How much bubble wrap would someone have to wrap themselves in to walk away unscathed if they were to use it instead of a parachute for a typical skydive? Assuming no problems breathing at altitude or from the bubble wrap constricting airflow.
All other factors being negligible. Just bubble wrap and gravity.
Terminal velocity for a skydiver is around 120 MPH. If you assume no change in terminal velocity due to the bubble wrap, it would need to be deep/thick enough to decelerate a human body from 120 MPH to a survivable impact speed. And that assumes the bubble wrap is efficient at dispersing the energy of the impact.
But the amount of bubble wrap needed would change the terminal velocity due to drag and density. I don’t know enough how to calculate that, but I picture something the size of a hot air balloon.
The net that this guy used should give you a good estimate for the deceleration needed. It’s basically the same problem with a different solution.
The pop would be deafening, so factor in industrial-strength ear plugs.
Didn’t Adam do it on Mythbusters? IIRC, getting dropped from just 15 feet or so required him to be covered in bubble wrap that was several feet wide.
ETA: Here’s the clip. Bubble Boy - Mythbusters for the Impatient - YouTube
I would assume if you wrapped yourself in enough bubble wrap to break your fall, it would also slow you down quite a bit. Whether or not that counts or is considered cheating, I suppose would be for the person asking the question to decide.
Might speed you up, if the layers of bubble wrap meant that you tended towards a spherical shape. Spheres are a lot more aerodynamically efficient than a flailing human body.
Flailing? Who do you skydive with?
Wouldn’t there be a problem with the bubbles rupturing due to the low pressure at high altitude?
How about instead of wrapping the diver in bubble wrap, we just make a landing pad out of the stuff?
120 MPH is 176 ft/s. Assume our diver can tolerate 10G of deceleration on landing, so that’s 322 ft/s^2. Time required to decel to zero speed is 0.547 seconds. Average speed during that period is half the max, i.e. 88 ft/s, so distance covered during that period is 48 feet.
So if you assume that our bubble wrap provides a constant decelerative force throughout the landing event, you need it to be 48 feet thick.
The most obvious problem with that model is that bubble wrap definitely doesn’t provide a constant force regardless of displacement: you’ll have zero G at the first moment of contact, and very high G by the time your speed goes to zero. If you want to keep the max G limit at 10, then you’ll need a much thicker bubble mattress, providing a longer decel period.
And if you actually wrap your diver in bubble wrap, then yes, you change the drag profile. As a rough estimate, aero drag for a falling object is proportional to the cross-sectional area: double the diameter, quadruple the CS area, therefore quadruple the drag for a given velocity. Except quadrupling the drag just means your diver slows down so that drag still equals weight. Drag is proportional to the square of velocity, so if you want drag to stay the same despite doubling the diameter, then the square of velocity needs to be reduced by a factor of four. So what you get is this:
doubling the diameter of your diver (using massless bubble wrap) results in terminal velocity being reduced by half.
Reducing your velocity by half means you have 1/4 of the energy to dissipate on landing, so you only need 1/4 of the stopping distance to keep your decel rate within limits.
So doubling the diameter of your diver means you only need 1/4 of the stopping distance you used to need.
For 120 MPH, I estimated 48 feet of decel at a steady 10 G. For the sake of argument, let’s assume bubble wrap really does provide a constant decel force, no matter how compressed. So if my diver is three feet across, and I wrap him in a 1.5’ layer of wrap (making him 6’ feet across), then he’s falling more slowly and I only need 12 feet of decel distance. Clearly not enough wrap yet. If I wrap my diver to make him 12’ across, then I only need 3 feet of decel. Clearly too much wrap.
So for 10G decel during landing it looks like you need a layer of wrap somewhere between 1.5 and 4.5 feet thick, and you need to control attitude so you don’t land head-first or feet-first. And again, this assumes constant rate of decel during the landing event, which is admittedly unrealistic. If you want to account for the real spring-rate behavior of bubble wrap, you may need to go with something close to that 4.5’ thick layer to keep the max decel under 10G.
You don’t have to be terribly high in order to achieve something close to terminal velocity - especially if your terminal velocity is drastically lowered by being inside a bubble-wrap cocoon. Jumping from a few thousand feet above sea level will do it - and you may have noticed that you can ship items in bubble wrap to Denver (elev. 5280’) without the packages exploding enroute.
Actually, bubble wrap probably does provide fairly close to a constant force, that being the force needed to rupture a bubble. One could doubtless engineer a bubble wrap where that force is approximately the force needed to decelerate our skydiver.
But you could do accelerations much greater than 10 gs. That’s approximately the limit for sustained acceleration, for a pilot who’s remaining in control of his airplane. But for very brief durations, and where you don’t need the person to remain conscious, you can go over 40 gs without major injury (Colonel Stapp’s highest run was at 46).
NASA used if for the Mars lander Opportunity earlier in the century:
“Opportunity arrived on Mars on January 25, 2004, and was drop-bounced onto the ground inside of a kind of heavy-duty bubble wrap.”
https://boards.straightdope.com/sdmb/newreply.php?do=newreply&noquote=1&p=22290606
But a sphere 40+ ft in diameter will have a lot more drag than a human body, flailing or not. Unless it has a density comparable to the human body, it will have a lower terminal velocity.
And bubble wrap has notably low density.
Me, possibly.
I did about 4 free-falls (hop-and-pops). Gave it up due to a combination of not being able to attain a consistent arch (flailing wouldn’t be entirely accurate but not unfair) and an onset of acrophobia.
The engineering of the bubble wrap would be critical. It would have to be designed to pop when a certain amount of force was applied at that force would have to be very small. Most bubble wraps as designed are meant as a cushion and are too strong. When layered they wouldn’t break from the force and would slow a body down way too fast and kill the person.
And on the other end of design would be if the bubble plastic was very weak. Then you’d have the body just crashing through layer upon layer never slowing down enough.
I suppose an exactly engineered bubble wrap could be designed to break easily when hit with a force of a 200 pound mass going 120mph and have a breakage resistance curve increase as the force decelerates. Problem then is calculating the surface area of contact the body makes with the bubble wrap. Big difference if he goes feet first or attempts a belly flop.
It would be interesting to see the calculations that went in to the engineering of the net that Luke Aikins used in his parachuteless skydive. From the picture I’d guess the net was approximately 100 feet high, so he probably had 75-80 feet of deceleration. The net is probably easier to design and test for deceleration than bubble wrap. Of course, you have to hit the net right on target.
The orientation of the faller would also matter for determining the survivable acceleration. The best case is with the faller’s back facing down (which also conveniently happens to be the orientation with the greatest surface area). Assuming you have some way of guaranteeing that, finding the surface area is easy.
Scream N Splat Skydiving
Motto: We’ll get you on the ground; that part will happen pretty definitely.
I measured three pieces of used bubble wrap I have lying around the house. It’s a bit subjective how much you should compress it to measure thickness but I folded it to double thickness (since the bubbles have a tendency to line up that way increasing the density) and dragged the bubble wrap through my calipers trying not to compress the bubbles too much (basically not more than I thought the bubble wrap would naturally compress if stacked a few feet thick). Each piece of bubble wrap had a small paper label, adding some mass and each piece was a bit smushed in some places, probably detracting from the measured thickness.
I came up with densities of 37g/L, 42g/L and 35g/L, with a mean of 38g/L.
This guy, trying to answer a similar question, came up with a density of 17g/L (0.017g/cm^3) but he’s a fancy-pants using brand new bubble wrap. Jumping Off a Building With Bubble Wrap | WIRED
I don’t doubt you but I don’t follow this. Why does this always end with a “very high G”? Doesn’t that suggest that the bubble wrap is useless in reducing the g forces on the skydiver? That can’t be right, since we know that you can pack pretty fragile things in a lot of bubble wrap and they survive completely indifferent shipping.
Massless bubble wrap? Do we live in a world of spherical skydivers? 
It seems more cautious to assume the worst possible orientation for the sky diver and work from there. Brace his neck and assume head first.
Many of the things we routinely pack in bubble wrap are actually capable of surviving more G than the human body - we are actually protecting against localised blunt impact rather than overall G forces.
That said, I am certain it must be possible to design a bubble wrap descent solution - I am not so certain that the benefit of the cushioning will outweigh the reduction in terminal velocity; that is, I suspect that before the point where sufficient cushioning is added, the assembly will already be a huge, slow-falling ball of packaging.
Pathfinder/Sojouner in 1997 was the first Mars lander to use airbags. But that was only for the last phase of landing. It also had a heatshield, a parachute, and retro rockets to slow it down enough to not be damaged when it bounced. Opportunity and Spirit’s landings were very similar, but because they were heavier, had to have bigger parachutes and extrastrong airbags.
My mental model of bubble wrap was that its spring behavior (force as a function of displacement) was due to compression of the trapped air, like the piston of an engine compressing the air in the combustion chamber: low force at first, and then very high force near the end of compression, with an exponential relationship. But of course bubble wrap can’t handle very much pressure before it ruptures, so my mental model is probably inaccurate. It seems likely that the spring force is more related to the mechanical properties of the plastic film that makes up the bubbles, and less due to the compression of the trapped air.
I just googled “bubble wrap force versus distance,” and found this Wired article, in which the author explores the properties of bubble wrap while attempting to answer a similar question. So it turns out that the spring force is a linear function of deformation, much like a conventional steel coil spring. This does still mean that you start with infinitesimal decel at the moment your cocoon first makes contact with the ground, ramping up to a max decel level at the moment your speed reaches zero.
The author was more thorough with his math than I was upthread. he assumed the jumper jumped from the sixth floor (20 meters up, impact velocity 20 m/s), and he chose a G limit of 31 for the landing. He determined that you’d need 39 layers of the small-bubble wrap, with a total thickness of about 14.2 cm.