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Let us suppose that we have people who for all intents and purposes are human, except for one (not so) tiny modification: they are able to exert enough muscular force and react fast enough that they can move their whole body, or their limbs independently, faster than the speed of sound, say $1800 \text{ kmh}^{-1}$ / $1118 \text{ mih}^{-1}$/ $500 \text{ ms}^{-1}$, and can accelerate to such speeds in as little as a few metres or so ($30\text{ kms}^{-2}$, or $3061\text{ g}$), without any ill effects to themselves. They can see where they are going and what they are doing; everyone and everything else would appear to be moving in slow motion. They have no special ability to generate thrust, they achieve such speeds by running or jumping or otherwise applying a force against another object.

However, let us also suppose that only their own bodies are protected from the ill effects of such speeds and accelerations. They could throw and catch something at said speeds, and while their bodies would no more be injured by performing such an action than ours would when throwing something, the things that they throw are not so protected. Any clothing they may wear is not protected either.

This ability is gained by magic, but I'm looking for answers that do not rely on magic, only science.

What would the effects on their possessions, the environment and any bystanders be should such a person use this ability?

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  • $\begingroup$ sonic booms would be dangerous $\endgroup$ – bowlturner Feb 11 '15 at 3:18
  • $\begingroup$ Remember that stopping is as intensive as the starting force. @bowlturner - could you generate sonic booms by waving your arm back and forth quickly? $\endgroup$ – Twelfth Feb 11 '15 at 21:32
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    $\begingroup$ Check you figures in km vs miles. $\endgroup$ – JDługosz May 17 '17 at 23:13
  • $\begingroup$ @JDługosz, Thanks for the heads-up. Fixed. $\endgroup$ – Monty Wild May 18 '17 at 2:53
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What would the effects on their possessions, the environment and any bystanders be should such a person use this ability?

A lot

You made me look up a new Order of Magnitude chart on Wikipedia: acceleration! Congratulations! I haven't needed that one.

3000Gs is roughly the acceleration of a baseball as its hit by a baseball bat. However, that is over a very short time period, and impacts a nice compact mass. Accelerating a purse to the speed of sound is going to be icky. The average purse weighs about 2kg. An acceleration of $30000 \text{m}/\text{s}^2$ on that is going to yield a force of 60kN on the poor pursestrap. For perspective, a climbing carbiner is rated to 20-30kN. Novice climbers who don't trust their gear are reminded that that is more than sufficient to hold a car. You'd need 2 of them just to hold a purse to you, and you'd probably want climbing-grade webbing for a strap. No designer leather here.

You'd probably want to rely on magic to accelerate these components with you, using the same magic that prevents these humans from turning to goo. However, we're going to need more magic. Humans are not exactly Sears-Haack bodies. This means that, once you're up to speed, the wave drag of the sonic boom behind you is going to be brutal. This drag is also not just concentrated on one point, so any clothing or equipment which was not ripped off by the acceleration is going to be subject to tremendous forces. Modern planes are designed to get through this region with many shockwaves as fast as possible: the X-15 used over 250kN of thrust from anhydrous amonia and liquid oxygen. This is probably another place for magic to come to the rescue.

Finally, consider newton's 3rd law: for every action there is an equal and opposite reaction. Not only do they need to withstand the abuse of acceleration, but whatever they're pushing against has to as well. Let's avoid having to play friction games, and give them a perfect vertical surface to accelerate off of. The suface of an average human's feet is roughly $0.02 \text{m}^2$. If we are accelerating a 100kg man at $30000 \text{m}/\text{s}^2$ like you say, we are looking at 150 MPa. Tossing that into Wolfram Alpha we see some comparisons:

  • 0.2 to 0.6 times the pressure of a water cutter
  • 0.5 to 2.1 times the maximum pressure in the chamber of a firing pistol
  • 1.8 times the pressure at the bottom of the Mariana Trench

Now we eventually have to move some object in the other direction to equalize things. In a perfect world, you'd just slow the rotation of the earth down, or make it wobble a wee bit. However, just how hard is this? Consider momentum balancing... momentum of your superhero moving forward must be matched with momentum of some object moving backwards. We don't want to have to kick an object backwards supersonic (that would upset the nearby gawkers). We need to kick a massive object slowly. A train locomotive will do nicely. A GE Genesis like you'd find on the front of an Amtrak train clocks in at 121,672kg. That's 1216 times more massive than our 100kg man, so it needs to go in the opposite direction 1216 times slower than our man. That's .4m/s. If you were to shove a Genesis sideways with that force, you'd lift it up on one set of wheels, with the other wheels dangling 1.6cm off the tracks*. If you aimed for the top of the train (the previous calculations assumed you shoved right at its center of gravity), 10 people kicking off at once could knock a Genesis clean off the tracks.

* Slight literary license. Train wheels are not actually fixed to the car. The car merely rests on top of them with enough weight that they're (usually) not going anywhere. However, I think this imagery is worth the slight inaccuracy.

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    $\begingroup$ Since they are accelerating by pushing against the ground, my gut sense is that they would end up about half a km up in the air after every 'step'... $\endgroup$ – Serban Tanasa Feb 11 '15 at 13:08
  • $\begingroup$ @ServanTanasa: Yeah, that's why I ran the math with them pushing against a wall. I also decided it would be fair to give them "magic shoes" which have a virtually unlimited coefficient of friction. That way they could just push forward, not up (but they'd still be bound by the strength of the material they're pushing on) $\endgroup$ – Cort Ammon - Reinstate Monica Feb 11 '15 at 15:11
  • $\begingroup$ Can you include the effects of being near a person who is generating a supersonic shock wave upon bystanders/environment? $\endgroup$ – Monty Wild Feb 12 '15 at 0:30
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    $\begingroup$ Wow, I did not expect how little trouble they cause. Wikiepdia's Sonic boom page says most sonic booms clock in under 1000 Pa. The record is 7000Pa, caused by a F-4 flying at 30m. No researchers were harmed by it. It appears organics are pretty resilient after all (glass doesn't fare as well because its brittle). I expected much more damage! $\endgroup$ – Cort Ammon - Reinstate Monica Feb 12 '15 at 2:39
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    $\begingroup$ I envisioned them throwing up roostertails of ablated terrain as they ran, and they'd be more climbing than running, as they'd be leaning forward so far. $\endgroup$ – Monty Wild Feb 13 '15 at 0:26
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As for the person...

It would feel like being in an endless vat of molasses. with insignificant acceleration due to gravity compared to wind resistance. I imagine that is how it would feel regardless of how strong your are, or are able to execute whatever move/thing you are doing. Gravity would be wayyyyyyy below your strength level hence not really being noticeable. The molasses is an air replica. Although I'm not super educated on supersonic fluid dynamics.

Now get your mind on that level or you will never execute it...

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  • $\begingroup$ No gravity? While I understand that such speed may allow you to move faster than the pull of gravity horizontally, shouldn't you still be confined to the Earth because you can't run straight up? $\endgroup$ – Zxyrra Feb 4 '17 at 5:46
  • $\begingroup$ Well, at top speed they're going just under half of escape velocity and accelerating over 30 times faster than an anti-ballistic missile, so I don't think gravity will have any noticeable effects compared to everything else. $\endgroup$ – matsjoyce Feb 4 '17 at 8:52
  • $\begingroup$ Welcome to the site, kevlar. Please note that science-based tag expects answers to be supported by scientific evidence. If you could link to some information indicating how gravity wouldn't apply to a supersonic body, the community would appreciate it. Otherwise, this may be deleted as inadequate. Feel free to take the tour to get a better understanding of how the site works. $\endgroup$ – Frostfyre Feb 4 '17 at 13:58

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