# Could Captain America Jump Without a Parachute?

I am moderately pumped up about the next Captain America movie: The Winter Soldier. The above clip is pretty exciting. It shows Cap jumping out of an aircraft without a parachute and then landing in water. Clearly this isn’t something I would do – but is it possible? Remember that Captain America’s super power is that he basically the strongest a human can be. He doesn’t have superhuman strength.

## How Fast Did He Hit the Water?

After Cap jumps out of the aircraft he is in a standard free fall position that skydivers use. In this position he will quickly reach terminal speed where the air resistance force pushing up has the same magnitude as the gravitational force pulling down. I always use a normal skydiver that has a terminal speed of around 120 mph (53.6 m/s) for this position. So, let’s just say that is how fast he is falling.

But wait! At the end of his free fall, he changes his position such that he is traveling feet first to hit the water.

Captain America in sky diving position and feet down position.

In this second position, his cross sectional area decreases which will make the air resistance force lower. This means that he will once again accelerate. Instead of estimating both the stand up cross sectional area as well as the drag coefficient, I will just use this site which estimates the stand up terminal speed at about 170 mph (76 m/s).

But would he have time to reach this new terminal speed? Let’s say that he starts at 53.6 m/s and then goes into the stand up position. My rough estimate from the video is that he was in this position for about 4 seconds before hitting the water.

If he were at stand up terminal speed, then the following would be true:

Since I know this terminal speed, I can solve for the product of ρAC (ρ is the density of air). There is one thing I need – the mass of Captain America. I am going to go with 90 kg. That means that the coefficients would be:

Now I can use this to model the speed of Cap after he changes position. Since the air resistance force depends on his velocity, the easiest method will be to just make a numerical model to calculate his speed during these 4 seconds.

This puts his water hitting speed at 67.2 m/s. Oh, yes – he did do that little flip in between but I ignored that. He was just showing off.

## Slowing Down In Water

Now comes the water part. This is pretty tough to estimate. The interaction between a body moving very fast and water isn’t really as a sky diving person. However, I am going to give this my best shot. Actually, I was going to start with some analysis of high divers jumping into a pool. I started to look at this fairly awesome high speed underwater video. It shows a diver going into the water, but I couldn’t get enough usable data to find the acceleration. So, I’ll just make a rough estimate.

I will use the same model for drag that I used in the air except that water has a much higher density (1.2 kg/m3 for air and 1000 kg/m3 for water). If I assume the drag coefficient and the cross sectional area for Captain America is the same both in the air and the water, then I get an AC product of 0.255 m2 (based on the stand up terminal velocity).

I will just ignore the messy part where he is part way in the water and part way in the air. Now I can go back to my numerical model and just change the density. Here is a plot of speed vs. time after he enters the water at 67.2 m/s.

I only plotted his speed until he slowed to 5 m/s. Really, it’s just the initial acceleration that I am looking at. Anyway, I just realized I ignored the buoyancy force. I think that’s ok since this is just an estimate and the buoyancy force probably wouldn’t be the normal model with all those bubbles and stuff.

Looking at the motion during the first 0.01 seconds, Cap starts with a speed of 67.2 m/s and ends with a speed of 34.2 m/s. Using a time interval of 0.01 seconds, this gives an average acceleration of 3300 m/s2 or 337 g’s. Is that too much? According to Wikipedia’s entry on G-force tolerance, humans can survive 100 g’s for very short time intervals. This is indeed a short interval, but quite higher than 100 g’s. I guess I should add that the highest recorded g-force survival was 214 g’s.

But remember – this is Captain America.

Maybe I should add some preemptive comments (haven’t done that in a while).

• This is dumb.  You are wasting your time and my time.  Who cares if he could survive the jump, he clearly did.  It’s just a movie.  Seriously, stop wasting my time.
• I think your estimate of the drag forces on Cap while in the water are totally wrong. (I think you might be right)
• Captain America isn’t just a peak fitness human.  He is awesome.
• Why didn’t you calculate how deep he would go? (I did – but my model only said around 2.5 meters and that didn’t seem very impressive)
• Batman is cooler than Captain America.
• It would be cool to explore the forces on a real actual person jumping in the water.  Maybe I will get a high speed underwater camera and set it up on an underwater tripod (with a length scale visible) to get good data. (Yes, please)
• The MythBusters already looked at this when they investigated dropping a hammer into the water before a person hits (to break the surface tension).  They found it didn’t help.  (I agree)
• What if Captain America had some type of special suit that protected him during impact with the water? (I don’t think it would help.  He still has to slow down and would still have the same acceleration.  The same is true for a crashing Iron Man.)
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