Tying Kinetic Energy to damage in D&D

[hamishspence]

I was idly speculating on some of the oddities of D&D damage, and wondered how much of a difference tying damage to kinetic energy would make.

For example- if you fall, the damage you do to yourself would be based on how heavy you are as well as how fast you're moving.

The mass of your weapon would make a big difference to damage.

And so on.

Might it fix some of the less plausible things?

[Yora]

One question: Why?

Would it improve the story, or the fun of winning encounters, to add complex calculations of velocity and mass?

[hamishspence]

Might fix some of the more broken things. Then again, it might not.

Done right- maybe it could bump up melee damage so that it scales well?

If, for example, a person Full attacking with a weapon can make 4 attacks per round, this would imply the weapon is moving very fast- so doing more damage.

[Eldan]

However, you should also calculate how fast you can swing that heavier weapon, and if it actually changes damgae

[hamishspence]

True- might give heavy weapons an even bigger bump than they have already- and make strength much less important than the speed the weapon is swinging at.

Maybe charging would allow you to add your speed to your weapon speed.

And, when set to receive a charge, you use the speed your enemy is moving at- and possibly their weight instead of the weapon's.

[Tetrasodium]

For example- if you fall, the damage you do to yourself would be based on how heavy you are as well as how fast you're moving.

The mass of your weapon would make a big difference to damage.

Gravity doesn't work that way on the first point. A feather doesn't fall slower than a brick because it's lighter, it falls slower because of how its structure impedes it's movement through the air. A 50 pound humanoid and a 300 pound humanoid both lack anything to impede their movement in any significant way unless it's one of the less common winged humanoids (i.e. raptorians) or they have featherfall or something. Both the 50 pound humanoid and the 300 pound humanoid have a bone and muscle structure capable of handling their weight in roughly the same level of effectiveness.

With regards to your point about weapon damage being affected by mass, that somewhat already exists when you consider the ridiculous mercurial weapons. It's certainly possible there is a book that says a lead core mace/morning star/etc gives it a nonmagical +1 bonus or something. Plus there is nothing that says it's not involved in creating magical weapons anyways, ECS (or a different eberron book) rattles off a bunch of magical items in the DMG that use various dragonshards in their construction when it's going over dragonshards and some interesting uses for them for example.

[Lapak]

I was idly speculating on some of the oddities of D&D damage, and wondered how much of a difference tying damage to kinetic energy would make.

For example- if you fall, the damage you do to yourself would be based on how heavy you are as well as how fast you're moving.

The mass of your weapon would make a big difference to damage.

And so on.

Might it fix some of the less plausible things?

The physics involved is complicated enough that you're likely to end up with equally wrong results through a much more difficult process. More mass doesn't mean more kinetic energy if the weapon is slow; note that real-world weapons weren't that heavy. More attacks does not mean any individual attack is moving faster; it might just mean that the attacker is better at creating or exploiting vulnerabilities in the enemy's defenses while the amateur flails around a bit. Falling damage is much more involved than just weight.

So any attempt to make damage accurately reflect reality would either require too much calculation every time someone gets hurt or would fail in its goal, I think. (And all of that leaves aside what 'damage' actually means in gaming, itself a topic of constant debate.)

[Snake-Aes]

Might fix some of the more broken things. Then again, it might not.

Done right- maybe it could bump up melee damage so that it scales well?

If, for example, a person Full attacking with a weapon can make 4 attacks per round, this would imply the weapon is moving very fast- so doing more damage.

I believe it will only complicate things more than it is worth. For example, how will you differentiate bludgeoning damage from piercing or slashing damage given the only difference between them is the area they are applied to?

[jseah]

Well, it seems logical to me to treat the idealized case of Object A of mass Ma travelling at speed Va collides with Object B of mass Mb travelling at speed Vb.

Shape and structure should be a matter of DM handwaving, so at best guidelines for those. D&D players cannot be expected to do complex fracture simulations on paper... =P

A good formula should also yield the same result if it was Object B moving towards Object A (in the same orientation of course), being that the situation is a simple frame shift of the original.


I have a houserule in my games correcting free fall speeds and dmg though. It always bugged me about how slow stuff falls in D&D.

Spoiler

Show

Falling damage does not cap
Falling speed is 180ft in round 1 and increases by 360ft per round for every round afterwards (180, 540, 900...)

Falling damage is 1d6 bludgeoning per 10lbs per 20ft falling speed.
Both the falling object and the object it hits take this damage.

[hamishspence]

I have a houserule in my games correcting free fall speeds and dmg though. It always bugged me about how slow stuff falls in D&D.

Spoiler

Show

Falling damage does not cap
Falling speed is 180ft in round 1 and increases by 360ft per round for every round afterwards (180, 540, 900...)

Falling damage is 1d6 bludgeoning per 10lbs per 20ft falling speed.
Both the falling object and the object it hits take this damage.

This is roughly the sort of thing I was thinking about- maybe something similar might apply to creatures which one might expect to attack via ramming- a whale, a swordfish, and so on.

Both the 50 pound humanoid and the 300 pound humanoid have a bone and muscle structure capable of handling their weight in roughly the same level of effectiveness.

In game, a 60 pound Medium humanoid and a 300 pound Medium humanoid with the same strength, can lift the same amount over their head.

While "lower terminal velocity" might account for some of the survivability of small creatures falling, "lower kinetic energy" probably also plays a big part.

[Snake-Aes]

Now take into account friction to determine the terminal velocity.

[hamishspence]

I did mention "lower terminal velocity" as part of it.

If you could have two creatures of roughly the same size and shape (but one weighing twice the mass of the other) while they'd hit at roughly the same speed, the heavier creature would take a bigger shock.

[Esser-Z]

The main issue is the gameslowdown that comes from doing all that phsyics. Also from some people ALREADY being afraid of the math there is, so adding more (especially complicated-looking, even if really not so hard) is not a very good idea.

Really, abstracting damage is fine. I do believe there are rules for heavier objects dealing more falling damage--I know Telekinetic Thrust takes this into account in a nicely simple way.

The mass of your weapon would make a big difference to damage.

I believe this is represented by different damage die sizes. A Greatsword does 2d6, while a Longsword does 1d8, because a greatsword is bigger.


Air resistance is mostly meaningless for most falling things--they're likely to be PCs or rocks or such, none of which have significant increased resistance, at least not for these purposes. So, falling speed is roughly constant (though I'm not sure how D&D handles fall speed and acceleration) for just about anything we care about. This is good.

Now, while mass doesn't matter for speed, it does indeed affect impact strength... This probably doesn't matter too much for PCs. Outside constructs and monsters, they usually weigh close enough to the same values to not have significant impact variance, I imagine. For heavier things, extra damage based on size (See the Telekinetic Thrust power again. It even takes the composition of the object into account!) sounds reasonable.

[grimbold]

i think this is accounted for in the fact that weapons can hit harder due to strength bonuses. Also bigger weapons tend to do more damage. The physics would be a pain if you really want to make it +1 damage w/ all 2handed or larger weapons.
maybe +2 for large weappons and scaling up on the same rate (+3 for huge, +4 for Gargantuan, i hope i got my size classes right)

[hamishspence]

True- might work better for things which are very obviously chunky, high speed objects.

I was thinking along the lines of

"given that a stone of X weight hurled at a target Y distance away by a hulking hurler does Z damage, how much damage should other weapons be doing relative to that?"

[Snake-Aes]

I did mention "lower terminal velocity" as part of it.

If you could have two creatures of roughly the same size and shape (but one weighing twice the mass of the other) while they'd hit at roughly the same speed, the heavier creature would take a bigger shock.

I'm not sure we talked about the same thing. Terminal velocity is the maximum speed the object will achieve. That is added to the fact many small creatures don't even take falling damage ever, just like small mice can fall from the top of a building and run like nothing happened.

[hamishspence]

And the reason they do that, isn't because their terminal velocity was much lower- but because their kinetic energy was much lower.

In D&D- if you drop a really tiny animal from a high place- splat. If you drop a much bigger animal from the same height, it has a chance to survive due to high hit dice.

When it should be the other way round.

[Esser-Z]

Aha, yes. The Falling Damage rules do have a nice simple approximation for increased weight=increased damage, and a clause for very light objects not doing any. This is good.

On the other hand...it completely lacks rules for how fast an object falls, or in game terms how far a falling object moves per round. This is harder to resolve than it would see, as D&D tends to not have much of a concept of acceleration. Hmm.

Hamish: That higher HD creature also has a much better chance (IE, pretty much 100%) of being stabbed with a sword. HP's... a mess.

[hamishspence]

Light objects- but not creatures. (A mouse falling on you from a great height won't hurt you, but the mouse is in deep trouble).

Maybe the rule should be expanded to include damage to objects and creatures from falling, not just damage from them.

[Snake-Aes]

Light objects- but not creatures. (A mouse falling on you from a great height won't hurt you, but the mouse is in deep trouble).

It wouldn't, really. the light build is the main reason they can drop high heights and not care.

[hamishspence]

It wouldn't, really. the light build is the main reason they can drop high heights and not care.

That's the way it works in real life- but apparently, not in D&D.

[Esser-Z]

D&D and real life don't match up in many, many ways.

This, like other things, can be blamed on residual magic.

As for those little animals and falling... A small rodent can be potentially badly injured from just a several foot drop, so...

[hamishspence]

Hence the idea of, if not making it match precisely, at least trying to make some things make a bit more sense.

As for those little animals and falling... A small rodent can be potentially badly injured from just a several foot drop, so...

That might be a case of rolling, and getting more damage than they have HP

[Terazul]

On the other hand...it completely lacks rules for how fast an object falls, or in game terms how far a falling object moves per round. This is harder to resolve than it would see, as D&D tends to not have much of a concept of acceleration. Hmm.

It has a few. For example, a stalling flying creature (who isn't moving his minimum speed) falls 150 ft in a round. And then 300 ft. And feather fall reduces falling speed to 60 ft a round. But yeah, I really don't see the benefit of trying to suddenly apply physics to everything. Especially when magic starts getting involved.

[Snake-Aes]

That's the way it works in real life- but apparently, not in D&D.

Then what are you doing trying to adapt real life into d&d? :p Because if "small creature dies but big one doesn't" irks you, it's kind of a double standard to forbid the small creature to not taking damage in the first place.

[hamishspence]

Mostly because the DMG says that for most things D&D worlds generally obey the same principles as the real one-

and the fact that they really don't, could maybe do with fixing.

It's more idle speculation than a serious attempt though.

Small creatures should be taking damage from falling- but much less than big creatures- so much less, that there should be a chance (if a small one) of survival.

[jseah]

^Redid the calculations to base them off 9.81m s-2.

Spoiler

Show

Falling damage does not cap
Falling speed is 190ft in round 1 and increases by 190ft per round for every round afterwards (190, 380, 570...)

Falling damage is 1d6 bludgeoning per 10lbs per 20ft falling speed.
Both the falling object and the object it hits take this damage.

Distance fallen is 570ft times number of rounds squared.

It's a bit more than this, but I can chalk up the shortage of a few feet to air resistance... or more honestly, plain laziness. =P

A slightly more accurate one would be to take damage based off relative speed of the two objects, but that gets into trigonometry so nvm.

EDIT:
This scales the damage with momentum.

[Eldan]

Obviously, you looking at falling damage from the wrong angle.


Let's first take into account that all matter in the universe is actually composed of differing amounts of fire and pneuma. We can assume that a small living creature and a large living creatures have both the same number of atoms of pneuma, as they are equally complex, and the same amount of fire spirit, as they are both equally alive.
Let us assume that the small animal is a mouse, and the large animal a horse.
The horse is not only larger, but also heavier than the mouse. Since they consist of the same number of atoms, we can therefore conclude that horse atoms are larger than mouse atoms.
Now, let us come to the issue of falling. As we all know, the pneuma of air is less dense than the pneuma of ground, as it's atoms are spread further apart.
It has been proven consistently by many great sages that all atoms are possessed by a strong love for each other, and that only random movements outside their control move them apart.
As we now look at the elephant and the mouse, they both have the same number of atoms, as I previously stated. Therefore they receive the same amount of love from the ground.

So they also fall at the same speed. I see no problems with this conclusion.


In related news: guess who just had a lecture on the history of life sciences, starting with a few noteworthy Greeks, Ionians and so on.

[Eric Tolle]

^Redid the calculations to base them off 9.81m s-2.

Spoiler

Show

Falling damage does not cap
Falling speed is 190ft in round 1 and increases by 190ft per round for every round afterwards (190, 380, 570...)

Falling damage is 1d6 bludgeoning per 10lbs per 20ft falling speed.
Both the falling object and the object it hits take this damage.

Distance fallen is 570ft times number of rounds squared.

It's a bit more than this, but I can chalk up the shortage of a few feet to air resistance... or more honestly, plain laziness. =P

A slightly more accurate one would be to take damage based off relative speed of the two objects, but that gets into trigonometry so nvm.

EDIT:
This scales the damage with momentum.

Actually, you've got some major problems with this formula, and it makes it no more accurate than regular D&D.

For a start, there has to be a cap on falling damage, based on air resistance. For a start, if there's no cap to falling damage, then obviously items are falling in a vacuum, and we need to use the suffocation tables before worrying about damage (actually those tables are inaccurate as well: roughly, in a vacuum creatures will pass out in 2-3 rounds (being generous), and start taking permanent damage in 20 rounds, and die immediately after that. please adjust your rules accordingly).

Secondly, for most purposes maximum velocity is going to be based on both the distance fallen, and the acceleration minus drag, a = (W - D) / m. The drag equation of course is D = Cd * r * V ^2 * A / 2 , so quickly working out the reference area and the Drag Coefficient ( Cd = D / (A * .5 * r * V^2) ) will give you the final equation. Terminal velocity then is going to be:

V = sqrt ( (2 * W) / (Cd * r * A)

See? No trig at all! And naturally easy enough to figure out in game when you have the right tables of mass, density and reference area printed out.

Note that the maximum velocity doesn't increase linearly according to mass, so basing damage directly on mass won't work.

Finally, maximum velocity is going to vary between 14 and 300 ft./round at most, so the velocity will usually be capped after one or two rounds (for most humanoids, one round is fine. So once we have all that, we can easily calculate the damage based based on the standard D&D velocity/impact tables.

Waitasecond...we don't HAVE "Standard D&D velocity/impact tables? Well no problem, we can probably just use your handy "Handbook of Engineering Fundamentals" to calculate that.

OK? Go ahead and reconfigure your calculator to encompass this new information. If you need some assistance, here's a handy Terminal Velocity Calculator.

And don't forget to show your work.

[jseah]

Eric:
Yes, I did assume a fall in a vacuum in my calculation.
I also generally try to avoid square roots in any calculations, calculating drag is a bit... >.>

Then again, it's nice to see someone else willing to put up the formulae, most especially since I don't know them.
Also, your link gives me a 404... =/

PS: the trigonometry I mention is needed for working out the relative velocity of two objects moving in arbitrary 3D space.
eg. working out the collision damage for a hero jumping out an airship and landing on a gliding dragon's back.
Trig (specifically cosine rule) might be needed to work out the relative velocity vector. Of course, that's if the dragon isn't going horizontal coz in that case the pythagoras theorem will do.