (3 GeV) per particle? Perfectly cromulent.

WRT Firefly's terraforming, I'd have to question its validity based simply on the fact that we don't know how extensive the terraforming really was or how much work they had to do to the planets (for all we know, the planets are mostly almost Earth-like and needed only some adjustments to make them livable). Let alone their actual tech base; we get the barest glimpse of the technology of the setting, and that through the eyes of a band of penniless outlaws working on the outer fringes of society - and they still have access to an engine capable of generating nuclear-grade explosions and engage in Casual Interplanetary Travel. I'd say we have too little information to reach a conclusion at this point.

As for why they didn't repair Earth, the specific phrasing used was that it was "used up" which indicates that most of the natural resources were expended already, so there's no point to repairing the atmospheric damage anyway.

About the Star Trek ships blowing up: isn't it very difficult to get matter and antimatter to combine in the specific manner required to cause the amount of destruction that's being described? You need to time the combinations fairly precisely, otherwise only the outermost antimatter will contact the matter, causing an explosion that will cause the matter and antimatter to scatter or be destroyed. They'll cause a big explosion, no doubt, but you can't assume every single molecule will interact.

I added a bit in the "Star Wars" tab under "Unitless Numbers", explaining that the figures regarding quintillions of droids were inflated in-universe and weren't just made up by the authors. Now, since I'm replying to other observations about droid numbers, I didn't want to delete them wholesale...but since those observations are inaccurate, is it OK to delete them?

• The Doctor Who episode "42" shows a ship falling into sun, starting only 42 minutes from hitting the sun. However, even at less than minute before hitting, the sun still has a distinct curvature!
  • Maybe they were falling really really fast.
  • The gravity on the surface of the Sun is about 100 g, or 980 m/s^2. Since the Sun's atmosphere is very thin, there is little resistance to slow your descent. Starting from rest, the altitude required to take one minute to hit the surface is over 3,000 km. This is about the same fraction of the Sun's radius as being 30 km over the surface of the Earth.

• In Doctor Who, the Slitheen scheme to use the world's stockpiled nuclear weapons to "reduce the planet to molten slag". In fact, the Earth gets more energy from the sun every hour than this. The effect would be tens of thousands of places reduced to slag and most of the planet unharmed, except by fallout.
  • Even worse than this is the episode "Journey's End" (season 4 spoiler), where 25 strategically placed nuclear bombs are meant to be enough to destroy the entire planet.
    • It would seem that nuclear technology in Doctor Who is meant to be that ridiculously powerful. May I direct you to the old series "Z-bomb", a UNIT bomb that destroyed the earth-like planet of Mondas.
    • In any case, each nuclear bomb would have had to have a yield of approximately 2,365,667,200,000,000 megatons, or 47,313,344,000,000 times more power than the largest nuclear bomb ever built. Assuming a fusion-type warhead, each of those bombs would probably weigh about 1,277,460,288,000,000,000 kg, much more massive than the asteroid theorized to have caused the extinction of the dinosaurs. Such a warhead, strategically placed, would be extremely difficult not to notice as it could be as much as three hundred miles across.
    • For that matter, the Dominators nearly manage to blow Dulkis up with a small, hand-held bomb, and Stahlman manages to reduce the Mirrorverse Earth to molten slag just by drilling into it in the wrong place. It would seem that in the Whoniverse, planets are Made Of Explodium.

...these are complete messes. Someone simplify them down?

Some of the examples in Literature are not from science fiction and have nothing to do with outer space at all.

• Unit numbers also fluctuated wildly between the series. The original series said there were only 12 Constitution-class ships, and showed little evidence of any others on Starfleet's possession; in The Next Generation there were intially only six Galaxy-class ships built, with another six on order, and a loss of 39 vessels against the Borg at Wolf 359 was apparently a total catastrophe that crippled Starfleet. By Deep Space Nine, the Federation was regularly committing as many as six hundred ships at a time to individual battles with the Dominion; and in response to questions about the unexpectedly-high registry numbers of Voyager and Defiant, Ronald Moore went on record as saying that Starfleet probably had at least thirty thousand ships.

Both the Constitution and the Galaxy were newly created top of the line ships during their perspective shows. While we don't see many other ship types in The Original Series, we do see plenty of other ships in The Next Generation.

As for the Borg attack crippling Starfleet, Commander Shelby also said that they would be able to get the fleet up in less than a year. That would suggest they can build at least 40 ships per year. You also have to take into account of how little time they had to prepare for the Borg attack. Considering how ships in Star Trek can only travel about a few light years per day at maximum warp, and Starfleet was more focused on exploration during this time, the ships gathered at Wolf 359 should only account for a small fraction of the entire fleet.

When the Dominion threat was revealed, Starfleet could have pulled back the ships that were sent on missions of exploration and diplomacy and gathered them closer to the wormhole. They could have also repaired and upgraded decommissioned ships.

No you absolutely can't. Not when tank-sized pieces of rock or metal structures far larger than the attacking ships themselves are blown to superheated shrapnel by fighter-scale weapons,

Watch the scene where the X-Wing does that, you'll notice the fighter produces a lot of sparks but no actual damage until that last couple of hits. Combined with the numerous shots where fighters don't produce nearly that much damage (see Anakin firing inside the TF battlecruiser here, the TIE fighter strafe here, and the Deflection Tower gangbang here, which took like a dozen shots before it blew up), and add the ANH novelization mentioning secondary explosions, Luke might have simply hit (and was shooting at) a vulnerable target that exploded more violently than he was expecting).

asteroids dozens of meters in diameters are completely vaporized by point-defense guns,

We've seen much higher rates of fire on Star Destroyers, including prequel era ships, suggesting those weren't the point defence weapons (especially since an asteroid managed to get through), and considering the yields stated, the fact that at least three Star Destroyers (including a Super Star Destroyer) couldn't shoot down one measly asteroid before it blew off the con tower of an ISD suggests more than simple self-imposed limitations. Also, what proof do you have that those were the Point Defence weapons? They have pretty bad rates of fire, bad spread, and if we're using the size of the bolt as a measuring stick, I'd like to remind you that author that proposes these figures also argues for invisible lightspeed Turbolasers, and the bolts we see are merely the equivalent of tracer rounds. If that's the case, then the size of the bolt is irrelevant to determining the kind of bolt it is. So if the bolts we see are merely tracer rounds and the damage precedes the bolt by a substantial margin, then the visible part of my anti-fighter bolt could be three times the size of my capital ship, and the visible part of my anti-capital ship bolt could be smaller than my fist, it makes no difference because the visible bolt has no destructive yield (at least compared to the actual weapon). Also, he based these "invisible light speed Turbolasers" on exactly one scene (see where the Star Destroyer is blasting the asteroids), where the destruction is a few frames before the bolt hits it, for a single asteroid. He uses this to deduce that all bolts are like that. It's that kind of "the exception is actually the rule and the rule is actually the exception" that he seems to base all his movie-based calculations on

above-mentioned secondary batteries of Inivisible Hand tear hundred-meter craters in the heavily armored hull of a Republican star destroyer

Funny, I see some clones not getting instantly mulched by those shots, and those don't exactly look like hundred meter craters, seeing as that would represent almost a tenth of the ship's length per crater. Also, if by "secondary", you mean "weaker", where's your proof for that?

(and hulls of SW ships are made from tougher materials than any we can imagine, as not only the fore half of Inivisible Hand survived a barely controllable atmosphere reentry, various apparenrly unarmored protrusions on it - including the bridge where the characters were - survived as well),

True they can take decent punishment, but the underside of the Invisible Hand got crushed under its own weight and needed fireships to not get completely screwed over, so it seems they aren't made of the indestructanium that some people like to throw around.

and so on. Heck, even SW ground artillery managed to carve up a landing pod over a kilometer in diameter, far bigger than any warship or arificial structure on Earth, like a watermelon. There are ample examples of firepower in kilotons and megatons range on screen and it is not possible to ignore them.

S-PHATs are some of the heaviest guns in Star Wars. You'll notice one of them breaking a ship in two in a single shot in ROTS, something no other weapon in Star Wars managed to accomplish, short of a Death Star. That's like saying "Heck, even ground based weapons were able to take out a Star Destroyer", when talking about the massive planetary Ion Cannon at Hoth. Also, that's not carving it like a melon. That's more like Julius Caesar getting ganged up by his former allies (yeah the ship got brought down, but it's not exactly the kind of dismemberment that you're describing).

If at times demonstrated firepower is lower, this means weapons in question were not firing on their maximum settings or generally were of inferior quality.

There's a difference between inferior quality and sending stuff against something that outclasses you by several orders of magnitude. What exactly was the point in lowering their shields and weapons in the Hoth asteroid belt to the point that they would feel threatened and suffer damage? The Imperials were feeling nice and wanted to give the asteroids a fighting chance? Or Anakin turning down his weapons (including his torpedoes) inside the TF Battleship? That would have been a golden opportunity to do as much damage as possible (unless we're subscribing to the "send things millions of times less effective than the enemy and not do anything approach").

If there not much waste heat, then the local Applied Phlebotinum can efficiently deal with it now (and by the way, IIRC 4.8 megatons is the yield of the Invisible Hand's ion cannons).

It says "Point-defence ion cannon delivers as much heat per shot as a 4.8 megaton bomb". Considering that an ion weapon is supposed to ionize (read: disable) the target, not melt it, I would assume that was waste heat. And 4.8 Megatons is about a thousand times as potent as the ships they're meant to disable. What's the point in having point defence weapons that are meant to disable ships, if all they're going to do is vaporize them?

Oh, and in movies fighters never manage as much as scratch a capital ship, unless its shields are taken down by other capital ships before. The Naboo squadron explicitly failed to dent the deflector shield on the Trade Federation's carrier, and the humongous wave of the imperial fighters in Ep.VI was entirely ineffectual.

Yes, two dozen fighters from an undermilitarized world facing off against a carrier with about 1500 escort fighters fail to do anything (except, you know, do some surface damage by crashing the enemy fighters into the ship, and Anakin blowing it the hell up), that's not exactly a resounding declaration that fighters are completely and utterly pointless against capital ships. Maybe if the Naboo had a few hundred ships they might have been able to do something). Meanwhile, in ROTJ, just about the first thing Lando ordered when facing the fighters was to "draw their fire away from the cruisers, and a few TIE fighters harassing the Medical Frigate was enough that they immediately dispatched Lando after them (please note, Lando expressly states right afterwards "only the fighters are attacking, I wonder what those Star Destroyers are waiting for", so it's not like they had capital ship support). This at the very least implies that fighters pose a decent threat when dispatched in sufficient numbers and don't have anything trying to stop them (like other fighters). Also, what's the logic in sending fighters to destroy enemy capital ships if they can't possibly take down the shields and do several million times less damage than just shooting it with a turbolaser? If the goal is to destroy the enemy capital ship, why wouldn't they just shoot it again with the capital ship guns, if the turbolasers are millions of times more powerful, and they've already shot it enough times that the shields are now breached? Don't give me any comment about disabling the ship. That's not what they were doing at Endor.

I remember Gary Sarli's take down of the sourcebooks in question. It was polite, and yet brutal, noting that the weapons (and consequently, the fuel requirements and the defences required to withstand said weapons) were at least 5 orders of magnitude greater than they needed to be, because the author in question made assumptions about the Base Delta Zero operation (which he apparently based the majority of his calculations on) that failed to take into account that it would be like 20 times as long (Caamas was rendered uninhabitable in about a day, not an hour), would have nearly 200 times as many ships (a 90 ship Force Superiority to clear out any opposition before the 100 ship System Bombard would completely destroy the planet from orbit, not a single, unsupported ISD Mark I having to do it by itself because they're not sending any support ships), and would require about 2000 times less energy (Assets of production like cities, mines, factories, arable land, droids, and people only need to be targeted, instead of the entire surface of the planet to a depth of one meter).

• There is a starfighter's stray blast vaporizing a big chunk of the Death Star hull, asteroids flash-vaporized with light turbolasers, handguns blasting walls apart... maybe an insistent man can shave off 2-3 orders of magnitude, but hardly more.

We see numerous shots of star fighters firing with less devastating effect (like inside the Trade Federation Cruiser and against the Death Star itself) and the novelization refers to secondary targets getting shot at and blowing up, and not even every shot of Luke's X-Wing produced those explosions in that very scene!

We also have seen much higher rates of fire from prequel era Star Destroyers while those flash vaporized asteroids could only get popped one at a time, and the screen was insufficient that at least one asteroid got through, suggesting those weren't the light turbolasers.

Plus, if they had the weapons' yield suggested in those books, that seemingly undamaged Star Destroyer that got wiped out by the asteroid could have easily withstood that rock or had its two buddies vaporize it long before it got close.

In "The Event", the aliens tried to release an especially nasty version of the 1918 flu virus to kill off most of the human race to "make room" for their 2.5 billion population they're going to bring from their planet which is threatened by their sun about to go boom. (About which the series writers are all over the map on what's going on.)

Make room? Ha! Wouldn't have to. Drop the lot in Alaska and nobody would even notice they were there. Or what about Texas? Texas could comfortably hold the entire current human population, with lots of room to swing a few billion cats...

The land surface area of the State of Texas, divided by the current estimated human population of Earth, equals almost 2,000 ft^2 per human. Texas, it is large.

After doing that bit of math a few years back, I've been wanting to see an author write a realistically super-populated world into a story. So here's the numbers to make it easy. :)

What would be interesting to see is a table comparing every super-pop SF story, with data on the population numbers, how high the buildings, whether or not it's total planet coverage or just the land, etc. Who came close? Who got it laughably wrong? Has any author got the numbers anywhere near right to match the descriptions in their stories? My bet is even in tales where the population is restricted to a few mega-arcologies, the buildings are still usually too large for the depicted population densities.

The total surface area of Earth could be divided into 2,745,191,623,680 – 2,000 ft^2 parcels, using this 196,940,400 I found for miles^2 for Earth's total surface area. Make that several trillion packed elbow to elbow in a multi-story building that covers an entire Earth sized planet. Even if necessary hallways, HVAC, water, sewer etc services uses half the space and cuts it down to 1,000 ft^2 per human, the 2,745,191,623,680 number is still the two-trillion pound gorilla in the room, and every individual still has plenty of space to rattle around in.

Science fiction authors have vastly undershot the mark, many times, in super-population dystopic tales. A 100 level building, and having to import *all* food and other resources, that just ain't plausible at all. With 1,000 ft^2 per person, that's 270 trillion, there's still gobs of elbow room, and the roof could all be covered in high density hydroponic farm.

More plausible, four story building, bottom floor all services, middle two floors living space, top floor food production. Cut the room size down to 200 ft^2 and again give 1/2 the space to etc and the pop per floor is 13,725,958,118,400 or 27,451,916,236,800 total. There we go! A mere 27.4 trillion beings in a world girdling building. Not quite 70,000 per mile^2.

The depiction of Coruscant in the Star Wars prequels, assuming that architecture is worldwide, would have to be at least double digit trillions - but the official-ish numbers are around 1 trillion permanent residents plus 2 trillion transients, tourists etc. Um, yeah, fail. Three trillion beings + mile high buildings everywhere = "poverty flat" is at least a whole floor.

Monaco's density is over 42,000 mile^2, so I suppose the 27.4T number could be within spitting distance of "packed in elbow to elbow", as long as it's kept to only two floors – but 200 square feet per person is ridiculously generous, in really dark and dingy dystopic Sci-Fi.

So please, somebody write a story about a super-packed planet with the population numbers to justify the scenario.

Um, on the explanation on how much it would cost to travel one light year. Doesn't one of Newton laws says that an object will keep moving unless otherwise acted on by another force. So if a force accelerates a spaceship to the speed of light, wouldn't it keep moving in that direction at that speed forever. You wouldn't need to spend more fuel other than the initial force to get up to speed. The car example is different as you have to constantly keep adding force in order to keep the car at the same speed because of FRICTION. Which you wouldn't have in space.

I contest the removal of the Empire Strikes Back backup hyperdrive thing, because not only were the RP Gs were introduced what, a decade after the fact, but George Lucas largely does not care about expanded universe material.

Just curious... if matter can't reach the speed of light, why even propose that a human in some mode of interstellar transport could go ten times faster...?

Kust to be clear: when I said the calculations in Irregular Webcomic were based on Coruscant being 200 times larger than it was, I was referring to its population being 200 times larger.

Most of the "unitless number examples" seem to be written on the assumption that when a number is given without units, it's an example of this trope, for no other reason. I think that's an error.

As I understand it, this trope is about numbers being massively incorrect in scale. For instance, saying that the Moon is more than ten miles away (true, but a massive understatement), or that the human population of Earth is less than a trillion (in fact it's less than 1/100th of that). If you get the size of the numbers wrong, in a big way, that's an example this trope. If you do it for numbers like population that are *unitless*, then it's a unitless number example.

"Unitless" is a technical term from physics and engineering for numbers that represent things like counts of objects, that do not require units of measure. The fact of a number being unitless isn't an error if that's the kind of number it is, and even if a number that should have units is quoted without them, that's not an example if "Sci Fi Writers Have No Sense of Scale". So: say the distance is a mile when it's a million miles, it's a distance example. Say the population is a thousand when it's a billion, it's a unitless number example. Say the time until the probe arrives is "three" without saying three what, and it doesn't belong in this trope at all.

I hesitate to just delete all the incorrect examples from the article because someone will think I'm vandalizing, but I'm noting it here in case someone else wants to make the attempt.

So, I noticed this little gem: "[...]Earth is seen with enough stars to look like a shot from Hubble."

Ignoring the fact that Hubble is never pointed towards Earth it made me curious about how much of the Earth HST would actually be able to see.

Finding a good source for the actual field-of-view of HST was a bit hard. While I'm sure it could be derived from knowing the area of the sensor, the area of the mirror and the focal length? (Or?) But calculating this would be a bit beyond my mad physics skillz... So finding a simple Fo V angle seemed much more simple.

What I found was this: http://acs.pha.jhu.edu/instrument/detectors/ which gave the Fo V for the most(?) wide angle instrument at 210 x 204 arc-seconds.

So, basic trigonometry gives us this:

Angle A == 204 arc-seconds ~= 0.05667 degrees

Height of HST (h) == 559 km

Side of area covered (x) == 2*(h*(tan A)) = 2 * (559 * tan 0.05667) ~= 1.1 km. (The '2' comes from the fact that we use a right-angled triangle and thus only get one half of the side.)

So, unless I've screwed up my math, or didn't understand the facts about HST the largest area of Earth that Hubble could picture is approx. 1 sq.km.

This is not taking either the curvature of the Earth into account, which could potentially increase the area covered minutely or the fact that from such a low orbit, even if you had the ultra wide-angle optics that would be required, you would still not be able to see more than significantly less that half the Earth. (To calculate this would require slightly less basic trigonometry, and is left as an exercise to the reader...)

1.21 gigawatts in everyday terms

I was curious (and bored and avoiding doing my laundry), so I started doing some back-of-napkin style calculations.

According to Wikipedia, gasoline contains roughly 8.89 kW*h/L (8.89 kilowatt*hours per litre).

Converting hours to seconds (8.89*60*60) yields 32004 kW*s/L.

Converting kilowatts to gigawatts yields 0.032 GW*s/L.

Again according to Wikipedia, the energy conversion efficiency of a combustion engine can vary from 10% to 50%. Let's split the difference and say 30%. That yields 0.0096 GW*s/L.

1.21 / 0.0096 = 126

So, burning 126 litres of gasoline per second in combustion engine(s) would be (very) roughly equivilent to 1.21 gigawatts.

My car gets roughly 30 MPG at a steady highway speed of 60 MPH. Google tells me 30 MPG is 12.75 litre/kilometer. Google tells me 60 miles is roughly 97 kilometers. An hour is 3600 seconds.

So, one hour at that speed (97 km / 12.75 L/km) yields 7.6 L. Per second, that is 0.002 L/s.

(There's probabbly a more direct way to get that result, but I get confused easy when juggling units.)

126 L/s / 0.002 L/s = 63000

So, 1.21 GW is (very very) roughly equivilent to the power output of 63,000 motor vehciles. I think.

More directly: Your typical hand-held hair dryer uses 1800 watts (in the US, anyway). (Why 1800? Because that's the maximum rating for a standard household outlet.) 1.21 GW / 1800 W = 672222. So roughly three-quarters-of-a-million hair dryers.

Of course, as people have nattered about on the main page, without knowing the duration of the usage, just knowing 1.21 GW isn't very useful. Running a 4 watt nightlight lightbulb for a year uses a lot more energy than running my hair dryer for five seconds.

Dammit, double-posted. Anyone know how to delete posts now?

What the heck happened, where did this page go?