Understanding Movie Physics Final Project: Captain America and Bucky's Helicopter (Captain America: Civil War)

Tug-of-War:

Captain America vs. Bucky and his Helicopter

Captain America: Civil War is an amazing movie that follows Cap on his journey to find and redeem his friend and stop a master mind from unleashing evil on the world, even if his own allies stand in his way. Ranging from topics such as psychological areas like brain washing to the realm of international politics, Civil War touches on many subjects that make a great movie. In our case, we will be studying the physics of the movie, specifically Cap's 'tug-of-war' scene with Bucky's helicopter.

In this scene, Cap is giving chase to Bucky as he is trying to escape. To make his getaway, the Winter Soldier jumps into a nearby helicopter and starts to take off; however, Cap is right behind him and jumps onto the leg of the helicopter, preventing it from escaping. Without anything to really keep him grounded, Cap is dragged to the edge of the building by the helicopter as Bucky is trying to get him off. Before being dragged all the way off, Captain America is able to grab onto a railing on the edge of the roof with one of his hands while still holding onto the helicopter and effectively stops Bucky from being able to escape, as he is able to hold back the massive force of the helicopter.

Just by looking at the scene, this action seems to be an amazing  feat for any man to accomplish, but just exactly how amazing of a feat is it? Let's see.

Our goal here is going to be to find the total amount of force Cap is applying to the helicopter to be able to hold it back. Posted below is a diagram of where each directional force is being applied in the scene: 

In the scene, we notice that the net force of the interaction is zero, as neither of the objects are moving or accelerating. This means that the net force of the interaction in both the x and y directions are zero as well. 

For the x-direction, this can be described as the force of Captain America (Fcx) and the thrust (Tx) cancelling each other out to equal zero (Fcx - Tx = 0), as they are both the same value (Fcx = Tx) but in opposite directions, which would indeed cancel out any movement in any x-direction as seen in the clip above. For the y-direction, it would be described as Cap's force(Fcy), the thrust of the helicopter (Ty), and the helicopter's weight (W), all cancelling each other out to equal zero (Fcy - Ty - W = 0).

In order to move ahead, we are going to have to estimate some values. For the thrust of the helicopter, we are going to assume that the helicopter has a weight of 12,000 lbs/5,443 kg which defines it as a "light helicopter" (a helicopter with a weight of 12,000 lbs or less), which possesses around 53,378 N of thrust power at the max weight. The helicopter in the movie seems to resemble many other types of light helicopters in size, so its safe to assume that it is has a similar weight and thrust values. Some trigonometry is also going to be used, so we are going to assume that, by looking at the scene, the helicopter is trying to move away from Cap at a 225 degree angle and the angle that Cap is pulling down on the helicopter is -45 degrees. 

In order to calculate the thrust in the x-direction, we must do some trig and multiply the total thrust by the cosine of the angle at which the helicopter is moving toward, that being 225 degrees, and we get a total of  -37,744 N. With the new Tx value, we can now actually find the total force of Captain America with a little shortcut thanks to the help of algebra. As stated before we know that Fcx = Tx and since we can figure out Fcx much the same as we did Tx by multiplying the total force of Captain America (Fc) by the cosine of the angle of which he is pulling down (-45 degrees) we can actually make a formula that solves for Fc by setting the Fcx and Tx equations equal to each other and isolating Fc. Worked out below: 

• After some calculations, we find that Cap is actually pulling on the helicopter with the exact same amount of force that the the helicopter itself is exerting! A total of 53,378 N which is equivalent to about 12,000 lbs of force! To put this into perspective, the highest world record of weight lifting was a total of 582 lbs lifted by a Russian man named Alexey Lochev. Cap topped this record by ALMOST 2000%! HOLY CRAP! Another way to look at it is that it takes about 4,000 N of force to break a human femur, and Cap applied about 13 times that amount in this scenario. It's amazing that he's not instantly killing every one his opponents that he fights with one punch. If it was in real life, then he certainly would be. Seems like Cap should be in the run for the title "Strongest Avenger," no?