Crawl Physics

[Igxfl]

The three basic units of measurement in Crawl are well known:
aum (mass)
aut (time)
tiles (length)

We can thus say that a wand masses at 10 aum, or that the typical Ticktocktomancer moves at .05 tile/aut.

These units reveal much more about the Crawl universe than it initially appears. Some brief consideration will reveal several important properties of the dungeon. For example:

Str is clearly a unit of force, and one Str equals the amount of gravitational force typically exerted on 30 aum, so the local gravitational field g is equal to .033 Str/aum.
This is an interesting conclusion indeed, since projectiles are never observed spending more than 1 aut in the air. Throwing a rock in an arc from just near the floor to just near the ceiling and back again should maximize the time it spends aloft, which is presumably necessary to obtain maximum range. Since this still takes at most 1 aut, the maximum height of the ceiling can be calculated as h = .5g(.5t)^2 = .5*.033*(.05)^2 = .00004125. Everything in Crawl would thus appear smooshed and pancake-like to us, although they are probably too used to it to notice, and don't think of "up" or "down" except as regards stairs. It is widely suspected that Cheibriados performs "Step from Time" by knocking his followers out and gluing them to the ceiling.

The entire main dungeon could be almost as thin as .00004125*27 = .00111375 tiles. However, it seems likely that side branches are discreetly sandwiched between the main floors, so that all of lair could be jammed in between D:10 and D:11, with all of Shoals then between Lair:4 and Lair:5. The stairways between D:10 and D:11 would then cut straight through all of the Lair levels, which are so thin that no one notices the gap. This explains how two adjacent stairways can lead to entirely different levels. These incredibly thin levels also explain more minor mysteries, such as the inability of a tengu to fly over an iguana,or even lob a projectile over it -- the ceiling is simply too low.

Lightspeed in Crawl is 8 tiles/aut. Nothing is observed moving faster that this, and 8 tiles is the universal limit of LOS because the light from objects outside of that range hasn't reached you recently enough to provide accurate information. This explains why Darkness and Nightstalker also change the range of projectiles -- these effects actually modify the speed of light, limiting the maximum velocity with which projectiles can be thrown.

There are a few exceptions to the lightspeed rule. Long-range teleportation occurs via wormholes through the Abyss (obviously). Teleportation delay occurs because it takes time to establish a wormhole, unless you use a trap, which keeps one up all the time. Detection effects, which can allow you to know things about faraway tiles before light can reach you, is the result of quantum entanglement, which is also suspected to be the underlying principle behind cursed equipment. These two loopholes in Crawl's natural law are the fault of Lugonu and Ashenzari, respectively, and Zin still refuses to invite them to parties.

And now, the question we've all been waiting for:
Q: If my Ogre can throw a large rock at near lightspeed, why can Iron Shot, travelling far more slowly, do more damage?
A: An Iron Shot weighs several hundred aum and barely fits in a single tile.
Q:If that were true, wouldn't it be more accurate?
A: Of course not. Since Crawl monsters are pancake-flat, it often flies right over them.

[Amnesiac]

this is hilarious

[Grimm]

Everything in Crawl would thus appear smooshed and pancake-like to us

And in fact does in tiles. Notice how everything is depicted from a side view and not top down as you'd expect. The character is literally crawling on his belly through the dungeon.

[Amnesiac]

crawling on his belly

More like on his back

[Grimm]

Well he flips around every turn so the CCTV can get his face. He doesn't want to die anonymously.

[tcjsavannah]

And in fact does in tiles. Notice how everything is depicted from a side view and not top down as you'd expect. The character is literally crawling on his belly through the dungeon.

Just like a bird. Delicious.

[Siegurt]

Out of curiosity, one of your initial assumptions is:

projectiles are never observed spending more than 1 aut in the air.

However, it takes a minimum of 3 aut to fire a weapon (That being a bow with finesse active), a full 10 to throw a large rock, now while it might only take 1 aut for a projectile to reach it's destination, I wonder what evidence you have for that.

One could assume that throwing a large rock takes a nearly full 10 aut to reach it's destination, whereas it's reasonable that casting a spell (A much more complicated operation than throwing a rock, you must admit) probably takes a large chunk of the 10 aut the entire operation takes, and the iron shot's velocity might be something close to the speed of light.

[Amnesiac]

Out of curiosity, one of your initial assumptions is:

projectiles are never observed spending more than 1 aut in the air.

However, it takes a minimum of 3 aut to fire a weapon (That being a bow with finesse active), a full 10 to throw a large rock, now while it might only take 1 aut for a projectile to reach it's destination, I wonder what evidence you have for that.

One could assume that throwing a large rock takes a nearly full 10 aut to reach it's destination, whereas it's reasonable that casting a spell (A much more complicated operation than throwing a rock, you must admit) probably takes a large chunk of the 10 aut the entire operation takes, and the iron shot's velocity might be something close to the speed of light.

wasn't it 0.2 with haste? same with a rock, it's 0.5 with finesse and 0.3-0.4 with haste

[DracheReborn]

Out of curiosity, one of your initial assumptions is:

projectiles are never observed spending more than 1 aut in the air.

However, it takes a minimum of 3 aut to fire a weapon (That being a bow with finesse active), a full 10 to throw a large rock, now while it might only take 1 aut for a projectile to reach it's destination, I wonder what evidence you have for that.

One could assume that throwing a large rock takes a nearly full 10 aut to reach it's destination, whereas it's reasonable that casting a spell (A much more complicated operation than throwing a rock, you must admit) probably takes a large chunk of the 10 aut the entire operation takes, and the iron shot's velocity might be something close to the speed of light.

On your first point, I think the fact that Finesse can cut a bow's delay in half strongly implies the largest part of the delay comes from wielding the bow, not from the projectile traveling to its destination. If Finesse actually increases projectile speed instead of bow wielding speed, then the damage should increase with Finesse right? But it doesn't.

I agree with your second point though, there's nothing that says it takes Iron Shot 10 auts to reach its target. Again using the logic that Haste can speed up Spellcasting, this seems to imply that majority of delay incurred is in the casting itself, not in the traveling time of the Iron Shot.

The bigger mystery to me is how projectiles (whether from spell or launcher) always take the same time to reach their destinations, whether it's at range 2 or range 8. This means either a) projectiles are traveling *very* fast, like say 3*10^8 tiles/aut, so the difference in delay to reach 2 tiles or 8 tiles is negligible; or b) that crawl is actually some weird hyperdimensional space where all points in the 2-D grid (at least in LOS) is actually equidistant to each other.

If (a) is true, this violates the postulate that lightspeed is the fastest thing in the (crawl) universe. Even mundane projectiles travel faster. If instead (b) is true, then the familiar 2-dimensional representation of crawl is actually a lie, in reality we should be able to move anywhere on the grid instantaneously, if only we had Lugonu's knowledge of loopholes.

Actually, my theory is that all of crawl is actually just a dream of Xom, and that when Xom wakes up all crawl would end. But this is an unprovable hypothesis (unless it actually happens of course)

[1010011010]

Thanks to this thread I actually ran some tests, there are a few assumptions, but I'm a physicist and that's what we do.

  Code:

human corpse 55 aum
real average human 62 kg

1 kg = 1.127 aum
1 aum = 0.887 kg

plate armour 65 aum
real plate armour = 20 kg

1 kg = 0.308 aum
1 aum = 3.25 kg

therefore the corpse is not complete or crawl armour is super heavy.

hill giant corpse = 170 aum
human = 55 aum

let's assume that both are of similar proportions, composition and loss of material on death

a hill giant is 170/55 times as large = 3.1 times.

therefore approximately 18 ft and 18ft in arm span

a titan (said to be big even for giants) is 320/55 = 5.8 times

by the same principle a titan is 35 ft tall and has a span of similar size.

a tile minimum size is thus 35 ft, to be able to fit a titan in one square.

current marathon record is 2:03:38 or 7418 seconds

that's  42.195 km or  42195 m in 7418 seconds

an average speed of 5.69m/s!

assuming your crawl character is running marathons not sprint, and at record pace, to be able to clear one tile in 1aut

is to run 35 ft (10.6m) at a rate of 5.69m/s

therefore 10 aut = 10.6/5.69 = 1.9 seconds.

a tile could be bigger, and a human could run slower. I would say this is a generous amount.


starve test
engorged at turn count 3648.7
starving at turn count 7311.7
death at turn count 7610.7

36630 aut till starving
39620 aut to die

Mahatma Gandhi survived 21 days without food, out hero cannot survive 2 hr, 5 mins, 27.8 seconds


[Igxfl]

Out of curiosity, one of your initial assumptions is:

projectiles are never observed spending more than 1 aut in the air.

However, it takes a minimum of 3 aut to fire a weapon (That being a bow with finesse active), a full 10 to throw a large rock, now while it might only take 1 aut for a projectile to reach it's destination, I wonder what evidence you have for that.

One could assume that throwing a large rock takes a nearly full 10 aut to reach it's destination, whereas it's reasonable that casting a spell (A much more complicated operation than throwing a rock, you must admit) probably takes a large chunk of the 10 aut the entire operation takes, and the iron shot's velocity might be something close to the speed of light.

Imagine a large pack of centaurs in which one centaur fires an arrow each and every aut. This is entirely possible in Crawl, if not distressingly common. You as a player, no matter which aut you happen to act on, will never get to take an action while one of the arrows is in the air. Thus, each arrow is in the air for 1 aut at absolute most.

[Siegurt]

Out of curiosity, one of your initial assumptions is:

projectiles are never observed spending more than 1 aut in the air.

However, it takes a minimum of 3 aut to fire a weapon (That being a bow with finesse active), a full 10 to throw a large rock, now while it might only take 1 aut for a projectile to reach it's destination, I wonder what evidence you have for that.

One could assume that throwing a large rock takes a nearly full 10 aut to reach it's destination, whereas it's reasonable that casting a spell (A much more complicated operation than throwing a rock, you must admit) probably takes a large chunk of the 10 aut the entire operation takes, and the iron shot's velocity might be something close to the speed of light.

Imagine a large pack of centaurs in which one centaur fires an arrow each and every aut. This is entirely possible in Crawl, if not distressingly common. You as a player, no matter which aut you happen to act on, will never get to take an action while one of the arrows is in the air. Thus, each arrow is in the air for 1 aut at absolute most.

Well, that does presume that the centaurs act as fast as they can and don't simply wait to start firing their arrows until you start some action (giving their arrows the full time that your action will take in the air) and that they don't simply act in response to your actions, however given the behavior of all things, it seems very probable that each arrow is in the air for <1 aut.

Next challenge to your hypothesis:

Throwing a rock in an arc from just near the floor to just near the ceiling and back again should maximize the time it spends aloft, which is presumably necessary to obtain maximum range. Since this still takes at most 1 aut, the maximum height of the ceiling...

When throwing or firing a weapon, it's true that flying close to the ceiling would maximize your range (With some allowances for projectile shape), however in this game you are firing *at* something not firing for maximum range. It's entirely possible in the craw universe, maximum range is, in fact, beyond your event horizon (LOS) perhaps things only spend <1 aut in the air because we aren't firing anywhere close to the maximum potential range, and the maximum potential range of a projectile would leave in the air for 2, 3, or 4 aut, but that would put it so far outside our perception range as to be unknowable. If there was a "throw a rock as high as you can straight up and count until it hit's the ceiling or comes back down" command we could verify this, but it doesn't look to me like you can verify this with the information available to you.

As I understand it the premise for your argument is "Since projectiles can only be in flight for 1 aut at max, it takes at most 1 aut for them to fly from floor to ceiling and back again" which presumes an action which cannot be taken (Throwing something up until it hits the ceiling) and therefore can not be verified.

While there is some anecdotal evidence which lends credence to your hypothesis that the world is near-flat (e.x. flying creatures not being able to fly over other ones) there are other possible explanations. (For example a tengu might not fly over a lizard for fear of the lizard suddenly gaining the ability to jump up and bite him in the nethers, or he's just to angry at the lizard and *must* go down and attack the lizard for behavioral reasons that have nothing to do with it being a physical impossibility)

Challenge #2:

The bigger mystery to me is how projectiles (whether from spell or launcher) always take the same time to reach their destinations

Why is this true? The current working theory is that it takes <1 aut for a projectile to travel from it's source to it's destination, which is between 2 and 8 squares away, there's nothing to say that that it doesn't take say, 0.2 aut for it to travel 2 squares and 0.8 aut for it to travel 8 squares, at least I've seen no argument to reason the contrary.

[le_nerd]

Projectiles do not travel widest when thrown as high as possible; have a look at http://en.wikipedia.org/wiki/File:Ideal_projectile_motion_for_different_angles.svg for comparison!

As for the weight/height of members of the species Gigantus, lets remember thehttp://en.wikipedia.org/wiki/Square-cube_law; if an ordinary human/hill giant/titan is 55 vs 170 vs 320 aum, we can come to the proportional height by taking the third root of their relative weights. This yields that a Hill Giant is 1.45 times as big, and a titan 1.8 times as big as a human.

Of course under the strange physics we would need other evidence that the square-cube-law is still valid; one could try and look at strength/carrying capacity and thereby muscular cross-section of average adult specimen. It should vary as the square root of the relational weights. For Felid/Human/Troll base strength is 4/8/15, with an added 2.3 averaged about all possible backgrounds. Weight is 20/55/155; relational strength with human baseline is 0.5/1/1.87. Values for the square rooted weight relations are: 0.6/1/1.67.

As we can see, it seems that the crawl universe holds to some degree to the square cube law but also that titans are pretty small. Deep water is not that deep at all!

[Igxfl]

Projectiles do not travel widest when thrown as high as possible; have a look at http://en.wikipedia.org/wiki/File:Ideal_projectile_motion_for_different_angles.svg for comparison!

I had assumed firing most projectiles at 45 degrees would hit the ceiling, but perhaps not.

Say a Magic Dart, capable of course of speeds up to 8 tiles/aut, doesn't hit the ceiling. Fired at 45 degrees, and assuming 1 aut in flight, its vertical velocity goes from .707*8 = 5.656 tiles/aut to 0 in .5 aut. Thus, g is 11.312 tiles/aut^2. Since we already know that g = .033 Str/aum, we can say that 11.312 tiles/aut^2 = .033 Str/aum.

Alternately written, 1 Str = 343 aum*tiles/aut^2.

Thus, a 3 Str Spriggan Wizard, given proper leverage, can accelerate a Titan corpse (320 aum) to a velocity of roughly 3 tiles/aut in 1 aut. In practice, however, they can only throw such corpses a single tile in 10 aut. Since the Spriggan presumably is able to shove on the corpse for the entire 10 aut to move it (it doesn't even get out of UC range, after all) the corpse is only accelerating by a = 2x/(t^2) = 2*1/(10^2) = .02 tiles/aut^2, meaning that only about .02*320/343 ~= .02 units of Str are being exerted on it.

I can only conclude that all surfaces in the dungeon are incredibly slippery. Objects and creatures in the dungeon are not usually observed sliding around, so it also appears that the air in the dungeon is incredibly thick. When running, characters appear to be sprinting in place cartoon-style while slowly gliding forward. This explains why Airstrike and Tornado deal so much damage, and why eyeballs and the like can just float in midair. Most "projectiles" are easier to dodge than one might expect because they move surprisingly slowly through this soup in a paper airplanes than arrows. Evasion basically happens in slow motion, and the Dodging and Weapon skills mainly involve learning to move more aerodynamically. Haste covers you in highly aerodynamic but slightly carcinogenic varnish. Swiftness makes your shoes slightly sticker.

This also offers a possible alternative to the lightspeed LOS hypothesis: air resistance makes travel faster than 8 tiles/aut practically impossible. There are also enough bits of opaque crud suspended in the air to prevent sight beyond this range (Sandblast uses "ambient grit", which can't mean ordinary dust). Darkness and Nightstalker just make the air thicker, slowing the maximum practically obtainable speed even more and allowing additional dirt to float around.

Q: Wait, your first calculation assumed ideal projectile motion, and then you use it to conclude ludicrous amounts of air resistance! I think you're full of shit!
A: Magic Dart is infinitesimally tiny and extremely dense, so it is virtually unaffected by air resistance. It moves quicker than almost anything else through Crawl's air-soup, which is why it always hits. However, casters still can't see beyond 8 tiles in order to properly target one.

[Lokkij]

I can only conclude that all surfaces in the dungeon are incredibly slippery.
[...]
the air in the dungeon is incredibly thick
[...]
the Dodging and Weapon skills mainly involve learning to move more aerodynamically.
[...]
Swiftness makes your shoes slightly sticker.
[...]
I think you're full of shit!
[...]
Magic Dart is infinitesimally tiny and extremely dense
[...]
Crawl's air-soup

You're so very crazy.
Marry me.

[Lokkij]

Since this still takes at most 1 aut, the maximum height of the ceiling can be calculated as h = .5g(.5t)^2 = .5*.033*(.05)^2 = .00004125. Everything in Crawl would thus appear smooshed and pancake-like to us, although they are probably too used to it to notice, and don't think of "up" or "down" except as regards stairs.

So we just deduced monsters are very flat because of the really low ceiling.

Q:If that were true, wouldn't [Iron Shot] be more accurate?
A: Of course not. Since Crawl monsters are pancake-flat, it often flies right over them.

How can we be sure this is possible? We didn't calculate the height of the monsters; it's entirely possible they fit in exactly, making it impossible for anything to fly over it.

Physicists, go!

[Siegurt]

Since this still takes at most 1 aut, the maximum height of the ceiling can be calculated as h = .5g(.5t)^2 = .5*.033*(.05)^2 = .00004125. Everything in Crawl would thus appear smooshed and pancake-like to us, although they are probably too used to it to notice, and don't think of "up" or "down" except as regards stairs.

So we just deduced monsters are very flat because of the really low ceiling.

Q:If that were true, wouldn't [Iron Shot] be more accurate?
A: Of course not. Since Crawl monsters are pancake-flat, it often flies right over them.

How can we be sure this is possible? We didn't calculate the height of the monsters; it's entirely possible they fit in exactly, making it impossible for anything to fly over it.

Physicists, go!

I think the conclusion goes the other way 'round' i.e. "If monsters took up the entire square, your iron shot couldn't pass through said square and also miss them"

The fact that you can miss implies that there's *some* space in which the two could occupy the same square without touching.

[Lokkij]

Since this still takes at most 1 aut, the maximum height of the ceiling can be calculated as h = .5g(.5t)^2 = .5*.033*(.05)^2 = .00004125. Everything in Crawl would thus appear smooshed and pancake-like to us, although they are probably too used to it to notice, and don't think of "up" or "down" except as regards stairs.

So we just deduced monsters are very flat because of the really low ceiling.

Q:If that were true, wouldn't [Iron Shot] be more accurate?
A: Of course not. Since Crawl monsters are pancake-flat, it often flies right over them.

How can we be sure this is possible? We didn't calculate the height of the monsters; it's entirely possible they fit in exactly, making it impossible for anything to fly over it.

Physicists, go!

I think the conclusion goes the other way 'round' i.e. "If monsters took up the entire square, your iron shot couldn't pass through said square and also miss them"

The fact that you can miss implies that there's *some* space in which the two could occupy the same square without touching.

You're right with your first point. However, how can we know all monsters have the same square-filling width? Monsters are classified as "big" and "small", and because the difference in height is negligibly small, their width would be larger. This means some monsters will not fill the whole square, which means the projectile can just fly past them. Igxfl assumed the projectile almost filled the whole square, but I can't see what he based that on. If it's because the projectile is so incredibly heavy, couldn't it just be extremely dense?

[Siegurt]

But if creatures fill the entire square from bottom to top, then what does it mean to be "flying"?

[Amnesiac]

I think 3d universe laws of physics don't apply to possibly a 2d universe of crawl. also flying or size of creatures doesn't mean the same thing in the universe of crawl, seeing how a bee and a giant or two bees can't fit into one tile. Tiles are either passable or not and that probaby doesn't have to do anything with size or height but with some kind of a passability property. For example flight makes you adjusted somehow to lava and water, so other species are adjusted to only one of them from the beginning. Evasion gives one a chance to be passable for projectiles, too. Well, I'm not in a mood to elaborate upon a subject, but what I wanted to say is - not so fast with judging by laws of physics that you can learn in our universe.

[1010011010]

seeing how a bee and a giant or two bees can't fit into one tile.

In Crawl, we respect personal space.

[Turukano]

We didn't calculate the height of the monsters; it's entirely possible they fit in exactly, making it impossible for anything to fly over it.

I'm not sure about this. Already Siegurt mistrusted your theory.

I think the conclusion goes the other way 'round' i.e. "If monsters took up the entire square, your iron shot couldn't pass through said square and also miss them"

The fact that you can miss implies that there's *some* space in which the two could occupy the same square without touching.

This is a hint the theory is dubious. But you can definitely prove it's wrong, it's a little test which doesn't take much time.

• Start a new game.
• Select TrHu with large rocks.
• Type 'ff' (depending on your settings you might have to confirm this). If your troll fits in exactly there will be no space between him and the ceiling and so he can't throw rocks on himself.
• Repeat previous step.
• Post your game at YAVP/YASD forum if you like.

[Lokkij]

the inability of a tengu to [...] lob a projectile over it

[Iron Shot] often flies right over them.

Well, something is wrong here.

[Confidence Interval]

Type 'ff' (depending on your settings you might have to confirm this). If your troll fits in exactly there will be no space between him and the ceiling and so he can't throw rocks on himself.

He could be holding them at arm's length and lobbing them at himself. I've just tried this with a paper ball and it is impossible. This suggests to me your test cannot definitively answer the question that you propose to use it to answer.

[Turukano]

Magic Dart is infinitesimally tiny

This is not right for an entire crawl game, it's only valid in the first 5.391* 10^-44 seconds after you entered the dungeon.

[rebthor]

I think 3d universe laws of physics don't apply to possibly a 2d universe of crawl. also flying or size of creatures doesn't mean the same thing in the universe of crawl, seeing how a bee and a giant or two bees can't fit into one tile. Tiles are either passable or not and that probaby doesn't have to do anything with size or height but with some kind of a passability property. For example flight makes you adjusted somehow to lava and water, so other species are adjusted to only one of them from the beginning. Evasion gives one a chance to be passable for projectiles, too. Well, I'm not in a mood to elaborate upon a subject, but what I wanted to say is - not so fast with judging by laws of physics that you can learn in our universe.

And yet there must be room for two monsters to move past each other because we can experience this with friendly summons and with pack creatures switching spaces. A conundrum.

[Amnesiac]

I think there is some other principle for that, like they pass through each other, because they are friends or something, because other monsters can't do the same.

[Grimm]

quantum entanglement

[Scrotar]

Good post, make more.

[Matanui3]

This also explains how mimics can pretend to be stairs going downward (and thus into the floor), if the concept of up and down is not really noticed.

Q: Wait, your first calculation assumed ideal projectile motion, and then you use it to conclude ludicrous amounts of air resistance! I think you're full of shit!
A: Magic Dart is infinitesimally tiny and extremely dense, so it is virtually unaffected by air resistance. It moves quicker than almost anything else through Crawl's air-soup, which is why it always hits. However, casters still can't see beyond 8 tiles in order to properly target one.

Or Magic Dart is magic, and thus unaffected by air resistance.
Also, it probably just flies straight, no angle required for max distance. All of the power it doesn't have in its damaging capabilities went into an advanced tracking system.

[BlackSheep]

This also explains how mimics can pretend to be stairs going downward (and thus into the floor), if the concept of up and down is not really noticed.