Cluster Ballooning and a Buoyancy Problem in Beginning Physics

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Cluster Ballooning and a Buoyancy Problem in
Beginning Physics

• Curious George and Lawn-chair Larry
• Neutral Buoyancy is hard to do.

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Fish gotta swim Birds gotta fly

• Can't Help Lovin' That Man
•     (Oscar Hammerstein - J. Kern, from Show Boat)

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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.co
  m/stupid/stupid1998-11.html

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• 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

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• 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.

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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

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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 m345 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.

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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
  dont know that it was 120 kg. It is an
  estimate.)
• LiftVB (0.9489 m345 42.7m3) (1.00 kg/m3)
  42.7 kg (or 418N). This is much less than the
  payload. 4 pts.

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Darwin award error

• LiftVB (0.9489 m345 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. )

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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 m3 B. 42 m3 C. 60 m3 D. 90 m3 E. 120 m3 F.
  150 m3 G. 240 m3

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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
• SF ma B-mHeg ?AirgV-?HegV (?Air- ?He)gV if
  this sum of forces is to be equal to the weight
  of the payload (mg120Kg g) then
• SF (?Air- ?He)gV 120kgg rewriting
• V 120/(?Air- ?He) 120kg/ (1.16-0.16)kg/m3 120
  m3. This was like problem 2-4 on HW.

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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/l
  awnchairman.html

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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
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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 4pr3/3. I used ratios to do the
  problem, but you can do it whatever way.
• Answ LiftVB (0.9489 m3(6/4)342 134.51 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.)

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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 leads to the problem on achieving stability
neutral buoyancy.

• 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.

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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.
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A little bit of extra lift has a big effect.

• SF ma ? B-mg ma a (134.51 kg g
  120kgg)/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.

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Humans dont 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.

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• Here is a more accurate HISTORY OF THE
  FLIGHTWhen 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.h
  tml

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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 2C/1000 ft.) Net effect_at_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.

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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?

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The balloon stretches out

• And keeps ascending
• Is there a limit?
• Image credit Paul Verhage. The image and next
  text is from http//www.universetoday.com/2006/0
  1/20/satellites-on-a-budget-high-altitude-balloons
  /

Paul Verhage is a teacher in the Boise, Idaho
school district.
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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.univ
  ersetoday.com/2006/01/20/satellites-on-a-budget-hi
  gh-altitude-balloons/

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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-altitu
  de-balloons/

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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.
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In summary,

• 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 cant 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

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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/?p4986
• John Ninomiya http//www.clusterballoon.org/

http//www.flickr.com/photos/omnibus/31588081/
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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/?p4986
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http//www.xenophilia.com/blog/?p4986
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http//www.couchballoons.com/default.aspx
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Fish gotta swim birds gotta fly
Application

• Bony fish can achieve neutral buoyancy in water.
  How do they do it?

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.