[Runequest] RQ3 Big explosions

Marko Perälä perala at student.uef.fi
Thu Nov 8 20:38:52 EST 2012

An RQ3 problem:
I find current rules for explosions to be unrealistic and unscalable. Basic idea with RQ3 explosions comes mostly from dwarf bowling ball and Call of Cthulhu.
Basically an explosion causes (x)d6 damage in random hit location that diminishes incrementally by d6 every (y) meters of distance from the center of explosion.
This approach works with small explosions, but it doesn't scale well. Here's why:
1) An unarmored human has on average 12 hit points. That means a solid hit of 4d6 damage is a fairly reliable kill. If the base damage is very high (10d6, 20d6, 100d6 etc.), the explosion has a kill zone almost to the very edge of explosion area, leaving only a small strip upon which it causes injury, but no death. In real life the opposite is true. The kill zone is relatively small, but there is a wide area, where injury is likely.
2) A regular human has vital locations head, abdomen and chest. This means any explosion, no matter how large an explosion is and how close a person is, is only lethal in 45% of the cases. In real life explosions have an instant kill range inside which an unarmored human has no chance of survival, regardless of how lucky he is - unless he's in a trench or bunker, but that's a whole different story. In case of a thermobaric explosion even those don't matter.
3) An explosion causes damage only in one location, leaving others intact. In real life explosions are blast waves that effect the whole body. This may apply to schrapnel damage, but even then if a person was hit by schrapnel in one location, he's likely to be hit in several.
4) Effects of explosions vary. Some spread scrapnel, some cause a fireball that ignites flammable objects, some have intense air burst that can yank lungs out through mouth (thermobaric weapons). There's even cluster bombs that combine hundreds of smaller explosions into a cumulative area attack. Does non-airtight armor even protect against pressure wave? I don't know how to rate these into generic formula.

Basically what I'm looking for is some kind of formula that allows me to calculate the effects of any sized explosion - and in any setting, modern as well as fantasy - from a stick of dynamite all the way to the biggest nukes. I'm not talking just about injuring PCs and NPCs. I want to be able to determine other effects of explosions, like how big a crater it leaves behind, how far away all the windows are broken, how far away the noise is heard, how far away buildings take severe damage and so on.
I have made some research in this department, here are my findings:
a) In physics there is a term intensity (not RQ3 sorcery) that states how powerful a wave (usually sound, works with blast wave) is at a distance. The intesity is divided by the square of distance. Basically, when distance is doubled, the intensity is diminished to one fourth. Any formula that incorporates accurate modelling of explosions should have a mechanic resembling something like this.
b) In RQ3 the hit points progression and therefore damage follow a logarithmic progression. Let's compare a human (CON 10, SIZ 10) and a giant (CON 100, SIZ 100). A giant has 10 times as many hit points, but according to Size equivalency chart in Runequest 3rd edition (Deluxe's chart ends at SIZ 48, but follows similar lines) it's body weight is about 104-105 tons compared to human's maybe 59-64 kilograms. That means 10:1 ratio with hit points, but 164:1 ration in body weight. The only way any object 164 times bigger than a human can take only ten times as much damage as a human is if that object was a big balloon - unless the damage scale is logarithmic.
c) In alternative systems, like GURPS (cumbersome and soulless system, but I like to refer to it thanks to simulationist approach and thorough research of it's makers) explosions' damage is handled by dividing damage with the 3*distance (sometimes just distance) to point zero. That's a fairly simple calculation. It isn't exactly the division by square of distance, but GURPS damage is also a bit logarithmic - though not as much as RQ3. GURPS also makes scrapnel a separate, secondary damage. This division scales pretty well, causing a core of intense damage and a wide area, where there is small damage. Something like this might work to solve problem number 1). However dividing the final damage can be cumbersome.
d) In RQ3 falling damage functions by injuring one hit location, but damage taken to total hit points is not limited to twice the hit location with limbs. That means a 100 meter drop is always lethal to regular human, regardless of what body part he landed on. This might work with large explosions to solve problems 2) and 3).

Using previous points it is possible to alter the mechanics for RQ3 explosions that make it easier to apply to variating circumstances.
Explosions should work like falling damage and damage should be divided by some variable related to distance. I don't like dividing the final damage, because it just causes a wide area of damage 1 zone. Maybe the instead of final damage the amount of d6s should be divided. That would create a damage d6-zone, 2d6-zone, 3d6-zone etc. That's more manageable. However then the divisor should be reduced by 3,5 or something.
So, the final formula should be something like:

d6 damage * (x) * 3,5 / (distance / (y))^2  #, ##
# rounded up at 0,5.
## (x) and (y) from the RQ3 formula, given in first paragraph.

So, with a Call of Cthulhu modern hand grenade (damage 4d6, increment 4 yd), we get:
d6 * 4 * 3,5 / (20 / 4)^2 = d6 * 14 / 25 = 0,56 => 1d6 damage at 20 meter distance.
d6 * 4 * 3,5 / (12 / 4)^2 = d6 * 14 / 9 = 1,55 => 2d6 damage at 12 meter distance.
d6 * 4 * 3,5 / (9 / 4)^2 = d6 * 14 / 5,0625 = 2,76 => 3d6 damage at 9 meter distance.
d6 * 4 * 3,5 / (8 / 4)^2 = d6 * 14 / 4 = 3,5 => 4d6 damage at 8 meter distance.

With regular explosion rules it would have been 4d6 damage upto 4 meter radius, 3d6 damage upto 8 meter radius, 2d6 upto 12 meters and 1d6 upto 16 meters. Seems like formula requires a bit fine tuning.
Let's try a bigger explosion, 75mm field gun from Call of Cthulhu 5.6 (10d6 damage, 2 yd increments).

d6 * 10 * 3,5 / (16 / 2)^2 = 35 / 64 => 1d6 damage at 16 meter distance.
d6 * 10 * 3,5 / (9 / 2)^2 = 35 / 20,25 => 2d6 damage at 9 meter distance.
d6 * 10 * 3,5 / (7 / 2)^2 = 35 / 12,25 => 3d6 damage at 7 meter distance.
d6 * 10 * 3,5 / (6 / 2)^2 = 35 / 9 => 4d6 damage at 6 meter distance.
d6 * 10 * 3,5 / (5 / 2)^2 = 35 / 6,25 => 6d6 damage at 5 meter distance.
d6 * 10 * 3,5 / (4 / 2)^2 = 35 / 4 => 9d6 damage at 4 meter distance.
d6 * 10 * 3,5 / (3 / 2)^2 = 35 / 2,25 => 10d6 maximum damage at 3 meter distance, although formula gave 16d6.

With bigger explosions we start seeing the pattern more clearly. There's a much greater increment at the low end of damage and closer to point zero the damage dice increase heavily. It isn't quite right, though. The damage dice seem to rise too beyond the maximum damage too far away from ground zero and reach atmospheric numbers under the first radial increment under the regular rules. We get more realistic damage progression with this, but formula needs still something to prevent it from topping too far out. With this it's still 4d6 damage at 9 meter radius. It's down from 12 meter radius with the old explosion rules, but still too deadly too far away (or rather doesn't spread it's non-lethal radius widely enough).
With old explosion rules the lethal range would have been 12 yd and non-lethal 8 yd beyond that. With this formula it's 9 meters lethal radius and 11 meters further of non-lethal. A step in right direction, but requires tuning.

Hmm...maybe I'm making this too complicated. What other ways would there be to handle this? Maybe the GURPS formula of would still work simpler, or maybe using a growing range increment (first 1-meter, then 2-meter, 3-meter, 4-5-6-... meter increments). Maybe it would be better to determine the maximum radius of effect first and then work backwards towards point zero. Maybe instead of increasing distance, the increments should be kept same, but damage halved every increment.
I just don't know how to solve this. The basic RQ3 formula works well with small explosions. Maybe I should just stick with that and avoid big explosions altogether. After all, scaling up is a common problem with pretty much all aspects of RQ3, not just this.

What do you think of this? Do you have suggestions to improve this formula? Did you think of something I never thought off? There's still the problem 4) that I don't know how to solve.

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