I How fast does a blastwave travel?

[Baluncore]

Since the wave started as a sudden increase across micrometres, does it remain such a sudden increase no matter how weak it gets? Or does it eventually spread out, and then how?

The explosion generates the heat and pressure. But once propagating outside the fireball, the shock front heat comes only from the pressure step. The shock front "self maintains" a step function until the temperature is attenuated sufficiently to approach the ambient speed of sound. The shock step then ceases to exist, as it becomes a gentle ramp.

A positive pressure step can become a self maintaining shock front. A negative pressure step cannot, it must always become a more gentle ramp as the speed of sound is falling.

 

[Baluncore]

As we have discussed on this thread, when the observer is close to an lightning strike, the sound is a crack. Further away, it becomes a rumble. I suspect the abrupt energy increase at the shock front becomes less and less sharp as the wave propagates outwards.

As the shock front propagates outwards, the energy density is falling continuously, and the step is reduced in amplitude over time. The virtually instant rise time of the step however, is maintained by the positive temperature step, so long as the wave remains a shock front.

The P and T step remains virtually instant and self-maintains that step, until the shock front slows to the speed of sound in ambient air. Only then does the step collapse into a sound wave ramp. If you are in the area covered by the shock step, you will hear only a click or a single crack as it passes.

If you examine Kinney and Graham, table XI, you will see the velocity of the shock front progressively falls to 343 m/s. The shock front step obviously ceases to exist at the end of that table.

In the atmosphere, high frequency sound is attenuated much more rapidly than low frequency sound. That is why distant thunder does not crack, it rumbles.

 

[snorkack]

As the shock front propagates outwards, the energy density is falling continuously, and the step is reduced in amplitude over time. The virtually instant rise time of the step however, is maintained by the positive temperature step, so long as the wave remains a shock front.

The P and T step remains virtually instant and self-maintains that step, until the shock front slows to the speed of sound in ambient air. Only then does the step collapse into a sound wave ramp.

But my point is that it should be impossible for the step to collapse, ever. Because so long as there is any wave at all, as long as there is any nonzero ΔP, then the wave crest should be travelling faster than the wave foot. When the sound gets weak and ΔP is small compared to total P then the speed of wave crest should approach that of wave foot, but not become lower. Since the wave starts as a steep step, it should remain a steep step. Collapsing a step into ramp would require the crest to travel slower than foot.

If you are in the area covered by the shock step, you will hear only a click or a single crack as it passes.

If you examine Kinney and Graham, table XI, you will see the velocity of the shock front progressively falls to 343 m/s. The shock front step obviously ceases to exist at the end of that table.

In the atmosphere, high frequency sound is attenuated much more rapidly than low frequency sound. That is why distant thunder does not crack, it rumbles.

Attenuation view gets an opposite result, yes. Since a steep step can be expressed as a sum of high frequency components, attenuating away these high frequency components should collapse step into ramp. The paradox here is that this model, reasonable taken alone, clashes with the model of speed/amplitude relations, which predicts no collapse. So how can a broken wave collapse?

 

[Baluncore]

Because so long as there is any wave at all, as long as there is any nonzero ΔP, then the wave crest should be travelling faster than the wave foot. When the sound gets weak and ΔP is small compared to total P then the speed of wave crest should approach that of wave foot, but not become lower.

We do not concern ourselves with the distortion of low energy audio waves in the atmosphere. An audio wave is different to a shock front. We assume an audio wave does not significantly change the air temperature as it passes. The shock front is assumed to have a temperature step sufficient to maintain that step. There will come a point where you must change your assumptions and terminology, where the shock front becomes an acoustic wave. You cannot extrapolate wave profile or behaviour across that transition.

The shock front step is a high frequency step, so it is attenuated by both the inverse square law, and by acoustic dispersion. So long as it has a sufficient temperature step, it will maintain that step.

The paradox here is that this model, reasonable taken alone, clashes with the model of speed/amplitude relations, which predicts no collapse. So how can a broken wave collapse?

The step collapses and begins to transform into a ramp, when the temperature step becomes insufficient to maintain that step. Based on our assumptions, that is when the shock front ceases, and the audio sound wave begins.

 

[snorkack]

We do not concern ourselves with the distortion of low energy audio waves in the atmosphere. An audio wave is different to a shock front. We assume an audio wave does not significantly change the air temperature as it passes. The shock front is assumed to have a temperature step sufficient to maintain that step. There will come a point where you must change your assumptions and terminology, where the shock front becomes an acoustic wave. You cannot extrapolate wave profile or behaviour across that transition.

The shock front step is a high frequency step, so it is attenuated by both the inverse square law, and by acoustic dispersion. So long as it has a sufficient temperature step, it will maintain that step. The step collapses and begins to transform into a ramp, when the temperature step becomes insufficient to maintain that step. Based on our assumptions, that is when the shock front ceases, and the audio sound wave begins.

But the thing is, wave profile and behaviour must be continuous across the transition, at least the lower derivatives. Both effects - self-sharpening due to amplitude dependent velocity and spreading due to preferential attenuation of high frequency - must be present on both sides of transition. So how do you analyze the balance of the two effects to predict exactly when the step collapses. What is the minimum temperature step for the shockwave to stay a step?

 

[Baluncore]

So how do you analyze the balance of the two effects to predict exactly when the step collapses. What is the minimum temperature step for the shockwave to stay a step?

You do not have to be exact. One model ends, another begins, wherever.
If it steps like a shock front, it is a shock front. Everything else is noise.

 

[Baluncore]

Both effects - self-sharpening due to amplitude dependent velocity and spreading due to preferential attenuation of high frequency - must be present on both sides of transition.

No. Self-sharpening due to temperature step dependent velocity is assumed to be absent in audio sound waves.

You have introduced a new term Spreading due to attenuation of high frequency; which suggests audio phase dispersion, which is present in acoustic waves.
https://en.wikipedia.org/wiki/Acoustic_attenuation

A shock front is not 100% efficient. Some energy is left behind, to become part of the following blast wave. That represents a loss of energy from the shock front, which reduces the step height, but not the step duration, as that is maintained by the temperature step while it continues to propagate.

It is the presence of a PT step that defines the presence of a shock front. That is fundamental to this discussion and cannot be denied, without departure from the observed reality.

 

[Squizzie]

Folks, can we take a pause and remind ourselves that unlike a water wave or the vibrations in a string, a pressure wave is a transverse wave and not a longitudinal wave. In a longitudinal wave the dimensions of wavelength and amplitude are the same: distance. In a transverse wave, like sound, they are different: distance and pressure respectively.
Whilst many analogies between the two are valid, not all are.

 

[Baluncore]

Folks, can we take a pause and remind ourselves that unlike a water wave or the vibrations in a string, a pressure wave is a transverse wave and not a longitudinal wave. In a longitudinal wave the dimensions of wavelength and amplitude are the same: distance. In a transverse wave, like sound, they are different: distance and pressure respectively.
Whilst many analogies between the two are valid, not all are.

I think you have that backwards.
A longitudinal wave is one where all the particles of the medium (such as gas, liquid or solid) vibrate in the same direction as the wave. Sound waves are longitudinal waves. When longitudinal waves travel through any given medium, they also include compressions and rarefactions.
Transverse waves do not travel through a gas.

 

[berkeman]

Thread closed for Moderation...

 

[berkeman]

Thread is reopened provisionally to see if OP @Squizzie understands the correction.

 

[Squizzie]

Thread is reopened provisionally to see if OP @Squizzie understands the correction.

Yes, I stand corrected. I had the terms backwards. The waves in water and a taut string are indeed transverse waves.
Sound waves through a solid, liquid or gas are longitudinal waves.
My apologies for the confusion and thank you for the opportunity to keep the thread active.
I have not heard back from Dr. Rigby on my request for clarification of his use of "particle velocity" in his explanation for the negative phase of the blast wave.

 

[Squizzie]

Here is a sloppy proof for a spherical sound wave, but it should give you the idea.
u is particle velocity,

Do you mean molecule velocity?

 

[Baluncore]

Do not mix your gas models. You must analyse the gas using statistical mechanics, or fluid mechanics.

Do you mean molecule velocity?

A "particle" of a fluid refers to a small volume, or parcel of the fluid, not to the statistical molecules that make up the fluid.

Your follow-up question to Dr. Rigby mixed the fields, which makes your question too complex to answer simply.

Please stay away from the statistical mechanics of molecules, while discussing the fluid dynamics of pressure waves. If you mix the statistical-micro-internal model, with the fluid-macro-external model, you will confuse yourself, and confuse the issue.

 

[Squizzie]

No, particle velocity. A sound wave moves at velocity c. It gives the air a particle velocity u at the continuum level.

Yes, a sound wave moves at velocity c, and that velocity is relative to an inertial frame of reference in which the medium is stationary.

Despite molecular theory and statistical mechanics establishing that the molecules are moving randomly at a mean speed of around Mach 1, with a mean free path of around 50 nm, the medium is considered to be stationary
In that frame of reference, air is considered as a continuum in which, to quote Gupta[1],
"This is called the continuum concept, that is, the matter is uniformly and continuously distributed and not made up of pebble-like molecules followed with space. "

There are clearly two realms in which the properties of gas, like air, can be studied: the thermodynamic, or "macroscopic" realm in which the gas behaves as a continuum and is described in terms of pressure, temperature, and density, and the molecular realm, in which it behaves like a collection of molecules and is described in terms of velocity, momentum, size and mean free path.

The two realms appear to be distinguished the size of the system under discussion relative to the mean free path of the molecules.
In the thermodynamic realm there is no useful concept of particles.
In molecular theory, the only particles are molecules. Therefore the use of particle velocity is not useful in the discussion of the velocity of sound waves in air.

In neither realm does it contain particles that are not molecules, so I am not sure in which context the term "particle velocity" is being used in the context of sound waves in air.

[1] Gupta S. C., (2011) Thermodynamics, Dorling Kindersley (India) Pvt. Ltd. p. 4

 

[Squizzie]

Your follow-up question to Dr. Rigby mixed the fields, which makes your question too complex to answer simply.

Yes I agree, but it was not me, but Dr. Rigby who appears to have mixed the fields by including "particle velocity" and "pressure" in the explanation.
I find it confusing, which is why I asked for clarification

 

[Baluncore]

Yes I agree, but it was not me, but Dr. Rigby who appears to have mixed the fields by including "particle velocity" and "pressure" in the explanation.

Dr. Rigby wrote: ..."The positive phase imparts a forwards particle velocity to the air. Pressure and particle velocity are two sides of the same coin, you can't have one without the other, so if a pressure is acting it is also moving the particles." ...

I believe you misinterpreted the term "particle" in the reply to mean "molecule", rather than "parcel". In doing that, you were confused by the answer, as it then mixed the models.

 

[Squizzie]

I believe you misinterpreted the term "particle" in the reply to mean "molecule", rather than "parcel". In doing that, you were confused by the answer, as it then mixed the models.

Nope, Dr Rigby used "particle" four times in his response. Here's a marked-up image of his email:

That's not me having "misinterpreted" him.
I suggested to him that the association with molecule would be incorrect.
I have not received further explanation of his use of the term molecule.

 

[Baluncore]

I suggested to him that the association with molecule would be incorrect.
I have not received further explanation of his use of the term molecule.

I do not see him use the term "molecule" anywhere in his reply. I think you are imagining it. That suggests that you have fixated in your head, that the term "particle" must, and can only mean, "molecule".

A large population, or a parcel of molecules, is one particle of fluid.

 

[Squizzie]

I suggested to him that the association with molecule would be incorrect.
I have not received further explanation of his use of the term molecule.

I have just noticed the error in my final sentence of post #160:

I have not received further explanation of his use of the term molecule

He didn't mention molecule. I didn't request clarification from him about the use of molecule - see my post #40:
"May I ask for clarification on your use of particle velocity please?"
The sentence should have read:
I have no received further explanation of his use of the term "particle".
That would explain the sceptical emojis from @weirdoguy and @Motore

 

[Drakkith]

I have replied:
"May I ask for clarification on your use of particle velocity please?
If you are referring to individual molecules as particles, then my understanding is that, according to statistical mechanics, the molecules are individually moving in random directions at a mean speed of around Mach 1, and that the pressure in the blast wave is being transmitted by the molecules imparting momentum to their neighbours through their collisions over the distance of the few nanometers of their mean free path. That is, the individual molecules don't travel any significant distances in the direction of the blast front, rather it is the transient concentration of these molecules that is the pressure wave that travels out from the blast centre."

Instead of a chemical explosion, imagine a spherical 'piston' that expands a short distance very rapidly, say at mach 5, pushing air out of the way and creating a spherical blast wave. There MUST be some way for this volume of displaced air to move outwards and dissipate into the rest of the air. This requires that some net molecular displacement occur. In other words, the average molecule MUST move some distance, perhaps a significant amount, away from the origin of the blast wave. This must occur not only near the piston's surface, but also much further away if the entire volume is to return to ambient pressure.

This would seem to imply that an outwards inertial effect exists, as there must be a net outwards molecules velocity (or else how could we have a net flow outwards to dissipate the high-density gas), resulting in an rarefaction and a negative phase to the pressure as the outwards moving gas has to be stopped and then compressed back to mean atmospheric pressure.

There is virtually no change with a chemical explosion. The rapid vaporization and combustion generates a high-pressure, high-temperature region that pushes outwards, just like the piston.

 

[Squizzie]

Instead of a chemical explosion, imagine a spherical 'piston' that expands a short distance very rapidly, say at mach 5, pushing air out of the way and creating a spherical blast wave.

Whilst there clearly are similarities between explosions and other methods of creating pressure waves, discussions about the differences can often lead to endless debates that do not apply to the subject at hand: explosive blast waves. At the risk of introducing one, the elephant in the room for me is that an explosion converts a very small volume of solid explosive into a massive volume of gas.
Please, may I request we stay on topic?

 

[Drakkith]

Whilst there clearly are similarities between explosions and other methods of creating pressure waves, discussions about the differences can often lead to endless debates that do not apply to the subject at hand: explosive blast waves. At the risk of introducing one, the elephant in the room for me is that an explosion converts a very small volume of solid explosive into a massive volume of gas.
Please, may I request we stay on topic?

It is on topic. The topic of this thread is not about the initiation of the blast wave, but how it propagates. It matters not whether it is generated mechanically, chemically, or thermally. I chose a slightly simpler example to minimize the number of factors to consider when illustrating my point.

At the risk of introducing one, the elephant in the room for me is that an explosion converts a very small volume of solid explosive into a massive volume of gas.

What about it?

 

[Squizzie]

It matters not whether it is generated mechanically, chemically, or thermally.

You may be right, you may be wrong, but don't you see that a discussion on this opens a further detour from the present subject which is the source of the negative phase of a blastwave, which is generally accepted to have been generated by a chemical or nuclear reaction?

 

[Baluncore]

At the risk of introducing one, the elephant in the room for me is that an explosion converts a very small volume of solid explosive into a massive volume of gas.

And that gas is very hot and expanded like a fireball. At first, it pushes air away from the site of the explosion, then the combustion products of the explosive cool and condense, and the air comes flowing back in.

 

[Squizzie]

And that gas is very hot and expanded like a fireball. At first, it pushes air away from the site of the explosion, then the combustion products of the explosive cool and condense, and the air comes flowing back in.

Are you offering this as a complete explanation for the source of the negative overpressure?

 

[Baluncore]

Are you offering this as a complete explanation for the source of the negative overpressure?

No. Just the part played by the fireball seen in the video of big explosions.

 

[snorkack]

I think that we could return to the example of squib load.
Yes, as you pointed out, if the bullet is stuck at the breech and the explosive load is normal then the pressure at the chamber will be above the normal live load pressure, which may result in barrel burst.
However, consider a squib which is a squib because it has abnormally small amount of explosive, but still some explosive. For example a cartridge that has just primer but no powder.

When the bullet is stuck at the breech and the explosion is not strong enough to either dislodge the bullet or burst the barrel, there will be no negative phase. Because the overpressure in the chamber will be released by slowly leaking out of the windage. Not enough inertia to produce overshoot and underpressure.
When the bullet slides freely but the explosion is too small to fill the length of the barrel, the bullet will travel partway along the barrel, and then continue travelling by inertia while underpressure is left behind. So the bullet is sucked back.

If the explosive load is sufficient then the smoke in the barrel is still under overpressure when the bullet exits the muzzle, and smoke will continue to exit the muzzle as a muzzle blast. But the inertia of muzzle blast will cause the smoke to overshoot, leading to underpressure in the barrel, after which air is sucked back into the barrel. This is demonstrated in that when a target is near the muzzle, pieces of target are sucked into the barrel, such as blood and pieces of brain.

 

[Squizzie]

I think that we could return to the example of squib load.

At the risk of repetition, can we keep to the topic: blastwaves?

 

[Squizzie]

No. Just the part played by the fireball seen in the video of big explosions.

I'm pretty sure that the condensation cloud does not appear until the blastwave has cleared the fireball.

 

[snorkack]

At the risk of repetition, can we keep to the topic: blastwaves?

I believe it very much includes a blastwave and illustrates how a blastwave forms and propagates! When smoke exits the muzzle as a muzzle blast, it is a blastwave. When a blank shot propagates along the barrel, it is a blastwave. When a squib load is stopped by a bullet seized in the breech, the blastwave is prevented from forming, or perhaps stopped after it has propagated across empty cartridge. The barrel, muzzle and free air outside the muzzle allow examining blast wave propagation in 1D and in 3D, and the transition from 1D to 3D.

 

[Squizzie]

Hot off the press, a response from Dr. Rigby:
"Particle velocity is a common term in fluid dynamics. It doesn't refer to velocity on the molecular level, more so it describes what happens to a "packet" of air (or "parcel", but I prefer the term "packet"!). Think differential calculus rather than statistical mechanics. You don't need to go down to that sort of scale when you have wavelengths in the order of metres. It's important to remember that the wave is moving, but the particles have considerable momentum and therefore move themselves, as can be seen in that YouTube video I linked in the previous email.
Sam"
I'm not sure how to reconcile "think differential calculus" with "you don't need to go down to that scale when you have wavelengths in the order of metres" .
Comments?

 

[snorkack]

Hot off the press, a response from Dr. Rigby:
"Particle velocity is a common term in fluid dynamics. It doesn't refer to velocity on the molecular level, more so it describes what happens to a "packet" of air (or "parcel", but I prefer the term "packet"!). Think differential calculus rather than statistical mechanics. You don't need to go down to that sort of scale when you have wavelengths in the order of metres. It's important to remember that the wave is moving, but the particles have considerable momentum and therefore move themselves, as can be seen in that YouTube video I linked in the previous email.
Sam"
I'm not sure how to reconcile "think differential calculus" with "you don't need to go down to that scale when you have wavelengths in the order of metres" .
Comments?

Again consider for example firing a blank.
The length of the barrel is tens of cm, and that will be "wavelength" of the blastwave.
But the front of the blastwave will be very much thinner. In the rear, there will be the smoke accelerating along the barrel; but in the front there will be the air that was in the barrel and is pushed ahead by the smoke.

The size of air molecule is in the order of 0,1 nm. The free path is in the order of 100 nm. A few of the molecules in the blastwave will be accelerated to speeds well above the speed of the blastwave; but they will collide with the molecules ahead of blastwave and be slowed down until the mass of ambient molecules get accelerated. So a region of, say, 1000 nm across will behave as a "packet". And it can be accelerated, compressed etc...

 

[Baluncore]

I believe it very much includes a blastwave and illustrates how a blastwave forms and propagates!

The best way to understand and analyse one dimensional shock fronts and blast waves is with the well understood technology of shock tubes, not by analogy to the interior ballistics of guns.
See:
https://vesselmechanics.mech.utah.e...Computational-shock-wave.-Thesis-2010-Lib.pdf

 

[Drakkith]

You may be right, you may be wrong, but don't you see that a discussion on this opens a further detour from the present subject which is the source of the negative phase of a blastwave, which is generally accepted to have been generated by a chemical or nuclear reaction?

No, I don't see my post as a detour.

 

[Baluncore]

I'm pretty sure that the condensation cloud does not appear until the blastwave has cleared the fireball.

The blast wave air is outside the fireball. The transparent shock front is initiated at the surface of the growing opaque fireball. The shock front then moves away from the fireball surface, leaving the massive outward blast wave of air, between the shock front and the fireball surface.

It is the later inward condensation collapse of the fireball, coupled with the outward momentum of the blast wave air mass, that pulls the partial vacuum and rarefies the air, that precipitates formation of the Wilson cloud. Note that the Wilson cloud grows at a rate dependent on the RH and the distribution of the partial vacuum. The Wilson cloud surface has a phase velocity, not a flow velocity. The cloud surface grows from the point of minimum pressure, inwards and outwards at the same time, but you only see the opaque outer surface coming towards you. Since the cloud forms where the slowly moving air is cooling, a shock front step cannot form, though the phase velocity of the cloud surface formation can be infinite in places.

Following the formation of the cloud, another lower step shock front may form, but this time travelling back from the blast wave, towards the original site of the explosion. As the rarefied air is heated, and the return shock front builds and accelerates towards the site of the original explosion, the Wilson cloud condensate is rapidly dissolved again into the air.

I believe that reasoning sufficiently explains the rapid formation of, and the rapid disappearance of, the opaque Wilson cloud, and why it is seen momentarily in the place that it is.

 

[Squizzie]

.
OK it's in a tunnel, so there are lots of reflections.
Use your "." and "," keys to step frame by frame (I measured the frame rate at 30/sec) through the second between 11:16 and 11:17.
You can see the fuse burn in two or three frames.
And then there are at least three clouds behind the first boom and cloud (reflections?)
[PS] take no notice of the commentary.

 

[Baluncore]

And then there are at least three clouds behind the first boom and cloud (reflections?)

I do not think that video adds anything to the discussion, unless you want to confuse the issue.
That is an uncontrolled experiment, deliberately misleading, for entertainment purposes only.

 

[Squizzie]

I think I have found the original video from a portuguese source that appears to be genuine. The sound is much better, and there are some interesting comments.

 

[Baluncore]

sound is much better, and there are some interesting comments.

How can you tell the difference between cloud formation and the refraction of light due to the change in density of the air as a positive pressure wave passes?

What can be added to this discussion by watching or discussing that unscientific video?

 

[Drakkith]

How can you tell the difference between cloud formation and the refraction of light due to the change in density of the air as a positive pressure wave passes?

It looks pretty clear to me to be cloud formation in the tunnel. A change in the refraction of light is basically not visible without specialized techniques (like Schlieren photography).

 

[Squizzie]

It looks pretty clear to me to be cloud formation in the tunnel. A change in the refraction of light is basically not visible without specialized techniques (like Schlieren photography).

Actually I think I can detect refraction caused by the secondary waves (but not the initial one). Look at the first light down the tunnel and step through the frames (".") towards the end of 0:03 (from about frame 20) and see the distortion of the cable hanging down.

Just for giggles, I timed the duration from the initial det-cord ignition frame to the arrival of the cloud at 30 frames = 1000 ms +/- 30. With det-cord detonation speed of 6,400 m/s and sound at 340 m/sec, I reckon the charge was around 300 metres down the tunnel.

 

[Squizzie]

I have been wondering if the negative phase observed in the blast wave from a detonation is the inevitable evolution of a sharp high pressure pulse into a longitudinal pressure wave according to wave mechanics, and a colleague with whom I have been sharing my thoughts showed me this demonstration and explanation of the Kamifusen Japanese paper balloon.
It seems it's possible to generate a negative phase from a mechanically induced pressure pulse.

 

[Squizzie]

By consolidating shock propagation data from two distinct sources [1][2] into a single chart using a log scale for both axes, the contrasting speeds associated with two distinct phases of an explosion, which contribute to the formation of a shock front, become clearly evident.

The detonation phase involves the expansion of hot gaseous products at an initial hypersonic speed. This speed eventually decays to the speed of sound, marking the transition to the blast wave. The blast wave detaches upon the completion of the detonation phase and then propagates as a pressure wave at the speed of sound in the surrounding air, or Mach 1.0.

The timing and location of this transition depend on the type and size of the explosion, with the blast wave originating within milliseconds of the detonation of a chemical explosion up to a few seconds of a nuclear explosion. In all cases, the blast wave propagates at Mach 1.0.

[1] Kenney G. F and Graham K. J, (1985) Explosive Shocks in Air, Springer Science+Business Media, LLC, Table XI
[2] Bethe H. A, Fuchs K., Hirschfelder J, Magee J., Pearls R. and von Neumann J. (1958) Blast Wave U. S. Atomic Energy Commission, p. 185 ("The Los Alamos report")

 

[Baluncore]

What is your definition of "Mack 1.0" and "the speed of sound"?

During the detonation phase, the shock wave accelerates, then it begins to decelerate as it expands and moves away, with the fireball well behind it. Why do you include the decelerating supersonic shock wave, as part of the detonation wave, when it is usually treated as being outside the detonation, as an early part of the blast wave?

 

[Squizzie]

What is your definition of "Mack 1.0" and "the speed of sound"?

(my emphasis)
What makes you think I am using a definition of Mach 1.0 and the speed of sound in any way other than established in physics textbooks?

During the detonation phase, the shock wave accelerates,

Unless you are referring to a behaviour in the first 0.007 milliseconds (7 microseconds) that is not documented in Kinney's data, can you identify any stage in either dataset that indicates an acceleration in the shock front?

Why do you include the decelerating supersonic shock wave, as part of the detonation wave,
when it is usually treated as being outside the detonation,

I have not found that to be the case in the literature I have accessed.

 

[Baluncore]

What makes you think I am using a definition of Mach 1.0 and the speed of sound in any way other than established in physics textbooks?

In all cases, the blast wave propagates at Mach 1.0.

Your post is really confused, because your classification of the distinct phases of an explosion, or your definition of Mach 1.0 must be wrong.

What is it with your fixation on, or worship of, Mach 1.0 ?
Mach is only needed, or useful, when it has a value greater than one.

 

[Squizzie]

This is all a bit vague and depends on what you mean by 'blast wave'. If we take a blast wave to be an explosively generated shock wave/front and the entirety of all of the effects seen as it passes by a region, then sure, it can last several seconds. I'd guess the sounds of a blast wave are generated mainly by the following (data taken from a 100g charge, so times may vary as the charge increases):

• The initial shock front, which, for small explosion sources at least, rises from ambient to peak pressure virtually instantly (much less than 1 ms).
• The decay of the shock front, which takes 3-4 ms.
• Sound waves generated by the interaction of the shock front with other objects as it passes.
• Vibrations induced in the audio equipment or your ear from the interaction of the shock front.
• Reflections of the shock front and other sound waves by terrain and local objects.

If you're far enough away not to have your eardrums or microphones blown out by the blast, then the end result should be a sharp crack as the shock front passes you followed by several seconds or more of induced and/or reflected sounds depending on the surrounding terrain. As the distance increases the sound should decay in amplitude and start to lose its high frequencies, ending up as a low-frequency 'rumble' that's often heard if you're very far away.

Reference for time values: https://www.mdpi.com/2076-3417/12/5/2691
Again, note that I don't know how the times change as explosive power increases. It could be that the durations increase, which is what I naively expect, but I don't know.

As you can see, after just 20 meters the blast wave has fallen from nearly 7,000 m/s to roughly the speed of sound at 340 m/s. Graph referenced from this article on Injury and death to armored passenger-vehicle occupants and ground personnel from explosive shock waves.

I have added the data from your Viano reference to the plot (in yellow) which shows a high correlation with the Kinney and Los Alamos data.

 

[Squizzie]

Your post is really confused, because your classification of the distinct phases of an explosion, or your definition of Mach 1.0 must be wrong.

What is it with your fixation on, or worship of, Mach 1.0 ?

I'm not sure it rates as "fixation" or "worship" , but the fact that it defines the speed at which a blast wave (or any pressure, density or temperature disturbance) propagates through air is pretty important.

Mach is only needed, or useful, when it has a value greater than one.

Then I wonder why the Mach number is displayed on an airliner's instrument panel.

 

[Baluncore]

Then I wonder why the Mach number is displayed on an airliner's instrument panel.

The Mach number there refers to the speed of an aerodynamic vehicle, not to the speed of sound wave propagation. The aerodynamics of the vehicle change as it approaches the speed of sound, which is slower in the cold at higher altitudes.