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.

Asteroid Belt: Not as Dense as Advertised

This is a scene that is repeated over and over again in movies, books, games and any other area where science fiction has a place. Our protagonists are in a ship, it's being pursued hotly by some alien doom vessel trying to destroy them, and their only chance at escape/survival is to dive into the asteroid belt and hope that the alien pilot can't keep up with the many collisions and flying rocks! Basically, flying through a scene that looks very much like this:


This scene has one very large mistake in it: space is very, very big. There are two consequences of this; the first is that it is unlikely that one will find an entire asteroid belt that is full enough of rocks to have this scene at all, but there will be more on this later. The second consequence is that most space flight "chases" are going to be taking place with the ships light seconds apart, with the chasing ship firing, and then waiting to see if the shot hit or not. There is a small subset of people who might enjoy that type of scene, and this is the type of person who likes submarine thrillers; who waits on pins and needles to see if the shot fired hits and if the ship was detected soon enough for the enemy to get their own firing solution. But for most people, having 20 minutes of movie waiting to detect an explosion five light minutes away would be pretty boring.

The truth of the matter is, although the asteroid belt is a comparatively densely packed part of space, there just aren't that many rocks in there. The entire asteroid belt of our solar system is only 4% the mass of the Earth's moon! Even more interesting, more than half of the total mass is contained in the four largest asteroids. What this means is that a spacecraft is not very likely to find an asteroid, let alone have to dodge around one. According to Alan Stern of Space Daily, there is a less than 1 in 1,000,000,000 (billion) chance that a ballistic trajectory satellite would hit even one of them when passing through the asteroid belt. To give some perspective on the amount of rock this is, if one were to smash up all the rocky planets in the solar system and place them in the asteroid belt, there would be 10,000 times as much rock as is in the belt right now. This would only bring a ship up to a 1 in 100,000, chance of hitting something when passing through the asteroid belts, assuming that the size distribution was similar to what it is now, and that the ship doesn't dodge. So, the odds of hitting a rock in the asteroid belt with a ballistic ship are similar to the odds of throwing a rock in the ocean and randomly hitting a whale. This would seem to be an unreasonable amount of rocky material to have in a single system. Real asteroid belts are hard to tell apart from the rest of the system from the inside.

So, the moral here is that if a chase scene of this type is needed, have it be near a planet. Maybe a moon broke up, maybe they've been dragging rocks nearby for mining purposes, maybe the planet just has unusually thick rings. But having an entire asteroid belt this dense is over the top.

Dragon*Con Photos

Here are all our Dragon*Con photos and these are from our Roomate. If you got to this site because I gave you a card, try to find yourself, and have a look at my site! Science Advising will continue later this month.

Dragon*Con Awesomeness

Hello to everyone who found this site because you got a random business card at Dragon*Con. If you don't need any science advising, please feel free to check out the site and see if anything amuses you. If you do, feel free to follow the email link and contact me. Also, I am going to be posting all the pictures I took at Dragon*Con for all to look at, so if you want to see yourself in your awesome costume, come and check it out!

Awesomeness Quotient

This is sort of general advice for anybody making anything science fiction. The degree to which you can get away with something that is scientifically unsound is proportional to how much more awesome it is than what real science would allow. In other words, if you have a plot device which requires bad science to exist, take a look at what real science would allow. If your device is much, much cooler than the real science, and isn't too unreasonable, you're probably good.

This can be represented by a simple formula:

Allowability = (Plot Device Awesome - Real Science Aweseome)/ Badness of the science

What this boils down to is, if your plot device is very awesome, and your science isn't too bad go for it. If, on the other hand, your plot device is kinda underwhelming, and/or the amount of bad science required to realize it is very high, then probably come up with a different plot device.

I'll give an example of each so you can see what I'm talking about. Let's start out with the bad science that doesn't in any way contribute to the story. What we are going to use is one of the worst science movies of all time, Mission to Mars. The scene which is the most guilty of this is the scene where the astronauts are transferring from their damaged space craft to an orbiting supply ship. Tim Robbins' character overshot the supply ship and was drifting off into space. His wife sets up her suit to use half of its fuel to try to thrust out to him and save him. Right there we have our problem. If you use half your fuel to thrust away from something in space, it takes the other half to stop. What they did was allow her to thrust away from the ship and then magically stop in space for her to be able to turn around and live! Let's try running this through our equation.

(Bad plot device - Both of them die ending the movie sooner!)/Terrible Scene = Shouldn't have been used.

Now, to help us feel better, let's give an example of a really good scene. The new Star Trek movie, love it or hate it, this movie had good science. Now, if you've seen this movie, you're probably wondering what I found to pick on. I admit, I didn't find this, it was pointed out to me by the most excellent Phil Plait. There was a scene where the Enterprise was coming up out of Titan's atmosphere to to ambush the Romulans. I know what you are thinking, this scene had some great science, Titan's atmosphere was the correct color, the Saturn images looked straight out of Cassini, what's the problem? Answer, Titan's orbit is in the same plane as the rings, you wouldn't be able to see them from Titan. However, let's just run that through the equation for this scene:

(Awesome view of Saturn's rings - Not seeing Saturn's rings)/Awesome Dramatic Scene = Must include in movie.

So, as you can see, even if the science is a little bad, you can use it in movies. Just try not to make the science types out there cringe.

Iron Giants Want Science Too (Spoilers)

The other day I was watching The Iron Giant. Now, this is basically a family movie about a giant robot from space that lands on earth and is damaged so it can't remember its purpose. This movie is overall a fantasy, and it doesn't worry me too much when it does odd things like have the robot eat metal. There was one thing that was bad enough to throw me a bit, and that was when the Robot heroically saves the town from the nuclear weapon at the end. Overall, I quite liked this scene, it showed the basic insanity of what was going on, and the self sacrifice was a nice touch, and I tend to think they did a very good job with it. It does bring to light one slight misunderstanding people have about how nuclear bombs work. Unlike conventional explosives, nuclear bombs won't be set off by an impact event as was shown in the movie.

In general, there are two types of fission warheads. The first type of warhead is what's called a gun-type warhead; basically you have two slugs without enough mass to go critical, but when brought together go supercritical and you get a large explosion. This type of nuclear bomb would, in fact, detonate just as was depicted in the movie. The other type of nuclear warhead is what is called an implosion type nuclear warhead. It uses much less fissile material, and instead has a series of explosive lenses which, when detonated very precisely, cause the fissile material to compress and go supercritical producing a nuclear blast. By 1957 the United States had switched to using almost entirely compression style nuclear warheads due to the fact that they use less fissile material, and are much safer to operate. Further, I was unable to find a single instance of the United States using a gun type warhead in a nuclear missile, they were only put into gravity bombs. Crashing into the side of one would almost certainly destroy the explosive lenses and prevent a supercritical explosion.

So, what does this mean for The Iron Giant and other movies of its type? The giant might have been blown apart when it destroyed the warhead due to the small explosions of the lenses inside the warhead, but there would not have been a nuclear blast as depicted. This is, admittedly, a very minor nitpick, but it was severe enough to pull me out of the story when it happened, so I thought it was worth mentioning. The Iron Giant was an excellent movie though, and I recommend you watch it if you haven't.

Speed Racer can really really go! (Oh Spoilers!)

I recently watched the film Speed Racer by the Wachowski brothers. Imagine my surprise that I really enjoyed the film! Overall, I think that the stunning visuals and bright colors, coupled with good to excellent acting force me to give this movie a bit of a pass as far as physics goes. But there was one scene that made me wonder if, even given the magical properties of car and driver, would be possible.

The scene in question takes place during a cross country race, which Speed has engaged in so that he might help the government with some investigations. At one point during the race, Speed's car is forced off the track! Not one to be stopped by a little setback like being forced down a cliff, he drives his car back up a nearly sheer cliff face! The question is, could even the Mach 5 have been able to achieve such a feat?

The answer should be no, probably not, but that would be boring. To find this answer though, we need to know two things. One, what is the primary force driving the car, and the second, what is the maximum force output that it's capable of. The answer to both questions can be found in how the car drives around normal turns.

In the movie, they state that the speed of the vehicles driving around the track is "800 km/h." We'll assume that this is a high end as we use this number to allow us to approximate the speed at which he goes around the turns. I'll guess he's going about half his maximum speed when taking the tight hairpin turns. If we assume that the Mach 5 can take a 10 meter radius turn at about 400 km/h, which is reasonable given what we see, then what would the acceleration be to keep him in the turn? Using the equation V^2/r, you find that the centripetal acceleration would be on the order of 200g. Notwithstanding that no human could survive that level of acceleration, this would at least be possible given a car made out of unobtainium and some magical drive system. It does tell us one important thing though: the primary motive system for the car is not the motors driving the wheels, but the thruster at the back of the car. To see why this is you need only look at how tires function. Tires rely on frictional forces between themselves and the road to provide the force on the car. The equation that describes this force is mu*normal force * gravity, where the normal force is the weight of the car and mu is what is known as the coefficient of friction. To provide the 200g's required, mu would have to be equal to 200, since the highest coefficient of friction that I could find was gecko feet, at 8, we can safely assume that this number is ridiculous. Now that we have all this, we can discuss the mountain climb.

We can see clearly in this scene that the mountain is not a sheer cliff, so there would be some small force holding his wheels to the ice. Combined with the spikes on his tires, this might be enough grip to allow him to control his ascent. Now, given that the nominal acceleration of the Mach 5 is 200g, minus 1g of gravity, he can not only drive up the cliff, but drive up it at 199g. Although the overall physics of this movie is silly with respect to the car, if you give them the Mach 5, the rest is surprisingly consistent. Well done, Wachowski's.