I should probably stop watching movie promos and trailers. Every time a new one comes out, two things happen. First, I get just a little more pumped up about the movie (which is the point of the clip). Second, I find something with some physics in it.
In this clip, we see the Winter Soldier jump onto a road from some type of bridge. It seems a bit far for a normal human to fall and survive.
Now for an analysis.
Because he dropped on purpose, I guess it would be called a "jump," not a "fall." Does it even matter? No. What does matter is the height. Here are three methods we can use to determine the drop height.
Just guess. There's nothing wrong with guessing. Maybe I should call it "estimating" instead. When I'm dealing with heights, I like to think of stories in a building. If I use the rough guideline of 10 feet per story, then I can put some limits on this drop height. It's clearly higher than one story but probably less than four. Let's go with a height of three stories or about 30 feet (9 meters).
Using the falling time. Once Bucky (the Winter Soldier) leaves the top level and falls, there is essentially only one force on him---the gravitational force. This means he will have a vertical acceleration of -9.8 m/s2. Since I also know his starting velocity of zero meters per second (technically, that is an assumption), I can use a kinematic equation to determine the height.
Here I set both the initial velocity and the final position to zero (m/s and m, respectively). Now I just need the time it takes for the Winter Soldier to drop the distance in the clip. I can determine this by examining the number of frames in the clip between leaving and landing (using Tracker Video Analysis). This gives me a free fall time of 1.578 seconds. Putting this value into the equation, I get a drop height of 12.2 meters (40 feet). OK, I'm pretty happy with my original estimate.
Using the impact speed. There are a few frames at the end of the fall that show Bucky as he lands. The nice thing about these frames is the camera view is perpendicular to the motion of the human and the camera is stationary. If I estimate the size of Bucky at 1.8 meters, I can scale the video and get the following position-time graph for the landing.
Looking at the part just before he hits the ground, Bucky's speed looks fairly constant (it shouldn't be constant but this is over a short time interval). From the slope of this line, I get a landing speed of 6.16 m/s. Now assuming he started with an initial velocity of zero m/s, I can use this final speed along with the free fall acceleration to find the height. I'll skip most of the details of getting this equation since I went over it several times before---but here are a bunch of examples.
Putting in my final velocity of 6.16 m/s, I get a drop height of just 1.94 meters. OK, that's not a very high bridge to jump from. In fact, I suspect there will be many vehicles that wouldn't be able to fit under such a bridge.
When Bucky collides with the ground, he goes from having some downward velocity to being stopped. Since this change in velocity takes some amount of time, he has an acceleration. If the acceleration is very high, it can be quite deadly to normal humans. Just a quick note---as far as I understand, the Winter Soldier is a normal human with a bionic arm. Other than the arm, he is just a normal guy with expert skills.
There are two ways I can estimate his impact acceleration. I can use the change in velocity along with the time of impact or I could use the change in velocity with the distance over which he accelerates. Assuming a constant impact acceleration, I get the following two expressions (in 1-dimension).
In the second expression, s is the distance over which the Winter Soldier travels during the landing. Oh, in both of these cases, the final velocity will be close to zero assuming he doesn't bounce (which would require a higher acceleration).
Now I need a few measurements. From the video I can determine the stopping distance (s) and the stopping time (Δt) with values of 0.196 meters and 0.125 seconds (he didn't crouch too far on landing---odd). I also need another value for the impact velocity. Of course the video shows him traveling with a speed of just 6.16 m/s, but what if he jumped off a 12 meter high bridge? In that case, he would be going 15.4 m/s right before impact.
OK, there are plenty of combinations of starting speeds and stopping distance (or time). Let me look at two cases. First, there is lowest acceleration landing. This of course would use the lower estimate of velocity (6.16 m/s) along with the time of 0.125 seconds to give an acceleration of 49 m/s2 or 5 G's. This is a survivable landing by just about any human (even me).
For the second case, I will use the higher impact speed along with the stopping distance of 0.196 meters. This gives an landing acceleration of 605 m/s2 or 61.7 G's. This most likely is not a survivable landing for a mere mortal. It's fairly difficult to predict exact damage from high accelerations, but NASA has done its best job trying to figure this out. Here is a plot showing the maximum acceleration humans can endure.
Clearly 61 G's is just too high for a safe landing.
Then what happened? OK, I have two options to explain this landing.
- The Winter Soldier has bionic legs to match his bionic arm. This doesn't really explain everything since the rest of his body would still have a super high acceleration but it at least gives an explanation as to how his legs can stop him during that jump. Or maybe he has some other body modification that allows him to survive these high g-forces. Nobody really knows what Hydra did to him to create the ultimate assassin.
- The other option is that the Winter Solider is falling while attached to stunt wires. This means that he is in fact not in free fall during his trip and thus moving at the much lower speed of about 6 m/s. Yes, it's true. I'm not completely delusional. I know that this is just a movie but it's not my fault that I just really like physics.
OK, I should point out that the clip also shows the Black Panther and Captain America making this same jump. Captain America is technically still a human such that he probably wouldn't survive this jump either. Black Panther is more of a mystery. In the comics he has all sorts of technology, so perhaps he could survive the fall.
If you really wanted to increase your chance of surviving this fall, your best bet would be to increase the distance over which you land. One way to do this is with a Parachute Landing Fall. In the PLF you don't try to land and stand up. Instead, you roll all the way to ground to greatly increase the distance over which you stop and thus decrease the stopping acceleration. Sure, you won't land looking cool like a superhero, but maybe you will at least be alive.
https://www.youtube.com/watch?v=gyWEtvGCykQ
