thequirkdetective

[thequirkdetective]

Announcement - Indefinite Hiatus

Despite our best efforts to keep this blog running with regular and high-quality updates, many factors, including school and the covid-19 pandemic, have hindered both our time and motivation for the project. The update frequency has been continually pushed back, so that now it seems laughable I initially planned to have an update every week. This blog was started in the summer holidays during the beginning of the pandemic, when I had a lot of time, and not much else to do. Back then an update a fortnight was easy. As school returned to my life, with added pressure due to moving into sixth-form, that goal became less achievable. I asked for help from a friend, who joined the project, and yet it was still nearly unattainable. We moved updates to once a month, and again kept missing our upload date from work, stress, and lack of motivation. This recent hiatus has been a godsend, and the thought of ending it now fills me with worry. As much as I would love to continue this blog, it is with a heavy heart that I am extending its hiatus indefinitely. It may be the case that I return to it one day, but that chance will be slim, and at the moment is entirely non-existent.

I hope you have enjoyed the content this project has produced.

[thequirkdetective]

Investigation 13: Elasticity – Danjuro Tobita

It’s almost the Christmas holidays as I write this, as well as being exactly halfway through December. Hopefully during the holidays we can catch back up to schedule, so this should be the last upload that isn’t on time. Let’s not dwell on it. Shall we?

Danjuro Tobita, better known as Gentle Criminal, has the quirk of elasticity. This allows him to make anything he touches elastic (in the sense of property, rather than material). I only learned when researching this quirk that his name is in fact a pun of the quirk in Japanese, where the standard Japanese kanji for ‘elasticity’ also translates as ‘gentleman’. This has nothing to do with the investigation, I just thought it was a cool fact.

The first problem we run into is that elasticity isn’t a set property at the molecular level. Different materials are elastic for different reasons, mostly due to the different ways the atoms and molecules within the substance are bonded together. For example, rubber is elastic because of its complex interlinked polymers that align when stretched. Most other substances deform elastically due to uniform deformation of their atomic structure. Which brings us to our second problem…

Nothing is perfectly elastic. Rubber and other elastomers are ‘elastic’ up to a point (around 10x their original length), but other materials can only deform slightly before they become plastic. Plasticity, in opposition to elasticity, is the property of a substance that retains its new shape when deformed, while elastic materials return to their original shape.

These two factors together make the effects of Gentle’s quirk highly irregular. To explain them, we first have to look at elasticity in more depth. So-called ‘perfect elasticity’ is described by Hooke’s Law, which states the force required to stretch or extend a material is directly proportional to the distance it is to be stretched or extended. This means to compress a spring to a quarter its length, one must apply twice the force required to halve its length, and so forth. This is (practically) true for all materials to a point. After that point, known as the yield point, the material stops being perfectly elastic, and begins deforming plastically. There are other stages between this and the material breaking, but these are unnecessary to discuss since no material that has been affected by the quirk has ever reached its yield point.

Let’s begin, as always, with the largest use of the quirk, here being the material that underwent the largest force and still remained elastic. The answer would of course be the air trampolines that redirected Izuku’s pellet of air[1], but the physics behind this interaction is possibly the most gratuitous and bloody murder of sense in the anime. I usually shy away from criticising the anime on its science, primarily because it’s a work of fiction about superheroes, but also because its purpose is a source of entertainment, and I bring the burden of applying science to it upon myself. In this instance however, I am allowing myself a small fracture in my usual composure to discuss why this scene is absolutely nonsensical.

Firstly, Izuku cannot create a bullet of air. To flick his finger is to create a pressure wave that spreads out from the point of creation at the speed of sound. No faster, no slower. If the finger is to move at a supersonic speed, the resultant pressure wave would create a sonic boom, and still travel at only the speed of light, still in a dissipating wave. Due to the properties of waves, their amplitude decreases with the square of the distance from the source. Thus Deku’s blast wave would not need aiming, and would also be barely a light breeze at such a distance as it is used.

Additionally, and most grievously, Gentle cannot create trampolines of air in the air. This is for the simple (yet often misquoted) fact of Newton’s Third Law. The classic, profound, smart-guy quip version is “every action has an equal opposite reaction”, but this is most likely only because the full answer is far more bloated. The law is in fact “when body A exerts a force on body B, body B exerts a force on body A that is of equal magnitude, opposite direction, identical type, and in the same line, as the force of body A on body B”. Quite a mouthful, but there’s a lot of subtle and important detail missing from the first, I’m sure you’ll agree. The problem here is that the created trampoline must exert a large force of Gentle to cause such acceleration (see Newton’s Second Law of Motion), and thus Gentle exerts a force on the trampoline, that causes an accelerate in the same proportion to the acceleration of Gentle as the ratios of their respective masses. Since air is a lot less dense than Gentle, and his quirk does not appear to add mass to a system, the trampoline would be accelerated backwards considerably fast before Gentle could gain any significant acceleration. It would be like trying to push yourself backwards by punching a balloon. Sure, the balloon is elastic, but it does not have enough mass to exert the required force. The only way this could work is if the trampolines were connected to the earth (thus the mass of the system is increased), but the only way this could occur is via more elasticated air. This does not happen because a) it is not seen – the elasticated air becomes slightly opaque (possibly a stylistic effect to show the action of the quirk) and there are no opaque structures visible, just a single floating disc, and b) these structures would be elasticated, and thus the system would be too flexible to exert such force over such distance.

Right, after that little rant, lets get back to the matter at hand. During the fight with Gentle and Deku there is a scene within a construction site that gives a lot of valuable information. This comes in the form of gratuitous quirk use, as well as an explicit statement of the quirk’s features: it cannot be turned off at will, and instead fades over time. This is odd when compared to almost all other quirks (if you need any examples, every other quirk investigated save one can be both activated and deactivated at will) and so it is likely it ties into the mechanism of the quirk’s action.

The scene contains two key uses of elasticity. Firstly, multiple steel girders are made elastic, and secondly a crane arm is made elastic. The former is useful because it is used by Gentle for movement, so the force on it and thus a lower limit for the yield point can be garnered. The second is useful because it showcases the flexibility of elasticated materials by how much the crane arm bends.

The steel beam bends about 1m each side of its equilibrium, which seems to be relatively unaffected by the quirk. The beam seems around 10m long, but thankfully the beams look like Universal Beams, which have standardised measurements including each type’s flange thickness, root radius, and most importantly, mass by metre and elastic modulus in each axis. Unfortunately there are almost 100 types, each of subtly different dimensions and properties. After downloading a spreadsheet and sifting through all types, I can confidently say the distinction does not matter, as the differences are all within the margin of error that arises upon attempts to measure the on-screen girder.

Let’s start with some maths. There’s no escaping it, and this time it’s back with a vengeance. Assuming the girder bends to approximate an arc (a section of a circle’s circumference) we can use some geometry to figure out the length of the original and stretched girders, and thus how much longer the latter is than the former. The unstretched we already know is around 10m long, and the centre bends ~1.5m from equilibrium. Since the ends are fixed, we know the chord subtending the arc is 10m long, and the distance bent (1.5m) is the distance between the arc and the centre of the chord. I won’t bore you with the details, but it turns out that the steel only increases length by 60cm, or one 60th its original length.

There isn’t much clear data on how elastic metals are (illustrated by the fact that a cursory search of “how far do metals stretch” gets 10 results in before some very different and nsfw questions come up instead, no points for guessing what they are) but there is an incredibly useful dataset courtesy of engineering toolbox, containing the ultimate tensile strength, yield strength or Young’s Modulus of almost every material you can think of. I’m not sure which engineer would need to compare the elasticity of compact and spongy bone, but I’m sure some day I’ll be glad the entry is there. For now we’ll look at the structural steel values, and thankfully all three are available. Let’s take a moment to discuss what they mean.

Young’s Modulus is the ratio of stress against strain, and has a fixed value for each material. Stress is the force per unit of cross-sectional area applied to the material, and the strain is the stretched length sure to such stress over the original strength. Yield strength is the minimum stress required to deform the material plastically, and ultimate tensile strength is the stress required to snap the material. Structural Steel has a Young’s Modulus of 200, so for every 200 MN of force per square metre of cross-sectional area, the beam will double in length. Sadly, these simple calculations are only applicable when the force and extension lie on the same line. In our case, the deformation is complex, non-shear, and therefore cannot be described at an angle relative to the force. In this case, we must apply the terrifyingly named Euler-Bernoulli Beam Theory. It contains some fittingly terrifying equations, included variable functions based on beam material, and second derivatives against two separate nested variables. However, in our scenario, the beam is supported at both ends (known as a simply supported beam) and we’ll assume it is uniform in density, elasticity, etc. Therefore we get an equation that looks like this: σmax = ymax F L / (4 I) where σmax is maximum stress at a given point, ymax is the distance from the point to the neutral axis, F is the force applied to the centre of the beam, L is double the length of the beam, and I is the ‘area moment of inertia of the cross section’. I have almost no idea what that last one means, but thankfully I managed to find an equation for it given different dimensions of a symmetrical I-shaped cross-section. There are two pieces of bad news. 1, it looks like this: Iy = (a^3 h / 12) + (b^3 / 12) (H - h), and 2, we now need to play a game of universal-beam ‘Guess Who’ to gain the correct dimensions.

The beam in the anime seems to be less than 500mm in depth, so that removes 47 possible types. Less than 500mm in width sadly doesn’t remove any more. However, we do know the beam is roughly larger than 150mm, since it larger than Deku’s hand span, which removes another 23. Averaging the rest gives us some dimensions we can use as an approximation of the beam. Thankfully, there exists a table of standard UK I beam dimensions and their respective area moment of inertia of the cross section. Comparing our values to the closest standard gives a value of 7440. Plugging this into the max strain equation, we find the maximum strain on the beam to be 0.79N per square metre. A strangely low number that says to me something must be wrong. The problem is we don’t know the value of F, and since I just used Gentle’s weight the formula treats the beam as incredibly flexible, since it bent so much under such little load. This is a problem, only solved by using a formula involving the Young’s Modulus E  of the beam rather than F. Such a formula is even more complex than those already seen, and is at such a level that I cannot understand how to apply it to the above scenario. Indeed, this post is already much over its due posting date at time of writing, and we have not talked at all about the quirk’s mechanism. Beam theory being as complicated as it is, and having spent now a good few days failing to apply it, I believe it is best we approach the problem from a different angle.

It’s safe to say the metal becomes not just more elastic, but more flexible, when the quirk takes effect. It takes a very large force to bend metal to the extent shown, and that metal would snap or at least bend plastically before that point is reached (sadly I cannot say which would occur). Therefore something about the molecular structure of the metal must change.

As previously discussed, metals and polymers bend differently at the molecular level, and this is because their very structures are different. Metal atoms bond by delocalising their outer electrons, creating positively charged ions attracted to a sea of negatively charged delocalised electrons. This is why metals shine – the electron sea is incredibly smooth, sub atomically so. Polymers bond via covalent bonds and inter-molecular bonds, creating discrete polymers that weakly attract each other. Gentle’s quirk must somehow make both these structures, and others, elastic in the same fashion.

The first answer is to weaken the inter-molecular forces within the structures, allowing polymers/molecules/any base elements to more easily move past each other within the material. Sadly, this just makes the material more ductile, which is the ease with which the material can be elongated via tensile force. To make something more elastic, the forces holing the molecules together must be made, for want of a better word, springier. Essentially, they must be able to act over a longer distance in order to pull the material back into shape after deformation. To do this simply would be to make the bonds stronger, but this would also make the material less flexible and denser. Instead, the force must somehow be spread across some distance profile, maintaining its magnitude at the standard distance of molecules from each other, but fall off slower as distance increases. The way to do this while retaining the other featured of the material is essentially fictional, and would even break thermodynamics (again) by being able to increase the Helmholtz Free Energy within a closed system. Since we’re now changing the mechanism by with one of the four fundamental forces of the universe functions, we can suppose the quirk changes the quirk in such a way ass to create perfectly elastic materials, since they already seem to have ridiculously high yield points.

Supposing this is the case, the question immediately arises – so what? The answer is that perfectly elastic materials have immense uses within many scientific circles. If a material returns to exactly the same state after deformation as it was in before, then it has the same energy. This means any object that hits it rebounds with the same kinetic energy as it started with, a phenomenon known fittingly as a perfectly elastic collision. Every other collision loses energy as heat, save for collisions that stretch the term for physics reasons, such as two orbiting objects. In our case purely elastic collisions have as many uses as elastic materials do, and possibly more. To have any material possible suddenly, even though temporarily, gain perfect elasticity will have material scientists drooling, and although I do not have the intelligence to think of any novel applications of such, asking one of them would I’m sure give you myriad answers.

Another fun application is heat-proofing. A material becomes liquid when the inter-molecular forces are partially overcome by kinetic energy, and gasses when the forces are broken completely. Since these forces are unlimited in distance, the objects would never be able to become gaseous, and would have very high cohesion (surface tension) when liquid. I’m again not sure of the applications of this, but it is cool nonetheless.

To conclude, Gentle Criminal’s quirk affects any material he touches, and changes the effect of the electrostatic forces within it, making them act across any distance, with a slight reduction in magnitude with distance. This works by having the force pull the molecules together from any distance, until they become close enough to be repelled by the electrostatic repulsion of the atoms. Any force applied may overcome the electrostatics for a distance, but will never cause yielding.

[1] Season 4 episode 85: School Festival Start!!

I hope you enjoyed this investigation! It’s almost Christmas as I post this, and as I’m sure you’re aware this post should have ben released on the 1st. I’m also sure you’re aware this has become a trend, and I’m sure you know reasons behind it. It is therefore with a heavy heart I announce we will be taking a hiatus for an undefined length of time. We have decided it is better to write a few posts as backup and prepare for posting, rather than desperately writing posts weeks after they’re due and apologising. We don’t have an idea of when we will be back, but we will. In the mean time, go have a Merry Christmas/Happy Holidays, and a happy new year. We’ll see you some time in 2021.

[thequirkdetective]

Investigation 12: Half-Cold Half-Hot – Shoto Todoroki

We’re finally back, despite the efforts of our teachers. Unfortunately, due to our new sporadic college workload we won’t be updating as consistently as we would like. I’m sure you don’t want to read through the details of how and why our uploads will be changing (the information will be at the end just in case), but the gist is we can still promise with as much certainty as it is possible to muster in these times that we will post at least one investigation a month. And here is the rather overdue next one!

‘The peppermint man’. ‘50/50’. ‘Two for the price of one’, ‘1-A’s pretty boy’, ‘the guy with the fiery childhood’, ‘icy spicy’, ‘season 1 budget movie villain’, ‘no but seriously what is with that first costume’. I am of course talking about Shoto Todoroki. I have been avoiding his quirk for a while now, since it basically gives us twice the work. But I decided now that we’re barely scraping by on our upload schedule, this was the perfect time to give us more to do. Let’s get down to business.

It’s safe to assume for the moment that the two halves of the quirk are complementary and caused by the same phenomenon. This is most likely not the case, due to the quirks coming form two unrelated people, but it is possible the quirks are reverse manifestations of the same effect. We already know multiple people can have the same quirk, so why not two people with opposite quirks?

The ice side is easier, so we’ll look at it first. When Todoroki uses this (preferred) side, he can lower the temperature around him, and/or create ice seemingly wherever he wants. The immediate question is ‘where does all the ice come from?’, and to answer that let’s see how much ice Todoroki can create.

During his infamous match against Sero, Todoroki creates a giant wall of ice and traps Sero within it[1]. The volume is immense, and immensely inconsistent. From one angle it barely brushes the front row, but when we see it from outside the stadium it has clearly reached metres beyond the top of the walls, and seems to have encased the top few rows of seating.

It appears at least 10 times as tall as Sero, who comes in at 177cm tall, according to the BNHA wiki (and I assume some officially licensed BNHA book of statistics). The ice is therefore around 20m high, at the very least. However, for another angle it looks twice the height of the stadium roof, which I estimate to be around 50m. Well, 50m is a good estimate for the average sports stadium, but this stadium seems at least twice as high on account of the odd curved roof. Let’s call 50m a good compromise.

The volume of any cone is equal to 1/3*π*r2*h, where r is the radius of the cone’s circular base, and h is the distance from the plane of the base to the top of the cone. This equation holds irrespective of slant, so we can apply it to an approximation of Todoroki’s ice wall. The radius of the base seems about 5x Sero’s height, or ~10m. Therefore, the volume of ice created is around 5200m3, 4% of the titanic, or 2.1 Olympic swimming pools. Since water expands when frozen, the block of ice contains 4800 cubic metres of water – 1.9 Olympic swimming pools. The question is, where on earth did all that water come from?

The first, and most obvious, answer is the air. Air can contain up to 4% water by mass. From this, we can calculate the volume of air that was cooled below 0°C (32°F). It comes out as 120000kg of air, equivalent to 147000000m3, 260x the volume of air contained within the sports stadium. If this volume were cooled in such a way, the effect would be first and foremost the crowd being cooled ridiculously fast, and almost dying from hypothermia. As the air cooled, the water would freeze, and fall as a sort of snow-mist, rather than condensing into a spectacular wall of ice.

A similar problem is seen if we examine the other quirk. It cannot simply cause heating since flames rise from Todoroki’s body, showing something is combusting. We therefore know the quirks involve changing the temperature of the surroundings, along with / by producing ice and fire.

The fire side is much more straightforward in this manner. Todoroki’s body produces a petrochemical that ignites due to the heat produced at the same time. The production of the chemical is both simple and arbitrary, most likely some hydrocarbon similar to petrol (gasoline). If you want to read about how this may be produced, it would be similar to Bakugou’s quirk, which I talked about al the way back in Investigation 4. The ice production is similar, since the body already produces water from the skin in the form of sweat. The real issue is the forced and rapid temperature change.

The body regulates temperature in two ways, based on whether it is too hot or too cold. If too hot, it sweats, which isn’t useful if trying to produce temperatures below 0°C. This is because sweating removes heat from the skin via the evaporation of the sweat, which requires an energy input known as ‘the latent heat of vaporisation of water’. As the sweat evaporates from the skin, it takes that energy with it, and the skin cools. Additionally, the body can dilate blood vessels close to the surface of the skin, meaning more blood flowing close to the surface. The heat this blood carries can then be transferred to the skin and to the surroundings via conduction and convection respectively. This is why you go red when you get hot – your body routes more blood to your skin.

If the body is too cold, it shivers, and the excess heat produced by muscle activity warms it back up. This is not very useful for producing temperatures high enough to light petrol, as muscles physically cannot work that fast – if they could there would be recorded cases of athletes suffering burns from exercise. Also, blood vessels close to the skin narrow, in an opposite effect to the dilation of vessels discussed above. However, if this were to cause such large heating as to ignite gasoline, the blood would have to be at a very high temperature, and thus when the quirk deactivates and the blood vessels narrow, lots of that incredibly hot blood is routed towards Todoroki’s internal organs, and he suffers heatstroke and/or internal burns. Not to mention the fact that the blood would burn whatever vessels it flowed through, and whatever tissues those were near, and no doubt cause heatstroke anyway.  We therefore need some other way of causing temperature change, something a little more drastic in effect, but less drastic in side-effect.

The barrier to this, of course, is that Todoroki appears mostly unaffected when he uses his quirks – no frostbite for a good while, and no extra burns. We do know Todoroki is capable of being burned, and he does get frostbite after prolonged ice-side use, but why not immediately if the heat comes from his body?

In fact, let’s go on a little tangent to prove Todoroki killed Sero. Just for fun. The concept of cryogenics is popular in sci-fi, but has one fatal flaw in practical terms – when the human body is frozen, ice crystals form in the cells and blood. Since ice has a larger volume than water, this causes the cells in question to expand and burst, leading to death. Also, ice crystals flowing through the blood tear the lining of the blood vessels and lead to haemorrhaging, and you guessed it, death. Additionally, frostbite occurs when bodily tissues fall below 0 and begin to freeze. Since Sero is unable to move, that means his flesh has completely frozen solid, causing Fourth Degree frostbite at least. No frostbite level exists for such injuries, because they usually cause death before treatment can be administered. If Sero were to be thawed, his skin would become black and mummified, and undergo a process known as autoamputation – his limbs would fall off. However, autoamputation is caused by lack of blood flow, since his blood vessels have been constricted and destroyed by the cold. This effect is seen everywhere, most notably around major organs such as the heart, lungs, and brain, where lack of blood leads to a heart attack, asphyxiation, and coma respectively. Sero would therefore suffer severe frostbite over his entire body, gain serious tissue damage in all his organ tissues, suffer internal bleeding if indeed his blood didn’t clot immediately, suffer a heart attack, fall unconscious, suffocate, and die. Not to mention the top row of the crowd who seem from certain angles to have got encased in the ice too, who would undergo similar symptoms. Many of the crowd would suffer frostbite of varying degrees, and many more would become hypothermic if the stadium wasn’t quickly reheated by Todoroki. Sadly, he only has the good grace to thaw Sero. Which, come to think of it, would kill him again. Rapid thawing of hypothermic individuals leads to ‘rewarming shock’, categorised as a drop in blood pressure after acute rewarming. It is unknown  I think you’re right Todoroki, you may have gone overboard.

Right, back to Todoroki. Another problem plaguing his quirk is thus: if the ice does not come from the air, it must also come from his body like sweat, but the volume of water created is over 2 billion times the volume of the average human body. Sadly, it looks like we have another conservation-law-breaker, this time violating conservation of mass. Todoroki does not weigh 120000kg (264555lbs, or 120 metric tonnes), or he would stand up on two feet and immediately start sinking through the floor, as well as being so dense and water-filled he could not move. In fact, he could stand on the second floor of a building, or even exist on soil, lest he collapse it or sink into it. It is impossible for him to store that much water within him, and so the question again arises: ‘where one earth does all that water come from?’.

Many times we see the ice appearing to rise from the ground, including during the Todoroki vs Sero fight, but this again is not a satisfactory explanation. Firstly, concrete has no water to be drawn out, and even if it did the amount of water is so immense that the volume of effect would be kilometres cubed. And how would Todoroki even draw water from the ground without being in a very different animated show?

The ice wall is (fittingly) posing a significant obstacle, so let’s turn our attention to the base cause of both effects, and see if it gives any insight. Many metabolic reactions release heat, including the reaction that causes muscles too move. These reactions are not meant to release heat (as a primary function), and the heat instead arises from their inefficiency. The benefit of this is the body’s ability to regulate temperature without having a designated function for producing heat. For us though, this is an issue.

However, one of the main sources of heat is digesting food. The process is only 25% efficient, and 75% of ingested food’s energy is released as heat. So, how much food would Todoroki have to eat to create the heat required for ignition?

The spontaneous ignition temperature for gasoline is 280°C (536°F), which means that if his Todoroki’s blood was to be raised to this temperature it would be 100°C above its boiling point, and would stop flowing through his veins. This is a problem. When blood ‘boils’, it doesn’t do so cleanly. It consist of many types of cells and proteins suspended in blood plasma. When the blood is heated past 100°C, these cells and proteins coagulate and precipitate from suspension. The temperature would also most likely render them denatured and thus unable to function (haemoglobin denatures at roughly 65°C). The plasma would then boil, causing bubbles to form in the blood that block arteries, known as gas embolisms. These cause symptoms such as loss of consciousness, vertigo, numbness, paralysis, and many other mental and physical symptoms. These would not have time to appear, as Todoroki would both asphyxiate from having no red blood cells (like anaemia, but the worst case of anaemia possible), or be killed as he is essentially cooked sous-vide by his own body.

Ok, back to the food. To raise a kilogram of water by 1°C, you need 1 Calorie of energy (not to be confused with 1 calorie, which is how much energy is needed to heat 1 gram of water by 1°C). Therefore, to heat the entirety of Todoroki’s body by 1°C you need around 66.4 Calories of energy. To heat to 280°C, this number becomes around 16800 Calories. Muscle efficiency brings it to 22400C, and finally divide by the calorific content of a Big Mac (other fast food burgers are available) to find out that Todoroki would need to consume 39927 Big Macs (£127000 here in the UK, $151000 in the US) to heat himself to the flash point of gasoline by shivering. This may be the most useless fact we’ve calculated thus far, but at least we did calculate it.

It seems therefore that the method of heating via blood is incredibly inefficient and unfeasible – after all, we didn’t even factor in the latent heat of water fusion. However, it rather sadly unavoidable, since when a body part is heated, blood flow carries much of that heat from the site of heating to the rest of the body, at least when the heating is as slow as shivering. If the heat were to be concentrated, and only one muscle fired, the energy requirement would be much less significant, but the strain on the individual muscle would be so large as to cause serious damage to the tissue. Also, if only 1/1000 of his muscles were used, it would still be the equivalent of 15 Big Macs (other fast food burgers are available), causing severe fatigue. It seems the generation of heat itself is another thing to be banished to the realms of fiction.

At this point, I fear the worst. However, we must strive forward and examine one last quality of the quirk that has been bugging me – why is Todoroki so unaffected by the temperature change?

Wood Frogs can survive temperatures as low as -18°C (0°F) for months at a time, by increasing the glucose content of their blood as a cryoprotectant. Granted, the woods frogs are usually cooled at a rate of at most 2°C per hour, but if the glucose was already present or more rapidly created, then the process could theoretically guard against much steeper drops in temperature.

The flame is more of a problem. Todoroki cannot secrete a fire-resistant substance from his skin, since it would mingle with the fuel, and either prevent ignition or have no effect. The fuel if in constant contact with Todoroki’s skin, so it must be the skin itself that is flame resistant. However, Todoroki has a prominent burn on his skin, that was inflicted after his quirk manifested, so his skin is not heat-resistant. It could reasonably be, however, that his face does not have heat-resistant properties. This could be for many reasons, including a lack of need since to produce flames from his face would damage his eyes and mouth, as well as the fact that these organs may be adversely affected by whatever causes the heat-resistance. This is most likely layers o heat-resistant material, for example silicone, or some other natural polymer, that insulates Todoroki’s internal organs from the heat and cold. This does however mean that any heat created by Todoroki’s body would not be able to travel to the surface of the skin and light the gasoline-like fuel, so the heat must somehow come from the skin. However, since the heat generation is impossible anyway, this is not an issue.

So, after discounting a lot of processed to impossibility, we have finally arrived at a semi-plausible explanation of Todoroki’s quirk. Either water or a hydrocarbon fuel is secreted from his skin, and then cells in his skin raise of lower the temperature accordingly, causing the water to freeze or the fuel to catch fire. This causes the effects seen in the show, but to prevent the temperature changes from damaging his body, Todoroki’s skin contains fire-resistant polymers, and his cells high glucose levels, to guard against high and low temperatures respectively.

[1] Season 2 Episode 20: Victory or Defeat

Warning – boring details of our lives incoming!

As you may have noticed, this upload is 16 days late. The reason, as you may also know, is our new schools. We’re both now UK sixth-form students, and squeezing this blog into our schedules has been a challenge beyond belief. The problem has been worsened by my decision to study 4 A-Levels, meaning I mostly work 9 hours a day, 7 days a week. Covid worsens matters yet further, piling on extra time and stress for each piece of work.

Each post here takes a good few hours to compile, research, cite, and write, clocking in at about 20 hours per post, at least. In addition to our mortal needs for food, drink, and sleep, we are in grave mental need of breaks and time-off for seeing friends, doing hobbies, or getting more sleep. I hope you can now see why our uploads have been unstable to say the least. We are working as hard as we can, but we are also aware that to push harder would increase stress, and decrease the quality of both this blog and our school work. I hope that you are patient with us during this time, and stick around for the content we do eventually produce.

[thequirkdetective]

Investigation 11: Zero Gravity – Ochaco Uraraka

This quirk is one I have a rather personal vendetta against. Despite the continuous pleas that it simply removes the force of gravity on any object, this is not consistent with the effects seen. However, lets start by taking on the quirk on its own terms.

Gravity exerts a force of 9.8N for every kilogram of mass an object has. Therefore, Uraraka’s quirk must exert exactly the same force in the opposing direction. At this point Physics begins to creak slightly at the seams. The quirk’s effects occur remotely (aside from the initial contact needed to activate the quirk), and so the force is non-contact. The quirk is used on concrete[1], and so cannot be magnetic or electrostatic. The only other option is gravitational (aside from things like nuclear forces which act over too short a distance), which would require the placement of an object of equal mass to the earth at an equal distance from the object, or an object with mass proportional to the square of the distance. Not only would this significantly affect the gravitational forces acting on every object within a sizeable area, by the time the object was far enough away to not be visible, it would be such a large mass as to throw the orbits of many objects in the solar system into chaos, most notably the orbit of earth.

The first logical conclusion of Uraraka’s quirk, then, is that she can control and exert a new type of fundamental force on any object she touches. This is a slight cop-out on our part, but also doesn’t explain every effect of her quirk that is shown.

In episode 7, Uraraka uses her quirk on a large concrete pillar, through the air as if it were a baseball bat. The issue here is that this manoeuvre would be incredibly difficult to pull off, and require immense strength.

The acceleration of an object due to a force is inversely proportional to its mass (F = ma). This essentially means if you kick a football (soccer ball) it will fly through the air, but the same cannot be said of a boulder. In the Tenya vs Ochaco scene, the concrete pillar acts as if it had negligible, or zero mass.

A good way to think about what ‘zero-gravity’ means, especially in simplified 2d scenarios, is to put the object on wheels. The force of gravity is then balanced by an upwards force, making a net force of zero, and the object is ‘floating’. The wheels simply negate the friction of the object with the ground. Now, imagine placing a stone pillar on a skateboard and swinging it like a hammer throw. The pillar won’t move easily, because it still has mass, and thus ‘inertia’.

Side note: inertia is in inverted commas here because it doesn’t actually exist. It is simply a property of mass arising from laws of forces and acceleration, like having weight or being made of matter. Sometimes, especially when learning physics, it is useful to express that property of mass with its own word, but you can always replace the word “inertia”, with “mass” and the sentence will still make sense (indeed, it will make more sense).

An argument could be made that Uraraka is just unusually strong, and thus could move the pillar. Due to intense hero training and martial arts skills this is almost certainly true, but as an explanation it is flawed for two reasons.

Number one: The pillar is around ten metres tall, and two metres by two metres wide, for an overall volume of 40 cubic metres, and a rough mass of 96 metric tonnes (106 tons). The pillar is swung such that its average speed reaches about 5m/s (11mph) in 0.5 seconds. And thus, thanks to the ever-useful Second Law of Motion, we know Uraraka must have exerted a force of 96 kN, the force of four amateur boxer’s punches. However, let’s not forget that the force was exerted on the end of the pillar, meaning the actual force required would be much, much greater, about 5x at least, which gives us a ridiculous force of 38 boxers’ punches. If Uraraka was standing on the ground trying to swing this weightless pillar, the forces requires would push her backwards before the pillar could reach such speeds, and that’s assuming she is even able to exert such impossible forces to begin with. This brings us onto…

Number two: Uraraka is not standing on the ground. She too is floating, though it seems it is due to the updraft from Deku’s blast (which, if it were able to lift 96 tonne concrete pillars, would have had to exert a force of at least 9.6 kN on Deku’s hand, but that’s for a later post). For her to swing the pillar, the pillar would swing her, due to Newton’s Third Law of Motion (there will be a test on these next week). This means that if she were to pull the pillar in a circle, the effect would be her spinning in the opposite direction, like pulling on the wall of an ice-skating rink. No matter the force Uraraka is able to exert, she has nothing to exert it on except the air, and the air resistance of the pillar far outweighs her own. It is simply impossible, in no uncertain terms, for her to swing this pillar.

It is for these reasons that we know something else must be the cause of Uraraka’s quirk effects, something deceptively simple and yet physics-breaking. Each force acting on an object, such as gravity, or Urakara’s pull, has been in proportion to the object’s mass.

If Uraraka’s quirk removed an object’s mass, then the immediate effects would be no gravitational force acting on the object. The force of gravity between two objects is proportional to both object’s masses, and since one is zero, the force will be zero. Success! Right?

Except for one thing. We should all know by now that a force creates an acceleration in inverse proportion to the object’s mass (F=ma, so a=F/m). However, the value of m is now zero, so the acceleration is undefined. This means that other objects cannot interact with the zero-gravity object, and it cannot be swung. Another, slightly larger, problem with this approach is that mass and energy are two parts of the same fundamental quantity, and that quantity is conserved. This means that when Uraraka’s quirk removes 96 tonnes of mass from the universe, she would introduce 96 tonnes of energy, which we can convert via E = mc2. It turns out this is around 9x1021 Joules, or the total energy released by the sun over 18 years. As a result of using her “Improvised Super Move”, she would immediately obliterate the entire Earth. And this doesn’t even take into account the fact that the mass can be returned, and somehow Uraraka has to channel into a pillar an amount of energy that would take 18 years to be generated by a comprehensive Dyson Sphere.

So, we’re at an impasse. Either the quirk doesn’t affect mass, which violates the effects seen in the show, or it does, and the show no longer obeys basic laws of physics. Hence my personal grudge.

We have been prone to conclude that conservation of mass simply does not exist in the BNHA universe, due to the existence of Momo Yaoyorozu and Yuuga Aoyama’s quirks. That does somewhat soften the blow of the destruction of mass, but we still have to figure out how the object is able to interact with other objects of mass. If we give F/m a value by tracking its limit as m tends to 0 we get F/m = infinity. Therefore if a single air molecule were to so much as touch the pillar, or the electrostatic forces between the electrons of the two objects were to exist, the pillar would immediately accelerate to an infinite speed, requiring infinite energy (which the universe does not have), breaking the cosmic speed limit of c (a quantity that is possibly the most fundamental in all of physics), and immediately smacking into another object, where the process repeats. It’s impossible to boil this down to a single sentence of slapstick apocalypse like “and then the world explodes”, because the only result would be the complete, immediate destruction of the entire universe, and not in any spectacular way, just that by whatever laws of physics are still desperately clinging to life in this mess of a scenario, the entire universe would cease to be, instantaneously, without any serenade or fanfare. Uraraka just causes the end of everything in less that an instant as soon as she uses her quirk.

This simple quirk vexes me beyond reasonable measure. It’s effects are so contradictory as to be completely unexplainable, no matter how many leaps of the imagination I take. I can’t give it any cause, because the options are either ridiculous inaccuracy or the destruction of the universe. Even the option of a compromise between the two – removing some mass and having a smaller upwards force to counteract gravity – doesn’t work, because the mass removed would still be immense enough to obliterate the world. Even to take off 10kg of mass would destroy the school in a release of energy equivalent to the largest nuclear device ever detonated. There is no physical way for Uraraka’s quirk to have the effects seen.

It is at this point we have rather thoroughly established that not only is Uraraka’s quirk impossible, but it also does not have so-called “zero-gravity” effects. So, we can now reverse-engineer the quirk, and see what Uraraka would be like if her quirk functioned ‘properly’.

To get started, lets assume that by “zero gravity” we mean negating or otherwise removing the force of gravity from an object without affecting its other characteristics, most easily by creating an equal force on the object in the opposing direction. This force would of course change based on the mass of the object and its distance from the earth’s centre, but lets just assume it can magically alter to be exactly the opposite of the object’s weight. Now, we come to our first problem with this new and improved quirk – it doesn’t work on Earth.

The forces pushing vertically on an object do not just include gravity. In addition to this, there is atmospheric pressure; the weight of the ~97km (60 miles) of air above the object. At sea level, this is exerted as a pressure of 101,325 Pa (14.7 psi), so for an object with a 1mx1m (3ftx3ft) cross-section, the force would be over 100,000N or 10 tonnes. However, using the term ‘weight’ was a bit disingenuous. The force is just caused by velocity of the air molecules, which is exerted in every direction. Therefore, every object around you, including your body, has 10 tonnes of pressure pushing on it in every direction at once. This is why depressurisation of a plane, or (much worse) a space ship, is so drastic, as this immense pressure is reduced as fast as the air can move, which is fast.

Now what has this got to do with zero-gravity quirks? The answer is that pressure increases with depth. This is the reason buoyancy exists. An object submerged in fluid gains an upwards force known as upthrust due to the bottom of it being deeper than the top, and thus having a larger pressure exerted on it. If this force is larger that the object’s weight, it floats. In our scenario, the object’s weight is zero. This means any object with its weight negated would float into the air (or more accurately, in the air), rising upward through the atmosphere until it reached the edge, where it would drift off into space.

So, let’s say this magic counter-balancing force is just enough to make the object stay stationary. What are some fun thing to do with your new anti-gravity powers? Well, not much. Aside from doing the cool science demonstrations they do on the ISS like drink an orange juice sphere (go google some of it, its pretty epic), there’s not really much application hero-wise. Sure, fling stuff at your opponents, but if you’ve got a good arm it’s near identical to throwing with gravity, except harder. Your brain is hardwired to throw stuff in gravity, so you would be fighting against it to try and hit anything more than a few metres away. Not to mention that air resistance is negligible so the speed of the projectile is the same whether zero-gravity-ed or not. The only difference would be if you happened to be using a weapon with a velocity of projectile that made gravity significant, like a bow and arrow or sniper rifle. The former is rather unusual, but the latter is very common. However, a sniper rifle round is also affected by wind speed, altitude, pressure, temperature and the spin of the Earth itself, so removing gravity doesn’t really solve your problems.

There’s no doubt the quirk would be somewhat useful; you could literally put stuff down in mid air and pick it back up later, exactly where you left it, but overall it isn’t too impressive, and would be a real nuisance whilst you get used to it. Couple that with the one thing we can shoehorn in from canon – a side effect of extreme nausea – and you’ve got a quirk that is usually a simple if finnicky convenience, at best an aid for firing a bow and arrow, and at worst a useless producer of vomit. But I guess it beats destroying the Universe.

[1] Season 1 Episode 7: Deku vs Kaachan

[thequirkdetective]

Important announcement: Investigation schedule

Hey guys! Sorry, there won’t be an investigation this week, but we do have a reason why.

This blog began at the start of Coronavirus lock-down, and as such we have had plenty of time to write and post the investigations. However, not only has school began again over here in the UK but we have both started new Sixth Form Colleges, and along with them have begun an increased workload compared to what we’re used to. This all means that we sadly won’t be able to keep up with our current rate of uploads.

However, there is good news! In addition to a ranking/investigation every month, we will occasionally be posting bonus investigations. These won’t be looking at any quirks, but instead things like features of the world of BNHA. We don’t yet know how long these will take, so don’t expect these to be reliably or frequently posted, but this is just a heads up that they are in the works!

Thank you for sticking with us despite our slow stream of content, and we hope that this new schedule is still satisfactory without interfering with our work and daily lives.

-Mod W

[thequirkdetective]

Investigation 10 (4/9/2020): Ranking 1

As we reach the lofty heights of 10 investigations, and look back on the 4 months this blog has existed, we have decided to begin a new type of post to consolidate all we have learned. Every 10 posts, starting with this one, all of our newfound knowledge will be collected together into an objective, inarguably correct BNHA tier list. The list will be ranked worst to best, with the each quirk/quirk holder being able to reliably beat those below them in a 1 on 1 match, and will expose what the true hero rankings should be.

There are a few rules. 1: This list is based on the quirks, not the characters. It assumes the characters are of equal skill level, and simply evaluates the effects of the quirks in combat. 2: some quirks may be able to defeat other quirks ranked higher than them. However, these are exceptions, not rules, and are usually down to strange interactions between quirk effects. 3: This list only contains quirks that have been investigated in ‘the Quirk Detective’ posts.

Please note: all discrepancies between this list and canon are the fault of lazy script writing, thus all criticisms should be forwarded directly to Kohei Hirokoshi. He must answer to my faultless research and reasoning.

With that out of the way, on to the list!

9: Compress – Atsuhiro Sako

The worst quirk on this list is, surprisingly, the one we last investigated. Although at first it seems rather powerful, it has one drawback that wasn’t covered in the investigation, namely the fact it required contact to activate. This was a rather insignificant feature of the quirk when investigated, but it becomes rather crucial when discussing fighting and overall effectiveness. The problem is that very few quirks on this list require contact, and thus the opponent can be fought from a distance. All the while Atsuhiro will be essentially quirkless and on the defence, only being able to use his quirk to compress incoming attacks (assuming he can react in time). It is true that if he could get into close range the fight would be over rather quickly, but all the other quirks make that incredibly difficult, and assuming two opponents of equal skill this quirk is certain to be the least effective.

8: All for One – All for One

Many of you will be understandably confused about the most notorious and powerful villain in all of BNHA being ranked the second lowest in this list. There is good reason for this, however. The issue is that All for One has multiple quirks, only one of which has been investigated. In future we may do an investigation of all the quirks All for One is known to possess, but that still wouldn’t be complete, since it is impossible to know how many quirks he has but isn’t shown to use. Additionally, this is a ranking of quirks rather than characters. Therefore, our only choice is to assume All for One possesses only his own quirk at the start of the fight. Here we hit the same issue as Atsuhiro Sako – the quirk requires physical contact. Again, if contact was to be achieved the fight would end near instantly as the circumstances flipped on their head, and the previous quirk-user would become quirkless and disoriented.

However, All for One does rank one above Compress because their fight would be slightly different. Since both need contact to use their quirk, they would both move into close quarters. Both quirks would activate at the same time, and All for One would be trapped in a marble. However, at the same time All for One takes Atsuhiro’s quirk, and frees himself from the marble. All for one is now able to use Compress against Atsuhiro, and trap him in one of his own marbles.

7: Frog – Tsuyu Asui

Tsuyu’s quirk is the last to require contact, but has the huge advantage of incredibly toxic mucous. Against any long-range opponent, Asui is more manoeuvrable than Atsuhiro or All for One, and thus has a slight advantage over them. Interestingly, Asui could defeat Mr Compress suing the aforementioned mucous, or in the worst case scenario become trapped in a marble and survive for about a week before she dehydrates, whilst Atsuhiro dies of Batrachotoxin poisoning in less than a day. However, she could not defeat All for One. If she manages to poison him, he could steal her quirk. This gives him her frog-like traits, including resistance to Batrachotoxin, whilst the residual mucous on her skin poisons her since she loses this immunity. The reason she is ranked higher than him is due to the slim possibility of her being able to defeat some of the lower ranking long-ranged opponents due to her impressive manoeuvrability.

6: Acid – Mina Ashido

Our first mid to long range quirk, Mina Ashido’s Acid is not very effective as quirks go. The range is not very substantial, and the quirk requires many hits to do significant damage to a target. It is also more effective at closer ranges, meaning an increased chance for the three quirks above to be used. There also aren’t many tactics that can be used to increase effectiveness, and the best appears to be the simple ‘drench the opponent in as much acid as possible from as far away as possible’.

5: Hardening – Kirishima Eijirou

I can already hear the pedants screaming that this quirk is the actual last one to require contact. To this I respond with further pedantry: this quirk does not require contact between the two individuals, and instead places a quartz barrier between them. This means Kirishima can use his quirk do beat up All for One without getting it stolen. This quirk is especially vulnerable to Compress, and would probably lose to it consistently, but it does offer extensive defensive and offensive capabilities against other quirks, namely the other three already discussed. Asui’s poison needs skin contact, and quartz is a silicate – exceptionally unreactive, and thus immune to Ashido’s acid. However, it does have one large drawback…

4: Electrification – Denki Kaminari

Quartz is sometimes electrically conductive, and in a very interesting way. It is composed of a crystal structure of SiO4 tetrahedra, with a central 2+ Silicon ion and four shared 1− Oxygen ions. Whenever an electrical current is passed across a quartz crystal, the oxygen ions move in one direction and the silicon the other, causing the crystal to deform. The reverse is also true – whenever a quartz crystal is deformed it gains a potential difference across its surface. This is called ‘piezoelectricity’ and is the reason quartz can be used as a timekeeping component electronic clocks and watches. However, this is only a property of certain types of quartz, and all other types are electrically insulating (and a dielectric, but that doesn’t matter for the DC current of Kaminari’s quirk). Sadly this doesn’t have much application to a fight between Kirishima and Kaminari, since the piezoelectric effect is too small to be noticeable on such large scales, but since we know that Kirishima can’t be entirely insulated by the quartz (there have to be gaps to allow movement) Kaminari’s quirk can be used against him. The effects on any enemy within a close enough range are spasms, disorientation, and possible unconsciousness and/or cardiac arrest. However, the effect is quite close range, and not necessarily fatal or long-lasting.

3: Explosion – Katsuki Bakugou

The first of our big 3 is Bakugou, with his ridiculously powerful yet still feasible ‘explosion’ quirk. This can be used at multiple ranges, and causes serious damage to opponents. Assuming he has a proper stance he can fling opponents back by tens of metres. If they land well they’ll just break a few bones, if they don’t then they’ll die. This quirk is incredibly effective during combat for manoeuvring, attacking directly, and creating environmental hazards. It can also force opponents back, meaning there is very little chance for anyone ranked below Bakugou to get within a good range of him. It does have the drawback of limited use, but so do most of these quirks, so it’s not much of a problem.

2: Creation – Momo Yaoyorozu

And here we get to the quirks that are sort of cheating. The top two can create energy or matter on demand by violating the current laws of physics, thus allowing them to theoretically do some pretty nifty stuff like time travel and power every house in the world. Momo’s quirk is second for a few reasons. 1: it takes some time to activate, 2: it rips portions of her skin off, and 3: it can only create objects with cross sections no larger than that of her body. This does allow her to throw nuclear warheads at her opponent, but sadly this pales in comparison to the number 1 quirk.

1: Navel Laser – Yuga Aoyama

Step aside One for All, it is with great pride and disgust that I proclaim Yuga Aoyama the most powerful quirk user yet investigated. The quirk can output a nauseating 28 gigawatts, enough to defeat a foe from orbit. Use a set of mirrors to snipe them from halfway across the globe! Shoot the floor and let the ride an expanding column of superheated gas and plasma! Burn things! The possibilities are endless with this quirk, and usually involve vaporisation of the opponent and tummy aches.

[thequirkdetective]

Investigation 9 (21/8/2020): Compress – Atsuhiro Sako

Atsuhiro Sako, villain name ‘Mr Compress’, has the ability to trap a large spherical area into a small marble-like object. Immediately, questions arise. Do the trapped objects stay the same mass? If not, where does the excess mass go? How are the objects compressed, and what state are they in whilst compressed? It’s time to find out.

Right off the bat, there is no way for the quirk to compress and expand an object without causing a large amount of damage. Being able to change the size of an object only through touch is impossible, and changing the volume of a space so drastically cannot be done without some way to increase pressure drastically, which would have intense heating effects, as well as requiring vast amounts of time and industrial machinery. The quirk’s main effect cannot be explained scientifically, which leaves us looking at not the mechanics of the quirk, but instead the effects, both intentional and accidental.

There are two mutually exclusive options as to how objects are stored whilst the quirk is in effect, and both are shown to occur at one point or another in the anime. On the one hand, Compress can hold the marbles in his hand and even on his tongue[1], showing they weigh much less than their expanded counterparts. On the other hand, people who are compressed by the quirk are conscious and can make decisions and move around, shown by Mr Compress’s ability to use his quirk on himself [1], and then cancel its effects whilst he is compressed. This means his brain at least is intact, and thus the objects are somehow just squeezed into a smaller area, with all their atoms intact.

Lets look at each of these possibilities in further detail. At the end of the Shie Hassaikai raid, Mr Compress uses his quirk to tunnel through the ground, excavating multiple spheres of concrete and earth to create a tunnel around 5m (15ft) across[2]. The marbles are about 1cm (0.4 in) in diameter, meaning the volume of the earth was reduced by 500 times. This means the volume was decreased by 125 million times, and thus the density increased  by the same number. If the quirk conserved mass, then the marbles would have a mass of 163 metric tonnes, and exert a pressure of  16 tN/m2 (16 teranewtons per square metre), the equivalent of 235 thousand hydraulic presses. Suffice to say, these marbles could not be held on the tongue.

Another explanation then, is some sort of delayed teleportation similar to Star Trek. Theoretically, Mr Compress could store the positions and states of every atom within the volume to be ‘compressed’, and then turn all the mass into energy. Then, this energy could be turned back into mass when the object is ‘expanded’. We can figure out the energy needed by looking again at the most significant use of the quirk: tunnelling into concrete. Mr Compress creates at least 5 marbles, each holding a 5m radius sphere of concrete and earth. Using the famous E=mc2 we find that this generates 7.3 zetajoules, or 7.3x1022 joules of energy. This is the energy of 7.8x1018 AA batteries, and if these batteries were laid end-up in a square, that square would measure 12 km on each side. It’s safe to say that this Star Trek method requires unfeasible amounts of energy storage, as well as some way of converting energy to mass and back again incredibly precisely and completely efficiently.

If we move even further into the realms of science fiction, (i.e. less emphasis on the ‘science’, much more on the ‘fiction’),  we can postulate on the quirk’s use of wormholes, pocket universes, or other similar theoretical physics terminology takes wildly out of context. Essentially, the quirk could transport the matter to an enclosed point in space, into a pocket universe, along a new dimension, or any other way to move the sphere of matter from the here-and-now. Before we continue, this is not possible under current understandings of physics, and is essentially sci-fi jargon with a thin façade of relativity and theoretical physics to cover it up. Theoretical physicists, if for some reason you’ve read this far, feel free to skip the next 6 paragraphs and replace them with the phrase “Mr Compress’ quirk is impossible”.

First, some terminology. Pocket universes are a possible explanation of the rough homogeneity in temperature across the whole universe, even in sections so far apart light should not have been able to travel from one to the other. The theory states the universe is constantly and rapidly expanding, and that certain regions stop inflating, and instead the energy within them condenses into matter. These new populated regions of space are called pocket universes.

Wormholes (often called Einstein-Rosen bridges to sound fancy) are theoretical structures that link two defined points in space time, and could allow travel between those two points.

In everyday life there are three spatial dimensions; x, y, and z. Relativity explains the universe with an extra dimension; time. However, it is possible that the universe, or certain sections of it, contain extra dimensions. Indeed, standard string theory requires 10 spatial dimensions for mathematical consistency, and bosonic string theory needs at least 26. Even stranger, some or all of these dimensions may be ‘closed up’: coiled in on themselves so much they essentially disappear.

Now, for some incredibly theoretical ways to explain both sides of Mr Compress’ quirk. It is possible wormholes could connect different universes or pocket universes. It is also likely the entrance to a wormhole is a sphere, in the same way that the entrance to a cave in a cliff is a circle (or similar), except in one more dimension. Therefore, if Mr Compress’ quirk creates a wormhole to a pocket dimension, then the matter would be transported into a different universe, unable to interact with our own. The matter also would not be able to escape the universe due to its expansion. The good news is that the sphere has about enough air for a trapped person to survive two weeks before carbon dioxide poising sets in. This is much less time than it takes to starve, so food is not an issue, but if the universe does not contain water the person would dehydrate in about one week. Another issue, although more a minor inconvenience, is that without a light source the inside of the universe would be pitch black – the blackest black possible, since no light would exist there.

However, we still haven’t explained the presence of the marbles. It is theoretically possible that a pocket universe could form around another pocket universe. It thus may be possible to force the formation of a pocket universe inside another. If this is the basis to Mr Compress’ quirk, it functions as follows. 1: A pocket universe is created within our universe. This pocket universe appears the size of a marble. 2: A wormhole is created, with one end centred on a point in our universe, and the other in the pocket universe. 3: The matter enclosed within the opening in our universe travels through the wormhole to the pocket dimension. 4: The wormhole collapses, and the transported matter is trapped within the pocket universe. 5: The pocket universe’s boundary is impassable, so it acts like a marble, with a completely reflective surface. 6: Another wormhole is created, and instead of transporting matter both ways, the pocket universe is collapsed. The implications of collapsing universes is slightly too maths-filled and strange to explore here.

And that is a possible explanation to Mr Compress’ quirk! Theoretical physicists, if you’re reading this, I’m so sorry. Non theoretical physicist, and any of this interested you, I would encourage you to research it yourself and debunk all the falsehoods crammed into this explanation.

Finally, I would like to look at some strange effects of the quirk, namely large gusts of wind. When an object is compressed or wormhole-d, it leaves a 2.5m radius sphere of empty space (hi theoretical physicists -I just mean a vacuum, not the absence of all the weird particles you’re so cagey about). This would be rather quickly filled with air, creating a large rush of wind inwards. The speed of this would vary significantly based on altitude, humidity, temperature and other factors. Once the space has been filled, there are a few possible options. If the air is going relatively slowly, then there would be a slight compression, and a small wave of pressure back outwards. If it is going faster, that small wave of compression becomes a supersonic shockwave. Faster still, and the air compresses, heating up the centre of the blast area. Faster still, and this heating causes nuclear fusion and a nuclear detonation.

A similar, if less drastic, version of this problem happens in reverse when the quirk is used again, and the matter is returned to its normal size. In this case, a volume twice atmospheric pressure is created as the trapped matter overlaps with the matter in the destination. If a person was transported, then this would cause air to become present within their body, a very unpleasant experience similar to what occurs when divers surface too quickly. Gas bubbles form in the blood, as if the person was a newly opened bottle of coke, and symptoms range in severity for joint pain, to rashes, to seizures, coma and death. This would be accompanied by a rush of wind outwards, though one much less severe than the shockwave when the object is first compressed.

In summary, Mr Compress’ quirk condenses matter down into a small area, most likely through the forced creation of a pocket universe within our own universe. The instantaneous creation of a wormhole transports a sphere of matter into the universe, where it is then trapped. When the object is ‘expanded’, another wormhole transports the contents of the marble universe into our universe, and the marble universe collapses, disappearing entirely.

[1] Season 3 Episode 45: What a Twist!

[2] Season 4 episode 76: Infinite 100%

If you liked this investigation and want to have a say in the next one, then make sure to send a recommendation for which quirk I should investigate!

[thequirkdetective]

Investigation 8 (7/8/2020): Acid - Mina Ashido

Mina Ashido’s quirk is rather simple in its effects, at least compared to some other quirks that we’ve investigated. However, many aspects of it need to be examined for a true understanding of it to be reached. The basic premise is Ashido’s ability to - secrete? emit? Is there a word for it that doesn’t sound awful? - acid from her body, with varying levels of both pH and viscosity.

The first thing to examine is the recurring theme of ‘How does [character] not get injured when they force [thing] from their skin?’, followed closely by ‘how does [character] get the materials to make [thing] in the first place?’. Both of these issues are especially pertinent in the case of potent, viscous acid.

To answer these burning questions, we need to figure out the chemical formula of Mina’s acid. Acids are defined simply as chemicals that protonate nearby chemicals, either by donating a proton or accepting an electron. They are then categorised by how readily they undergo this process, via pH values, defined as -log(H+), with H+ being the molar concentration of hydrogen ions, or the number of moles of hydrogen ions per litre of acid. Superacids have a pH less than 0, meaning more than 1 mole of hydrogen ions per litre.

The body already produces a strong acid in the form of concentrated hydrochloric acid (HCl). The main use of this acid is to kill any bacteria in ingested food, as well as create the optimal pH for digestive enzymes. In the stomach, the pH varies between 1 and 2, but when it is first produced it is at a concentration of 160mM, or a pH of 0.8.  The production of such acid is courtesy of parietal cells in the digestive tract. These could theoretically be present on Ashido’s skin, conveniently giving it a pleasant pink-red colour. Sadly, the acid secretion would be rather different from the effects shown in the anime; more a sweat-like dribble than a “super geyser”[1]. In addition, it wouldn’t be grey or viscous, instead water-like in consistency and colour. Also, the acid could cause similar problems externally is it can do internally, such as ulcers and gastrointestinal bleeding. Overall, this system of acid production would not be pleasant nor very useful, doing as much damage to the user as it does to any villain. This means the quirk must have extra effects if it to function as shown.

Mina’s acid being concentrated HCl makes sense for a few key reasons. Firstly, it is easy to produce in the body, needing only chlorine ions and a proton pump. Also it can corrode concrete, although the reaction is slightly messier than the concrete simply disappearing, involving more black chemical waste and chlorine gas than the anime shows.

The first discrepancy between our current model and the quirk proper is the viscosity of the acid. Compounds only become acidic when dissolved in water (mostly, and certainly in the case of HCl), so a viscous solvent would not solve the problem. Instead, the acid must be mixed with a viscous substance. It’s impossible to say for certain what this substance is (the body has many viscous fluids to choose from, and I can’t find any studies detailing hydrochloric acid’s reaction to bodily secretions) but it’s feasible that a compound exists that can fulfil the role and be easily produced.

The next issue is one of velocity. Mina’s acid can be forcefully thrown outwards, rather than just dribbling downwards. A lot of this can be achieved by Mina increasing the viscosity of the acid and flinging it off herself, but it is apparent there is another factor at play. The possible explanation is the possession of slightly modified parietal cells, which possess some sort of valve or seal that can restrict the flow of acid and create a high-pressure flow in a similar way to covering a hose nozzle with your thumb.

The final issue is burns (there isn’t a synonym that starts with ‘v’, sadly). Exposure to acid with a pH of 0.8 is not known to be pleasant; it causes serious chemical burns, especially if the acid in question is oozing from ones skin. The solution that the human stomach employs is a thick mucous membrane that gets replenished as it is destroyed. We already know from Tsuyu Asui that layers of mucous are not animated in BNHA, so it is entirely possible Mina’s skin is similar to the human stomach lining. This, as stated previously, would explain its pink colour, as well as provide a (rather disgusting) answer to what the viscous substance in Mina’s Acid is.

However, skin isn’t the only exposed area of the human body. This is where we get to the second strange aspect of Mina’s appearance; her eyes. Rather than the standard white, she has a black sclera, and is thus I’m sure the envy of goths everywhere. She also has yellow irises, but coloured eyes seem to be standard in the world, either due to the art style or some side effects of quirks in general. Chemical burns on eyes cause them to become bloodshot, but not black. Black eyes can occur in rare and severe cases of hyphema - when blood fills the anterior chamber of the eye, between the cornea and iris. However, this would only affect the iris and pupil, and not the sclera. The complementary injury to hyphema is a subconjunctival haemorrhage, and in this case Mina’s sclera would turn a dark shade of red, near black. It occurs due to a burst blood-vessel in the eye, and affects the whole eye, save the iris and pupil. These aren’t anything to worry about, and can even be caused by sneezing too hard, but they usually go down in a week or two. The fact the blood has clotted to black in Mina’s eye, as well as its permanent colour, points towards regular exposure of the eye to acid, causing regular haemorrhaging. The blood in the conjunctiva then clotted, leaving Mina’s eyes black. This is good news for any extremely dedicated Mina cosplayers, but do note that this method is in no way recommended, and in fact strongly discouraged, by The Quirk Detective. Just get contacts if you’re desperate.

Mina’s horns don’t seem to relate to her quirk, and neither does her pink hair. Indeed, the fact Mina has hair shows either that her scalp has hair follicles and thus doesn’t produce acid, or she wears a wig. If her hair is natural, the hue may be caused by genetic inheritance from her parents (it is possible that the traits caused by a quirk can be passed down without the quirk’s effects) or simply Mina dying her hair. Her horns also could be inherited from a parent.

In conclusion, Mina’s quirk is caused by her skin being similar to a stomach lining – producing mucous and hydrochloric acid. These mix and become Mina’s Acid, capable of dissolving, skin, muscle, and if concentrated enough, concrete. Her ‘skin’ is coated in a layer of mucous to protect it from chemical burns, but overuse of the quirk could damage this lining. Her eye colour is possibly due to overuse of her quirk as a child. Repeated exposure to acid caused blood vessels to rupture in her eye, causing a subconjunctival haemorrhage. If the bleeding continued and the eye was not allowed time to heal then the blood would clot and become a layer of near black colouring over the sclera. Her horns seem to have no cause, and are likely inherited from one of her parents. Her hair colour is the same, and may either be inherited like Midoriya’s or dyed like Kirishima’s.  

[1] Season 3 Episode 52: Create Those Ultimate Moves

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Investigation 7 (24/7/2020): Navel Laser – Yuga Aoyama

Aoyama’s quirk is an interesting one, that I have been pondering for quite a while. On the surface it’s a simple power; being able to shine a large, wide laser beam from one’s bellybutton, but upon deeper inspection the quirk reveals itself as rather powerful, with enough energy in the beam to launch the user backwards[1]. So how much energy is a laser of those capabilities actually outputting?

The ability of the laser to propel Aoyama backwards is most likely the largest consumer of energy throughout the quirk’s many uses. The basic principle is the same as that of a rocket: accelerate an object in one direction, and you will accelerate in the opposite direction, at a rate proportional to the ratio of the object’s mass to your mass. The problem with this approach is that photons do not have any mass, since they travel at the speed of light. They do, however, still exert momentum, equal to Planck’s constant over the photon’s wavelength. Aoyama’s laser is blue, with a wavelength around 470nm, and so the momentum of each photon is 1.4x10-27kgm/s.

Usefully, Aoyama uses his quirk to move in a race, where we are given his precise time, and the distance travelled. Rather unhelpfully, it takes him two bursts to finish, and the bursts are unequal. Judging by the features of the building in the background, the first burst takes him 43m. When he hits the ground, Mina is about 7m behind him, and since she finishes in less than 5.51 seconds, we can assume she is running at a rather impressive 10m. This means she covers that 7m in 0.7 seconds, and the whole 43m in 4.3 seconds. Since Aoyama crashes down 0.7 seconds before, he covers the 43m in 3.6 seconds, his average velocity therefore being just under 12m/s. Assuming a constant acceleration, his initial velocity would be 0m/s, and his final velocity a rather swift 24m/s. This is reached in 3.6 seconds, so the acceleration given by the laser is 6.7m/s2.

Approximating Aoyama’s mass as 50kg, the momentum he needs is 335kgm/s. The number of photons required for this is 2.4x1029, emitted over 3.6 seconds, with a rate of 6.6x1028 photons per second. To figure out the power output of this laser, we need to multiply the number of photons released by the speed of light, then the Planck constant, then divide that total by the wavelength of light. This gives us a power output of 2.8x1010 watts, or 28 gigawatts. According to Doc Brown from Back to The Future, this is enough energy to travel back in time 25 times over. The Three Gorges Dam in China has the largest power output of any commercial power plant, at just over 2000MW. Aoyama’s laser, if powered solely by Three Gorges Dams, would need 12 to be fired at full power. To get an even better sense of scale, we can show the number of laser pointers Aoyama’s laser is equivalent to: if we lay out laser diodes, each 1x1mm, in a square, with the same power usage as Aoyama’s laser, each side would be over 2.3 million km on each side; 260 times the height of Mt. Everest or six times the distance from Earth to the Moon.

In fact, there is a laser 7000 times more powerful than Aoyama that is currently built and in operation. The Laser for Fast Ignition Experiments (LFEX) is used for fusion energy experiments, and draws 2 petawatts of power. However, it’s only ever fired for 1 trillionth of a second, leading to a total energy output of 2000 Joules. Although Aoyama has a lower power consumption, the total possible energy output is 14 million times greater.

There is no possible way for Aoyama to power the laser due to the eye-watering power consumption, so that must immediately be written off to fiction. So now Aoyama has a 28 Gigawatt laser that can be fired in 1 seconds bursts. What sort of uses does this device have?

Firstly, the laser has a radius of ~1/4m, so an cross sectional area of 0.2m2. Since Aoyama can fire the laser in 1 seconds bursts, he can, at any time, pump 28 gigajoules of energy into any 0.5m radius circular area, be it a tree, a building, or a passer-by. Lets say he point the laser at a large block of ice. How deep would the resulting hole be?

The ice reflects around 2/3rds of the light, meaning in 1 second it absorbs 18.7 gigawatts of energy. Adding together the latent heat of fusion and vaporization, and the specific heat capacity multiplied by 100, gives the amount of energy to melt 1kg of ice at 0°C, heat it to 100°C, and boil it, which comes in at 3008510 joules. Then, divide the energy output of the laser blast by this figure to get the mass of ice that can be vaporized by the laser (remembering to factor in reflection), to find that the laser can melt 3.1 tons of ice. Going back to our ice block example, the resultant hole from 1 second of laser exposure would be 17.2m deep, not taking into account the ice indirectly melted by the cloud of steam.

Now that strange example is figured out, we can take a look at the effects of the same exposure of a human body. The average specific heat capacity of a human is 3470J/kg°C. Assuming a 50kg student or villain took the full force of it across their whole body, they would be heated to 161,000°C, around 1/10th the surface of the sun.  This is of course assuming the student/villain stands there and absorbs all of the energy released. This is improbable, not least because they would be pushed backwards by the force of the light. Also, the laser is much more likely to vaporize a clean hole through them. However, the effects of acceleration, incredible amounts of heat, and a large hole vaporized through one’s torso would most likely lead to death. The problem arises when the careless misuse of the quirk leads to the laser shining on unwanted objects and people. The use of the laser as a method of movement in the 50m race is a good example.

The laser slowly loses efficacy with distance, as the light spreads out and is scattered in the air. Blue light is especially prone to scattering, which is the reason the sky is blue and sunsets are red. However, with a 28 gigawatt laser Rayleigh scattering is pretty insignificant, and the growth of the laser’s cross-section is based only on the focus of the laser. This means that the beam would still be immensely powerful when it met whatever obstacle first crossed its path; and in the case of the 50m race that obstacle would be a patch of woodland. The trees at the edge would be hit first and hardest, absorbing the brunt of the laser, heating up quickly and causing the sap in the wood to boil and expand, exploding the tree outward. This process is repeated a handful of times as the laser rips inwards, splinters and shards of burning wood flying outwards in all directions. Then, once the laser has lost significant energy to heating it would start to burn through a few more trees, setting them on fire and most likely causing a forest fire that burns down the whole patch of woodland.

In addition to woodland conservation, Aoyama’s laser has a few other applications, some that would undoubtedly pay much more than hero work, and would be much more beneficial to the world at large. Since Aoyama uses so much energy and does not need to eat the appropriate amount of carbohydrates (92 thousand slices of cake or 30 thousand servings of pasta) he can violate conservation of energy. With the right apparatus, this could create infinite energy to supply to the whole world, with enough to spare to create wormholes and travel back in time, allowing everyone to live in a post-scarcity utopia (a trait shared by Yaoyorozu, meaning there are now two students who could end world hunger forever but are instead just training to beat up petty criminals). In the short term, Aoyama could get a job in physics, replacing one of the incredible powerful lasers at one of the many fusion power research facilities and supplying 2000x the energy those lasers can, furthering fusion research and helping to create a fusion reactor to supply Japan with huge amounts of clean energy. Or he could look at being a power source for space ships. The idea of beaming energy to space ships and stations has been around for a while, the basic idea being firing a laser at a vessel, which then absorbs the energy with something akin to solar panels, but the issue has always been placing large enough lasers outside the atmosphere to prevent Rayleigh scattering and then finding a way of powering them. Aoyama could solve this problem by either being portable enough to be flown into space or the upper atmosphere and using his quirk there, or even just having a laser powerful enough to still supply enough power despite Rayleigh scattering. This could allow humanity to travel outwards to the stars with minimal need for batteries and no need for any energy generators, in turn meaning less fuel is needed for each vessel. Engines such as ionized xenon drives could be used to propel the ships using only electricity and lightweight xenon gas, making space flight cheaper than it has ever been.

Even in the hero business, Aoyama’s quirk could make quick work of any villain, vaporizing them in less than a second. In offensive capability Aoyama is near unmatched, and utilising mirrors could mean taking out multiple targets at once, or precisely targeting the laser to within millimetres. In fact Aoyama doesn’t even have to move, just fire his laser at a series of precisely calibrated mirrors and lenses, controlled electronically. Orbital mirrors could allow the neutralisation of targets from orbit, with a system similar to the Strategic Defence Initiative developed by the US in 1983, using a system of terrestrial lasers and orbital and ground-based mirrors to take down incoming ballistic missiles. Except this time the laser is much more powerful and created by a high-school student rather than a large nuclear detonation.

There’s not much to conclude about the quirk itself here, apart from the fact that Aoyama can, in spite of all known physics, produce a 28 gigawatt laser from his bellybutton with no side effects other than mild IBS. The practical applications of this laser are immense, and I am just scratching the surface of what this could be used for. However, the used seen in the anime are reckless, and would have caused untold damage and likely significant loss of life.

[1] Season 1 Episode 5: What I Can Do for Now

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Investigation 6 (10/7/2020): Hardening – Eijiro Kirishima

This time, we’re going to be tackling a quirk I have been thinking about for a while now; Hardening. This allows Kirishima to “make his entire body [as] hard as a rock”[1]. The quirk is mainly used for defence but does also make Kirishima’s body rough and sharp, which causes his attacks to be more dangerous to opponents. We’ll look at the exact composition of Kirishima’s hardened body, as well as the systems that allow the body parts to both harden and soften.

Firstly, we need to know what Kirishima’s hardened skin is made of, and to do this we need to know how much force it can withstand.

The largest easily measurable force Kirishima withstands is when he is crushed underneath a few robots in the sports festival [1]. It is difficult to tell how many robots of which type(s) he is caught under, but we can do the maths on both types, and see how they compare, starting with the largest robots. These are in fact the same model as the one Deku punched in the entrance exam due to it nearly crushing and killing Uraraka[2] (I’m not sure how UA spun that one in the risk assessment to allow them to make a reappearance). In any case, whatever fate would have befallen Uraraka instead turns its gaze to Kirishima in season 2, but rather than being steamrolled Kirishima instead undergoes the more abrupt and deadly force of a robot in freefall. He survives (unsurprisingly, or this investigation wouldn’t have much data to work with), due to his quirk.

The whole scene plays out with the contestants of the obstacle course race coming across a group of the aforementioned giant robots. Todoroki (no doubt fuelled by chronic daddy issues) freezes the robots and gets through, but makes the decision to freeze them in such positions as to cause them to fall over. Ignoring the rather worrying possibility of Todoroki deliberately killing the entire student body of UA (get mad in the notes), only two people are caught underneath the ensuing pile: Kirishima and Tetsutetsu. The actual moment of impact isn’t shown, but a few seconds afterwards, an unnamed student declares that they see someone trapped in the rubble, and Kirishima bursts upwards in a shower of metal and testosterone, followed closely by Tetsutetsu.

This shows, in the most basic interpretation, that quirked-up Kirishima is harder than a UA robot, since if he were less hard he would be immediately crushed. Sadly, material science is a little more nuanced than that. The exact definition of ‘hardness’ is difficult to pin down, and the stresses would not be equal across Kirishima’s whole body. This blog doesn’t have access to laboratory grade material simulation software (yet), so we can’t see the exact forces involved in a student-robot collision. We can, however, estimate the rough pressures Kirishima’s body withstood after being mercilessly crushed by Todoroki.

There are no viable references for discerning the height of the robots in season 2, so let’s go back to their first appearance in the entrance exam [2]. The scene where Deku punches on of the robots in the face gives us a nice tall building in the background, which we know from earlier is about 15 storeys high (50m or 164ft). Deku jumps upwards until he is level with the robot, and gives the robot a good whack. It topples backwards, his bones shatter, and he is accepted into UA, all due to his incredible feat of self-sacrifice for his love interest. However, in the many, many different shots between the jump and the impact, the height of both the boy and the robot’s head varies from level with the roof to well above any of the surrounding buildings. This is in part due to camera angles and fisheye effects, but whatever the reason it is difficult to say for certain how tall the robot is. Let’s approximate between the two extremes, and say it’s around 55m tall (180ft). The area of the base of the robot is, you guessed it, difficult to get a proper estimate of. This is mostly due to it being framed close-up or surrounded by clouds of ice and dust. Taking this into account, along with the fact that I have strayed way too deep down this rabbit hole, allows us to approximate the robot’s base size as the same as the surrounding buildings’, since it is shown in front of one and nearly blocks it from view. This means the robot is around 15m x 15m x 55m (49ft x 49ft x 180ft). Piling on another wild guesstimate of average density gives us a robot with a mass of ~4000 tonnes (~4400 tons). Now, we can use a bit of physics to figure out the force the robot exerts on Kirishima.

We now need to use what is fast becoming the most useful equation in these investigations: F = ma. We now know m, but we have yet to find a. Fortunately, it has an equation: ΔV/t, or the change in velocity over time. Unfortunately, since the robot topples sideways, we cannot use simple acceleration due to gravity. We have to get velocity in a slightly more roundabout way.

The velocity can be found with two equations, using the principle of conservation of energy (we’re ignoring air resistance, as is traditional in physics). In the process of falling, the robot’s gravitational potential energy gets converted into kinetic energy, and so if we know the amount of energy converted, we can find out the resultant speed. Gravitational potential energy is given by , or mass x gravitational field strength x change in height, all relative to the centre of mass. Pairing this with the kinetic energy equation ( ½mv2, or ½ x mass x velocity squared), and using conservation of energy, we see , so . Rearrange, and voilà: sqrt(2gΔh) (a very nice equation that serendipitously does not contain mass). The robot has a large, heavy base, so lets say the centre of mass starts 20m (66ft) up. Then, the robot falls and the centre of mass ends ~5m (16ft) from the ground. Now we know is 15m (49ft), and is, at least around sea level, 9.8m/s2. Therefore, if a 0-point robot toppled over, it would hit the ground with an average speed of 17m/s (38mph).

Now we can work out , if we approximate the distance it took for the robot to stop. It fell onto soil and kicked up quite a dust cloud, so lets say it embedded 1m down. Assuming uniform deceleration across the 1m of distance, comes to 144.5m/s2, and is a whopping 5.78×108 N, spread over ~750m2 (8073ft2), giving 770667 Pa (112 PSI), or 7.5x atmospheric pressure.

The smaller robots seem to be no more than 10m tall, so the force of their fall is only 10m/s (22mph). This means the force is a measly 50N, and the pressure 0.5Pa (7×10−5 PSI). Now, finally, we can find out what these numbers mean in terms of Kirishima’s quirk.

The pressure would be spread over ~1m2 of Kirishima, meaning the force on him is anywhere from 0.5N to 770667N depending on the type of the robot. The issue with this calculation is that it assumes the fall of both robots is distributed evenly between the ground and Kirishima, so the forces would actually be more in the range of 50N-770667N, the equivalent of balancing a weight on your head with a mass of 5-80000kg (11-176370lbs). A force of 770667N is about the force a house exerts on its foundations, but the shock needs to be taken into account. It’s the difference between having a house resting on concrete, and dropping half the house from 10m onto the same concrete. From this example it becomes rather clear which one does more damage.

Due to this, as well as the sheer magnitude of the resultant forces, we can rule out Kirishima being crushed by the largest robots. Such a robot would flatten almost anything in its path, including Kirishima, no matter what his quirk made his body into. This also explains his quick escape; he was underneath a small robot and only had to dig through a metre (3ft) or so of robot wiring and metal panels.

Kirishima’s quirk is continually compared to rock [1], which to me says silicates. Silicates are the predominant compounds in the earth’s crust, and are mostly responsible for giving rocks their hardness (sorry geologists and material scientists, but I do have to end this somewhere). The question now, as with many other investigations, is where the silicates originate. Many health food such as spinach, soy, and bananas contain high amounts of silicon dioxide, also known as silica or quartz. However, a much more efficient way to increase silica intake is sand. Sand is mostly silicon dioxide, and is also fairly easy to ingest, making it very useful for such purposes as turning into rock at will. We’ll figure out which one Kirishima employs later on.

In the Shie Hassaikai raid, Kirishima’s quirk is shown to deflect a quirk-destroying bullet[3]. These bullets are hollow, and do not cause nearly as much damage as a standard metal bullet so it may not be the case that Kirishima is fully bulletproof. This does make sense; granite shatters easily upon contact with a bullet and the quirk-destroying bullets did not give Mirio an injury comparable to a bullet wound. The ‘bullets’ instead act more like flying syringes. However, Kirishima does also defend against a rapid succession of punches from Kendo Rappa[4] using his quirk. This is again feasible, since it is akin to Rappa successively punching a brick or granite wall. Therefore, Kirishima’s hardened body is made of some silicate, most likely akin to quartz – the primary compound in both granite and sand, with trace amounts present in food.

This means that Kirishima’s body can in some way store silica, and then reconstruct it onto or into the surface of the skin. Silica is notoriously insoluble, only trace amounts dissolving in water or acids, and the main viable solvents for dissolving it being hydrofluoric acid or hot alkaline solutions. It’s the same story  for pure silicon. However, if Kirishima’s body were to absorb silicon as an ion (a common way to absorb minerals) then the compound could be made soluble in some interesting ways.

Detergents are used to make oil and grease soluble in water, by having a hydrophobic end that binds to dirt, and a hydrophilic end that is attracted to water. The detergent molecules then surround dirt particles and make them hydrophilic, forcing them into suspension (not technically solution). A similar mechanism could be used to lift silicate ions into suspension in Kirishima’s bloodstream. These would collect in Kirishima’s cells. Then, all it takes is the degradation of the ‘detergent’ molecules to force the silicates out of suspension, where they then crystallise. This essentially turns the inside of Kirishima’s cells into rock, if given a few tweaks.

The first main problem is that the silicate ions would not necessarily create silica unless they were introduced to oxygen ions. This can be fixed by the other chemical required – one to denature the detergent molecules. The whole process involves ionised molecules that bind to silicon ions and bring them into suspension in Kirishima’s blood. They travel to his cells, and collect there. The activation of the quirk is in fact the release of a specialised chemical which breaks down the ionised molecules, releasing the silicon ions. This chemical could then also contains oxygen ions which bond to the silicon, creating silica within Kirishima’s skin cells. Then, when the quirk is deactivated, the silica is broken down and more ionised molecules are released to bring the silicon back into suspension.

The only remaining problem with this system is movement. Turning all of Kirishima’s skin into rock would lock up his joints and prevent him from moving his limbs. The solution to this is leaving some of the skin cells at points of motion un-hardened, allowing certain areas of skin to stretch and flex whilst still gaining some defensive advantages. This does leave Kirishima with a few relative weak points at his shoulders, elbows, knees, and hands, but overall, this mechanism fulfils the brief almost to the letter: turning his body into rock. It also means that it simply strengthens his skin, and does not create a new layer of rock. This has the added benefit of transferring any damage to his hardened form onto his normal body, for example a large chunk of rock being blasted off would leave a large chunk of his flesh missing once the quirk was deactivated.

Finally, we need to establish the source of the silicate ions. It is most likely diet, but is eating silicon-rich foods enough to provide the amount of silicate required? 

Kirishima’s quirk manifested when he was quite young [4] , let’s say 3 years old since he can’t remember the event very clearly. At this point just his hand and arm could harden. The amount of silicate required can be calculated by the surface area of the affected area multiplied by the thickness of Kirishima’s skin.

The average surface area of a man’s hand is ~0.1m2 (1sq. ft). Kirishima is a toddler at this point, so a 0.1m2 area would cover his upper arm too, as shown. Skin is around 1mm thick on average, so the volume of silicate required for the first manifestation of his quirk is ~0.26g (0.009oz) of silica, the same amount as present in 40 bananas. This is a very feasible amount of silica to have ingested in three years, and if Kirishima made a habit of eating silica rich foods he could have enough silicon ions to harden his whole body in 10-15 years, depending on the thickness of the hardened skin. This matches with the anime, because his quirk was not very strong and could not activate across his entire body when he was in middle school [4] . In fact, the quirk could even manifest throughout most of Kirishima’s cells, leaving a few un-hardened for movement, and the amount of silica needed would still be plausible to intake over such a time period provided his body’s ability to absorb it.

Another fun effect that corroborates with the source material is silicon-rich foods like spinach being prone to wearing teeth down, possibly leading to the strange, sharp teeth Kirishima possesses. Most likely he has them filed due to their continual wearing.

In summary, Kirishima’s body can absorb silicon ions, using detergent-like ionised molecules to force the ions into suspension. Then, the silicon is carried through the bloodstream to Kirishima’s cells. When his quirk is activated, a molecule, most likely some kind of enzyme, is released that destroys the ions responsible for keeping the silicon atoms in suspension. This causes them to react with the oxygen ions present in the cells and enzyme, creating silicate crystals within Kirishima’s cells. Some muscle cells are left without crystals in order to preserve movement, and some skin cells are kept softened for the same purposes. When the quirk is deactivated, more ionic molecules are released which bring the silicate back into suspension, softening the cells again.

[1] Season 2 Episode 16: In Their Own Quirky Ways

[2] Season 1 Episode 4: Start Line

[3] Season 4 Episode 68: Let’s Go, Gutsy Red Riot

[4] Season 4 Episode 72: Red Riot

 If you liked this investigation and want to have a say in the next one, then make sure to send a recommendation for which quirk I should investigate!

[thequirkdetective]

Investigation 5 (26/6/2020): Frog – Tsuyu Asui

This time, I’m going to be looking at Tsuyu Asui’s quirk ‘Frog’. This quirk is different from others I have covered, since it doesn’t have a specific effect, but is more a summation of many different effects, namely abnormalities in Asui’s body that mimic a frog’s anatomy. I will therefore be looking at exactly how many frog traits Tsuyu possesses, and how they affect her body.

The first ability to look at is Tsuyu’s super move, aptly named ‘Camouflage’, which allows her to match the colour and heat of her surroundings in order to avoid detection[1]. Sadly, although many frog species exhibit camouflage, few are so-called ‘active’; where the appearance of an animal changes based on surroundings, and none to the extent seen in the show. However, some frogs can change colour, going from light to dark and even changing shades from brown to green to black. This behaviour is mainly to regulate body temperature or display the mood of the frog (a practice shared with chameleons who, despite common knowledge, never change colour to blend into their surroundings), but can sometimes be used for camouflage. The drawback is that the resultant colour change is never as accurate, varied, or substantial as Tsuyu’s. However, when first shown using the move, she says “I’ve finally reached a new level of control”, most likely meaning she used to only be able to colour change simply, like frogs, but has now learned to accurately control it for camouflage.

Almost all frogs who can change colour are tree frogs, and so we can assume that Tsuyu’s abilities are related to the biology and anatomy of this group. Rather fittingly, tree frogs don’t actually belong to any one species, genus or even family, but instead all share similar traits. It is these traits, as well as the fact tree frogs spend most of their time in trees, that make a frog a tree frog.

Using this information, we can now evaluate all of Asui’s canon abilities in relation to tree frogs. The first thing to examine is her ability to leap like a frog[2], which simply calls for slightly more developed leg muscles (Tsuyu has the canonically thiccest thighs) since she leaps rather than running. Another slight change to her anatomy is webbed feet to aid swimming. This webbing does not extend to her hands, which are mostly human-like, save another ability: climbing.

Tree frogs climb through two means: the active grasping of thin branches, and the suction on smooth surfaces caused by their fluid filled toe pads, known as gripping and adhesion, respectively. Tsuyu is seen climbing up a rock face[3] with the use of both her fingers and tongue (which we’ll cover later), the sheerness of the rock meaning she is not gripping, and so must have a frog’s toe pads to gain adhesion. The sticky-ness of these pads is caused by channels in their surface that flow with mucous, which both cleans the surface of dust and dirt to increase adhesion, and makes the toe sticky. Therefore, Tsuyu’s fingers have channels, either the channels of her fingerprints or a frog-like hexagonal lattice of grooves, that fill with sticky mucous and allow her to climb surfaces.

The final ability shown in the anime is Tsuyu’s tongue, which differs slightly from a frog’s. Frog tongues are used to capture prey by their rapid extension, made possible with two different groups of muscles. The muscles in the tongue contract and stiffen, and muscles in the base of the tongue force the tongue out of the mouth like a spring. Tsuyu’s tongue can extend quickly, but can also be controlled whilst extended, presumably by developed muscles in the tongue’s structure. These unique muscles are extraordinarily strong, and can be used to lift the weight of a person. This isn’t entirely unfeasible since some frogs can lift 3 times their weight with their tongue. But since Tsuyu isn’t the size of a tree frog, how large, and how heavy, is her tongue?

An answers.com user states the mass of the average human tongue is 70g (2.5oz) for men and 60g (2.1oz) for women. I’m unsure of the accuracy and legality of this information, but it seems good for a rough estimate. Tsuyu’s frog tongue is 20m (65.6ft) long[2] , and an average human tongue is 8.5cm (3.3in). This means Tsuyu’s tongue is 23.5x longer than a human’s tongue, and thus is ~23.5x as massive, coming in at an astounding 1.5kg (53oz), and that assuming it has a normal tongue with. The strain on Tsuyu’s jaw to even bear the weight of such a tongue would be significant, and the force in its extension could easily dislocate it, especially since frogs’ tongues are positioned at the front of the mouth. This injury has not yet occurred in the anime, and so it is likely Tsuyu has substantially strong jaw muscles and tendons. The position of the tongue is also noteworthy, being mounted to the front of the bottom jaw and curled backwards into the mouth. This would make standard speech nearly impossible, leading to a significant speech impediment, as heard in the anime. Tsuyu’s speech also has a nasal quality in the anime, most likely due to a frog’s inability to breathe through its mouth.

When Tsuyu explains her quirk, there are two abilities she mentions offhandedly, as they are seemingly unimportant to the situation her, Midoriya and Mineta were in. These are being able to regurgitate her stomach “so [she] can clean it”, and secreting a toxic mucous that “just stings a bit”.

As a quick YouTube search will confirm, some frogs do regurgitate their stomachs in a truly ghastly display, for urgent expulsion of anything they should have thought twice about before ingesting, usually poisonous things like certain insects. To examine how a human would perform such an action, we must compare this with human vomiting. Fair warning, the following section is not for anyone with a weak stomach.

Humans vomit by closing the sphincters to and from the stomach, before contracting the diaphragm and stomach muscles to build up pressure. The oesophageal sphincter is then opened, releasing the pressure, and expelling the stomach’s contents. The mechanism of so-called ‘full gastric eversion’ is not as well understood, but it is believed that similar pressures created by the diaphragm (or vocal sac, as we will see later) eject the stomach, which is retracted by essentially ‘sucking’ it back in. The main structure that prevents full eversion in humans is the oesophagus, which is made out of hard cartilage. Frogs have a soft oesophagus to allow eversion, and thus Tsuyu must have a slightly different internal structure to account for this. Her stomach must sit where the lungs and heart usually are to limit the length of oesophagus that must be everted, meaning the other organs move downwards. The liver also would most likely sit normally in respect to the stomach, and lie above it. This means Tsuyu’s duodenum and the first section of her small intestine proper lie behind the lungs, flat to the spine. It is possible her internal organs near fully resemble those of a frog, with a large vertical liver and stomach squeezed to the left of the chest. The internal organ structure of a frog is something that will be explored in full later on

Finally, her last ability that is mentioned is a toxic mucous, that apparently only causes a mild stinging sensation. The mucous has not yet been used in the main anime series (neither has the full gastric eversion, for rather obvious reasons), but I am told it has some use in both the anime and one of the movies, but we will not look at those here, mainly because I haven’t seen them.

Most poisonous frogs secrete Batrachotoxin, from the Greek ‘bátrachos’ meaning frog (the chemical also goes by the catchy name ‘3α,9α-epoxy-14β,18-(2′-oxyethyl-N-methylamino)-5β-pregna-7,16-diene-3β,11α,20α-triol 20α-2,4-dimethylpyrrole-3-carboxylate’, because biochemists seem to be incapable of naming things well). This is a compound that binds to and opens the sodium channels of nerve cells leading to permanent paralysis, seizures, and death; a symptom far from that of Tsuyu’s mucous. Some species secrete toxins other than Batrachotoxin, but all secrete some kind of lipophilic alkaloid, which all have the same effect on the nervous system to varying degrees. Almost all frogs gain these toxins from their diet, the only exception being the Corroboree Frog, which produces its own alkaloid, pseudo-phrynamine, without ingesting anything toxic.

The toxin Tsuyu secretes is therefore most likely some kind of sodium channel opener. These have some use as painkiller in low doses, but the therapeutic dose is dangerously near the lethal dose, and the dose given via contact with skin is not accurately controllable. There is no dose of any known lipophilic alkaloid that “just stings a bit”, so Tsuyu was either wrong about the symptoms, or lying. She could not be able to produce toxin at all, or can produce an incredibly potent neurotoxin, but the significance of her misinforming Deku about such a toxin is left to the reader’s discretion.

One last canonical effect of Tsuyu’s quirk is hibernation due to cold[4]. In Episode 55, Tsuyu is wrapped in a blanket created by Yaoyorozu in order to keep her warm, but this is in fact not necessary. The hibernation response lowers a frog’s metabolism, allowing it to survive sub-zero temperatures whilst using only the food stores present in the frog’s body. This means that in her hibernating state, Tsuyu could survive nearly indefinitely in temperatures that would kill the other class members, and so Tsuyu is the last one who would need that blanket. In fact, it may even be detrimental, since hibernating frogs ‘breathe’ through their skin, in a process known as cutaneous respiration. Hibernation can get so drastic as to stop the frog’s lung and heart, appearing entirely dead, and using only simple gas exchange and glucose stores to retain a semblance of life. At these temperatures, parts of the frog such as the extremities, skin, bladder, and body cavity freeze, but a sort of biological antifreeze keeps the vital organs free of ice. When the temperature rises again, the frozen body parts thaw, and the frog comes out of hibernation completely unfazed.

If hibernation is possible, then its hot weather counterpart, called aestivation, is also viable. The process involves an animal shedding a few layers of live skin to create a waterproof seal around itself and prevent water loss. The only body parts left exposed are the nostrils, which are used to breathe, since the skin is sealed up. Tsuyu hasn’t yet been exposed to an extended period of drought, but if it were ever to happen she may be able to bury herself underground and create a protective seal of her own skin around herself.

A rather prominent aspect of frog anatomy to be covered is the vocal sac. This is the bag of skin and muscle on a frog’s chin and neck that allows a frog to croak, but it is mainly used as a diaphragm. In fact, frogs don’t have an internal diaphragm, and mechanically breathe by expanding their vocal sac to pull air out of their lungs, contracting it to push that air into the environment, before expanding again to take a new breath through their nose, and contracting to push it into their lung. However, in most circumstances frogs breathe through their skin and mouth lining via simple gas exchange, which can even be done under water. A frog’s relatively low metabolism allows this to be sustainable for indefinite periods of time.

Here we get back to the question of Tsuyu’s internal organs. If they were identical to a frog’s, she wouldn’t be able to talk until adulthood, and even then, only via croaking. Her ability to talk (as well as her lack of any notable vocal sac) means she must at least have some sort of internal diaphragm to inflate and deflate her lungs. If her respiratory system is more human, then she would have two large lungs, but if it were more frog-like she would have two small, inefficient lungs, and mainly breathe through her skin. Her digestive system may be of varying levels of complexity, from the simple single-intestine system of a frog to the multi-intestine system of a human, and a frog’s respiratory system mixes oxygenated and deoxygenated blood, and thus is less efficient, but more easily allows cutaneous respiration. Interestingly, frog and human skeletons are remarkably similar, so Tsuyu’s bones wouldn’t be significantly different whether they mimicked frog or human anatomy.

Of course, this is all rather binary, and there are plenty of areas to mix human and frog traits, or even have body parts that are some mix of human and frog, for example a slightly larger liver or shorter large intestine.

To conclude, Tsuyu’s anatomy is a mix of human and frog, with her most prominent frog-like traits being her larger legs, webbed toes, sticky mucous for climbing, enlarged, frog-like tongue, and secretion of potently toxic mucous. She also goes into hibernation in response to cold, and therefore likely undergoes aestivation in hot and dry conditions. She breathes like a human, using an internal muscular diaphragm, with the possibility of addition cutaneous respiration being available to allow her to breathe underwater.

[1] Season 3 Episode 59: What’s the Big Idea?

[2] Season 1 Episode 10: Encounter with the Unknown

[3] Season 3 Episode 41: Kota

[4] Season 3 Episode 55: Class 1-A

If you liked this investigation and want to have a say in the next one, then make sure to send a recommendation for which quirk I should investigate!

[thequirkdetective]

Investigation 4 (12/6/2020): Explosion - Katsuki Bakugou

This investigation will cover the quirk of the most famous/infamous character in the BNHA fandom: Katsuki Bakugou. His ‘explosion’ quirk allows him to “secrete nitro-glycerine-like sweat”[1] from his skin and detonate it at will, and he uses the resultant explosions for direct close-range attack, movement, and illumination. The main detail to be examined therefore is the synthesis of the substance within Bakugou’s body.

To begin with, we’ll look specifically at the compound Nitro-glycerine. It is described by Encyclopaedia Britannica as “a colourless, oily, somewhat toxic liquid having a sweet, burning taste”. How exactly the taste of nitro-glycerine was discovered is not explained, and neither is the dubious use of the word “slightly”, but the entry does describe the exact stages of the decomposition of the molecule. Its extreme instability lies in its high nitrogen content. Diatomic nitrogen molecules form triple covalent bonds, and are thus very stable. Therefore, the nitrogen in its state within the nitro-glycerine molecule is unstable, as it ‘wants’ to form strong, stable triple-bonds. As the nitrogen is released from the molecule, energy is given off as heat, which allows the carbon and hydrogen atoms to react with the oxygen, releasing yet more heat. It is this second step, facilitated by the high oxygen content of the molecule, that makes nitro-glycerine so powerful as an explosive.

The instability of the compound creates difficulty – since it is in such a high energy state, it takes a lot of energy to synthesise. The commercial synthesis of nitro-glycerine involves heated nitric and sulfuric acids, but can be done at home, in an experiment not for the faint of heart (or perhaps the opposite, but we’ll get to that later). The ridiculousness of such an experiment can be summed up by a forum post by an amateur chemist using the phrase “only 65-70% concentrated HNO3 [nitric acid] and 96-98% concentrated H2SO4 [sulfuric acid]”. It’s safe to say that such a reaction is infeasible within biological environments, and most likely any environment without a few dozen blast shields and fume hoods. However, the main pathway is simply the nitration of glycerol, where each of the three hydroxide (OH) groups are replaced with a nitrate (NO3) group, and the mixture of sulfuric and nitric acid only exists to create protonated nitric acid (nitric acid with an additional H+ ion). It is this that reacts with the glycerol in an endothermic reaction, so if the two can be gathered from food then nitro-glycerine can be synthesised within Bakugou’s body.

Glycerol, referred to in the food industry as glycerine, is used as a preservative and sweetener, and as such can be found in a handful of foods, such as dried fruits, soft drinks, and icing. Despite this, the average intake of glycerol per day is rather low. Additionally, I have yet to come across a food containing nitric acid in both high enough quantities to be used for nitro-glycerine production and low enough quantities to be safe, or indeed containing nitric acid at all. The role of nitric acid in the reaction is rather indirect, though, and a safer way to obtain the nitronium (NO2+) ion could be found, specifically via nitric oxide (NO). This compound can be obtained via the ingestion of many foods, including red meat, beetroot, garlic, and dark chocolate. The compound would then bind to a protonated oxide ion, and become the desired nitronium ion.

It is important to note that when explaining his quirk, Bakugou uses the phrase “nitro-glycerine-like”. The pronunciation is ambiguous in the dub (either “secrete nitro-glycerine-like sweat, or “secrete nitro-glycerine like sweat”), but the subtitles reveal the former to be true, and therefore we know that the substance that is produced is not pure nitro-glycerine. Nitro-glycerine, despite the name, is in fact not a nitro compound, but a nitrate ester. These compounds all have the property of explosive, smokeless decomposition, but are again synthesised using nitric acid. The intake of nitric acid is unlikely to be the ingestion of the compound in solution, due to the acid’s tendency to corrode biological tissues. Bakugou’s internal organs have not yet been shown in the anime, but it is safe to assume that he does not internal chemical burns by drinking acid. The issue is therefore one of acquiring the acid (interestingly, passing electricity through moist air creates small amounts of nitric acid, a technique that could be completed with the help of Denki Kaminari) and somehow ingesting it without causing large amounts of corrosive damage to the digestive system. Therefore, the compound would most likely be synthesized rather than ingested in its native form. The synthesis of nitric acid involves the reaction between nitrogen dioxide and water, releasing nitric oxide and nitric acid. This nitric acid can then be reacted with glycerine to produce nitro-glycerine (although glycerine is relatively rare in the body and diet), or an alcohol to produce a corresponding nitrate ester. These esters are all to a certain degree explosive, especially methyl and ethyl nitrate, created with methanol and ethanol, respectively. Since methanol is incredibly toxic to humans (there’s a reason people don’t drink methylated spirits and tell you about it), it can be assumed the substance secreted by Bakugou’s skin is ethyl nitrate (formula C2H5NO3).

Now the exact compound and method of synthesis is known, we can look at some of the possible side-effects of such a quirk. The first, which has been theorised by a few different fans, is the fact that nitro-glycerine is used to treat high blood pressure. At first it may seem that this problem is irrelevant, since it is expressly stated the compound created is not nitro-glycerine, but the treatment works via nitro-glycerine’s decomposition into nitric oxide, catalysed by the enzyme mitochondrial aldehyde dehydrogenase 2. It is then the nitric oxide which causes vasodilation, not the nitro-glycerine. This is a problem due to nitric oxide’s role as a by-product of Bakugou’s production of ethyl nitrate, and thus any of the compound that enters the blood stream would be absorbed by the blood vessels and cause lowered blood pressure. This could become dangerous, as low blood pressure creates dizziness, fatigue, nausea, and in extreme cases, loss of consciousness. Usually, low blood pressure (also known as hypotension) does not need treatment, but chronic hypotension can be treated via medication to alleviate the symptoms.

Another minor issue is the lack of normal sweating. Sweat lowers body temperature by evaporating, taking energy from the skin and cooling it. Ethyl Nitrate would perform similarly to normal sweat in this scenario, with any slight differences in energy change regulated by the amount of ethyl nitrate which is secreted (just like how the amount of sweat people secrete is based on temperature). However, it would make especially sweaty areas of Bakugou’s body dangerously flammable. It should also be noted that only Bakugou’s hands are every depicted as having explosive potential, so either Bakugou only sweats through his hands, leading to incredibly clammy, flammable and dangerous hands in any slightly warm environment, or sweats normally, leading to the possibility of his explosions spreading across his whole body. If he just sweats from his hands, this also explains the disproportionately large frequency and size of explosions he can release.

It hopefully should be rather evident that sweating explosive compounds and causing them to spontaneously detonate on one’s skin is not good for one’s bodily wellbeing. The immediate worry is one of burns from temperature increase. Ethyl Nitrate burns with 1348922 Joules per mole. I can’t find any measure for the average amount of sweat on someone’s hands, but it’s safe to assume it’s only a few ml and so the explosion of jus the residual sweat on Bakugou’s hands wouldn’t do much damage to the skin, since the heat isn’t very high or prolonged. The frequent detonation of small amounts of sweat would at worst cause hardening and callousing of the skin. But what about large quantities of sweat?

One of the largest (and first) uses of Bakugou’s quirk in combat seen is when the gauntlets integrated into his hero costume are used against Deku. They allow the storage and voluntary detonation of large volumes of Bakugou’s sweat, leading to a large explosion with significant offensive capabilities. But as Newton’s third law of motion states, every action has an equal and opposite reaction. In this case, a force of equal magnitude to the one exerted on the opponent, but in the opposite direction (along Bakugou’s arm). The magnitude of such a blast could be calculated by estimating the volume of storage in the gauntlet. The gauntlets stretch across the length of Bakugou’s forearms, and have a similar width. If we approximate them to a cylinder of length 30cm (12 inches), and width 20cm (8 inches), the volume of the gauntlets is ~9500cm3. Of course, some of this space is taken up by Bakugou’s arm, so simplifying his arm to a 10cm wide cylinder (to account for some beefy forearms), the volume reduces to ~7000cm3.

Let’s then estimate that 75% of that volume is sweat storage, so the final value for the volume of sweat each gauntlet comes to approx. 5250cm3, or 5.25 litres (1.2 gallons). This amount of liquid would weigh nearly 6kg (13.2lbs), not an easy feat to swing around with one arm, let alone jump and do acrobatics with (but again, we’re observing that Bakugou has some large muscles). We know the detonation of Ethyl Nitrate releases 1348922 Joules per mole, and 5.25 litres of Ethyl Nitrate is the equivalent of 64 moles. Therefore, the explosion of one full gauntlet releases 86.3 MJ of energy, equivalent to 20kg (44lbs) of TNT.

With proper preparation and placement, 1kg of TNT can be used to destroy a small vehicle. The explosions caused by many amateur bombs are equivalent to around 10kg of TNT. It is safe to say that if the entire gauntlet were detonated at once, the building would suffer catastrophic structural damage, most likely leading to at least partial collapse, and both Deku and Bakugou would be immediately killed (its seems All Might may have been on to something here). Although the damage caused by the use of the gauntlet is severe, it does not equate to the detonation of 20kg of TNT, and therefore we can deduce that only a portion of the total capacity of the gauntlet was detonated. The question is, how much?

After examining the many different controlled explosions usefully uploaded to YouTube, I estimate that the explosion Bakugou unleashed in episode 7 equated to roughly 10kg (22lbs) of TNT, or half of the maximum force of one gauntlet. The exact force exerted by the explosion is near impossible to accurately calculate, since the gauntlets direct the blast in a line, the dimensions and material of the corridor are not fully known, and well as many other factors come into play, not to mention I can’t find an equation that includes all of the terms ,corridor dimensions’, ‘material of corridor’, ‘width of gauntlet barrel’ and ‘weight of Bakugou and Deku’. However, we can turn to Newton again to figure out the damage to Bakugou’s arm. It is here we recall Newton’s third law of motion. It means that the force applied to Bakugou is at least the same magnitude as the force applied to Deku, and almost certainly much more since some of the force that would have hit Deku instead goes into destruction of the building. According to the BNHA wiki, Bakugou is 172cm tall, and we can see he is ~2.5 wall-tile-widths from the floor. This means the tiles in the scene are around 69cm wide and tall. Japan uses the metric system for all but traditional craft, and so it is likely the tiles are some round number of centimetres, let’s say 75cm. After the blast travels past and destroys ~35 tiles, 26m or 85ft (this seems rather far away for ‘close quarters’ combat, but here we are), it hits Deku and blasts him backwards, through the door behind him which sits 20 tiles (15m or 50ft) away. The blast is then immediately shown damaging the outer wall of the building, creating a roughly circular hole three windows wide. Afterwards, we see Deku standing in a new room, with the walls now tiled differently, but the width of each tile is the same 75cm when we compare them with the identical floor tiles. This shows us he is 7 tile-widths (5m or 16ft) from the door, having travelled a grand total of 20m (66ft).

The wind speed required to blow the average person off their feet is 45mph, the speed of a significant tropical storm. To work out the force of such a breeze, and thus the minimum force Deku was hit with, we must multiply the surface area of Deku’s body in m2, the wind speed in m/s, and the density of the air in kg/m3, giving us a final measurement of kgm/s2, or Newtons. Substituting in the numbers gives us approximately 50 Newtons of force as a minimum. Assuming this force was exerted over 1 second, we can see that 1 Deku 1m/s isn’t a realistic way to blow through a solid door. Let’s go bigger.

The magnitude of a force in Newtons can be calculated by multiplying the mass of the object the force acts upon and the resultant acceleration of the object due to the force (this is Newton’s Second Law of Motion). Since Deku starts at rest and acceleration is change in velocity over time, his acceleration is simply half his final velocity. The velocity now needs to be measured, which can be done via the approximate momentum need to break down a door.

The Enforcer is a modern battering ram used by the British Police do just that. It weighs 16 kg, and assuming it can be swung at ~15m/s (lets be conservative, Deku doesn’t need any more broken bones) the momentum it carries is 240kgm/s - this can also be understood as exerting a force of 240 Newtons on the door. For Deku to exert the same force, assuming he has an above average body weight[2] of ~75kg, he would have to be travelling at 3.2m/s. Let’s round up to 5m/s to account for his flight through the air and short trip beyond the door, since going at 2.3m/s would keep one airborne for long. This means that he has a force of 45kg × 5m/s acting upon him when hit by the blast, a force of 225 Newtons. Going back to Newton’s Third Law of Motion, this means Bakugou’s arm recoils under at least ~500 Newtons of force, since the blast originates from the gauntlet, (we’re being conservative and saying around 50% of the force missed Deku). Now we must find out the damage that this force would cause.

500 newtons is a lot of force, but it’s not the only thing to keep in mind. Boxers can punch up to 2500N, but the force doesn’t last long, maybe a tenth of a second. The main thing to focus on is impulse, and we can see that punches have an impulse of only 250kgm/s. The explosion force on Bakugou’s arm is applied over a significant time, giving an impressive impulse of ~1500kgm/s, or 6 boxer’s punches at once. The force required to dislocate a shoulder at the deltoid is around 85 Newtons, which means it’s not looking good for Bakugou’s tendons. However, the human shoulder can support a lot of force. People can dead-hang an excess of 100kg for an impressively long time, the equivalent of 980 Newtons (do note that this is in the opposite direction to our scenario, and does not carry a very high impulse). Even with the sudden shock, it’s doubtful that the 500N of recoil would do anything more than a possible dislocation (again, we’ve got serious muscle to take into account), which whilst being immensely painful would not be fatal or irreparable. But since half the force was enough to fling Deku through the air, even with adequate bracing Bakugou would near certainly be accelerated backwards and into the wall only a meter or two behind him, causing severe damage to his back, ribs, limbs, skull, and gauntlets. The headwear and shoulder guards of his costume may absorb some of the impact, but depending on their structural rigidity would probably do more harm than good, especially the sides of the mask which would be rather dangerous at high velocities.

Either way, Bakugou would be quickly propelled backwards, as if standing right next to an explosion of 10kg of TNT (a rather direct parallel) or being hit by 100 golf clubs simultaneously, if he were to unleash half of the possible blast of one of his gauntlets. Firing eve one, let alone both at full power would rival many modern-day chemical explosives, and would certainly be fatal to Bakugou and anyone within a considerable radius.

To conclude, Bakugou’s body uses nitrogen dioxide and water to create nitric acid, which is reacted with ethanol to produce ethyl nitrate. This is the explosive substance that Bakugou sweats, and it facilitates the explosions he can produce. Small amounts of the compound, as present on Bakugou’s skin, could be detonated, but to little effect. However, the storage of the compound allows significant explosive potential, with half of one gauntlet having the rough explosive power of 10kg of TNT, the equivalent of one small conventional bomb.

[1] Season 1 Episode 7: Deku vs Kaachan

[2] Season 1 Episode 3: Roaring Muscles

If you liked this investigation and want to have a say in the next one, then make sure to send a recommendation for which quirk I should investigate!

[thequirkdetective]

Investigation 3 (29/5/2020): Electrification – Denki Kaminari

For this investigation, I will be examining the quirk that has become rather notorious in the BNHA community – Denki Kaminari’s ‘Electrification’. This is mainly due to the quirk’s overuse temporarily inhibiting the user’s cognitive ability. The quirk itself allows Kaminari to create a voltage between different areas of his body or the ground, allowing him to electrically shock opponents via contact, proximity or through some conductive medium. Therefore, to explain this quirk we first need to understand electricity.

‘Electricity’ is simply the movement of charge. Most commonly this charge is the delocalised electrons in wires, but it can also be soluble ions, or any moveable charged particle. When a potential difference (most commonly called ‘voltage’) is induced between two points it creates forces that act upon the charges and, if the charges are delocalised, move them. If the charge is negative, then the charge will be forced away from the positive terminal and towards the negative, and vice versa.

To create a potential difference, one must separate differing charges. A common demonstration of this is rubbing a balloon on a jumper, where the action physically takes electrons from the jumper and adds them to the balloon. This creates a positive charge in the jumper, and a negative in the balloon. A wire with flowing current has a potential difference across it too. Potential differences can be visualised as slopes, where the charges roll from the top to the bottom. In the case of the metal wire, the negative end is the elevated end of the slope, and the negative electrons ‘roll’ down to the positive end. However, if there were flowing positive charges, those would ‘roll’ the other way.

Knowing this, we now need to understand how electricity is generated. The first port of call is power plants, where either burning fuel, or decaying radioactive isotopes boil water which drives a turbine. The turbine can also be driven by wind, flowing water, or even the movement of waves. The turbine is attached to a magnet, which spins inside a coil of wire, inducing a potential difference across the coil. The physics of this is rather complex for a blog post, so I won’t explain it here. The issue with this for Kaminari is that it requires both a magnet and wires to exist and be actively rotated within his body. However, not all electricity requires moving parts.

Alkaline batteries use a chemical reaction between two chemicals involving the loss of electrons from one chemical and the gain of electrons by the other. The chemicals are each connected to one terminal, and when they are connected with a wire, the electrons flow between the two, and the reaction occurs. The downside of this method for use by the quirk is twofold: 1, the process is irreversible, so only a certain amount of power can ever be generated by the quirk, and 2, the chemicals used are highly corrosive to organic tissue.

Rechargeable batteries operate on the same principle, but with a stronger and opposing potential difference the reaction reverses; the electrons are dragged from the negative ions back to the positive. These batteries do suffer the same drawback as disposable ones, however, regularly employing cadmium compounds in their reactions.

In principle, any redox reaction could be employed to generate voltage, reversible or not. Redox reaction is the umbrella term for any reaction involving the movement of electrons, from the words reduction, meaning the gaining of electrons, and oxidation, the loss of electrons. If Kaminari’s cells contained two reactants of a redox reaction, their connection through a conductive medium could create a voltage. Then, if the reaction were irreversible, the spent chemicals could be disposed of, and replaced via ingestion. If the reaction were reversible then it could be possible for Kaminari to literally recharge via a large DC current, such as the output of an AC to DC power converter. Sadly, sticking his fingers into a power outlet will not suffice, since all electricity supplies in Japan and most of the world are AC. The products can also be disposed of and renewed in the same manner of excretion and ingestion. Interestingly though, due to redox reactions being balanced, any electricity created in this way will ground back to Kaminari.

One possible candidate for the redox reaction is respiration. This reaction is the one that supplies cells with energy (or more specifically ATP) and allows them to carry out their functions. It’s an exothermic redox reaction, and so can be used to generate a potential difference, albeit with a few changes in biology. Firstly, in cells the electrons are carried by molecules called electron shuttles. These ‘pick up’ electrons from the glucose and deposit them into the oxygen, forming CO2 and H2O. If the electrons shuttles were replaced by a conductive medium, then they would flow through that medium, creating electricity. Since the reaction is exothermic, it will give off energy rather than require it, and so will cause a potential difference. The question now, is how much potential difference?

In season 1 of the anime, Denki uses a large discharge of electricity to stun and incapacitate surrounding villains[1], one of the largest uses of his quirk. The area of effect covers a sphere roughly 10m in diameter. The dielectric breakdown of air (how much electricity it takes to ionize it) is roughly 3 million volts per metre, so the voltage of this move is around 30 million volts, or a third of an average lightning bolt. Now, to work out the voltage given by the breakdown of one mole of glucose, we turn to the Nernst Equation, which gives the approximate voltage of any electrochemical cell. The equation is as follows: where is the voltage given, is the standard electrode potential () at room temperature, 1atm pressure, and 1mol/dm3 concentration, is the gas law constant; 8.314J/K/mol, is the temperature in Kelvin (assumed to be 298.15K), is the number of moles of electrons transferred in the reaction (every molecule of glucose transfers 12 electrons), and is Faraday’s constant, of 9.649×104C/mol. Unfortunately, it is impossible to calculate the value of   in this reaction, as no one seems to have published the reduction potential of glucose. However, we can estimate that a maximum voltage from one mole of glucose could be no more than around 10 volts. We could be out by a factor of 10 either side, but since we’re working with numbers in the millions this shouldn’t matter too much. Now, under this assumption Kaminari needs to react 3 million moles of glucose to generate the voltage seen. This is ~54050 tonnes of glucose, meaning Denki needs to eat, convert, and somehow simultaneously metabolise 55000 tonnes of sugar. Sadly, we have again reached the impasse of the human body’s limited use as an energy source, and must therefore conclude that the method of generating the energy the quirk harnesses are fantastical. However, once the energy is generated, it obeys the laws of physics perfectly.

This means that the quirk somehow creates 3o million volts of electricity, which somehow needs to find its way out of Denki’s body. As previously stated, the energy created here is equal to a third of the energy in a lightning bolt, and all of it passes through Denki. When someone is struck by lightning, they can be affected in many ways, including most commonly a large heart attack, but also include loss of consciousness, dizziness, confusion, memory loss, temporary paralysis, hearing loss, cataracts, and physical injuries from the force and temperature like burns, broken, fractured or dislocated bones, neck injuries, and lung damage. To work out how many of these apply to Kaminari, we have to find out what happens when he lets loose a full 30-million-volt blast. The air around him becomes immediately ionised – it heats up and expands, creating a large shockwave and loud bang in the same way lightning causes thunder. A lot of the charge is immediately grounded if Kaminari is standing on something earthed, but it spreads through the ground and shocks anyone standing nearby. The shockwave of ionised air spreads outwards, heated by the electricity. The force of the blast won’t be enough to knock someone over unless they are very close, but it may cause superficial burns to skin and clothing, as well as almost certainly bursting the eardrums of anyone in the near vicinity, causing pain, dizziness, and of course loss of hearing. Even those whose eardrums survive will likely gain some kind of hearing loss, the severity of which rises the closer they are to the epicentre. Kaminari suffers the maximum possible severity of all these effects since he is the epicentre. His hearing would be severely damaged, and prolonged, high voltage quirk use could cause permanent hearing loss. The force of the shockwave will also cause blunt trauma to different areas of his body, and the millions of volts that flow through his body will almost certainly cause a heart attack, and some kind of memory loss or brain damage (this is the only symptom shown in the anime). Interestingly enough, some people who have been struck by lightning had it flow around them, simply blowing their clothes off and leaving few signs of injury, though both a specially designed hero costume and the show’s age rating could help prevent this.

In conclusion, Denki Kaminari’s Electrification quirk somehow generates voltage in Kaminari’s body, up to around 30 million volts. A discharge such as this one creates a shockwave of ionized air, burning anyone immediately next to Kaminari, and causing hearing loss to anyone in the vicinity. The electricity mostly spreads through the ground, shocking anyone nearby and causing pain, convulsions, and possible heart attacks and mild brain damage. Kaminari is hit with the brunt of the shockwave, and he most probably gains broken or fractured bones, burst eardrums, memory loss, loss of consciousness, and more seriously, immediate cardiac arrest.

[1] Season 1 episode 11: “Game Over”

If you liked this investigation and want to have a say in the next one, then make sure to send a recommendation for which quirk I should investigate!

[thequirkdetective]

Investigation 2 (15/05/2020): All for One – All for One

Spoilers: season 3

Note: Throughout this investigation, ‘All for One’ will refer to the person, and ‘AfO’ will refer to the quirk

 For the next investigation, I decided to look at a villain quirk. At first, I wanted to investigate Decay �� Tomura Shigaraki’s quirk – but realised too late that the research would involve exposure to many, many manga plot points not yet covered by the anime. Since I have not yet read the manga, I will instead look into the next best big bad in the series so far – All for One – whilst trying desperately to forget all of the spoilers I saw. Since All for One is now dead (in both the anime[1] and manga as far as I know), spoilers should not be an issue. His quirk also allows me to talk about the causation and mechanic of (almost) every quirk in the series – genetics.

(Please note I am not a geneticist. My knowledge of genetics is very sparse, as you may have guessed from the fact that I am not using it not for the good of humanity but instead for a Tumblr post about My Hero Academia. If you are a geneticist, I am incredibly sorry for butchering your subject of study. If you are a supervillain trying to steal people’s genes, this is not how that really works. And also, that’s bad. Don’t do that.)

AfO allows the user to take the quirk of others from contact with them, as well as give any quirk that the user has onto someone else in the same manner[2]. Quirks are not fully explained in the anime, simply stated as “the next stage in human evolution”, and it is even explicitly stated “no-one knew what was causing these quirks”[3]. However, due to the link with evolution, it is highly probable that the quirks are caused by genetic mutation. There could be a number of causes for this mutation, such as a virus, high levels of pollution, increased UV levels, or any other mutagen. If this is the case and quirks are genetic mutations, then AfO allows the alteration of a person’s DNA. The reading and writing of DNA withing cells is still not fully understood, but it is known that DNA encodes amino acid sequences that are synthesised into proteins. This is the sole function of DNA, but the number and complexity of proteins it can encode, as well as additional features that allow it to carry out its function more effectively are what make it so essential for life.

DNA is much more complicated than this incredibly brief explanation shows, but essentially AfO can do two things: 1) Find out which gene(s) cause the quirk to be exhibited, 2) replicate those genes in every cell of his own body / the body of chosen recipient, and 3)  remove the genes from the victim’s body without causing any damage to the surrounding genetic material. Whether All for One is giving or receiving the quirk (it is, naturally, arbitrary), I will usually assume he is receiving it for the sake of consistency.

The first is relatively easy, since the quirk gene would have certain defining traits, including rarity (AfO could check the DNA against a database of other victims), and lack of inhibition. If a sample of skin were taken for a victim, the DNA could be accessed by AfO, examined, and the gene identified.

Now for figuring out how AfO takes the gene from the victim, and how the gene is given to the recipient. The latter is the easiest to theorize about, so we’ll tackle it first. It is possible that the quirk genes are not entirely removed from the victim, but are instead inhibited. Genes are inhibited all the time during the normal functioning of DNA, but this is usually by another gene. It is possible another gene is inserted into the person, but the feasibility inserting genes into others will be explored when tackling how All for One gains the quirk. Instead, it could be that a molecule is bonded to the gene. Genetic inhibition this way is categoric of some poisonous mushrooms, notably the Destroying Angel, Amanita bisporigera, which contains amatoxin. This inhibits cells’ ability to read DNA, but it works by binding to the protein that reads the DNA (RNA polymerase II), not the DNA that is being read. Instead, a protein that binds to the gene is needed, otherwise the victim will simply have the symptoms of amatoxin poison, and die. A possible contender is one that mimics the RNA copy of the gene that is created whenever the gene is ‘used’, which would bind permanently to the bases. Two are needed, each having the opposite bases of the other in order to bind to both strands of the double helix. However, this only works when the DNA is opened. For that to happen, the DNA must be being read. If three proteins are used, one to open the gene, and the other two to bind to the strands, then the gene could be rendered unusable.  However, advances in genetic engineering have given rise to CRISPR-cas9, a programmable protein that can selectively remove strands of DNA, and allows only 1 protein to be used. The molecule can remove DNA sections, and cause a cell’s repair proteins to mend the DNA, whilst also adding sections of DNA. The ability of CRISPR to add sections is useful for All for One gaining the quirk, whilst the victim can have the relevant section of DNA removed by a different CRISPR molecule.

CRISPR-cas9 is ‘programmed’ by changing its nucleotide bases, causing it to bind to different sections of DNA. Therefore. AfO needs to create a custom CRISPR molecule for every use of the quirk. This can be done if a section of the victim’s DNA is acquired, and it may be possible for CRISPR to be created in cells in a similar way to protein synthesis, where a complementary RNA copy of the gene is made, before being passed to a ribosome, where complementary codons are attracted to the RNA. If the RNA copy is passed to a CRISPR molecule, that molecule will then bind to any complementary gene, and since the RNA was created due to it being complementary to the quirk gene, the CRISPR molecule will bind to the victim’s quirk gene.

This also allows easy reproduction of the quirk gene since a copy of it has been acquired and reproduced already. AfO just needs to spread the gene throughout All for One’s cells and add it to the nucleic DNA. This is seen most commonly in bacteria, and they achieve it any one of three ways: transformation, where a bacterium picks up a loose section of DNA from its environment, transduction, where a virus randomly moves a plasmid from one bacteria to another, and conjugation is where two bacteria use pili to replicate and share DNA.

Conjugation seems promising. Once any one cell in All for One’s body contains the new gene, it could be spread quickly throughout the whole body. However, it does need to exist at least for a short while as an isolated strand, to be picked up and replicated by a cell’s pilus.

The next option is transformation, where specialised cells in All for One’s body pick up the gene and begin to replicate it, releasing copies into the bloodstream to be transformed into all other cells. This is relatively easy for each individual cell, and only needs All for One to have lymph node-like structures for gene replication.

However, all of these have the drawback of not allowing quirks to be passed from All for One to others. This can be solved by transduction. Suppose AfO creates two viruses, one that strips the quirk gene from the victim’s cells, and the other that adds the gene to All for One’s cells. The first can simply be a carrier of a specialised CRISPR molecule that can remove the quirk gene. The virus also needs to replicate itself, and that can be done by every infectious virus, so is not really an issue. Another virus is then needed that is a carrier of a different CRISPR molecule, and the quirk gene, so that the gene can be inserted into All for One’s DNA. This virus also needs to reproduce, in the same fashion as other viruses.

This method gives the added benefit of side effects. In the anime, the side effects of AfO, as seen in his victims, are drowsiness and nausea. These symptoms could be caused by two different causes (or both in tandem). The first is the immune response the viral infection that removes their quirk gene. The second the removal of the gene itself, since serendipitously, similar symptoms are shown in the first stages of amatoxin poisoning via Destroying Angel mushrooms. The later symptoms are caused by the removal of cells’ ability to divide, so they would not be caused by AfO.

However, the removal of genes in general has a few drawbacks, namely any quirk that causes a change in the body’s cells. In the same way that inhibiting the gene for hair colour won’t change someone’s hair colour immediately, people with altered bodies would only slowly feel the effects of AfO. The side-effects would hit as fast as anyone else’s, but their bodily changes would only set in over time, as their cells divided. This unfortunately has a high chance of bodily disfigurement, since at any one point some fraction of a person’s cells would be ‘normal’, and the other half quirk-exhibiting, which could lead to a change in bodly structure as the body regrows.

To conclude, AfO contains a few separate systems. All for One begins to use his quirk by in some way acquiring the DNA of the victim, probably via touch. The DNA in the sample is examined against a database of other victims’ genetic material, and the quirk-causing gene is found. A CRISPR molecule removes the gene, (we’ll call it CRISPR 1), and the victim is infected with viruses containing copies of CRISPR 1, which divide rapidly and strip the cells of the quirk gene. Next, a CRISPR molecule that can alter All for One’s DNA (CRISPR 2) is contained within another virus containing the gene. This spreads through his body, inserting the gene into his cell’s DNA. At this point, the victim begins to feel the effects of both the viral infection and the genetic tampering, and becomes faint and nauseous, whilst All for One gains mild symptoms from the viral infection. As the viruses spread through the two bodies, the victim’s quirk is stripped from their DNA to become waste protein, which is then disposed of by the body, whilst All for One’s cell’s gain the quirk as the nucleic DNA is cut, the new gene inserted, and the whole strand mended together.

[1] Season 3 episode 49: ‘One for All’

[2] Season 2 episode 33: ‘Listen Up!! A Tale from the Past’

[3] Season 1 episode 1: ‘Izuku Midoriya: Origin’

If you liked this investigation and want to have a say in the next one, then make sure to send a recommendation for which quirk should be investigated next!

[thequirkdetective]

Investigation 1 (1/05/2020): Creation – Momo Yaoyorozu

The first quirk I am investigating is Creation, an Emitter type that allows the user - Momo Yaoyorozu - to turn ingested lipids into objects[1] and release them from her skin. The first thing to note is that any material can be made with this quirk, as long as its atomic composition is known. Since lipids are carbohydrates (molecules that do not contain every known element) this means the quirk can alter the structure of the atoms of carbon, oxygen, and hydrogen, rearranging the protons, neutrons, and electrons to create new elements.

In the first part of the UA Sports Festival Yaoyorozu creates a fully functioning cannon and cannonballs[2]; one of the largest displays of her quirk in the anime. A cannon typically weighs around 3,500kg (7,700lbs), and a cannonball has a mass of roughly 17.5kg (39lbs). In the episode Yaoyorozu fires 4 cannonballs, as well as describing the creation of the weapon as “a piece of cake”. The total weight of the cannon and 4 cannonballs is 3570kg (7870lbs), meaning Yaoyorozu had to have created them from the same mass of lipid in her body under the law of the conservation of mass. Yaoyorozu looks very slim on account of the fact she should weigh 57x the healthy weight for her height, and she should have lost over 8 metric (8.8 tons) tons during the creation of the cannon, so we can safely assume the mass of the objects does not come directly from the lipids she consumes, as described. If it did, and somehow originated from a single meal, she could eat a meal, and use it to create a 3570kg (7870lbs) version of the same meal. She can then eat 1 serving of that, burn the rest as fuel and repeat, violating the laws of thermodynamics and creating infinite free energy for everyone, solving world hunger, and allowing everyone to live in a post scarcity utopia. (This has not occurred in the anime as of the end of season 4)

Since we have established the source of the objects cannot be directly from lipids, we must question what the source actually is, and whether there can be any credibility to this ‘lipid’ explanation. If the objects were created from other matter that has been reformed by Yaoyorozu’s quirk, then there has to be a cannon-sized hole in something nearby, which there isn’t. The mass could come from the air, but the volume needed to supply the same mass as a cannon is ~3 million litres, or 1/10 of the air within the UA Sports Stadium. This volume is not only infeasible to consume, alter, and emit in such a short space of time, it would also create a large wind, with Yaoyorozu acting as a vacuum. This alone would most likely be enough to topple the robots without the use of the cannon.

Another option is the use of energy. Since mass is just a from of energy, Yaoyorozu could be harnessing some source of energy and using it to generate mass. Although this is theorised to be impossible under the standard model of particle physics as it changes the number of quarks in a closed system, the possibility remains in other theoretical models of physics. This process has the added benefit of explaining the ability to create any element, since the entire process hinges around the creation of individual quarks. To calculate the energy required for the cannon creation, we turn to the most famous equation in Physics; . This tells us that the energy stored in matter is equal to the matter’s mass (in kg) multiplied by the speed of light (in m/s) squared. Plugging in the numbers shows that the energy required to form a cannon and four cannonballs is…

320855598809043897480 joules.

The destructive capability of harnessing this much energy can be demonstrated via the detonation of 41256 Tsar bombs – the most destructive weapon humanity has ever created. This is enough Tsar Bombs to fill almost 5000 large warehouses.

If this energy were to be gained via the standard way humans gain energy – eating and respiring using the ingested glucose – Yaoyorozu would have to eat a meal before the obstacle course with a calorie count of 76686328587247580kcal. To put this in perspective, this equates to 36 trillion skyscrapers worth of bacon, or enough bags of crisps to give everyone in the world 2500 tons of Walkers cheese and onion (or Lays if you’re American). Of course, this method of energy generation is bound to be less efficient than directly altering lipids, since the human body is not 100% efficient at generating energy from mass. The same line of reasoning can describe why Yaoyorozu doesn’t gain the energy from radioactive sources, since these are not 100% efficient either. The only process that does turn mass into energy with 100% efficiency is the annihilation of antimatter and matter. Sadly, reversing this process a) required double the amount of energy, as you need to make two copies of the object, one made of antimatter, and b) will cause the matter and antimatter copies to annihilate immediately, releasing the same amount of energy you just put into creating them – 82,512 Tsar Bombs. Needless to say, this would vaporize a large chunk of the continent and plunge the world into a nuclear winter which would cause the extinction of all life on earth.

It seems there isn’t a way of creating the cannon that’s fully adherent to canon, and I believe there isn’t a way of creating one compliant our current understanding of the laws of physics. In order for Yaoyorozu to create such a large object, she would have to have at least the same amount of mass to transmute, and since nothing / no-one in the scene ends up with a cannon-sized chunk of them missing, it appears the creation of the objects within Yaoyorozu’s body is something we have to relinquish to the realms of fantasy.

The releasing of the objects, however, is not.

Human skin is comprised of many layers. We do not know for certain which layer the object is created in, but whichever it is, the layers above will be stripped away as the object grows in size and is ejected from the body, so it makes sense for it to be as close to the surface as possible. Here, we may still find a kernel of truth in the ‘lipids’ claim. The hypodermis contains a layer of fat lying beneath the epidermis and dermis and just above the muscle called the subcutaneous fat layer. It could be that ‘made out of lipids’ is a simplification of the fact that the objects originate from the layer of skin where some of the lipids in the body are stored. The downside of this is that any object originating in the hypodermis must then punch through the epidermis and dermis to be used, leaving a large, deep graze more akin to a terrible burn, or being flayed alive. Additionally, sizeable portions of skin would be ejected from the body. This would of course be both unsightly and inconvenient. Seeing as large amounts or gore do not erupt from Yaoyorozu when she uses her quirk[2] , we are again calling the feasibility of canon into question.

If the object is created in the live cells above the subcutaneous fat, then the quirk does not properly create objects from lipids. However, I think this is a detail we can let slide if it means leaving most of Yaoyorozu’s skin attached to her body.

Most.

The topmost layer of skin is called the epidermis, which itself is comprised of multiple layers. The very bottom layer, known as the stratum basale or stratum germinativum, is comprised of dividing keratinocytes. The keratinocytes are then pushed to the surface, undergoing cornification. By the time the cells have reached the surface, they are bound husks full of keratin, their surface covered in a cornified cell envelope. The layers above the stratum basale are thus in various stages of cornification and cannot carry out any function. Therefore, the shallowest layer of living cells that can hypothetically produce objects via quirk are the cells of the stratum basale itself. The cells may not have enough blood flow to gather the required nutrients, but as discussed previously, the objects cannot be created from raw matter. The object creation occurring in the basal layer does mean any cells above this layer are forcibly removed whenever an object is created. However, this isn’t as bad as if the quirk manifested in the hypodermis, and simply leaves a light graze.

So, after all this research we can finally understand Yaoyorozu’s quirk. It activates at will, with Yaoyorozu thinking of an object she wishes to create, and then the basal cells in Yaoyorozu’s skin collect the chemicals required from an unknown source and begin construction. The resultant object pushes its way through the epidermis, finally emerging with a graze in its wake, and dead skin covering its surface. Prolonged use of the quirk could lead to scarring due to the continued trauma of the basal cells, however this is not permanent, as it is conveniently removed upon use of the quirk.

[1] Season 1 episode 11: ‘Game Over’

[2] Season 2 episode 16: ‘In Their Own Quirky Ways’