A Question of Scale

Finally watched Pacific Rim...and while there were any number of things wrong with this movie*, I decided to pick on what I think was the largest, that being the question of the size of the participants in the extra-worldly monster battles, I'm pretty sure that we have a problem here. The basic problem here is that you can't build things that big which move quickly. Now, I could get into a discussion of the Kaiju, as they are far and away the most ridiculous thing about Pacific Rim, but they get a pass due to the fact that they are extra-dimensional engineered beasts(read magic). The Jaeger's on the other hand were created entirely with good old fashioned Technology, just like mom used to make.

 

 That wonderful beast up above is the movie's main character Gipsy Danger. Unfortunately, many of the technical aspects of her construction were left out of the movie, and have not been subsequently released, but there are a few things that we do know. First off, she stands a towering 79 meters tall, which is about the same as the length of a Boeing 747-400. This is a very tall thing, to put that into perspective, if she stood at the base of Niagara falls, there would still be 28 meters of robot visible above them. Gipsy's mass was also made available to us, and she is a heavy beast, coming in at 1980 Tons of Kaiju fighting giant robot. This is almost 5 times the maximum takeoff weight of the Boeing 747-400 we listed above. The amount of energy required to move this mass is fairly staggering. This brings us to our first question, can Gipsy Danger survive a jump? This would require forces in excess of those used to propel the space shuttle, but that might be able to be accomplished for short periods of time. This is assisted by the fact that Gipsy does not jump in a ballistic manner, but fires some sort of jet out of her back in order to complete the jump. This would allow for relatively possible accelerations. But would the force applied be survivable for an object of her size? Gipsy appears to be able to reach a maximum height of 14 or so meters, assuming that the downward fall is still being slowed by her jets, we can estimate(I just am guessing, but it will give us order of magnitude) that she comes down with an acceleration of 5 m/s^2 giving her a final velocity of 12.1 Meters/Second. Not too fast, about 20 miles per hour. She then comes to rest fairly quickly in about 1 second. This gives a force of about 2*10^7 newtons. So the question is, could her legs survive that much force? It turns out we can solver this fairly easily if we make a few assumptions. First off, let's assume that Gipsy's legs are made of alloys at least as good as steel, and that they have been engineered in such a way that the forces will be applied in such a way that it compresses the steel. Steel is very strong in compression, with a yield strength of at least 500 MPa. Since we know that the force will be on the order of 2*10^7 newtons, how large of a piece of steel would you need to not deform under these circumstances? A quick trip to Wolfram alpha tells us that the steel bar would need a radius of about half the size of a medium pizza! Gipsy's legs are easily larger than this, and could therefor comfortably accommodate such a blow. Now, I know what you are thinking, what about shear forces? Well, the shear strength of steel is much lower than the compression strength, coming in at as little as 1/10th the strength, which means that if Gipsy is ever hit sideways properly, her limbs will fall off, but since that is pretty much what happened in the movie, we'll let that go.

 

The actual scale problem we have is with using the tanker as a baseball bat in the Otachi fight. If you assume that the ship is about the same length as Gipsy, you get an 80 meter ship. I ship of that length might easily mass 400 to 1000 tons(a quick wikipedia search got me these numbers) Realistically, Gipsy's arms probably could handle the strain, though I have my doubts that the ship could, but more importantly, that's like a full grown adult swinging a 50 pound hammer. Gipsy should be pivoting around this thing, not swinging it like a bat. I'm actually forced to admit that this is a bit of a nit pick, but honestly, I had to find something wrong.

 Overall, they did a shockingly good job with the forces involved with giant robot's, putting Gipsy Danger at just about the right size to be possible, but large enough to be suitably epic in scale. Giant robots fighting alien extradimensional monsters is a wonderful thing, but please don't use ships as bats, especially when you have awesome chain swords. It's silly.

Avenging Science

So, I'm sure many of you have seen the avengers. It was a fun movie, but like all superhero movies, it's not a place that you would expect to go for scientific accuracy. And you would be correct. The main thing that caught my eye, since it couldn't be explained away using either Magic or Tony Stark(see magic) was the giant flying aircraft carrier. This guy here:

That is not a particularly practical looking piece of flying equipment, and I can pretty much guarantee it's only use to is make Samuel L. Jackson look even more badass. The question though is not should you use a giant awesome flying aircraft carrier, of course you should, but is the one depicted physically possible. The first thing we need to look at is the force required to keep that in the air. As you can see in the image, the carrier has 4 ducted turbofans. I have tentatively estimated that the average speed of the air going through the fans it ~.3 times the speed of sound at sea level, or 100 meters per second. Since the mass of the carrier must be assumed to be on the order of the mass of the USS enterprise

(I'll assume 50000 tons for our purposes), we can figure out what surface area of fan is required to move that much air. The force needed to keep a 50000 ton aircraft carrier aloft is about 4.5*10^8 newtons. Now, we have to compare that to the force actually able to be produced by the ducted fans. At the speed discussed, they would produce about 6.4*10^3 newtons of force per square meter, that means you need 69740 or so square meters of area to get your lift. Or 17435 m^2 per fan. Which comes out to a radius of 75 Meters. Unfortunately, as we can see from the image, the radius of those fans is closer to 15 meters, so how fast would the air have to be moving? The answer is something like 1200 meters per second, which is significantly faster than the speed of sound. And sadly impossible. Unfortunate that we have found that this isn't really possible, but let's assume that they can generate the speed needed, how much power is required? That's relatively easy, since we know how much air we are moving at what speed. Assuming we use the larger turbines, that means moving 69740 cubic meters of air at 100 m/s. Since the energy of the air moving past the turbine in 1 second is 1/2 m*v^2, the power required would be about 1 gigawatt, or 5 times the output of the Enterprise. This is actually not terribly impossible, but if you instead assume that they are using the turbines shown, the energy goes up to an impossible 12 gigawatts. Which is unavailable to any craft of that size today. Once again a movie has shown us the impossible. But then again, it did manage to make Samuel L. Jackson look cool using a bluetooth headset, so I suppose we will have to forgive the director.

Whoops

Apparently I haven't posted to this blog in forever. Possibly longer than that in internet terms! This has been a terrible mistake. In an attempt to remedy this, I need to watch more movies with questionable science. I suspect that Avengers might be a good place to start. Wish me luck.

Bullets and Sense

Almost every action movie, animation, TV show or anything with guns in it has something wrong with it. I'm not talking about the fact that only heroes can aim, and I'm not talking about the fact that bullets don't have that much momentum. No, we have the much simpler to fix problem that automatic firearms generally don't have that many bullets!



Take, for example, the weapon pictured above. That is an FN P90. This weapon is pretty standard for military and counter terrorist forces throughout the world today, and is very popular in movies, due in large part to it's futuristic look and wide availablity. But there is a problem with how they are used, let me show you:

Carter's P90

Watch the video, and pay attention to the number of seconds she is firing on full automatic for. By my count it's about 6 seconds. But with that firearm she only has a 50 round clip, at 900 rounds per minute, the clip would be empty in 3.3 seconds! This is the problem that I'm talking about. Even in movies where they remember to reload at all, they forget that most assault rifles and sub machine guns will run out of ammunition in less than 5 seconds with full automatic fire. Just casually glancing through wikipedia, I couldn't find a single assault rifle or SMG with more than 10 seconds of continuous fire on full auto.

So remember, if your protagonists or antagonists use their weapons at full auto, they'll probably need to reload every 3-5 seconds.

Elementary Mistakes (Spoilers ahead)

I recently saw a movie in theaters that hit a bad chord with me, because it's allegedly a movie based upon reason and logic. As has likely been deduced from the title of this post, this movie was Sherlock Holmes. Although I have few complaints with the movie overall, there was one scene in which terminology was so out of place that it distracted me from the story they were trying to tell.

There was a scene where Nefarious Villain was attempting to use a wireless device to poison the British Parliament, and take over England. Although the device itself was fantastical, there was no particular reason why it wouldn't work. It should be mentioned that the device had a magnetic "anti-tamper" field, which was probably impossible to generate at the time, but we're talking about the entire technological expertise of a country being directed at it, so we'll give them the benefit of the doubt. So, what is the problem? To discover the error, we have to take a look at the year in which the movie takes place.

During the movie, there are scenes of the Tower Bridge in London clearly being constructed. Since the Tower Bridge was opened for service on June 30th of 1894, it can be safely assumed that the movie takes place, at the latest, in 1894. The problem arises from the fact that Holmes described the device used to activate the poison dispenser as a "Radio" device. The first documented use of the word radio can be tracked to 1897, and while Sherlock is quite the detective, he never claimed to be prophetic.

Getting historical details right is just like nailing the science—there are usually details that can be corrected to avoid conflicting with the facts, without harming the story-telling.

You too could be Joss Whedon

So far I've mostly harped on things in movies or video games that are bad, but it can be important to point out examples of good in science fiction as well.

There is one common issue in science fiction that is more drawn to light by the few shining examples where it was done correctly, rather than the majority of shows and movies that flagrantly ignore reality.

This issue is sound in space.

Any person can think of three or four shows where this is done incorrectly. This is usually because some high level person on the show forced them to include it because otherwise "it just doesn't seem realistic." The reason that this doesn't seem "realistic" to these executives is that they grew up in an atmosphere. In space, where there is no medium for sound to travel in, you can't hear anything. As the saying goes "In space, no one can hear you scream."

So, what are some movies and shows that did it right? First off, as was hinted at by the name of this post, Firefly. Whenever there was an outside shot of a ship that wasn't on a planet, the only sound you heard was music. This is a perfect example. It doesn't require annoying silence, and it worked quite well, dramatically.



Another example of someone doing it right, scientifically at least, was 2001: A Space Odyssey. In the extended director's cut, there was a scene where one of the crew was outside of the ship for about 10 minutes. During the whole scene, the only sounds are the hissing of air from his space suit life support system, and some communications. It made the scene feel very desolate and creepy, but it was paced a little slow.

There are ways, however, of using the silence of space for good dramatic effect. In the most recent Star Trek movie, the first battle featured some poor red-shirt getting fwooshed out of a hole in the hull of the ship. As the sad crew member transitioned from the pressurized interior of the ship to the vacuum of space, all the crazy exploding battle sounds stopped. It made for a very clear contrast, emphasizing how hectic the inside of the ship was.

Another interesting example of sound in space was the climactic explosion of the Nostromo in Alien. Although there was sound in that scene, the sound was reasonable, given the situation. A nice ballpark amount of atmosphere needed to carry sound is that on the surface of Mars (about 1% of Earth's). Using that as a benchmark, the vaporized ship would have provided an envelope of sound approximately 15 km in radius.

Finally, if external ship sounds are necessary for the story, take a page from the movie Event Horizon. The entire film took place in the upper atmosphere of Uranus. Not only are there most of the hazards and issues of being in space, but there is also some nice creepy clouds, lightning, and most importantly, sound.

It is absolutely beyond me why movie makers continue to insist that sound in space is required by audiences. There's no dramatic reason for it that couldn't be accomplished in a more realistic manner. For most scenes, an accurate portrayal would help to highlight the stark unfamiliarity of space. Hopefully more people will be like Joss in the future.

Physics: It's not a Game (Gamer)

I recently saw a movie which reminded me why I'm doing this. The movie was Gamer. This was a pretty bad movie, but the biggest problem it had was a very serious tendency to ignore the laws of physics when it comes to certain objects. Most notably amongst these was Newton's Third Law of motion, and bullets.

Newton's Third Law is a very simply stated law: For each action there is an equal and opposite reaction. What this means is that if something is pushed on, that thing will push back on the thing doing the pushing just as hard as it is being pushed on. Overall this is a very positive thing. I imagine it would be problematic if an object pushed on the ground, but it only pushed back with half of the force. The ground would be unable to support the object, and it would sink! There are other consequences of the Third Law however. The problem is, this applies to any object feeling force, including a bullet being fired out of a gun. The bullet feels a large force as it is accelerated down the barrel of the gun, this force is then transferred through the firearm to the person holding the weapon. Which brings us back to Gamer.

In Gamer, there is a scene where the main character is attempting to rescue his lady from her job. There are people chasing him, and one of these people corners him in front of a doorway. The villain fires a gun at him, and he is propelled back with enough force that he is first knocked off his feet, then destroys the door behind him. Despite his rather epic flight through the door, the man who fired the gun barely had to brace it and recovered almost instantly to grab the lady. There are all kinds of things wrong with this scene, but we'll take them one at a time.

All of the problems stem from one thing: bullets aren't very massive objects, and people are. To propel a person back a projectile requires a lot of momentum, and the only way a bullet has that kind of momentum is if it's going very very fast. Normally a bullet going very fast wouldn't be stopped by a person, but the hero was wearing body armor, so it's assumed that the bullet transferred all it's momentum to the hero. So the question is, how fast would a bullet have to be going to pack enough momentum to throw a person back. It turns out that the equation is very simple:
Mass of the bullet multiplied by the speed of the bullet has to be equal to the mass of the person and bullet together multiplied by the speed of the bullet and person together, after the impact. This can be represented by:
Mbullet*Vbullet = Mboth*Vboth
So, by filling in the rest of the variables, the speed of the bullet before it hits the hero is known. First, assume that the hero flew back at 5 meters per second, or about 11 miles per hour. Since he was knocked off his feet and through a door, this might be on the slow side, but it will work well enough for our purposes. Then assume that, being a large man, he massed about 100 kg. Next, we need a mass for the bullet. Since a NATO standard 7.62mm round masses .01kg we can take that to be a fairly close approximation of the bullet used. Solving for the speed of the bullet we get that it would have to have been going 50 kilometers per second, or 112,000 miles per hour. This number is roughly 4.5 times the speed required to shoot and object into space and have it never come back. Now, there are objects which travel at this magnitude of speed which people see all the time, they are meteors, tiny bits of rock which occasionally fall through the atmosphere. The thing is, most meteors are very small, and at these speeds even sand grain sized meteors are visible from the ground, 50-60 miles away! So, imagine something that's emitting as much light as a bright meteor, but is only several feet away. Catching on fire due to the intense heat and being blinded by the light would be larger problems than just getting shot at.

Now that the bullet speed is known, it's time to take a look at the effect this would have on the person. The problem here is that the gun had to push the bullet up to that speed, so one of two things should have happened. Either the man holding the gun should have been thrown back at the same speed that the person hit with the round was, or (and this is much more likely) the gun would be ripped from his hands and hurled back itself. If the gun massed about the same as and M16, it would have been hurled backwards at 320 miles per hour.

The worst part about all of this is that the scene could have been easily achieved without the use of the impossible bullets. An explosive device planted in the elevator would have the same effect of being surprising and knocking the protagonist back, but it wouldn't have required breaking the laws of physics to achieve. So lets leave the really high speed stuff to meteors and keep bullets in the realm of the reasonable. It's odd though, in the scene just after the one discussed, they had a very interesting Newton's Cradle, kinda like this one, only full of scantily clad women:
Odd how you can have such a good example of physics in a movie next to a complete lack of it.