Idle musings about nukes in 4E...

[PK]

No great wisdom here -- just playing around with some numbers and felt like doing it out loud.

Since explosions have been changed to vary proportionately with the square of the explosive weight (rather than directly with its weight), overkill attacks do a lot less damage than they did in 3E. Given that ST-based damage has effectively gone down at high lift levels as well (it hasn't, but since you need a lower ST to lift a lot now, elephants and the like have a lower ST and do less damage), this is obviously intentional.

Take nukes, for example. In 3E, a suitcase nuke (1-kiloton) did 6d x 4,000,000 dice of damage. But the damage was quartered every 64 yards and sealed or vehicle DR was squared against it. After 12 quarterings, the average concussion damage would be down to 5 points, giving the nuke an effective blast radius of about half a mile.

In 4E, that same suitcase nuke does 6d x 2,828 dice of damage, a rather huge difference. But DR is never squared and the damage is divided by 3 x the distance from the blast, in yards. The rules also expressly limit the zone of destruction to twice the dice of damage, in yards, which means the suitcase nuke can theoretically harm everything in a 19.3 mile radius. At half a mile (the range at which the 3E nuke would be doing 5 points of damage), the 4E nuke does an average of 59,388 (average damage roll) / 3 x 3520, or 5 points of damage. Heh. Funny, that.

At 19.3 miles, it won't even do a point of damage, of course. I suppose the reason to include that maximum was for super attacks that took more than one level of Explosion. If this nuke attack was built with Explosion 3, the hard limit of 19.3 miles would matter, because otherwise it could theoretically affect anything out to over 33 miles (with an average damage roll).

I like the new explosion rules quite a bit. It was a HELL of a lot easier to figure the effects of the 4E nuke than the 3E for this little thought exercise, and I like that the concussive damage has a smoother curve -- it starts off high and gradually tapers off.

Oh, and in case anyone needs to know and is too lazy to do the math, a 1-megaton nuke (reasonably typical for missiles, etc.) does 6d x 89,429 dice of damage, though you could just add an extra micron or two of fissionable material and round that sucker up to 6d x 90,000. Your players won't notice, believe me. :)

[DrTemp]

Originally Posted by Rev_Pee_Kitty

[...]
At half a mile (the range at which the 3E nuke would be doing 5 points of damage), the 4E nuke does an average of 59,388 (average damage roll) / 3 x 3520, or 5 points of damage. Heh. Funny, that.
[...]

Well, that's still a broken arm or leg to most people, or a major wound, and that from heat (thus a great chance for infection here). Also remember that radiation damage is a different thing.

Not too unreasonable, I'd say.

[Diogenes]

It seems that the 3e rules are actually more realistic, regarding nuclear bombs.

And speaking of radiation: In chemical bombs, it's heat (IR) light (VIS), and possibly a little ultraviolet (UV), and that's it. Nuclear bombs span the whole gamut from electromagnetic pulse to hard gamma. You can expect something in the blast radius of an nuclear bomb to be burnt, blinded, and irradiated at the same moment, not to mentioned disabled if electrical and not shielded. No radio receiveing. No mobile phone.

[Rupert]

That depends on the bomb - the bigger the bomb the less the prompt radiation matters. With a little wee 10kT tactical nuke you could suvive the heat and blast to get sick from the promt radiation dose you also took. With a nice big 1MT bomb, if you suvived the blast you were well out of reach of the prompt radiation pulse.

[Diogenes]

I said nothing about intensity of a particular frequency band, so you might be right about the details, but you could could still get something of everything - it indeed depends on the bomb and the distance.

[Allister MacLeod]

Originally Posted by Rupert

That depends on the bomb - the bigger the bomb the less the prompt radiation matters. With a little wee 10kT tactical nuke you could suvive the heat and blast to get sick from the promt radiation dose you also took. With a nice big 1MT bomb, if you suvived the blast you were well out of reach of the prompt radiation pulse.

Why is that? Does the kinetic output go way up faster than the radiation output for bigger bombs, or does the blast carry further because it diminishes slower than the radiation? (I'd expect inverse-square for the radiation, but I'm not familiar with how concussion damage spreads out)

[lwcamp]

Originally Posted by Allister MacLeod

Why is that? Does the kinetic output go way up faster than the radiation output for bigger bombs, or does the blast carry further because it diminishes slower than the radiation? (I'd expect inverse-square for the radiation, but I'm not familiar with how concussion damage spreads out)

Basic things to worry about with nukes, and how they propagate in an atmosphere:

Prompt radiation - this is the gammas and neutrons directly created by the fission or fusion reactions. They account for roughly 1% of the bomb's total energy. Gammas and neutrons, like all radiation, become less intense as they spread out from a point source (say, the bomb) with an inverse square relation with distance. However, gammas and neutrons are also absorbed by the atmosphere, roughly half of all gammas and neutrons will be absorbed for every half kilometer traveled. This leads to a falloff something like
I=I_0 exp(-r/(0.5 km)) (1/r^2)
where r is the distance from the detonation, I is the intensity at distance r, I_0 is a constant, and the exp() function is the exponentiation of e (the base of the natural logarithm). The exponential falloff quickly cuts the prompt radiation intensity down to harmless levels at distances of more than a few kilometers.

Fireball - the fission fragments and fusion reaction products will be traveling very quickly, and heat up the nuclearly reacting materials to very high temperatures. These are so hot the peak of their radiated light is in the soft x-ray part of the electromagentic spectrum. The atmosphere is pretty much opaque to soft x-rays, so these get rapidly absorbed, heating up the adjacent part of the atmosphere to soft x-ray hot temperatures, which then radiate and heat up the next layer of air, and so on. This results in a sphere of air that is so hot it can vaporize just about anything. This is called the fireball. Its range is limited because each time the x-rays get absorbed, they are re-radiated at lower energies and the layer cools somewhat. The rate of radiation goes up very sharply with temperature (it is proportional to temperature to the fourth power), so eventually the fireball cools enough that the radiation diffusion process I described above is no longer very important. Depending on the size of the nuke, fireballs range from a few tens of meters to a few hundereds of meters across, with some big nukes generating fireballs a couple of kilometers across.

Thermal radiation - hot material radiates not just at the peak output of the electromagnetic spectrum, but also at all lower energies as well (but just not with as much intensity). Thus, the fireball radiates light to which the atmosphere is transparent (near UV, visible, and infrared). It is so intense it radiates a lot of this. This thermal radiation, and it can cause burns to unprotected skin, set clothing and easily flamable objects alight, and scortch just about everything that is only slightly flamable (or, at close ranges, even scortch non-flamable substances). In clear air, the intensity of this radiation falls off with an inverse square law.
I = I_0 (i/r^2)
If there is haze or mist or dust in the air, this can scatter the light, resulting in something closer to the exponential falloff you get with prompt radiation - except that the light is not abosrbed, it just gets scattered in another direction and can thus still increase the intensity of light (making for a complicated calculation of the intensity). About half of a nuke's energy is emitted as thermal radiation.

Blast - Hot air tends to expand. The fireball is very hot. In its initial stages, the fireball is growing faster than the air can respond, but eventually it cools off and slows down enough so that it is no longer overtaking the blast waves it would otherwise emit. At this point, it emits a shock wave that is so intense the shock itself can vaporize matter. However, shock waves don't just spread out like radiation, the also continuosly loose energy to the matter they travel through (heating it up in the process). The dynamics of shocks are very complicated, but at the distances we would care about, where the shock wave is not instant-death but is intense enough to cause injury and break structures, the intensity in the shock tends to fall off as an inverse cube of the distance
I = I_0 (1/r^3)
The shock wave not only causes a sudden jump in pressure, it causes the air to move with it, producing a strong wind flowing away from the detonation. This, of course, creates a region of lower pressure when much of the air has moved away, so after the wind blows away, it will then blow back to fill the void it left. The combination of shock and wind is called the blast wave. People tend to be highly resistant to shocks, but the wind can easily blow over buildings. The wind can also pick people up and throw them, and bits of the smashed buildings can injure or kill people, either by falling on them and crushing them or because slivers, shards, and sticks made by blowing the building apart are picked up by the wind and blown into (or through) people. About half of a nuke's energy takes the form of a blast wave.

Radioactive fallout - The fission fragments and neutron activated material from the bomb casing are now a vapor rising into the air with the fireball. Eventually, the fireball cools, and these highly radioactive substances can start to condense out. If the fireball evaporated much stuff on the ground, this stuff will condense out around the radioactive particles and fall out of the sky. This creates a swath of area downwind that is contaminated with radioactive junk, and can cause acute health problems for several days or weeks. On the other hand, if the fireball did not touch the ground, it has no vaporized solids or liquids to condense out around the radionucleotides. These continue to rise with the fireball into the stratosphere, where they eventually condense into fine suspended particles that are blown about the globe in the jet streams. For a few bombs, this dilutes the radioactive stuff so much you don't have to worry about it. Global nuclear war might bring the concentration up enough to cause probelms, however.

A consequence of this for large nukes is that people will be killed by the thermal radiation at distances where the blast and prompt radiation have dwindled to harmless intensities. Thermal radiation resistant structures, such as masonry or concrete buildings, can survive at distances much closer to the bomb than can wood buildings or exposed people, since they must be smashed by the blast wave. For smaller nukes, the blast becomes correspondingly more important, to the point that the Manhatten Project era bombs had about equal effect from blast and thermal radiation, and there were reports of victims sickening from radiation poisoning (since the wartime bombs were detonated as airbursts, they would not have had much in the way of radioactive fallout, so I am guessing the sickness was caused by prompt radiation).

Luke

[PK]

Originally Posted by DrTemp

Well, that's still a broken arm or leg to most people, or a major wound, and that from heat (thus a great chance for infection here). Also remember that radiation damage is a different thing.

Not too unreasonable, I'd say.

Didn't think it was. I was saying that it's funny that the 3E and 4E damage at max range is identical, despite their calculations being so different.

[Luther]

Originally Posted by lwcamp

Basic things to worry about with nukes, and how they propagate in an atmosphere:

When lwcamp replies, he sets the bar. High.

Thanks for the post :)

[lwcamp]

Originally Posted by Luther

When lwcamp replies, he sets the bar. High.

Thanks, Luther!

I guess my post raises the question of how to model these things in GURPS. Let's look, for example, at the Mike bomb, the first thermonuclear bomb tested. It completely evaporated a small island on a coral atol, leaving a crater 60 m deep, 1,500 m across. It had an estimated yeild of 10.4 megatons.

A 10 megaton blast will have a 50% casualty radius for thermal radiation of about 25,000 m, and will ignite fabric out to about the same radius. For the blast, the 50% casualty radius is about 7,500 m. The blast will cause moderate to severe damage to structures out to about 15,000 m.

If half of Mike's energy went into its blast, the usual formula for explosive damage for a given yeild gives a blast wave doing 6d x 200,000 cr ex. This does not match actual lethal range from 10 megaton blasts. We see we would be doing lethal damage out to 70,000 m. This is to be expected - the scaling of damage falloff to base damage of explosions assumes an inverse square reduction of intensity. To get the approximate inverse cube falloff of blast waves, we can use the folowing method. First, find the range modifer corresponding to the range from the bomb. Multiply this by 1.5. The range corresponding to this new range modifer is the what you divide the damage by. 7,500 m is range modifier 21. 1.5 x 21 = 31.5, rounded down to 31. This corresponds to a range of 200,000 m, so using this method, mike would cause about 2d damage at 7,500 m - a reasonable value for 50% casualties. Because nukes cause winds that last longer than the blasts of conventional explosives, we could say that the blast causes double knockback, but only 1/2 injury. Anything that is anchored to the ground and thus unable to be knocked back takes double injury instead of 1/2 injury. The blast wave is supersonic, we are probably not too far off at pegging its speed at 400 m/s, although it will be traveling faster where it causes more damage and approaching 330 m/s (the speed of sound) as its damage drops to zero.

Thermal effects are less efficient energy wise at causing damage than mechanical effects such as the blast wave. We can thus put the thermal damage at 1/5 the blast damage, or 6d x 40,000 burn. Since the thermal radiation is stopped by even thing barriers, we will give it an armor divisor of (0.1) - but it will have its full effect for igniting that barrier! For thermal radiation, just use the normal GURPS rules for damage falloff from explosions. This will cause an average of 10 points at a range of 28,000 meters - in good agreement with the 50% casualty range and the ranges for ignition.

It will take about 50,000 HP of damage to penetrate 60 meters of stone. This means the fireball will be about 6d x 2400 burn with an area effect of 1,500 meters.

If we straightforwardly apply the GURPS radiation rules, we end up with 6d x 50,000,000,000 toxic (radiation) damage, with the damage falling off with the square of the range, and roughly halving the damage every 500 meters (an extra 250 meters can be treated as -1 per die). This gives an average of 42 rads at 5 km and 1/3 rad at 6 km.

The fallout would occur in a 3,000 meter wide swath downwind. This would inflict toxic (radiation) damage to anyone entering the contaminated area. Roughly, it would cause 1 rad per cycle at various intervals - 1,000 cycles at 10 second intervals, 1,000 cycles at 1 minute intervals, 1,000 cycles at 1 hour intervals, and 1,000 cycles at 1 day intervals would seem to model the time scale of the decay of the radiation (it would cause 1 rad every 10 seconds for 3 hours, 1 rad every minute for 17 hours, 1 rad every hour for 41 days, and one rad every day for 3 years).

If we desire to apply the standard GURPS explosion rules for all effects, we can model Mike as
blast: 6d x 4000 cr ex (double knockback, half wounding to unanchored victims)
thermal radiation: 6d x 40,000 burn ex (armor divisor (0.1))
fireball: 6d x 2400 burn (area effect 750 meter radius)
prompt radiation: 6d x 200,000 (but you really do have to halve the damage every 500 m for radiation to match reality at all).

To extend this to other nukes
blast: 6d x 200 x cube root of (yeild in kilotons) [falloff as explosion]
or
6d x 3000 x square root of (yeild in kilotons) [faster falloff described above]
thermal radiation: 6d x 400 x square root of (yeild in kilotons)
prompt radiation: 6d x 2,000 x square root of (yeild in kilotons) [falloff as explosion with additional exponential falloff]
or
6d x 5,000,000 x yeild in kilotons [inverse square falloff with additional exponential falloff]


Since it is late, I will ignore the fireball and fallout for now.

Luke