I guess some people will do anything to get on television. In the media blitz last week, nobody seemed to pause to wonder whether the escaped helium-filled contraption would in fact have sufficient buoyancy to carry a 40-pound boy to a height of 7000 feet. Let's apply some physics to the case.
When talking buoyancy (which is a result of a difference in pressure between the top and bottom of a submerged object), it's all about Archimedes's Principle: The buoyant force acting on an object submerged in a fluid is equal to the weight of the fluid displaced by the object.
In the case of a helium balloon, the fluid being displaced is air, and the volume of displaced air is equal to the volume of the balloon. Therefore, the greater the volume of the balloon, the greater the buoyant force acting on it. Mathematically B = DVg, where D is the density of displaced air (1.3 kg/m3), V is the volume and g is the acceleration due to gravity (9.8 m/s2). In order to lift off of the ground, the upward buoyant force must be greater than the downward force of gravity acting on the contents of the balloon, including the helium, the balloon material, any attached components, and any small boys that publicity-obsessed parents may claim to be on board. According to Newton's Second Law,
B - Mg = Ma
Mg is the weight of the balloon and contents and therefore B must be greater than Mg for the balloon to achieve an upward acceleration of a.
Without being able to perform direct measurements, we can make a rough estimate of the volume of the rig from the video. We're going to approximate the shape to be that of an "oblate spheroid" with a volume V = 4/3πb2c with b being the horizontal radius, and c the vertical radius of the balloon.
Estimating a = 2.2 meters, and b = 1.0 meters we get V ≈ 20 cubic meters.
resulting in a buoyant force of
B = (1.3 kg/m3 )(20 m3 )(9.8 m/s2 ) = 255 Newtons or 57 pounds.
Is it enough? Well, assuming a smallish six-year-old boy weighs about 40 pounds, and because the weight of helium (D = .18 kg/m3) in the balloon will be
W = Mg = DVg = (.18 kg/m3 ) (20 m3 )(9.8 m/s2)
= 35 Newtons (8 pounds) it appears that we're right on the borderline. We've got 9 pounds left over.
Assuming our volume estimate is in the ballpark, the boy could have been lifted off the ground, if the balloon material and any attached components weighed less than about 9 pounds. Fortunately this was never actually put to the test.
Adam Weiner is the author of Don't Try This at Home! The Physics of Hollywood Movies.
CNN reported the thing was held together with scotch tape.
I know! Let's build a bigger one and launch the parents!
Well, at least the father is gonna be charged.
Innocent until proven guilty. Why is anyone making judgments when their only source is the media?
You forgot to take into account the high altitude and cool air temperature. You need to solve for density using the specific gas constants of helium and air, the ambient temperature, and the ambient pressure which, at 5000', is only about 84% of what it is at sea level. This makes a very big difference.
I disagree with your assessment of the balloon's dimensions, but even at that size, the total upward force on the balloon's materials and payload would be a little less than 40 pounds. And that assumes that the balloon is completely filled with helium, which it didn't appear to be.
You also forgot to check the results of your work against reality. If the net upward force on the balloon and its payload was actually 255 N, and the empty balloon weighed 9 pounds (4 kg), the resulting upward acceleration (neglecting drag from the atmosphere) would be almost 64 m/s/s, or 6.5 times the acceleration due to gravity a falling object experiences. In the video of the launching balloon, the upward acceleration is clearly less than 1 g.
the father has some loose screws.
authorities said it was a hoax, publicity stunt, will be charged for the crime.
meyaht: they're *criminally* innocent, but so was OJ. We're making judgments because that's what brains are for.
Meyaht: Maybe because the media is CNN and not the laughable Foxnews!!!...
I understand the family already accepted it was a publicity stunt!
The first time I looked at the drama and after initially seeing the size of the balloon I also wondered about if that is even possible. I have done some work on trying to get a balloon on Mars and have done some calculations using helium gas in my tests.
See "The Martian Windsurfer" here:
If he didn't use pure helium then your calculations would be even worse, most cheap helium the kind you fill up balloons with are mostly air with a small percent of helium. Industrial strength helium, close to 98 percent by volume you can buy at a welding shop but the cost is much more than for just an experimental intended flight without passengers??
I think the above calculations are way too conservative. I would have guessed about a maximum of 20 pounds of lift using 98 percent by volume or more of helium after adding the weight of the balloon and the gondola into the calculations leaving a - 20 pounds deficit when adding the six year old into the mix. Remember the gondola would have to also be strong enough to hold a 40 pound child.
So by first looking at it I thought the balloon should never get off the ground if the six year old was in the gondola.
The balloon is patently smaller than your estimates. Cutting to the chase, I get a net lift of about 10 pounds, even with generous assumptions of %Helium, altitude, temperature, etc. And, that flying Mylar Tea Bag was partially collapsed at launch, by at least 25% (probably 1/3), so not even 10 pounds. And, the video at launch indicated such.
But aside from any detailed calculations, you could instantly see that (1) the thing was so slow and light on takeoff, there was no way it even held a cat, let alone a boy, (2) all the shots at altitude showed the Tea Bag tilted, with the collapsed portion drooping the lowest, exactly *not* like it would be if a kid was jammed into the "gondola" (which would have been hanging pendulously if Master Falcon was present), (3) the fact that the father, who has made a few of these things, absolutely knows all this and could not ever have mistaken a delicate, lightweight bag for one loaded down with his junior primate, and (4) given the fact that he had edited video of the launch ready and formatted for release, that it all points to this guy being a hoser, and anyone who freaked out about it after seeing the evidence fresh and on TV got hosed. The authorities need a few guys with the common sense to (A) consider the source, (B) check the facts, and basic math, (C) decide that the Tea Bag will come down of it's own accord, (D) understand that knocking it down if it did have a kid in it could be a Bad Thing, and (E) call a professional balloonist, who would've straightened them out at a glance, or at told them to follow it with a squad car and meet the Faux Foil Flyer when it settled gently, emptily to the ground (which is a good place to keep one's feet).
Hey - the hoaxer should also get a citation for littering, and for creating a Helium spill...
I think the charges should Really Fit the crime. Creating a public disturbance, pay me for my time in wasted concern on that day, 50 bucks, times however many people. Class action of citizens vs. balloon boy's dad.
After he pays the emergency svcs of course.