D&D General Is this a fair trap?

[Democratus]

This is totally where I'd hoped this thread would go!

 

[AbdulAlhazred]

Haha, and it gets a lot worse from there . Gels are non-linear fluids. The maths behind their motion gets very heavy with tensors and co and contravariance, and other such matters.

Re: Your reply to my reply. Yeah, there would be an initial splat, I'm guessing a pretty violent one, with the block stopping very suddenly and a narrow edge of GC material being forced upwards along the narrow edge. Afterwards, probably not very much, just a slow ooze of the GC material up around the edge. Maybe nothing at all, depending on how much shear(?) is needed for the GC material to stop acting like a solid. The block might not create enough pressure to get the GC material to flow.

For the initial impact, I'm thinking the impact time will be a lot less than 1/10 of a second. But that just adds more to the idea of there being an initial violent splat. If there were a simple transfer of energy and momentum (basically, making the GC material a big seesaw), we could estimate how quickly the GC material that is ejected is moving. But, I have no sense of how much of the energy and momentum are transferred to the surrounding rock (or back to the rock that was dropped).

TomB

Well, you COULD assume that the block stops almost completely to start with. Suppose it ejected 1/20th of the volume of the cube? Given that cube has less than 1/2 the density of rock, then it would have to have 40x the velocity. We said 8 meters/sec for the block, so 320 m/sec! Even if I'm generous by an order of magnitude, the stuff is moving at 40 mph roughly. It should manage to travel a pretty fair distance! It COULD well be traveling at several HUNDRED mph. At that point, it is likely to simply travel as far as whatever wall is in the way, underground.

 

[Xetheral]

Well, you COULD assume that the block stops almost completely to start with. Suppose it ejected 1/20th of the volume of the cube? Given that cube has less than 1/2 the density of rock, then it would have to have 40x the velocity. We said 8 meters/sec for the block, so 320 m/sec! Even if I'm generous by an order of magnitude, the stuff is moving at 40 mph roughly. It should manage to travel a pretty fair distance! It COULD well be traveling at several HUNDRED mph. At that point, it is likely to simply travel as far as whatever wall is in the way, underground.

Of course, the farther it spreads the less dense the spray. Even if we assume dead cube stuff is still harmful (after being subjected to a sudden, massive pressure change no less) at some point it's going to be too finely dispersed to be dangerous.

We're firmly out of the rules here, so the DM just needs to decide how dangerous they want the corpse of a cube to be. Just remember that the more dangerous it is, the more valuable the residue will be to the party when they collect it for later use.

Edit: also, your velocity calculation is flawed, as you're not taking into account the direction of the momentum vectors. You can't just assume the magnitudes of the vectors will be conserved. (And since the block and cube aren't a closed system, the initial momentum of then block isn't going to be conserved in the final momentum of the cube anyway.)

 

[Mannahnin]

Historically I usually see dead cube residue treated as losing its paralytic qualities fairly quickly, but not instantaneously.

 

[Istbor]

I'm still not seeing a single scenario which avoids all four of the failure modes for the Yellow Mold that I described. There's just no way around the facts that it only has a 50% chance to go off, and only hits on top of the block (assuming this ludicrous magic rope, magic pulley scenario which is not in the original somehow results in an impact strong enough to trigger it, which is questionable).

Honestly at this point I feel like we should be calling Mythbusters.

Hell, maybe we should do a Mythbusters of old-skool traps? I.e. first we analyze them exactly as written, and probably a lot of them fail, but then we figure out how we could make them work.

If you call your show Trapbusters, and you have an electric personality and high-enough Charisma score, you will have an avid viewer in me.

 

[Xetheral]

Nobody ever explains how the monsters on level 2 manage to get food and such, they just do. This is a given.

I do!

If there is no way for monsters in a given locale to get food, I simply won't put monsters there that need to eat.

More broadly, I won't put any monster anywhere unless there's a good reason for it to be there.

 

[tomBitonti]

A naive analysis:

17 m/h ~ 25 f/s
times
1/10s (or 1/20s or 1/100s)
2.5 f (or 1.25 or f 1/4 f)

The block is almost a cube: 10 f by 10 f by 9.9 f.

0.1 f are shaved off of the front and back of the cube (and not the sides).

A section of the GC with a top area 99 sq ft is displaced by the downward motion of the cube.

The displaced GC material is ejected along the sides of the cube through an area of 1 sq ft.

Based on the relative cross sections (99 sq ft vs 1 sq ft), the material must be ejected at 99x the speed of the descending cube. That is, initially, 25 f/s * 99, about 2475 f/s, or about 1700 mph, decreasing to zero as the block is slowed. This speed is absurdly high. I expect that losses due to an initial shock wave and due to viscous heating would reduce this speed.

How long the block takes to decelerate will be related to energy transfers to the ejected material.

TomB

 

[Xetheral]

Based on the relative cross sections (99 sq ft vs 1 sq ft), the material must be ejected at 99x the speed of the descending cube. That is, initially, 25 f/s * 99, about 2475 f/s, or about 1700 mph, decreasing to zero as the block is slowed. This speed is absurdly high. I expect that losses due to an initial shock wave and due to viscous heating would reduce this speed.

This type of analysis doesn't work either, due to the issue of "choked flow". You can't simply make an opening smaller in order to increase the flow velocity arbitrarily high. I don't know enough fluid dynamics to calculate whether the flow would be choked here, but given the 99-1 ratio you've created, I'd be surprised if it wasn't choked.

Physically, if the opening is too small, the post-impact velocity of the block will simply be limited by the maximum flow rate of the dead cube stuff.

 

[AbdulAlhazred]

This type of analysis doesn't work either, due to the issue of "choked flow". You can't simply make an opening smaller in order to increase the flow velocity arbitrarily high. I don't know enough fluid dynamics to calculate whether the flow would be choked here, but given the 99-1 ratio you've created, I'd be surprised if it wasn't choked.

Physically, if the opening is too small, the post-impact velocity of the block will simply be limited by the maximum flow rate of the dead cube stuff.

Yeah, if the flow rates are beyond a certain point. So, I previously approached this as a momentum transfer, with the assumption that (at least as a first approximation) all the momentum of the falling block was transferred to the cube. However we can approach it in a completely other way which is probably even better.

The block can be thought of as a hydraulic cylinder with an area of approximately 90 ft^2, and the reacting cylinder would then have an area of 10 ft^2. With a ratio of 9:1 the pressure on the reacting side is 9x that on the acting side (it is just like a lever with a 9:1 ratio, basic hydraulics). We established that the PASSIVE pressure on the cub was on the order of 14 PSI, so the passive pressure must be 140 PSI, roughly. This is still enough to eject material with considerable velocity, and only accounts for the block's weight, not its initial downward momentum.

Surely during the deceleration phase the pressure MUST be considerably greater. Here @pemerton calculated the pressure at 100 PSI at the moment of impact, which would imply 900 PSI outflow. Your average power washer is putting out no more than 250 PSI, tops. I think a 10 ft^2 outflow at 900 PSI is going to be a pretty big outflow! Granted, it is probably only happening for a very brief time. Pemerton stated 1/10th of a second for his pressure calculation, so it is a short, but high volume, squirt.

Honestly, if the average speed during deceleration is 4 m/sec and it is 0.1 sec long, then the travel must be .4 meters, which means roughly 5 m^3 or about 50 ft^3 of material was displaced, at decreasing pressures. That should be enough to thoroughly wet anyone or anything within a few meters of the trap. It would certainly be on the order of having a bucket of slime dumped on you!

I also think that the GC slime has to have SOME effectiveness, if only for a very brief time. After all, contact with it is paralyzing, and it certainly doesn't have time to change its bulk chemical composition much in the brief instant it is being splashed... I guess you could suppose that the effect is actually requiring a reaction of some sort involving some complicated dynamic chemical process. More likely the cube stores some of the 'toxin' in its body somehow, or a couple of simple precursors that form a 'binary toxin'. I'd be happy to rule that the save you got was at a bonus. The effect would also probably end fairly quickly, though for the purposes of the trap that probably doesn't matter MUCH.

 

[Ruin Explorer]

Granted, it is probably only happening for a very brief time. Pemerton stated 1/10th of a second for his pressure calculation, so it is a short, but high volume, squirt.

Whilst I don't buy the physics you're going on, even in this scenario, the spray would be pretty much entirely vertical. It would hit the ceiling then spray back down, so you'd probably get the 5' squares on the two shaved sides, and nowhere else.