In my second year studying Physics, we were required to present a talk about Physics. A short talk, about 10 minutes with 5 minutes for questions. So this is what I decided to talk about: Imagine a someone jumps out of a plane with helium balloons, would they make it? - Yep, titled Splat?
This by the way, was one of the motivations for IN[SCI]TE that Andy and I co-founded. Anyway lets jump right in, - pun intended - jumping out of a plane with a bunch of helium balloons is a stupid idea; and no, not because it’s dangerous, but because it doesn’t work. This is because the pressure needed by the balloon to slow down the jumper at high altitudes would be ineffective at lower altitudes (atmospheric pressure at lower altitudes is higher so would squeeze the balloons, smaller balloons means less air resistance and a smaller buoyancy force). And the ideal pressure to slow down the jumper at low altitudes would pop the balloon at high altitudes.
So the solution is, no not to dismiss our poor jumper from this barbaric experiment, but to give our jumper a pressurized helium tank and some weather balloons to be inflated on the way down. This solves our high altitude / low altitude problem. It makes it possible for the balloon to have less pressure at higher altitudes and more pressure at lower altitudes, this helps keep the balloons’ sizes constant and at their maximum.
I won’t go into details on here, I will include the presentation (nice pictures and a few equations), the report (no pictures :( and a lot of equations) and the matlab code. I’ll just quickly mention what concepts I used: the foces acting on the balloon are gravity, buoyancy and air resistance. The Mooney-Rivlin Model relates the pressure inside the balloon to its radius, and so volume. The Bernoulli Equation and the Continuity Equation together describe how fast the balloons inflate from the tank (up to a constant, by modeling how the balloon inflates on the ground we can find that constant).
I was actaully surprised with the results, so the jumper lands with a speed of 60kph. This is actually not that large a speed, compared to no balloons at all which is 270kph! Or the speed had the balloons been pre-inflated: 200kph! So I looked at car collision stats, survival rates for car collisions at 60kph are: 40% fatality, 50% sustained severe injury, 10% survived with only slight injuries. So there you go, very bleak, here are the files!