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I am working on a character that has multiple superpowers that work in a matter similar to My Hero Academia and has been transported to a world of magic. I am trying to figure out how some of these powers would interact and affect the world around him.

For example, the power to freely manipulate your weight into the multiton range, alter the vector of anything you touch (including accelerating yourself and other objects into the massively hypersonic range), and the ability to turn yourself into an indestructible, immobile crystalline statue. What would happen then if, say, the character found himself surrounded by enemies and made the panicked decision to hurl himself up into the troposphere, increase his weight into the hundreds of tonnes range, then sent himself back down at his enemies at mach 50? Exactly how much of an oopsie is this?

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  • $\begingroup$ Please edit the question to limit it to a specific problem with enough detail to identify an adequate answer. $\endgroup$
    – Community Bot
    Commented Oct 16, 2022 at 3:39
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    $\begingroup$ A better question is what do you want to happen, and then how heavy and fast does the object need to be for that to be plausible. $\endgroup$
    – kaya3
    Commented Oct 16, 2022 at 3:48
  • $\begingroup$ a few issues, you are in the troposphere right now. A fall from the highest part of the troposphere will only get your guy up to around 600m/s and that is ignoring air resistance. so he is falling two orders of magnitude too fast. making him heavier does not make gravitational acceleration any faster. the moon dropped at the same altritide would still only reach 600m/s $\endgroup$
    – John
    Commented Oct 16, 2022 at 20:39
  • $\begingroup$ Note that one of the powers my character possessed was the ability to manipulate the vector (that is to say momentum, direction, velocity, and inertia) of anything his body touches at will and he can push this power into the massively hypersonic range. The issue about the pull of gravity not being enough to provide the required acceleration to reach mach 50 doesn't apply here. The question is exactly how much damage my character is going to do when he turns himself into a 3.4 meter, 330000 ton indestructible statue hurtling to the earth at mach 50? $\endgroup$
    – Grant Pflum
    Commented Oct 17, 2022 at 0:51
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    $\begingroup$ Gonna be hard to aim at that speed from that height. Gonna be hard to see with the wind. I bet he misses clean and makes a crater nearby. Hopefully his ego can withstand the enemies that panicked him coming to the edge of the crater and guffawing, because he missed, and now he is naked because he blew his clothes off with the 17 km/second wind., and he has a big tattoo that says "THE TOUHGEST!" on his chest. $\endgroup$
    – Willk
    Commented Oct 17, 2022 at 2:16

3 Answers 3

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You said the character can "increase his weight." By this I assume you mean he becomes more dense without increasing his size; he's still the same size as a human. Furthermore you said that he can become indestructible, so he's not going to break up on impact.

This means your character is not like a meteor hitting Earth, and not like a nuclear explosion, because he will not release all his energy at once on impact. Instead, he will punch a deep hole in the ground, gradually slowing over a distance of 70m to 300m as he passes through the rock. His kinetic energy will be released gradually along the length of this hole, and the blast radius on the surface will be fairly small. The impact will spray molten rock back up out of the hole.

In a collision at mach 50, the speeds and forces are so great that the tensile strength of the rock he is passing through doesn't matter very much. As a result, we can use Newton's approximation for the impact depth. We can assume he is passing through granite, with a density of 2.6 g/cm^3. The distance he travels through the granite depends on his orientation on impact. If he hits feet-first or head-first, then we might estimate his cross-sectional area to be 2 ft^2 (1860 cm^2), which means he will penetrate 300m deep. If he belly-flops, we might estimate his cross-sectional area to be 9 ft^2 (8360 cm^2), which means he will only penetrate 70m deep.

His impact energy will be about 2 * 10^13 J, or 5 kilotons TNT, which is about a third of the energy of the bomb dropped on Hiroshima. But it will not devastate nearly as large an area, because most of the energy will be dumped harmlessly deep underground.

It's difficult to say how much destruction there will be on the surface. For one thing it depends on his body orientation; head-first or feet-first will naturally result in a smaller crater. To truly answer this question we would need to do an appropriate fluid dynamics simulation. However, we can safely say the energy reaching the surface to cause damage will be only a small fraction of his initial kinetic energy. If we say that 10% of his initial kinetic energy is released as a surface blast, then we can use nukemap with an 0.5 kT detonation to get some idea of the damage: a crater 30m radius, 10m deep; a fireball 60m radius; heavy blast damage in 170m radius; moderate blast damage in 360m radius. Thermal radiation radius can be ignored, because the ground would act as a shield.

The real damage radius could be a lot less than this because what energy does reach the surface will be guided upwards by the shape of the hole, instead of spreading out horizontally.

There would also certainly be lava and rocks raining down from the sky in a large radius, but again, difficult to say what the radius of this effect would be without a fluid dynamics simulation.

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    $\begingroup$ Since you mention the ground absorbing most of the impact, we can assume up to a magnitude 5.6 Earthquake. keisan.casio.com/exec/system/1346229131 So, while the blast may be small, the resulting Earthquake could have a much bigger radius than an equivalent nuke. $\endgroup$
    – Nosajimiki
    Commented Oct 17, 2022 at 13:54
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    $\begingroup$ He's going many times the speed of sound in Granite. And as an invulnerable person, the speed of sound in the impactor is a bit of a division by zero problem. This is going to be outside of the newtonian impactor range of validity? $\endgroup$
    – Yakk
    Commented Oct 17, 2022 at 16:38
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    $\begingroup$ @Yakk The assumption of Newton's approximation is that for the guy to stop, he has to transfer his momentum into the rock directly in front of him, and the speed is high enough that the material strength of the rock won't be a factor, only its mass. These assumptions are met. What the wikipedia article says about a top speed for the approximation to be valid is because at high enough speeds the impactor would break apart, which isn't an issue here because he's indestructible. $\endgroup$
    – causative
    Commented Oct 17, 2022 at 16:52
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    $\begingroup$ You mention punching a hole, but the matter that he's punching through has to be moved out of his way some how: It's going to be pushed down and sideways at supersonic speeds, and the rock will be pulverized and heated by this process, but you seem to assume the rock he hits will simply cease to be. The rebound will throw much of the displaced material into the air. This is going to look a lot like a meteor impact, even if the "meteor" itself doesn't break up. The ground is also shattered by a meteor - which is why craters are larger than the impactors. $\endgroup$
    – Sarah Messer
    Commented Oct 17, 2022 at 18:11
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    $\begingroup$ We can calculate how much energy will be released at each depth from 0 to 300m, because the projectile will slow at a uniform rate with depth (because in Newton's approximation it bleeds momentum at a uniform rate with depth). As a result the energy released per meter will decrease linearly with depth, with twice as much energy released in the first meter as in the 150th meter. In the first 10 meters he will go from mach 50 to mach 50 * (290/300), so 7% of his energy will be released in the first 10 meters if he hits feet-first. $\endgroup$
    – causative
    Commented Oct 17, 2022 at 19:26
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Mach 50 is 17,150 m/s. That is 17.15 km/s. At this speed, each kg of matter has $1.47 \times 10^8$ Joules of energy. This is the equivalent of 35 kg of TNT. Your 330,000 pounds at Mach 50 is thus 149,685 kg at Mach 50, equivalent to 5.238 million kg of TNT, or 5.238 kilo-tonnes. This is round-about one quarter of the energy of the atom bomb used on Hiroshima.

Note that he cannot achieve this just by falling. You need to assume he can generate this energy somehow. Falling from near-Earth orbit will at most get you something like 5 km/s, compared to your 17. So you would get something less than 10 percent of the energy here.

Also note that, assuming a density similar to water, your character has a diameter round-about 60 meters. So the energy will tend to be highly concentrated. So the tendency will be to punch a hole rather than blast the surface. The energy will tend to disipate in making a crater. There is an impact crater calculator on line. Depending on the assumptions about the ground and the angle of impact, the crater will be something like 1.4 km across.

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    $\begingroup$ If a character has a super power to "increase his weight," I would assume this means he just becomes more dense without increasing his size. Furthermore he is stated to have the power of indestructibility. As a result he will not hit like a nuclear explosion - he will punch a small, deep hole in the ground. $\endgroup$
    – causative
    Commented Oct 17, 2022 at 7:31
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    $\begingroup$ @causative The nuclear explosion will be the ground exploding, not him. If you hit something hard enough, it goes off like a bomb; bombs are, in a sense, just stuff hitting each other really hard. The real question is how invulnerable is the super -- are they completely inelastic? If so, we run into division by zero problems. Then how compressible is the ground; I could imagine extremely exotic reactions going on. How hot does plasma-ground have to be to move out of the way fast enough for the super to penetrate? $\endgroup$
    – Yakk
    Commented Oct 17, 2022 at 16:22
  • $\begingroup$ @Yakk At speeds like that, bedrock acts like a liquid. It will get out of the way. Yes, the rock is going to explode when he deposits energy into it, but most of the energy will be released deep underground instead of causing damage on the surface. $\endgroup$
    – causative
    Commented Oct 17, 2022 at 20:51
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It's a big badda boom, but not too bad in the grand scheme of things. Meteorites with this sort of energy hit the Earth every year or so. Such meteorites usually air burst, but in your case it would create a crater the size of which would depend on the assumptions you make.
https://en.wikipedia.org/wiki/Impact_event#Frequency_and_risk

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