Don’t know how many of you have been following this story, but basically a 20ft diameter by 6ft high balloon allegedly picked up a 6 year old boy and floated him around Colorado. When the balloon landed, they couldn’t find the boy. There is speculation that there may have been a gondola or some such under the balloon.
I’m wondering is how much lift would a balloon of that size have? Would it be enough to lift a 6 year old? A 6 year old and a gondola?
10ft ^2 * pi * 6ft = 1884 cu ft
1884 cu ft * 28.3 liters/cu ft = 53317 liters
1 liter = 1.113 gram of lift per wikipedia
53317 * 1.113 = 59341 grams
59341 grams / 1000 = 59.3 kg
59.3 kg * 2.2 lb/kg = 130 lb
Well, a 20 foot diameter cylinder 6 feet high has a volume of 1,884 cubic feet. Helium weighs 0.011 pounds per cubic foot, and air weighs 0.0807 pounds per cubic foot (at STP). I figure the lifting capability to be close to 132 pounds. Assume the balloon and gondola doesn’t weigh too much, sure it could lift a small child.
If those dimensions are right its gonna be close…first because the thing weighs something…and second, to me it doesnt look like cylinder, but more like a “classical” silver disk UFO shape, which is going to drop the lifting capacity to somewhere around 70 percent of that give or take.
Its close enough (if the numbers are right) that it almost sounds like it was DESIGNED to just lift a kid. That may not amuse the authorities.
Well…that saucer doesn’t have the volume of a cylinder. Probably about 1/2 to 1/3 of that, since it tapers down to a point along the edges. Also, the lifting power of helium depends on the air temperature and altitude. This was flying around Denver, at 8,000 ft. I imagine the lifting force mentioned above is for helium at sea level.
If the thing was capable of lifting a child, and the child fell out at some point, then I think it would have climbed a lot higher than 8,000 ft. So my guess is that they’re going to find the child hiding somewhere and this was either a practical joke or the kid released it by accident and then hid because he’s scared to face the music.
At least, let’s hope so.
If I had time, I’d do the math on the lifting power of the helium at ground level and at 8,000 ft, and from that we could tell whether a balloon which could barely lift a child at ground level would only go to 8,000 ft sans child. But we’d have to know the rough empty weight and whether they were talking about 8,000 ft above ground level or above sea level. My guess is the latter, which means the thing only rose 3-4,000 feet above ground level at best with no child in it.
Turns out there was no kid inside so the balloon was only lifting itself. (cite)
Boy has yet to be found though.
Other places (such as Whack-a-Mole’s cite) say it is only 5 ft tall. That comes out (using El Cheapo’s formula) to around 108 lbs.
The balloon looked like a mushroom with a stem-like protrusion coming down from the saucer-like cap. I don’t know if that stem thingy is included in the final height.
The density of air is less at 8,000 feet, true, but so is the density of helium. I figure that to be more or less a push. More important is the shape of the balloon. I didn’t look at the story and went on the dimensions given. A saucer shape is going to have, as you said, a third of the volume of a cylinder. We’re down to an object barely capable of lifting its own weight.
Shadowfyre, Shadowfyre, Shadowfyre…no-no-no.
You cannot resolve your quarrels with the babysitter in this fashion.
Why?
That thing looked like a saucer but still, why can’t it just be considered a squat cylinder (e.g. think of taking a drinking glass and cutting it across 2" down from the top)? This thing wasn’t 'a perfect cylinder but pretty close.
(Note I am asking…I hated geometry in high school)
It’s actually two cones face to face, and the formula for the volume of a cone is 1/3PIr^2*height.
The husband and I got out the engineering software we use to design our own flying objects (so far nothing big enough to lift a person, but that’s largely a matter of finances. The physics work at any scale)
Assuming the “mushroom stem” is not included in the volume, and it’s 20 feet x 5 feet, the volume would be around 1047 cubic feet and could, assuming pure helium in the envelope, lift around 65 pounds. Total. That would be envelope, “pod”, boy…
However, from pictures it looks like it may not have been fully inflated to maximum volume. Also, any contamination with normal atmosphere will also reduce the lifting power, so I’m guessing that even under ideal conditions it’s not going to lift a full 65 pounds.
If the “mushroom stem” was part of the height dimension we’re estimating lifting capacity at, oh, around 39 pounds total.
Likely, the real number is somewhere in between those two.
It would have to be a really small six year old.
I don’t think the kid was on board. I think daddy’s toy got away from the kid and he went an hid.
There are different grades/purity of helium available, and of course this did not occur at sea level nor at 70 degrees. Nor do we have barometric pressure and other atmospheric numbers for the actual location(s) so of necessity there’s rounding and estimation.
My question is how long before we see an episode of CSI based on the incident.
The density of the helium would not decrease, because it’s in a sealed bag - unless the bag was only half full on the ground and expanded as it went up. But if the bag was empty enough on the ground that there was room for major expansion of the helium, then we have to decrease the lifting power estimate even more.
I have no idea how full it was - when I saw the footage, it had been flying for a while and clearly had some leakage.
The thing that struck me watching the footage is just how bad the news media is. That episode got full coverage for over an hour, and yet none of the talking heads thought to ask these questions. After it landed, they were still reporting eyewitnesses saying something fell out of it, and they were wringing their hands about the little boy plummeting to his death.
Why can’t a network with the resources of FOX or CNN have real technical experts handy who can answer questions like this? Or more importantly, how come these supposedly highly educated talking heads are so ignorant of basic math and physics that it didn’t even occur to them to ask the right questions?
Here is a youtube video of Mythbusters lifting a 40lb 4 year old with carnival balloons.
At about 1:50 you get a good shot of the volume of balloons required and it is much more that I would have thought. I think they said it was about 3500 balloons.
My first impression when seeing the ‘saucer’ balloon for the first time on the ground, was it was no way big enough to lift a six year old.
BTW, here are some pictures of Cluster Balloons sized to lift an individual person.
Here’s a video of the balloon landing. It doesn’t look big enough to me.
Just got word on our local news… apparently the child was found hiding in their attic.
That little btd.
This is what gets me. If the father designed and built this thing, he musta (or shoulda) known how much this thing could lift.
Any half assed “backyard engineer” woulda known damn well right off the bat whether his kid could floated away on the thing or not.
I smell prank for profit or one really stupid balloon maker.
What sort of flying saucer “engineering” software are you using???!! And why is there such little faith in the public sector that you all think this wasn’t considered immediately, despite the fact that you all obviously thought of it? Okay, so maybe I can see the lack of faith in the public sector, but is everyone here so full of themselves that they think no one involved in the rescue would have done those calculations?
The formula for an oblate spheroid (flying saucer shape) is ::V = 4/3 * pi * [(radius at width)(radius at width)] * radius at length::
This spheroid measured 20 feet wide by 5 feet tall (or long), so the formula looks like this: Volume = 4/3 * pi * (10’ * 10’) 2.5’, which when solved is 1046.67 cubic feet of Helium. At an approximate lift of 28.2 grams per cubic foot, that’s enough Helium to lift about 65 pounds. All that was needed was enough to get him a few feet in the air, and then the wind would have taken him like a kite for a while. Even if it wasn’t fully inflated, the idea that he could have been in the balloon while improbable, was definitely possible.