Four identical quadruplets leap from a plane…

Factual Questions
1

…and plummet towards a placid lake far below.

They have just carried out a daring aerial robbery and some clutch their loot. Alas, they have forgotten their parachutes.

The leader, addressed by his brothers as “Control”, or “A”, carries nothing. He strikes the water at terminal velocity. As I understand it, he cannot displace the water below him fast enough to decelerate at a safe speed.

Brother B drops a single heavy object just before he hits the water. Perhaps it is a bag of gold coins, weighing about as much as him, say 100kg. It strikes the water a fraction of a second before him.

Brother C has the same bag of coins, but opens it. Hundreds of small heavy objects, weighing in total 100kg, strike the water just before him.

Brother D has a different idea. He grabs a single, long vertical object of 100kg. Perhaps it is a spar from the stricken plane. He hurls it down like Zeus’ thunderbolt and it strikes the water just before him.

Is brother B, C or D any more likely to survive than brother A / Control? That is, do the objects that hit the water before them displace the water and / or break surface tension so as to reduce the deceleration experienced by B, C and or D? If so, which of B, C and D has the best plan?

Assume if relevant:

  • I’m really only interested in the effects of the objects striking the water on the survivability of the fall.
  • Every person and object travels at the terminal velocity for a person falling through air (about 200km/h for a belly-down skydiver).
  • No object interacts with any other, except insofar as it affects the water that each person strikes. Eg person D does not collide with the spar.
  • The pilot of the plane and any other victims of the heist packed their parachutes that day. They survived just fine.
2

Mythbusters did a partial on this one at least:

Multiple drops with a heavy hammer falling headfirst (not as much mass as your spar, but closest) seemed to have minimal effects. Possibly some (the tests varied a lot), but nothing substantial and certainly nothing survivable.

3

The idea that surface tension is like a skin on the top of the water is, basically, incorrect.

Imagine that you have two rooms, one on top of the other.

In the lower room, there’s a series of air pumps forcing more air into the room, to raise the pressure.

In the upper room, you have a large mass of wood spheres that are immersed in a gooey, shampoo-like substance.

Now, if you opened a hole in the connecting floor, you’d expect the weight of the spheres and shampoo to cause everything to start falling down through the hole but, between the high air pressure and the impermeability of the goo, the spheres and goo just dangle a bit from the top of the ceiling, like a blister. There’s no skin to the blister, it’s just a bunch of goo being held up by the air pressure.

If you wanted to jump into a pool of wood spheres and goo, jumping onto it flat would suck. The spheres are nicely resting on top of one another in a lattice, they’re not going to move easily out of your way. They’re relatively incompressible.

If you poked a stick in, though, you might be able to wedge into the lattice without too extreme of resistance.

Overall, this is an issue of how to efficiently move into and through a lattice of hard objects that are mildly connected to one another by a goo.

Slapping a steak doesn’t work to penetrate it. Cutting a steak with a sharp object, like a knife, does work. The knife is as effective against the first 1mm as it is at the 2nd and 3rd millimeters because the angles and pressure points are all still the same. (Ignoring friction on the sides of the blade.)

Shooting a steak with a pellet gun just before your slap isn’t going to do much to make it more penetrable unless you REALLY blast that thing away. And, at that point, ricochets and shrapnel might be the new concern.

4

I suspect the problem is that a human hitting the water at terminal velocity is on the margins of survival. Usually just over.

The La Quebrada Cliff Divers hit the water at about 28 meters per second. They do this time and time again without injury. People jumping from the Golden Gate can survive - so long as they enter the water vertically - and that is an entry of 38 m/s.

Terminal velocity is 54 m/s, so more again. But not wildly.

So, what kills people? For the Golden Gate we have the problem that those jumping are intent in dying. Some might change their mind half way down, but things are grim no matter what. About half die. This cite has this to say about the nature of injury:

An earlier study noted that those entering the water vertically had a much greater chance of survival. The much lower rate of deceleration likely being the differentiator.

If you are intent in surviving don’t hold your breath - hemothorax/pneumothorax is the inevitable outcome if you do. Don’t belly-flop. You will break.

And do anything you can to reduce the decelleration. Which is where we came in. What is remaining that will kill you is your internal organs slamming about and tearing themselves off other vital bits. Hearts don’t pump well if they have torn themselves off their aorta etc. (Which is the classic third impact of car accidents.)

Dropping at terminal velocity, your task is to reduce the deceleration to something less than jumping off the Golden Gate Bridge. Preferably down to something akin to jumping off the cliffs at La Quebraba. Could a 100kg object punch a large enough hole in the water in front of you to give you a fighting chance? You want it to be just far enough in front of you that when it decelerates you don’t plough into it, but close enough behind that there is an appreciable hole in the water. It is making a hole that matters. Just disturbing the surface isn’t going to help.

I’m going to bet that this is doable, and brother B could survive. I doubt any of the others do.

I remember the Myth Busters episode. It really bugged me just how sloppy their methodology was and how useless the results were. One learnt nothing except that they were driven by time and not results. But their myth was that the dropped hammer stirred up the surface enough to prevent injury. That isn’t going to help.

5

I wonder if the first impact created a foam, or even just a lot of bubbles, if that would help.

6

A foam is a good cushion but creating a foam timed just perfectly to decelerate a falling body is going to be nigh impossible. It also might not work because you basically want to generate a material that has a sufficient density to slow the body’s velocity just right to maximize the deceleration over the maximum possible timeframe. In the midst of an explosion and the then the rapid collapse of the foam under gravity, ensuring a proper density under compaction below the falling body might not be possible.

With a structurally sound foam, like a sponge, the lower layers are basically going to stay where they are, ready to catch and push back against the falling body. That’s not true with aerated goo and wooden spheres nor aerated water, all held up by nothing but inertia.

Plausibly, you could create a large surface area micro-bubbler under a body of water and create a continuously frothy material that acts like a structural foam. But, also plausibly, the bubbles would simply all merge and become one giant hole in the water and not create a foam.

I think I sent a letter into the Mythbusters asking them to test it, but they didn’t. (And I assume the New-Busters haven’t either - but I haven’t watched.)

7

That’s my thinking. Making a lot of bubbles will lower the average density, producing the lower deceleration you’d need to survive. I’d guess that the one who dropped all the coins as a loose mass would produce more bubbles, because each individual coin would cause its own splash, with subsequent mixing of air and water.

8

I believe the minimum distance needed to decelerate from a freefall to zero is something like 12 meters. So even if you could survive the fall you’d be the equivalent of a 3 story building below the surface of the water. Hopefully you can hold your breath long enough to resurface.

9

All four should have dropped whatever they were holding, then taken off any clothes they could wave around to slow their descent, then lined up one above the other with enough distance in between so the splash created by the previous brother hitting the water lessens the impact for the next one. Perhaps the 2nd, 3rd, or 4th brother survives that way. But I have brothers and we would all hit the water together in the midst of fighting over who would hit the water first.

10

I’ve seen a training device for teaching diving (those Olympic divers have to start somewhere.) it was a bunch of pipes on the floor of the pool (deep end, duh!) and just before the student dives, they release a blast of air so the surface is foamy. But then, the water is foamy for a decent depth too, hence less dense. As a result, belly flops or other incorrect entry are far less painful. I’m not sure dropping a bagful of coins would produce the same result. It would make for a less flat/solid surface, but the resistance after entering would be close. Would the coins sink out of reach in time or would you impact them at almost 54m/s just under the surface (being much smaller, and less weight vs surface area, they would slow down fairly soon on entry). The bank would get many of their gold coins back from the coroner after she did the autopsy.

11

Stuntmen use airbags much shorter than that.

12

Suppose terminal velocity is 55 m/s, and an acceptable rate of deceleration is 50 gees (totally survivable for a healthy adult under good conditions). Then the deceleration time is 0.11 s, and the distance about 3 meters. So yeah, totally fine.

But that’s assuming broad support, like what you’d get with an airbag. Hitting the water vertically would increase your distance, but 50 gees is probably too much in that configuration. I don’t have any data available, but I don’t think I’d want to exceed 20 gees in that case.

13

Okay, let’s say instead of a 100kg object, Brother B drops a 100kg bomb. Or to be exact, the bomb impacts the water and explodes one or 2 seconds ahead of B. This churns up the water (and creates a lot of foam) just as B strikes the surface. How does that affect the deceleration?

14

I don’t think stuntmen reach terminal velocity speeds. The one guy that did skydive and land in a net I remember the net being some 3 stories+ above the ground.

15

Well it appears there is some proper science on the question.

Tl;dr: done right, experimentally there is up to 78% reduction in deceleration with a sphere preceding you into the water. Done wrong and the deceleration is worse.

16

So let’s say B forms his bag of loot into a perfect sphere, drops it at the perfect time, and contorts himself into a similarly perfect sphere.

He achieves the maximal benefit in terms of deceleration, as in Francis Vaughan’s paper.

Does that render the fall survivable?

In other words does B get away with the loot (whatever he can collect from the lake)?