When objects fall

[arscott]

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.

Momentum is vastly important in collisions. But it's usefullness is in determining movement after collision. for instance, say we have two spheres, moving towards eachother at 10 m/s, one with mass 20 and the other with mass 10. momentum equals mass times velocity, so
the momentum of the first sphere is 200 mkg/s and the momentum of the second sphere is -100 mkg/s (it's negative because it's moving in the opposite direction of the first sphere. This will become important pretty quickly)

In any collision, momentum is always conserved. So if these two spheres collide, the total momentum of the result would be 100 mkg/s. But that momentum could be expressed in different ways. It might mean that the spheres remain in contact and travel at 33 m/s in the direction that the heavy ball was traveling. It might mean that the heavy ball stops but the light sphere bounces and goes 100m/s in the opposite direction. It might mean that both spheres bounce, the heavy one moving away at 50 m/s and the light one at 200 m/s. whatever happens, momentum is contained.

But momentum doesn't really matter much with our specific example. The reason? it's a gravity problem. Gravity is an attractive force exerted by each object in the universe on every other object in the universe. So that means as the earth pulls us towards it, we pull it towards us too. Fortunately, the earth is so much bigger than us that it's safe to ignore that fact in basic falling problems (like the one in my previous post). But it also means that when you gain momentum by falling towards the earth, the earth gains that same momentum by falling towards you. And when you hit, those momentums cancel out.

This assumes no bounce (as did my previous post), but if you've hit the ground hard enough to bounce significantly, then it's probably a moot point.

but the damage dealt isn't determined by momentum. It's deformation.
When you hit the ground, your directional kinetic energy is tranformed into different types of energy. Some is transformed into heat. Some is transformed into sound. But the greatest part of it is removed by the work applied by the stopping force over the deformation distance (or in game terms, 1d6 per 10 feet fallen).

 

[mmadsen]

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 32 feet, but if you fall for twice that time, then you'll fall four times that distance, or 128 feet.

If you fall for one second, you start your fall with a downward velocity of 0 ft/s, and you hit with a velocity of 32 ft/s -- after falling 16 ft.

 

[arscott]

damn! I'll fix that. I also used s(t) = 32t^2 for the position instead of s(t) = 16t^2. But even with the number change, the conclusion remains the same.

 

[Agback]

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

Until they reach terminal velocity, yes.

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

Certainly. It would be too bizarre if they behaved differently from objects with which the players are familiar.

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

I'll assume that you mean 'what are they?' They don't represent things because they aren't symbols.

No-one is quite sure, because they don't answer when spoken to. The Sun says that they are his siblings, but that the family isn't close any more. And he turned out to be right about all the planets revolving around him, even though everyone though it was just egocentricity. So for the time being we'll accept his account. The planets and the moons, on the other hand, are things like the world, except different, so you can converse with them as you do with Gaia. And then there is Indarian….

4. Does water conduct electricity?

Not very well, unless it has an ionic substance dissolved in it.

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

They are consistent.

 

[Agback]

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.

Those two things work out to be exactly the same. Do the math.

After falling for t seconds at an acceleration of a ms^-2, an object has velocity v = at, and has travelled a distance d = 0.5 at^2. Having velocity v, the object has kinetic energy E = 0.5 mv^2 = 0.5 m a^2 t^2 = m a 0.5 a t^2 = m a d.

Thus a constant acceleration produces a gain in kinetic energy per unit mass that is proportional to the rate of acceleration and proportional to the distance travelled under acceleration.

 

[Agback]

but the damage dealt isn't determined by momentum. It's deformation.

That's right. It takes a given amount of energy to produce a given deformation in a given material.

Sure, a bullet of high energy may miss a vital organ. And a slow-moving train may exert only forces that are less than the strengths of the materials of a body, so that one is pushed out of the way rather than injured. Circumstances may allow that much of the energy of an impact will go into, say, deforming the crumple zones of your car, so that less goes into deforming your ribcage. So, it is possible that the energy that goes into debilitating deformations of a person's body my be less than the total energy of a collision, but it can never be more.

If successive blows of a fist or blugeon do damage that [is random but consistent and] adds up linearly, it is consistent that falling damge ought to be [random but with mean] proportional to distance fallen.

 

[Agback]

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.

More accurtely still, transfer of momentum per unit time is 'force'. Impulse equals forces times time (or more accurately, the integral of force through time), and is equal to the change in momentum.

You remember those car safety engineers you mentioned. I used to work for one. He described his art as directing energy into the strucutural members of the car so that it didn't go into the passengers.

 

[fusangite]

Why would I? I'm curious what you do with physics that adds to your game.

For me, a world is a whole package. For most of history, human beings have thought this way and, I believe, still do to a larger extent than we acknowledge. It used to be that the physics of the universe were simply the logical entailment of one's philosophy. In order words, physics and metaphysics have only recently diverged. Or at least we pretend they have diverged. The original philosophy of the Epicureans held that the universe was unintentional, eternal, essentially random and composed of atoms -- they needed to believe the universe was this way in order to justify their semi-hedonistic philosophy of how people should live. Similarly, the Platonists believed the the cosmos was a pale reflection of a perfect immaterial universe made of ideas (forms).

It is only since the scientific revolution that we have reversed this order and tried to figure out the physics of the universe independent of our philosophy. But I don't think this really works. The fact is that as science has determined our universe to be unintentional, random and composed of atoms, people who accept these scientific conclusions have tended to adopt a startlingly large proportion of Epicurean philosophy. Similarly, we find that more and more of the committed Christians of the world are increasingly diverging with science when it comes to questions of science when these scientific truths seem to imply a non-Christian ethical system.

In other words, I believe that it is in the nature of people believe that they reside in a consistent and intrinsically moral universe.

When I run a game, I want my campaign universe to exhibit the same internal consistency that pre-modern people would have demanded of it, first, because it helps to give my campaign worlds a pre-modern feel and second, because when I build a world, a build a consistent whole.

Also, on a more practical level, my players are sufficiently creative that they throw me genuine curve balls where I have to figure out what happens when a magic spell or item interacts with something the rules haven't planned for it to interact with. I don't trust myself to wing it every time that happens because if I do, I'll likely end up with a very inconsistent world.

Finally, and most importantly, in a game where there is magic, I want the magic to actually fit in with the rest of the world's properties. I'm no enamoured of the idea that magic should function as some kind of trump card that temporarily suspends or invalidates the system of physics by which everything else runs. I prefer worlds where magic is a consistent part of a single overarching system of physics rather than a series of isolated yet incredibly frequent moments where the laws of the universe go into retreat. Every culture in which magic has been practiced (or believed to be practiced) has understood magic as part of its system of physics not a separate principle that periodically shuts physics down.

 

[fusangite]

Supplementary Question

I would like to add a question #6 to my list, if people do not mind. It relates to people's responses to the water-electricity question, especially Agback's.

6. How many elements are there in your D&D world? Are there four or are there the 100+ that we have? If there are not 4 or 5, how do you make elementals work in your game?

EDIT: And as for the stars question, I'm interested in what the stars are not what they represent. Sorry for my poor wording there.

 

[Gez]

6. How many elements are there in your D&D world? Are there four or are there the 100+ that we have? If there are not 4 or 5, how do you make elementals work in your game?

Element and energy are synonym. They are the building blocks of the universe. They are countless. The most well-known are:

1. Air
2. Chaos
3. Corrosion
4. Darkness
5. Earth
6. Electricity
7. Entropy (aka negative energy, or decay)
8. Evil
9. Fauna
10. Fire
11. Flora
12. Force
13. Frost
14. Goodness
15. Law
16. Light
17. Magic (aka lei)
18. Vitality (aka positive energy, or lifeforce)
19. Sentience (aka Soul, or Mind)
20. Silence
21. Sound
22. Water

The list is debated, of course. People think every duality (light/darkness, death/life, good/evil, male/female, etc.) should be excluded, other that every one should be included. Some sages lump together darkness, cold, and silence on one side, and light, fire, and sound on the other.

Some argue that the perfect number of element is 256 -- 4 to the power of 4, as 4 is a magic number.

It's believed there are elementals and energons for each of these elements, elemental corresponding to the material aspect, and energons, to the energetic aspect, of the element. Everything has matter and energy, including themselves -- matter has energy, and energy has matter.

Combined with wonky planar anomalies, this leads to interesting things. The elemental planes, for example, are dimensions, not full-fledged planes. They are merely another way to look at the universe, ignoring normal spatial dimensions (so the "geography" of elemental planes do not match with the material plane) and everything that's not the concerned element. But this technique can be used for non-elemental planes as well -- Caleor the Elder, in his time, was famous for his discovery of the "coloural planes", where instead of phasing yourself with only a particular kind of matter, you phased you in a particular shade of color, and found yourself floating in a sea of things of the same color.

EDIT: And as for the stars question, I'm interested in what the stars are not what they represent. Sorry for my poor wording there.

Who knows?