Falling damage and physics [D&D 3.5e]

[Mastikator]

Yes I know that combining physics and D&D kills catgirls, but they're dying for the greater good.

I was thinking about kinetic energy and falling damage. Shouldn't falling damage be squared? I mean, lets look at basic Newtonian physics, the energy of velocity is velocity^2*mass, if a rock hits you at double speed it smashes into you four times as hard. Shouldn't the same general rules apply to falling damage?

Here's my new (improved) version of falling damage:
The damage you take from falling is distance (in feet) / 10, rounded down, squared, # of d6's. So falling 10 feet is still 1d6, but falling 20 feet is now 3d6, and then 9d6. It increases very fast and high distances become increasingly lethal. (yes, I know my explanation sucks, my wording is bad today)
(If I remember correctly) the terminal speed is achieved in 150 feet, so that's 225d6 damage.

In my opinion this not only reflects reality more accurately, since damage from falling is not linear, you're not twice as hurt from falling twice as long, but quadruple after all (in reality). This also is more balanced, since it makes it a lot harder to survive long falling distances (a high level fighter can easily survive falling from orbit and taking only 15d6(52 damage), but 225d6 (787 damage) is a different level of "ow")


So which am I wrong about? D&D or physics?

[Yuki Akuma]

Nothing says that someone with 20 hit points is twice as tough as someone with 10.

[Kurald Galain]

It strikes me that how much being hit by a falling object hurts depends not on kinetic energy, but on momentum, which is linearly dependent on velocity.

Then again, velocity itself should not increase linearly as you fall, but exponentially.

So you and the system are both wrong

[Johel]

We could... but then, we would have to use an open scale and account for the friction of air, too.

In most situation, saying that a brick falling from the ceiling causes 1d6 damage is a way to say "-Watch out !! This dungeon is old" while taking 20d6 from a crumbling ceiling is a way to say "-Rocks fall, everyone die people might survive".

The system can be abused (Bags of Holding, full of 2lb iron balls, dropped 500 meters above a thickly packed army...or a market square) but in most situation, it's not relevant to spend 10 minutes calculating the damages. Better go with a handful of 1d6 with pseudophysic.

D&D is about roleplay, not science/economics simulation.

[Spiryt]

Don't forget mass.

Rat won't be hurt much from falling 100 feet, but an Umber Hulk will *SPLAT*

So, come one bring on the math

[Mastikator]

@Kurald Galain, velocity increases linearly in a free fall (technically it increases exponentially since you're getting closer to the gravitational center, making the acceleration greater, but in Earth-terms, it's linear).
The length you'll cover will increase exponentially.

Basically, you'll fall at an accelerating rate of ~9.5meters/s, making your velocity 9.5m/s/s, So by the time you've fallen for 5 seconds you're falling at a rate of 5*9.5 m/s, or 47.5m/s, and have fallen (5seconds)^2 * 9.5meters/second/second, or 237.5 meters.


I'm all for rounding and making quick calculations to quicken the time. You could just use the old system, but multiply the number of dices by itself. So 1d6 becomes 1*1d6 = 1d6, 2d6 becomes 2*2d6 = 4d6, ... 6*6d6 = 36d6 and so on. Those aren't complicated to make. At least they don't seem so to me.

[Kurald Galain]

@Kurald Galain, velocity increases linearly in a free fall

Oops. In other news, my recall of physics increases exponentially as I drink more coffee

Nevertheless, my point about momentum still stands.

If you don't mind tables, you could also use those as a system for falling damage. For instance, Paranoia uses something like this. Also, it's a much more Fun system than D&D, because The Computer says so! Praise The Computer!
{table]Height|Not hurt|Lightly hurt|Seriously hurt|Dead|Vaporized
5m|1-10|11-18|19-20
10m|1-5|6-16|17-19|20
100m|1|2-3|4-15|16-19|20
Orbital|-|-|-|1|19-20
[/table]

[Tyrmatt]

It strikes me that how much being hit by a falling object hurts depends not on kinetic energy, but on momentum, which is linearly dependent on velocity.

Then again, velocity itself should not increase linearly as you fall, but exponentially.

So you and the system are both wrong

Velocity only increases up to terminal velocity, which is not an exponential. You would have to live in a frictionless world for this to occur.

Second Law.
Observed from an inertial reference frame, the net force on a particle is equal to the time rate of change of its linear momentum: F = d(mv)/dt. Since by definition the mass of a particle is constant, this law is often stated as, "Force equals mass times acceleration (F = ma): the net force on an object is equal to the mass of the object multiplied by its acceleration."

Force = Mass x Acceleration. When mass is fixed and acceleration has a maximum, the force a given falling object can acquire is limited.
Which when you take terminal velocity into account, does in fact mean that by the system of D&D hitpoints, yes you can can survive a fall from orbit. Force cannot increase past a certain point when mass is fixed and accelleration has reached it's maximum.

Rat = 0.5KG X (theoretical max) 55m/s (180ft/s is terminal velocity) = 27.5 Newtons force applied to the rat. Now divide that over the maximum possible area the rat can make itself when it hits the ground. Assuming totally equal dispersion of force, compare this value to the number of newtons needed to break bones, cause shock trauma injuries etc.

Now a fighter
Fighter = Mass ~80kg + full plate (20kg) 100kg x 55 m/s = 5500 Newtons.
In order to effectively work out the damage, you need to work out from a base point, e.g. a mace of weight 2kg being moved at a certain velocity by someone of Strength X does X Newtons damage and the appropriate dice damage to go with that. Then divide the Newton damage into the Newton falling force to give you the correct indication of how many D6's SHOULD be applied.

Note that this assumes that the acceleration is near instantaneous for simplicity's sake. Since terminal velocity is in effect, this won't be an issue as this only deals with falls that come from heights where terminal velocity can be reached.


If you want an accurate representation of someone falling, come up with rules for broken bones and internal injuries, not increased fall damage.

[bosssmiley]

Yes I know that combining physics and D&D kills catgirls, but they're dying for the greater good.

<trim science waffle>

So which am I wrong about? D&D or physics?

D&D is a game, not a physics simulator. d6 damage/10' is an acceptable break from reality.

If you look at rates of acceleration and suchlike greek letter mumbo-jumbo, then falling damage as written holds up until about the 60-70 feet. Anything else is just rounding errors and really not worth the brain space.

That said, the old Dragon Warriors RPG did falling damage per Newton. It went something like 1, 2, 3, 4, 5, 7, 10, 15, 20 for 1-10 yards.

[ericgrau]

By conservation of energy the kinetic energy produced is equal to the potential energy at the height which is proportional to the height. i.e., if you fall 4 times as far your kinetic energy (and initial potential energy) is still 4 times as much and your velocity is twice as much to match (2 x 2 = 4). So, by real world physics, the damage should be proportional to height.

Death of catgirls is actually fairly rare, due to most people's poor recollection of their physics classics. Perhaps we need a new meme involving Newton rolling in his grave whenever anyone attempts to kill a catgirl.

[Mastikator]

Lets try common sense instead. Because common sense should apply in games.

Which is more painful, falling 10 feet 5 times, or falling 1 time 50 feet. In game-terms it's 5d6 either way, in reality it's a difference between life and death.

[ericgrau]

That's a rather extreme example as 10 feet is far more likely to be negated, and a jump check that even a commoner might pass will do it even in game terms. It's also fairly anecdotal. I mean are we going to get anyone to volunteer to break their legs 5 times to compare to the guy with broken bones all over from falling off a 5 story building? Technically people survive both all the time, but even if they do you better believe the ambulance will be rushing either way.

[Signmaker]

Lets try common sense instead. Because common sense should apply in games.

Which is more painful, falling 10 feet 5 times, or falling 1 time 50 feet. In game-terms it's 5d6 either way, in reality it's a difference between life and death.

That's debatable. Falling 10 feet assumes that we're not landing how we intend to (hence falling, not jumping as an athlete or tumbling as a stuntman), so that can be quite painful, even lethal (as 1d6 should be to a commoner). Doing it five times in succession is even moreso painful. A fifty foot drop still leaves a chance for survival, but you're likely to be crumpled regardless. So it's more or less a tossup, but close enough in "Ouch" factor that falling rules can get away with it.

[Mike_G]

Lets try common sense instead. Because common sense should apply in games.

Which is more painful, falling 10 feet 5 times, or falling 1 time 50 feet. In game-terms it's 5d6 either way, in reality it's a difference between life and death.

As a Paramedic, I've seen a lot of very bad 10 foot falls.

One guy did die from a roughly 15' fall off the back of a tactor-trailer. Most people don't "survive" a 10 foot fall onto hard ground in such a way that they can get up and keep slaughtering orcs. Falls of 20 feet or more will pretty much always be incapacitating, in that you break something that will keep you out of combat/adventuring if not kill yourself.

Realistic modelling for falls is too mcuh work, and would involve the results of "Winded, Broken arm/leg, Paralysed, and Dead."

Not really any fun for a dungeon crawl.

[Pigkappa]

@Kurald Galain, velocity increases linearly in a free fall

Velocity increases linearly with time, but not with travelled distance. The speed just before hitting the ground is sqrt(2*g*h) (if h is small enough; otherwise, friction should be considered).

if you fall 4 times as far your kinetic energy (and initial potential energy) is still 4 times as much and your velocity is twice as much to match (2 x 2 = 4). So, by real world physics, the damage should be proportional to height.

Nope. The damage should be proportional to the force that's crushing you, and that's proportional to your momentum, not your kinetic energy. That is, it should be proportional to sqrt(E), and therefore sqrt(h).

Nevertheless, I think the rules work quite well for common distances. If you fall down for 3 kilometres, the DM should better decide what happens instead of applying the common rules.

[Yuki Akuma]

At distances like that it doesn't matter if you fall three kilometers or three thousand kilometers - you're going at the same speed. (You hit terminal velocity at about 500 meters - much higher than D&D's 200 feet, but there you go.)

People have survived falls that high. You can fall out of orbit and land safely in one piece not-dead if you survive the friction.

[Signmaker]

People have survived falls that high. You can fall out of orbit and land safely in one piece not-dead if you survive the friction.

Usually due to an obscene amount of luck, and possibly having attempted some form of drag increase. Not something as ridiculous as Angels and Demons, but hey, at that point, any small chance is better than just splattering.

[Yuki Akuma]

Good thing about falling distances that high - you have time to aim. Aim for trees.

[Signmaker]

Good thing about falling distances that high - you have time to aim. Aim for trees.

Anything that yields/breaks, really. Ergo, not the ground. Trees just happen to be nicely noticeable from a bird's view. =)

[Radar]

(...)
Nope. The damage should be proportional to the force that's crushing you, and that's proportional to your momentum, not your kinetic energy. That is, it should be proportional to sqrt(E), and therefore sqrt(h).

Nevertheless, I think the rules work quite well for common distances. If you fall down for 3 kilometres, the DM should better decide what happens instead of applying the common rules.

Damage is proportional to the energy dissipated in the crash. Actual forces applied to crashing objects depend highly on their stiffness and is relevant only, because there needs to be some treshhold tension applied to the bones, muscles, skin etc. to damage them.

[ericgrau]

Velocity increases linearly with time, but not with travelled distance. The speed just before hitting the ground is sqrt(2*g*h) (if h is small enough; otherwise, friction should be considered).

Yeup. And the square of that velocity - proportional to kinetic energy - is directly proportional to height. FWIW terminal velocity is 120 mph which takes at least 450 feet to reach. D&D caps at 200 feet, go figure.

Nope. The damage should be proportional to the force that's crushing you,

Probably, at least in part.

and that's proportional to your momentum, not your kinetic energy. That is, it should be proportional to sqrt(E), and therefore sqrt(h).

No.

EDIT: Ninja'd, but I have a link.

[Signmaker]

I believe the relevant terms required are Force, Impulse, Momentum, Stress.

That is to say, a fall (and the subsequent crash) creates a change in momentum, whose force can be determined via the Impulse-Momentum theorem (knowing the impact time would be important here, but it can usually be estimated). From that force (and the affected area), the stress can be determined. If that stress is above the yield stress of the material, expect it to either permanently deform or even break (depending on material type). Because the human body is so complex and I so lacking of knowledge of it, I can't really help with the calculations, but that should be how it works. From a basic engineering standpoint, at least. Feel free to toss around the physics for the first three terms however you'd like.

[oxybe]

you know, it's folks like you that put us discount catgirl salesmen out of business.

y'all and your "physics" and "verisimilitude" and "realism". back in my day we had rainbow hurling elven princessess fighting tentacle poop monsters and we LIKED it! bah humbug!

now leave me while i clean up this mess...

[Yuki Akuma]

you know, it's folks like you that put us discount catgirl salesmen out of business.

y'all and your "physics" and "verisimilitude" and "realism". back in my day we had rainbow hurling elven princessess fighting tentacle poop monsters and we LIKED it! bah humbug!

now leave me while i clean up this mess...

What a constructive post.

[Worira]

What a constructive post.

What a constructive post.

[Maroon]

Hit points are an abstraction, not a direct measurement. The best way to approach the problem of falling damage would be through statistical analysis of real-world cases, cross-referencing chances of survival of trained versus non-trained sky-divers with high-level versus low-level characters, but that would require actual work to be done.

[Yuki Akuma]

What a constructive post.

I'm glad you agree.

[Darrin]

I was thinking about kinetic energy and falling damage. Shouldn't falling damage be squared? I mean, lets look at basic Newtonian physics, the energy of velocity is velocity^2*mass, if a rock hits you at double speed it smashes into you four times as hard. Shouldn't the same general rules apply to falling damage?

In the original AD&D/1E rules, the falling damage was supposed to be exponential. The first 10' = 1d6, the second 10' = 1d6 + 2d6, the third 10' = 1d6 + 2d6 + 3d6, and so forth. (There was probably some sort of cap to represent terminal velocity, but I can't recall exactly). However, the rules were worded badly enough that everyone who read them thought it was just a straight linear progression, each 10' = 1d6 damage, so 30' = 3d6. Since then, everyone has been playing that way because its very easy to remember and easy to calculate on-the-fly.

And I think in this particular case, over 30 years of playtesting has somewhat proven the point that "simple to remember" and "faster play" trumps accurate real-world physics.