Download
1 / 31
310 likes | 448 Vues
Cluster Ballooning and a Buoyancy Problem in Beginning Physics. Curious George and Lawn-chair Larry Neutral Buoyancy is hard to do. Fish gotta swim Birds gotta fly. Can't Help Lovin' That Man (Oscar Hammerstein - J. Kern, from Show Boat ).
E N D
Cluster Ballooning and a Buoyancy Problem in Beginning Physics Curious George and Lawn-chair Larry Neutral Buoyancy is hard to do.
Fish gotta swim Birds gotta fly Can't Help Lovin' That Man (Oscar Hammerstein - J. Kern, from Show Boat)
Darwin “Honorable mention” 1982. Balloon question This question and some of the language is derived from the Darwin Awards: (Lawn Chair Larry did not win the DA. He lived.) http://www.darwinawards.com/stupid/stupid1998-11.html
Lawn Chair Larry “hatched his weather balloon scheme while sitting outside in his "extremely comfortable" Sears lawnchair in 1982. He purchased 45 weather balloons from an Army-Navy surplus store, tied them to his tethered lawnchair dubbed the Inspiration I, and filled the 4' (1.22 m)* diameter balloons with helium. Then he strapped himself into his lawnchair with some sandwiches, Miller Lite, and a pellet gun. He figured he would pop a few of the many balloons when it was time to descend.* I added the metric length
“Larry's plan was to sever the anchor and lazily float up to a height of about 30 feet above his back yard, where he would enjoy a few hours of flight before coming back down. But things didn't work out quite as Larry planned. “When his friends cut the cord anchoring the lawn chair to his Jeep, he did not float lazily up to 30 feet. Instead, he streaked into the LA sky as if shot from a cannon, pulled by the lift of 42 helium balloons holding 33 cubic feet of helium each. He didn't level off at 100 feet, nor did he level off at 1000 feet. After climbing and climbing, he leveled off at 16,000 feet.”
Many people assume that this is an urban legend. (I wrote) However, the incident actually occurred, but most sentences, from the Darwin award, are inaccurate or misleading. The account has, in fact, been embellished in the manner of urban legends. There was no beer, only soda. There were items that showed planning: ground crew, ballast water, CB radio, spare glasses and a parachute etc. I found better sites on the internet but I knew to look for them because of Physics 123.http://www.markbarry.com/lawnchairman.html
Cutting to the Chase, it was the balloons. Now you can do it, too. A. Calculate the total volume of helium in m3 in the 45 4-foot diameter balloons as reported above. ____________m3. (This is not physics, only math.) 0.9489 m3*45 =42.7 m3 4pts. A few people used 4 as radius and were off by a factor of 8. That should have given you too much lift in part B and been a clue.
B. Calculate the “lift” in kg of the balloons (in the space below). I am using lift here to mean the mass that can be lifted. This will show that the total buoyant force for the “45 balloons” before launch was inadequate to lift him and his equipment. Assume 120 kg for the pilot and payload and use the density numbers from MC problem #16 above. (I don’t know that it was 120 kg. It is an estimate.) Lift=V*B= (0.9489m3*45 =42.7m3) *(1.00 kg/m3) = 42.7 kg (or 418N). This is much less than the payload. 4 pts.
Darwin award error Lift=V*B= (0.9489m3*45 =42.7m3) *(1.00 kg/m3) = 42.7 kg (or 418N). This is much less than the payload. 4 pts. There is really no way to get around the fact that there is not enough balloon volume. The values for the density of air & He are less than the ones I have in the packet, 1.29 kg/m3. There is a reason for that. I used the ideal gas law to calculate density based on it being a hot day in LA. (I estimated, 32 C, without any data. )
As an aside, this was MC16. A balloon is to be filled with helium and used to suspend a mass of 120 kilograms in air. (Think lawn-chair aviator.) If the mass of the balloon is neglected, which of the following gives the approximate volume of helium required? (The density of air at sea level at 90ºF is 1.16 kilograms per cubic meter and the density of helium is 0.16 kilogram per cubic meter.) • 22 m3B. 42 m3C. 60 m3D. 90 m3E. 120 m3F. 150 m3 G. 240 m3
Answer I supplied to 16 Balloons lift by displacing air. The amount that they can lift is proportion to the product of the volume they displace * the difference of the weight of the air and the weight of the helium: ΣF =ma =B-mHeg = ρAirgV-ρHegV = (ρAir- ρHe)gV if this “sum of forces” is to be equal to the weight of the payload (mg=120Kg *g) then ΣF = (ρAir- ρHe)gV= 120kg*g; rewriting: V= 120/(ρAir- ρHe) =120kg/ (1.16-0.16)kg/m3 =120 m3. This was like problem 2-4 on HW.
What went wrong in the DA? They got their info from newspaper articles rather than interviews. They interpolated. 4-foot balloons. Note that they calculated (rather than measured) the volume of the balloons & inserted it.) (33 cu ft is what you calculate for a 4-ft sphere.) (I calculate, too.) The 45 number comes from some articles. The New York Times reported they were 6-ft balloons. And that he shoot out them out to avoid continuing the accent beyond 16000 ft. He had a radio and camera. (as quoted in) http://www.markbarry.com/lawnchairman.html
The lawn chair. There are 13 gallon jugs. (1 gallon H2O = 8 lb. so > 40 kg ballast was possible.) “It still has 13 of the 35 water jugs still on it, along with the tethering cables.” Mark Barry
C. Now redo the problem of calculating lift with the facts. There were only 42 balloons and they were 6 ft (not 4 ft) diameter. How much total lift do they generate? The volume of a sphere is 4πr3/3. I used ratios to do the problem, but you can do it whatever way. Answ: Lift=V*B= (0.9489 m3*(6/4)3*42 = 134.51 m3) *(1.00 kg/m3) = 134.51 kg (or 1318. N) 6 pts. (Comment: 6 ft is nominal. If the balloons were over filled then the lift would be larger.)
This leads to the problem on achieving stability: neutral buoyancy. D. Extra credit: What will be the initial acceleration upward? You may neglect the mass of the helium and just use the payload. Neglect air resistance. BTW, Larry lost a pair of glasses on the way up. He shot out balloons while he went up to not go too high. He landed with about 35 balloons left, having dumped ballast. This is a very shaky and speculative part of the problem, but it is interesting. This leads to the problem on achieving stability: neutral buoyancy. I ask for initial velocity knowing that there was also terminal velocity which could be estimate from the reports.
These pictures show that 1. there was preparation/ substantial payload weight2. the balloons were big. 3. that they were stacked in tiers 4. this would not have been hard to spot.
A little bit of extra lift has a big effect. ΣF = ma ► B-mg = ma; a = (134.51 kg* g – 120kg*g)/120 kg = 0.121 g. g stands for gravitational acceleration at earth. (If you multiply it out it is 1.18 m/s2.) He reported an ascent speed of ~1000 ft/min ~17 ft /s = 5.5 m/s. He could have reached most of this “terminal velocity” in ~10 s even with this small imbalance of ~15 kg. With a tiny 1.5 kg imbalance he might reach this in ~100s.
Humans don’t have much experience with continued acceleration. We might think with such a tiny imbalance we would not go high. But evidence is that he had a large imbalance. “After his crew purposely cut the first tether, the second one also snapped which shot Larry into the LA sky at over 1,000 feet per minute.”
Here is a more accurate HISTORY OF THE FLIGHT:When Larry Walters was 13 years old, he went to a local Army-Navy surplus store and saw the weather balloons hanging from the ceiling. It was then he knew that some day he would be carried aloft by such balloons. This obsession would be with him for the next 20 years. On July 2nd, 1982, Larry tied 42 helium-filled balloons to a Sears lawn chair in the backyard of his girlfriend's house in San Pedro, California. With the help of his ground crew, Larry then secured himself into the lawn chair which was anchored to the bumper of a friend's car by two nylon tethers. He took with him many supplies, including a BB gun to shoot out the balloons when he was ready to descend. His goal was to sail across the desert and hopefully make it to the Rocky Mountains in a few days. But things didn't quite work out for Larry. After his crew purposely cut the first tether, the second one also snapped which shot Larry into the LA sky at over 1,000 feet per minute. So fast was his ascent that he lost his glasses. He then climbed to over 16,000 feet. For several hours he drifted in the cold air near the LA and Long Beach airports. A TWA pilot first spotted Larry and radioed the tower that he was passing a guy in a lawn chair at 16,000! Larry started shooting out a few balloons to start his descent but had accidentally dropped the gun. He eventually landed in a Long Beach neighborhood. Although he was entangled in some power lines, he was uninjured. http://www.markbarry.com/lawnchairman.html
Does one level off? Does buoyancy decrease for helium balloons with altitude? The air is less dense at high altitude. So for a given volume there is less lift. Use the ideal gas law. Now there are two effects. Air pressure decreases with elevation. So the density of air, n/V, goes down. But some of the decrease is offset by temperature decrease (dry-air lapse rate = 2°C/1000 ft.) Net effect:@16000 ft. P≈ 9/16 sea level. Temperature 0.9T sea level; so density of air = 0.625 sea level. Delta Density of air-helium would be 0.8125 - 0.1125 =0.7 kg/m3. For a fixed volume then there is less lift.
for a given/fixed volume … But is the volume of a (weather) balloon fixed? What determines the radius of a balloon? the amount of gas in it, the pressure outside and to a lesser extent the elasticity of the envelop. As a balloon ascends and the outside pressure drops what happens?
And keeps ascending Is there a limit? Image credit: Paul Verhage. The image and next text is from: http://www.universetoday.com/2006/01/20/satellites-on-a-budget-high-altitude-balloons/ The balloon stretches out Paul Verhage is a teacher in the Boise, Idaho school district.
Balloons break. . . Eventually “Ascent rates for the balloons vary for each flight but are typically between 1000 and 1200 feet per minute, with the flights taking 2-3 hours to reach apogee. A filled (latex) balloon is about 7 feet tall and 6 feet wide. They expand in size as the balloon ascends, and at maximum altitude can be over 20 feet wide. “The flight ends when the balloon bursts from the reduced atmospheric pressure.”http://www.universetoday.com/2006/01/20/satellites-on-a-budget-high-altitude-balloons/
Could Larry have died? “Verhage said his highest flight reached an altitude of 114,600 feet (35 km),” Continuing, “Near space lies begins between 60,000 and 75,000 feet (~ 18 to 23 km) and continues to 62.5 miles (100km), where space begins. "At these altitudes, air pressure is only 1% of that at ground level, and air temperatures are approximately -60 degrees F," he said. "These conditions are closer to the surface of Mars than to the surface of Earth." http://www.universetoday.com/2006/01/20/satellites-on-a-budget-high-altitude-balloons/
He lived because he shot out balloons And controlled ballast. He dropped his gun at some point on the way down and that meant he had to come down.
“Unlike traditional hot-air balloons, which possess vents for easy altitude control, cluster balloons rise uncontrollably, expanding as they go.” http://en.wikipedia.org/wiki/Cluster_ballooning Allred: You can’t make yourself heavy. Even the smallest amount of positive buoyancy could take you up and up. The only way to get rid of it is to release helium. “Cluster balloonists must periodically cut balloons loose (disregarding where the balloons end up) to maintain altitude and descend.” wiki In summary,
This has turned to a sport called cluster ballooning http://en.wikipedia.org/wiki/Cluster_ballooning One of the most recent manifestations is Ken Couch (from Bent Oregon) who did 193 miles on July 7, 2007 almost reaching ID. http://www.couchballoons.com/default.aspx & http://www.xenophilia.com/blog/?p=4986 John Ninomiya http://www.clusterballoon.org/ http://www.flickr.com/photos/omnibus/31588081/
Man flies 193 miles in lawn chairJuly 11th, 2007 · · “Last weekend, Kent Couch settled down in his lawn chair with some snacks — and a parachute. Attached to his lawn chair were 105 large helium balloons. With instruments to measure his altitude and speed, a global positioning system device in his pocket, and about four plastic bags holding five gallons of water each to act as ballast — he could turn a spigot, release water and rise — Couch headed into the Oregon sky. http://www.xenophilia.com/blog/?p=4986
Application: “Fish gotta swim; birds gotta fly” The gas bladder (also fish maw, less accurately swim bladder or air bladder) is an internal organ that contributes to the ability of a fish to control its buoyancy, and thus to stay at the current water depth, ascend, or descend without having to waste energy in swimming. http://en.wikipedia.org/wiki/Gas_bladderBTW, shark store lots of oil to help their density. Bony fish can achieve neutral buoyancy in water. How do they do it?
