3 ms·

Unless I'm missing something they forgot to account for the fact that dimensional analysis will only give you a result up to a constant. This should be somewha

Unless I'm missing something they forgot to account for the fact that dimensional analysis will only give you a result up to a constant. This should be somewhat obvious as otherwise you'd get a different result with different units (and no SI units won't save you here, those just work for several common equations in physics not ones you came up with yourself).

johnbcoughlin 6y ago
it's not really dimensional analysis. the same methodology was used to estimate the Trinity blast.
- vladTheInhaler 6y ago
  IIRC dimensional analysis lets you put constraints on the form of the equation, by requiring that the variables form dimensionless groups. But you still have to include the right variables, and then measure the values of those dimensionless quantities under different conditions (for instance the Reynolds number for different velocities or length scales) to figure out how the groups scale relative to one another. But I'm sure that data already exists for the situation in question. It would just be a matter of estimating the values from the video and dropping them into the equation.
- contravariant 6y ago
  It is dimensional analysis provided you can justify that the constant should approximately be 1. This is what G. I. Taylor did for the fireball of the trinity test. And apparently it does end up being close to 1. I do worry about the accuracy of this a bit, but looks like it could in theory work.
sinab 6y ago
The underlying assumption in this analysis is that the constant is 1. Maybe I should have clarified that in the thread.. Thank you for pointing it out!
- contravariant 6y ago
  Okay looks like there is some justification for that assumption given by G.I. Taylor. By the way with your data it looks like you get a better fit if you assume your first image is not at 50ms but rather 38 ms. A line fit between t and r^(5.2) gives a slope of 1.6 10^13. This gives 4 kt if you use the lower estimate of 1 kg/m^3 for the density of air. I do worry you may have overestimated the distance slightly, as these numbers are frankly ridiculous, and with a power of 5 even small errors grow quickly.
  - sinab 6y ago
    Absolutely, I do think it is an overestimate. The angle of the video makes it hard to accurately estimate the size of the ball, and as you rightly pointed out an epsilon difference in size gives epsilon^5 differences in energy, so size estimates are extremely important.
hanche 6y ago
You should be able to determine the constant experimentally by running controlled experiments. Preferably with smaller amounts of explosives. (It’s been too long since I read Taylor’s paper. I thought he had relied upon such experimental data, but it appears I misremembered.)

johnbcoughlin 6y ago

it's not really dimensional analysis. the same methodology was used to estimate the Trinity blast.

vladTheInhaler 6y ago
IIRC dimensional analysis lets you put constraints on the form of the equation, by requiring that the variables form dimensionless groups. But you still have to include the right variables, and then measure the values of those dimensionless quantities under different conditions (for instance the Reynolds number for different velocities or length scales) to figure out how the groups scale relative to one another. But I'm sure that data already exists for the situation in question. It would just be a matter of estimating the values from the video and dropping them into the equation.
contravariant 6y ago
It is dimensional analysis provided you can justify that the constant should approximately be 1. This is what G. I. Taylor did for the fireball of the trinity test. And apparently it does end up being close to 1. I do worry about the accuracy of this a bit, but looks like it could in theory work.

sinab 6y ago

The underlying assumption in this analysis is that the constant is 1. Maybe I should have clarified that in the thread.. Thank you for pointing it out!

contravariant 6y ago
Okay looks like there is some justification for that assumption given by G.I. Taylor. By the way with your data it looks like you get a better fit if you assume your first image is not at 50ms but rather 38 ms. A line fit between t and r^(5.2) gives a slope of 1.6 10^13. This gives 4 kt if you use the lower estimate of 1 kg/m^3 for the density of air. I do worry you may have overestimated the distance slightly, as these numbers are frankly ridiculous, and with a power of 5 even small errors grow quickly.
- sinab 6y ago
  Absolutely, I do think it is an overestimate. The angle of the video makes it hard to accurately estimate the size of the ball, and as you rightly pointed out an epsilon difference in size gives epsilon^5 differences in energy, so size estimates are extremely important.

hanche 6y ago

You should be able to determine the constant experimentally by running controlled experiments. Preferably with smaller amounts of explosives. (It’s been too long since I read Taylor’s paper. I thought he had relied upon such experimental data, but it appears I misremembered.)