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/stup
id/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= (0.9489 m3*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= (0.9489 m3*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.)
A. 22 m3 B. 42 m3 C. 60 m3 D. 90 m3
E. 120 m3 F. 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 = (ρAirρHe)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/lawnc
hairman.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 weight
2. 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 ArmyNavy 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?
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.c
om/2006/01/20/satelliteson-a-budget-high-altitudeballoons/
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/satellit
es-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/satellit
es-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.
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 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
This has turned to a sport called
cluster ballooning
http://en.wikipedia.org/wiki/Cluster_b
allooning
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/def
ault.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 chair
July 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
http://www.xenophilia.com/blog/?p=4986
http://www.couchballoons.com/default.aspx
Application:
“Fish gotta swim; birds gotta fly”
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_bladder
BTW, shark store lots of oil to help their density.