How many pillows would you need to survive a fall from a church tower?

Question

The praised Dutch book "Koning van Katoren" features an 18 year old who wants to become king of his country of Katoren, which had been under the regency of half a dozen evil ministers for his whole life. The ministers gave him a series of impossible tasks, like curing a plague and cutting down a dangerous pomegranate tree which drops actual grenades. He miraculously succeeded in every task, and the exhausted ministers eventually ordered him to just jump down a church tower.

But by this time he has become so popular with the people of his kingdom, that thousands of them travel to the church in question, all carrying their bed pillows. They pile them up high before the tower, and when the boy finally makes the jump, his fall is literally cushioned and he survives without any injury.

The tower's height is never stated in the story, but the tallest and most famous church tower in the Netherlands is the Domtoren at 112 meters tall. Because he did not jump from the actual roof, but rather from the highest balcony, let's say he fell 100 meters.

How many pillows are needed to cushion his fall and leave him unscathed? A rough order-of-magnitude estimation is fine: I am curious if it would have been closer to a thousand people that showed up, or more like a hundred thousand.

Answer 1

Okay, from a height of 100 meters, the faller will reach a speed of 44m/s. Human terminal velocity, for a spread-eagle position like skydivers, is 53m/s, so drag is going to play a big role here, especially if he goes spread-eagle. Call it 32 m/s of landing speed.

If our hero wants to stop in ten meters from this, assuming roughly constant acceleration, he will stop in 0.625 seconds and will experience a bit over 5g. This is survivable, especially if he goes back-first.

I don't know the angle of repose for the pillows that the townspeople are using. Let's just assume that it's 45 degrees, because it makes the math easier. The volume of a cone with a radius and height of 10 meters is just over 1,000 cubic meters, or about half the size of an Olympic swimming pool. That's a lot of pillows. You could reduce this by using the wall of the church to support half a cone.

You could get a smaller cone by making it steeper, but that involves binding the pillows together, and you don't want to do that. See, when stunt performers fall onto airbags, the bags vent pressure to slowly catch the performer and prevent bouncing. In the same way, our hero is going to just explode the pillows out as he lands.

Accounting for the increased density of the pillows as they stack is difficult, but I doubt the volume of the pillows out of the pile will be more than twice the volume of the pile. This conveniently cancels out the factor of 1/2 that we get from building the stack against the church.

1,000 m³ of pillows. A rough estimate from the pillows on my bed gives about 7-10 pillows/meter. You're talking 7-10,000 pillows in play here, which may not be from the same number of people, since one person can bring multiple pillows to the church.

Answer 2

Without having the information to crunch numbers on this... I'm going to call it plausible, but only if the commoners have enough knowledge of physics.

What you really need is to absorb energy slowly. For this to happen, your pillows will have to be able to "give" a lot, and quickly. Now, the good news is we are presumably talking about down pillows, as opposed to modern stuff, which does have quite a bit of "give", especially if someone knows enough physics to tell the peasants to take out some of the stuffing first.

That said, your best bet would be if you can somehow construct the sort of air bag that professional stunt performers use. Failing that, your hero is probably better off jumping into a series of awnings that will rip as he hits them. It's not inconceivable that a bunch of peasants could arrange to erect such structures, though it starts to stretch belief that the evil ministers will just look the other way. Another option (that could be used in addition to all of the above) would be for the hero to hold one or more pillow cases over his head to use as a makeshift parachute. This almost surely wouldn't be enough on its own, but might slow his fall enough in combination with other methods.

See also https://www.reddit.com/r/NoStupidQuestions/comments/8wqy7o.

That said, the one thing that will really help is if the pile of pillows is built against the side of the church to form a slope. This way the pillows are absorbing some of the hero's energy, but they are also working to redirect his downward momentum into sideways momentum. If you can do that over a sufficient distance, you can survive a fall onto concrete (how to avoid friction-related issues is left as an exercise for the reader).

If the pile of pillows forms a relatively steep slope against the side of the church, and the hero hits it right, and his clothes don't shred from the friction, I would say it's plausible that, between the friction of sliding down the slope-of-pillows and the cushioning effect of the same, he could survive.

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On the other hand, since the height of the tower isn't known... it might be as little as, say, five stories, if this is a smaller, local church.

Answer 3

I don't believe he can walk away from this, period.

Look at Itmauve's answer--stopping in 10 meters causes 5g of acceleration--done right, this is fine. But can you actually punch 10 meters into a pile of pillows? A quick look in the closet indicates that arranging pillows to make a human-size/shape landing (in a jump you would have extras because you don't have perfect but they aren't hit, they're irrelevant to this) weighs at least 10% of my body weight. That means a stack of 10 pillows will equal my body weight--and at that point I've shed a minimum of half my velocity--in little more than a meter. Survival is questionable, walking away isn't going to happen.

Now, you probably can find some fluffier pillows but the effect isn't going to be huge as pillows are engineered for human body weight--a pillow which has too much give is not going to be pleasant to use.

For those who aren't getting what I'm saying: While it is not an inelastic collision the end result is functionally the same. The jumper is going 32 m/s, he hits pillows of his own weight moving 0 m/s. The end result is 2x his weight moving 16 m/s--I do not care exactly what the collision looks like, I'm looking at the start and end points and seeing him shed 16 m/s in the space of 1 meter--and that's far above the danger threshold even in an optimum deceleration curve.

Answer 4

A 100-meter jump would break current world records for free-fall jumps. I do not believe this would be possible with pillows.

Dar Robinson currently holds the world record for the highest free-fall jump in a commercial film at 220 ft (67 meters). That's 33 meters short of the church jump. That's with several safety precautions, practice, and training. He also did a 311 feet (95 meter) jump onto an airbag.

Luke Aikins set a record for the highest jump without a parachute at 7,620 meters. He landed in a specially made net, not a pile of pillows.

Why I'm doubtful a pile of pillows would allow you to walk away from a 100 meter fall

The "airbag" was probably something like BigAirBag, which has 2 stages. One is a soft stage to slow you down, the second is a firmer stage to stop you.

Even with 21st-century technology, we don't do 100 meter falls without a parachute that often. This answer points out that hundreds of years later walking away from a 100-meter fall would still be quite note-worthy, and that even professional stuntmen would likely not attempt this.

Answer 5

If you want a really quick rule of thumb for things like this, which assumes no air resistance, and an ideal substance absorbing your fall (which produces the same deceleration at all levels of compression) then you can just use potential energy. The kinetic energy gained in the fall is mgH for mass m, acceleration = g, starting height = H. Suppose an object can survive ng deceleration, starting at height h. Then, to come to a stop at ground level, m(ng)h = mgH. Simplifying, this gives h = H/n

If you assume that a boy can survive a 10g deceleration, for example, without injury then in your example h = 10.

A normal pillow, uncompressed, probably has a height of between 10-20 cm. Assuming the lower height it could be as few as 100 pillows. In practice, of course, that wouldn't be stable so let's assume a triangular based pyramid 100 pillows high. That gives 1/6*100*(100+1)*(100+2) = 171700 pillows. That's quite a large village then.

However, if we assumed 50g deceleration (50% survivable for a child based on a mention in http://www.madsci.org/posts/archives/2003-11/1068660102.Bp.r.html though I haven't got the original source) and 20cm thick pillows then we need just 10 in height, which would be a pyramid of just 220 pillows. In practice, of course, pillows will not stack well, or decelerate evenly so the answer is definitely much higher than this.

In short, the answer is that (a few) thousands is probably enough for survival but hundreds of thousands may be closer to the mark if he is to walk away unscathed.

Answer 6

there is not enough information given to calculate the number of pillows, like what are the pillows made of and what is their size.

and the distance from the jump to where the pillows start, if the stack is 90 meters high then he will not accelerate much before his fall is slowed.

given enough of the right pillows it is feasible.

Answer 7

The physical process of piling up pillows may be a problem. The people will need to pile up the pillows in a pyramid like shape and the process of stacking may determine how stable it the stack is while people are passing pillows up the stack to the top, as well as how well the stack of pillows cushions the protagonist when he jumps.

Did you ever hear of the Bent Pyramid?

The Bent Pyramid is an ancient Egyptian pyramid located at the royal necropolis of Dahshur, approximately 40 kilometres south of Cairo, built under the Old Kingdom Pharaoh Sneferu (c. 2600 BC). A unique example of early pyramid development in Egypt, this was the second pyramid built by Sneferu.

The Bent Pyramid rises from the desert at a 54-degree inclination, but the top section (above 47 metres) is built at the shallower angle of 43 degrees, lending the pyramid its very obvious 'bent' appearance.[4]

Archaeologists now believe that the Bent Pyramid represents a transitional form between step-sided and smooth-sided pyramids (see Step pyramid). It has been suggested that due to the steepness of the original angle of inclination the structure may have begun to show signs of instability during construction, forcing the builders to adopt a shallower angle to avert the structure's collapse.[5] This theory appears to be borne out by the fact that the adjacent Red Pyramid, built immediately afterwards by the same Pharaoh, was constructed at an angle of 43 degrees from its base. This fact also contradicts the theory that at the initial angle the construction would take too long because Sneferu's death was nearing, so the builders changed the angle to complete the construction in time. In 1974 Kurt Mendelssohn suggested the change of the angle to have been made as a security precaution in reaction to a catastrophic collapse of the Meidum Pyramid while it was still under construction.[6]

https://en.wikipedia.org/wiki/Bent_Pyramid1

The outer casing and much of the structure of the Maidum Pyramid collapsed sometime during the period of ancient Egypt, possibly while it was still being built.

The collapse of this pyramid during the reign of Sneferu is the likely reason for the change from 54 to 43 degrees of his second pyramid at Dahshur, the Bent Pyramid.3

https://en.wikipedia.org/wiki/Meidum#Pyramid2

the Maidum Pyramid is made out of rocks, and yet it collapsed. Obviusly a pyramid made out of soft and flexible pillows would have a much greater tendency to shift and thus collapse and would have to be built much more carefully.

You may remember the fairy tale of "The Princess and the Pea":

The story tells of a prince who wants to marry a princess but is having difficulty finding a suitable wife. Something is always wrong with those he meets and he cannot be certain they are real princesses because they have bad table manners or they are not his type. One stormy night a young woman drenched with rain seeks shelter in the prince's castle. She claims to be a princess, so the prince's mother decides to test their unexpected, unwitting guest by placing a pea in the bed she is offered for the night, covered by huge mattresses and 20 feather-beds. In the morning, the guest tells her hosts that she endured a sleepless night, kept awake by something hard in the bed that she is certain has bruised her. The prince rejoices at her bruised back. A huge wedding takes place in the palace. The prince couldn't believe that he found his true princess. Only a real princess would have the sensitivity to feel a pea through such a quantity of bedding, so the two are married. The story ends with the pea being placed in a museum, where according to the story it can still be seen today unless someone has removed it.

https://www.google.com/search?q=the+princes+and+the+peaa&oq=the+princes+and+the+peaa&aqs=chrome..69i57j0l7.6990j0j7&sourceid=chrome&ie=UTF-83

Recently I did something vaguely similar. I put another mattress on top of my mattress and box spring. And apparently the flexibility of the two mattesses combines to make a somewhat unstable platform which sometimes threatens to slant too much and roll me off the bed.

So I wonder about the stability of three mattresses one on top of the other, and four mattresses one on top of the other, and so on.

So how stable will ten pillows one on top of the other be, or twenty, or thirty or forty, and so on?

If the protagonists needs a pile 200 pillows high to survive his fall, but the pile keeps sliding down and collapsing whenever they try to pile higher than 100 pillows, he will be doomed.

In my opinion, the protagonist would be much more likely to survive a jump into a pile of pillows from a ten meter church tower than from a hundred meter tower.

And if he lands on a flat topped pyramid (or half pyramid leaning against a church) much more than about ten meters tall, his landing is likely to cause the pyramid of pillows to collapse and spill out and he might get buried by pillows during that collapse and his friends might have to frantically dig him out of the pillows before he suffocates.

So I can imagine a story where a technological or magical time traveler keeps going back in time to the protagonist's jump off the tower, each time getting the people to build the pile of pillows a different way in the hope that this new arrangement might save the protagonist.

Answer 8

If the pillow tower is near the height of the original fall, and people stand at the top of the tower to receive him in a “trust fall” like catch, you can make it happen.

Human ladder with a pillow base.

Answer 9

Pushing the boundary of the definition of "pillow," I would go with very slippery pillows. There's little need for compressibility because I'm going to arrange them in a catenary or perhaps log curve (I'm too sleepy to apply the calculus to verify maximum vertical delta-vee applied throughout the slide). The fellow's total speed will slowly decrease because the slide is not frictionless, but he'll exit the slide moving horizontally and at worst will suffer abrasions. Wear some thick leather clothes.

Answer 10

He miraculously succeeded in every task, and the exhausted ministers eventually ordered him to just jump down a church tower.

This phrasing is ambiguous as to whether it's "they ordered him to jump, such that his jump is from a church tower", or "there was a church tower such that they ordered him to jump from it", i.e. whether the choice was up to him which tower to jump from, or they chose a specific tower. If the former, I'm sure there are church towers from which he could have jumped safely.

If the latter, it's quite complicated. It's not like every situation is either perfectly safe or perfectly lethal. There are people who have died from falling one meter, and others who have survived falling from airplanes. A thousand pillows would be in the "survivable, if lucky" range, but I don't think a 100m fall could be made riskless. Another answer assumed 10m of pillow compression, but that invokes further problems. For one, now you have the risk of being smothered under 10m of pillows. For another, just because you have an average deceleration of 5g doesn't mean you have a maximum of 5g. Almost all of the deceleration would be at the end. To produce an maximum of 5g would require a stack much more than 10m high.

If I had to jump off a tower, I would certainly prefer jumping into pillows over jumping onto concrete, but I wouldn't voluntarily do either.