In recognition of the latest Batman installment, The Dark Knight, coming out on DVD in December, I took a look at a selection of scenes both new and old. Sometimes Batman displays a solid understanding of physics, but some sequences are enough to make any physics teacher groan.
In the world of comic-book heroes, I’ve always liked the fact that Batman doesn’t really have a super power; he uses tools and equipment to give him an advantage over his enemies. I’m not the first to examine the science behind Batman, of course; MythBusters has devoted substantial air time to testing the practicality of several of his gadgets, including the use of a cable and grappling hook to help the Batmobile make a high-speed 90-degree turn. (It doesn’t work, by the way, so don’t look for one at your neighborhood auto parts store.)
The Dark Knight picks up right where Batman Begins left off, and Christian Bale continues in the role of Bruce Wayne/Batman. Heath Ledger plays The Joker—his final film performance—and is frightfully good at portraying madness. The storyline is too complex to relate here, but involves crooked cops, the mob, moral dilemmas, and many, many explosions.
Roughly midway through the film, a reluctant potential witness has fled to Hong Kong. Batman is able to collect him by having an airplane pluck them both right out of a downtown skyscraper then reel them into the plane. My initial reaction was incredulity; I thought it was pure movie fantasy. A little research revealed, however, that the U.S. military has a system designed to pick up a single person in pretty much the same manner depicted in the movie, and it was developed more than 50 years ago. Time magazine even ran an article about it in 1964. The key to the process is spreading the force over a large part of the person’s body while keeping the force small enough to avoid causing internal injuries or making the person black out. The military system does this by using a special jumpsuit/harness and a very elastic nylon rope.
Here is one way to think about the physics: Batman has to change from being at rest to moving at the same speed as the airplane, very quickly. This is a large change in his momentum (mass × velocity). The change in momentum is equal to the product of the force causing the change times the time the force is applied:
FΔt = Δmv.
You can either exert a large force over a short time:
FΔt = Δmv
or exert a small force over a long time:
FΔt = Δmv.
Protecting Batman from injury means choosing the second option and exerting a smaller force over a longer time. The force × time quantity is known as impulse, and the impulse-momentum relationship is key to understanding collisions. Safety belts and airbags in cars are there to extend the time of a collision so that the forces on passengers are minimized. Using an elastic rope for the airlift operation means that the force on the person being picked up can be small enough that Batman will be all right. Careful observers will note that in the movie Batman was holding onto another person during the lift, so there was a correspondingly larger mass, and therefore larger force required to lift them both. I did not find any evidence of a double lift like that ever being done by the military, but it is plausible.
A recurring trick of Batman’s is to use his cape to glide around Gotham City (or Hong Kong) after dropping from a tall building. I appreciate the fact that he is not generally shown to be able to fly; he drops off a building and lands on a lower building later. He trades some of his gravitational potential energy for some kinetic energy, and he’s not able to return to his initial height, in much the same way that classic roller coasters never get back to the height of the first hill. Hang gliders are able to climb by using thermal updrafts and/or wind patterns near mountains, but their wings are much larger and lighter than Batman’s cape. All the same, to be a truly successful glider, Batman would need a bigger wing than his cape makes for him in the movies.
While the cape is a bit too small to really work, some films in the series completely abandon physics in favor of spectacular visuals. Batman and Robin is perhaps the “best” example (and is considered by some to be the low point in the film franchise). Leaving aside the acting and the less-than-inspiring dialogue, it includes some of the worst movie physics I have seen.
It begins at the very beginning: the climax of the initial battle involving Batman (George Clooney), Robin (Chris O’Donnell), and Mr. Freeze (Arnold Schwarznegger) places all three on a rocket headed skyward. Robin makes the journey on the outside of the rocket, holding on with suction cup handles even though there would tornado-strength winds acting to push him off. Inside the rocket, Freeze traps Batman with icy handcuffs, then proclaims “Can you feel it coming? The icy cold of space. When you reach 30,000 feet, your heart will freeze and beat no more.” That's about 5.7 miles up —in metric, 9 km. There are two big problems here. Most scientists consider “space” to be at least 160 km (100 miles) up. [The international space station is about 300 km (190 miles) up.] Second, while it is cold at 9 km, it’s only about -40°C, which is not cold enough to freeze Batman’s heart quickly, particularly given his thick rubber Batsuit. The lack of oxygen in the thin atmosphere at that height would be more of a problem, but that gets no mention in the movie.
Freeze exits the rocket to glide to Earth using rigid wings. Robin breaks into the rocket, cuts the icy handcuffs restraining Batman with some sort of heat gun, and both eject from the rocket standing on small surfboard-shaped doors. I addressed free fall in my review of Journey to the Center of the Earth, but here is a quick recap of the issues that come up in this scene. It takes a long time to fall to Earth from a great height. Even though terminal velocity is around 190 km per hour (120 mph), that’s “only” 3 km (2 miles) per minute. Falling 9 km (30,000 feet) would take nearly three minutes, but that makes for dull movie footage, so Robin plunges away from the rocket down to a building in just 30 seconds. That is only long enough to fall about 1.5 km (5000 feet). (Check out the free-fall research web page for more details and some amazing stories of survival.)
The science does not get any better as Batman and Robin continues, but I will leave that as an exercise for those with the time and fortitude to watch the rest of the movie.
Jacob Clark Blickenstaff is Assistant Professor of Physics and Assistant Director of the Center for Science and Mathematics Education at the University of Southern Mississippi. He can be reached at firstname.lastname@example.org.
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