Trinity
Our exploration of the physics of explosions starts with Trinity, the first nuclear test of July 16th 1945. Throughout the series we periodically come back to this example, enriching the description of this historic explosion by progressively adding layers of measurements at different time and length scales.
In the first episode, we introduce a subset of pictures of the test used by G.I. Taylor in his famous 1950 paper.
These pictures were declassified in a report by J.E. Mack, the head of the optical team at the Trinity test (except for the pictures from 1.08 to 1.93 ms, which Taylor obtained from Mack's unclassified report, through his connexion with the Ministry of Supply). These pictures allowed Taylor to construct a plot of the explosion radius over time.
We thank Anna Part (Atomic Heritage Foundation, National Museum of Nuclear Science & History) and Alan Carr (Los Alamos National Laboratory) for helping us track all the pictures used by Taylor and taken by Mack and his team.
Taylor showed that this data set follows a power law, where the radius of the explosion is proportional to time to the power 2/5. Taylor understood that this rather strange exponent was a direct consequence of the interplay between the energy of the explosion and the density of the surrounding medium.
The full set of pictures acquired by Mack and his team was finally declassified in the 1980s, complementing the time range studied by Taylor from 0.1 ms to 100 ms after detonation.
The disks are from Mack's 1946 report declassified in the 1980s, complementing Taylor's data from his 1950 paper (squares).
In this time range, the extension of the explosion follows the 2/5 scaling predicted by the interplay of energy and density.
Mack's 1946 report also included very detailed measurements of the explosion beyond the 100 ms time range studied by Taylor.
This more complete trajectory of the shock front of the explosion includes data from Taylor and Mack, and data beyond 1s obtained through pressure measurements, curated by Kenneth Bainbridge. (see Episode 8)
These extended measurements reveal that the front of the explosion departs from the 2/5 scaling at short (Episode 5) and long times (Episode 4).
Considering the combined effects of the mass and energy of the bomb together with the density and pressure of the surrounding medium leads to the "Explosion Domain", including six scaling laws and five special space-time points (Episode 6) governing the dynamics of explosions.
Any of the special points can be used as logarithmic origin, such that its time and size can be used as units more objective that the second and meter. In addition, the four mechanical parameters of the domain combine to form a single dimensionless index, constant for a particular explosion. Using objective units and a number base built from the index (Episode 7), a fully objective representation of the Trinity explosion can be given:
The first tab of the spreadsheet below gives the evolution of the radius of the shock front for the Trinity explosion, together with the values of the four parameters of the domain (Energy, Mass, Density and Stress). The last tab of the spreadsheet gives the values of a number of additional quantities derived from the parameters (index, radix, some objective units before and after taking into account the dimensionless perfactors , the deltas, etc). See DATA page for more details.
