Buoyancy

The most commonly used keyword to tag stories on this site is “floating”. Second is “helium”. So clearly there’s some interest in the subject. It’s fairly common for people in inflation stories to be filled with helium to the point of becoming airborne. How much helium this requires varies widely from story to story.

So today we address the question: How much helium would it really take to make someone float?

Short answer: a lot.

The long answer involves some math.

If an object is heavier than the volume of fluid it displaces, then it sinks. If it’s lighter than the volume of fluid it displaces, then it floats.

Helium is lighter than air. If a balloon is filled with enough helium that the combined weight of the helium and the balloon is less than the weight of the air that would take up the same amount of space, then the balloon will float.

The density of helium is 0.172 g/l. The density of air is 1.225 g/l. The difference between the two is helium’s lifting power; d_Air - d_He = 1.053 g/l. Converted into less civilised units, it comes out to 0.0657 lbs/ft³

Let’s run the numbers for a typical inflation subject, Nikki. Nikki’s a cheerleader so she’s quite slim, weighing in at a mere 115 pounds. She’s 5’4” and has perky B-cup breasts that she really wishes were bigger and she’s certainly impulsive enough to experiment with imprudent and unconventional means of enlarging them, possibly involving magic, experimental chemicals, and or compressed gas. But that’s for another post. What’s more relevant for now is that she also has long blonde hair, a beautiful face, and a tendency to make nasty comments to nerdy sociopaths who have access to large quantities of helium. Oops.

115 lbs/(0.0657 lbs/ft³) = 1,750.38 cubic feet.

If we were to fill Nikki with 1,800 cubic feet of helium, certainly over her strenuous and high-pitched objections, she would be a slightly buoyant sphere 15 feet in diameter.

Take a moment to contemplate how huge that is for a moment. Nikki would be towering at almost three times her normal height.

Those of you who aren’t gaping in awe about how massive Nikki has become are probably thinking “Hey, Kane, haven’t you overlooked some stuff?” And the answer, of course, is “Yes.”

First, I’m ignoring Nikki’s initial volume. That’s actually not a problem when we’re dealing with such huge volumes. In her uninflated state, Nikki takes up about two cubic feet of space. It’s negligible once Nikki’s blown up.

But I’m also ignoring internal pressure. Since you can’t actually inflate a person to Nikki’s size in real life, how much pressure her body exerts in its attempt to return to its normal shape is up to whoever’s writing the story. The above calculation assumes that Nikki’s body isn’t offering any resistance. This is the “weather balloon” scenario; Nikki would be quite soft and squishy. But since the feeling of pressure is central to so many inflation stories, let’s explore a few other scenarios

First, the “party balloon” scenario. I could only find one experiment online where the pressure inside a latex balloon was measured as it was inflated. Right before it burst it was a pressure of about 1 psi above ambient pressure.

As helium is compressed its lifting power decreases, meaning we’ll need more of it to get Nikki off the ground. And while Nikki would definitely notice an increase in pressure of 1 psi, the effect on lift is negligible. We’d need an extra 24 cubic feet of helium to get her to neutral buoyancy. The 1800 cubic feet used in the weather balloon scenario would still be enough to get her off the ground, albeit a bit more slowly.

Let’s say Nikki fills up to the pressure of a volleyball (~4.5 psi). That still wouldn’t do much. Well, it wouldn’t have much effect on her buoyancy; I’m sure Nikki’s really feeling the pressure at this point. We’d only lose 5% of our lift. We’d need an extra 100 cubic feet of helium and Nikki would increase in diameter by about 3 inches wider to achieve neutral buoyancy.

We’d need to pump Nikki up to a pretty high pressure for it to have a significant impact. At the pressure of a car tire (~ 30 psi), we lose about 30% of our lift. We’d need to fill her up with over 2600 cubic feet of pressurized helium to make her weightless. That would make her about 17 feet across and definitely give her that “look out, she’s going to explode” feeling.

And if she does blow, you’ll want her to have floated far away by then. That much gas under that much pressure will create quite an impressive boom. But for now we’ll deflate Nikki and let her get back to cheerleading practice. We may need her assistance in future writings.