# Dear Evil Engineer: How many balloons do I need to make an elephant fly?

Image credit: Dreamstime

The Evil Engineer consults with the owner of a flying circus, who wants to trade in their custom pachyderm jetpacks for an airier mode of aviation.

Dear Evil Engineer,

I own a flying circus – by which I mean not a barnstorming troop but, quite literally, a circus that flies. My clowns, acrobats and circus animals wear kerosene jetpacks throughout the performance, ensuring an excellent view for all members of the audience. However, I’ve found that the loud noise of their customised jetpacks tends to alarm my dancing bears, elephants and poodles, preventing them from performing to the standard I expect.

I’ve come up with an idea for an alternative mode of flight: gigantic helium balloons, which I could additionally monetise as advertising space. So, how much helium will I need to lift a dancing elephant? And is this helium shortage I keep hearing of going to cause a problem – is there enough helium for my dozen elephants to continue performing?

Yours,

A showbiz villain

Dear villain,

I cannot pretend to know much about managing circuses, but this sounds like a fine proposal to me. Anyone who would not pay to see a dozen elephants drifting through the air to the strains of ‘Entrance of the Gladiators’ is incapable of enjoyment and not worth your consideration.

To know how much helium is required to lift an elephant, we must first calculate how much lifting force helium provides. For this, we must use Archimedes’ principle: a body, wholly or partially immersed in a fluid, experiences buoyancy equal in magnitude to the weight of the fluid displaced by the body. The average density of air at sea level is 1.2kg/m3 while the density of helium at atmospheric pressure at 0°C (standard temperature and pressure) is 0.18kg/m3. Looking at the difference between these two densities, we can say that when a cubic metre of helium displaces a cubic metre of air, this exerts an upward force equivalent to the weight of a 1.02kg mass (weight of 10.2N).

How many cubic metres of helium will you need to support the weight of an elephant? It depends, of course, on what species of elephant you employ. But the adult mass of an elephant ranges from around 5,000kg (Bornean elephant) to 6,000kg (African bush elephant). Supporting a single African bush elephant would require 6,120m3 of helium.

This would require you to fill a spherical balloon with diameter of around 23m to support each of your elephants (or, alternatively, using 560,000 standard party balloons). At approximately £100/m3, your troupe of elephants will use approximately £7.34m of helium. This is not to mention the much larger circus tent you will need to buy to fit all those giant balloons inside. Is it worth it? Perhaps. I’m the Evil Engineer, not the Evil Entrepreneur, so don’t ask me.

Next, the matter of the helium shortage. There is disagreement about whether this is a cause for panic or not. Helium shortages of the sort we hear about in the news are, however, cyclical; we are in the middle of what is being called ‘Helium Shortage 4.0’. Although these shortages are influenced by a variety of events, they are all, in part, related to the clumsy handling of the vast US helium stockpile.

In 1925, the US Bureau of Land Management started to reserve all helium found on federal land, which became an essential resource in the 20th century, such as a coolant during the Space Race. This led to the (expensive) accumulation of a Federal Helium Reserve in the Bush Dome in Amarillo Texas, which stood at one billion cubic metres in 1995. After the US Congress passed the Helium Privatization Act 1996, the government was forced to start selling its helium at below-market prices to clear its debt. With the US flooding the market with cheap helium, industry players had little incentive to invest in helium discovery or recycling. This resulted in sluggish expansion in helium supply, and supply problems during periods of increased demand, such as with booms in semiconductor manufacturing. The last of the Federal Helium Reserve is expected to be sold in September.

In spite of some interventions to stop distorting the helium market (such as a 2013 law which permitted the federal government to sell helium at market price), there remain few helium suppliers. This means that, whenever problems arise at a helium facility, we can expect supply disruptions and price spikes – which will of course affect your bottom line. The current helium shortage can be linked to the closure of a natural gas plant in Russia following an explosion coinciding with the closure of two plants in Qatar for scheduled maintenance. These shortages tend to be rectified in time; a recent shortage was relieved after a rich new helium deposit was discovered in Tanzania.

We are not – by any means – running critically low on helium. Recent studies have even suggested that the gas, which is produced by radioactive decay, may be collecting in natural gas reserves in larger quantities than expected. This does not change the fact, though, that helium is a finite resource – once released into the atmosphere, it is uneconomical to recapture and eventually escapes Earth altogether – and eventually we will run out. How long until then? In 2014, the US Department of the Interior estimated there are 1,169 billion cubic feet (3.3 million cubic metres) of helium reserves left on Earth: enough for another 117 years.

So, how does this match up to your needs? The world’s helium reserves – according to the Department of the Interior estimate – could support the flight of around 5,400 African bush elephants, which is fewer flying elephants than you may expect.

Yours,

The Evil Engineer

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