However, a study from 1963 suggested that, if detonated 28 miles
(45 kilometers) above the surface of the Earth, a 10,000-megaton
weapon could set fires over an area 500 miles (800 kilometers)
in diameter. Which is to say, an area about the size of France.
If thousands of such gigaton bombs were developed then MAD (Mutually Assured Destruction) would be more taxpayer efficient because we could simply stop funding expensive rocket and submarine weapons delivery systems, as they would only add an unnecessarily complicated step to the process. Just detonate your gigaton arsenal on your own nation's soil. When an animal is in great pain and cannot be saved, we usually consider the most compassionate course of action to euthanize. So in the event of MAD, just instantly vaporize your own population to spare them a few months of clinging to life with radiation sickness, starvation, cannibalism, and the lawless raping and murdering of the earth's final warlords. The multiple gigaton bombs detonated on your own soil will ensure the agonizing death of all your enemies that don't similarly self-euthanize.
The scientist Edward Teller, according to one account, kept a blackboard in his office at Los Alamos during World War II with a list of hypothetical nuclear weapons on it. The last item on his list was the largest one he could imagine. The method of “delivery” — weapon-designer jargon for how you get your bomb from here to there, the target — was listed as “Backyard.” As the scientist who related this anecdote explained, “since that particular design would probably kill everyone on Earth, there was no use carting it anywhere.”
The article is a brilliant piece of writing, but scattered through it, you can gather the bits and pieces of math that would describe why it's not strategically practical.
- Bomb weight / size scales roughly linearly with bomb yield. How are you going to get that massive bomb over to France? The aircraft required to haul it over would be exceptionally vulnerable. If you want to use a rocket, you'd need something on the order of the Apollo Saturn-V rocket to lob it over (especially for 1960's technology), and that rocket would as well would be vulnerable on the launch pad. Good luck hiding it while you fuel it up. Defending nuclear weapons (cough silos / subs cough) was/is no small task.
- The troposphere (which accounts for the main density of the atmosphere) is only about 13 miles in height, on average. It's thinner near the poles and thicker near the equator. But anyhow, past a certain yield, you literally really do blow a hole in the atmosphere. At that point, the atmosphere acts like a tamper, channelling much of the additional yield into outer space.
To which end, Sakharov was right. The big bombs were massive publicity stunts, and to the degree that the Soviet leadership pursued them, they were wasting money on propaganda projects.
>So in the event of MAD, just instantly vaporize your own population to spare them a few months of clinging to life with radiation sickness, starvation, cannibalism, and the lawless raping and murdering of the earth's final warlords.
Life tends to not want to die. And somehow they seem to survive enormous catastrophes against all odds. The dinosaur killing asteroid was ~100 million times more powerful than the Tsar Bomba. Yet we're here.
The bigger threat is from the firestorms that throw so much soot into the atmosphere that it's ruined for our kind of life. But that probably still wouldn't get rid of life on Earth.
It's radically different surviving in a hostile environment (limited sun, cold weather, limited food) than one that will literally kill you by interacting with it.
Indeed, from the other comment about Teller's "Backyard" bomb it seems Kubrick's satire was more truth than fiction. The cigar smoking Ripper in the film was based on the real life Curtis LeMay, who it was later revealed really did want to start WWIII by bombing Russia, reasoning that America should strike before the Soviets developed effective retaliation, nipping the problem of Mutually Assured Destruction in the bud as it were.
No one consents to nuclear war though, unless we imply consent through the actions of the elected government. In which case I don't see how that's different.
There was plenty of technical headroom left for making more fearsome weapons in the early 1960s. Fortunately, the pace of innovation plummeted after atmospheric testing ended, and none of the later nuclear weapons states have surpassed the high water mark set by Cold War era superpower rivalry. Chuck Hansen's book The Swords of Armageddon is a fascinating account of the vast hidden empire of the post war Atomic Energy Commission, and how it developed atomic weapons so far beyond the early atomic bombs used on Japan. And then again optimized thermonuclear weapons so far past the early hydrogen bombs.
They quit making bigger booms because there was no need for them. Two factors are at work:
1) Square-cube law. You do more damage with a collection of smaller warheads than with one big one with the same total yield.
2) The Earth isn't flat. Once a boom gets big enough the area of damage doesn't go up much as the shockwave ends up separating from the ground and the atmosphere above the bomb just ends up blasted off. Note that this does *not* limit the usefulness of big bombs detonated high up for thermal and EMP effects. Very big booms in low orbit could be very nasty with total surprise.
Less than you'd think. At the scale of object which poses a serious collision risk to Earth, nuclear weapons could (at best) break up the object, but would have no realistic chance of significantly reducing the mass/momentum of the object. Unless you can break it up into dust (which at that scale you can't), most of it is still going to land on Earth and do just as much damage.
Actually, one recent work on n-body gravitational methods found that "nuclear explosives remain an indispensable element
of the planetary defense portfolio." [0]
In particular, although these dispersion methods (as you pointed out) don't typically reduce the impact energy to zero, they offer a roughly 2 order-of-magnitude decrease in impact energy while requiring only month-scale warning.
In contrast, diversion techniques which can reduce the impact energy to 0 (e.g. by shifting the impactor to 'miss' our planet) can require decade-scale to accomplish their goal.
Why a decade? Is the idea that we can only nudge it slightly, so we have to go 10 years towards it so that the nudge compounds to a large enough distance to miss?
A point to keep in mind: even if it arrives as a literal dust cloud, an asteroid impact at ~20--40 km/s has all the kinetic energy of the original solid impactor, and the only way for that energy to be expended is in either thermal energy (frictional force against the atmosphere) or kinetic transfer (from impact).
It was from a reply to a question I'd asked recently here on HN that an eyewitness to the Chelyabinsk impactor reported on the heat of that event. Even as the impactor largely broke apart and vaporised 20--40km above the Earth, it shed a huge amount of heat over a large area. Not enough to be lethal, but enough to be felt.
A larger mass would deliver correspondingly more energy. And energy is conserved.
>the only way for that energy to be expended is in either thermal energy
Correct, much of the atmosphere would become superheated, perhaps to plasma, and radiate the energy away non-directionally. So only half would radiate toward the surface -- not that that's a whole lot of help.
Note that for an asteroid reaching terminal velocity, that's already largely the radiative pattern for thermal energy and the bulk of the energy transfer. That is, for Chelyabinsk, roughly half the heat radiated directly to space.
For a sufficiently large single impactor ... there's also an ejecta cloud, and for sufficient sizes (e.g., Chixulub+), that also results in atmospheric warming by a similar mechanism, though from secondary rather than primary fireballs. Several descriptions of the K-T mass extinction go into this mechanism in detail. Even at the antipodes, most exposed terrestrial life would have been subjected to at the very least uncomfortable, and probably lethal, heat.
I've had the experience of feeling radiated heat from a bushfire (and a relatively small one at that), and even at 100s of meters distance, it could be distinctly felt, with the sense that this wasn't just a nearby small heat source (a radiator or firepit), but a large conflagration. The prospect of a wall of flame sweeping down a hillside, or of a sky on fire, is slightly more real to me since that.
If an object started off as a 10-km rock, and was pulverised to a dust cloud, that dust cloud will disperse across thousands of kilometres, some of it likely missing earth entirely.
Area of impact for original rock: 78.5 km2
Area of impact for a 1000-km dust cloud: 785,398 km2
Asteroids that struck 65 million years ago had 3×10 ^23 joules
In case of dusk cloud, that's 382,000 Megajoules per square meter impacted
A column of air with a cross-sectional area of 1 square centimetre (cm2 has a mass of about 1.03 kilogram
A square meter of air column weighs ~10 tons
Heat capacity of air is 1.0035 joules per gram per degree centigrade
So it's 10 MJ to heat up 1 m^2 of atmosphere by 1 degree
So if all the energy was absorbed, converted to heat, and evenly distributed vertically (unrealistically), it the atmosphere would heat to 38,000 degrees. If this is in the right ballpark, then radiation will dominate this equation, which I can't estimate. Upper atmosphere will be heated to a glow, and will radiate away most of this energy. Whatever happens, not a happy scenario.
For a dust cloud 5,000 km in diameter, situation is quite different: 3,821 megajoules per square meter, that's 382 degrees rise per square meter. For comparison, the Sun provides 115 Mj/m2 per day.
I would anticipate that in case of 5000 KM dust cloud there wouldn't be a major loss of life - the atmosphere doesn't conduct heat very well, so most of it would be stuck in upper atmosphere and radiated away. I think a realistic 'space dust cloud' would disperse very quickly to greater than earth radius, but it's not going to be uniform dust.
Note that following pulverisation, the dust cloud would be under the effect of the gravitational field of the cloud itself, and tend to re-coalesce.
The initial pulverisation would presumably result in a distribution of velocities amongst particles. Some of those would achieve escape velocity and leave the cloud. Some would not.
Time to re-coalesce would depend on the total cloud mass and maximum extant itself. In total, it would be relatively quickly.
The resulting re-agglomerated impactor would then resemble a rubble-pile or the World's Largest Dust Bunny. It would be significantly disrupted by both tidal forces and interactions with the atmosphere, though of course, how greatly it is disrupted by atmospheric friction would again be a function of mass.
I don't think it will coalese, surface gravity of ceres is 0.2 metwrs oer second, and ceres is 500km across. Gravity of 10 km rock will be measure in cm or mm. Any process that will pulveriae an asteroid is going to give those dust particles a lot of energy
I've somewhat deliberately left the pulverising mechanism unspecified.
But the point remains: under the influence of the cloud's own gravity a cloud of merely separated particles will re-coalesce. You can look up in the night sky much of the time to see an example of this yourself, the Earth's moon.
And again, depending on the mechanism, a fair fraction of particles, quite possibly / probably the majority, will approach the original centroid of the mass.
In practice, pulverising planets and/or planetoids is likely a challenging proposition. Early experimentation on animal models tends to support this hypothesis:
Though the point remains that what you've got to do is avoid impacting the asteroid entirely, whether it's a single solid core or a dispersed dust-cloud. Or more precisely, the total delivered energy has to be considered and kept to a survivable maximum.
That said, I'm now wondering what it would look like to suddenly have a sub-lethal dust-cloud impact Earth. I imagine there'd be an initial few stray shooting stars, then a rapidly-growing glow as the dust struck the atmosphere. Hrm...
I am in favor of numbers in a discussion like this, even if wrong, (and I am not a physicist) they're more interesting than without.
- The asteroids considered a threat to the Earth start at about 460 feet in diameter. This is about an order of magnitude less (in diameter, not mass) than the impact that got the dinosaurs but would still probably be a lot worse than anything in recorded history, if it hit land or sea. It's said to be about a 10,000 year level.
- Density is uncertain, but I found a figure of 2.7 g / cm^3 as a mid range.
- This equates to 3.9 million metric tons or more being probably what we would want to do something about.
- Freeman Dyson wrote a paper in 1968 or so, about nuclear pulse rocket design, that described a hypothetical spacecraft that would mass forty million metric tons.
- It would, however, accelerate very slowly; at 0.00003 g (supposedly).
- But that's really not so slow.
- Ignoring orbital mechanics, because I just can't right now, if something is headed for Earth, it should be enough to move it by one radius in some direction...right?
- Earth is something like 7926 miles in diameter, and 6.4 megameters is ~half that.
- d = 1/2at^2, 1/2a = 0.000147 m/s^2, so divide the radius by 0.000147, take the square root, and I get ~209,000 seconds.
- That is...2.4 days!
- However, it presumes a one megaton bomb going off every 100 seconds, for a total of around 2,100.
- That sounds like a lot. On the other hand, it's less than 3% of the nuclear bombs the US has produced since 1945.
- However they would have to be custom designed, is my impression, as "nuclear shaped charges" and not just recycled warheads.
- The asteroid might have to be reinforced on the size that was being pushed. The spacecraft design included a 1mm thick sheet of copper to absorb thermal energy.
- However, if the asteroid was four and not forty million tonnes, then less time and fewer explosions would be needed, I would assume. Would it be ten times less? I'm leaving that as an exercise for the reader.
Here in Blighty, during the early cold war we built fall-out shelters and equipped a civilian force with "Green Goddess" fire engines to enable them to extinguish fires from nuclear flash.
Yet this all stopped after development and adoption of the Hydrogen Bomb..... because unlike nuclear weapons (kT yield), trying to defend against thermonuclear weapons (MT yield) is pointless. This was a very real and honest defence policy.
Of course civil defense against the H bomb isn't pointless. In fact, the bigger the bomb, the larger the perimeter zone where survival becomes a matter of knowing how to react appropriately.
"Duck and cover" won't work if you're too close to the fireball, but most people won't be.
...Huh. On an EXTREMELY tangential note, I wish I'd known about this when I was drawing a political cartoon comparing California to a burning building which [redacted] was turning a "Green New Deal" ("Green Dream or whatever") fire engine away from. Tracing and recoloring a random US fire truck didn't quite have the same kick this would have.
It's worth noting, in case anyone thinks that we somehow slowed down testing with the atmospheric test ban...that we went on to conduct 1,352 nuclear weapon detonations. That's roughly 3/4 of all nuclear testing. It really is mind-boggling that we set off so many.
But really, how much more do you want? The US upped the ante several times, developing all kinds of more advanced super weapons, as well as modes of delivery, the first long range bombers, the Hydrogen bomb, ICBM's, MIRV, the Neutron bomb ... I mean, as you say it was FAR beyond the early atomic weapons. And they're continuing with development, in secret of course ...
A missile shield that actually works will actually precipitate a nuclear conflict, because it means an end to MAD. If you know that your adversary will become invulnerable to your counter-strike in three months, the optimal game-theory solution is to strike him today.
Optimistically, military planners are aware of this, and are just doing pork barrel spending.
Pessimistically, military planners don't care about this, and are actively working on 'winning' a nuclear war.
This doesn't really follow IMO and is a result of deep oversimplifications.
Even if you make those simplifications though: If your choices are pre-emptive strike where MAD applies now (near-total destruction) vs. live to 3 months from now, where you have a post-MAD world where one adversary dominates, the post-MAD dominant adversary no longer has the incentive to pre-emptively strike since they aren't worried about a pre-emptive strike from their adversaries since they'd have an effective missile defense system.
> If you know that your adversary will become invulnerable to your counter-strike in three months, the optimal game-theory solution is to strike him today.
Striking today means MAD happens and your country gets wasted. That only makes sense if the shield-building adversary is some sort of psychopath who wants to see you dead.
The 3 big nuclear powers don't seem to be that stupid. Maybe the calculus would be different with Israel vs Iran or India vs Pakistan, where the conflict has religious aspects.
> That only makes sense if the shield-building adversary is some sort of psychopath who wants to see you dead.
Or if they may become a psychopath who wants to see you dead - in the name of self-defense, of course. Or if they think that you are a psychopath who wants to see them dead. Or if they think you may become a psychopath who wants to see them dead.
It's difficult to assure your counterparty that you will never behave in a psychotic manner in the future - or to assure yourself that they will not.
If you're not planning on starting a nuclear war, and you assume that your adversary isn't going to, either, why do you need a missile shield, anyways? MAD is a necessary and sufficient deterrent. If you're building a shield, you are very conspicuously betting that at least one of these two assumptions is no longer true...
> Or if they may become a psychopath who wants to see you dead - in the name of self-defense, of course. Or if they think that you are a psychopath who wants to see them dead. Or if they think you may become a psychopath who wants to see them dead.
These assumptions better be strongly supported by evidence, if one's going to decide to get their country annihilated by attempting a first strike.
Striking first won't protect the country from a hypothetical future attack, it will just make it happen now. I don't really see a sane reason to do it if the threat isn't considered immediate.
Which is precisely why during the
Cold War there was a treaty limiting anti-missile defence (ABM Treaty). Who wants to guess which side withdrew from it in 2002 under a war criminal leader?
The Swords of Armageddon was only ever available digitally (first on CD-ROM, then as download). Hansen's widow used to sell it after his death but she is no longer responding to sales requests. Or at least mine was ignored early this year. You can find it on Library Genesis.
U.S. Nuclear Weapons: The Secret History is sadly missing from LibGen, but it appears to be available as a digital checkout from the Internet Archive. It's a good companion book to Swords because it went through a professional editing-publishing cycle. Swords is a lot longer and rawer, with a higher ratio of text to illustrations.
This is by Alex Wellerstein, who is unparalleled when it comes to writing about nuclear weapon history. His occasional blog http://blog.nuclearsecrecy.com/ is an excellent read.
I read this every time I see a link to it. Slotin's exposure incident really resonates with me for some reason, it plays in my head like a movie and I'm Slotin. I can just imagine ears ringing and a metallic taste in my mouth as my brain slowly comes to grips with the fact that I'm a dead man walking. (For some reason i have a stuffy nose too)
The other thing I come away from this thinking is that our bodies are way better at dealing with damage from radiation than we give them credit for.
I'm left wondering if women would make for statistically better bomb putter-togetherers. If the account on Wikipedia is to be believed, it sounds like a true Darwin award with only a screwdriver separating him from certain death.
You mean because women would be more careful and less inclined to show off as daredevils? That could well be.
Then again you got girls using Radium as makeup [0], so who knows what way they'd find to screw up. (I'm aware they didn't know the Radium was dangerous and am mostly joking.)
Depictions of the Tsar Bomba usually focus on the huge mushroom cloud, which is awesome (in the original "causing awe or terror" meaning of the word). However, I think the geometric simplicity of the fireball is even more effective at inspiring awe.
For a brief moment, the sky was filled with the light of a human-made star.
The Tsar Bomba idea is revived in the Poseidon nuclear very large torpedo which is estimated to have up to 100Mt yield and intended to hit large oceanside cities. Interesting that back then Saharov proposed such weapon and was shamed and shut down by the USSR Navy along the lines that "Navy fights enemy forces and is against such a clear attack on civilians". 50+ years later here we're - the Poseidons are put in service. It goes slow and deep - about 30 knots cruise at 1000m depth, beyond detection - and it would take it days to reach the enemy shores from several thousands miles distance, yet the idea here is that it will still come and assure the destruction, pretty much Kubrik style ( or that StarTrek episode where they were trying to stop the large autonomous space torpedo which was on its way to the target).
I read about Poseidon a few weeks after it first became public, so it's been a bit now.
Do we happen to have any indication as to whether or not the US military/DoD is internally at all seriously scared/concerned about it?
I've been anecdotally told by a very old DoD engineer who was somewhat familiar with things - that when the soviets first came out with their heavily armored multi-hull submarines, there was actually great concern about the fact we didn't at the time have technology to ensure two torpedos could near simultaneously hit within the required radius to pierce all the way through.
A lot of engineering hours went into making the targeting systems of the torpedos capable of doing so. Or maybe he was full of shit, who knows.
It just seems like Poseidon is quite the threat, but we haven't heard too much concern about it yet.
“Now I am become Death, the destroyer of worlds” - J. Robert Oppenheimer's thoughts on witnessing the first atomic bomb test. A quote from the Bhagavad-Gita.
That bomb was finally measured to be 'only' 20 kilotons. [1]
God I hope one of these is never dropped in anger.
That's what he thought, and afterwards said he thought, and it's a great quote. What he actually said at the time according to his brother Frank Oppenheimer was "It worked!"[0]
I think it’s ambiguous grammatically, but I read “one of these” as one of the much bigger ones discussed in the article. “One of those” for me would have been a reference to the previous sent me, i.e. to a Hiroshima/Nagasaki sized one.
Can you really say those were dropped in anger? From what I’ve read they were dropped to avoid the cost to American lives a ground invasion would bring. Several warnings were given to Japanese leadership to avoid a bad outcome, which were not heeded. The first bomb itself did not result in a surrender either. To me the motivation was less about anger and more about practicality.
"In anger" in these contexts usually means "trying to kill people", as opposed to "in testing or training". It does not mean that the people who did so were angry at the time.
Would have been easy to drop one on, say, Tokyo bay if you wanted intimidation. But the US also wanted reliable data on the effects to buildings and people.
I really wouldn't be so sure. Even after destruction of Hiroshima and Nagasaki, the Japanese military still opposed surrender, in fact the day before the Emperor was supposed to announce it there was an unsuccesful coup attempt to prevent it.
So no, I don't think just detonating the bombs "harmlessly" would have have had the same effect. In fact hitting a target just slightly off the mark(like Tokyo Bay) would have been presented as American incompetence and failure of aiming.
Were the atomic bombs really all that different from the systematic fire bombing of Japanese cities?
I think what got Japan to surrender was a certain common sense in the emperor and some of the elite that a final last stand wouldn't do them much good. Especially not with the Soviets joining in.
> Only a few months later, in July 1954, Teller made it clear he thought 15 megatons was child’s play. At a secret meeting of the General Advisory Committee of the Atomic Energy Commission, Teller broached, as he put it, “the possibility of much bigger bangs.
At this point where anything bigger creates a threat that goes beyond nations, what kind of person even proposes this. "This is child's play, there's much more effective ways to destroy the planet"
It’s not that easy to destroy the planet. The 1815 eruption of the Mount Tambora volcano released about 2000 times more energy than the 15 megatons TNT released by Castle Bravo [1]. The asteroid that killed the dinosaurs was equivalent to about 3000 Tamboras.
What's really surprising to me is that right below Chicxulub in intensity on that list are the recent Indian Ocean earthquake in 2004 and the one in Japan in 2011. They're both only about 1/10th the total energy, but still it's a lot more than I would have guessed.
(I live in the vicinity of the Cascadia subduction zone, which will probably experience something similar some time in the next couple hundred years.)
I think hydrogen bombs tend to be cleaner. Or at least, they have a higher ratio of heat/kinetic energy versus radioactive fallout. The long-term environmental contamination of a few large hydrogen bombs probably wouldn't be as bad as a lot of smaller fission bombs. (I'm not an expert though. And either way you'd probably want to hide in a hole in the ground for awhile at least if you aren't and can't get far upwind.)
Wasn't there talk about a 1 Gigaton bomb? When asked how to transport it, they said it's not necessary because it would basically destroy the planet anyway. I remember reading something like this
It's literally in the article. US was working on a gigaton bomb, but even it was only used as a means to ignite a 10 gigaton bomb. The exact damage caused by such a thing is extremely hard to estimate though.
It is hard to know what horrors nuclear weapons have prevented and what horrors they may cause in the future. So far I would say they have been a net positive, but tail risks are a bitch.
But certainly it would be much better to just have a few dozen nuclear weapons per country to stop WWII like events than the thousands that the US and Russia still have that might cause a serious nuclear winter event killing most of the people on Earth.
From your link Sakharov had similar musings:
“Have Soviet and American atomic scientists helped to keep the peace? After more than forty years, we have had no third world war, and the balance of nuclear terror... may have helped to prevent one. But I am not at all sure of this; back then, in those long-gone years, the question didn’t even arise. What most troubles me now is the instability of the balance, the extreme peril of the current situation, the appalling waste of the arms race... Each of us has a responsibility to think about this in global terms, with tolerance, trust, and candor, free from ideological dogmatism, parochial interests, or national egotism.”
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The "continuing to browse this website" seems shady. Can someone explain how this is even supposed to work? Is there a timer that expires? If I scroll at all am I opted in?
Also, is this even legal in jurisdictions that require a cookie opt-out? I thought I read some language about required a positive user interaction to accept tracking.
> The "continuing to browse this website" seems shady. Can someone explain how this is even supposed to work? Is there a timer that expires? If I scroll at all am I opted in?
I would be surprised if it "works", or if they do anything other than tracking you from the first moment until you opt out.
The EU of course, there are international agreements, frameworks and even extraditions for such scenarios.If the US can extradite Ukrainians for hosting a torrent tracker, surely the US would extradite people refusing to follow EU law and violate user privacy and consent (joking of course, that would never happen).
So you're saying people can be punished simply for ONLY following their own country's rules for a website hosted solely within that country? Can you cite any precedent for this especially in the US?
No website is "hosted solely in a country" by default. When your website is available to the world, apparently according to the US, you're liable under any jurisdiction out there:
That's why there are so many shitty american middle-of-nowhere Daily Star Gazettes that block EU visitors with a laughable "our EU visitors are important for us". It seems that they agree with GDPR that it covers them if they serve anything to EU citizens.
Which again, is absolutely terrifying, but I've read in several places now that it probably doesn't exist outside of some blueprints for a thing that could maybe be built. Like, the whole idea of "poisoning" it with a cobalt load so that it would produce deadly contamination for hundreds of years is just straight up vilanious, it truly is the ultimate destruction weapon in design)
Hydrogen bombs are endlessly fascinating and horrifying. The physics and engineering that goes into them is amazing, especially when it boils down to triggering alternating dominos of progressively larger fission and fusion reactions.
>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.
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.
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.
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.
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.
>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.
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.
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.
That's a thought about killing an entire planet by burning it's atmosphere. Cliche thing but "burning hole in atmosphere". Reminds me like ants on a rock.
(via https://news.ycombinator.com/item?id=29039900, but there's no real thread there)