Da Na Na Na Na Na Na... BATMAN!

December 8th, 2010

THE DARK KNIGHT: 180 DEGREE TRUCK FLIP
The seventh highest-grossing film of all time was released in 2008 in which Christopher Nolen directed a masterpiece which was nominated for eight academy awards. In the city of Gotham, the Joker is the most prominent antagonist which must be stopped by Batman in the most recently released movie about the superhero, The Dark Knight. This movie was a sequel to Batman Begins which was released in 2005.
This research paper applies a broad range of physics topics to a single scene; namely the different forces in effect in this scene, action and reaction and their effects in collisions, acceleration and its role in assessing the overall plausibility of the scene, as well as different forms of energy illustrated within the scene such as kinetic and potential energy. The particular scene that will be used in order to convey all of the above ideas is just over half way into the movie (1 hour and 18 minutes in). Filmed in downtown Chicago, Batman latches a cable onto the front of a semi truck being driven by the Joker. Batman then rides his bike swerving through numerous light posts. When the cable inevitably runs out and is knotted through numerous light posts as well as other things, the truck has nowhere to go which then causes the cab end of the truck to stop, while the trailer of the truck flips up and over the cab. This scene can be found by searching “Batman truck flip” on Youtube.com.

Einstein's Theory of Relativity is that all motion is relative to what you define as a fixed point. This is just a way of saying that different people may say different things about the motion of the same object, depending on what they perceive as the fixed point to reference the motion against. For example, in this scene Batman is riding his bike at let’s say 80kp/h, while the truck is traveling at 70kp/h. Although Batman is only traveling 80kp/h to someone else who has their fixed point set as the ground, the Batman may perceive his speed at upwards of 150kp/h, because that is how fast he is headed towards the truck. This is called relative velocity; a perceived velocity of an object in relation to a fixed point, which is most often the ground.
In order to be able to determine whether this scene is plausible, we first, we need to consider the strength of the cable used by Batman. The trucks themselves on average weigh between 16,000-20,000 lbs. The trailers (empty) add another 15,000 lbs. So the total weight for the truck and trailer would be roughly 33,000 lbs. In kilograms, this would be equal to around 15,000kg. According to the EngineeringToolbox.com website, the diameter of a steel cable which would have a safe load of 29.7kJ would need to be at least 5/8 of an inch. The minimum breaking strength in this wire would be 33,400 lbs. Therefore, the minimum diameter of the wire that would have needed to be used by Batman would have to be at least 5/8 of an inch.
With a maximum safe load figured out, it will now be possible to determine what would have happened in a real life scenario if Batman had actually latched a cable onto the front of a truck and then twined it around lamp posts. Is this scene busted, plausible or confirmed? Is the strength of the cable employed by Batman strong enough to withstand the speed of a semi truck traveling at 70kp/h and cause it to come to a complete stop within an instant? But how about the truck performing a full 180 degree flip? If the cable used was not strong enough, how strong would one actually need to be to make this scenario into something more realistic and plausible? And if it actually was able to withstand the forces it was presented with, what would actually happen to the truck if it would not flip over the way that it did?
Another notion presented in this scene of The Dark Knight is the law of inertia. Inertia is the property whereby all objects remain in motion or at rest, until acted upon by an external force. Forces that may overcome inertia are air resistance, friction, gravity, or applied forces. During this particular scene, the predominant force that stopped the truck was a (supposedly) stronger opposing force, in which the cable was being tied and knotted around numerous lamp posts among other things. Other forces which would affect the truck in a situation such as this would be the friction of the tires running against the ground, as well as the air resistance against the truck, seeing as how they are not necessarily all that aerodynamic. But regardless, one of the key points pertaining inertia would be present; objects in motion remain in motion. This would mean that although the front end of the truck may have come to a stop due to the cable, the back end of the truck would still continue moving forward.
Different forms of energy had been used in a few instances in the scene. Kinetic energy, the energy of motion, was present in both of the moving vehicles. To calculate the actual kinetic energy produced by the truck, we need its mass and velocity. Again, the trucks themselves on average weigh between 16,000-20,000 lbs, with the empty trailers adding another 15,000 lbs. So the total weight for the truck and trailer would be roughly 33,000 lbs, or equal to around 15,000kg.
The next step would be to find out the velocity of the truck. The velocity is the rate at which a given object is changing its position. Velocity measures motion in a specific direction, as opposed to acceleration which measures change in the velocity. To find out the velocity of an object in motion, we divide distance (d) by time (t).
As previously noted, we’ll assume the truck is travelling at 70km/h. For this part of the scene, we will calculate the velocity of the truck only from when Batman started heading towards it on his bike. At 1:17:52 he started towards the truck which then came to a stop at 1:18:16. So the truck was travelling for a period of 24 seconds, causing the truck to have travelled a total distance of 0.464 kilometers in that time, or 464 meters. The speed of the truck would have been equal to 19.3 meters per second.
KE = Energy (in Joules) m = mass (in kilograms) v = velocity (in meters/sec) t = time (in seconds) d = distance (in meters)
KE = (½)mv2 and v = d/t v = 464m / 24s = 19.3m/s.
KE = (½) 15,000kg x 19.3m/s
= 7,500 x 372.49 = 2,793,675 joules.
Remember, according to the EngineeringToolbox.com website, a cable with the diameter of 5/8 of an inch would be able to have a safe load of 29.7kJ and would have a minimum breaking strength of 33,400 lbs; the rough estimated weight of the truck in question. That being stated, since the cable used by Batman to would have been sufficient to put up with the amount of force needed to stop the truck, it would also therefore be strong enough to flip it over as well, seeing as how this would put less force on the cable as opposed to just stopping it.
But whether the way of flipping this truck over is actually possible depends on where its center of gravity is, as well as the comparison of the truck’s initial and final kinetic energies.
The center of mass is a point in an object in which its mass is concentrated. If the truck’s trailer’s center of mass is placed closer to the bottom front end of the truck, it would be easier for it to flip over in the way it did. Because of inertia, the back end of the trailer would continue forwards even though the front has stopped. And if the very back of the trailer was lighter than somewhere closer to the front of the truck, there is a greater likelihood of the back end of the truck lifting off the ground.
Where the Center of Mass Should Be

Acceleration(a) = velocity(v)/time(t) a = 19.3ms /24s a = .804m/s/s
Force (F) = ma
F = 15000kg x .804 = 12060 N
Assuming the truck is 13’ tall, The initial kinetic energy (in this case, the energy the truck had while moving at its full speed of 70kp/h) is equal to ½ (m)(v)2 + mghi.
(1/2)15,000 (19.3)2 + 15,000 (9.8)2 (13) = 2793675+1911000 = 4,707,675 joules.
Final kinetic energy = mghf
(15000)(9.8)(60)
= 8,820,000 joules
Basically, the possibility of this truck flipping head-over-heels seem more and unrealistic; if it were able to flip in such a way, the initial energy would need to equal, if not exceed that of the final energy. But in this case, the final energy of the truck is almost twice as much as the initial.
In conclusion, this scene in The Dark Knight is busted; Batman would not be able to latch a cable onto the front of the truck causing it to flip 180 degrees up and over its cab. Although the cable used may have been strong enough to withstand the forces exerted by the truck, the other physical properties in affect on this truck would still not enable it to defy the laws of physics. So if the cable was strong enough, how about the truck itself? Would the part of the truck that the cable had been attached to not just break under the severe forces? My hypothesis would be that it would have just broken straight off, letting the truck to keep on heading straight through downtown Chicago. The actual way this stunt was performed was not by stopping within an instant via a cable. Stunt coordinator Paul Jennings had used a piston which fired from the bottom of the truck (later edited out), giving the truck the upward lift it needed to perform a 180 degree flip. On the front end of the truck were attached “teeth” (also later edited out, of course) which dug into the ground at the front of the truck, enabling the front to stay in a position as the back end of the truck, propelled by the force from the launch of the piston, shot up straight and then over the front end. In the first picture below, you are clearly able to see the smoke from the launch of the piston.