# I bet he broke the sound barrier

(Spoilers for the Dark Knight Rises.)

At the end of the movie, Batman and his allies fail to stop the nuclear bomb, so he flies it out over the bay to prevent it from wiping out Gotham. People on the Internet correctly noted that this is definitely underestimating the range at which nuclear weapons can cause Bad Stuff to happen. But there definitely exists some distance such that the bomb going off at that range wouldn’t hurt anyone in Gotham to any instantly noticeable degree.

At the football scene, Dr. Scientist states that it’s a neutron bomb with a blast radius of six miles. Bane said it was a four-megaton bomb, and those numbers do not go well together. I’ll take the nuclear physicist’s word over Bane’s, and we can find out how far Batman must have gone.

I don’t fully understand why the equations I’m using are the right ones (I would have expected inverse squares instead of weird fractional exponents), but Wikipedia cited this as a source so it probably works. Anyway, for a neutron bomb (unlike most nuclear weapons) half the energy goes to radiation and does not affect the size of the blast radius. If the blast radius (in km) is (Yield/2.5kt)^.33, then a six-mile blast radius means 2410 kilotons. Double that, because half the energy is going into radiation instead of blast, and it’d take a 4.82 megaton bomb. So Bane wasn’t that far off after all.

We can determine how far Batman would have to fly it. It was obviously over six miles, or everyone watching it would have been blasted backward and very possibly killed just from the air. But it must have been even farther than that, because there were unprotected humans with a clear line of sight to the blast. When it went off, they cheered. They didn’t appear to have been covered in burns or struck blind or anything.

For a 4.8 Mt neutron bomb, the thermal radiation would hand out third degree burns within about a ten-mile radius. But the other effects of the thermal radiation reach go further than that.

The people on the bridge were all watching Batman fly the bomb away. And they were looking directly at it when it went off. (Note: Never do that.) Fortunately for them, it went off during the day instead of at night. Dilated pupils would be a bad thing. Unfortunately for them, it was a pretty clear day. A one-megaton nuke would temporarily blind people from 13 miles away. That’s for a regular nuclear weapon where 5% of the energy goes to radiation. For a neutron bomb, that number is 50%, leaving proportionately less for thermal radiation. (To make up for that, the neutron radiation is worse, but that has a smaller range anyway.)

Since a two-megaton neutron bomb would blind people from a bit over 13 miles, a 4.82-megaton one would blind people from 13√(4.82/2) miles away.  That’s a bit over 20 miles. Hopefully he flew it farther than that, but any closer and the kids in the school bus would definitely not have been cheering. So this gives us a good lower bound on his speed.

The timer on the bomb showed 1:57 when Batman attached it to his flying car. Then he kissed Catwoman and told Commissioner Gordon his not-remotely-secret-anymore identity and started the car, and by the time he took off it had been over 40 seconds. That leaves less than 77 seconds for him to fly it more than 20 miles. Apparently the Bat can fly at 935 miles an hour, which is well over the speed of sound. So I win my bet, muahaha.

Maybe there are other effects with wider reaches. Like, Gotham is probably going to have some severe fallout problems later. If there are effects that would show up on screen as soon as the bomb goes off and have a wider range than the flash blindness, Batman would have had to take the bomb even farther. But 20 miles in 77 seconds gives us a lower bound: He must have gone at least that fast.

(And it just occurred to me that I should be timing from when he passed the bridge instead of when he took off, since the bridge is where the people were. But the movie didn’t show the timer position for that, so I’ll just say it’s definitely significantly higher than 935 and use that number anyway.)

Incidentally, if he covered that much distance in that little time, then his average acceleration was 20/77*3600/77 miles per hour per second. Or 5.4 m/s^2, about half a gee. Which is much more survivable than I was expecting.
But the air resistance against the giant spherical bomb would be .5*1.225 kg/m^3*(418 m/s)^2*.47*π*.75^2 = 88.885 kiloNewtons. That’s about ten tons of force just from the air pushing back against the bomb. And the hovercraft can apparently fly at over 935 miles an hour while dragging that behind it. Too bad it got nuked, because that must be a seriously awesome machine.

# Why C-3PO is Secretly the Main Character of Star Wars

A long time ago (in internet time, not galactic time), someone challenged me to write this post. Past-me gave it up as impossible, so I’m doing it instead.

The first clue is in the fact that C-3PO keeps turning up around important people. This isn’t much of a clue; after all, diplomats and politicians are the ones who use protocol droids the most and it makes sense that the same droid would be passed around among those people. But it is important to note. It means that C-3PO knows more about what’s going on in the galaxy than nearly anyone else.

He is, after all, one of only four characters to appear in every movie. Nobody saw all the events depicted, and barely anyone was in a position to even find out about all of them. But it’s a safe bet that C-3PO is one of them. Talking to the people who just happened to be the witnesses to the plot of Star Wars is literally his job as a communicator, and nobody bothers to hold their tongue around the protocol droid. It’s like how nobody notices the mailman, except more so. But don’t just take my word for it; have an example. When Anakin and Padme were secretly married, who saw it? Nobody, not even C-3PO, said or implied it was unusual for him and R2-D2 to know highly volatile secrets.

The movie makers thought of this. They didn’t want to leave someone  around from the prequels who could tell Luke and the rest everything. So they inserted a line, “have the protocol droid memory-wiped.” We have no reason to think the order wasn’t carried out. But what’s missing is, they didn’t do the same to R2-D2. Maybe because he’s not shaped like a human so it doesn’t occur to them that he might know things. And who does C-3PO talk to more than anyone else? Clearly this is not an effective memory wipe.

Speaking of R2-D2, his continued presence is sort of surprising. Diplomats and senators might be likely to employ a protocol droid, but what possible use could they have for an astromech? It’d be like if a real-world dignitary hired a personal assistant and a full-time mechanic. Nevertheless, R2-D2 is always around wherever C-3PO is. The most likely explanation is that C-3PO is able to convince his employers to go slightly out of their way to use that particular droid. That’s not hugely significant, but it does require him to have more influence than he appeared to use in the movies (i.e., none).

So by the start of the original trilogy, the droids know what happened in the prequels. This is our first clue that there is definitely some plot going on. They could have simply told Luke or the Rebels about Darth Vader’s backstory. They could have at least informed Luke that they’ve seen the name Skywalker before. But they didn’t. They never once even say the word “Jedi” or let slip that they fought in the Clone Wars. This means that they are consciously, actively trying to keep a low profile even from the Rebels, even while they try to make sure they win. This also explains why C-3PO uses the voice he does. He has an artificial voice box; he could sound like James Earl Jones if he wanted to. He picks the least intimidating, most ignorable voice possible. Nobody notices the mailman, and they definitely don’t pay attention to a protocol droid.

And most importantly of all, C-3PO knew what would happen on Endor. There was no obvious reason for him to go there, but he never once asked “why am I going along.” A shiny and definitely not camouflaged protocol droid in the middle of a secret military operation? Something’s up. C-3PO as he was portraying himself to the Rebels would have liked nothing more than to not go to Endor, and it’s not like anyone would insist on it or even suggest it.

But when they got there, they found that someone had trained the Ewoks into a fighting force capable of interfering with stormtroopers. You didn’t think hunter-gatherers could do that on their own, did you? That’d take someone like a Clone War veteran or two. It couldn’t have been a member of the Alliance; they didn’t even know the Ewoks existed. But they have somehow set up an effective resistance. Some of the traps the Ewoks used were useful only against AT-STs, meaning they were built and invented recently. (The thing with all the logs rolling down the mountainside could knock over anything big, but the two tree trunks swinging down simultaneously would be useless against a predator or anything else capable of looking sideways.)

And what’s the first reaction of the Ewoks when they see C-3PO? They recognize him. What’s the alternative, that they start worshipping anything shiny? They must have seen plenty of Imperial machinery, but didn’t have that reaction then. And they didn’t react much to seeing R2-D2, which is also why we know it’s 3PO behind this particular plot and not R2. Well, that and the fact that R2-D2 doesn’t speak the language.

Also worth noting is that C-3PO tells Luke that it’s “against his programming to impersonate a deity.” This is an obvious lie. Luke had other things on his mind at the time, but the viewer has the time to notice that a droid’s programming is not analogous to ethics. If it were against 3PO’s programming, it wouldn’t be that he considered it wrong or unpleasant; it’d be impossible. He would no more be able to impersonate a deity than my calculator can tell me 2+3=6.

Finally, there is one detail hiding in plain sight throughout all of the original trilogy. Every time 3PO introduces himself, he calls himself “C-3PO, human cyborg relations.” As a droid built in a nine-year-old’s garage, he can only really be said to have one relation: Anakin Skywalker. And at the time of the original trilogy, Anakin Skywalker is indeed a human cyborg. C-3PO knew Darth Vader was Anakin Skywalker before George Lucas did. And now you can’t unsee it.

So obviously C-3PO is up to something involving both lying to the Rebels and saving their bacon. What is it? I wish I knew. One thing’s for certain, though. There’s a lot more to this droid than you see.

# In Which the Cucumber Gets Unconstitutionally Sentenced to Use a Sippy Cup

Note: All references to legal rules are either U.S. ones or Tennessee ones. This is because at the time that this Silly Song came out, the studio was based in Nashville. And what are the odds that there are TWO towns populated by anthropomorphic vegetables?

Bumblyburg has some really scary legal practices.

The first relevant line in that video was Larry’s, “Spilling soda’s not a crime; if it is, I’ll do time.” He’s factually wrong with that conditional, but it’s just a figure of speech. Nothing to see here.

Cue the judge.

Order! Order, in the court! I judge you the clumsy sort. By the dictates of our law I sentence you to safety straws.

Larry’s entire trial takes about thirteen seconds, counting the ominous pauses. Not cool. He never had a chance to defend himself, and he never got a lawyer or a jury or anything else like that. But the worst part is, what is he even on trial for?

Based on Larry’s figure of speech earlier, this is meant to be a criminal prosecution. He’s not suing the restaurant to prevent them from giving him the titular tableware, and this isn’t an appeal up the chain of command. (Because of course “judge” comes after “maitre d’.” Obviously.) It’s pretty clearly supposed to be a criminal trial. Especially since criminal charges are the only things that actually result in sentencing. I’m not going to say Larry’s sentence was disproportionate to his behavior, but there were some pretty severe irregularities.

Larry doesn’t have a right to a jury in this case. He only automatically gets one if the crime is punishable by six months in prison, which this isn’t. A few states do include that right for small offenses, but Tennessee is not one of them. So, despite appearances, there’s no problem with lack of jury. But there are quite a few problems, any one of which could give him a winning appeal.

Thing One: What were the charges?
Larry appears to be on trial for whether he’s going to spill. If that’s the charge, these proceedings are very questionable. Maybe we could give the Bumblyburg legal system the benefit of the doubt, and assume that a) Spilling soda is in fact a crime in this jurisdiction, and b) they were accusing him of some specific instance of spillage in the past. Or however many counts of it, based on the number of spills since the statute of limitations kicked in. But without the judge saying what he’s guilty of, this is a problem.

Thing Two: Where is the judge getting his information?
The judge just appeared out of nowhere and convicted Larry at the drop of a gavel. Perhaps the judge saw the whole thing and was convicting Larry based on his own knowledge, but that would also be an issue. A judge can never preside and act as a witness in the same case. This is so bad that it is one of the things where an appeals court can overturn the trial even if no lawyer makes an objection. (This is convenient for Larry since he didn’t get a lawyer.)

Thing Three: No lawyer.
Larry should get a lawyer. Period. It’s a criminal charge, so he’s entitled to a defense. There wasn’t a prosecutor either, so at least it went both ways, but that doesn’t exactly help. Larry is just going to accept what the judge hands down, because he doesn’t know there are rules keeping loose cannon judges like this guy in line. There are all kinds of cases about why you need a defense lawyer, what kind of lawyer, how much lawyer, and so on. No lawyer is not really an option, and we didn’t see Larry waive his right.

Thing Four: No actual evidence.
This one is a bad case of prosecutorial epic fail. They have a room full of witnesses and some written records, and they didn’t bother using any of it in the trial. So Larry never got a chance to refute it, let alone offer his own evidence. This kind of undermines the entire point of a trial, and that’s not even an exaggeration. They could have proven him guilty; there was more than enough evidence for that. But they didn’t. Fortunately, there’s another issue: Since it’s not on the record, then when Larry appeals the decision the higher court will see that the lower one used no evidence whatsoever to convict. Could they have done it any worse?

Thing Five: Improper use of character evidence.
What exactly were the facts that the judge used against Larry? None. Just “I judge you the clumsy sort.” This is using a character trait to establish conformity therewith on particular occasions. It’s saying that since he’s a clumsy kind of guy, he therefore must be guilty of spilling on whatever particular incidents he’s accused of. This is exactly how you are supposed to avoid using character evidence, and it’s that judge’s job to make sure it doesn’t get used that way. Fail. Since Larry was convicted on literally no other evidence except this, the appellate judge would have to grant the appeal for this reason, too.

Larry isn’t going to get off on a technicality; he’s going to get off on all the technicalities. Fortunately, he didn’t have to bother with the appeal because a phone call from the governor put everything right.

Thing Six: the pardon.
First of all, a stay of execution* comes from a court, not a governor. Not a hugely important mistake, considering this scans better. What governors can actually do is pardon people. This is good news for Larry; it means that not only does the punishment get cancelled (and permanently), but the crime is officially both forgiven and forgotten. If it ever comes up again, he doesn’t have a record of a prior conviction for spilling.

The down side is that this legal system is terrifying. You can just be minding your own business or trying to convince someone to do you a favor, and then BAM! A judge comes out of nowhere and convicts you for something you didn’t know was a crime. I hate it when that happens to me. The only way out is if the governor personally pardons you within the thirteen seconds it takes for the trial. He probably spends all day waiting by the phone in case he needs to undo this judge’s latest exploit.

The only way it would be worse than having the law enforced hilariously unevenly would be if they actually did apply it to everyone. Any crime of the magnitude of spilling soda or worse is automatically prosecuted and punished with no defense. The only way you can escape it is by knowing the governor. This is not a friendly legal system.

*Execution refers to execution of the sentence, not necessarily to the death penalty. Literal execution was never supposed to be on the table in this case. But then, neither was the grape juice.

Note: I flipped a coin to decide what pronouns to use for the governor, since it’s never specified in the Silly Song. It came up female. But then I realized that if VeggieTales were to have a generic political authority figure, they would cast Archibald Asparagus, Mr. Nezzer, or Madame Blueberry. Only Archibald hadn’t already been shown, so I decided he was the governor and used male pronouns.

# Falling Enterprise

SPOILER WARNING: Star Trek Into Darkness is still recent enough that I need to warn you.
SPOILER WARNING WARNING: Eventually I’ll do to these warnings what J.J. Abrams did to the colon in the title.

Picture the scene: a spaceship falls helplessly toward Earth, only to regain power at the last minute. It falls through a cloud, then ascends slowly from below it with triumphant music in the background. Or maybe it hits the ground in a crash landing and the beleaguered characters step off it accompanied by the same triumphant music. Either way, the audience cheers and nerds reach for their calculators.

In Star Trek Into Darkness, there was one throwaway line saying how far from Earth the Enterprise was before they started falling. I’m pretty sure it ended in “hundred thousand kilometers,” but it could be any number of hundreds of thousands. If anyone knows, I’ll update the math; if not I’ll wait until the next time I see the movie. EDIT: Bad Astronomy says it was 237,000 (which doesn’t end in “hundred thousand” when spoken), and that this number is probably a mistake.

But it’s canonical now, so we’re stuck with it. On the up side, now that we have the information we need the math is solvable . The distance is stated (237,000 km), and gravitation is pretty well understood. F=GMm/r^2, and F=ma, so the acceleration of the falling ship is GM/r^2.

G=6.67×10^-11, M=5.97×10^24. Hopefully, anyone in charge of piloting a starship is at least marginally familiar with those numbers. We can plug those in and we get that, at any given time, the Enterprise is accelerating by (3.985×1014)/r^2 meters per second per second, where r is its distance from the center of the Earth.

Normally, the acceleration due to gravity is a constant; the famous 9.81 m/s^2. That’s what you get if you plug in the radius of Earth (about 6,371,000 m) for r, since most of the falling things we care about are at or near the surface. So their distance from the center of the earth before and after the fall is pretty much the same, and it’s OK to round them off to the same number and say that g=9.81.

In this case, the Enterprise is falling 237,000 km, which actually is a lot compared to the 6,370 km radius of Earth. So we don’t get to treat the acceleration due to gravity as a constant. It’ll start off slow, because the gravity pulls weaker on the ship when it’s farther away, and get gradually faster toward the 9.81 number that we all know and love. (Yes, it won’t ever actually be accelerating that fast because that only happens at the surface and by that point there’s air resistance, but really? Air resistance? We can ignore that.)

Unfortunately, I did not have any idea how to set up that equation. I think I used to, and there’s definitely some way to do it using integrals, but I couldn’t manage it. If anyone wants to, your solution will be more precise and elegant than mine.

What I did instead was try to estimate it. First approximation: pretend it was falling at the same speed as things fall at the Earth’s surface. Since we know it’s falling slower, it’ll take at least that long to reach the surface. With acceleration of 9.81 m/s^2 and h=237,000,000 m, it takes √((2.37×10^8)/9.81)=4915 seconds to hit the surface. That’s eighty-two minutes, or about an hour twenty: way longer than what it seemed to be in the movie, but potentially short enough to maintain dramatic tension. We don’t know how long that character was in that place doing that thing. But remember, this was an absolute minimum.

Second approximation: Think of it in two halves. For the first 118,000 km, use the acceleration due to gravity that the Enterprise will be experiencing when it reaches the halfway point. For the second 118,000 km, use the surface gravity. At 124,000,000 meters from the center of the Earth*, the acceleration due to gravity is 0.02592 meters per square second. At that much acceleration, it would take √(124,000,000/.02592)=69160 seconds, or nineteen hours twelve minutes. But that’s just to get halfway. The second half will be quicker, though. At Earth surface gravity, a=g=9.81 m/s^2, which is way bigger than the .0259 from earlier. And the ship is already moving in a downwardlyish direction at 0.02592/s^2 x 69160 = 1793 m/s.

With initial velocity of 1793 m/s and acceleration of 9.81 m/s^2, it would take 3378 seconds, or about 56 minutes, to travel the final 118,000,000 meters and reach the surface. When hitting the surface, it would be traveling at a pulverizing 34,930 m/s, which is over one hundred times the speed of sound.

The total time there is about twenty hours, mostly from the first half of the distance and a bit from the rest. This is plenty long enough that nobody was actually in a hurry for what they were portrayed doing. Now, the precise number is definitely going to be more than 20 hours. That number came from assuming that it’s falling faster than it actually is. For the first half, it’s too far away for gravity to give it the kind of acceleration we assumed. For the second half, as soon as it was close enough to get the accelerate we had already been crediting it with, we increased the amount we assumed. So we know it’s over six hours.

The same thing works for finding an upper bound. For that, we just assume an acceleration that we know is lower than the true one. One good candidate for that is the starting value of G*M/r^2 where r is the starting distance from Earth’s center, or 243,000,000 m. That gives an acceleration of only 0.00675 m/s^2, which would take it 132200 s = a day and a half to fall half the distance to Earth. If we then switch acceleration values to the actual acceleration at 118,000,000m from the surface, we get a=0.02592 m/s^2 with an initial velocity of 892 m/s. It takes them 52484= 14.5 hours. The total in this estimate is 50 hours, and it’s moving at 2245 m/s. The real answer will take less time and be moving faster.

(This was basically a Riemann sum with n=2. You see why I wish I had figured out how to set up the integral, and I’m still feeling stupid for not managing it. This could have all been done as one problem and ended up with a better answer.)

So, the time it takes is somewhere between twenty hours and fifty, and at the end it’s moving somewhere between 6.5 and 100 times the speed of sound. Bad news on the way-too-long-for-dramatic-tension front and worse news on the not-killing-everybody front.

Wikipedia tells me that the Enterprise (NCC 1701-E where this one was A, but it should be close) has a mass of 3,250,000,000 kg. This would of course result in the Enterprise being annihilated on reentry, so it was handwaved by Scotty getting the shields running in the nick of time, or something. Plugging in that mass for an asteroid, I’m told** that the impact would blast a crater 4.5 miles deep and twelve across. This would  also kill the main cast.

Now, you might be thinking that I assumed the spaceship was at rest relative to the Earth when it started falling. I did. But if it didn’t, then it would either be moving toward the Earth and fall even faster and more fatally, or it would be moving away from the Earth and still end up crashing even harder. It’d just take longer for Earth’s gravity to turn it around, and then it’d be dropping from higher. Assuming that the ship isn’t moving relative to Earth is actually the nicest thing I could do. As for the true answer, well, it had come out of warp without getting a chance to move, so whatever the velocity is when it drops into normal space, that’s how fast it was moving.

Now let’s look at what would have to happen in order to save the Enterprise and the day.

Obviously if they’re going to turn it around it has to be at the last minute, for the same reason that all timers must be showing 0:01 when their bomb is disarmed. It has to be in Earth’s atmosphere, because otherwise it isn’t recognizably a Close Call.

So that means the turnaround has to happen within, say, 100 km from the surface. Any more and it happens in Space, which isn’t as excitingly last-minute. It’d probably be lower, but this gives us a good maximum altitude. The problem is that it would cover the distance from space to surface in less than ten seconds. (Probably a lot less, but that Purdue site says that 11 km/s is the minimum for objects freefalling from outside Earth, so let’s use that.) It’s got to decelerate from 11,000m/s to 0 in ten seconds

That kind of sudden stop, at 1100 m/s per second, is extremely unsurvivable. Everyone on the ship would be instantly transmogrified into a bloody pulp smeared across what used to be the floor, assuming the floor doesn’t collapse when the weight of literally every part of the ship increases by a factor of 112.1. Fortunately, it’s established that Star Trek ships have “inertial compensators,” which, well, compensate for inertia. We know this because of the lack of frequent transmogrifications into bloody pulp. So we can assume that machinery was working and the people in the ship were in no danger from a deceleration several times worse than ramming your car into a wall.

No, I’m more concerned with the effects on the Earth. The ship has a minimum of 3,250,000,000kg*1100m/s=3.575*10^12 kg*m/s of momentum. That’s three and a half trillion. Trillion, with a T. And the ship isn’t stopping by some magic futuristic technology; they specifically say that they’re using thrusters. In other words, rockets. Sure, they use deuterium fusion reactors instead of combustion to power those rockets, but they’re ultimately working by good old opposite reaction. So they have to blast out a lot of mass really fast to take care of that momentum. If the exhaust is moving at 3×10^8 m/s, which you may recognize as THE SPEED OF LIGHT, then they’d still need to be blasting down more than ten (metric) tons of helium per second at relativistic speeds.***

Since this is taking place in Earth’s atmosphere, it would be a ten-second explosion bigger than anything you want to be around. Helium is usually not very scary, but in this case it’s tons of plasma blasting down at you at a significant fraction of the speed of light, followed shortly by the world’s biggest sonic boom for good measure. It won’t be anywhere near planet-destroying, but it’d still be incredibly destructive. And the Enterprise is definitely not going to gently fall through a cloud and rise back up. Maybe it could avoid being obliterated by the shock wave from the helium thing, but I don’t like the survival chances of anyone standing underneath. And this is what happens if they don’t crash.

Good thing there isn’t an even bigger ship crash-landing at the same time and aiming to cause as much damage as possible. That would suck.

*”distance from Earth” usually means distance from the surface. So I added 6000km in some of the calculations to approximate the Earth’s radius because sometimes the number is measured from the center.

**OK, so this is kind of an extreme case and I don’t know if the Purdue people set it up to be able to handle this. Especially since, to simulate the ship not breaking up in the atmosphere, I told the asteroid calculator a diameter of 1m and an incredible density. 6207042780 kg/m^3, to be exact, since a sphere of that size and density ends up with the mass of the Enterprise. Anyway, accuracy of this simulation is not guaranteed but the point is that ouch.

***Not really. This is using Newtonian math because I don’t feel like doing relativity calculations right now, but the total momentum of all that helium will still be 3.575 trillion N*s. The speed and mass there are definitely going to be big numbers. It would be a very good idea to be somewhere else.

# Balloons!

When I was a kid, I heard about the buoyant force. Specifically, I heard that the more air/water/fluid something displaces, the more force there is pushing it upward, and if that’s more than the weight of the thing then it’ll float up. Sound right so far? Well, I interpreted that to mean that if you drop a rock off a really high cliff, it’ll eventually move enough air to make it stop falling. And the reason why there aren’t a bunch of rocks that have displaced enough air to float around must be because there isn’t a tall enough cliff on Earth. I may have tried to impart that knowledge to some impressionable younger siblings, and I may have been shot down by their inexplicable common sense in the face of revealed scientific truth. Well, that’s my embarrassing backstory for the day; on to the present.

Someone asked me how many balloons it would take to lift a house. Obviously it’s a lot more than Pixar says, but how much more? As you might expect the answer is “more balloons than you’ve ever seen,” and in fact it takes tons of balloons. Like, literal tons.

According to the masters of internal capital letters and empiricism known as the MythBusters, 3500 balloons lifts a 44-pound three-year-old. That means one balloon can lift about an eightieth of a pound, which is…not a lot. But it’s more or less right. Helium weighs 0.1785 kg/m^3, air weighs 1.225 kg/m^3, so a balloon can pull hard enough to lift 1.225-0.1785= 1.0465 kg per cubic meter of balloon.

If a normal party balloon has a diameter of ten inches, it takes up 8.58*10^-3 m^3 and can lift a 8.98*10^-3 kg mass. (That’s an order-of-magnitude estimate assuming a spherical balloon, just to see what a reasonable number looks like. It’s not supposed to be right, just close.) So one balloon would lift 0.0198 lbs, which is reasonably close to the actual number. So, balloons don’t lift very hard and it’ll take a lot of them.

It’s easy to overestimate the strength of buoyancy. Try this: If gravity were to suddenly stop affecting you, would you float away or would your clothes be heavy enough to hold you down? I tested this,* and it’s not even close. It’d be perfectly safe, except maybe in strong winds. Point is, being pushed upward by air displacement is really weak. But you knew that already because you paid close attention to those numbers.

For some reason, the Internet doesn’t always say how much fictional characters weigh. But guesses are still allowed. Carl Fredricksen is 78 years old, the median weight for men that age is about 170 lbs, so it would take over 13,500 balloons to lift him. That’s a lot more than is remotely likely, and that’s just to lift him.

Now I’m going to go out on a limb and say that his house weighs more than he does. Number: 80,000 lbs. That’s another 6.4 million balloons. Since the ratio of lifting power of the helium to mass of the helium is 1.0465 to 0.1785, that means that the balloons lifting 80,000 pounds would themselves weigh 13.6 thousand pounds. That gives them a mass of over six and three quarters tons. (Things I did not know: The ton, the 2000 lb one, is a unit of mass not weight.) To lift that house, you’d need enough helium to be two or three times heavier than your car. Good luck with that.

Google tells me that the balloons themselves also weigh a few grams, meaning it would take some extra helium to lift all that rubber. And that party balloons are often filled with a mixture of air and helium, meaning it’d take even more of them to get the same amount of lift. I’ll ignore those and just stick with the 6,400,000 number; it’s already too big.

Let’s say Carl Fredricksen’s balloon-blowing powers allow him to inflate and tie off one balloon per second. And that it takes him no time at all to set them all up to come out the chimney in perfect formation. Then that many balloons would take him six point four million seconds to prepare, otherwise known as two and a half months.

Which leads to the next question: When they dramatically came out the chimney, where were the balloons coming from? Inside the house. So when they, being balloons, were pushing upward, what stopped them? The house. If they could pull hard enough to lift the house, they should have done that as soon as he inflated them. Besides which, there obviously isn’t enough space for all those balloons in the house. The obvious answer (in case the implausible conveyance, younger sidekick, treating physics as optional, tweed, and bow tie didn’t tip you off) is that Carl is a Time Lord and the balloons were stored somewhere bigger on the inside. But that’s a bad idea both for intellectual property reasons and also because I should stop using that as the explanation for everything. More likely it’s just a suspension of disbelief thing. In this case, those balloons can apparently suspend both that and the house.

There are a few reasons why this is even harder than the 6.4 million balloons. For one thing, that represents the number it’d take to support the weight of the (empty) house. It’s not enough to both pull it upward and break it off the foundation. So he’d need a lot more balloons, and I can’t say how much of a lot more.

The other reason is that party balloons are not a good method for long-distance travel. When a balloon goes upward, it expands as the pressure around it decreases. Eventually, the pressure gets low enough that the balloon expands enough that it pops. The balloons Carl used are full even at the start, and they’re not made of anything unusually strong, so they’ll do that at a pretty low altitude. And they’re close enough together that they don’t have much room to expand. This is why actual balloonists don’t use those even though it’d be cool.**

The moral of the story is to always do the math first before doing anything like that, just in case physics decides to pay attention that day.

*This was a Noodle Incident that I will not explain except to say that in the course of testing the hypothetical question I lost my only key ring but not the keys on it. Empiricism may have unexpected side effects. Consider sticking with math, which has less.

**There is at least one person who built a replica of the house and lifted it with balloons. The main differences were that he used bigger, less tightly filled balloons than his fictional counterpart did and it was a much smaller and lighter house that was basically just a box and so it would be much less impossible and I’m just jealous.

# How to Suck at Being Evil

Welcome to the ancient and secret Order of the Sith. As the latest in a long line of apprentices and masters, it will be your task to take over and then rule this galaxy through sheer force of evil. And the Sith can tell you exactly how best to be evil.

As a certified evil person, you are free to ignore the constraints of morality and do whatever helps you regardless of what other people think. Don’t do that. Instead, make sure to always go out of your way to be evil, especially when it hurts you. How else will people know you were serious about being evil? One of your generals was foiled by the protagonists? Kill him. This will encourage his replacement to avoid doing anything ever, just in case it fails. Your apprentice got defeated? Have someone kill him and recruit that guy. Your new apprentice will know that means you’re perfectly trustworthy. You have ridiculous amounts of energy available? Put it into a planet-destroyer. Science has shown that this is the best possible use of 10^32 Joules.

Murdering billions of people simultaneously is a well-known way to make the survivors hate you. Don’t worry about that; you are completely invincible and can feel free to kill billions whenever your child misbehaves.

If your unstoppable superweapon gets stopped, you must learn from your mistake. Build another one. And of course you should include the same alleged “weakness;” you know it’s unstoppable so it’s not like there’s any extra risk. Besides, it even lets you know their battle plan in advance.

Many evil overlords recommend maintaining a public image masquerading as someone who isn’t puppy-murdering evil. They’re wrong. Straight-up informing people not to trust you can’t possibly go wrong. Then you can feel justified in doing exactly what you said you would whenever you feel like Altering The Deal.

On that note, make sure to use a suitably terrifying appellation. Every name creates a strong first impression. You want one that says not only “please don’t laugh” but also “I am one hundred percent super trustworthy definitely.” This is why all names should be obviously evil. It should be something evil-sounding, like “Darth Nefarious.”  If your name is Darth Fluffypants, nobody will be quaking in fear, and it’s obviously either quaking or laughing. There is no middle ground.

The most important thing to remember is that there are always two Sith. One master and one apprentice. Since the Sith are in possession of hoards of ancient lore, they must make sure to pass it down safely so that none of the knowledge or skill gets lost. The master teaches the apprentice everything he can before the apprentice gets around to murdering him. This guarantees that no information gets lost between generations, and also that they can always trust one another.

Since you know you and your apprentice can trust one another, feel free to do everything in your power to make him want to betray you. Torturing his long-lost son in front of his eyes might be a good start. Make sure your monologue includes talking about how you don’t need your current apprentice anymore. Since no apprentice Sith has ever turned on his master before, this is completely risk-free.

On the subject of turning on former masters, always remember that you are unbeatable. If someone who you know is more experienced tells you that you can’t win because he has the high ground, he’s wrong. Period. Like Henry Ford says, if you think you can do it you’re right, and if you think you can’t do it you’re still right. So you have to always believe that you will win, and then you’ll never wind up dismembered and on fire and left for dead by the good guys.

While trying to take over the galaxy, you need to be where all the powerful people are. If there are people known to be able to see the future or sense what people are thinking, go live next to their headquarters. They probably won’t notice anything.

Finally, you must always gloat. If you have an enemy at your mercy, make sure to gloat. Make sparks by slashing your lightsaber against the ground for no adequately explained reason. Even if he is uninjured and has superpowers, there is no possible way he could interfere.

With all these advantages you will gain from being Evil, you cannot fail to conquer the universe. By doing exactly what they did, you will succeed where the last few thousand failed!