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It's no secret that super-speed comes with a slew of nigh-mystical secondary powers to protect both the speedster and their surroundings. There are common exceptions when writers want the speedster to dish out damage, but there are also nearly universal rules like abolishing conservation of momentum so that city roads aren't regularly destroyed by footsteps.

One aspect I haven't heard much about though is the speedster's lack of effect on air. Like how a moving car generates wind that can be felt by passers-by, a speedster should not be able to run closely by other people without them even noticing. If we do not hand-wave this away with yet another speedster perk, how fast CAN a speedster go before they injure or push people just with air pressure and wind? Analogies by real-world examples of fast objects are welcome.

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    $\begingroup$ Can you be (much) more specific about the target results? I can be "pushed by the wind" by a sprinter if he/she runs in front of my toes. What, (very) specifically, are you using as the basis of judgement? What exactly does injury and being pushed around mean? How tall & heavy is the target person? Are they athletic or naturally agile? What are they wearing? What are the current weather conditions? Does the target know the speedster is coming (prepared for the effect)? There are a LOT of things that affect this question. I'm thinking 2 paragraphs of explanation. Until then, VTC:Unclear. $\endgroup$ – JBH Sep 19 '19 at 23:43
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    $\begingroup$ BTW, welcome to the site. This is normal. We like to give well-thought-out answers, which means we need well-thought-out questions. The close vote isn't a punishment, is a hold to keep well meaning but often too enthusiastic users from posting less than well-thought-out answers. This is a good question, it just needs some expanding and clarification to make it a great question. $\endgroup$ – JBH Sep 19 '19 at 23:45
  • $\begingroup$ Given that a car generates enough Air Pressure to move people around, I would randomly pick a number around 150-200KM/H. You will also hit a hard limit at the speed of sound (1200km/h), where your speedster is producing a Sonic Boom. $\endgroup$ – Shadowzee Sep 20 '19 at 1:18
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This is going to be difficult to solve even with a solid definition of damage, because there are just so many variables involved. I really doubt you will be able to get a specific answer no matter how much detail you give. This is the kind of question NASA would solve with wind tunnel tests and weeks of supercomputer time. So consider my answer as a really rough guess.

If we're including hearing loss as damage, then your limit for observer safety is the speed of sound. Sonic booms will cause hearing loss, whether it's from a bullet, a jet fighter, or The Flash.

If we're not including hearing loss it gets a lot tougher. As things move through the air, they leave a pressure wave behind them. The faster you move, the higher pressure the wave. Also however, the larger your surface area, the higher the pressure. Last, the closer you pass by the sensor, the higher the pressure will be. Fighter jets will break windows if they go super sonic near them. So since your speedster is much smaller than a fighter jet, he can either go faster, or go the same speed but closer than the fighter jets. On the opposite end of the spectrum, bullets often are several times faster than fighter jets, and yet you won't even feel one pass by you by more than a few centimeters. Note in this video, he shoots through the gaps of a card house, and it barely budges. So a quick google search tells me that the speed of sound is 331m/s, which I'll take as the minimum for my jet fighter example. Another quick google search tells me the muzzle velocity of that 50 caliber rifle in the video is about 931m/s. Recall, my argument is that your speedster is smaller than a jet, and larger than a bullet, so he will have a pressure wave that's bigger than the bullet, and smaller than the jet. So this means your safe speed limit is somewhere between 331m/s and 931m/s.

This will vary with the weather by the way.

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    $\begingroup$ +1. The only thing I would add is that the distance between the cards and the bullet is very small when measured in bullet widths. If we scale that up to human size, I think it would be fair to say that your speedster can go faster than your safe speed limit as long as the potential victim is more than an arm span away from his path. $\endgroup$ – Henry Taylor Sep 20 '19 at 2:05
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    $\begingroup$ +1. Love your answer, just a few details to add. 1) the sonic barrier varies by elevation, so the runner does not have to go as fast as a fighter jet to create a sonic boom. 2) the shockwave is determined by the transonic area or "drag force" of the object, not its total area. A bullet and a fighter jet are both designed to minimize this area. The bullet is effectively a pinpoint travelling through the air (slightly larger but not much thanks to its stabilizing spiral flight pattern) and the fighter plane's drag is actually close to that of a person, so the speedster would be more disruptive. $\endgroup$ – HA Harvey Sep 20 '19 at 4:06
  • $\begingroup$ Bullets in general are slower or equal to fighter jets: 300-800 m/s for most bullets vs up to 600-1000 m/s for jets (that one with 1000 m/s was a reconnaissance aircraft, actually). And bullets loose speed very quickly, unlike jets. $\endgroup$ – ksbes Sep 20 '19 at 7:10
  • $\begingroup$ Adding to ksbes's comment, one of the reasons that missles are preferred over bullets with modern fighter jets is that the jet risks running into it's own bullets if it fires the gun while travelling at high speeds. $\endgroup$ – krb Sep 20 '19 at 10:30

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