A question about really big explosions

The Silence and I · Post by **The Silence and I** » 2006-11-13 03:37pm

Lets say you have a powerful starship(s) in orbit of a planet. A city below has raised a theater style shield powerful enough to hold off the starship(s) for many seconds of bombardment. Assume the weapons used are large hydrogen bombs (at least double digit MT each) and many dozens have been fired into this shield for the last minute or two. Lets say the shield is something like 30 km above the surface (atmosphere is Earth like).

Over the course of the bombardment several GT worth of energy has been released, and shortly after bombardment stops, the shield fails from mechanical stress. What happens to the surface below?

I expect significant thermal radiation will immediately heat things up seriously, but I don't know enough about fireballs and shock waves. Will the rising fireball never touch the ground? Will it expand downward enough to touch the ground? Will any shock waves propagate downward now the shield is gone? How different is this situation than simply detonating many such bombs at 30 km without any shield?

Admiral Valdemar · Post by **Admiral Valdemar** » 2006-11-13 03:48pm

Everything around the outside of the shield dies in the quickest possible way. Assuming the shield is simply a field of atomic force, minus the atoms, then the detonations simply get directed outwards from the dome. The fireball, shockwave and radiation is all there, but blocked by this force field and so doesn't propagate in all directions evenly.

The Silence and I · Post by **The Silence and I** » 2006-11-13 03:56pm

Admiral Valdemar wrote:Everything around the outside of the shield dies in the quickest possible way. Assuming the shield is simply a field of atomic force, minus the atoms, then the detonations simply get directed outwards from the dome. The fireball, shockwave and radiation is all there, but blocked by this force field and so doesn't propagate in all directions evenly.

I'm not concerned with the area outside the shield. I'm interested in what happens on the ground directly below the shield, after it fails.

I know the detonations are directed differently, it is the details I'm curious about. After the shield dome fails, what happens to the city? Due to the magnitude of energy involved the fireball in the sky will persist for many minutes, but does it ever touch the ground? Does the city experience a shock wave?

Icehawk · Post by **Icehawk** » 2006-11-13 04:53pm

If the sheild fails just after the ships finnish bombardment then even with the nuke explosions still burning high in the sky nothing really bad should happen below as the atmospheric blast waves from the explosions and most of their initial radiant energy would have still been redirected away by the shield before it failed. Also with the explosions happening 30kms up, the people in the city below may end up feeling some heat and wind from the remaining burn of the explosions, but I don't think they'd be in any real danger at that point.

IIRC the US extensively tested high altitude airbursting nukes for defeating soviet bomber formations and I don't think they caused any major problems for the ground below when they were detonated high up.

Post by **Darth Wong** » 2006-11-13 05:41pm

Why should we expect anything to happen to the surface below, if the shield doesn't fail until after all of these explosions?

Admiral Valdemar · Post by **Admiral Valdemar** » 2006-11-13 05:54pm

Maybe he means residual radiative effects. The ground should be pretty molten at that point if the bombs detonated around the city and not just at the apex of the shield, but it won't do shit compared to getting nuked without the field. You're just left with some hot, gusty winds and surrounding ground that is mainly trinitite.

Seggybop · Post by **Seggybop** » 2006-11-13 06:12pm

According to the calculator on the main site, a 5GT explosion would have a fireball lasting around 200 seconds. That's probably long enough that when the shield went down the city could still get cooked. However, this isn't a single several GT bomb but many smaller ones, so a lot more energy would probably have been dispersed already when the shield failed. Still, it can't be too good in the city as hot gases loaded with fallout rush in from all sides.

Icehawk · Post by **Icehawk** » 2006-11-13 07:18pm

Where exactly is fallout going to come from if the explosions were 30kms up against the sheild?

Seggybop · Post by **Seggybop** » 2006-11-13 07:59pm

It would assume they were attacking from all sides instead of continually bombarding the same point on top of the shield. Spreading them out would reduce the chance of incoming bombs being destroyed by explosions before reaching the target.

The Silence and I · Post by **The Silence and I** » 2006-11-13 08:08pm

Seggybop wrote:According to the calculator on the main site, a 5GT explosion would have a fireball lasting around 200 seconds. That's probably long enough that when the shield went down the city could still get cooked. However, this isn't a single several GT bomb but many smaller ones, so a lot more energy would probably have been dispersed already when the shield failed. Still, it can't be too good in the city as hot gases loaded with fallout rush in from all sides.

That's what I'm getting at. There is still a hell of a lot of residual energy in the air 30 km up. Perhaps enough to glow visibly for around 30 seconds after the shield fails.

Can I assume this fireball which will be visible for around half a minute will not pose a danger to the city below? Most of the bombardment was at the apex of the shield dome, so it can be assumed this fireball is fairly compact (read: not spread thinly over many square km).

FYI I'm not too concerned by radiation, this is more of a short term 'does the city cook to death or not' question.

Elheru Aran · Post by **Elheru Aran** » 2006-11-13 10:03pm

How well does heat energy go through the shield?

Singular Intellect · Post by **Singular Intellect** » 2006-11-13 10:57pm

Elheru Aran wrote:How well does heat energy go through the shield?

I'm guessing that would depend entirely on the shield's efficiency at absorbing and redirecting the impacting energy.

We certainly wouldn't know how the shield does do it's 'stuff', but if there's a described mechanism by which the shield operates, we could get a clearer picture.

So far, it's only been established there;s a shield and not much else. Unless the OP auther wishes to clarify.

The Silence and I · Post by **The Silence and I** » 2006-11-13 11:27pm

Elheru Aran wrote:How well does heat energy go through the shield?

The shield, so long as it functions, is assumed to protect the city (I assumed the word "shield" would imply that. Damn you star trek!). So no significant heat energy passes through the shield while it functions.

To make things more clear:

Lets say the bombardment lasts 60 seconds. Every second 500 MT worth of explosives are detonated at the apex of the shield dome, for the full 60 seconds, in the form of twenty five 20 MT bombs per second. The total energy released is 30 GT, over 60 seconds, from 1500 bombs. At the 60th second firing stops. At the 61st second the shield fails from mechanical stresses. What happens to the city below?

Post by **Ghost Rider** » 2006-11-13 11:33pm

The Silence and I wrote:
Elheru Aran wrote:How well does heat energy go through the shield?
The shield, so long as it functions, is assumed to protect the city (I assumed the word "shield" would imply that. Damn you star trek!). So no significant heat energy passes through the shield while it functions.

To make things more clear:

Lets say the bombardment lasts 60 seconds. Every second 500 MT worth of explosives are detonated at the apex of the shield dome, for the full 60 seconds, in the form of twenty five 20 MT bombs per second. The total energy released is 30 GT, over 60 seconds, from 1500 bombs. At the 60th second firing stops. At the 61st second the shield fails from mechanical stresses. What happens to the city below?

Still a little too vague. What exactly knocks the shield down?

An overload on it's generator, some technobabble reason of energy dispersal because of something of yet another factor, what?

The Silence and I · Post by **The Silence and I** » 2006-11-14 12:36am

Why the hell does it matter what takes the shield out? All you need to know is the shield works while the bombs are going off, and stops working moments after the last bomb explodes. The generators do not explode and annihilate the city, what possible effect on the outcome can the method of failure have?

As it is I already told you, vaguely, what takes out the shield: mechanical failure from stress. Something shorted, overloaded, melted, broke or otherwise failed and the shield ceased to exist.

The Silence and I · Post by **The Silence and I** » 2006-11-14 01:04am

As I think about it I am beginning to think it might be safe enough to assume this bombardment may be modeled with one big 30,000 MT explosion at the 60th second. The duration of each individual bomb is 17.3 seconds, but they are going off an average of every 1/25 second, and at the same general location. I suspect not very much energy from the first bomb will dissipate before the second explodes and traps much of its energy within the same region, and then the third explodes and the fourth and so on. So the 'yield' will go up with each bomb, and before any significant energy can dissipate, the last bomb has exploded. Can anyone tell me if this is a safe assumption? I'm reading up on nuclear weapons now, but I'm playing catchup and nothing I'm likely to find will go over a scenario remotely like this one.

A 30,000 MT bomb will produce a 465 second fireball (roughly) and the thermal radiation radius is 800 km. So I guess there will be plenty of thermal heating going on down on the city after the shield fails, for the next seven minutes or so (more, I suppose, at 465 seconds thermal emission is down to 10% of peak, and 75% of total energy has dissipated)

The fireball, being an air burst, would be about 33 km in radius if there was no shield interfering with things, and would envelope the city. However there is a shield, which will redirect the fireball. This will probably initially make it larger, the same way a ground contact fireball is larger than an air burst, but mere moments later the shield (the 'ground') vanishes. I want to know if the fireball will expand toward the ground significantly, after the shield fails. How close will it come to the city? Is there any air shock (I imagine not, as that should be reflected by the shield before it fails--but I'm not content with imagining, that's why I'm asking)?

Post by **Surlethe** » 2006-11-14 01:12am

If you can justify modeling it as one big burst a second before the shield goes down, you might try comparing the air pressure above the shield to the air pressure below it. That will dictate the reaction of the air upon the disappearance of the shield: air will flow from high pressure to low pressure, and if it does so quickly enough, you could have a boom on your hands.

Also, see if you can figure the temperature of the firebal and its distance from the city upon dissipation of the shield; that'll tell you how much energy the city absorbs before the fireball disappears.

The Silence and I · Post by **The Silence and I** » 2006-11-14 03:09am

Surlethe wrote:If you can justify modeling it as one big burst a second before the shield goes down, you might try comparing the air pressure above the shield to the air pressure below it. That will dictate the reaction of the air upon the disappearance of the shield: air will flow from high pressure to low pressure, and if it does so quickly enough, you could have a boom on your hands.

That helps a bit. Pressure above the shield will be far higher than below, that's what creates and sustains the shock wave which will be traveling up and out from the shield dome at very high velocity. This means the fireball will travel downward, although I'm still not sure how far. Because a lot of energy was initially radiated outward and upward by the shield I suppose the fireball won't quite reach the city, but I'm really not sure.

**********

As I understand things the fireball is the iso thermal core of the explosion, which after both the breakaway point and the second pulse becomes visible for the rest of its duration, and apparently comprised of light, rather than hot gases (this makes only a small amount of sense to me--due to its high temperature I would think it would be expanding due to its hot gases as much as its radiative expansion).

The higher the yield the longer it takes to reach the second pulse, and at 0.9 seconds for 1 MT a 30 GT bomb would reach its second pulse well after 1 second after detonation. The shield's presence however might cause the second pulse to occur much sooner, because the shield will reflect the shock front away. So the city can start cooking as soon as the shield drops, maybe (--well, yes it can, because this is not really one giant bomb but 1500 detonating over 60 seconds).

The core of the fireball will continue to expand, but is no longer spherical in shape thanks to the shield. With a flattened bottom this iso thermal core might expand oddly. I'm confused by the iso thermal core. It is very hot, yet I read that it does not expand as quickly as the shock front after the breakaway point, despite being hotter than the shock front. This confuses me...

Anyway, it seems to me neither the fireball nor the shock front will quite reach the city, but they don't need to as the thermal radiation will be quite lethal. Sound fair to those that know more than me?

Also, see if you can figure the temperature of the firebal and its distance from the city upon dissipation of the shield; that'll tell you how much energy the city absorbs before the fireball disappears.

Seeing as the thermal radius for something this big is 800 km, I feel safe in assuming the city is charred into a crispy wasteland of burning buildings and flesh.

Ariphaos · Post by **Ariphaos** » 2006-11-14 06:16pm

The Silence and I wrote:As I think about it I am beginning to think it might be safe enough to assume this bombardment may be modeled with one big 30,000 MT explosion at the 60th second.

There's a major difference. This high up, the fireball is basically a plasma ball, which dissipates -extremely- fast (there are videos available of similar altitude nuclear tests).

However, not only that, but the first blasts clear atmospheric material out of the way for the next, making their potential destructive effect that much weaker. The end result of your initial scenario is: A few aurora-style effects, but all in all, not much to the city below or the surrounding lands. Maybe some EM interference for awhile.

The Silence and I · Post by **The Silence and I** » 2006-11-14 11:19pm

Xeriar wrote:
The Silence and I wrote:As I think about it I am beginning to think it might be safe enough to assume this bombardment may be modeled with one big 30,000 MT explosion at the 60th second.
There's a major difference. This high up, the fireball is basically a plasma ball, which dissipates -extremely- fast (there are videos available of similar altitude nuclear tests).

This makes sense, I was never sure how high those tests were.

However, not only that, but the first blasts clear atmospheric material out of the way for the next, making their potential destructive effect that much weaker. The end result of your initial scenario is: A few aurora-style effects, but all in all, not much to the city below or the surrounding lands. Maybe some EM interference for awhile.

Heh. Hindsight... this sounds good to me, thank you Xeriar

drachefly · Post by **drachefly** » 2006-11-15 03:06pm

Out of curiosity, what raised the question?

The Silence and I · Post by **The Silence and I** » 2006-11-15 10:52pm

drachefly wrote:Out of curiosity, what raised the question?

I'm writing a story where a situation much like this one comes up, and I wanted to be scientifically accurate within reason.

The capitol city of a planet is captured by the bad guys(TM), and the good guys(TM) come to save it. The time interval allows the bad guys to set up a theater shield which is 30 km high at its apex, preventing the orbiting fleet from saving the day. I needed to breach the shield, which has a capacity roughly around 30 GT under the circumstances of this particular bombardment, and it is important to the story what happens to the city below after it fails. Very important...

Winston Blake · Post by **Winston Blake** » 2006-11-17 07:30am

The Silence and I wrote:All you need to know is the shield works while the bombs are going off, and stops working moments after the last bomb explodes.

The fireball radius for a 30GT blast is going to be about 33km, so if it's delivered over 60 seconds the fireball must be smaller than this. However, this is misleading since the shield must absorb a bit less than half of the X-rays produced (assuming they detonate on impact), and almost none of the rest of the X-rays will be directed downwards. The fireball will only be about half the original yield, and its centre will be about half a radius above the dome apex. This means when the dome disappears, the bottom of the fireball will be about 13 km above the city, and it will last more than 5 minutes.

Based on the equationshere about the temperature of the sun delivering power to earth, and taking the fireball temperature as 10,000K I get 1.8e16 W being delivered to the circle beneath the dome shield. Chemical explosives apparently reach 5000K, so we might assume the fireball temperature is between 5e3 to 10e3 K, so putting 5000K into that gives 1.1e15 W. This is between 390 kW/m^2 and 6.4 MW/m^2, utterly frying the city. However, it might be less if the shield fails long enough after the last bomb that the fireball can rise further up into the sky.

Also, if the shield is still on for a few seconds after the last explosion, the burst of heat/radiation from all the bombs will have missed the city. However, the blast waves from the last few bombs will still be on their way down to the ground as they wrap around the dome. When the shield dome disappears, these will probably expand out again somewhat and hit the city.

The good guys can avoid all of this by using magic nukes which direct most of their energy down into the shield. Also, if the shield reflects or reradiates energy rather than absorbing and 'disappearing' it, the situation for the city gets much, much worse.

Winston Blake · Post by **Winston Blake** » 2006-11-17 07:39am

Xeriar wrote:
The Silence and I wrote:As I think about it I am beginning to think it might be safe enough to assume this bombardment may be modeled with one big 30,000 MT explosion at the 60th second.
There's a major difference. This high up, the fireball is basically a plasma ball, which dissipates -extremely- fast (there are videos available of similar altitude nuclear tests).

However, not only that, but the first blasts clear atmospheric material out of the way for the next, making their potential destructive effect that much weaker. The end result of your initial scenario is: A few aurora-style effects, but all in all, not much to the city below or the surrounding lands. Maybe some EM interference for awhile.

Huh. I probably should've read this first. I was using Darth Wong's calculator for the fireball radius and duration. Now that I think about it, that must be designed only to handle heights of a few km at best. Maybe the fireball will dissipate fast enough that by the time the shield fails, there's nothing left. The residual train of blast waves is still a problem though, but I don't know how powerful they'd be for a high-altitude detonation.

Wyrm · Post by **Wyrm** » 2006-11-17 03:10pm

The Silence and I wrote:Why the hell does it matter what takes the shield out? All you need to know is the shield works while the bombs are going off, and stops working moments after the last bomb explodes. The generators do not explode and annihilate the city, what possible effect on the outcome can the method of failure have?

As it is I already told you, vaguely, what takes out the shield: mechanical failure from stress. Something shorted, overloaded, melted, broke or otherwise failed and the shield ceased to exist.

Actually the way the shield goes down is important. The energy absorbed by the shield in the attack has to go somewhere when the shield goes down. If that somewhere is the shielding mechanism itself, then the shield generator may explode into a great fireball with the total energy dumped into it by the bombardment. If the energy is released from the shield itself, be it in the form of direct heating of air trapped in the region the shield operates or radiation to be subsequently absorbed by the surrounding air, then depending on how how much energy is ultimately released, this could cause its own form of nastiness as searing winds convection-bakes everyone.