When objects fall

[Baron Opal]

Originally Posted by fusangite
1. Do objects accelerate towards the earth as they fall in your world?
2. Do objects have Newtonian trajectories when they are thrown?
3. What do the stars that people see in heavens actually represent?
4. Does water conduct electricity?
5. Are your world's physics based on a consistent model or do you just make them up as you go?

1. Provisionally. If an object is too high up the earth powers are no longer able to pull the object toward them. They fly in the upper air. As "too high up" is just higher than the highest mountain, it doesn't come up often. I use the arithmetic falling damage.

2. Yes, but as the Earth does not turn beneath them, people do not have the Artilleryman's Dilemma.

3. The legions of the 10,000, lead by the Archangel Polaris. They watch the outer Dark for incursions from the Far Realms.

4. Yes.

5. Both. I attempt to be consistant from an Aristotolean paradigm, taking into account my world's myths. My physics are more "Gloranthan" than Neutonian.

Baron Opal

 

[Mishihari Lord]

That said, gravity on my world works different than in the real world. Instead of gaining a certain velocity per unit time (i.e. 9.8 m/s/s), a falling object gains a certain amount of kinetic energy per unit mass per distance fallen. This conveniently explains why falling 100 feet does exactly twice as much damage as falling 50 feet.

Umm, that actually is how it works in the real world. Change in potential energy = mgh = kinetic energy =1/2 mv^2

 

[Samuel Leming]

So, I thought I would ask:
1. Do objects accelerate towards the earth as they fall in your world?
2. Do objects have Newtonian trajectories when they are thrown?
3. What do the stars that people see in heavens actually represent?
4. Does water conduct electricity?
5. Are your world's physics based on a consistent model or do you just make them up as you go?

1). Yes, but it depends what plane you're on.

2). Yeah. People expect it. On some planes it doesn't work that way.

3). Represent? Like in meaning? The stars mean different things to different cultures. In my game the stars of the prime material plane are much as they are in real life, only smarter. In the astral plane the bright twinkly lights are the projected souls of these same stars. They're watching you.

4). Depends on what's in the water. Sea water will conduct electricity. Water taken from the center of the elemental plane of water would be an insulator until it's contaminated.

5). I make it up based on what I've seen of the real world and how I think a fantasy world should work. I like to think I'm consistent.

Sam

 

[arscott]

The mistake we're making here is that we normally think of falls in terms of time, but d&d handles them in terms of distance. falling acceleration in earth-normal gravity is about 32 feet per second squared*. so if you fall for one second, then you'll fall 16 feet, but if you fall for twice that time, then you'll fall four times that distance, or 64 feet.

But if you fall for ten feet, then you've fallen for ten feet. and if you fall for twice that distance, then youve only fallen twenty feet.

Here's how it works:

t is the time, in seconds, that you've been falling, starting a t = 0
m is the mass of the object in question, in pounds mass
s(t) is you the distance you've fallen with respect to time, in feet, starting at s(0)=0
v(t) is your velocity, in feet per second. v(0)=0
k(t) is your kinetic energy in feet squared per second squared times pounds mass

velocity is the derivitive of positon with respect to time
kinetic energy is velocity squared times mass over two

one of the major laws governing physics is the conservation of energy. energy never increases or decreases, it just changes forms.

at the starting point, all of your energy is potential. That basically means that the energy used to raise the you above the floor is stored inside you, ready to be released when you begin to fall.

Next is kinetic energy. Thats the energy in your motion.

After that it gets messy. When you hit the ground, your kinetic energy is transformed into all kinds of energy. The effects of that energy are represented by damage in the D&D world.

So the amount of damage you take is proportional to your kinetic energy when you hit the ground. And since we want to find out how your damage varies with respect to the distance you fall, we're trying to find the derivative of your kinetic energy with respect to your position.

you position the distance you've fallen, so
s(t) = 16t^2

your velocity is the derivitive of that with respect to time, so
v(t) = d/dt 16t^2
v(t) = 32t

your kinetic energy is the square of your velocity times mass, so
k(t) = (32t)^2*m/2
k(t) = 32m * 16t^2

but there's a 16t^2 in there. that's the position. so we can just say
k(t) = 32m*s(t)

we're trying to the derivitive of kinetic energy with respect to position, so we can just differentiate both sides with respect to s(t)
dk(t)/ds(t) = d/ds(t) 32m*s(t)
dk(t)/ds(t) = 32m

the derivitive is a constant, which means the relationship is linear. If you fall twice the distance, you take twice the damage. which is exactly how it's represented in d&d.

What's interesting to note is that the mass doesn't cancel out. Thus, the larger you are, the more kinetic energy you have. But given that big creatures take no extra damage from Area effects despite taking up a greater portion of the effected area, you could argue that hit-points are already adjusted for size.

Of course you could also argue that your gnome should only take 1/6th damage from the fall 'cause he's 1/6th the mass of everyone else, but I'll leave that up to you and your DM.


*pardon my use of imperial units in a discussion of physics, but it's a hell of a lot easier this way 'cause the important figures are a power of two. plus, that's what d&d uses.

Edit: Aaagh. I spent three hours on this thing. Now I remember why I switched majors to Theatre Arts.

Edit two: I initially made an error regarding the equation for position, which is s(t) = 16t^2, not s(t) = 32t^2. madsen this out. It is now fixed.

 

[hong]

Theorem: like any movie, any post is improved by the mention of pants.

Proof: observe.

As evidenced in some of my recent contributions, over the past few years, I have become more and more convinced that the pants of the worlds described in the core rules of D&D 3.5 are governed by Aristotle's physics. There is the matter of there being 4 pairs of pants instead of 100+, the fact that a number of pants have fixed GP values pegged to real world physics and the fact that when pants fall, the falling damage increases arithmetically instead of geomatrically; plus, unlike present-day physics, Aristotelian physics offers a number of solid theories for how pants work. Obviously, this is pretty convenient when one is faced with pants problems that arise in your game that are not covered in the core rules such as what happens when water and pants interact, the trajectory of thrown pants, the nature of the universe beyond the upper waistline, or the consequences of dumping a bunch of unexpected crap into your pants. But I get the sense that very few people view pants in D&D the way I do.

 

[diaglo]

what goes up. must come down when it takes 25% of its hps in damage.

or what goes up must come spiralling uncontrollably down when it takes > 50% of its hps in damage

 

[D+1]

1. Do objects accelerate towards the earth as they fall in your world?

One current theory at The School of Ancient Knowledge holds that damage resulting from falls is caused by uncontrolled elemental forces of air and earth, occasionally air and water.

2. Do objects have Newtonian trajectories when they are thrown?

Who is this Newtonia you speak of? If you mean do they have arcing trajectories, yes. But so rarely do the severity of the arcs matter that they are routinely ignored.

3. What do the stars that people see in heavens actually represent?

There are currently 43 recorded theories and 11 verified, yet conflicting firsthand accounts.

4. Does water conduct electricity?

I do not understand your question. The element of water has many effects as does the element of fire. Water, for example, can be breathed by many creatures, but fire can only be breathed by elemental creatures of fire. Lightning generated by spells travels in a straight line through the element of air but in water has different effects.

5. Are your world's physics based on a consistent model or do you just make them up as you go?

It was once posited that there is but a single, consistent, physical model that governs all aspects of the world but the myriad of conflicting experimental results and continued discovery of new theories and new effects conclusively disproves this notion. There are many physical models that govern the world and they are often inconsistent.

 

[Voadam]

Ummm, the damage system for falling in D&D does apply acceleration - it is the increased velocity that imparts the increased damage.

The stupid ! damage, where 10 ft. does 1d6, 20 does 3d6 is pretty ridiculous from a real world standpoint, most people the real world will walk away from a 20 foot fall, in D&D that would knock most people (not PCs, but Joe Bloke the 1st level Commoner) into negative hit points. Of course the difference in surviving a 20 foot fall vs. surviving a 30 foot fall are pretty large, so while Joe Bloke will likely survive a 20 foot fall, 30 foot will still knock him into the negatives.

The Auld Grump

*EDIT* ! in this case is the symbol for this kind of increase, not an exclamation...

Assume a level 1, 10 Con commoner or wizard with 2 hp. 3d6 damage from a 20 foot fall with ! damage = an average of 10.5 damage, knocking them to -8.5 damage, which is at risk of dying but not dead. 30 feet would be average of 21 damage killing them. This seems to fit your survival at 20 but not 30 foot falls better than arithmetic falling damage. Arithmetically a 10 foot fall will knock them to -1.5, 20 feet to -5, 30 feet to -8.5 and 40 feet to -11 and dead.

So in arithmetic damage a commoner will not walk away from a 10 foot fall and the average adventurer can walk away with little problem from ridiculous heights.

So under either model low level people do not walk away from any falls, the difference comes with mid to higher level PCs and hp creatures when they fall significant distances (20, 30 or more feet).

With accelerating damage falls from significant heights are still serious for higher level characters. IMO arithmetic falling damage makes falling from significant heights insignificant for PCs. Jumping off of cliffs onto rocks a hundred feet below should not be so viable an option for high level non-flying mortals not employing magic to aid them.

 

[AuraSeer]

Umm, that actually is how it works in the real world. Change in potential energy = mgh = kinetic energy =1/2 mv^2

I should explain that in my gameworld, the term "kinetic energy" means something different. Neither mgh nor mvv/2 is a meaningful equation, because the very concepts of motion,position, and energy have different physical underpinnings. Conveniently, this prevents the physicist and engineer players from arguing about what is possible.

There is a concept that works kind of like potential energy, only backward. It depends not on gravity, but on the force that lifted the object from the ground. If an object's mass changes in midair, and the now-heavier object falls to the ground, it does damage for its original mass. (For instance: if you throw a pebble and immediately polymorph it into a boulder, it does damage as a pebble. If a druid in hummingbird form changes into a rhino and drops on an enemy's head, the enemy may be startled but will take no damage.)

 

[Umbran]

...the derivitive is a constant, which means the relationship is linear. If you fall twice the distance, you take twice the damage. which is exactly how it's represented in d&d.

Except that in the real world, transfer of energy is in no way the whole story. Frequently, transfer of momentum (or, more accurately, transfer of momentum per unit time, or "impulse") is what determines what happens.

There is a reason why there are mechanical engineers who get paid lots of money to design cars to deal with various impacts - collisions of real objects get very complicated very quickly. The D&D system is a pleasantly easy abstraction, but likening it to real-world physics is probably not a good idea. The analogies fail quickly.