# The Mathematics of Black Panther

The Mathematics of Black Panther

In 2018, I watched the excellent Marvel film Black Panther which has just broke \$1 Billion in the box office worldwide!

The film had a number of themes including the question – What if an African country, named Wakanda, lead the world in technology? The film offered a cinematic picture of this, with an important emphasis on the STEM subjects.

Now one of the most interesting characters in the film is Shuri.  Wikipedia describes the her character like this

Shuri the princess of Wakanda, designs new technology for the country. She has “an innovative spirit and an innovative mind” who “wants to take Wakanda to a new place.  Shuri is a good role model for young black girls as well as being one of the smartest persons in the world.

Now one of the technologies that Shuri design was Black Panther’s suit. The suit can distribute  the kinetic energy from an impact. The idea is that the kinetic energy will not be focus on one area but move to another part of the suit where it can be absorbed. Okay, nice Hollywood science fiction stuff or is it? Watching this scene took me back to my postgraduates days, when I was doing a MSc in Industrial Mathematical Modelling at Loughborough University. Here, I did a dissertation on the “Impact on an Adhesive Joint”.

The mathematical model I had to create was to show how material behaved in aggressive impact circumstances.  My placement was at a Material Start up firm ran by three PhD Material Scientists. They had this crazy idea that if you create a design a composite material, it would be able to take an impact, by distributing the kinetic energy away from the impact zone to places for which it can be absorbed. Sounds familiar? But materials under impact react like this simulation!

Materials under high impact tends to buckle and fracture. The future Black Panther’s suite is not looking good. Nevertheless, one of the key skills of a mathematical modeller is to listen to the subject matter experts and turn their knowledge into a mathematical form. Then by solving the mathematical form we will see if we have created a viable solution that can be applied to a real world problem.

Material Scientist are very familiar with the stress-strain graph

The three PhD Material Scientists argued that under impact condition if we could minimise the stress and strain the material would remain in its elastic region. In the elastic region, once the stress has been removed the material will return to its original size and shape.  The three PhD Material Scientists wanted to know was there a mathematical way to test out their idea; that there is a material design that can deflect an impact. By using the Wave Equation with an Impact forcing term, it was argued that the kinetic energy is distributed away from the impact zone fast enough so that the material remains in the elastic region

The figure below shows the schematic from the original MSc dissertation.

The Impact Force was represented by a triangular pulse forcing term of impact duration ‘a’.

Now was interesting in the film, Black Panther suit, made up of nanomites started to disintegrate when it was hit by a sufficient force, like the horn of a Rhino or a point blank grenade launcher. The sharp energy rised forced the nanomites apart. Okay not so Hollywood, but in my dissertation research it was identified that the interface is where the composite material was most likely to fail.

However, if the interface remained in place, the adhesive layer serves as the entity to absorb the energy by bouncing the reflective wave  between its boundaries. So theoretically, a Black Panther suit might actually work. Well done Shuri!

This was one of my first mathematical models, and the dissertation did receive a distinction. At the time of thought the idea of a impact absorbing composite material as crazy but after watching Black Panther, it motivated me to have another look at my MSc thesis.  Though I don’t think I can invent the Black Panther suit, I hope that this film inspires children all over the world to greater and better things in STEM.