I've been watching the coverage of a 6-year-old boy who supposedly climbed inside his father's hobby weather balloon and floated away. News helicopters followed its progress over the eastern plains of Colorado as it was whipped back and forth over the plains as about 3,000 feet above ground level (AGL). The whole time I was asking, "Why hasn't somebody done the calculation about whether such a craft was capable of lifting itself and a 6-year-old boy?"
The reporters said the saucer-shaped, mylar balloon was about 20 feet in diameter, and it looked to be maybe 3 feet high at the center.
The volume for a cylinder 20 feet in diameter (10 foot radius)* and 3 feet high is about 942 ft^3. That converts to about 26.7 kiloliters. Helium has a lifting force of roughly 1 gram per liter at sea level and 60 degrees, so that means 26.7 kg, or about 58.8 pounds.
A typical 6-year-old boy weighs about 45 pounds per a government website I consulted. The picture of the boy shows he was no fatty, so assume 45 pounds.
The balloon itself had its own weight plus the weight of a small equipment gondola underneath, so assume maybe 3 pounds. That leaves around 55 pounds to lift. Since the balloon had less volume than a cylinder, and it was partially collapsed, it might have had 70% of the cylinder's volume at most, so that leaves around 38 pounds of lifting force.
It seems to me that there is no way that balloon could have lifted the boy, so the entire event was overplayed. Oh well, it made good news. Too bad that the news people don't have enough science savvy to even do a sanity check.
Maybe I'm wrong. What do you think?http://www.cnn.com/2009/US/10/15/colorado.boy.balloon/index.html* Typo correction 10/16/2009, in response to Voltamancer's comment. Yes, I used 10 feet as the radius in my volume calculation
- Kirt Blattenberger
RF Cafe Progenitor & Webmaster