In the new Pixar film Up, a crotchety old man named Carl ties thousands of balloons to his house and proceeds on an awesome flying adventure to South America. This left several Explainer readers wondering: Just how many balloons would it take to lift a house?
Between 100,000 and 23.5 million. The lower figure comes from the Wired Science blog, which took a crack at the calculation last week. After consulting with a house mover, Wired estimated that Carl's home in Up would be about 100,000 pounds. (Most houses weigh between 80,000 and 160,000 pounds.) Given that 1 cubic foot of helium can lift 0.067 pounds, it would take 1,492,537 cubic feet of helium to lift the house—or about as much as would be contained in 105,854 balloons, each 3 feet in diameter.
This figuredoesn't account for the weight of the balloons themselves, however. A 3-foot latex balloon—which is bigger than your average party balloon but smaller than the ones used in the extreme sport of cluster ballooning—might weigh about 1 ounce. So 105,854 of them would add 6,615 pounds to the weight of the house. The weight of the strings also needs to be taken into account. (A Wired Science commenter estimates that "non-optimal rigging" would require about 1,800 pounds of rope.) The Wired piece noted that it would take more balloons to lift Carl's house above the cloud cover, but according to experienced cluster balloonists, that's not necessarily true. If the balloons are made out of an elastic material like latex and haven't been fully inflated beforehand, they'll expand as they rise into the thinner atmosphere, which should keep the house rising steadily.
If Carl were trying to use regular old party balloons to fly his house, he'd need a whole lot more. A typical party balloon—11 inches in diameter, with 26 inches of curling ribbon—can lift 4.8 grams, or about 0.17 ounces. Assuming these flimsier balloons could withstand the strain—and not counting the extra string that would be involved—it would take more than 9.4 million balloons to lift Carl's house.
Meanwhile, Up co-director Pete Docter recently told Ballooning magazine that techniciansat Pixar estimated it would take 23.5 million party balloons to lift a 1,800-square-foot house like Carl's, though it's unclear exactly what size balloon they were using to make their calculations. (In the film, the animators used 20,622 balloons for the liftoff sequence, but most of the other floating scenes have just 10,297.)
These figures all assume that Carl's house is simply being lifted off the ground. In the movie, however, Carl's house rips free from its foundation, which would likely require a dramatic increase in the number of balloons needed. (Consider that in a storm situation, shifting a house clean off its foundation requires wind speeds of around 120 mph, which is what you'd find in a Category 3 hurricane.) Plus, if the cluster were big enough to have that much lifting force, the house wouldn't leisurely float away after being unmoored, as it does in the film—it would shoot off like a rocket. Another physicist has taken issue with the manner in which the balloons were deployed in the film, noting that Carl didn't seem to have factored in the need for an anchor to keep the house weighed down until he was ready to unleash his balloons.
Bonus Explainer: Is it legal to set off in a flying house? Not without the proper certification. Most cluster-balloon systems, which carry a solo flier in a harness or chair, are considered ultralight vehicles, like hang gliders or para-gliders. Under Federal Aircraft Regulations, the pilots of these vehicles must follow certain rules, such as flying only during daylight hours and staying out of particular airspaces. But Carl's house would clearly surpass the 155-pound cutoff for unpowered ultralight vehicles, which means he'd need to have his house certified as an airworthy experimental aircraft by the Federal Aviation Administration. Inspectors would probably use guidelines designed for "manned free balloons" to determine whether Carl's house was safe for American skies.
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Explainer thanks Rhett Allain of Southeastern Louisiana University, John Ninomiya of Clusterballoon.org, and Jonathan Trappe of ClusterBalloon.com.