# Glass hitting water at terminal velocity [closed]

I have a setting where technically sophisticated but underequipped humans are resorting to improvised chemical weapons in a war against Lovecraftian monsters, and am trying to figure out the exact mechanics of using a jar of concentrated dioxin as a chemical bomb. So...

Will a 20 liter glass jar full of liquid reliably shatter if it hits water at terminal velocity? A human hitting water at terminal velocity will die; I'm not sure how glass compares.

If so, from what height would you need to drop such a jar for it to reach terminal velocity?

## closed as off-topic by Vincent, Hohmannfan, fi12, Aify, Xandar The ZenonMar 2 '16 at 4:47

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• How thick is the jar? Why are you modelling your monsters as bags of water? Don't they have exoskeletons or internal structures? I'm trying to suggest that you need to specify the situation in much more detail if you want a credible answer. – WhatRoughBeast Mar 1 '16 at 16:38
• Did you need to create three brand new tags for this question? Wouldn't science-based and weapons work? – Frostfyre Mar 1 '16 at 16:54
• @WhatRoughBeast I don't know how thick the jar needs to be; enough to safely contain twenty litres of fluid during transport and handling. How thick is that? The monsters aren't being dropped; they're Deep Ones and suchlike, but the important thing is that they live in the water and will get sick and die if the dioxin contained in the jars is successfully delivered to their habitat. – rwallace Mar 1 '16 at 16:55
• Although your motivation for asking thus question is for worldbuilding, your inquiry is about real-world physics. Belongs on physics.SE IMO – NauticalMile Mar 2 '16 at 4:03
• @NauticalMile for the record, I think this would need a bit of rewriting to be appropriate on Physics. Right now it reads like a "please calculate [thing] for me" kind of question, which we don't like, but it could probably be rewritten into a "I tried to calculate [thing] and got confused about [conceptual issue]" kind of question which would be a lot better. – David Z Mar 2 '16 at 15:50

# Compressibility of water

The old "hard as concrete" saying has much to do with the fact that water resists compression very well. Thus, if the jar hits the water (at less than terminal velocity, even if the glass is quite thick), the water will not compress enough to provide much cushion, so the glass will shatter. At slower speeds, the effects of breaking surface tension (think: water "getting out of the way" or making a splash) would allow the jar to splash into the water.

# Dioxin liquid

Unfortunately, your specification of "liquid dioxin" creates a slight problem:

I don't know which dioxin you are referring to, but TCDD is a commonly known one, so I'll go with that.

TCDD is solid at room temperature, and unfortunately not very soluble in water ($0.2 \mu g / L$), which only allows for $4\mu g$ of dioxin in your 20L delivery container, which probably wouldn't kill anyone by the time it's further diluted in the target body of water. (Lethal dose in rodents varies between $1-1000 \mu g/kg$).

To wit, it would probably take in excess of twenty such canisters to kill a single human-mass monster and that's if they somehow managed to ingest all of the toxin from every jar, which is very, very unlikely given the delivery method. Clearly, they'll need the concentrated solid.

If you do have TCDD in a concentrated solid form, I'd suggest (er, in your fictional world!) to simply drop that. When it hits the water it will slowly dissolve, but would have a better chance of staying concentrated enough to do some damage.

# Dioxin solid

TCDD is a crystalline solid. I've never seen it (and hope I never do!) but it would probably lend itself to small-ish crystals, granules, or ground up powder (the finer the grind, the more readily it would dissolve). To continue with the "jar" delivery method, I'd fill up the 20L jar with the powder, and then flood it with water. The water won't dissolve more than a few micrograms of the powder (see above), but it will give your package more heft and make it more likely to shatter the glass on impact.

# Water hammer design

If you include an air gap so the liquid/solid combination can move inside the jar, you can achieve a "water hammer" effect to help break the glass:

The idea is that in between the top (poison) layer and the air (better yet, partial vacuum) compartment at the bottom, there's a relatively thin barrier that will break easily when the jar hits the water, which will cause the poison to accelerate and rapidly hammer the bell at the bottom and blow it out. The fins of course keep the vessel on a stable orientation during free-fall.

The concave bell shape on the bottom might help transmit more of the shock to the glass, but it's certainly not essential. You could use ordinarily-shaped jars.

While you don't need this kind of design, it's still simple, and it would improve the reliability of your characters' poison bombs and/or allow them to drop them from lower heights.

# How high?

Not very.

With the above design, and 20kg of accelerating poison to help break the jar, a drop of a few meters on relatively calm water would suffice. Thus, your characters will want to handle them carefully, which would include careful packaging and carrying protocols (not to mention hazard pay...).

At drop distances of even tens of meters (30 feet), the jar will be moving fast enough to virtually guarantee the destruction of the vessel.

For even greater reliability (or use in cases where free-fall delivery may be unavailable), simply include a low-yield "slow" explosive (modern "smokeless" gunpowder would be sufficient, since it contains its own oxidizer). It needs only break the glass, so a tiny amount will suffice (or just use a bullet, if your characters have modern ammunition). Almost any kind of detonation trigger will do (contact, altitude, even a timer/fuse), since you don't care when it blows up, as long as the good guys aren't holding it at the time, right?

• Great detail. Love the visuals. Nice answer! – AndreiROM Mar 1 '16 at 21:50
• Bonus points for the water hammer: what-if.xkcd.com/6 – thanby Mar 1 '16 at 22:38
• Thanks! @thanby, that's definitely one of Randall's finest. Anyone with older plumbing is likely familiar with the water hammer effect, so it's an easy crowd pleaser. ;-) – type_outcast Mar 2 '16 at 2:51
• Really good break down. However... in reference to your final line; these days (Post World War 1) how often do the "Good Guys" use chemical agents? – Blade Wraith May 14 '18 at 10:20
• @BladeWraith Thanks! If you think "good guys" using chemical agents in a fictional world is bad, I've covered everything from using giants as slave labour, to Santa vaporizing all the Christian children (and launching an extreme nuclear winter), to putting pants on centaurs. And I'm not the only one. Welcome to Worldbuilding.SE! – type_outcast May 15 '18 at 13:56

Actually I don't think you need to get it to terminal velocity, just put some steel ball bearings in the jar, maybe need to have them loosely attached to the different sides, so when the container strikes the water, (at whatever angle) the steel projectiles will slam into the glass shattering it.

• It seems to me that would work if the jar were empty, but not when it's full of fluid that would cushion the movement of the ballbearings? – rwallace Mar 1 '16 at 16:57
• The liquid would slow down the bearings but I think they can still move fast enough to do the deed, unless the the liquid is very viscous. – bowlturner Mar 1 '16 at 16:59
• @bowlturner You should just embed small chunks of dense metal such as lead directly into the glass. When the glass impacts the difference in inertia will cause high stresses in the glass around the metal so you can get it to break in a multiple locations in a controlled fashion. So if you drop directly on monster make the bottom break and use pointed pieces of something hard to get maybe some penetration. For bigger splash you can break the top. This actually works on metal containers, but using an explosive charge is always much better. – Ville Niemi Mar 1 '16 at 21:42
• One may attach the bearing below the jar, it wouldn't break off while gradually accelerating in the air yet it will hit the jar when it's slowed down abruptly by the water. – Dallaylaen Mar 1 '16 at 22:34
• @Dallaylaen Expanding on that idea... A spiked plate with the spikes touching the bottom of the jar would be similar, it would take the impact on its lower surface and focus it on the points of the spikes, giving you a pretty reliable puncture. – thanby Mar 1 '16 at 22:36

Yes, it will probably break especially if it's designed to break on contact with water.

This sounds very similar to egg drop competitions held in science programs all over the world. The competition is to see who can make a container that will prevent a common chicken egg from breaking when dropped from a high height (usually hundreds of feet). There are various techniques to building a vehicle to preserve the egg...but the egg isn't my point.

This Mythbusters video shows that while hitting pavement hurts way worse than hitting water, a crash landing on water is still lethal. If dropping from 600 ft is enough to break bone, then that's certainly enough energy to shatter glass.

If these would-be god killers decide to make the jar a three inch thick(76.2mm) sphere, they stand a very poor chance of it breaking open. However, if they make it just 1/16 inch (1.58mm) thick in a non-spherical shape, they stand a pretty good chance of breaking open on contact with the water.

Terminal velocity is completely dependent on the surface area, center of gravity and weight of the jar. A jar shaped like a javelin will fall far faster than a jar shaped like a parachute.

Dispersal problems with impact on water's surface

If this jar is supposed to be a weapon of mass destruction, then having it shatter on impact is less effective than having it explode some height above the water then disperse the dioxin over a broader area. If the Lovecraftian monster is submerged then a cloud of dioxin in the air is only minimally dangerous unless they come up for air within the dioxin cloud.

• 3 inches are 76.2 mm, not 72. 1/16 is closer to 16mm. (nitpicking, but still) – njzk2 Mar 2 '16 at 4:28

well, water is supposedly as hard as concrete when a human at terminal velocity hits it, and i imagine that a glass jar filled with fluid would have a comparable speed, so it makes sense for it to shatter on impact. if there is something moving in the water to disrupt the surface tension, however, there wouldnt really be anything for the water to break against (except the thing moving), so it might not work that great as a direct weapon. can you clarify how they hope to use the jars (are they dropping them directly at swimming eldritch abominations? and what form is the dioxin in?). either way, this probably would not be the most effective way to disperse a chemical weapon; additionally, if you have the means to either accelerate the jar to a high enough speed or get high enough to drop it, than you should probably have some other sources of attack available.

• I've heard the claim about water being as hard as concrete, but how true is it? Sounds like an exaggeration. The jars are not expected to hit individual creatures; they're intended to be weapons of mass destruction. I don't really know anything about forms dioxin takes; I'm just assuming it will dissolve in water. The stuff could be sprayed, like crop dusting, but then some of it would get on the aircraft, which would create problems; it needs to be delivered without contaminating the aircraft or poisoning the pilot. – rwallace Mar 1 '16 at 16:59
• the reason that water seems "as hard as concrete" at the moment of impact isnt necessarily due to the strength of the water, but rather the relative weakness of the other materials involved: at a certain speed, there is enough energy present that it doesnt really matter what the glasses are made of, especially it they are dropped from airplanes. im think that the parts about the dioxin dissolving are correct on your part (or that the audience will believe so). – Duncan Urquhart Mar 1 '16 at 17:14

I believe this totally depends on the jar, it's thickness etc.

Think of it this way, you could drop a thick-walled perfume bottle out of a plane and it'd probably be undamaged when it hits water.

On the other hand a very large jar made of paper-thin glass is unlikely to survive the impact.

Height for reaching terminal velocity would vary based on the density of the substance inside and the shape of the jar.

• Right. So assume the substance inside has the density of water, and the jar is thick enough to hold twenty litres of it during transport and handling, but no thicker than it needs to be for that. – rwallace Mar 1 '16 at 17:22
• What you need is momentum. The perfume bottle wouldn't break because it would have very little momentum. A 20L bottle of liquid would be much easier to break, even from a relatively low height, especially if it is shaped to do so. It wouldn't have to be super-thin. – thanby Mar 1 '16 at 22:42