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[noodle0117]

I have been thinking about this little question for quite some time now, but haven't really come to a conclusion. It feels a little awkward trying to explain this on a physics forum, but hopefully my ideas will be a bit more understandable on a game forum.

If I were to implement a hit-point system for a game where you lose health based on how hard you get smashed around by different objects, which formula makes a more accurate depiction of the amount of "damage" you receive?

Assume all objects are rigid bodies (no deflation, deformation, bending ect.)

Damage = Change in (1/2 * mass * velocity^2)
(formula for change in kinetic energy, 1/2 constant optional)

- or -

Damage = Change in (mass * velocity)
(formula for change in momentum)

Also, I know there will undoubtedly be many more constants to consider, but for ease of reading, I'll just keep the formulas bare and simple.

[da_nang]

Well, it's all about the force, not the velocity, that causes damage, isn't it? A change in velocity can occur at different rates, so I'd probably go with change in momentum but tie it in with force through impulse.
For example:

Damage ∝ dI/dt = d(mv)/dt or Δ(mv)/Δt for the average force.

Additionally, you can also take into consideration the jerk and yank.

There's also pressure, of course. Ice can shatter if a large enough force is distributed on a small surface.

[Sergarr]

Use the second one, the first one wouldn't work because otherwise you'll get stuff like a boucning object (velocity => - velocity) recieving no damage.

EDIT:Ninja'd

[noodle0117]

One of the main things that keep me from just thinking the change in momentum is the "correct" formula for damage is because of this trope: http://tvtropes.org/pmwiki/pmwiki.php/Main/KineticWeaponsAreJustBetter.

[da_nang]

One of the main things that keep me from just thinking the change in momentum is the "correct" formula for damage is because of this trope: http://tvtropes.org/pmwiki/pmwiki.php/Main/KineticWeaponsAreJustBetter.

It all depends on the rate of change. You can have all the time in the world to slow down a fast object but the change in kinetic energy would still be the same and you probably wouldn't get even a scratch.

[acetech09]

A bit of context about the type of damage would be great. Because, depending on the target, a grain of salt at 500m/s might be much more lethal than a thrown table.

You did ask for help in a DF forum, you know. Where damage can never be that simple.

[Another]

Why would you not combine the two?

I was thinking about this subject previously and some kinds of damage can be inflicted by bone crushing heavy relatively slowly moving objects and other - by kinetic energy released from point of impact of a bullet. Why not use a_1*m*dV+a_2*m*d(V^2) for some coefficients a_1, a_2? (Which IMHO should also depend on the surface area of impact and other local geometrical and material characteristics.)

[noodle0117]

Why would you not combine the two?

I was thinking about this subject previously and some kinds of damage can be inflicted by bone crushing heavy relatively slowly moving objects and other - by kinetic energy released from point of impact of a bullet. Why not use a_1*m*dV+a_2*m*d(V^2) for some coefficients a_1, a_2? (Which IMHO should also depend on the surface area of impact and other local geometrical and material characteristics.)

That... is actually quite a nice idea, although I'd probably require a lot of fiddling with constants to get it just right.

It all depends on the rate of change. You can have all the time in the world to slow down a fast object but the change in kinetic energy would still be the same and you probably wouldn't get even a scratch.

Ah, forgot to include it in the thread post, but this is assuming all calculations occur in a given (presumably short) timeframe.

As to the context of the type of damage, I'm thinking of making a 2D physics based combat game similar to Hammerfight, except with a much more significant use of guns and kinetic ranged weaponry. Ammunition comes in all forms from tiny bullets to heavy ballista bolts to massive cast-iron cannonballs. Ideally, I would model all projectiles under a single formula, but doing so seems rather tricky if I want all projectiles to deal "realistic" amounts of damage.