I How fast does a blastwave travel?

[vanhees71]

https://en.wikipedia.org/wiki/Sonic_boom

 

[Squizzie]

Kinney et. al. refer to "negative overpressure" only once, in Figure 1.1 C , reproduced in post #53, in the context of the pressure distribution in blast wave where, as explained on p. 90 :
"The overall pressure configuration then consists of an abrupt pressure discontinuity followed by positive and negative pressure phases as indicated by Curve 4 of Figure 6-2. ".
I suspect that the white cloud observed in the Beirut explosion images is the condensation that occurs due to the temperature drop associated with the adiabatic expansion of humid air to below its dew point in the "negative pressure phase" described above. However I can't find any reference to that phenomenon in Kinney or the textbooks I have read.
I would be interested to hear of any source that describes it in a scientific manner.

 

[renormalize]

I suspect that the white cloud observed in the Beirut explosion images is the condensation that occurs due to the temperature drop associated with the adiabatic expansion of humid air to below its dew point in the "negative pressure phase" described above. However I can't find any reference to that phenomenon in Kinney or the textbooks I have read.
I would be interested to hear of any source that describes it in a scientific manner.

Wikipedia states (https://en.wikipedia.org/wiki/Condensation_cloud):
"A transient condensation cloud, also called a Wilson cloud, is observable surrounding large explosions in humid air."
And there is a link to this article: https://cen.acs.org/safety/industrial-safety/chemistry-behind-Beirut-explosion/98/web/2020/08.
With this info, perhaps you can find references to the scientific literature you seek.

 

[Baluncore]

However I can't find any reference to that phenomenon in Kinney or the textbooks I have read.

The condensation cloud is only visible after large explosions, say about 500 kg TNT. It does not get attention because it is transient and a minor part of the explosion.

The condensation cloud has a smooth surface, marked by the transition to lower pressure. It appears to expand in place, from the air, without mass flow of material. Shortly after, it dissolves back into the air, again without mass movement. What could it be but atmospheric moisture?

https://en.wikipedia.org/wiki/Cloud_chamber#Invention

 

[Squizzie]

I am indebted to Wikipedia for its reference to Glasstone, Samuel and Philip J. Dolan. The Effects of Nuclear Weapons, U.S. Dept. Of Defense/ Dept. Of Energy; 3rd Edition (1977) for its analysis of this cloud (also referred to as a "Wilson cloud").
That paper associates the cloud's appearance to the blast wave propagating through humid air, and the cloud being formed in the "negative phase" of the blast wave where the air pressure drops below the ambient pressure, as illustrated on p.84 :

and, on p.43:
"During the compression (or blast) phase, the tem-perature of the air rises and during the decompression (or suction) phase it falls. For moderately low blast pressures, the temperature can drop below its original, preshock value, so that fi the air contains a fair amount of water vapour, condensation accompanied by cloud formation will occur"

It is left for the reader to connect a) the existence of the temperature drop with that associated with the adiabatic expansion of gas, and b) the formation of the cloud due to the temperature falling below the dew-point of the humid air, but I think the formation of the cloud is well explained.
The mystery for me now is the source of this "negative phase". The presence of the overpressure is easily imagined as the result of the rapid expansion of the hot detonation gases . But what is the source of the negative phase, where the pressure drops for about the same duration as the compression phase, and only starts to appear at some time and distance from the detonation?

It is referenced in both Kinney and Glasstone, but is not explained.

 

[renormalize]

The mystery for me now is the source of this "negative phase". The presence of the overpressure is easily imagined as the result of the rapid expansion of the hot detonation gases . But what is the source of the negative phase, where the pressure drops for about the same duration as the compression phase, and only starts to appear at some time and distance from the detonation?

Search for info on blast waves:
https://en.wikipedia.org/wiki/Blast_wave
"In fluid dynamics, a blast wave is the increased pressure and flow resulting from the deposition of a large amount of energy in a small, very localised volume. The flow field can be approximated as a lead shock wave, followed by a self-similar subsonic flow field. In simpler terms, a blast wave is an area of pressure expanding supersonically outward from an explosive core. It has a leading shock front of compressed gases. The blast wave is followed by a blast wind of negative gauge pressure, which sucks items back in towards the center. The blast wave is harmful especially when one is very close to the center or at a location of constructive interference. High explosives that detonate generate blast waves."

 

[Squizzie]

Search for info on blast waves:
https://en.wikipedia.org/wiki/Blast_wave
"In fluid dynamics, a blast wave is the increased pressure and flow resulting from the deposition of a large amount of energy in a small, very localised volume. The flow field can be approximated as a lead shock wave, followed by a self-similar subsonic flow field. In simpler terms, a blast wave is an area of pressure expanding supersonically outward from an explosive core. It has a leading shock front of compressed gases. The blast wave is followed by a blast wind of negative gauge pressure, which sucks items back in towards the center. The blast wave is harmful especially when one is very close to the center or at a location of constructive interference. High explosives that detonate generate blast waves."

I guess my question is along the lines of conclusion 4 of the paper[12] linked in the Wikipedia article :

It would appear that the Friedlander equation provides a close correlation with the experimental data, but it doesn't explain what appears to me anyway, as wholly counterintuitive, why the high pressure zone of the blast wave is followed by this low pressure zone.

 

[Baluncore]

The mystery for me now is the source of this "negative phase". The presence of the overpressure is easily imagined as the result of the rapid expansion of the hot detonation gases . But what is the source of the negative phase, where the pressure drops for about the same duration as the compression phase, and only starts to appear at some time and distance from the detonation?

Atmospheric pressure is greater than zero, so there can be positive and negative pressure excursions. After a disturbance, while an equilibrium is being restored, the pressure can be expected to oscillate about atmospheric pressure. The positive and negative phases have the same periodic duration, simply because they are parts of the same oscillation.

 

[renormalize]

...but it doesn't explain what appears to me anyway, as wholly counterintuitive, why the high pressure zone of the blast wave is followed by this low pressure zone.

Do you think it's counterintuitive that a region of rarefaction (low pressure) follows every region of compression (high pressure) in an ordinary sound wave in a fluid? If not, shouldn't an impulsive (shock) wave in that fluid similarly have low pressure follow high?

 

[Squizzie]

Do you think it's counterintuitive that a region of rarefaction (low pressure) follows every region of compression (high pressure) in an ordinary sound wave in a fluid? If not, shouldn't an impulsive (shock) wave in that fluid similarly have low pressure follow high?

Yes, counterintuitive.
Especially as we now have the Friedlander equation that doesn't have any wave-like e^{ix}, e^{-ix} components.

 

[Baluncore]

Especially as we now have the Friedlander equation that doesn't have any wave-like e{ix}, e{-ix} components.

Do not forget that; e^iz = cos(z) + i⋅sin(z)
https://en.wikipedia.org/wiki/Euler's_formula

 

[Squizzie]

Do not forget that; e^iz = cos(z) + i⋅sin(z)
https://en.wikipedia.org/wiki/Euler's_formula

Precisely, but Friedlender's equation has no i term!

 

[Baluncore]

The Friedlander equation is an approximation to the pressure of a blast wave. Blast waves do not follow the Friedlander equation as a law.

It seems that Friedlander simplifies the analysis by assuming the wave is damped to one cycle. It predicts the rarefaction, and we should expect the integral of the pressures above and below atmospheric pressure will be proportional.

 

[sophiecentaur]

The shockwave will lose speed as it travels

But will the wave maintain its profile until it slows to sonic speed. The 'wave' is surely more of a pulse which will disperse as soon as it's formed and you then have to ask which bit of the wavefront counts in the speed calculation?
If you observe a pulse, launched from a supersonic event, at various distances from its formation then is it not true that the pulse will spread out in time / distance? Can there be an answer to the OP question? I know that many people claim that the sonic boom they hear is actually a shock wave (don't ask for references) but PF has discussed this several times and my memory tells me that the wave acquires sonic speed very near the plane's path.

Any images of suitable graphs available?

 

[Baluncore]

If you observe a pulse, launched from a supersonic event, at various distances from its formation then is it not true that the pulse will spread out in time / distance?

The thing that defines a shock wave is that it is self-sharpening, as the higher pressure and temperature at the back of the pressure step, continuously catches up with the lower temperature at the front.

Once the compression and heating is sufficiently attenuated by inverse square law, the sharp step, falls to sonic velocity, and begins to take the form of a ramp, with attenuation of the high audio frequencies in the spectrum occurring more rapidly than the low.

By definition, the speed of an explosively generated shock-front is supersonic, due to the local heating in the front.

 

[hmmm27]

Once the compression and heating is sufficiently attenuated by inverse square law, the sharp step, falls to sonic velocity, and begins to take the form of a ramp, with attenuation of the high audio frequencies in the spectrum occurring more rapidly than the low.

I think the confusion is why form an (outwards) ramp. If it were an "ideal gas" all'round, without any of the normal variations in molecular velocity, would it stay a sharp step ? (gradually attenuating).

 

[Baluncore]

Sound waves are assumed to travel at sonic speeds, and do not assume heating of the air, during passage of the pressure wave.

If a pressure step increases the temperature, the pressure wave will be self-sharpening, with a supersonic speed.

There must be a transition defined between those two distinct models.

 

[Baluncore]

https://en.wikipedia.org/wiki/Rankine–Hugoniot_conditions

 

[sophiecentaur]

Once the compression and heating is sufficiently attenuated by inverse square law, the sharp step, falls to sonic velocity,

The inverse law must depend on the shape of the generating object - a sphere if it's an explosion but not for all shock waves. (Close to an aircraft or in a tube) This is hard stuff - that link of yours is not bed-time reading.

 

[Baluncore]

This is hard stuff - that link of yours is not bed-time reading.

The theory gets hard when you try to apply it to every possible case of supersonic flight, shock tube, and explosion.

If we can limit discussion to supersonic explosions, near the Earth's surface, then it can be discussed in this thread, without too much confusion.

 

[Squizzie]

@Baluncore I'm not sure that the Rankine–Hugoniot conditions (at least as summarised in Wiki) can be reconciled with the measurements reported in Kinney and Glasston.

 

[vanhees71]

But will the wave maintain its profile until it slows to sonic speed. The 'wave' is surely more of a pulse which will disperse as soon as it's formed and you then have to ask which bit of the wavefront counts in the speed calculation?
If you observe a pulse, launched from a supersonic event, at various distances from its formation then is it not true that the pulse will spread out in time / distance? Can there be an answer to the OP question? I know that many people claim that the sonic boom they hear is actually a shock wave (don't ask for references) but PF has discussed this several times and my memory tells me that the wave acquires sonic speed very near the plane's path.

Any images of suitable graphs available?

But also shock waves propagate with the speed of sound. What's moving with faster-than-sound speed is the source, which leads to the formation of the Mach cone.

 

[sophiecentaur]

But also shock waves propagate with the speed of sound. What's moving with faster-than-sound speed is the source, which leads to the formation of the Mach cone.

OK. So you connect a microphone to an oscilloscope. You display the sound of a sonic boom going past. Later, you record the microphone output using a loudspeaker source. Would you expect a different scope trace? Could you call what the loudspeaker produced a shock wave?

If you use a pair of microphones then the spacing of the two pulses will give an idea of a 'speed'. The wave front of the sound approaching the ground is tilted and the pulse spacing gives a supersonic 'virtual' speed? But that happens for all waves when you look from off the propagation axis. You can even measure an 'instant' / infinite speed when a stationary source is directly overhead the mid point of the microphones.

The pulse speed is the rate of actual energy transfer, normal to the wave front.

 

[Squizzie]

From the context of my OPs , where I referred to the Slo Mo Guys' C4 experiment and the Beirut explosion, I was clearly using the "term shock" wave to refer to what I now recognise is more appropriately described in the technical literature as a"blast wave" with a "shock front".

The subject of the shock wave generated by an object like a jet plane or a bullet travelling at a supersonic speed is a fascinating subject, but, as pointed out by @Drakkith at #39, it is a quite different physical phenomenon from that generated by an explosion.

Could I respectfully request @vanhees71 , @sophiecentaur , that we confine responses on this thread to the discussion of the blast wave/ shock front from an explosion and perhaps submit your thoughts about the shock wave from a plane or bullet on a separate thread. Unfortunately a brief search of PF indicates that earlier threads on the subject are mostly closed, so maybe you should start a new thread.

As I indicated in #71, I think there is a way to go on this one.

 

[sophiecentaur]

Could I respectfully request @vanhees71 , @sophiecentaur , that we confine responses on this thread to the discussion of the blast wave/ shock front from an explosion

Fair enough. I still have to ask when one should say the sound of an explosion is just a sound and not a shock front?
Near an explosion, is there a point where the ejecta is travelling at supersonic speed? Is this just a play on words and definitions. A detonation will carry with it, material that is more dense than the air it flies through so is it valid to talk in terms of gas laws and air temperature to set what we call the speed of sound.

There must be loads of data for videos of detonations in which at least a mean value for the speed of the 'blast wave' can be measured and also the speed of the 'bang' that's left over.

 

[Squizzie]

I still have to ask when one should say the sound of an explosion is just a sound and not a shock front?

And that's a very good question.

From rough estimations from the Slo Mo video it seems that the shock front is travelling at about the speed of the bullet (~Mach 1) when it impacts the target at the same time as the bullet, and from the Beirut explosion video, it appears to travel to the cameraman at around Mach 1 . So my feeling is that once it has departed the extreme temperatures of the explosion, it is a sound wave.

Normally, however, we associate the term sound wave with a sound that persists for a while: the note from a piano can be sustained over a period of seconds, and that of a violin, for as long as the bow is being drawn over the string. In the case of a blast wave, the duration of the sound of the blast wave: the bang! is of a very short duration (did you see Oppenheimer?)

But the duration of the blast wave is considerably longer - see videos of an atomic explosions, when the dust surges forward and back over a period of a few seconds.

So maybe the sound of the explosion is contained in the shock front, but blast wave, immediately behind the front, travelling at roughly the same speed as the shock front, can persist for a few seconds.

 

[berkeman]

From the context of my OPs , where I referred to the Slo Mo Guys' C4 experiment and the Beirut explosion, I was clearly using the "term shock" wave to refer to what I now recognise is more appropriately described in the technical literature as a"blast wave" with a "shock front".

The subject of the shock wave generated by an object like a jet plane or a bullet travelling at a supersonic speed is a fascinating subject, but, as pointed out by @Drakkith at #39, it is a quite different physical phenomenon from that generated by an explosion.

Could I respectfully request @vanhees71 , @sophiecentaur , that we confine responses on this thread to the discussion of the blast wave

Should I edit your thread title from "shockwave" to "blastwave"?

 

[Baluncore]

I'm not sure that the Rankine–Hugoniot conditions (at least as summarised in Wiki) can be reconciled with the measurements reported in Kinney and Glasston.

They are discussing the same subject.
Your lack of certainty, is your problem.

The Wiki page theory assumes that the temperature increase is significant, from which it follows that the speed of sound will increase as the wave front passes.

Kinney and Glasston were presenting the supersonic wave front velocity, from which they could estimate the momentary temperature rise of the shock front.

So my feeling is that once it has departed the extreme temperatures of the explosion, it is a sound wave.

If you can hear it, it is a sound wave. Feelings do not come into it.

We are discussing the step front wave that travels at greater than M 1.0

Any claim you make that the shock-front travels at exactly M 1.0 denies the thermal step that makes it special.

It remains a self-maintaining shock-wave until the velocity falls to M1.
The bandwidth of an audio recording system is clearly insufficient to reproduce the self-sharpening pressure step.

 

[sophiecentaur]

From rough estimations from the Slo Mo video it seems that the shock front is travelling at about the speed of the bullet (~Mach 1) when

You asked to restrict the discussion to detonations and you're back on flying objects. Which do you want?

Normally, however, we associate the term sound wave with a sound that persists for a while:

I don't. Our hearing has to deal with many percussive sounds, lasting for a few milliseconds. Do we make a distinction between that and your violin bow playing a minim length G? If I'm picky, I'd say that the speed of an endless note would be very hard to measure without some interruption / modulation as a marker. Kids measure the speed of sound by clapping their hands and counting the time for multiple echos from a wall.

So maybe the sound of the explosion is contained in the shock front, but blast wave, immediately behind the front, travelling at roughly the same speed as the shock front, can persist for a few seconds.

What you seem to be describing is the effect of dispersion. for a large source, a lot of air can be displaced and the resulting wave can travel a long way (across a town) and do damage (windows) at around 300m/s.

Alternatively, for very sub sonic speed. Did you ever see / own one of these?

 

[Squizzie]

Should I edit your thread title from "shockwave" to "blastwave"?

Yes, please.

 

[Squizzie]

You asked to restrict the discussion to detonations and you're back on flying objects. Which do you want?

I'm talking about the blast wave from the C4 explosion. I offer the trajectory of the bullet simply as a visualisation of the speed of sound.

 

[Baluncore]

I offer the trajectory of the bullet simply as a visualisation of the speed of sound.

The speed of a bullet is quite irrelevant to the speed of sound.

Some bullets are supersonic, at Mach 2.5, others are subsonic, at Mack 0.4

 

[Squizzie]

The speed of a bullet is quite irrelevant to the speed of sound.

Some bullets are supersonic, at Mach 2.5, others are subsonic, at Mack 0.4

In the case of the quoted video, the bullet is reported at 8:09 to be travelling at
387 m/sec which is Mach 1.1 in air at NTP.

 

[Squizzie]

Alternatively, for very sub sonic speed. Did you ever see / own one of these?

May refer you to my earlier post, requesting that discussion be constrained to explosive blast waves on this thread?
The air cannon is indeed a fascinating device, and the vortices it generates are an endless topic for discussion, but perhaps on a separate thread?

 

[Squizzie]

The bandwidth of an audio recording system is clearly insufficient to reproduce the self-sharpening pressure step.

Could I ask you to elaborate on "self-sharpening pressure step" please, and how it applies to blast waves?
I am not familiar with the term. A Google search comes up with pages about sharpening knives, ChatGPT doesn't recognise it but Bard provides :
"A self-sharpening pressure step is a type of pressure step that is used in adsorption processes to improve the separation of different components in a gas mixture."
so I'm not clear about what you are describing.

 

[sophiecentaur]

The air cannon is indeed a fascinating device, and the vortices it generates are an endless topic for discussion, but perhaps on a separate thread?

The relevance is the possibility of carrying 'destructive' power through the air, slowly.

 

[berkeman]

May refer you to my earlier post, requesting that discussion be constrained to explosive blast waves on this thread?
The air cannon is indeed a fascinating device, and the vortices it generates are an endless topic for discussion, but perhaps on a separate thread?

The relevance is the possibility of carrying 'destructive' power through the air, slowly.

If you folks want a separate discussion, please start a different thread. Thanks.

 

[Baluncore]

Could I ask you to elaborate on "self-sharpening pressure step" please, and how it applies to blast waves?

That is fundamental to the discussion here.
The speed of sound is proportional to the square root of temperature. So the speed of sound is faster in hotter air than colder air. The speed of sound is an immediate function of temperature, not of pressure.

The pressure wave generated by an explosion causes heating of the air.
The back of the shock-front is hotter than the front of the shock-front, so the back of the wave catches up with the front of the wave. That keeps the wave steep. I call that self-sharpening.

That pressure and temperature wavefront step will continue, until the compressive energy is no longer able to significantly heat the air. The speed will then be restricted to Mach 1, it will become a normal sound wave.

Look at table XI in Kinney and Graham. It shows that the velocity, Mx, of the shock-front, resulting from the detonation of 1 kg of TNT, is supersonic throughout the 500 metre passage of the blast wave.

Any supersonic blast wave must have a sufficient pressure step to cause a temperature rise, or it would not be supersonic.

Your persistent demands that, the shock-front of a blast wave must travel at the speed of sound, demonstrates a rejection of the fundamental step assumption that defines, and makes a shock-front special.

You are caught in a self-contradiction, a paradox of your own making. Once you understand the self-sharpening effect of the pressure step, you will understand what makes supersonic shock-fronts so interesting, and so destructive.

 

[Squizzie]

The back of the shock-front is hotter than the front of the shock-front, so the back of the wave catches up with the front of the wave. That keeps the wave steep. I call that self-sharpening.

But don't both Glasstone and Kinney suggest that, if anything, the back of the blast wave travels more slowly than the shock front, causing the back of the blast wave to lag further and further behind the shock front, rather than catch up as the blast wave travels away from the blast?

 

[Drakkith]

So maybe the sound of the explosion is contained in the shock front, but blast wave, immediately behind the front, travelling at roughly the same speed as the shock front, can persist for a few seconds.

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.

But will the wave maintain its profile until it slows to sonic speed. The 'wave' is surely more of a pulse which will disperse as soon as it's formed and you then have to ask which bit of the wavefront counts in the speed calculation?
If you observe a pulse, launched from a supersonic event, at various distances from its formation then is it not true that the pulse will spread out in time / distance? Can there be an answer to the OP question? I know that many people claim that the sonic boom they hear is actually a shock wave (don't ask for references) but PF has discussed this several times and my memory tells me that the wave acquires sonic speed very near the plane's path.

Any images of suitable graphs available?

Here's a graph of the pressure and velocity of a blast wave from 15 kg of TNT:

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.

 

[Baluncore]

But don't both Glasstone and Kinney suggest that, if anything, the back of the blast wave travels more slowly than the shock front, causing the back of the blast wave to lag further and further behind the shock front, rather than catch up as the blast wave travels away from the blast?

It seems you insist on confusing the back of the shock-front with the back of the blast-wave. Are you a troll?

All your attached plots show the supersonic shock-front as a singular step function of pressure. That maintains its steepness, but the step is reduced in height as energy is lost. Later, things will happen at subsonic speeds.

You need to stop insisting, that the complex system must fit into your oversimplified model. If the theory is too complex for you, then walk away before your head explodes.

 

[Squizzie]

It seems you insist on confusing the back of the shock-front with the back of the blast-wave. Are you a troll?

I am trying desperately not to be.
I think of the shock front as the time and location of the arrival of the blast wave. It is an instant in time after which the air pressure starts to rise abruptly from ambient to an overpressure value above ambient.
The size of this overpressure depends on a number of factors including the nature of the explosion and the distance from the source.
The increase in pressure occurs over a very short distance and period of time: it is shown in the images posted at #34 as being vertical, but, as we know, it can't be exactly vertical, but its duration is smaller than the resolution of the plots. Unfortunately the plots have no scale on either axis, so it's hard to tell from the plots.
Kinney and Graham, when discussing "Thickness of the Shock Front" describe a shock plane and suggest:
"A representative thickness for a shock plane, as given by equation (4-23) for Mx= 2, is about 0.00025 mm. From equation (4-24), this corresponds to about twice the mean free path for a molecule in the upstream air."
I am confused about your interpretation of "shock front" in your post #88: "The back of the shock-front is hotter than the front of the shock-front"
[EDIT]
I read further in Kinney p. 50, that :
"The shock front of a blast wave is in many ways a determining factor in its behavior. The concern here is with shock fronts in air, which for present purposes may be considered as conforming to the specification of an ideal gas. The physical feature which uniquely characterizes a shock phenomenon is its abrupt occurrence in a Iamina of effectively zero thickness."
This seems to suggest and accord between "shock plane" and "shock front".

 

[Drakkith]

The increase in pressure occurs over a very short distance and period of time: it is shown in the images posted at #34 as being vertical, but, as we know, it can't be exactly vertical, but its duration is smaller than the resolution of the plots. Unfortunately the plots have no scale on either axis, so it's hard to tell from the plots.

For the 100g to 400g charges in my first reference in post #90 the rise time was less than 1 μs.

 

[Baluncore]

The increase in pressure occurs over a very short distance and period of time: it is shown in the images posted at #34 as being vertical, but, as we know, it can't be exactly vertical, but its duration is smaller than the resolution of the plots.

The front of that shock is in ambient air, while less than ¼ um behind, (one nanosecond later), the back is subjected to full pressure. If it is not vertical, then it will make itself vertical, because the back will overtake the front.

 

[Squizzie]

For the 100g to 400g charges in my first reference in post #90 the rise time was less than 1 μs.

I noted from the reference that :"The width of the shock front is only very small ",
and that :
"The transducers have a measuring range of 344.7 kPa, rise time less than 1 μs",
but I didn't see any specific reference to the size of the shock front. I am not familiar with the specification of transducers, so do I understand correctly that that implies that the duration of the shock front had to be less than 1 μs?
I have no doubt that the shock front has a very short duration, but 1 μs does seem a bit short!
In just one of the plots I can detect a 1 px step in the shock front, but the resolution of the plot is not high enough to ascertain if it indicates a slope in the line, or is an artefact of the image production.

 

[Squizzie]

But this whole concentration on the characteristics of the shock front has diverted from my search for a reason for the source of the condensation cloud's "negative overpressure" that we digressed from after post #60.

 

[Drakkith]

I have no doubt that the shock front has a very short duration, but 1 μs does seem a bit short!
In just one of the plots I can detect a 1 px step in the shock front, but the resolution of the plot is not high enough to ascertain if it indicates a slope in the line, or is an artefact of the image production.

My mistake, I didn't look closely enough. Looking closer now, I can see a step in the vertical line on the 100g charge too. A quick and totally non-rigorous count gives me about 16 steps over about 0.5 ms, or about 30 microseconds per step. Does a 50 microsecond rise time sound more reasonable?

 

[Baluncore]

I have no doubt that the shock front has a very short duration, but 1 μs does seem a bit short!

Does a 50 microsecond rise time sound more reasonable?

Over 40 years ago, when I was measuring the velocity of Mach 7+ shock fronts in a reaction tube. I used resistive sensors made from 0.2 mm wide gold leaf, mounted flush against the wall of the shock tube. The gauges were heated by the shock front as it passed, with their resistance rising in proportion to absolute temperature. The speed was measured accurately by the elapsed time between sensors.

It took about 100 ns for the narrow shock-front to cross the 0.2 mm wide sensor. The step transition then took another 50 ns to complete, as it was limited by the speed of the electronics.

As computed in chapter 4, of Kinney and Graham, I would expect the rise-time of the shock-front to be closer to 1 ns. The instrumentation is much slower than the shock front.

 

[Squizzie]

Folks, this analysis of the shock front is fascinating, but could I implore you to return to the question of the source of the low pressure in the back of the blast wave?
Contributors to this thread have provided evidence that It appears in all the experimental papers (Glasston, Kinney & Graham, Filice & collaborators), it is visible as a condensation (or Wilson) cloud in videos including the Beirut explosion, and is closely modelled with the Friedlander equation.
It has been suggested that it is the expression of a heavily damped oscillation, which is interesting, but there seems to be little independent evidence for that and the absence of an oscillating term in Friedlander equation would not support that view.
The plots of the experimental data would indicate the locus of the low pressure approaching atmospheric pressure asymptotically with time.
@renormalize queried my view that the presence of this low pressure was counterintuitive, by analogy with a pressure wave in a fluid, but as I said, there appears to be no evidence of an oscillation in the experimental results or the mathematical modelling.
I would expect the high pressure in the blast wave to decay exponentially to atmospheric pressure, but it doesn't, and I have yet to discover why.

 

[Drakkith]

I would expect the high pressure in the blast wave to decay exponentially to atmospheric pressure, but it doesn't, and I have yet to discover why.

Is that not what the graph in post #90 is showing?

Folks, this analysis of the shock front is fascinating, but could I implore you to return to the question of the source of the low pressure in the back of the blast wave?

In a normal sound wave, the compression and expansion phases have negligible energy transfer and the entire cycle of the wave leaves the medium with virtually no gain or loss of energy. I suspect that a blast wave is somewhat different as some form of energy loss has to occur for the air to cool and moisture to condense. Radiative losses maybe?

On the topic of blast waves, I stumbled across this extremely in depth report on nuclear detonations from Los Alamos from the 1940's. It may or may not be of use but I thought it was interesting and related to the topic. Here's the link: https://apps.dtic.mil/sti/tr/pdf/ADA384954.pdf