Chew
Senior Member.
Some commentators have claimed the Tianjin explosion was caused by a tactical nuke. However this does not fit with the known scaling laws of the effects of nuclear weapons. They seem to think a small nuke is exactly like a big nuke, only smaller and cuter.
Glasstone and Dolan (1977) wrote the definitive work on the effects of nuclear weapons and I cite their work throughout.
The blast radius increases with the cube root of the yield. The prompt ionizing radiation radius increases to the 0.19 power of the yield. The radius of the fireball of a surface burst increases to the 0.4 power of the yield. The time after detonation of the peak of the thermal radiation output increases to the 0.44 power of the yield. And the duration of the fireball is 10 times the time of the peak thermal output. That means if you time the duration of the fireball you can calculate the yield. This compilation video of the explosion includes a security cam with a timestamp.
The fireball lasts for 22 seconds so the peak thermal power occurred at 2.2 seconds after detonation. Plug in the numbers for the time of peak thermal radiation output and it comes up with a yield of 8.2 megatons!!!
http://www.fourmilab.ch/etexts/www/effects/eonw_7.pdf#page=35
Another way to estimate yield is to measure the radius of the fireball. thunderf00t did that in this video and came up with a radius of 75 meters:
Section 2.127 describes the scaling and constants of the radius of the fireball:
http://www.fourmilab.ch/etexts/www/effects/eonw_2.pdf#page=45
For a surface burst that radius would indicate a yield of 0.66 kilotons. But that yield would give a fireball duration of 0.34 seconds.
Since two extremely well-studied phenomena of nuclear weapons give incredibly huge discrepancies in yield (8200 and 0.66 kilotons), and the observed fireball radius and fireball duration are mutually exclusive, it is very safe to say this explosion came no where near to obeying the scaling laws of nuclear weapons and therefore it was not caused by a nuclear weapon.
Glasstone and Dolan (1977) wrote the definitive work on the effects of nuclear weapons and I cite their work throughout.
The blast radius increases with the cube root of the yield. The prompt ionizing radiation radius increases to the 0.19 power of the yield. The radius of the fireball of a surface burst increases to the 0.4 power of the yield. The time after detonation of the peak of the thermal radiation output increases to the 0.44 power of the yield. And the duration of the fireball is 10 times the time of the peak thermal output. That means if you time the duration of the fireball you can calculate the yield. This compilation video of the explosion includes a security cam with a timestamp.
The fireball lasts for 22 seconds so the peak thermal power occurred at 2.2 seconds after detonation. Plug in the numbers for the time of peak thermal radiation output and it comes up with a yield of 8.2 megatons!!!
http://www.fourmilab.ch/etexts/www/effects/eonw_7.pdf#page=35
Another way to estimate yield is to measure the radius of the fireball. thunderf00t did that in this video and came up with a radius of 75 meters:
Section 2.127 describes the scaling and constants of the radius of the fireball:
http://www.fourmilab.ch/etexts/www/effects/eonw_2.pdf#page=45
For a surface burst that radius would indicate a yield of 0.66 kilotons. But that yield would give a fireball duration of 0.34 seconds.
Since two extremely well-studied phenomena of nuclear weapons give incredibly huge discrepancies in yield (8200 and 0.66 kilotons), and the observed fireball radius and fireball duration are mutually exclusive, it is very safe to say this explosion came no where near to obeying the scaling laws of nuclear weapons and therefore it was not caused by a nuclear weapon.