How fast does a blastwave travel?

[Squizzie]

TL;DR Summary

Popular science and posts on this forum suggest shockwaves travel faster than the speed of sound, but the The Slow Mo Guys youTube video of a bullet and a C4 detonation seems to indicate that even the shockwave from a C4 detonation travels at the speed of sound.

I read on Wikipedia , Encyclopedia Britannica and threads on this forum that shockwaves travel faster than the speed of sound, but when I watched this youTube video, it appears that even a shockwave from a C4 detonation travels at about the speed of sound.
I have extracted a couple of frames at around 14:03 during the 100,000 frames/sec video of the explosion. We can see the detonation front moving at around 10x the speed of the bullet.

The bullet's velocity is reported at 1250 ft/sec which is around Mach 1.1, so the detonation front must be travelling at around Mach 10. Does the observation, at 12:10, that the shockwave and the bullet arrive at the target, some 5 metres down range, at about the same time, indicate that the shockwave is moving at a similar speed as the bullet, i.e. the shockwave from the detonation is propagating at Mach 1? (the shockwave has had a bit of a head start as it was being generated at Mach 10 the first few microseconds)

 

[Drakkith]

The shockwave will lose speed as it travels, eventually turning into a normal sound wave that moves at the speed of sound. I don't know how quickly the shock wave in the video loses speed though.

 

[hmmm27]

Most (explosive-based) bullets travel quite aways before they go subsonic ; I guess that was a pistol round, probably coming out of a (relatively) short barrel. C4 (the actual explosive component) is very fast, detonating at IIRC 17k ft/sec, give or take. (Wp says about 1.5x as fast).

I'm not sure where you're getting "Mach10" for the expanding gas as it leaves the barrel right after the bullet (ie: the "shockwave"). Interesting that it hits at the same time as the bullet, but maybe they did some quick calcs and tried a few times with different ranges before they got it to match.

Waves travel at the speed of sound once they've been let loose and having nothing pushing them. Detonations are different : their front of the shockwave is actually the air that's getting shoved along.

 

[Baluncore]

It is the gas composition and temperature, not the pressure, that determines the speed of sound.
The gas temperature is proportional to the average kinetic energy of the molecules, KE = ½⋅m⋅v². So the speed of sound is proportional to the square root of temperature.

The explosive combustion products, form an expanding fireball, that compresses the air that surrounds the explosives. That air compression raises the temperature of the air, until the speed of sound in the air, is the same as the outside of the expanding fireball. The speed of that shockwave in air can therefore greatly exceed the speed of sound in what was initially cool air.

At some distance, the increasing surface area and volume of the shock wave, reduces the pressure and cools the gasses, so the shock wave quickly falls to the normal speed of sound in air. The shockwave sounds like a click, lower frequency waves only begin to appear at much greater distances, like the rumble of thunder.

Meanwhile, the combustion gasses and air have momentum and continue outwards, which reduces the air pressure below atmospheric at the site of the explosion, giving the fireball and surrounding air, a partial vacuum.

Condensation of water in the air, due to that depression, shows as a white expanding hemisphere in photographs of bomb explosions. The transparent shockwave may be seen as a distortion of the background, well outside that expanding condensation cloud.

Single engine propeller aircraft, flying through explosion fireballs, after shooting down flying bombs from about 100 metres range, were inverted, because the engine and propeller torque is not countered by the wings in the low pressure at the centre, half a second after the explosion.

The fireball shown in the video may have been at a lower than normal pressure, since the shockwave had passed, ahead of the combustion gasses. I would recommend an optical technique to make the density of the shock wave visible, against a detailed background, while setting up the timing for that devious bullet experiment.

 

[Squizzie]

I'm not sure where you're getting "Mach10" for the expanding gas as it leaves the barrel right after the bullet (ie: the "shockwave").

When I said the "detonation front", I was referring to the C4 detonation, not the bullet. At 8:09 they display the speed of the explosion at 3326 m/s , that's around Mach 10 in air at STP, and the speed of the bullet at 387 m/s , which is Mach 1.1

 

[Baluncore]

When I said the "detonation front", I was referring to the C4 detonation, not the bullet.

The composition (molecular weight) of the C4 combustion products, and their temperature, determines the early average velocity of the initial fireball front.

A detonation front travels through the raw explosive material, prior to, and triggering, the chemical reaction and energy release. It starts at the detonator, booster, or gaine.

The fireball front is a mixing, or inter-fingering, of hot combustion products with air being pushed out of the way.

The fast and bright sparks, could be grains of aluminium dust from commercial C4, burning in air ahead of the fireball front. Commercial explosives contain a chemical indicator signature, that can be traced back to the manufacturer and batch number of the explosive material.

 

[Squizzie]

I have conducted further research on the experimental determination of the speed of shock waves in air and found this video of the August 2020 Beirut Ammonium Nitrate explosion
youtube.com/watch?v=QQkmJI63ykI&t=792s
A brief investigation in Google Earth identifies the camera position to be approximately 670 metres from the warehouse, and the shockwave taking 2 seconds to reach that location, giving a speed of around 340 m/sec - Mach 1
Explosion at #13:12

Arrives at the camera location at 13:14

Estimate of the camera position:

Distance from explosion: 677 metres:

I am primarily interested in the speed of the shockwave as it travels through the air beyond the explosion.

 

[Baluncore]

I am primarily interested in the speed of the shockwave as it travels through the air beyond the explosion.

Then you will need to use some technique that highlights the changes in density, well ahead of the flame front, such as Schlieren photography.
https://en.wikipedia.org/wiki/Schlieren_photography

 

[Squizzie]

Then you will need to use some technique that highlights the changes in density, well ahead of the flame front, such as Schlieren photography.
https://en.wikipedia.org/wiki/Schlieren_photography

Don't we calculate the distance to the lightning by counting the seconds between the flash and the bang and multiply it by the speed of sound (~1/3 km/sec) ?
Isn't the thunder clap the shockwave from a bolt of lightning?

 

[Squizzie]

Here are a couple of points
P_s/P₀ Shock Velocity/Sound Speed
1.15 1.06
1.92 1.34
2.83 1.60
3.80 1.84
4.82 2.07

I am not sure what the context of these numbers is or what they represent.

 

[hmmm27]

Isn't the thunder clap the shockwave from a bolt of lightning?

It stops being called a "shockwave" when the wavefront goes subsonic slows to the speed of sound(local atmosphere).

"Thunderclap" is open to (mis)interpretation, but I've noticed that there always seems to be a boom, and sometimes a crackling sound that precedes it.

 

[Baluncore]

The velocity of the shockwave is falling throughout its journey, until it becomes a normal sound wave. Shockwaves are hot steps, hence they can travel faster than sound in the standard atmosphere.

If you hear more than a click, the lightning is far away, and the wave will be travelling at the normal speed of sound, Mach 1.

 

[hutchphd]

Is the "crackle" supersonic? (This has always made me wonder. Is it partially electromagnetic or ground conducted?)

 

[Baluncore]

Is the "crackle" supersonic? (This has always made me wonder)

As the air-path breaks down to a plasma, the velocity of the point of breakdown is supersonic, but the sounds travel at Mach 1.

Each segment of the breakdown plasma makes a dipole radiator of the step sound of air expansion.

The sum of all the energy radiated by all segments is directional and positional, so it sounds different, depending on the observer location.

The crackle starts with the nearest breakdown, later breakdowns from further away then reach you. That is why the crackle starts loud, and then fades due to inverse square law.

 

[Squizzie]

As the air-path breaks down to a plasma, the velocity of the point of breakdown is supersonic, but the sounds travel at Mach 1.

I understand that the thunderclap is caused by that column of air that heats and expands explosively as it becomes plasma and then collapses.
Does that mean that beyond the column of plasma, the shockwave is travelling at Mach 1?

 

[Baluncore]

Does that mean that beyond the column of plasma, the shockwave is travelling at Mach 1?

Not quite the correct terminology. A shockwave ceases to exist at Mach 1.
For a shockwave to propagate, there has to be sufficient compressive energy to heat the air, to maintain the speed of sound above Mach 1. The back of the shockwave is pushing the front, maintaining the step transition.

A short distance outside the plasma or fireball, expansion will have cooled the gas, which can then be treated as having a fixed temperature. The step in pressure, is then deemed to be, too small to heat the air.

 

[hmmm27]

Is the "crackle" supersonic? (This has always made me wonder. Is it partially electromagnetic or ground conducted?)

Never crossed my mind, before. Doesn't seem that reasonable that it would be supersonic for miles, but lightning doesn't seem particularly reasonable in the first place. But...

As the air-path breaks down to a plasma, the velocity of the point of breakdown is supersonic, but the sounds travel at Mach 1.

so I guess just normally propogating noise : oh, well. A long "Boom" sounds pretty specific to a linear-source shockwave collapsing into the subsonic sonic region (ie: a "sonic boom", but not just a point source like an aircraft).

 

[hmmm27]

I am interested in learning more about this claim, and I would appreciate it if you could provide me with a reference to the source material.

You mean like a dictionary ? or Wikipedia.

 

[Squizzie]

Not quite the correct terminology. A shockwave ceases to exist at Mach 1.
For a shockwave to propagate, there has to be sufficient compressive energy to heat the air, to maintain the speed of sound above Mach 1. The back of the shockwave is pushing the front, maintaining the step transition.

A short distance outside the plasma or fireball, expansion will have cooled the gas, which can then be treated as having a fixed temperature. The step in pressure, is then deemed to be, too small to heat the air.

But wasn't the phenomenon that struck the camera operator 2 seconds after the Beirut explosion, described in my post #10, a shock wave?

 

[Baluncore]

But wasn't the phenomenon that struck the camera operator 2 seconds after the Beirut explosion, described in my post #10 a shock wave?

I have conducted further research on the experimental determination of the speed of shock waves in air and found this video of the August 2020 Beirut Ammonium Nitrate explosion

The explosion would have produced a shockwave initially, but an average of Mach 1, over two seconds, suggests that it did not remain a supersonic shockwave for long, it was the decaying step transient.

The explosion was not a point source, and there were reflections, so the radiation pattern would have been subjected to constructive and destructive interference.

Listen to the sound of the step. Was it a click, or were lower frequencies present? Was the audio system capable of reproducing the spectrum of a shockwave?

 

[hmmm27]

But wasn't the phenomenon that struck the camera operator 2 seconds after the Beirut explosion, described in my post #10 a shock wave?

Shocked the h*ll out of the cameraman, I'd imagine.

(Opinion) supersonic within the building, at least until the walls blew out.

Maybe "pressure wave" might be a better term for that scenario, once it got to the cameraman. You don't need supersonic to trash nearby buildings and break windows further out.

@Baluncore : "click" ?

 

[Squizzie]

You mean like a dictionary ? or Wikipedia.

No, an Acceptable Source as recommended by PF
"Acceptable Sources:
Generally, discussion topics should be traceable to standard textbooks or to peer-reviewed scientific literature. Usually, we accept references from journals that are listed in the Thomson/Reuters list (now Clarivate):"

 

[Baluncore]

A 760 mph, 1230 km/h, gust of wind can do a lot of damage. Buildings are simply not designed to withstand half a bar of ram pressure, or 1050 pounds per square foot. That is ten times the design specifications.

While propagating as a shockwave, the step is "self-sharpening", it sounds like a single instant click as it passes, once the energy is lost to expansion, it becomes a ramp and many lower frequencies can be heard as a thud.

 

[Squizzie]

The explosion would have produced a shockwave initially, but an average of Mach 1, over two seconds, suggests that it did not remain a supersonic shockwave for long, it was the decaying step transient.

The explosion was not a point source, and there were reflections, so the radiation pattern would have been subjected to constructive and destructive interference.

Listen to the sound of the step. Was it a click, or were lower frequencies present? Was the audio system capable of reproducing the spectrum of a shockwave?

But consider the white dome we see expanding from the same Beirut explosion.

This is the phenomenon that was captured on camera in my earlier post.
This is what travelled at Mach 1 from the explosion.
Isn't this a shockwave travelling at Mach 1?

 

[hmmm27]

While propagating as a shockwave, the step is "self-sharpening", it sounds like a single instant click as it passes, once the energy is lost to expansion, it becomes a ramp and many lower frequencies can be heard as a thud.

Yeah, that seems to be on the list of "last things you'll ever hear".

Isn't this a shockwave travelling at Mach 1?

Does your opinion of the meaning of "shockwave" in a physics setting have definable boundary limits on velocity ?

[edit: mostly garbage removal, based on a temporary brainfart that wave propogation goes subsonic]

 

[Drakkith]

This is the phenomenon that was captured on camera in my earlier post.
This is what travelled at Mach 1 from the explosion.
Isn't this a shockwave travelling at Mach 1?

No, that's not the shockwave. Look at the white circular area at the water. I believe that's the shockwave. The white dome is water vapor condensing into droplets in the low-pressure phase of the explosion. This takes place up to several hundred milliseconds after the peak overpressure part of the wave passes by.

 

[Baluncore]

This is what travelled at Mach 1 from the explosion.
Isn't this a shockwave travelling at Mach 1?

No. That is condensation of water in the air. It results from the pressure falling below one atmosphere following the outward momentum of the shock wave. The shock wave is well ahead of that cloud of condensate.

The buildings and trees that are hit by that white hemisphere are wet, like it has rained sideways on them from the direction of the explosion.

I do not recommend the practical experiment, but some people have been standing behind solid trees when 1000 lb bombs have detonated, they hear the click as the shockwave passes, then a couple of seconds later they look around the tree to find everything wet, while the cloud dissolves back into the air in front of them.

 

[hmmm27]

Isn't this a shockwave travelling at Mach 1?

pic#4: the light-blue sliver on the left of the steam ball ; IMO, that's either your shockwave or the leading edge of the low-pressure zone.

 

[Squizzie]

Just look at these images.
There's the orange smoke from the explosion shooting up and then hanging there.
There's the white dome appearing after the appearance of the orange smoke and then quickly obscuring the orange smoke.
Is it steam, water vapour or cloud (water droplets)? Is it hot or cold? High or low pressure? Does it delineate a boundary? Does it leave trees wet?
Then there's the silver disk expanding on the water.
What is it?
Why is it silver?
Is it the base of an invisible shockwave?
Does the shockwave contain wind gusts of 760 kph?
And those four frames are captured over about one second!
Which brings me back to my opening question and I realise that there isn't even solid agreement on what a shockwave really is.
The Slo Mo Guys seem to think there are two shockwaves generated in the C4 explosion.
Is it the thunderclap I hear 3 seconds after seeing the lightning?
Is it the white cloud or the silver disk in the Beirut explosion?
And we haven't even started to talk about the double-bang of the supersonic aircraft!
This is such a fascinating subject that I can't believe it is not covered in standard textbooks or scientific papers.
Or is it?

 

[Squizzie]

At the popularization level try Shock Waves and Man by Glass.
There is also a large technical literature.

Do you have some links to the technical literature please? I have dug through my physics texts and can't find anything that goes into detail.

 

[Squizzie]

Thank you for the references, I think I have my answer.
Anderson, being an aerodynamicist, only focuses on the shock wave's interaction with the supersonic body, and I was unable to find any reference to its speed of propagation in his book.
I was unable to source a copy of Punty.
But Kinney And Graham provides the answer in Table XI, from which I have graphed the data.

After 1000 milliseconds the shock wave travelled 343 metres. That's Mach 1.0 at NTP.

 

[Baluncore]

After 1000 milliseconds the shock wave travelled 343 metres. That's Mach 1.0 at NTP.

No. That is the blast wave from a reference explosion: 1 kg, TNT.

 

[Squizzie]

No. That is the blast wave from a reference explosion: 1 kg, TNT.
The shock wave is very limited in that case. It certainly does not travel 300 metres.

Kinney and Graham appear to use "blast wave" and "shock front" interchangeably.
From p. 1
"The material presented here on explosive blast and shock gives essential background concerning the physics of the blast wave. It describes in relatively simple manner generation of a blast wave with its shock front, its transmission through the atmosphere, its interaction with a variety of structures and objects, and typical structure responses. Preliminary to this study of explosions is a description of explosive blast and shock in the atmosphere."
Do you have an alterrnative interpretation?

 

[Baluncore]

Look at the table XI. Column 5 is velocity; m/s.
The velocity, out to the first millisec is falling rapidly;
13500, 8730, 6920, 5870, 5150, 4610, 4180, 3830, 3530, 3280, 3060,
2870, 2700, 2540, 2410, 2280, 2170, 2070, 2067, 1980.
All those shockwave velocities are greater than mach 1.
At 7 us, v=13500, = mach 39.0
At 1 ms, v=1980, = mach 5.8
It falls to M1 = 343 m/s at 400 metres.
Because of the log scale, your average over 1 second, will downplay the initial high temperature and velocity shockwave.

 

[Squizzie]

Look at the table XI. Column 5 is velocity; m/s.
The velocity, out to the first millisec is falling rapidly;
13500, 8730, 6920, 5870, 5150, 4610, 4180, 3830, 3530, 3280, 3060,
2870, 2700, 2540, 2410, 2280, 2170, 2070, 2067, 1980.
All those shockwave velocities are greater than mach 1.
At 7 us, v=13500, = mach 39.0
At 1 ms, v=1980, = mach 5.8
It falls to M1 = 343 m/s at 400 metres.
Because of the log scale, your average over 1 second, will downplay the initial high temperature and velocity shockwave.

Your extract only looks at the first 0.46 millisecs, less than half a millisecond.
Although I didn't make it clear, my question about the speed of the shockwave related to human scales: I'm talking handfuls of seconds, not sub-millisecs, and assumed that would be the viewpoint of the man-in-the-street when they read about the speed of shockwaves.
But now that I understand that your interpretation includes the examination of the first 1/2 millisecond of the explosion, then yes, it could be said that shockwaves travel faster than the speed of sound.
I prefer my view that at any survivable distance from an explosion, the blast wave, shock front or shockwave will travel from the site of the explosion to your position at Mach 1.