What-If 0062: "Falling With Helium"

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What-If 0062: "Falling With Helium"

Postby Quicksilver » Tue Sep 10, 2013 8:34 am UTC

http://what-if.xkcd.com/62

"What if I jumped out of an airplane with a couple of tanks of helium and one huge, un-inflated balloon? Then, while falling, I release the helium and fill the balloon. How long of a fall would I need in order for the balloon to slow me enough that I could land safely?"
- Colin Rowe

Image
Seems legit.
Avoiding a high-speed landing is, unsurprisingly, the key to survival. As one medical paper[1] put it,

It is, of course, obvious that speed, or height of fall, is not in itself injurious ... but a high rate of change of velocity, such as occurs after a 10 story fall onto concrete, is another matter.
Speed itself is still a factor though, isn't it? and A bit from my RSS feed that's not on the official article for some reason:
The lesson: Don't mess with medical examiners. They're apparently pretty hardcore.
Last edited by Quicksilver on Tue Sep 10, 2013 10:26 am UTC, edited 1 time in total.

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Re: What-If 0062: "Falling With Helium"

Postby Klear » Tue Sep 10, 2013 9:00 am UTC

Quicksilver wrote:and A bit from my RSS feed that's not on the official article for some reason:
The lesson: Don't mess with medical examiners. They're apparently pretty hardcore.


It is there - note 5.

Also, this reminded me how Click and Drag was more awesome than Time...

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Re: What-If 0062: "Falling With Helium"

Postby rhomboidal » Tue Sep 10, 2013 9:09 am UTC

I love the Armchair Airman. Sometimes you have to break Man's laws in order to better understand Nature's. Or to just do some crazy amazing stuff.

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Re: What-If 0062: "Falling With Helium"

Postby Diadem » Tue Sep 10, 2013 9:11 am UTC

The bit with Wolfram Alpha was pretty awesome.

I'm sure over at Wolfram headquarters they are laughing very hard right now, wondering if they get more free publicity by keeping a world famous cartoonist banned, or by unbanning him :)
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Re: What-If 0062: "Falling With Helium"

Postby Klear » Tue Sep 10, 2013 9:28 am UTC

rhomboidal wrote:I love the Armchair Airman.


I prefer the Anti-Air Chairman

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Re: What-If 0062: "Falling With Helium"

Postby teelo » Tue Sep 10, 2013 10:33 am UTC

Where the hell are the jokes about ones voice changing pitch due to helium :(

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Re: What-If 0062: "Falling With Helium"

Postby ps.02 » Tue Sep 10, 2013 11:02 am UTC

Quicksilver wrote:Speed itself is still a factor though, isn't it?

Acceleration (i.e., the quick deceleration at the end) is what causes the injuries that will kill you: going from 120 mph to zero in a small fraction of a second. Speed is only an indirect factor, in that the speed you achieve will determine how much acceleration you will endure at the bottom. Speed would be a more direct factor if you were a meteor or a Space Shuttle, where the air resistance would literally burn you up. But free fall is orders of magnitude slower.
Randall wrote:The biggest consumer rental helium tanks are about 250 cubic feet, and you'd need to empty at least 10 of them to put enough air in the balloon to support your weight.

Aside from using the inexact term "air" for helium, does he mean "support your weight" completely, or just enough to, along with the drag from the balloon size and shape, slow your terminal velocity to something plausibly survivable? 'Cause it sounded like the former, which would be disappointing, since the real question is the latter.

Too bad he didn't go into specifics of how much buoyancy, how much drag, and how much terminal velocity we're actually talking about. Those kinds of specifics are usually what What If? is about.

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Re: What-If 0062: "Falling With Helium"

Postby Lazy Tommy » Tue Sep 10, 2013 11:11 am UTC

ps.02 wrote:Too bad he didn't go into specifics of how much buoyancy, how much drag, and how much terminal velocity we're actually talking about. Those kinds of specifics are usually what What If? is about.


I have a feeling that if you really want to answer the question definitively, you need to take into account how the pressure from falling at high speed is going to squeeze the balloon, make it hard to inflate, and maybe even raise the pressure inside the balloon to the point where it doesn't provide enough buoyancy.... And all that is assuming that the balloon doesn't simply tear.

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Re: What-If 0062: "Falling With Helium"

Postby Klear » Tue Sep 10, 2013 12:12 pm UTC

ps.02 wrote:Aside from using the inexact term "air" for helium, does he mean "support your weight" completely, or just enough to, along with the drag from the balloon size and shape, slow your terminal velocity to something plausibly survivable? 'Cause it sounded like the former, which would be disappointing, since the real question is the latter.

Too bad he didn't go into specifics of how much buoyancy, how much drag, and how much terminal velocity we're actually talking about. Those kinds of specifics are usually what What If? is about.


I wonder what is the speed that can be considered safe. People occasionally survive falls at terminal velocity, though that heavily depends on what kind of surface you hit. There has to be quite a difference between "slows you enough to ensure your survival" and "allows you to hover".

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Re: What-If 0062: "Falling With Helium"

Postby Introbulus » Tue Sep 10, 2013 1:06 pm UTC

Of course they will unban him, once they see the perfectly worded explanation for why he is doing these calculations.

That is, the two word explanation. In the name field.

That will explain everything.
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Re: What-If 0062: "Falling With Helium"

Postby waveney » Tue Sep 10, 2013 1:09 pm UTC

Diadem wrote:The bit with Wolfram Alpha was pretty awesome.

I'm sure over at Wolfram headquarters they are laughing very hard right now, wondering if they get more free publicity by keeping a world famous cartoonist banned, or by unbanning him :)


For those who don't realise - Mathematica is produced by Wolfram...

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Re: What-If 0062: "Falling With Helium"

Postby Klear » Tue Sep 10, 2013 1:09 pm UTC

He should have added:

"Unban me quickly! It's a matter of life and death!"

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Re: What-If 0062: "Falling With Helium"

Postby nitePhyyre » Tue Sep 10, 2013 1:15 pm UTC

ps.02 wrote:Too bad he didn't go into specifics of how much buoyancy, how much drag, and how much terminal velocity we're actually talking about. Those kinds of specifics are usually what What If? is about.
Well, he was going to, but then he got banned.
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Re: What-If 0062: "Falling With Helium"

Postby cellocgw » Tue Sep 10, 2013 1:32 pm UTC

+1 for the "AAAAAAAAAAAAAAAA"


But, -0.001 for not having BHG say, "But what if we tried MORE HELIUM?"

Besides, I bet 3/4 of the way down the balloon will turn into a bunch of petunias. Then what?

And, finally, what if you climb on top of the balloon just before impact, turning it into a giant mattress?
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Re: What-If 0062: "Falling With Helium"

Postby Zassounotsukushi » Tue Sep 10, 2013 2:35 pm UTC

I was disappointed with this one! I need hard numbers. What is the buoyancy to drag ratio?

drag coefficient should come from a simple sphere, Cd = 0.47

The buoyancy is dictated by the ratio of densities, but we have several complications.

  • The expansion affect the Helium temperature, which impacts its density
  • The balloon itself has some weight

I would still prefer to ignore these factors. So the basic idea is:

Image

The density difference is (1.097 kg/m^3). The base density of air is (1.3 kg/m^3). We know gravity, and now I've defined everything else. The remaining unknowns are the velocity and the radius of the balloon. For that, we'll have to add one more bounding equation which takes into account the mass of the falling person. I'll use 100 kg for this, to be the standard human. This is a fairly large human, so it can either represent a nerd carrying extra equipment, or a marine with no extra equipment.

The force balance is simply:

Image

Plug in the expression from above and we'll have an expression with v and R. This is what we want, because R can be adjusted to obtain a certain value of v.

Image

Now that's better. Here is the Google search string to get the velocity with a radius of 2 meters:

Code: Select all

sqrt( (2*(9.8 m/s^2)*(100 kg)-(9.8 m/s^2)*(8/3)*Pi*(2 m)^3*(1.09 kg/m^3) ) / ((1.3 kg/m^3)*0.47*Pi*(2 m)^2) ) = 12.7 m/s


Now here is the velocity for the full range of radii.

Image

At around 2.7 meter radius, the thing just stops. The above equation goes imaginary because it is no longer falling - it is floating. Here is a comparison of the drag and the buoyancy.

Image

This is the juicy stuff I wanted to see. As the balloon gets bigger, the drag component drops off and the buoyancy gets larger. There's little impact from the buoyancy up until a radius of about 1 meter. After that, the cross-over happens fairly fast. But in a volume-based view it would be a good bit more gradual. Ignore the parts beyond 2.6 meters, it's junk. The thing is moving up after that point.

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Re: What-If 0062: "Falling With Helium"

Postby taemyr » Tue Sep 10, 2013 4:32 pm UTC

The to note in this installment is that xkcd is apparently incorporated.

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Re: What-If 0062: "Falling With Helium"

Postby keithl » Tue Sep 10, 2013 5:14 pm UTC

taemyr wrote:The to note in this installment is that xkcd is apparently incorporated.
Presumably to limit liability, if empiricists read the comic.

Added: You can look up xkcd inc. at http://corp.sec.state.ma.us/corpweb/CorpSearch/CorpSearch.aspx.

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Re: What-If 0062: "Falling With Helium"

Postby Anachronism » Tue Sep 10, 2013 5:41 pm UTC

Zassounotsukushi wrote:I was disappointed with this one! I need hard numbers...


So, using your numbers and an LD50 of about 16.94 m/s, we get a radius of 1.7m, or 20.6 m^3 of helium. Amazon sells a helium tank regulator that claims the tank is full at 2000 psi (though NASA uses one at 4800 psia), or around 136 atm, so our daredevil would only need a tank of around 0.15 m^3 to fill his balloon. Seems totally doable. Any volunteers?

Sorry for lack of citations, but keep getting flagged as spam with them in.

edit: math typo
Last edited by Anachronism on Wed Sep 11, 2013 5:00 pm UTC, edited 1 time in total.

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Re: What-If 0062: "Falling With Helium"

Postby Yoshisummons » Tue Sep 10, 2013 6:10 pm UTC

You an only post links if you already had 5 posts to your account previously. The tanks they sell with such a high pressure are mostly made of very heavy materials. I can already see the Bond movie where the bad guy tosses Bond out of a jet in flight tied to a helium tank to kill him but Bond uses it to escape disaster :) .
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Re: What-If 0062: "Falling With Helium"

Postby gmalivuk » Tue Sep 10, 2013 7:46 pm UTC

Anachronism wrote:
Zassounotsukushi wrote:I was disappointed with this one! I need hard numbers...


So, using your numbers and an LD50 of about 16.94 m/s, we get a radius of 1.7m, or 12.1 m^3 of helium. Amazon sells a helium tank regulator that claims the tank is full at 2000 psi (though NASA uses one at 4800 psia), or around 136 atm, so our daredevil would only need a tank of around 0.09 m^3 to fill his balloon. Seems totally doable.
Except that most of the actual tanks I've seen listed for sale seem to top out at 300 cubic feet worth of gas, and you're saying you'd need over 400.
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Re: What-If 0062: "Falling With Helium"

Postby rmsgrey » Tue Sep 10, 2013 8:17 pm UTC

The medical examiner may be hardcore, but his reading comprehension may need work - yes, being hit by a car is not very similar to being hit by the ground, but, here in the UK, and in many other places, buses have vertical (or near-vertical) fronts - being hit by one of them would be like being hit by a 10' high brick wall rather than a car.

So, yeah, good information, but not really relevant to the point being responded to...

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Re: What-If 0062: "Falling With Helium"

Postby Anachronism » Tue Sep 10, 2013 9:00 pm UTC

gmalivuk wrote:
Anachronism wrote:
Zassounotsukushi wrote:I was disappointed with this one! I need hard numbers...


So, using your numbers and an LD50 of about 16.94 m/s, we get a radius of 1.7m, or 12.1 m^3 of helium. Amazon sells a helium tank regulator that claims the tank is full at 2000 psi (though NASA uses one at 4800 psia), or around 136 atm, so our daredevil would only need a tank of around 0.09 m^3 to fill his balloon. Seems totally doable.
Except that most of the actual tanks I've seen listed for sale seem to top out at 300 cubic feet worth of gas, and you're saying you'd need over 400.


That's because you made the mistake of limiting yourself to party supply stores in a "What If" thread. PSI-PCI sells a 4105 in^3 tank that pressurizes to 310 bar. So 20.8 m^3 at STP? More than enough for our balloonachute.

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Re: What-If 0062: "Falling With Helium"

Postby Anachronism » Tue Sep 10, 2013 9:05 pm UTC

Yoshisummons wrote:You an only post links if you already had 5 posts to your account previously. The tanks they sell with such a high pressure are mostly made of very heavy materials. I can already see the Bond movie where the bad guy tosses Bond out of a jet in flight tied to a helium tank to kill him but Bond uses it to escape disaster :) .


Please, a Bond villain would totally use a "titanium-lined, graphite epoxy overwrapped pressure vessel" and it's only 23.5 pounds of fun! At that weight, most people wouldn't even have to dump the tank to land safe-ishly. I still totally watch your movie though.

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Re: What-If 0062: "Falling With Helium"

Postby gmalivuk » Tue Sep 10, 2013 9:43 pm UTC

Anachronism wrote:That's because you made the mistake of limiting yourself to party supply stores in a "What If" thread.
No, I was looking on ebay. I doubt many party supply stores sell 300 cubic feet of gas.

PSI-PCI sells a 4105 in^3 tank that pressurizes to 310 bar. So 20.8 m^3 at STP? More than enough for our balloonachute.
Sure, if you're talking about higher pressure than was previously mentioned. A 67L tank is significantly short of the 90L you quoted before.

And your 20.8m^3 assumes the gas would stay the same temperature (in addition to using 1bar instead of the real pressure at STP), which doesn't seem like a good assumption if you're decompressing it fast enough to fill a balloon during your fall.
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Re: What-If 0062: "Falling With Helium"

Postby Wnderer » Tue Sep 10, 2013 9:56 pm UTC

But what if you heat the helium?

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Re: What-If 0062: "Falling With Helium"

Postby dalcde » Tue Sep 10, 2013 10:20 pm UTC

rmsgrey wrote:The medical examiner may be hardcore, but his reading comprehension may need work - yes, being hit by a car is not very similar to being hit by the ground, but, here in the UK, and in many other places, buses have vertical (or near-vertical) fronts - being hit by one of them would be like being hit by a 10' high brick wall rather than a car.

So, yeah, good information, but not really relevant to the point being responded to...


I guess you did not read the whole thing:
http://boards.straightdope.com/sdmb/sho ... stcount=40
A person hit by a bus would actually be run over. There would be two separate sets of injury. The first would be when the kinetic energy of the bus struck the pedestrian. Mass times velocity squared. This is the closest approximation to the ground that your example offers. The likelihood is that they would incur lots of fractures, but not be killed by simple impact. If they were killed, the injury I have seen most often, in my autopsies as a medical examiner, is rib fractures, with the free ends of the ribs bending inward at the moment of impact, to perforate heart and lungs. This is a vanishingly rare injury in fatal falls.

If they are then run over, they incur compression injuries beneath the tire marks, which makes them, in layman's terms, squuushed. They are not squshed the same way that people who land after high falls are squished: very different sets of internal injuries. This is not what you wanted from your example.

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Re: What-If 0062: "Falling With Helium"

Postby dalcde » Tue Sep 10, 2013 10:26 pm UTC

Klear wrote:He should have added:

"Unban me quickly! It's a matter of life and death!"


http://xkcd.com/135/

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Re: What-If 0062: "Falling With Helium"

Postby keithl » Tue Sep 10, 2013 11:07 pm UTC

gmalivuk wrote:And your 20.8m3 assumes the gas would stay the same temperature (in addition to using 1bar instead of the real pressure at STP), which doesn't seem like a good assumption if you're decompressing it fast enough to fill a balloon during your fall.
You may be thinking about air, which has a positive Joule-Thomson coefficient - it cools when it expands. Helium has a negative J-T coefficient - it heats up (and is temporarily less dense)! I was thinking the same thing, but looked it up. A clever posting (assuming cooling) shot to hell, and deleted.

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Re: What-If 0062: "Falling With Helium"

Postby ps.02 » Tue Sep 10, 2013 11:25 pm UTC

gmalivuk wrote:And your 20.8m^3 assumes the gas would stay the same temperature (in addition to using 1bar instead of the real pressure at STP), which doesn't seem like a good assumption if you're decompressing it fast enough to fill a balloon during your fall.

About how long does the fall take? I mean, it's possible to build some ugly linear equations (are there any other kind?) involving many gradients:
- Deceleration due to drag and buoyancy
- Warming and expansion of the helium from contact with the (also warming as you fall) air
- Increasing buoyancy of the helium as air density rises (or...does this cancel out as the balloon shrinks for the same reason? I'm not smart enough to know)
But if the fall takes long enough for deceleration to bring you down to a steady state (the new terminal velocity), then we can ignore all that.

Random thought: could you increase your maximum safe terminal velocity by inflating a second, smaller, balloon beneath you? Small enough to not flip over during the descent, but large enough (and strong enough) to cushion your fall?

keithl wrote:Helium has a negative J-T coefficient - it heats up (and is temporarily less dense)!

Mind blown. OK, just assume I edited the above text accordingly.

Anachronism wrote:Please, a Bond villain would totally use a "titanium-lined, graphite epoxy overwrapped pressure vessel" and it's only 23.5 pounds of fun! At that weight, most people wouldn't even have to dump the tank to land safe-ishly. I still totally watch your movie though.

Surely the movie would be named What-If 0062, or How I Learned to Stop Worrying and Love the Tank.

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Re: What-If 0062: "Falling With Helium"

Postby rmsgrey » Tue Sep 10, 2013 11:48 pm UTC

dalcde wrote:
rmsgrey wrote:The medical examiner may be hardcore, but his reading comprehension may need work - yes, being hit by a car is not very similar to being hit by the ground, but, here in the UK, and in many other places, buses have vertical (or near-vertical) fronts - being hit by one of them would be like being hit by a 10' high brick wall rather than a car.

So, yeah, good information, but not really relevant to the point being responded to...


I guess you did not read the whole thing:
http://boards.straightdope.com/sdmb/sho ... stcount=40
A person hit by a bus would actually be run over. There would be two separate sets of injury. The first would be when the kinetic energy of the bus struck the pedestrian. Mass times velocity squared. This is the closest approximation to the ground that your example offers. The likelihood is that they would incur lots of fractures, but not be killed by simple impact. If they were killed, the injury I have seen most often, in my autopsies as a medical examiner, is rib fractures, with the free ends of the ribs bending inward at the moment of impact, to perforate heart and lungs. This is a vanishingly rare injury in fatal falls.

If they are then run over, they incur compression injuries beneath the tire marks, which makes them, in layman's terms, squuushed. They are not squshed the same way that people who land after high falls are squished: very different sets of internal injuries. This is not what you wanted from your example.


You're right, I assumed that Randall's quote was not misleading.

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Re: What-If 0062: "Falling With Helium"

Postby gmalivuk » Tue Sep 10, 2013 11:52 pm UTC

keithl wrote:
gmalivuk wrote:And your 20.8m3 assumes the gas would stay the same temperature (in addition to using 1bar instead of the real pressure at STP), which doesn't seem like a good assumption if you're decompressing it fast enough to fill a balloon during your fall.
You may be thinking about air, which has a positive Joule-Thomson coefficient - it cools when it expands. Helium has a negative J-T coefficient - it heats up (and is temporarily less dense)! I was thinking the same thing, but looked it up. A clever posting (assuming cooling) shot to hell, and deleted.

Air, along with everything else I've ever witnessed the decompression of (i.e. other coolants and things in spray cans and the like). It seems so counterintuitive that some gases would behave otherwise, but I guess that just goes to show once again how lousy intuitions are when doing science about things outside everyday experience.
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Re: What-If 0062: "Falling With Helium"

Postby Khrushy » Wed Sep 11, 2013 2:26 am UTC

The most surprising part about this one was discovering that the Wolfram team haven't yet flagged or banned Randall's IP for earlier crazy requests.

I'd be really interested to see what queries they have listed under his IP.
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Re: What-If 0062: "Falling With Helium"

Postby flogge » Wed Sep 11, 2013 3:13 am UTC

High pressure helium tanks have lots of extra energy that you could use to pull in air as well as helium. Just use a venturi or possibly a micro-turbocharger if it's more efficient to draw in ambient air along with the helium. You get a mixed-gas balloon with less bouyancy/volume but you cut the amount of tank you are carrying at the beginning.

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Re: What-If 0062: "Falling With Helium"

Postby Tattle » Wed Sep 11, 2013 7:20 am UTC

What if you were to climb on top of the balloon, would that make a fall more survivable?
Hilarious to see Randall got banned from Wolfram Alpha, I'm surprised it hasn't happened before.

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Re: What-If 0062: "Falling With Helium"

Postby Zassounotsukushi » Wed Sep 11, 2013 1:19 pm UTC

Now that I look at the question again, it seems to be mostly focused on the release rate of the gas into the balloon.

I guess the balloon could supposedly inflate to infinite size (for the sake of argument), and we're only interested in the time it would take for the inflating balloon to break your fall. It's kind of implying using Helium balloons to base jump. This is all more complicated than I took it for.

But now - what if you could climb on top of the balloon right before you hit the ground? That seems like it would be awfully unstable, but you would get the balloon to cushion your fall. In fact, it seems like it would be a better idea to do this with air. Don't bother slowing down much. Just inflate a makeshift bouncy pad.

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Re: What-If 0062: "Falling With Helium"

Postby kventin » Wed Sep 11, 2013 1:28 pm UTC

Zassounotsukushi wrote:But now - what if you could climb on top of the balloon right before you hit the ground? That seems like it would be awfully unstable, but you would get the balloon to cushion your fall. In fact, it seems like it would be a better idea to do this with air. Don't bother slowing down much. Just inflate a makeshift bouncy pad.


What if you used hydrogen and ignited it right before you hit the ground?

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Re: What-If 0062: "Falling With Helium"

Postby keithl » Wed Sep 11, 2013 3:04 pm UTC

kventin wrote:What if you used hydrogen and ignited it right before you hit the ground?
Not prudent. Unless you are a Nazi. Do I get Godwin's Law points for this?
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Re: What-If 0062: "Falling With Helium"

Postby rmsgrey » Wed Sep 11, 2013 3:38 pm UTC

keithl wrote:
kventin wrote:What if you used hydrogen and ignited it right before you hit the ground?
Not prudent. Unless you are a Nazi. Do I get Godwin's Law points for this?

That was the envelope rather than the hydrogen igniting that caused the problem...

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bmonk
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Re: What-If 0062: "Falling With Helium"

Postby bmonk » Wed Sep 11, 2013 4:59 pm UTC

kventin wrote:
Zassounotsukushi wrote:But now - what if you could climb on top of the balloon right before you hit the ground? That seems like it would be awfully unstable, but you would get the balloon to cushion your fall. In fact, it seems like it would be a better idea to do this with air. Don't bother slowing down much. Just inflate a makeshift bouncy pad.


What if you used hydrogen and ignited it right before you hit the ground?

You might survive--unless you got trapped in the fireball.
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Re: What-If 0062: "Falling With Helium"

Postby davidstarlingm » Wed Sep 11, 2013 6:20 pm UTC

Zassounotsukushi wrote:But now - what if you could climb on top of the balloon right before you hit the ground? That seems like it would be awfully unstable, but you would get the balloon to cushion your fall. In fact, it seems like it would be a better idea to do this with air. Don't bother slowing down much. Just inflate a makeshift bouncy pad.

Like in the opening chase scene from MI4?

bmonk wrote:
kventin wrote:What if you used hydrogen and ignited it right before you hit the ground?

You might survive--unless you got trapped in the fireball.

Is it possible to time a blast wave such that it will slow you down to a not-particularly-dangerous impact speed without causing significant injury?

I mean, if movies and TV are to be believed, a blast wave is more than capable of flinging you across a room without much more than ringing in your ears. I'm guessing this is theoretically possible. One could then conceive of a Rapid Deceleration Gun that you pointed toward the ground while falling, then fired; it would have to measure the distance to the ground and the current airspeed, then fire a charge that would explode with the correct force to completely cushion your landing.


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