The Dark Knight, the action-infused sequel to Batman Begins, dominating the box office in recent weeks, it’s clear that the revitalization of the new Batman franchise is no fantasy. In my opinion, The Dark Knight doesn’t quite come up to the level of its predecessor—its relentless action sequences left me a bit numb after a while, and the constant quick cutting in these scenes gives the audience too much to absorb all at once. Nevertheless, it’s got some very good performances (notably, the late Heath Ledger’s much acclaimed portrayal of the psychopathic Joker), an intricate plot and dramatic psychological conflict.
Meanwhile, the action sequences, and the use of technological gadgetry are on par with a James Bond movie, and
The Dark Knight provides an ample springboard to apply some Hollywood physics. There are so many chases, collisions, jumps, flights and explosions it’s easy to highlight a few of these for some exciting physical analysis. We’ll also take a look at some of the fancy gadgets and discuss the physics (or lack thereof) behind them: There’s a lot there. So let’s highlight some relevant scenes. Click
here to delve into “The Physics of Batman.”
Adam Weiner is the author of Don’t Try This at Home! The Physics of Hollywood Movies.
The Batmobile (or the Tumbler as it is called in this newest incarnation) is actually a real car, or more accurately several different cars that were built specifically as prototypes for the movie. No CGI here, not even the flames ejected from the rocket engine. All of the scenes with the Batmobile that we see in The Dark Knight were filmed using these prototypes. When the Batmobile is racing along city streets, that’s one of the “race versions” which were constructed around a stripped out NASCAR race car at a cost of about $250,000 each. These are high performance vehicles capable of accelerating to 60 mph in 5 seconds. They are each equipped with special suspension systems similar to those found in Baja racing trucks, and in order to help the car negotiate high speed turns, each rear wheel is equipped with extra brakes that can be activated separately with hand levers. Engaging the supplemental brakes on only one side provides a greater net torque on the car and a tighter turning radius compared to normal braking. The prototype is also outfitted with a rugged steel frame, which, with the aid of the suspension, allows the car to execute 30-foot jumps without crumpling on impact. And it attains a top speed over 100 mph. There is also a much less outfitted “opening version” that they use to film Batman getting in and out of the vehicle. The “jet version” is one of the race versions outfitted with propane tanks that ignite for scenes involving rocket thrust, and there is even a miniature version which they film jumping ravines and other obstacles. However, the scene in Batman Begins where he jumps through the waterfall was actually filmed using the “race version.” It really can jump!
Even outside the world of the film fantasy, this is one pretty fantastic vehicle, but what about the fictional Batmobile? It has a some features not currently found on the prototypes – missile launchers, machine guns, bullet proof armor plating, and several fully automated modes such as “loiter”, “intimidate”, and “stealth”. In addition in The Dark Knight, we are introduced to the “Batpod”—that motorcycle-like vehicle that can be ejected from the left side of the vehicle. After the car undergoes a “catastrophic failure” following a run-in with a 20-ton tractor trailer, the Batpod gets spit out for the first time into the streets of Gotham. (We’ll discuss that collision below.) Now in Batman Begins there was a brief scene where the Batmobile apparently engages a cloaking device while in “stealth” mode. The vehicle completely disappears from the view of pursuing vehicles for a few seconds after Batman pushes a button on the dashboard. It was a little disappointing that this feature didn’t appear in the sequel because as implausible as it may seem, recent research into a fascinating new class of materials called “metamaterials” suggests that this may actually eventually be feasible. These fabricated materials strangely have negative refractive indices for specific frequencies of electromagnetic radiation. When light or other frequencies of e-m radiation enter a “normal” material at an angle to the surface, the waves refract outwards at a higher angle. For a metamaterial, with its bizarre negative index of refraction, the waves are bent inward. Let’s say you have a pear sitting on a table behind a piece of metamaterial. The general idea is that unlike with normal materials (where the light coming from the pear will either be reflected off of the material or refracted outward), in metamaterials the light rays diverging from the pear with actually bend around the metamaterial and re-converge. The result is the light from the pear will_ appear_ to be travelling directly towards you. You’ll see the pear but not the obstruction in front of it! Laboratory experiments using single frequencies of microwave radiation have demonstrated this phenomenon successfully, however they don’t yet know how to make a metamaterial that will work simultaneously with multiple frequencies, or for frequencies in the visible spectrum. Even if it could be figured out, though, there is still would be a drawback: While someone outside a metamaterial Batmobile can’t see in, someone inside also can’t see out. This could make driving in traffic a problematical proposition even for Batman.
Fantastic Mr. Fox
One of the eye-popping techno wonders from the latest Batman installment involves the use of cellphones to “see” inside of buildings. When Lucius Fox plants a cellphone in Lau’s office building, the modified phone somehow creates a map of the buildings interior by using a “high frequency pulse” to create an image. Fox tells Bruce that it works just like sonar. Well to be more accurate he should have called it radar because that’s what it is. Sonar is when you reflect sound waves off of objects to determine their location. Radar is when you use electromagnetic radiation usually at microwave frequencies to do the same thing. Since cellphones emit and receive e-m radiation in the radio wave/microwave frequency range (for cellphones the frequencies are usually between about 800 and 2000 MHz) if you tried to use them as imaging devices then that’s radar. There are many different types of radar designed for different purposes including military defense, meteorological applications (the Doppler radar they use to image precipitation), police radar, geologic applications (ground penetrating radar); the list goes on. But, not surprisingly, none is capable of coming close to the level of 3-D resolution and the depth of penetration that Fox’s is able to achieve. The more layers the radiation penetrates the more it is absorbed and scattered. This makes resolving and interpreting the reflected signals extremely challenging. Nevertheless it’s an interesting idea extrapolated from existing technology and maybe with some stunningly sophisticated futuristic signal processing algorithm we can make Fox’s dream a reality.
In a morally ambiguous maneuver Bruce has created a control room which receives and records all cellphone signals from calls across the city. He uses this as a last resort to locate the rampaging Joker. Well it turns out that technology (used by emergency 911 centers) does exist which can triangulate within a 100-meter radius or less the position of a cellphone caller using overlapping signal monitors. Bruce takes this further and claims that he can triangulate the Joker’s position as long as he talks “within range of a cellphone”. This is actually another quite interesting idea, which while it may not be prohibited theoretically, would likely be extremely challenging to make work in practice. We’re not sure what Bruce means when he says “within range” but let’s examine how this might work along with some of the technical issues. At first glance we may have a major problem relating to sound energy. The energy of a sound wave falls off as the square of the distance from the source. So if you were to stand ten times further from a cellphone microphone than you normally do when you make a call, the sound energy would be one hundred times as small. If the Joker is a significant distance away from a cellphone—say 50 feet or so—it would be not only extremely difficult to pick up his voice, but anyone standing closer to the phone, like the person making the actual call would be generating thousands of times more sound energy into the microphone completely obscuring the Joker’s signal. And yet there is a fascinating (disturbing?) potential solution to this obstacle. Apparently the FBI has used a technology which can remotely activate a cellphone’s microphone and eavesdrop on nearby conversations whether or not the phone is turned on or whether or not the owner is making a call. We imagine Bruce Wayne has the resources to obtain this kind of classified surveillance technology, and all he needs to do is install the appropriate software on every cellphone in Gotham. (It’s not unlikely that the Joker and his employees at least have cellphones with them.) Now we’re getting somewhere. Finally Bruce will require a sophisticated voice processing algorithm that can single out the sound wave pattern of the Joker’s voice from the tens of thousands of voices being monitored. This is not a trivial task but speaker identification technology is still in its early stages. Who knows what might eventually be possible?
What could be better than taking a dive off of a tall building, freefalling for several seconds, and then before you hit the street extending your bat wings so that you glide safely to the ground like a flying squirrel? It’s similar to hang gliding but with a lot less complicated rigging. So why don’t your everyday thrill seekers use some form of bat wings instead of all that equipment? The answer is simple—because their arms aren’t strong enough. Let’s analyze the magnitude of forces your arms would have to be capable of exerting in order to successfully use a pair of hi-tech bat wings. We’ll take an example from The Dark Knight. When Bruce leaps from the building across from Lau’s he falls for 4 or 5 seconds before opening his wings. For a free fall of four seconds, neglecting significant air resistance, and assuming an acceleration due to gravity of 9.8 m/s2 we can calculate his velocity just before he extends his bat wings: v = v0 + at = 0 + 9.8m/s2 (4s) ≈ 40 m/s Air friction would reduce this speed somewhat, but for a fall of 4 seconds not by that much, so neglecting it is a reasonable approximation. Now if you look at the scene carefully you can see that when Batman spreads his wings he moves into a circular path and his motion goes from vertical to mostly horizontal. It is the force of air resistance (which increases dramatically when he opens his wings) that pushes him into the circle and therefore it acts as a centripetal force during that part of the motion. To hold his arms out without buckling Batman has to exert the same force back on the air (that’s Newton’s 3rd Law at work). So while he moves in his circular trajectory we can calculate the force that will be exerted on Batman’s arms. From the scene we estimate that Batman moves into a circle of radius 20 meters or so and that he has a mass of 80 kg. If his speed remains relatively constant as his direction changes we can approximate the force acting on Batman’s arms as he sweeps through the bottom of the arc. We get: F = mg + mv2/r = 80 kg (9.8 m/s + [40 m/s]2 /20 m) ≈ 7200 N or about 1600 pounds. This means that Batman has to be capable of holding 800 pounds on each of his extended arms. Imagine lying on your back on a workout room bench holding your arms out and then having about 800 pounds of weights placed on each one. Imagine what that would do to your rotator cuffs. Now tell me that Batman doesn’t have super strength. (Interestingly in a scene early in the movie he bends the barrel of a gun with his bare hand. That’s something we’re more likely to expect from Superman!) On the other hand there is a way out of this. As Fox explains in Batman Begins, those wings are made of some fantastic and unknown material that somehow has the ability to transform loose, flexible fabric to completely rigid batwings when an electric current is applied. Now this rigidity won’t do anything to help Batman’s arms, but if there are some hinges that connect the wings to the bat suit (and it is in fact these hinges that are doing the supporting rather than Batman’s arms, which he could use only to steer) then those wings might work after all!
To put it delicately, sometimes the directors in action films get just a little overzealous and feel the need to include unnecessary or flagrant violations of basic physics. While Batman does a decent job of staying close to the boundary between the absolutely impossible and the merely highly improbable (thus allowing us to entertain interesting discussions about surveillance techniques and stealth technology), it does consistently fall prey to a particular action-movie physics and physiology cliché related to sudden stops and starts. For example, recall the adrenaline-charged moment from The Dark Knight when the Batmobile collides head-on with the Joker’s tractor trailer rig. Here’s the recap: The big rig is hauling along at highway speed. Batman comes straight at it from the opposite direction at what looks to be a similar speed, smashes into the truck’s undercarriage, and drives it upwards and backwards. At first glance it looks like the scene may violate the principle of conservation of momentum, since the greater momentum of the truck should push the car backwards rather than the other way around. However, if the Batmobile’s tires maintain solid contact with the road and continue to propel the car forward during and after the collision, while the truck’s tires are lifted off of the ground, then it could be possible. Nevertheless, consider the acceleration of the truck when the Batmobile plows into it. The velocity changes from 50 mph forward to maybe 20 mph backward in a fraction of a second. Now let’s say you’re the Joker, standing in the cargo bay of the trailer. According to Newton’s First Law he should continue to move forward at a speed of 50 mph indefinitely unless acted on by an outside force. The outside force would be the front wall of the trailer. Now I don’t know about you, but how he’s able to withstand a head-on collision with the wall at a relative speed of 70 mph and continue with the rest of the movie is hard to imagine. Of course, this immunity to the effects of the large forces that result from sudden accelerations is all too common in the action genre, and we see it frequently in The Dark Knight. Have some fun looking for more bone-crushing examples when the movie comes out on DVD!
There is a stunning moment in The Dark Knight that occurs just after the head-on collision we discussed in the previous slide. Here, Batman strings one of his utility cables in front of the oncoming big rig (anchoring the cable around some lampposts). When the truck hits the wire, its forward motion is abruptly halted and the force of impact launches it into the air where it completes a full 180-degree flip, landing on its back. It’s a spicy meatball of a scene. Now it’s certainly possible to start an initially non-rotating object spinning, as long as a net torque is applied to the object. And the cable will apply a torque if it impacts the truck below its center of mass. However, the cable is going to break before it ever gets the rig spinning. Here’s why. By looking at the linear acceleration of the truck as its forward motion is brought to a halt, we can estimate the force that is exerted on it. Let’s assume that the tractor trailer has a mass of 15,000 kg, is moving initially at a speed of about 22 m/s (50 mph), and in the collision its forward motion is stopped in a tenth of a second. This gives a force of F = ma = mΔv/Δt = 15,000 kg (22m/s/0.1s) = 3,300,000 N or 742,000 pounds acting on the vehicle By Newton’s third law, that must be the same force experienced by the cable during the collision. For reference, in an episode of “Myth Busters,” a moving car rips through a steel cable like it’s made of paper. But clearly Batman’s cables are a lot better than that. Did Fox fabricate an appropriate material in the laboratory that can withstand the force? At present the highest tensile strength yet measured is that of carbon nanotubes, which can withstand a tension of 63 billion newtons (63,000,000,000) per square meter of cross-sectional area before rupturing. Wow! That sounds pretty promising, and although researchers have not been able to produce a cable made out of carbon nanotubes on a macroscopic scale, let’s assume Fox has. Unfortunately Batman’s cables don’t have a cross-sectional area of an entire square meter. They’re compact and portable and appear to have cross-sections much closer to a square centimeter, at best. 63 billion newtons per square meter converts to 63,000 N/cm2. That’s not nearly enough. So unless the R&D; department at Wayne Enterprises has come up with something truly phenomenal, Batman’s cable is going to snap, and the Joker is going to escape (assuming he survived the earlier collision with the front wall of the cargo bay).
Mr. Fox (Morgan Freeman) epitomizes one of the two typical scientist types we see represented on the big screen. These archetypical cinematic eggheads can be categorized as follows: a) “The Jack of all Trades” who, in addition to being (usually eccentrically) brilliant, is a physicist, a biologist, and an engineer all at the same time. He can build any type of complicated highly technical equipment by himself, often without any government funding; and because he works alone and rarely publishes his results no one believes him when his groundbreaking and innovative theory provides the only insight into saving the world from some final apocalyptic disaster. (If the character is female, she’s usually about 23 years old, stunningly beautiful, and an expert in martial arts.) We contrast the Jack of all Trades with: b) “The complete idiot”. This is the narrow-minded scientist with no imagination, and limited ability to see the big picture. Often it takes someone with no scientific background but with real-world experience, grit, and practical knowhow to come in and get the job done when the scientists just can’t get it right. We see a classic example of this in the movie Armageddon, where NASA scientists can’t figure out how to make a drill work. Therefore, in order to save Earth from an impending planet-destroying asteroid impact, the government decides to crew the space shuttle with a bunch of oil riggers with various endearing psychological problems in order to drill a hole in the asteroid (the right way!) and blow it up with a nuclear bomb. These guys are the only ones who can do the job because they have real-life experience, unlike those idiot scientists. Now clearly Fox falls into the first category of scientist. He seems to always work alone, brilliantly creating or modifying fantastic gadgets (a lot of the equipment has been mothballed from various classified military projects) for Batman to use as crime-fighting aids. Fox does mention the R&D; department from time to time, but where are they? When he’s not with the board of directors for Wayne Enterprises, we find Fox isolated in his giant cavernous laboratory. In Batman Begins not only does Fox handle all of the formidable engineering duties, but when Batman is exposed to an insanity-producing psychotropic drug, he demonstrates his versatility by coming up with an “antidote” within a few hours. We see variations of the Fox type of scientist pretty often in the movies; however they are essentially non-existent in real life. It’s pretty hard to get a Ph.D. or gain expertise in one single very specialized area, let alone stay up-to-date with developments in four or five unrelated disciplines. Try it if you don’t believe me.