4 ms·

I didn't get the justification for the Trinity test calculation being within an order-of-magnitude of the actual value (putting aside, of course, the fact that

I didn't get the justification for the Trinity test calculation being within an order-of-magnitude of the actual value (putting aside, of course, the fact that it turned out to be very close!) To me, this experiment would seem analyzable in the same way: suppose we have a loudspeaker with a line of microphones stretching away from it. The speaker emits a pop, and 25 ms later, we record how far the sound has traveled. Clearly, we are going to get the same distance for pop intensities varying over several orders of magnitude. Given the knowledge that the speed of sound in air (though not necessarily that of shockwaves?) is independent of its intensity, this is not surprising, but what physical insight justifies taking the calculation given in the text as being an order-of-magnitude estimate? I would have thought it would require additional inputs, such as empirical evidence of fireball size from conventional explosions. Enrico Fermi famously estimated the yield on the spot by measuring how far the blast wave moved small pieces of paper, but that seems to depend on more than just dimensional analysis. https://www.tandfonline.com/doi/epdf/10.1080/00295450.2021.1927627 https://www.tandfonline.com/doi/epdf/10.1080/00295450.2021.1...

deleted 3y ago
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mannykannot 3y ago
There is more detailed explanation of the calculation here [1]. Having derived the equation E = C''ρR⁵ / t² the author writes "Taylor had experimental data that indicated that C′′ ≈ 1.033 for air." This author goes on to say that in the frame taken at 16ms, the fireball radius was about 100m, giving a yield of about 10 kilotons. This is a little less than half the actual figure, and, interestingly, it is about the figure Fermi arrived at from his impromptu experiment. It is a good estimate in that the method does not account for energy radiated away without contributing to the blast [2]. The article on Taylor's calculation mentions that other frames give higher estimates closer to the total yield (as is the case for the 25ms frame used in the original dimensional analysis article posted to HN, which gives an estimate of about 20 kilotons), but that seems to suggest a rather low precision for the method, unless there's a reason for expecting it to be more accurate after a longer interval (perhaps the dependency on the fifth power of the radius favors measurements taken when the fireball is close to its largest size?) [1] [PDF] https://www.wtamu.edu/~dcraig/PHYS4340/070119_bombscale.pdf https://www.wtamu.edu/~dcraig/PHYS4340/070119_bombscale.pdf [2] https://www.tandfonline.com/doi/epdf/10.1080/00295450.2021.1927627 https://www.tandfonline.com/doi/epdf/10.1080/00295450.2021.1...

deleted 3y ago

[deleted]

mannykannot 3y ago

There is more detailed explanation of the calculation here [1]. Having derived the equation E = C''ρR⁵ / t² the author writes "Taylor had experimental data that indicated that C′′ ≈ 1.033 for air." This author goes on to say that in the frame taken at 16ms, the fireball radius was about 100m, giving a yield of about 10 kilotons. This is a little less than half the actual figure, and, interestingly, it is about the figure Fermi arrived at from his impromptu experiment. It is a good estimate in that the method does not account for energy radiated away without contributing to the blast [2]. The article on Taylor's calculation mentions that other frames give higher estimates closer to the total yield (as is the case for the 25ms frame used in the original dimensional analysis article posted to HN, which gives an estimate of about 20 kilotons), but that seems to suggest a rather low precision for the method, unless there's a reason for expecting it to be more accurate after a longer interval (perhaps the dependency on the fifth power of the radius favors measurements taken when the fireball is close to its largest size?) [1] [PDF] https://www.wtamu.edu/~dcraig/PHYS4340/070119_bombscale.pdf https://www.wtamu.edu/~dcraig/PHYS4340/070119_bombscale.pdf [2] https://www.tandfonline.com/doi/epdf/10.1080/00295450.2021.1927627 https://www.tandfonline.com/doi/epdf/10.1080/00295450.2021.1...