## Full of hot air!

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.

Image credits:
Upper – AP Photo/Red Bull Stratos, Luke Aikins
Lower – Gizmodo

Molecular astrophysicist, usually found writing frenziedly, staring at the sky, or drinking mojitos.
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### 56 Responses to Full of hot air!

1. aerychtest says:

Reblogged this on aerychtest and commented:

2. Wow! What a funny post! 1.6 million people running around talking in a squeaky voice at each other would be a funny sight to see.

3. That’s so pointless, yet so clever. I give up. But I love the silly science bit.

4. Hmm… Now I’m totally flummoxed. Being old and feeble of mind may be the issue, but I recall reading, lo those many years ago, that something could not fall faster than 127 miles per hour on the Earth. Clearly this is wrong, do you know what bon mot of science might have misdirected me? Thanks!

5. vyvacious says:

I love your mesh of worlds, both comedic and science-y. I’m a nerd at heart so this post truly reaches out to me. Now if only I could combine some crazy science with my love of baking and Batman…maybe then I’ll be freshly pressed too! :P

It’s a fun way of seeing the world… And hmmm… I don’t know about baking and Batman together, but the two separately can totally be done. Actually someone’s already done some Batman science

• vyvacious says:

Yes it is :)

Well, I’ve managed to accomplish it to some extent! :P

Ooh, thanks for the interesting read!

6. amaya ellman says:

Although I graduated with a physics degree, I never realised blogging about anything even remotely scientific could work out so cool. Keep up the good work.

I guess that’s just the way things are taught. “It’s not supposed to be fun.” Frankly, I still don’t buy that. These things can and should always be fun. :)

7. I saw the video of Mr. Baumgartner falling from outer space. What an amazing feat and you have included data and introspective of such a feat to make it even more spectacular. Thank you for your post!

I always enjoy looking at things from a slightly different angle… :)

8. :-)

9. refugeekni says:

Reblogged this on refugeekNI and commented:
I found this educational, completely baffling and wonderful. So wonderful.

S.

10. Cool post, funky info! Thanks!

11. well that was a great equation!

12. Hilariously informative! Kudos for making me laugh and remember how much I love physics/loathe chemistry. Congrats on being freshly pressed!

Thank you, and I’m glad you enjoyed it!

Well what do you know! Science is FUN!!

14. Now that would be worth the price of admission! :)

Wouldn’t it? :)
Oh, just imagine Midsummer Night’s Dream… “Methinks I was in love with an ass!”

15. Gwenniesmom says:

Congrats on FP!! I LOVED reading this. It was silly, entertaining, but most of all informative. :)

Thank you so much. Glad I accomplished what I set out to do! :D

16. wesleybeath says:

Very original, great post.
A very fun take on a bit of maths and science.

Maths and science should be fun, IMHO. Any less is doing it wrong. :)

Always time for more silliness! :)

18. Pingback: Full of hot air! | birdmanps

19. Congratulations on being pressed.

I am rather surprised no one has taken Red Bull to task for wasting all of that Helium …. what with the world wide shortage which is supposedly holding back our economy.

:)

Thank you for a light hearted look at falling from the lowest edge of space.

ghost.

Thank you! :)

It’s interesting, you’re not the first person I’ve seen who’s said that. The trouble is that, despite being the second most abundant type of atom in the entire Universe, our planet is naturally deficient in helium. Simply speaking, Earth’s gravity isn’t strong enough to hold on to helium, so any helium entering the atmosphere is essentially lost permanently. There’s no way of getting it back, and it’s guaranteed to escape into space. By now, all the helium on Earth is created by radioactive decay of heavy elements in Earth’s crust.

Couple that with the fact that the rubber which makes up balloons actually contains pores. Helium atoms are tiny, so they can escape quite easily from the pores in your average balloon (which is why they’re usually shriveled up by the day after a party). Basically, every balloon which is ever filled is helium lost to our planet.

It would be interesting, perhaps, to work out how many helium balloons are filled every day on Earth. Unfortunately, it would also be hypocritical for anyone who’s ever been to a birthday party (myself included) to criticise Red Bull for wasting helium… Of course, if anyone were to invest in space travel, there are some conveniently large supplies of helium in some other parts of the solar system. ;)

Glad you enjoyed my post. :D

• I enjoyed your post. And I recommend we send you to go get some helium.

:)

20. Reblogged this on stephenfranano.

21. segmation says:

I never thought of this mathematically! Awesome!

I’m pretty sure you can find some odd mathematical ways to think about pretty much anything if you look hard enough. I suggest we all keep on looking! :)

22. Very well written post! That whole expedition was mind blowing in a way, so many factors and outcomes came into play! Congrats on being Freshly Pressed!

Thanks! To be honest, I think the thing I admired the most was the sheer audacity of an event like this. The fact that no matter how ludricrous it sounded, Baumgartner was going to do it anyway! Sometimes I just love the things that people are capable of…

23. Very nice post, well written and good with explaining the basics of the math and science involved with out getting too over technical.

24. liamodell1 says:

Congratulations on being FP! Great post! Helium is such an intriguing thing, isn’t it? :)

Thank you. :)
And yes, definitely. I may have written about helium once or twice before… ;)

25. nmbpro says:

I watched in amazement as Felix Baumgartner fell to the earth breaking the sound barrier and have been bursting at the seams to write a post about the science of it all. So when I saw this post on freshly pressed, I thought to myself, I more or less know what this one is about, but let me go ahead and read it anyway. Having just finished reading it, I have to say thank you for the surprise. I wasn’t expecting such a light and fun way to write about a mathematically dense subject. It was such a pleasure to read.

26. rebecca2000 says:

Congratulations on being Freshly Pressed. I love this silly science data. Great post!

x,
Becca

Thank you! :)
And I think the line from classic Doctor Who says it best – “What’s the point of being grown up if you can’t be childish sometimes?”

27. 3arn0wl says:

I was thinking that his jump would make the mother of all Terminal Velocity questions. Can’t seem to lay my hands on the necessary data though. :(

Oh? I’m intrigued… What data do you need? I might be able to lend a hand… :)

• 3arn0wl says:

Is his terminal velocity known? How long did it take for him to reach it? Do we know the exact height he fell from, and have you got an accurate time of the complete fall?

It would be very interesting (not to mention useful) to build a velocity / time graph – maybe even over the film of him falling.

Oh, interesting. Baumgartner’s jump was apparently from an altitude of 39045 m, with 4:19 spent in freefall. Though the actual calculation isn’t quite so trivial. After all, terminal velocity has to do with the restraining force exerted by the air – but that would vary with pressure. The troublesome part is the fact that from the altitude at which Baumgartner jumped, the relationship between pressure and altitude isn’t linear…

So actual terminal velocity will vary non-linearly with altitude similarly to the way pressure does. If you graph it, you could work it out though. I’d be interested to see what you find! :)

• 3arn0wl says:

Oh! More complicated than my ability then! Ah well!! :/

Thanks for the post and the reply.

Heh… sorry. Didn’t mean to scare you off. You could probably approximate it pretty well by calculating the terminal velocity every 5 km… But no worries. :)

You’re welcome!

28. Baribal says:

What a coincidence. After the Baumgartner jump I was thinking of the drones in Alien Planet again, and how hard they’d be to build on a budget. Obvioulsly, the hydrogen in the balloons would have to go, probably in favor of hot air, but after a bit of googling it seemed to me that they could only produce 100g of lift per cubic meter balloonsize per 30°C temperature difference to the outside. Do you have some idea what the drone tinkerer on a budget could use to generate enough lift to float enough equipment to search for intelligent life on Earth?
(Or some ideas about tests for sapience. The movie wasn’t too detailed on that part.)