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[khearn]

I just dropped the first four volunteers from test group #3. They were positioned on 4 hatches in the center 4 squares of my 4x4x30z test chamber. All 4 fell at the exact same speed the entire way down, with no lateral motion at all. So the varied speeds and movements in my earlier tests appear to have been imparted by the retracting bridge.

All 4 test subjects completed the test in 44 ticks. All 4 were completely dismembered. One upper arm actually flew up 6 z-levels before falling back down. That's a new league record.

Based in the falling time to the various levels, I'd estimate that the value of g is 0.0315 ± 0.0005 z-levels/tick²

So the time to fall d z-levels would be √(2d/0.0315).

I think I'll extend my test chamber farther downward and see if parts bounce higher. By my calculations, falling the 119 levels that I have room for should take about 87 ticks. At that point they would be falling about 2.75 z-levels per tick. I did see a number of times in this and the previous test when a dwarf would skip level. For instance, they were on level 11 after 35 ticks, and level 9 after 36 ticks. They were never on level 10. Of course, Toady may have established some terminal velocity. If so, I can say that it is higher than 1 z/tick, probably higher than 1.3 z/tick.

I'm also planning on doing some tests with goblins, as soon as some volunteers show up. I expect the first group pretty soon.

[Tryble]

On a slightly more boring note, a goblin standing on a raising bridge will, when the bridge is raised, go flying and may have enough momentum to suffer some nasty injuries.

I witnessed a goblin die from suffocation after being flung by a bridge of mine that was on level ground.

[khearn]

I just did another drop of 4 volunteers down 30 z-levels. It gave almost exactly the same results. Everything was exactly the same on the way down, but one test subject's head set another new league record by flying up 11 z-levels before falling back down.

edit: I observed the head falling back down, and was surprised to see that it fell at a constant rate of 1 z per 6 ticks. I started watching at level 10, and it fell at that rate all the way down to level 0. No acceleration at all from when I started counting ticks. That is also much slower than a dwarf falls. After 10 z-levels, the dwarves were moving at just barely over 1 tick per z-level. So body parts seem to follow different falling rules than living creatures.

[Graknorke]

I noticed this as a thing in adventure mode too, so it's universal. Before a human could take about 6z levels before suffering serious damage, but I recently jumped the same distance on a peasant-level adventurer and only got a broken arm and stunning rather than the full-body shatterfest that would normally happen.
Although looking at mass DOES seem to show the actual mechanics, that light creatures can take seemingly indefinitely long falls.

[misko27]

After reading khearn's tsting, I was inspired to do a little bit of my own regarding animals, with a eye to speeds and landig on one another. I first threw a dingo, who started at a speed of approximately 7ticks a z-level, then accelerated to, uh, 1 or 2 ticks a z-level it alternated, I read that as 1.5) very quickly. He incurred severe injuries, and should by all rights be dying soon. My next subject was a alpaca, to be thrown on top of his body from the height of 12 z-levels (until my miners are free enough to make the pit bigger). He started at a rate of approximately 6 ticks a z-level, and quickly accelerated to a speed of 1 tick a level. Here, the dingo sustained more bruising, but surprisingly less damage then I would expect, the alpaca was uninjured. I once dropped a grackle (which is what? something small I know...) onto a llama, and it shattered the bone, so I expect falling-onto damage is based on number of things that hit it, as the alpaca had multi-hits.

Any suggestions? I have quite alot of animas, and will continue testing.

[Urist Da Vinci]

...
Although looking at mass DOES seem to show the actual mechanics, that light creatures can take seemingly indefinitely long falls.

Are you sure? Mass didn't affect falling damage in previous versions.

Also, I just tested dropping groups of mountain gnomes, cats, giant tigers, and giants in the arena 8z-levels. There wasn't a noticeable difference between the damage that each creature suffered.

[MarcAFK]

In real life cats have a minimum height they need to be dropped in order for their automatic realignment system to engage, any drops below this height may cause impact on any vunerable parts of the creatures anatomy, falls over this height will generally cause the object to land on it's 4 impact absorption pads. There should be no upper limit to survivable drop height as most cats have fairly low terminal velocities, though there may be a difference between naked or highly pelted variants, or between lean and well developed(fat) creatures.

[khearn]

I just dropped 2 dwarves down 59 z-levels. They took 62 ticks until impact. Both were fully disassembled, as expected.

Only one was immediately reported as dead, the other is missing. I guess one lived enough longer to report the first one as dead? Seems unlikely, since they both fell at the exact same rate. Probably a list processing artifact. They were on level 19 at tick 61, but still showing a blue background indicating they were still in flight. So if one got processed before the other within the tick, the second one would be in the same square and still falling when the first one's impact was processed. Then the second one was processed and there was no one alive nearby when his impact was handled, so he was marked as missing. That's my guess.

Based on the new data, I now calculate the value of g to be .032075 ± .000015 Z-levels/tick². I also noticed that there appears to be a slight vertical offset in the level. The timing of the changes from one z-level to the next makes it look like the dwarf started out around 0.3 tiles below the top of the starting point. I'm guessing that's the top of the dwarf's head, and he doesn't appear in the next tile down until the top of his head is below the bottom of the tile he is leaving.

What I mean is that he appears on the first level down when my calculations (based on the value of g above) say he should be at .079, And he appears on the second level when he should be at 1.94, and so on. But if I go with a higher value of g to make those number work, then he ends up way off later on. So i played around with values of g and with offsets and found:
with g at 0.3205, no offset value would work all the way from level 0 to level 59.
With g at 0.3206, an offset of 0.31 worked all the way down.
With g at 0.3207, 0.30 or 0.31 worked.
With g at 0.3208, 0.29 or 0.30 worked.
With g at 0.3209, only 0.29 worked.
With g at 0.3210, no offset worked all the way down.

So that's what I'm basing my estimate of g being .032075 ± .000015 Z-levels/tick² on. It's somewhere between .3206 and .3209, because those are the only values that work.

However, if one assumes that the offset is exactly 0.300000, then g can range from 0.320646 to 0.320881, which gives an estimate of 0.3207635±.00001175 z-levels/tick². That's based on the assumption that Toady has defined the dwarves' height to be a nice round 70% of the height of a z-level. But if he picked a nice round number like that, why did he pick such an odd number for the value of g? It probably becomes a nice number when you convert it into the correct units.

Each tick is 72 seconds (based on 1200 ticks/day). Assuming g is 9.8m/sec², that would make each z-level something like 1500km, which obviously isn't the case. But if you make each level be 2 meters (so a dwarf is 1.4 meters), then you get a g of .000012 m/sec², which is also unreasonable. So whatever we get won't be reasonable because of the time factor. So Toady must have just picked something that would work for gameplay purposes (which is exactly what he should have done).

When I do longer drops I should be able to narrow it down more. Not that anyone is likely to really care about digits 5 or more places to the right of the decimal point.

Whichever value of g you pick from the ranges I've narrowed it to, you still end up with the dwarves moving at 1.99 z-levels per tick when they've fallen 59 levels. I need to dig deeper to see if they'll eventually get going faster than 2 levels per tick. But so far they seem to be continuing to accelerate at a constant rate all the way down. No sign of wind drag.

Nothing bounced more than 2 z-levels up this time, but the only thing that got that high was moving sideways fast enough to hit a wall there, so that probably explains it. the one I saw go up 11 levels in a previous test went all the way up in the same tile that it started. and only moved one tile sideways once it started down. The item I watched this time also took 6 ticks for each level it traversed, both upward and downward. When I get down to the bottom level that I can dig to, I'll probably dig our a nice 40x40x20z chamber so I can let parts fly as far as they want to go without hitting walls.

At this point I'm going to continue digging downward, and I'm also going to start dropping other creatures, plus some inanimate objects to see if they fall differently. Based on the way limbs and heads fly, I suspect it may be the case. Or maybe the bouncing body parts are just using old code made for this special case and Toady missed it in the parabolic arc changes.

[612DwarfAvenue]

Dwarf Fortress: Where people do serious mathmatical research on fall damage values, in doing so also determining the best depth:damage ratio to improve space efficiency for shafts designed to kill via fall damage.

_{I love you guys <3.}

*Meaning, the shafts are just deep enough to do the job, leaving more room for other stuff, instead of being overly deep and taking up space.

[Quietust]

Toady stated in the Future of the Fortress thread that tiles are supposed to be 3 meters tall and 2x2 meters in area. Perhaps this could be used to determine the time scale being used in fortress mode...

[crazysheep]

Toady stated in the Future of the Fortress thread that tiles are supposed to be 3 meters tall and 2x2 meters in area. Perhaps this could be used to determine the time scale being used in fortress mode...

Or we could determine all the physical constants! Who knows, with quantum mechanics already implemented, we might be able to break the speed of light!

[misko27]

Okay, in regards to dropping things on invaders, I did some tests, and frankly I wish I had better news. Only 5% of the dwarves hit their intended targets, as it turns out they have the ability to dodge out of the way, and the fall stuns the dwarves, leading to a massacre of the participants. It terms of armor, it avoids direct injury but keeps them stunned, which in a combat situation could be the difference between life and death. Dropping things is also ineffective, but has a higher rate due to the ability to kill them with sheer nuber of things being dropped, and shows a accuracy of 20%. Dropping can be extremly deadly if done right appearantly. More work to be done

[MarcAFK]

20%, so 5 steel anvils per tile?

[khearn]

Dropped a goblin thief last night. Other than the fact that he started out one z-level lower, everything was the same. When he was being led to the test chamber, I 'v'->'f'ollowed him and stepped it tick by tick. He went from being on the ground at level 0 to being falling at level 1 (numbers increase downward) in 1 tick. But from there everything worked exactly like a dwarf dropped from a hatch on level 1.

I'll drop some animals soon, but first I have to sort through a wave of 33 dwarves that just arrived. I have to pick out the useful ones to become members of the research staff, then put the rest into test groups, being careful to get all the members of a family into the same group. I also have to put anyone from a family with children onto the research staff, since I can't order children into the test chamber, and I don't want children around whose parents have been involved in testing. They tend to get upset and cause disruptions.

[khearn]

I've switched to tests that are a little more useful than just determining the value of g. This time around I dropped 10 dwarven test subjects down 5 z-levels. All were individually positioned on hatches, so there were no interactions between subjects during the course of the test. They took 19 ticks to complete the test. The landing surface was a retractable bridge made of chalk blocks.

Each test subject took 3, 4, or 5 hits on impact. Four subjects took 3 hits each , three subjects took 4 hits each , and three subjects took 5 hits each, for an average of 3.9 hits each. One test subject had his skull pushed through his brain and became an ex-test subject immediately. Four of them took spinal damage (either upper or middle) and are expected to suffer the effects of respiratory failure quickly and pass on to Armok's Final Test Chamber. One had a rib pushed through a lung. One had a shattered hand bone. The remaining three had various bruises, including one bruised arm bone and a bruised liver. All surviving test subjects were stunned.

Hit location	Damage	Count
Head	skull->brain	1
Head	upper spine	2
Throat	bruised throat	1
Upper Body	middle spine	2
Upper Body	bruised lung	2
Upper Body	rib->lung	1
Upper Body	bruised liver	1
Lower Body	bruised guts	4
Lower Body	bruised stomach	2
Lower Body	bruised pancreas	1
Upper Arm	bruised bone	2
Hand	shattered bone	2
Upper Leg	bruised muscle	11
Lower Leg	bruised muscle	6
Toe	torn skin	1

Note that there were no broken bones in arms or legs. The only broken bones at this height were in two hands and one skull. But there was still 50% immediate/short term fatality because of all the spinal damage.

TL;DR: 5 z-levels gave 10% immediate fatalities, 40% short term fatalities, 10% extreme pain, and 40% merely bruised. 100% were stunned.