This video brilliantly applies Fermi estimation to bridge the gap between infant physiology and planetary-scale physics. It proves that even the most absurd internet memes can be subjected to rigorous thermodynamic scrutiny.
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How Many Coughing Babies Would it Take to Defeat Omni-Man?Added:
On a scale of powerfulness, Omni Man and a coughing baby are basically on opposite ends of the spectrum. Omni Man is ridiculously strong and the power of a coughing baby is almost zero.
Almost zero. Omni Man might be strong, but he's not A coughing baby's power level is not zero. Small as one coughing baby may be, if you add enough of them together, their combined strength could defeat Omni Man.
To put it in more mathematical terms, there exists some number n such that for all numbers greater than n, that many coughing babies would defeat Omni Man.
The only question is, what is that n?
How many coughing babies would it take to defeat Omni Man? Unfortunately, we can't find an exact answer, but we can find a lower bound for how many coughing babies it would take to defeat Omni Man.
Step one, we got to figure out just how powerful a coughing baby actually is.
The critics might tell you that the reason why the hydrogen bomb versus coughing baby meme became so popular is because humans are at their weakest when they are infants. Likewise, humans are also especially weak when they are sick.
So, if a baby is coughing, that implies it is sick. Therefore, you have a sick human in its weakest form, a coughing baby. What they fail to understand, however, is that a cough actually contains kinetic energy. So, by giving us this idea of a coughing baby, they have actually given us something that we can directly quantify. There are several academic studies that dive into the fluid dynamics of the human cough, looking at flow rates, velocities, turbulence, and everything in between.
Although there was some level of variation in the numbers reported by these studies, they all generally talk about the average velocity of the human cough being between 10 and 15 m per second, and the average volume of the human cough being between 1 and 5 L of air. Here in this video, we will be using 2 and 1/2 L of air as the average volume of the typical adult cough. And the average velocity of the air in the adult cough is 11.7 m per second. Links in the description to the studies that reported these numbers. So, putting it all together, we can find the approximate kinetic energy of an adult cough using the formula T = 1/2 mv^2.
For the mass of the cough, we simply multiply its volume by the density of the air, because the density of air does not actually change all that much relative to ambient pressure in a cough.
Putting it all together, we find that the average adult cough contains about 210 mJ of kinetic energy. Now, at least the last time I checked, human babies are smaller than human adults, meaning that their coughs will not contain as much kinetic energy. So, we are going to make what I think are some pretty reasonable assumptions about coughs.
Let's assume that the volume of air in your cough is approximately proportional to your lung capacity, and that the velocity of your cough is approximately proportional to the strength of your diaphragm. Now, looking at what the baby's lung volume actually is, lung volume is approximately proportional to body weight. A 6-month-old male baby weighs approximately 8 kg, whereas a full-grown adult weighs about 90 kg.
Therefore, the baby is approximately 9% of the adult's overall body weight, meaning it has about 9% the overall lung capacity of an adult, or just a little bit over a fifth of a liter. Looking at the velocity of a baby's cough now, we know that pressure is equal to force divided by area. Interestingly enough, the overall pressure that a baby's diaphragm can generate is about the same as that of an adult's, which then implies that the overall force that a baby's diaphragm can generate is approximately equal to the cross-sectional area of the baby's diaphragm multiplied by the force output of an adult's diaphragm divided by the cross-sectional area of the adult's diaphragm. The cross-sectional area of your diaphragm is proportional to your height squared, and we go ahead and assume that the force output of the diaphragm is more or less proportional to the cough velocity. If a 6-month-old baby is approximately 37% the height of a full-grown adult, that means that a baby has an average cough velocity of about 1.65 m/s.
Putting it all together, that means that the baby's cough contains about 0.366 mJ of kinetic energy. However, to be fair, the adults in those studies were voluntarily coughing >> [cough] [clears throat] >> as opposed to coughing at their full strength.
When a baby coughs, it's probably going to be coughing a lot more vigorously relative to its body size than the adults did in that study. So, we'll be generous and say that the baby's cough is approximately 1 mJ of kinetic energy.
The next step is to figure out just how strong Omni-Man is, and we can do that by taking a look at some of his greatest feats. Now, hopefully I don't have to say it, but be warned, spoilers ahead.
One of Omni-Man's most impressive feats that I feel like just gets looked over way too often is his ability to simply hover here next to a black hole. Not only does he seem completely unfazed by the sheer amount of energy that he is fighting against right now, but at a certain point, a spaceship the size of a semi-truck starts to move towards the black hole, and Omni-Man is able to just casually move them away. Now, full disclosure, I haven't actually taken any general relativity courses. Last semester I did take a tensor calculus course where we spent the entire semester building our way up to be able to talk about the Schwarzschild metric.
But luckily, Omni-Man and this spaceship here seem to be far enough away from the event horizon of this black hole that we don't actually need a whole lot of relativistic corrections. This is the Paczynski-Wiita approximation used to find the effective gravitational potential energy for an object between three and 10 Schwarzschild radii away from a non-rotating black hole. Now, this black hole pretty clearly seems to be rotating, but you'll see how we can kind of sort of work around that a little bit here in a minute. If we assume that this black hole here has a mass that is comparable to that of Sagittarius A* which is the supermassive black hole at the center of the Milky Way, and assuming that this spaceship is roughly the mass of a semi-truck, we can go back to our potential field approximation. Big M is the mass of Sagittarius A*, and then multiplying by little m, which will be the mass of the semi-truck. If we look back at the shots from the show, they seem to be maybe a diameter and a half away from the black hole, which is about three Schwarzschild radii. So, overall, Omni-Man seems to be able to successfully fight against 10 to the 21 joules of potential energy here.
However, that's only if the black hole was not rotating, which again we said it likely is rotating. Paczynski-Wiita will underestimate the potential by a factor of six or more. So really, this whole sequence demonstrates Omni-Man's ability to resist 10 to the 22nd joules or more.
That's about 100 times current annual global energy consumption. However, this still isn't anywhere near Omni-Man's most impressive feats. In season 1 of Invincible, Omni-Man casually remarks about redirecting an asteroid the size of Texas away from Earth. If we take that to imply that the asteroid's diameter was more or less the same as the width of Texas, say the distance from El Paso to Houston at 1,085 km. If we assume the asteroid was spherical enough that 4/3 pi r cubed is a good approximation for its volume, that means that the asteroid was approximately 669 million cubic kilometers, or 669 quadrillion cubic meters. Assuming this was a near-Earth asteroid on the slightly denser side, that implies that it had a density of more or less 4,000 kg per cubic meter. Hence, it weighs around 2.67 sextillion kilograms.
Near-Earth asteroids tend to have orbital velocities of around 20,000 m/s, which means that Omni-Man faced down against an object with a kinetic energy on the order of 10 to the 29 to 10 to the 30 joules of kinetic energy, and just casually redirected it. Now, that is pretty impressive, but it pales in comparison to what is arguably his most impressive feat, that being the destruction of the planet Viltrum. Now, granted, he did do this with the help of two other notable Viltrumites plus Space Racer's Infinity Ray, but even if you divide this feat evenly three ways, which let's be frank, it probably wasn't an even three-way split between Mark, Thaddeus, and Nolan, assuming Viltrum is similar in volume and mass to Earth with a gravitational binding energy of 2.49 * 10 ^ 32 J, that means that this feat of Omni-Man was on the order of 10 to the 32nd joules of energy. And then he still had energy left over to fight Thraag. So, we can safely assume that in order to defeat Omni-Man, you would need upwards of one decillion joules of energy. Now, back to the babies. We generously said that one baby cough contains about one millijoule of kinetic energy, which means that you would need a whopping one decillion baby coughs in rapid succession in order to defeat Omni-Man.
If each baby coughs 10 times, that is a minimum of 100 decillion babies needed to defeat Omni-Man. Of course, then you have to figure out how you're going to get 10 to the 35 coughing babies all close enough to Omni-Man at the same time to kill him, but we can figure that out another time. If you want to know what the ideal air-to-water ratio is inside of a water bottle for a water bottle flip, then click this video appearing on the end screen right now.
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