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28 February 2009

How many balloons to lift the Nachoboy?

Saturday brought with it the Nachoboy’s sixth birthday party. I undertook a strategically important job: getting the Nachoboy* out of my wife’s hair while she prepared for the onslaught of 14 kids.

When the boy and I returned from Taco Bell,** the living room was crowded with Helium Balloons. Milo and another small human grabbed the balloons, and the other adults joked with me about the balloons lifting the kids away. So, of course, I had to estimate the number of balloons that could actually lift a six-year-old.

The Nachoboy weighs about 45 pounds, which equivalent to a mass of 20 kg.*** Thus, we need 200 N of lift.

Estimate #1: Buoyant Force Analysis

Archimedes’ Principle states that the buoyant force is equal to the weight of the displaced fluid – so, we need the balloons to displace 200 N (equivalent to 20 kg) of air to lift the Nachoboy. Air has a density in the neighborhood of 1 kg/m3. That makes 20 cubic meters of balloon volume.

Each balloon has a diameter of a bit less than a foot. If we call the radius 10 cm, then the volume of a balloon is .004 m3. (That’s using the equation for the volume of a sphere, (4/3)πr3. It helps to approximate π = 3.) Then, 5000 balloons give us the 20 cubic meters.

Estimate #2: Spring Scale Measurement

I grabbed a spring scale from my classroom. The 13 balloons I could gather in the living room pulled up with about half a newton of force. So, call it 25 balloons to the newton of buoyant force… that gives an experimental estimate of 5000 balloons. It seems our estimates are at least self-consistent.

Estimate #3: Use internet research

First of all, crazy people have in fact levitated themselves with helium balloons for transportation purposes. Most recently, we have a
Mr. Couch from Oregon. But that doesn’t answer the question about numbers. In the picture at the link above, it’s possible to count his balloons, but they seem quite large, and inferring a reasonable scale is difficult.

Not surprisingly, the Mythbusters worked on this very problem, except that they levitated an adult. They only needed 6000-7000 balloons, a number consistent with our order of magnitude estimates above. The pictures at their
slide show of the demonstration show balloons of approximately the size I was considering.

What have I figured out? Well, this won’t work for use at the science demonstration show that the Atlanta Cracker (Woodberry's AP chemistry teacher) and I do each spring for prospective students. On the other hand, we’re starting to look into the price of helium and balloons. It might be worth spending the time and money to capture us lifting Milo on video, and posting the video online. More on this topic eventually, if we do end up filling 5000 balloons.

Or, maybe we should just levitate the cat instead of a kid.


* The Nachoboy is also known as Milo Cebu Jacobs, my six-year-old. The name comes from my other blog, Nachoman's Baseball. Check out some old columns now; I'll be writing there again once the season starts next month.

** The Taco Bell in question is attached to an enormous playground. Funny, I would rebel nastily if someone charged admission to a playground. However, I wholeheartedly support the Taco Bell playground, even though it’s $10 down the drain for lunch every time I take Milo there.

*** Don’t start on me with the “20.45 kg.” We’re making an order of magnitude estimate. I’m happy if I get the number of balloons right to within a factor of 5 or 10. The whole point is to figure out the feasibility of the experiment. If it’s going to take 100,000 balloons, well, we’re never going to actually do that. If it only takes about 20 balloons, we’re having liftoff this afternoon. All numbers here are good to a maximum of one significant figure – and that’s all we need.

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