One of my favourite things to do from time to time on this blog is to answer peoples’ random silly science questions with… well… random silly science. And a friend of mine asked me a brilliant question the other day. A question about squeaky voices and helium balloons. Really really big helium balloons!
❝How many people could have had silly voices using the amount of helium in Felix Baumgartner’s balloon?❞
This past week, a man named Felix Baumgartner successfully managed a sky dive from 39 km up in the atmosphere and actually managed to break the sound barrier during his descent – the only human ever to do so without any kind of vehicle. Impressively, the balloon which Baumgartner jumped from, the Red Bull Stratos itself, was one of the largest balloons ever constructed. According to Gizmodo (who are usually quite a reliable source) the balloon was made to hold 834497 cubic metres of helium.
Well ok, so they got the value in m3 (sic) wrong in their infographic there (that’s actually the volume of the balloon used by the previous record holder). Sloppy, Gizmodo. Very sloppy. Let’s go by the value in the article text though. 8.34 x 105 m3 is a lot of gas. But there’s a missing piece to the puzzle here.
Nowhere does it say if this is the balloon’s volume at ground level or at maximum altitude. Gasses are squishy things, and the same amount of gas would take up much more space high up in the atmosphere where the pressure is lower – 39 km is actually above most of the stratosphere, above the ozone layer too. Unfortunately, I can’t seem to find anything about this, so let’s assume that publicity people do what they always do and that’s the balloon at maximum size. So I’ll need to work a little gas equation chicanery to figure out what volume of helium that is at ground level…
It’s a pretty simple bit of maths, actually. Basically for any given set of conditions, the pressure multiplied by volume, divided by temperature always equal a constant. Change any one value, and the others have to change too. So let’s assume standard conditions at ground level (101325 Pa of pressure and about 20°C). Conveniently, I found an article (which I’m arbitrarily going to trust implicitly) telling me that at 39 km, Baumgartner’s balloon would have had 434.6 Pa of pressure and a rather chilly -57°C. Cool. Let’s put the temperatures in Kelvin and crunch numbers.
So at ground level, the balloon is a slightly less impressive 4852.36 m3. Which is nevertheless, still rather a lot of gas. Enough to make a lot of people talk in a squeaky voice?
The average human lung volume is about 6 litres. But that’s total volume – and you’re never going to take in 6 litres in even your deepest breath, on account of the fact that your lungs are never completely empty. The deepest breath you can draw is called your vital capacity, which is on average 3 litres, or 0.003 m3. Ok, this calculation is easy now.
So Felix Baumgartner’s balloon used enough helium for over 1.6 million people to talk in a squeaky helium voice! But wait, there’s more…
❝You could go one step further & work out what percentage of the complete works of Shakespeare could be spoken with it.❞
I can say in all seriousness – that is a performance which I would like to see! My friends ask me the best questions…
So Shakespeare, as we all know, was a rather prolific chap, who wrote a grand total of 43 works, contining well over 884000 words in total (the exact quoted number varies slightly from place to place). Apparently, that makes about 118400 individual lines of text. Which is a lot, sure, especially if you assume that any good actor takes a breath before each line. But remember, there are over 1.6 million breaths of helium to be taken from that balloon.
In short, courtesy of the Red Bull Stratos balloon, you could give 13 hilariously funny enactments of Shakespeare’s complete works, and still have enough helium leftover to do your favourite ones again.
Just imagine watching Hamlet. I don’t think I’d be able to take the character seriously ever again!
Incidentally, and a bit misleadingly, despite the event being being touted as a jump from “the edge of space” the actual edge of space is rather higher up – the Kármán Line, situated at an altitude of 100 km. Arbitrary, perhaps, but that’s the cutoff that’s typically used to determine whether an aircraft is actually in space or not.
Upper – AP Photo/Red Bull Stratos, Luke Aikins
Lower – Gizmodo