3 ms·

>A 100-megaton bomb releases 10 times more energy than a 10-megaton bomb, but it does not do 10 times more damage. This is because the blast effects of explosio

>A 100-megaton bomb releases 10 times more energy than a 10-megaton bomb, but it does not do 10 times more damage. This is because the blast effects of explosions scale as a cubic root, not linearly. So a 10-megaton bomb detonated at an optimal altitude might do medium damage to a distance of 9.4 miles (15 kilometers) from ground zero, but a 100-megaton bomb “only” does the same amount of damage to 20.3 miles (33 kilometers). In other words, a 100-megaton explosion is only a little more than twice as damaging as a 10-megaton bomb. Area scales as square of radius, so (assuming the radius calculations are right, the ratios are approx cube root of 10 which is napkin-level correct) more than 4x as much area is effected (incinerated). Doesn't change much about the political/historical issues, but you would fail high school math for this.

yunohn 5y ago
> Area scales as square of radius (…) Yes, but they’re referring to volume - which does scale as a “cube”. Bombs detonate in 3D, not 2D - moreso when aerial/aquatic. > but you would fail high school math for this This seems quite vitriolic and uncalled for.
- skyechurch 5y ago
  But they are referring to a radius of a surface area on the Earth being destroyed, which goes as radius^2 (or ~volume^2/3 if you detonate in optimally). >This seems quite vitriolic and uncalled for. I apologize if this sounded too harsh, but "The Bulletin of Atomic Scientists" should not make basic errors like this. It was a very interesting historical article, but when you miss stuff like this, which is simple to catch, I wonder about the journalistic fact checking, which is considerably harder.
  - CapitalistCartr 5y ago
    It's not a mistake at all. They understand nuclear yields fine. The exact effects are complicated by wave reflectiins off Earth, changes in the atmosphere at different altitudes, etc. but basic cube law is a decent approximation. The bomb fills a volume of space, the cube of the increase of the radius of damage. The radius of damage is a linear measurement.
    - skyechurch 5y ago
      It is a mistake. The bomb does not damage a radius, it damages an area which is quantified by a radius squared. Again, this is high school geometry, not controversial, and maybe there are factors not explained which make this correct in a sense (maybe "damage" is a term of art which varies by the square root of area destroyed? Seems unintuitive, but I'm not an expert in atom bombs or much of anything.) It's a silly error which in no way undercuts anything in the article afaict, but it annoys because it is very simple and obviously true by unit analysis. I make silly errors too, as we all do, present company excepted. But it does undercut my confidence in the more far difficult journalistic work being done, which I cannot interrogate with my limited mathematical skills and pretty much have to take on faith. To me it speaks to the question of whether I "learned something" or "read some words". This is a very boring digression and I take full responsibility for making a ticky-tacky point, which I have now I believe fully explained and contextualized.
      - pdoege 5y ago
        I don't think it is true that bombs damage an area. For example, when I worked on ADF nukes we were interested in the volumes necessary to destroy targets located in 3D airspace. Similarly underwater explosions caused spherical and columnar affects depending on yield and depth.
      - CJefferson 5y ago
        I bomb exploded near the surface of the earth will, in effect, explode as a hemisphere, which is why there is a cube root. If you could somehow make the force spread only over the surface of the earth it would be radius squared, but that isn't what happens -- most of it goes into the air. You could think about what would happen in space (a spherical explosion), then consider what would happen as it got closer to the earth.
        skyechurch 5y ago
        >In evaluating the destructive power of a weapons system, it is customary to use the concept of equivalent megatons (EMT). Equivalent megatonnage is defined as the actual megatonnage raised to the two-thirds power: >EMT = Y[^]2/3 where Y is in megatons. >This relation arises from the fact that the destructive power of a bomb does not vary linearly with the yield. The volume the weapon's energy spreads into varies as the cube of the distance, but the destroyed area varies at the square of the distance. Src: https://www.atomicarchive.com/science/effects/energy.html https://www.atomicarchive.com/science/effects/energy.html It's just geometry, or dimensionality, you cannot directly compare 1D and 2D quantities. Type mismatches are often bad in programming, but always fatal in physics.

yunohn 5y ago

> Area scales as square of radius (…) Yes, but they’re referring to volume - which does scale as a “cube”. Bombs detonate in 3D, not 2D - moreso when aerial/aquatic. > but you would fail high school math for this This seems quite vitriolic and uncalled for.

skyechurch 5y ago
But they are referring to a radius of a surface area on the Earth being destroyed, which goes as radius^2 (or ~volume^2/3 if you detonate in optimally). >This seems quite vitriolic and uncalled for. I apologize if this sounded too harsh, but "The Bulletin of Atomic Scientists" should not make basic errors like this. It was a very interesting historical article, but when you miss stuff like this, which is simple to catch, I wonder about the journalistic fact checking, which is considerably harder.
- CapitalistCartr 5y ago
  It's not a mistake at all. They understand nuclear yields fine. The exact effects are complicated by wave reflectiins off Earth, changes in the atmosphere at different altitudes, etc. but basic cube law is a decent approximation. The bomb fills a volume of space, the cube of the increase of the radius of damage. The radius of damage is a linear measurement.
  - skyechurch 5y ago
    It is a mistake. The bomb does not damage a radius, it damages an area which is quantified by a radius squared. Again, this is high school geometry, not controversial, and maybe there are factors not explained which make this correct in a sense (maybe "damage" is a term of art which varies by the square root of area destroyed? Seems unintuitive, but I'm not an expert in atom bombs or much of anything.) It's a silly error which in no way undercuts anything in the article afaict, but it annoys because it is very simple and obviously true by unit analysis. I make silly errors too, as we all do, present company excepted. But it does undercut my confidence in the more far difficult journalistic work being done, which I cannot interrogate with my limited mathematical skills and pretty much have to take on faith. To me it speaks to the question of whether I "learned something" or "read some words". This is a very boring digression and I take full responsibility for making a ticky-tacky point, which I have now I believe fully explained and contextualized.
    - pdoege 5y ago
      I don't think it is true that bombs damage an area. For example, when I worked on ADF nukes we were interested in the volumes necessary to destroy targets located in 3D airspace. Similarly underwater explosions caused spherical and columnar affects depending on yield and depth.
    - CJefferson 5y ago
      I bomb exploded near the surface of the earth will, in effect, explode as a hemisphere, which is why there is a cube root. If you could somehow make the force spread only over the surface of the earth it would be radius squared, but that isn't what happens -- most of it goes into the air. You could think about what would happen in space (a spherical explosion), then consider what would happen as it got closer to the earth.
      - skyechurch 5y ago
        >In evaluating the destructive power of a weapons system, it is customary to use the concept of equivalent megatons (EMT). Equivalent megatonnage is defined as the actual megatonnage raised to the two-thirds power: >EMT = Y[^]2/3 where Y is in megatons. >This relation arises from the fact that the destructive power of a bomb does not vary linearly with the yield. The volume the weapon's energy spreads into varies as the cube of the distance, but the destroyed area varies at the square of the distance. Src: https://www.atomicarchive.com/science/effects/energy.html https://www.atomicarchive.com/science/effects/energy.html It's just geometry, or dimensionality, you cannot directly compare 1D and 2D quantities. Type mismatches are often bad in programming, but always fatal in physics.