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?)
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
[2] https://www.tandfonline.com/doi/epdf/10.1080/00295450.2021.1...