Back of the Envelope Nuclear Blast Strength Estimation
Back of the Envelope Nuclear Blast Strength Estimation
tldr: Order of magnitude estimation using archival footage provides reasonable estimates of nuclear bomb strength
tldr: Order of magnitude estimation using archival footage provides reasonable estimates of nuclear bomb strength
In school most people have had to guess the number of jellybeans, candies, etc. in a jar. In estimating this number one will likely have to ask questions such as "what is the volume of the jar?", "what is the volume of a bean?", and "how tightly to the beans fit together?" Fundamentally what one is doing in this simple example is asking what features matter and how they relate to one another. This line of reasoning is the core of dimensional analysis and order of magnitude problems.
In school most people have had to guess the number of jellybeans, candies, etc. in a jar. In estimating this number one will likely have to ask questions such as "what is the volume of the jar?", "what is the volume of a bean?", and "how tightly to the beans fit together?" Fundamentally what one is doing in this simple example is asking what features matter and how they relate to one another. This line of reasoning is the core of dimensional analysis and order of magnitude problems.
Following this reasoning one can ask more complicated, and perhaps more real world relevant, questions such as:
Following this reasoning one can ask more complicated, and perhaps more real world relevant, questions such as:
- How many phones will be sold this year?
- How quickly does a tire lose tread?
- How much resistance does a ship have in water?
For fun I dug into a question the great minds of the 40s and 50s were asking: How strong is an atomic bomb?
For fun I dug into a question the great minds of the 40s and 50s were asking: How strong is an atomic bomb?
Using the same sort of reasoning as the jelly bean estimation problem one can get an expression for the energy of a nuclear blast based on its fireball radius over time. Using the expression one can then look at images of a blast over time, such as in the plate series below, and estimate a bomb's energy.
Using the same sort of reasoning as the jelly bean estimation problem one can get an expression for the energy of a nuclear blast based on its fireball radius over time. Using the expression one can then look at images of a blast over time, such as in the plate series below, and estimate a bomb's energy.
In 2017 Lawrence Livermore Lab released archival footage of bomb tests; what once was a national secret you can now watch on Youtube. I wrote a quick image processing script to get the radii of blasts over time in these videos. Using the radii over time, the strength of the bombs was estimated. The estimates derived with my order of magnitude, back of the envelope, calculation showed reasonable agreement with the rough strength figures quoted in the videos.
In 2017 Lawrence Livermore Lab released archival footage of bomb tests; what once was a national secret you can now watch on Youtube. I wrote a quick image processing script to get the radii of blasts over time in these videos. Using the radii over time, the strength of the bombs was estimated. The estimates derived with my order of magnitude, back of the envelope, calculation showed reasonable agreement with the rough strength figures quoted in the videos.
