# Is this report accurate, or how can I improve it?

Scene description

In the movie, Captain America: Civil war, we are shown a scene where the avengers are fighting each other in an airport. In this scene, we see War Machine flying away from Ant-Man. To catch him, Ant-Man grows to many times his original height in order to reach and grab War Machine by the feet, before flinging him through the air. He then kicks a bus that almost hits Vision and Black Panther.

Assuming that Mass also increases

The movie explains the Ant-Man’s ability to shrink and increase in size through the use of Pym particles. These are a rare group of subatomic particles that shrink/increase the distance between atoms to make objects bigger or smaller, however the number of atoms stays the same. By this definition, it is implied that no matter the size, the Ant-Man will always have the same mass, as he has the same number of atoms.

If this were to be true, then if Ant Man’s mass is staying the same, but his volume is shrinking or expanding, the factor that is changing is his density. Density = mass / volume = m/V). According to marvel.com, Scott Lang (Ant Man) weighs 190 lbs (86 kg) and is 6’ (1.83m) tall in his original human form. In the Ant-Man and the Wasp trailer we hear Lang bragging about how he can grow to 65 feet (19.81 m). However if his mass were to not change, this would mean his density would be 0.787 kg/m3. Since the density of air on earth is approximately 1.225 kg/m3, Ant-Man would end up floating away. This is also backed up when we see giant Ant-Man crash into a plane and make a dent, which would be impossible if his mass was only 86 kg. Therefore, is safe to assume that either this scene is inaccurate, or Pym particles somehow find a way to increase the mass of objects. However if this was the case, then multiple inaccuracies would be encountered with the square cube law.

Square cube law

The square cube law is a physics principal discovered by Galileo Galilei in 1638. It states that when any object grows in size, its surface area increases by a squared factor while the volume grows by a cubic factor. For example, if there was a cube with a dimensions of the surface area would be 6 m2, and the volume would be 1m3. However if the length of each side of the cube was doubled, the surface area would become 24 cm2, and the volume would become 8m3. Even though we only multiplied the length of the cube by 2, the surface area increased by a factor of 22, and the volume increase by a factor of 23. This essentially means that if an object is scaled up, it will have proportionally a lot more insides than outsides, and this can cause a number of problems.

Support

One important problem that Ant-Man would encounter due to the square cube law, is the effect of his drastic weight increase. A 19.81 m tall Ant-Man would weigh 109 093 kg. While this means his muscles are also growing and gaining strength, the problem is that strength only scales with area, not mass. I.e. when finding how strong a bone is, the length/volume isn’t important, as the determining factor is the width/cross sectional area. The same applies to muscle strength, so while Ant-Man is 1266 times his normal weight, he only has 117 times his normal strength. To support this additional mass, a lot of extra internal infrastructure would be necessary, and while large dinosaurs may have adapted to this, humans weren’t designed to handle this weight. Ant-Man would not be able to stand, as his bones would snap.

Mitochondria

Life on this planet is based on cells, which do vary in size, however, are similar in dimensions across all species. For example a whale wouldn’t have bigger cells than a butterfly, however it would have many more of them. Cells need energy to stay alive, and to source this, they convert food and oxygen into chemical energy. However doing this causes them to heat up, reaching 50° Celsius in human skin cells, and some cells have up to 2000 mitochondria radiating heat into the cell. This means that animals with more cells will produce more heat, and this heat can only leave an object via its surface. Giant, Ant-Man will have 1266x more cells, however only 117x more surface area for the heat to leave through. This would cause his internal organs to heat up very quickly, and since as a human he is not adapted to losing this heat, he would likely explode.

Voice

A person’s physical size also affects the frequency/pitch of their voice. However, when Ant-Man grows in size, we hardly hear a difference in his vocal range, despite his vocal tract becoming 10.83 times longer. Assuming Scott Lang has the average male vocal tract length of 0.17 m, his vocal tract length when he is big will be 1.84 m. Since the vocal tract is an open ended pipe, the wavelength () of the wave that is the fundamental frequency will be 4 times the length of the tract (see diagram.)

To find the fundamental frequency (f), we need to divide the speed of sound (c) by the wavelength. Assuming the air is a regular density and the temperature is around 20 °C, the speed of sound is 343 m/s. This would give us a fundamental frequency of 46.58 Hz. So realistically Ant Man’s voice should sound more like a low, inaudible smudge of sound.

Conclusion

As explained, there are many scientific inaccuracies in the airport scene of Captain America: Civil war. When Ant-Man grows to 65 feet, he must also increase in mass to prevent him from floating away. However then he will encounter problems with the square cube law. His weight increase would mean that Ant-Man shouldn’t be able to stand, as his bones would snap. Additionally, an increase in size would mean that Ant-Man would have many more cells, and he would realistically have exploded. Even if these 2 problems were overcome, Ant-Man’s voice should still be far lower than what we hear.