First, some rough numbers.

A human falling off a table has an energy about 800 foot pounds. A car crashing into an unforgiving object at 30 mph with a "crumple distance"* of 2 feet exhibits 172,848 foot pounds of energy.

The former would result in "no damage" that would need to be resisted, the latter would probably total an Americar (3500 pounds of weight, which is pretty typical for compact cars today).

An F-16 traveling 300 miles per hour with a 10 foot "crumple distance" would have 13,391,493 foot pounds of energy. Even at a 100 foot deacceleration distance, the energy is still 2,678,298 ft-lbs. Bringing any aircraft to a complete stop is going to be Bad News Bear for everyone involved. Of course, an F-16 has a much higher top speed than that (Mach 1.2 at sea level)...

Now, onto collisions with objects that can move.

QUOTE

**Momentum**

An object which is moving has momentum. The amount of momentum (p) possessed by the moving object is the product of mass (m) and velocity (v). In equation form:

p = m • v

**Impulse-Momentum Change Equation**

In a collision, a force acts upon an object for a given amount of time to change the object's velocity. The product of force and time is known as impulse. The product of mass and velocity change is known as momentum change. In a collision the impulse encountered by an object is equal to the momentum change it experiences.

Impulse = Momentum Change

F • t = mass • Delta v

Some heavy math is involved, but roughly speaking, when two objects collide, the new velocities are equal to the old velocities, but on the opposite objects (ignoring mass). Two pool balls that collide head on bounce off each other, transferring the momentum from A to B and from B to A. Add in differences in mass, and the larger object changes less.

Car hitting a person:

30 miles per hour, hitting a stationary person (200 pounds) results in the car slowing down by 3.5 mph and the person flying off at almost 56 mph! (assuming an elastic, frictionless, collision).

Using the same calculator I did above, this results in about 6784 foot pounds of energy on the person and 469 on the car.

This sounds about right, hitting someone with a car at 30 mph is pretty fatal for the pedestrian** and not too damaging to the car (dent in the hood, cracked windshield if the pedestrian went over rather than under, neither of which are representative of a "box" of damage in Shadowrun--yes a shattered windshield probably should be, but we have to consider the fact that glass is fragile as all getout and the simulationist nature of the game doesn't respect that).

Real physics equations using game values:

Object

_{1}will have to be the object with the

*lower*of the two body scores (so an 8 body troll being hit by the 4 body Dodge Scoot, the dodge scoot is object

_{1}and will use the first equation, the troll the second.

Note: for velocities, these are not relative. If the two objects are moving towards each other, then the lower value needs to be multiplied by -1.

v'

_{1}= (Body

_{1}- Body

_{2}) / (Body

_{1}+ Body

_{2}) * (Speed

_{1}- Speed

_{2}) + Speed

_{2}

v'

_{2}= (2 * Body

_{1}) / (Body

_{1}+ Body

_{2}) * (Speed

_{1}- Speed

_{2}) + Speed

_{2}

(And then absolute value the results, because negative damage values are meaningless, although negative velocities are valid)

Hmm...offhand this isn't

*too*shabby and the math, while detailed, isn't that hard (we'll be rounding to whole values in the end, so approximating 3/13 * 10 to "about 2.5"--3 divided by 12 is 0.25, times 10--will be sufficient). Pull out a pocket calculator if you really need to.

Though because speed values are almost already the square-root of their real world mph values...and because the v' values we end up with are what we're going to want as our damage-inflicted values, we need to tweak a few things.

v'

_{1}= (Body

_{1}- Body

_{2}) / (Body

_{1}+ Body

_{2}) * (Speed

_{1}- Speed

_{2}) + (Speed

_{2})

^{2}

v'

_{2}= (2 * Body

_{1}) / (Body

_{1}+ Body

_{2}) * (Speed

_{1}- Speed

_{2})

The lower body object is now taking a pile of damage, especially when hit with a very fast moving object (a speed 10 object will obliterate anything it hits).

The higher body object now only has to deal with the collision of mass, rather than taking a pile of damage based on its own speed (a speed 10 object hitting a pigeon doesn't give two shits).

The +speed on the end was there in the original equation for the larger mass object retaining most of its original velocity (which we actually don't care about for our purposes).

One last change needs to be made.

DV

_{Body (lower)}= (Body

_{lower}- Body

_{higher}) / (Body

_{lower}+ Body

_{higher}) * (Speed

_{lower}- Speed

_{higher}) + (Speed

_{higher})

^{2}

DV

_{Body (higher)}= (2 * Body

_{lower}) / (Body

_{lower}+ Body

_{higher}) * (Speed

_{lower}- Speed

_{higher})

(And round up; rounding normally is fine as well, it makes a difference of 1DV, which doesn't impact the general results much, given the variable nature of the damage resistance rolls)

Now rather than stipulating that Object

_{2}is the one with the higher body (which plays havok with Speed

_{2}being 0 when the stationary troll is hit by a careening Dodge Scoot), we instead go "ok, use the larger value here, the lower value there, regardless of which of the two objects are involved." In the case of a tie, both objects use the first equation.

The awesome thing about this is that it works for barriers too. Simply substitute (barrier rating / 2)*** for the body.

A couple of examples, ramming Joe Shadowrunner (Body 4, Armor 9):

Dodge Scoot (Speed 3, Bod 4)

Suzuki Mirage (Speed 6, Bod 5)

Ford Americar (Speed 3, Bod 11) (Yes, it has a top speed of 30 mph)

GMC Banshee (Speed 8, Bod 20)

**Dodge Scoot**

DV

_{Joe, Scoot}= (4 - 4) / (4 + 4) * (0 - 3) + 3

^{2}

Both Joe and the scooter resist 9 damage. It's a pretty bad collision, given that the scooter was traveling 30 miles per hour, but no one is killed.

**Suzuki Mirage**

DV

_{Joe}= (4 - 5) / (4 + 5) * (0 - 6) + 6

^{2}

DV

_{Suzuki}= (2*4) / (4 + 5) * (0 - 6)

Joe resists 37 damage, which kills him instantly. The Suzuki resists ~5 DV, which damages the car, but not enough to impair its function. This is pretty reasonable, considering that it was a compact car traveling 120 miles per hour.

**Ford Americar**

DV

_{Joe}= (4 - 11) / (4 + 11) * (0 - 3) + 3

^{2}

DV

_{Americar}= (2*4) / (4 + 11) * (0 - 3)

Joe has to resist 11 DV, which puts him in the hospital, but he'll live. Soccer Mom's minivan however, is pretty much unharmed (2 DV). Given the sheer mass of her vehicle and low speed, this isn't all that surprising. Heck, even a Body 8 troll won't do much more than dent the grill (3 DV) and she can plow through chain link fences all day long (1 DV).

**GMC Banshee**

DV

_{Joe}= (4 - 20) / (4 + 20) * (0 - 8 ) + 8

^{2}

DV

_{Banshee}= (2*4) / (4 + 20) * (0 - 8 )

...Joe's dead. Not even edge can save him now. He'd have to resist 70 DV down to a mere ~14 in order to survive. Still, it's better than the 180 DV he'd have to face by RAW!

The Banshee doesn't even notice (3 DV). A Body 12 dragon might do it some damage though (6 DV, but the dragon would be toast, resisting 66 DV). An 8 Body troll on trollerskates skating towards the Banshee as it hits him will have a noticable effect though (6 DV).

This probably isn't the most accurate thing in the world, but I think I can live with it.

*Aka stopping distance. This value determines how much acceleration the object exhibits.

**

QUOTE

Hitting a pedestrian at a speed of over 30 miles per hour results in more serious injuries and fatalities -- yet a driver can severely disable a pedestrian in a crash where the driver is traveling only 10 miles per hour.

A 10 mph collision ends up giving our pedestrian about 877 foot pounds of energy, which is roughly equivalent to falling off a table, but neither takes into account the impact surface. The numbers I found for falling off the table made note of this and that it was possible for the person to still take a severe injury in that short of a distance.

***Chain link fence has a barrier rating of 4. This would be too large of a value when trying to ram it with a Dodge Scoot, as the scooter probably should be able to break through a chain link fence at top speed.

References:

Impact force (the 800 footpounds for falling off a table)

Cars hitting immovable objects (calculator)

Head-on collision calculator (calculator)

Converting from Newtons to Footpounds (unit converter)