Kinetic energy release equation

[Fitz]

OK, now that my evil master villain knows that if he accelerates a one tonne rock towards the Earth at 6G it will take an hour to get there and be travelling at about 210,000m/sec when it arrives.

 

So how big is the explosion?

 

If I recall correctly, in the HSR it says that an object can do no more than its DEF plus BODY damage when it impacts on something else -- i.e. if it's thrown. This equation seems to fall down a bit when you start dealing with Intergalactic Space Bugs who are tossing asteroids at Buenos Aires.

 

Or does it? What am I missing?

[Fuzzy Gnome]

I think the Evil Master Bug needs to just buy a 0.5 * 1000 * 210000^2 J RKA, maybe with Mega range and area. Bulky OAF or OIF 1-tonne rock, extra time 1 hour, etc.

[Agent Escafarc]

This would be one of those cases where common sense takes over from the straigh reading of the rules. I would figure something out using the move through rules for a starting point or just call it a plot device, pick a large number of DCs and move on.

[Fuzzy Gnome]

Or about 5 kilotons

[DigitalGolem]

The object body table (Fred p 304) gives a Body of 10 for an 800kg "unliving" object. The material defense table (same page) gives concrete a Def of 6. I'm not sure what type of rock we're talking about here; its def may be higher. So if you use the Def+Body you get 16 DC's, perhaps more. That's more than enough to kill any normals caught in the blast (-4 Body), take out light vehicles and un-armored buildings. I'd use the Explosion and Mega-scale advantages appropriate for the size of the blast, but I'm not sure exactly what scale to use. I guess the next question is, will this thing wipe out a single block, or half the city?

 

Oh, and don't forget the Double Knockback advantage; can't have a decent meteor strike w/o flipping a few cars end-over-end down the city streets!

 

Alternately, you can ignore the Def+Body limit, and use the move-thru velocity of 105,000 hexes/segment, which gives you 35,000d6 "normal" damage. Apply the Explosion advantage to this, and you get a blast radius of (I think) 70km, without using Megascale. Hope you've got lots of dice!

 

Enjoy.

 

DGv3.0

[Lupus]

Sorry for coming into this topic late. I haven't had the time to scan boards much later.

 

Quoting from http://www.seds.org/pub/faq/Space_FAQ_04_13_-_Calculations

COMPUTING CRATER DIAMETERS FROM EARTH-IMPACTING ASTEROIDS

 

Astrogeologist Gene Shoemaker proposes the following formula, based on studies of cratering caused by nuclear tests. Units are MKS unless otherwise noted; impact energy is sometimes expressed in nuclear bomb terms (kilotons TNT equivalent) due to the origin of the model.

 

D = Sg Sp Kn W^(1/3.4)

Crater diameter, meters. On Earth, if D > 3 km, the crater is assumed to collapse by a factor of 1.3 due to gravity.

 

Sg = (ge/gt)^(1/6)

Gravity correction factor cited for craters on the Moon. May hold true for other bodies. ge = 9.8 m/s^2 is Earth gravity, gt is gravity of the target body.

 

Sp = (pa/pt)^(1/3.4)

Density correction factor for target material relative to the Jangle U nuclear crater site. pa = 1.8e3 kg/m^3 (1.8 gm/cm^3) for alluvium, pt = density at the impact site. For reference, average rock on the continental shields has a density of 2.6e3 kg/m^3 (2.6 gm/cm^3).

 

Kn = 74 m / (kiloton TNT equivalent)^(1/3.4) Empirically determined scaling factor from bomb yield to crater diameter at Jangle U.

 

W = Ke / (4.185e12 joules/KT)

Kinetic energy of asteroid, kilotons TNT equivalent.

 

Ke = 1/2 m v^2

Kinetic energy of asteroid, joules.

 

v = impact velocity of asteroid, m/s.

2e4 m/s (20 km/s) is common for an asteroid in an Earth-crossing orbit.

 

m = 4/3 pi r^3 rho

Mass of asteroid, kg.

 

r = radius of asteroid, m

 

rho = density of asteroid, kg/m^3

3.3e3 kg/m^3 (3 gm/cm^3) is reasonable for a common S-type asteroid.

 

For an example, let's work the body which created the 1.1 km diameter Barringer Meteor Crater in Arizona (in reality the model was run backwards from the known crater size to estimate the meteor size, but this is just to show how the math works):

 

r = 40 m Meteor radius

rho = 7.8e3 kg/m^3 Density of nickel-iron meteor

v = 2e4 m/s Impact velocity characteristic of asteroids in Earth-crossing orbits

pt = 2.3e3 kg/m^3 Density of Arizona at impact site

Sg = 1 No correction for impact on Earth

Sp = (1.8/2.3)^(1/3.4) = .93

m = 4/3 pi 40^3 7.8e3 = 2.61e8 kg

Ke = 1/2 * 2.61e8 kg * (2e4 m/s)^2

= 5.22e16 joules

W = 5.22e16 / 4.185e12 = 12,470 KT

D = 1 * .93 * 74 * 12470^(1/3.4) = 1100 meters

 

More generally, one can use (after Gehrels, 1985):

 

(Snipped because I couldn't format it into a table)

 

The Hiroshima explosion is assumed to be 13 kilotons.

 

Finally, a back of the envelope rule is that an object moving at a speed of 3 km/s has kinetic energy equal to the explosive energy of an equal mass of TNT; thus a 10 ton asteroid moving at 30 km/sec would have an impact energy of (10 ton) (30 km/sec / 3 km/sec)^2 = 1 KT.

So, using the thing there for working out kilotons, Fuzzy Gnome is in the ballpark - around 5 kilotons.

 

This gives an explosion far below Hiroshima. That's a heck of a lot less than 20d6 RKA, which is the number more approxipate for megaton-scale explosions. So using a simple move-through is pointless, especially as it's a linear damage adder rather than a logarithmic one. If you want, you can work out the crater diameter could be worked out from the above equations, and work backwards to an impact damage and explosion. (Keep in mind that crater diameter is the area of earth that's disrupted, not the limit of damage.) I'd personally put it at 10d6 killing or so, with a couple of increases to explosive radius. That'd be enough to create a sizeable area of destruction of earth, while creating goodly devastation elsewhere.

 

Anyway, hope that's some use. I mostly posted here 'cause I really like that page, and find it very useful in games.

[DigitalGolem]

"Add to Favorites" click

 

thanks for posting that link!

 

DGv3.0

[Kristopher]

I'm not sure how to justify giving an 800 Kg mass the same BODY as a human being, which averages less than 100 Kg and is more sensitive to damage than many inanimate objects.

[Bartman]

Originally posted by Kristopher

I'm not sure how to justify giving an 800 Kg mass the same BODY as a human being, which averages less than 100 Kg and is more sensitive to damage than many inanimate objects.

This is just a built in bias of the system. All living things are given a huge body bonus over what raw mass would indicate. If people were treated like everything else in the system, they would have 5 body and would die when they reach 0 body. But then we would be playing GURPS and rewriting our characters every few adventures.