# How fast is the shockwave of a nuclear bomb from 2-5m away?

Namely, would my superhero who can fly to the moon in minutes like Superman be able to outspeed the point-blank detonation of a nuclear bomb, thus defusing nearly all tension from any conflict not involving other spandex-clad freaks of nature? Or would they still be caught in it?

Note that although I compared them to Superman, this character CANNOT fly faster than speed of light. I just want to know if they can fly faster than the speed of nuke.

• Ehhhh when you get to the point where people compare you to Superman even in jest, that level of destructive power usually isn't a problem (although the effects of acute radiation poisoning could be an interesting angle to explore). This is more like a kryptonite bomb meant to act as an unavoidable delivery system for the superhero's achilles heel. Sep 9, 2016 at 2:45
• This appears to be about story/plot development, rather than about the construction of the world in which the story occurs. Sep 11, 2016 at 5:04
• Looking at this almost two years later, I suppose I'm less convinced that it's off-topic. It's not really about building a plot; it's just asking "Assuming my superhero is extremely fast, can he outrun a shock wave?" - which doesn't seem that story-based. Jun 14, 2018 at 23:19
• A shockwave travels at the speed of sound or a single digit multiple thereof. If your hero can reach the moon from Earth in minutes, it shouldn't be a problem. Jun 15, 2018 at 6:18
• lol. @HDE226868, in what way is someone asking if his superhero can outrun a shockwave somehow not seeming "that story based"? Jan 11, 2020 at 1:11

The blast wind at sea level may exceed one thousand km/h, or ~300 m/s, approaching the speed of sound in air.

-

About 5% of the energy released in a nuclear air burst is in the form of ionizing radiation: neutrons, gamma rays, alpha particles and electrons moving at speeds up to the speed of light.

• A bit singed were you? Sep 9, 2016 at 1:26

Here, we need to use the Sedov-Taylor solution (the section was originally more detailed, but I see, regrettably, that edits have been made). You can fine the original paper by Taylor here, although it's not the best introduction to the solution; I'd recommend these notes instead.

The radius of the wave at a time $t$ is $$r(t)=\xi_0\left(\frac{Et^2}{\rho}\right)^{1/5}\tag{1}$$ for energy $E$, density $\rho$ and constant factor $\xi_0$. Differentiating, we find $$v(t)=\frac{2}{5}\xi_0\left(\frac{E}{\rho t^3}\right)^{1/5}\tag{2}=\frac{2}{5}\xi_0^{2/5}\left(\frac{E}{\rho}\right)^{1/2}r^{-3/2}$$ It's safe to assume that $\xi_0\approx1$, for our purposes. Air density at sea level is roughly 1.225 kg/m$^3$. Now, the Trinity test released about 10 kilotons of TNT in the form of the blast. Plugging this in, we see that at $r=2$ m, we get $v=882,000$ m/s, while at $r=5$ m, we get $v=209,000$ m/s.

This is a lot higher than the value quoted in Mazura's answer, but I'll note that once we get out to about a quarter mile from the center of the explosion, the blast wave slows to speeds more like that one - in the hundreds of meters per second.

This is a wee bit simplified. If you want to look at the Sedov-Taylor solution in much more detail, I'd recommend scrolling through these slides, which are extremely detailed - and also not light bedtime reading.

It turns out that your superhero has his kryptonite: the Rope Trick Effect.

See those odd protrusions from the otherwise smooth explosion? That's known as the Rope Trick. It's caused by the ropes which tethered the nuclear bomb to its test site. When the bomb goes off, there's enough radiative heating to vaporize the ropes before the blast wave actually reaches them. (nuclear tests which are not tethered never show this effect)

This effect can be mitigated by painting the ropes white, or covering them in aluminum foil. However, at a point blank distance of 2-3m, that radiative heating is going to be quite intense! Hope your superhero is wearing their asbestos underwear!

A superhero capable of flying to the Moon would have a speed of 2124.44 km/s (assuming a flight time from Earth to the Moon of three minutes). Therefore, if the blast wave has a velocity of 300 m/s, then the answer of his escaping the shock wave is easily.

Considering the question concerned itself with the shock wave and not any problems with radiation, it is safe to assume the superhero is radiation-proof. Something that is common enough in Superman level superheroes. He might glow in the dark afterwards.

The OP in the comments section suggested the nuclear detonation was intended to disseminate a substance that is the Achilles' heel of the superhero in a manner that would it unavoidable delivery system.

So it's back to the drawing board, silly old mad scientist, this nuclear bomb powered delivery system scheme won't work.

• Therefore, if the blast wave has a velocity of 300 m/s, then the answer of his escaping the shock wave is easily. Wellllllllll, he might not be able to get moving fast enough. I can't start off at a run, and my first bazillionth of a second might be pretty dang slow. Remember, he's only 2 to 5 meters away, as an established premise. Jan 11, 2020 at 1:06
• @tgm1024--Monicawasmistreated Indeed! But considering he can fly to the Moon in minutes, his rate of acceleration will be high. A quick calculation, based on my assumptions above, shows his acceleration is ~47 km/s/s. Therefore, the time for him to travel 2 metres is 42.4 microseconds, assuming uniform acceleration. A lower initial acceleration might be a problem, but probably not. Still an excellent point. Thanks! Jan 14, 2020 at 7:05
• He also needs a good reaction time, not those 0.3 seconds mere humans have ,,, Jan 3, 2021 at 23:11

The speed of an atomic bomb explosion shock wave. Plotting the radius of the expansion versus time, the slope gives the velocity of expansion. Examination of the time lapsed photographs shows at about 0.05 seconds the faint outline of the shock wave separating from the blast wave (hydro-dynamic separation) can be seen. This occurs at a velocity of about 1000 metres /second or Mach 3.