Shock wave data from nuclear tests

[Squizzie]

TL;DR Summary

Where are the results of the smoke mortar measurements of the shock wave in nuclear tests?

Smoke mortars were used in nuclear tests to measure the passage of the shock wave. The passage of the shock wave could be detected by the sunlight reflected from the smoke trails being refracted through the shock wave, and high speed cameras were used to record this passage, enabling the scientists to accurately measure the passage of the shockwaves through the smoke.

This is widely reported in publicly available reports. Unfortunately the reports I have retrieved only describe the process, but not the results.

I would be grateful if anyone could let me know where I could find some of the results?

 

[renormalize]

I would be grateful if anyone could let me know where I could find some of the results?

It's pretty easy to find blast-wave smoke data using Google. For example, see Fig. 4 in this 1964 article by J.M. Dewey:
https://apps.dtic.mil/sti/tr/pdf/AD0611648.pdf

 

[Squizzie]

Thanks, but I don't think Dewey's report used the refraction of the light as a measure.
A search for "refraction" only returned one result, in Section 6 p. 377:

"This refraction will give a slight shift to the image of the trail, but calculations based on an assumed density variation behind the shock indicated that the apparent displacement would be less than 0.1 % in the region of interest and, in fact, only 0.3 % at a shock strength of 200 atm. This point was also checked experimentally by attempting to detect any apparent shift of the marker boards as they were developed by the wave. No such a shift could be measured."
P.S. It was visible in his later report

 

[renormalize]

Thanks, but I don't think Dewey's report used the refraction of the light as a measure.

Good point. So instead, how about this report analyzing both direct and refracted photography of the shock-fronts arising from 8 atomic tests in Nevada conducted during Operation Teapot in 1955, with yields ranging from 1 to 43 kilotons of TNT:
https://apps.dtic.mil/sti/trecms/pdf/AD0611253.pdf
From pg. 19:

Direct photography was used on 4 shots, refractive smoke photography on 3, and both methods were employed for 1 blast.
(Aside: a quick perusal of the results shows that all the blast-fronts yielding velocity data were supersonic out to the measurement limits, as much as 1.2 km from ground zero. )

 

[Squizzie]

Thanks, lots of interesting reading.
On which page do you get that info please?

 

[renormalize]

On which page do you get that info please?

Shock velocity vs. distance data from https://apps.dtic.mil/sti/trecms/pdf/AD0611253.pdf:

• Shot 4: Fig. 3.8 pg. 40 and Table 3.3 pg. 41
• Shot 8: Fig. 3.25 pg. 60 and Table 3.12 pg. 61
• Shot 12: Fig. 3.38 pg. 75 and Table 3.20 pg. 74

And a correction: I said in post #4 that velocity data extended out to as far as 1.2 km (4000 ft) from ground zero. But the actual maximum distance is 0.9 km (3000 ft).

 

[Squizzie]

OK, And at this stage I'm working the numbers with no conclusions.
Looking at test 12, I think table 3.20 and fig 3.38 were calculated, not measured:

I'm still looking for the measured values.

 

[renormalize]

I'm still looking for the measured values.

But there are no directly "measured" values of velocity (or overpressure) available from film (or video) records. All that any single frame shows is the instantaneous location of the shock front and the time-stamp of when that frame was taken; i.e., $d \text{ vs. }t$ data. The collection of all the frames frames has to be "processed" to extract velocity data, as described in Section 1.1:

You should read and understand Sect. 1.1. It's basically a more sophisticated version of differentiating the spline-fit to $d \text{ vs. }t$ (that we discussed privately) to get the shock velocity and then using an empirical formula to derive the overpressure from that velocity.

 

[Squizzie]

Yes indeed, velocity is very difficult to detect directly. To detect velocity, it is necessary to detect sequential values of position and time, which was specifically the objective of the shock-wave photography that was introduced in Sect 1.1:

It specifically states "detect and locate in space and time".
My quote in #7 above clearly indicates that the values in Table 3.20 and plotted in Fig 3.38 were "obtained from Equation 3.4":

Equation 3.4 deduces speed (U ) from distance (R).
Table 3.20 and Fig 3.38 do not report measured values, but values calculated fro equation 3.4.

 

[Baluncore]

Equation 3.4 deduces speed (U ) from distance (R).
Table 3.20 and Fig 3.38 do not report measured values, but values calculated fro equation 3.4.

NO.
See page 75. "The arrival-time data were then fitted to Equation 1.1, Section 1.2, and the constants obtained by this fitting process are:
a = 966.374
b = 1420.296
c = 0.010475
The constants are valid over the entire range of from 600 to 3,000 ft. "

See page 18. "A complete explanation of the equation and method of fitting may be found In Reference 5."

The data was gathered and analysed, then the equation was fitted to the real data by selecting the parameter values needed to minimise the error. In effect, the real data was smoothed by finding the parameters for that equation.

 

[Squizzie]

The copy of
5. Moulton and Hanlon, Peak Overpressure va DisUnce in Free-Air. Operation IVY, VT-613, March 1953, 3RD. that I have accessed from https://apps.dtic.mil/sti/citations/AD0363573 is almost unreadable.
This is the derivation of equation 3.4 which is very hard to read:

Does anyone have a more legible copy?

 

[Squizzie]

NO.

Actually, YES (and it didn't use parameter c):

 

[renormalize]

Nice graph of the slopes of the tangents to the radius vs. time curve; i.e., the measured velocities of the shock front! All supersonic, just as I stated.

 

[Baluncore]

Actually, YES (and it didn't use parameter c):

c is the constant of integration in Equation 1.1, Section 1.2 on page 16.
After differentiating, the parameter values are used in Equation 1.2 on page 18.

See page 16. "Equation 1.1 is fitted to the data by the method of least squares on IBM computer equipment. Upon differentiation, the following equation is obtained for the instantaneous shock velocity, U:" Equation 1.2

Do you still believe, and insist, that shock waves travel only at the speed of sound?
Your anger at finding yourself in the wrong universe is apparent from your approach.

 

[Squizzie]

Nice graph of the slopes

Thank you

of the tangents to the radius vs. time curve; i.e.,

The graph is simply the graphical representation of equation 3.4 :

Where I have generated 30 values which I have plotted on the X-axis, from 500 to 3,400 in increments of 100 and evaluated a corresponding value that I have plotted on the Y-axis using the equation $y = 966.4 * ( 1 + \frac{1426.3} { x} )^{1.5}$

I read that the constants (966.4 (a), 1426.3 (b) in the equation were obtained as explained on pp. 71, 74:
"The absolute time for each film was found by plotting the first data point from the HOL films on the data supplied by BG4C- for flreball radius versus time (see Fig. 3.37). The arrival-tine data were then fitted to Equation 1.1, Section 1.2, and the constants obtained by this fitting process"
The derivation of equation 1.1

remains elusive as the referenced Moulton-Hanlon paper is, as I noted above, illegible.

the measured velocities of the shock front! All supersonic, just as I stated.

I think you have misunderstood that the purpose of my exercise was to demonstrate that, as was explained in the paper, the the data in table 3.20 and the plot in Fig 3.38 were arithmetical evaluations of equation 3.4 and did not represent experimental data, and certainly not measured velocities.

I am still looking for the experimental results that I initially enquired about.

 

[Squizzie]

Do you still believe, and insist, that shock waves travel only at the speed of sound?

I remain conflicted on the subject.
On the one hand there is a large body of work supporting nonlinear acoustic theory which demonstrates mathematically the existence of supersonic pressure waves.
But on the other hand there is little experimental evidence for the existence of such waves.

Feynman, iIn Vol I Chapter 51, introduces shock waves in section 51-2 with the statement 'Wave speed often depends on the amplitude...' However, I am perplexed by the absence of a mathematical treatment of the topic. Apart from an unclear scenario involving 'little bumps of pressure' superimposed on an object moving through the air, I cannot locate any mathematical analysis of the subject.

The subsequent paragraphs in Chapter 51 discuss water piling up in shallow channels, which the author ultimately dismisses with the statement: 'The point here is not that this is of any basic importance for our purposes.' Unlike previous chapters that offered a qualitative or historical coverage of a topic accompanied by a mathematical model, I am unable to find any relevant mathematical analysis for shock waves in Chapter 51.

Despite the promising introductory statement 'Wave speed often depends on the amplitude,' the subsequent content provides only a qualitative and, frankly, confusing treatment.
Could you assist me in locating any relevant mathematical analysis for shock waves in Chapter 51?

 

[Baluncore]

I think you have misunderstood that the purpose of my exercise was to demonstrate that, as was explained in the paper, the the data in table 3.20 and the plot in Fig 3.38 were arithmetical evaluations of equation 3.4 and did not represent experimental data, and certainly not measured velocities.

But they do represent the real data, because it must be processed before analysis and presentation.

Each data point has a time and a position, and each has a statistical error in time and position. If the data points were used raw, they would yield noisy velocity data between each two adjacent points. It would not be possible to say when the velocity actually had the computed value, or where it did.

By employing least squares estimation, to fit the real data to the equation, the equation can be differentiated and the velocity at any point can be computed. Gone is the switchback noise and the unknown synchronisation error of time zero, which was out by c= 10.475 ms.

That was how the smooth velocity curve was generated accurately and correctly from the noisy raw data.

Nice graph of the slopes of the tangents to the radius vs. time curve; i.e., the measured velocities of the shock front! All supersonic, just as I stated.

But on the other hand there is little experimental evidence for the existence of such waves.

Your denial of the evidence is evident and nonsensical.

 

[renormalize]

I think you have misunderstood that the purpose of my exercise was to demonstrate that, as was explained in the paper, the the data in table 3.20 and the plot in Fig 3.38 were arithmetical evaluations of equation 3.4 and did not represent experimental data, and certainly not measured velocities.

Let me turn this into a freshman physics question: suppose an instructor hands you a table or graph containing ordered pairs of times and distances, representing an experimental record of the motion of a body moving in one dimension. They then ask you use this data to calculate the speed of the body as a function of time. Don't these calculated results constitute a measurement of the body's speed at various times? Other than possible inaccuracies introduced by the method of calculation (e.g., finite-differencing, curve-fitting), is there any reason to believe that an actual speedometer carried by the body would somehow record speeds different than these calculated ones?

 

[Squizzie]

Let me turn this into a freshman physics question: suppose an instructor hands you a table or graph containing ordered pairs of times and distances, representing an experimental record of the motion of a body moving in one dimension. They then ask you use this data to calculate the speed of the body as a function of time. Don't these calculated results constitute a measurement of the body's speed at various times? Other than possible inaccuracies introduced by the method of calculation (e.g., finite-differencing, curve-fitting), is there any reason to believe that an actual speedometer carried by the body would somehow record speeds different than these calculated ones?

Yes, no argument. Finite differencing is the way to do that.
The problem with the data in table 3.20 and the plot in Fig 3.38 from the TEAPOT report is that it's not the result of finite differencing.
As my spreadsheet demonstrates, it's the plotting of the Moulton-Hanlon equation using parameters (a and b) derived from "first data point from the HOL films on the data supplied by BG4C- for flreball radius versus time (see Fig. 3.37)."

That is not finite differencing!
It inevitably yields a curve that is asymptotic to the value a (= 966.4) and with the values provided fin Shot #12, yields a supersonic speed for any value of R up to around 5,000 ft.

I am looking for the experimental data.

 

[renormalize]

Feynman, iIn Vol I Chapter 51, introduces shock waves in section 51-2 with the statement 'Wave speed often depends on the amplitude...' However, I am perplexed by the absence of a mathematical treatment of the topic. Apart from an unclear scenario involving 'little bumps of pressure' superimposed on an object moving through the air, I cannot locate any mathematical analysis of the subject.

@Squizzie, you've been repeatedly advised to refer to acoustics textbooks that are more advanced than the Feynman lectures. Try Pierce chapter 11:

 

[renormalize]

Yes, no argument. Finite differencing is the way to do that.

But finite-differencing is not the only way, nor usually even the best way, to extract the derivative of a curve. By adjusting parameters, you can fit a smooth function to your data and then differentiate that function to get the derivative. That's exactly what Moulton and Walthall do with their three parameters $a,b,c$ in eq. (1.1). Their velocities are every bit as much experimental measurements as those found via finite-differences.

 

[russ_watters]

I am looking for the experimental data.

I'm seeing dozens and dozens of pages of raw data in the link. Example below. What's the problem? Do you think the input data was faked or something? I really don't understand what's difficult to understand about curve fitting a bunch of distance and time data. But if you don't want to do the curve fitting and prefer to see a noisy version, then just plot the raw data as-is, with a basic conversion of distance and interval time to velocity.

 

[Drakkith]

I remain conflicted on the subject.
On the one hand there is a large body of work supporting nonlinear acoustic theory which demonstrates mathematically the existence of supersonic pressure waves.
But on the other hand there is little experimental evidence for the existence of such waves.

What? Your previous thread had multiple sources of evidence. You just made a graph showing a supersonic velocity in post #12. You linked me two videos of supersonic blast waves in our private conversation.

 

[boneh3ad]

I remain conflicted on the subject.
On the one hand there is a large body of work supporting nonlinear acoustic theory which demonstrates mathematically the existence of supersonic pressure waves.
But on the other hand there is little experimental evidence for the existence of such waves.

Feynman, iIn Vol I Chapter 51, introduces shock waves in section 51-2 with the statement 'Wave speed often depends on the amplitude...' However, I am perplexed by the absence of a mathematical treatment of the topic. Apart from an unclear scenario involving 'little bumps of pressure' superimposed on an object moving through the air, I cannot locate any mathematical analysis of the subject.

The subsequent paragraphs in Chapter 51 discuss water piling up in shallow channels, which the author ultimately dismisses with the statement: 'The point here is not that this is of any basic importance for our purposes.' Unlike previous chapters that offered a qualitative or historical coverage of a topic accompanied by a mathematical model, I am unable to find any relevant mathematical analysis for shock waves in Chapter 51.

Despite the promising introductory statement 'Wave speed often depends on the amplitude,' the subsequent content provides only a qualitative and, frankly, confusing treatment.
Could you assist me in locating any relevant mathematical analysis for shock waves in Chapter 51?

Linear and Nonlinear Waves by Whitham

Now please stop casting spurious doubt on established, extensively observed science.

 

[Baluncore]

@Squizzie
A "squizzy" is an Australasian colloquial expression meaning to "take a quick close look".

Go ahead and surprise us, by taking a closer look at -
Table 3.19 the numbers,
Figure 3.36 the plot with the finite difference noise and missing data, and
Figure 3.37 the log-log plot.

 

[russ_watters]

I'm seeing dozens and dozens of pages of raw data in the link. Example below. What's the problem? Do you think the input data was faked or something? I really don't understand what's difficult to understand about curve fitting a bunch of distance and time data. But if you don't want to do the curve fitting and prefer to see a noisy version, then just plot the raw data as-is, with a basic conversion of distance and interval time to velocity.

View attachment 339115

@Squizzie
Just to make sure this data is usable(readable/works/lines up, etc.), I did what I suggested above in Excel. Plotting the film 28284 data on PDF page 60, with a simple velocity calculation, yields a noisy version of the velocity vs distance graph and table on pages 62 and 63, respectively. Don't like filtering/fitting? Fine, the raw data proves the main point you're disputing (velocities above the speed of sound). I strongly recommend you try this.

 

[Squizzie]

@Squizzie
Just to make sure this data is usable(readable/works/lines up, etc.), I did what I suggested above in Excel. Plotting the film 28284 data on PDF page 60, with a simple velocity calculation, yields a noisy version of the velocity vs distance graph and table on pages 62 and 63, respectively. Don't like filtering/fitting? Fine, the raw data proves the main point you're disputing (velocities above the speed of sound). I strongly recommend you try this.

Thanks, as you suggested, I have transcribed the data from Table 3.11 (Shot 8, films 28284 and 28282) into a spreadsheet.
I note that the number of data points ( #28284:19, #28282:17) correlates well with the number of smoke rockets used in the test (20). (I could not find any explanation for the missing data points).

I did the same with the data for Shot 12 in Table 3.19, but when I found that, from the same number of smoke trails (20), the number of data points reported in films #28389 and #28390 have 48 and 64 data points respectively, I concluded that some of the data may have been generated by interpolation of the raw data.

I'm now looking at Shot 8.

P.S. Here's the transcribed data for Shot 8. Any errors are accidental.

 

[Frabjous]

I did the same with the data for Shot 12 in Table 3.19, but when I found that, from the same number of smoke trails (20), the number of data points reported in films #28389 and #28390 have 48 and 64 data points respectively, I concluded that some of the data may have been generated by interpolation of the raw data.

I prefer to read the text to learn that on shot 12 and some others, they used direct shock photography.

 

[Baluncore]

I did the same with the data for Shot 12 in Table 3.19, but when I found that, from the same number of smoke trails (20), the number of data points reported in films #28389 and #28390 have 48 and 64 data points respectively, I concluded that some of the data may have been generated by interpolation of the raw data.

There is absolutely no evidence for that conclusion.

The high speed camera fixed the time of the samples. If the intercept of the shock with a smoke trail could not be clearly identified in an image, then it is statistically better to leave that unreliable data out, than it is to guess or interpolate in the raw data.

With finite differences, missing data will aggravate the noise and reduce the time resolution, which is probably why you may be tempted to guess it, by splitting the difference.

The least-squares curve-fitting process, however, will jump over any missing data points, (that have a statistical weight of zero), to correctly interpolate through that part of the curve later. That is another reason why LS curve-fitting was used to process the data.

 

[Vanadium 50]

here is absolutely no evidence for that conclusion.

As they say, if the data doesn't match one's iconoclastic beliefs obviously the data is wrong,

Oops...almost forgot....IBTL.

 

[berkeman]

Oops...almost forgot....IBTL.

Thread closed for Moderation...

 

[Drakkith]

Thread will remain locked. Thanks everyone.