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ASMRB House Rules

Version 1.5
January 9, 2000

16.0 Damage and Penetration Calculations

The destructive performance of projectiles and explosives, and the perforation resistance of armor, are not currently described by a single complete theory. Terminal ballistic simulations employ several empirical descriptions and modeling rules to provide estimations of the interaction of 'threat' and protection.

The basic description of damage potential is known as Cranz' Model Law. Developed in the 1920s during a study of explosive effects, this relationship proved applicable to a wide range of ballistic effects as well. The central statement of Cranz' Law is that the energy applied to displace target material is proportional to the displaced volume times a specific energy characteristic of the material. This material characteristic generally has larger values for 'better' armor substances.

Another useful relationship states that the cavity diameter formed in armor by a perforating projectile is proportional to the projectile diameter.

For ballistic projectile attacks at high velocities, both Cranz' Law and the cavity relationship require adjustment due to the change in dynamic mechanical processes in both the projectile and the target. During the transition from rigid perforation, to shattering perforation, and finally to plastic (hydrodynamic) perforation as velocity increases, the cavity diameter gradually increases by a factor of 2; also, up to 20% of the kinetic energy of a ballistic projectile is expended in breaking up the projectile itself. However, the energy required to displace a given volume of armor decreases as more favorable dynamic processes occur.

At very low velocities, under 25 meters per second or so, the ability of most materials to mechanically deform over wide areas comes into play, increasing the affected volume and decreasing the possible penetration.

This system uses 'Damage Class' (DC) as the measure of destructive energy. The Damage Class scale is based on powers of two, with 25 joules chosen as DC Ø; each doubling of this energy adds 1 DC.

Note that only the highest Damage Class effect of an attack with multiple effects should by applied against a target's Body, after all armor penetration. If two effects have the same Damage Class, add 1 to that DC and apply the result. This rule mostly affects explosive shells.

Example: a delay-fused artillery shell strikes Gothmog, a giant monster ravaging downtown Tokyo. The shell is listed as having a 6d6K attack due to its kinetic energy, with a Piercing value of 5, fired at Speed Class 2; and an explosive damage value of 16d6 normal. Gothmog has DEF of 25, Speed Class 1 armored hide.

His armor is reduced by 8 points (due to the Piercing and Speed Class of the shell) to 17. The 6d6K kinetic energy portion of the attack is rolled for 22 points; thus 5 points gets past his hide. Once inside the monster, the shell explodes; the normal 16d6 explosion is increased to a DC 20 Killing attack due to being an internal explosion. The resulting 6.5d6K roll results in 21 points of damage. Thus Gothmog takes 21 Body, not 26 Body, before subtracting his Damage Ignorance of 13 . . . net result, 8 BOD lost.

The effects of velocity on penetration ability are simulated by assigning a Speed Class to all attacks and defenses. Each level of Speed Class difference represents 3 points of 'Piercing' against DEF for the attack, if the attacking Speed Class is greater. Only Speed Class Ø attacks lose 'Piercing' against DEF with a higher Speed Class.

Speed Classvelocity rangetypical damage vector
up to 25 m/sechand to hand attacks, thrown weapons
S126 - 500 m/secshotguns, pistols, SMGs, archery weapons
S2501 - 1,200 m/secrifles, machine guns, autocannons, WW2 tank guns
S31,201 - 3,000 m/secmodern tank guns, explosively formed projectiles
S43,001 - 12,000 m/secshaped charges, railguns, orbital deadfall ordnance
S5over 12,000 m/secmeteors, ASAT weapons

Example: a Hellfire missile warhead detonates in contact with the hull of a BMP armored personnel carrier. The missile's shaped charge warhead is a Speed Class 4 attack; the BMP's steel hull is Speed Class 2. Thus, the Hellfire missile will subtract 6 points from the 16 DEF of the BMP's hull, due to Speed Class advantage.

16.1 Ballistic Projectile Attacks

This section (16) deals with projectiles which produce damage from the kinetic energy of their flight, and which undergo no explosive form changes until after penetrating armor. Note that, against ballistic projectiles, sloped armor gains protection as follows:

additional DEF for target = 3.5 * log2(1 / cosine Ø)

Ø = angle inclined from vertical, degrees

This DEF bonus may also apply versus some non-ballistic attacks, as well. This value may increase by 1 or 2 DEF for certain types of projectiles (esp. APDS) at large angles (over 45deg.).

16.11 Damage Class

For projectiles, Damage Class is found with these formulae:

DC = log2(E / 25)

E = energy, joules

E = (m * v2) / 2000

m = mass, grams
v = velocity, meters per second

Round fractions of .9 or less down. Almost all ballistic projectile attacks are resolved as Killing Attacks.

Example: a BRI sabot slug, with a mass of 28.8 grams, is fired from a 12 gauge shotgun at a velocity of 560 meters per second. The muzzle energy is 4516 joules, or DC 7, normally rolled as 2d6+1.

16.12 Piercing

Normally, armor penetration is assumed if the Damage Class (DC) of the attack is greater than the defense value (DEF) of the target. However, the penetrating performance of a particular attack can be affected by the dimensions, form, material, construction, etc. of the projectile. The 'Piercing' (Pc) of an impacting projectile is subtracted from the DEF of the target. The basic formula for determining Piercing values is:

Pc = 3 * log2((8 * m) / (11 * p * d3))

m = mass, grams
d = diameter, centimeters

This yields the Piercing value for lead core, metal jacketed ammunition directly. For other types of projectile construction apply the following modifiers:

modtypical material
-3wood, plastic, rubber
-2radically expanding projectiles (i.e., jacketed hollow point)
-1unjacketed soft (unalloyed) lead
0full metal jacket, hard lead, generic HE rounds
+1solid copper
+2solid bronze, steel flechettes, steel core rounds, generic AP rounds
+3tungsten or tungsten carbide core, depleted uranium, African Grand Slam

Note that when perforating multiple defenses, a projectile retains its full Piercing value as long as it retains its basic form. Also, negative Piercing values are certainly possible - they add to the target's DEF (if any - negative Piercing will not provide resistant defense against a Killing attack). A normal (non-killing) attack with negative Piercing would increase the target's PD by the amount of the Piercing.

Example: the AP round fired by the KPV autocannon is a 64.4 gram, 14.5 mm diameter projectile with a hard steel core. It thus has a Piercing value of 9.

16.13 Stun Modifier

The Stun Modifier represents the tissue destruction and shock affect of an attack on a living target. When determining the Stun Modifier of soft or tumbling projectiles, use this formula:

Stun Modifier = log2((8 * m) / (11 * p * d))

m = mass, grams
d = diameter, centimeters

The Stun Modifier of hard, non-expanding, or armor piercing projectiles is calculated as follows:

Stun Modifier = log2(2 * d2)

d = diameter, centimeters

Some types of projectiles adjust either of the above basic figures as follows:

modprojectile type
+1radically expanding projectiles, generic HE rounds or exploding bullets
+2jacketed multiple projectile rounds (Glaser, Mag-Safe, etc.)

The efficiency of jacketed hollow point bullets is a subject of some uncertainty in the technical press; generally, the older the design, and the lower the muzzle velocity, the less likely it is that a JHP round will gain the +1 for 'radically expanding.'

Example: a typical .44 Magnum bullet with a mass of 15 grams produces a Stun Modifier of +1.64, which for consistency is rounded down to +1.

Example: the AP projectile for the KPV autocannon, with a mass of 64.4 grams and a diameter of 14.5 mm, will produce a Stun Modifier of +2.07, which rounds to +2.

16.2 Chemical Energy Attacks

This section describes the effects of attacks by explosives, fragments, shaped charges, and explosively formed projectiles (EFPs).

16.21 Explosions

The damage class in the core hex of an explosion is found using this formula:

DC = 13 + 1.2(log2(yield))

yield = kilograms TNT equivalent

This is the 1 meter radius, or 'in-hex' damage. Damage at range is adjusted by one of the following calculations:

Unconfined areas
DC at range = core DC - (3 * log2(range, meters))
Areas confined to 2 dimensions

(example: underneath a low ceiling)

DC at range = core DC - (2 * log2(range, meters))
Areas confined to 1 dimension

(example: a pipe, or a long hallway)

DC at range = core DC - log2(range, meters)

Persons exposed to explosions can also reduce the damage they receive by taking shelter or assuming protective positions, as follows:

-1 DCdodge
-2 DCcrouch
-3 DCprone
-1 DChalf cover
-2 DCfull cover
-3 DChalf shelter
-4 DCfull shelter

Explosions 'at range' will be Piercing Ø, Speed Ø, rolled as 'normal' (non-Killing) damage. Explosions in contact with the target are rolled as 'Killing' attacks, modified as follows:

contact conditionadd. damageadd. piercingadd. stun
simple contact; ground placed untamped+1 DC2 Pc+1 Stun
well-placed contact; elevated untamped+2 DC4 Pc+1 Stun
tamped; 'squash head' (HESH or HEP)+3 DC6 Pc+2 Stun
internal (inside armor or target)+4 DC8 Pc+2 Stun

Any explosion which comes within 3 points of penetrating a barrier will cause some amount of spalling on the far side of the barrier.

Example: the M229 HE warhead for the 2.75" rocket has a mass of 7.7 kg, assumed to be equivalent to TNT. The core damage is 19d6 normal dice; if detonated in the open, at 8 meters range the damage will be 10d6.

16.22 Shaped Charges

The Damage Class value of a shaped charge is:

DC = 9 + (3 * log2(d))

d = diameter, centimeters

This will be resolved as a Killing Attack. The Piercing value of a shaped charge is based on the precision of its construction:

modshaped charge construction
+3dual purpose (i.e., includes fragmentation), cheap
+6 standard
+9improved (best current)

All shaped charge attacks are Speed Class 4.

The calculation for Stun Modifier of shaped charges is:

Stun Modifier = log2(4 * d2)

d = diameter, centimeters

The secondary explosion produced by a shaped charge is:

DC = 2 + (3 * log2(d))

d = diameter, centimeters

This explosion is produced on the 'outside' of the target, and follows the usual rules for explosions from section 16.21; the effect of a successful (i.e., penetrating) attack by a shaped charge into an enclosed vehicle (on the other side of the perforated barrier) is a DC 3 explosion for each point of damage past the barrier.

Example: the HEAP warhead for the 90mm recoilless rifle produces a 6d6K attack, with 6 Piercing, a Stun Modifier of +8, and a secondary HE effect of 15d6 normal (core explosion damage).

Example: the M3 shaped demolition charge is an 18 kg, 22 cm diameter weapon. It will produce a 7d6+1K attack, with 3 Piercing, a Stun Modifier of +11, and a secondary HE effect of 18d6 normal (core explosion damage). It will penetrate approximately 1.6 meters of reinforced concrete.

16.23 Explosively Formed Projectiles

The damage done by an EFP is calculated by this formula:

DC = 3 * log2(d)

d = diameter, centimeters

This will be resolved as a Killing Attack. Piercing values are taken from the following table:

modEFP construction
+5standard steel liner
+6standard tantalum liner
+8advanced steel liner (maximum performance)
+9advanced tantalum liner (best current)
+11very advanced tantalum liner (maximum performance)

All EFPs are Speed Class 3. The calculation for Stun Modifier of EFPs is:

Stun Modifier = log2(d2 / 8)

d = diameter, centimeters

For comparison purposes, a 1 centimeter diameter EFP fires a 0.33 gram projectile with about 0.66 grams of explosives.

Example: the MBB 20 cm diameter off route mine has a mass of about 8 kg, and will produce a 6d6+1K damage projectile, with 5 Piercing, and a Stun Modifier of +5.

16.24 Fragmentation

The damage class of explosively propelled fragments is derived using the formulae in Section 16.1, using the mass and velocity of the individual fragments. If actual fragment characteristics are not know (as is likely), approximations can be found:

fragment velocity, m/sec = 1700 * ln( mweapon / mfragments,total ) * (RE)0.5

ln = natural logarithm
RE = relative effectiveness of explosive filler

Relative effectiveness of the explosive filler in modern weapons may be assumed to be 1.25 if the actual value is unknown. For calculations in the Shadowrun campaign, use a RE of 1.8; for 2300AD, use RE of 2.0.

If the mass of the individual fragments is unknown, use 3.2 grams; this number is not too accurate for weapons with a total mass under 10 kilograms. Typical modern hand grenades project fragments of about 0.5 grams mass.

The Speed Class of fragments is never larger than 2; if a value of 3 or more is produced with the velocity formula above, reduce the Speed Class to 2. Piercing values for fragments is usually Ø for properly designed weapons; impromptu fragmentation or secondary missiles will almost never have piercing values above Ø, and will usually have lower Speed Class as well. The Stun Modifier for individual fragments is usually -1, but the 'group hits stun modifier' rule is used.

Example: the M117 aircraft bomb has a total mass of 374 kg, with a filling of 180 kg of Minol-2 (RE = 1.3). It produces fragments with an initial velocity of 1300 meters per second, with a Speed Class of only 2. Assuming the fragments to be 3.2 grams each, they will do 2d6 damage. Piercing value will be Ø, and the Stun Mod will be -1.

Fragments may achieve hits out to a distance known as the effective range, or burst radius. As a general rule, for explosive/fragmentation weapons with a total mass of 10 kilograms or more, the burst radius will be:

effective range, m = ( mweapon,total, kilograms)0.6

The burst radii of weapons below 10 kilograms mass will tend to be greater than the values produced by this equation.

All fragmentation weapons have an OCV based on the density of fragments at the effective range. Typical values range from Ø for small modern weapons such as hand grenades, to -9 for old aircraft bombs. Specifically, an OCV of Ø represents a pattern density of 1 fragment per square meter. For weapons producing a spherical fragmentation pattern, the surface area of the burst zone will be:

surface area, meters2 = 4 * p * (effective range, meters)2

The pattern density is therefore:

pattern density, frags/meter2 =  #fragments,total / surface area

The OCV at the effective range can thus be easily calculated:

OCV = 2 * log2(pattern density, frags/square meter)

For weapons with non-spherical burst zones (Claymore mines, and other directional charges), the calculation of the surface area will of course change to the appropriate geometrical formula.

All fragmentation attacks are given an effective range, and an OCV at that range. For spherical fragmentation patterns (such as are produced by hand grenades, for example) each halving of the distance from the effective range adds 4 to the OCV. Planar fragmentation (as in claymore mines, for example) adds 4 to the OCV for each halving of the effective range, until the point at which the pattern's narrowest dimension (usually height) becomes smaller than the target: from that point on, each halving of the range only adds 2 to the OCV. For convenient figuring of whole OCV bonuses, note the following:

OCV modfraction of range
+1 OCV0.84 x any given range
+2 OCV0.71 x any given range
+3 OCV0.60 x any given range
+4 OCV0.50 x any given range

Each x 1/2 multiple of human size subtracts 4 OCV; each x 2 multiple of human size adds 4 OCV; technically, the OCV modifier is:

Area mod to OCV = 4 * log2(area, m2).

A hex has an area of about 4 x human size (about 4 square meters). 'Human size' is figured as 1 square meter of area normal to the fragmentation path. 'In-hex' range is assumed to be 1 meter; direct contact adds +2 OCV more than 'in-hex' range. Each die of Unluck adds +1 to the OCV; each die of Luck subtracts -1 OCV.

Fragmentation attacks are made against a DCV of Ø; neither DEX-based DCV nor skill levels raise this number. Characters in Dodge will gain the usual bonus to DCV for that maneuver (+3 or +5 for some martial artists). Also, the following DCV modifiers for position should be used:

actionDCV modusage notes
Crouch:+1 DCV;can be combined with Dodge or Diving for Cover; Crouched characters get only 1/2 of their usual movement.
Prone:+2 DCV;can be combined with Dodge or Diving for Cover; Prone characters must take a 1/2 phase to get to their feet.

To resolve the attack, compare the OCV of the weapon at the range of the target to the DCV of the target, and make an attack roll. If the roll is successful, one or more fragment groups strike the target; if the attack roll is unsuccessful, no fragments strike the target. For each 2 points the attack roll is made by, one additional fragment group strikes the target.

Note that fragments use the 'group hits Stun mod' rule: every group above the first which strikes the target adds +1 to the Stun modifier of each group.

Example: Major Thornton is standing next to his car when an M26 fragmentation grenade explodes 1 hex away. The M26 has an effective fragmentation range of 8 hexes, and a listed OCV of -2. At 1 hex range, the Major is at 1/2 x 1/2 x 1/2 of the effective range; the attack thus adds 3 x 4 = +12 to the listed OCV, resulting in an OCV of 12 - 2 = 10. A 7d6 normal explosion is also produced; after resolving the blast damage, the referee determines that since the character was not in Dodge, his DCV is Ø. The referee, making the attack roll of 21-, comes up with a 13: only 5 frag groups strike the Major. The groups are listed as doing 1 point of damage, with a -1 Stun modifier; the 'group hits' rule will adjust the Stun mod to -1 + 4 = +3. For role-playing purposes, it should be noticed that each extra fragment group above the first represents a doubling of the number of nominal, actual fragments striking the target; thus the referee might describe the effect of this attack by noting that the character has been punctured between 9 and 16 times! As a typical modern fragmentation hand grenade produces from 400 to 1200 fragments, Major Thornton can consider himself lucky.

The referee rules that the portion of the car within 1 hex range of the grenade is a three times man sized object for the purposes of this attack, thus adding 6 to the OCV of the attack. Making the attack roll of 27- (since the car also has a DCV of Ø), the referee rolls an 10, and the car is struck by 9 frag groups. With a Piercing value of Ø, and doing only one point of damage, the fragments are unlikely to penetrate even a cheap plastic car body; again for role-playing purposes is should be noted that a few hundred 'dings' have been put in the car's body (between 129 and 256 'dings', if a count is made). Other portions of the car, further away than 1 hex from the grenade, will take another few dozen hits.

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Document last modified Friday, June 01, 2001