How Many Balloons Would It Take To Lift a House?
The physics of Pixar's Up.
By Nina Shen Rastogi
Posted Thursday, June 4, 2009, at 6:35 PM ET
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 figure
doesn'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 technicians
at
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.
Explainer
thanks Rhett Allain of Southeastern Louisiana University, John Ninomiya
of Clusterballoon.org, and Jonathan Trappe of ClusterBalloon.com.
Nina Shen Rastogi is a writer and editor in Brooklyn, N.Y.
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