Balloons and more

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Balloonsand more

• Physics of Modern Devices
• January 26, 2009

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Observations about Balloons

• Balloons are held taut by the gases inside
• Some balloon float in air while others dont
• Hot-air balloons dont have to be sealed
• Helium balloons leak even when sealed

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5 Questions about Balloons

• How does air inflate a rubber balloon?
• Why doesnt the atmosphere collapse?
• Does air around a balloon exert a force on it?
• Why does a hot air balloon float in cold air?
• Why does a helium balloon float in air?

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Question 1

• How does air inflate a rubber balloon?
• How does air occupy space?
• How does it push on the balloons elastic skin?

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Airs Characteristics

• Air is a gas
• It consists of individual atoms and molecules
• Its particles are kept separate by thermal energy
• Its particles bounce around in free fall

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Air and Pressure

• Air has pressure
• Air particles transfer momentum when they bounce
• Each momentum transfer/bounce involves forces
• Air particles exerts forces on container walls
• Average force is proportional to surface area

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Air Pressure and Density

• Air has density
• Air particles have mass
• Each volume of air has a mass
• Air pressure is proportional to density
• Denser particles hit surface more often
• Denser air ? more pressure

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Pressure Imbalances

• Balanced pressure exerts no overall force
• Forces on balloons sides cancel
• Unbalanced pressure exerts overall force
• Forces on balloons sides dont cancel
• Forces push balloon toward lower pressure
• Air pressure also pushes on the air itself
• Air itself is pushed toward lower pressure

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Question 2

• Why doesnt the atmosphere collapse?
• If air has weight, why doesnt it fall to the
  ground?
• Why is the air more dense at lower altitudes?

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The Atmosphere

• Air near the ground supports the air overhead
• The atmosphere is in stable equilibrium
• Air pressure decreases with altitude
• Each layer of air experiences an upward force
• This upward force balances the layers weight
• Supporting itself structures the atmosphere
• Air pressure is highest near the ground
• p0 p
• Air density is highest near the ground
• ?0???

p, ?
p0, ?0
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Variation of pressure with altitude
Exponential!
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Question 3

• Does air around a balloon exert a force on it?

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The Buoyant Force

• Because of the atmospheres structure,
• air pressure is
• stronger near the bottom of a balloon,
• weaker near the top of the balloon,
• so air pushes up harder than it pushes down,
• and this imbalance yields an upward buoyant force
• The atmosphere pushes upward on a balloon!

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Archimedes Principle

• A balloon immersed in a fluid experience an
  upward buoyant force equal to the weight of the
  fluid it displaces

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Why dont people float in air?

• If a person displaces 0.08m3 (2.8 ft3) of air,
  what is the buoyant force he/she experiences?
  Compare to their weight. Assume a mass of 65kg.

FB
W
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Buoyant Force, cont
sink
float
hover
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Question 4

• Why does a hot air balloon float in cold air?
• Why does a cold air balloon sink in cold air?
• What is the difference between hot air and cold
  air?

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Room-Air Balloon in Air

• A rubber balloon filled with room air
• weighs more than the room air it displaces
• experiences a downward net force in room air
• sinks in room air
• FB
• Its average ?? ? of room air

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Air and Temperature

• Air pressure is proportional to temperature
• Faster particles hit surface more and harder
• Hotter air ? more pressure

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Hot-Air Balloon in Air

• A rubber balloon filled with hot air
• contains fewer air particles than if it were cold
• weighs less than the room air it displaces
• experiences an upward net force in room air
• floats in room air
• FB W
• Its average ?

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Hot Air Balloon

• A hot air balloon has three essential parts
• the burner, which heats the air
• the balloon envelope, which holds the air
• the basket, which carries the passengers.

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Balloon Pilot Controls

• Piloting a balloon takes skill, but the controls
  are actually very simple.
• To lift the balloon, the pilot moves a control
  that opens up the propane valve.
• This lever works just like the knobs on a gas
  grill or stove
• As you turn it, the flow of gas increases, so the
  flame grows in size.
• The pilot can increase the vertical speed by
  blasting a larger flame to heat the air more
  rapidly.

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Another Pilot Control

• Hot air balloons also have a cord to open the
  parachute valve at the top of the envelope.
• When the pilot pulls the attached cord, some hot
  air can escape from the envelope, decreasing the
  inner air temperature.
• This causes the balloon to slow its ascent.
• If the pilot keeps the valve open long enough,
  the balloon will sink.

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Ballooning Weather

• Can a hot air balloon lift more on a hot day or a
  cold day?

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How big?

• Hot air balloons range in size.
• The smallest, one-person, basket-less balloons
  have less than 1,000 m3 (35,000 ft³) of envelope
  volume.
• At the other end of the scale are the balloons
  used by large commercial sightseeing operations
  that carry well over two dozen people and have
  envelope volumes of up to 15,000 m3 (600,000
  ft³).
• Most balloons are roughly 2,500 m3 (100,000 ft³)
  and carry 3 to 4 people.

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How high?

• Even if pilot heats the air very hot, balloon
  wont rise forever.
• At higher altitudes, air is thinner and pressure
  decreases both inside and outside envelope.
• Balloon weight decreases
• Buoyant force decreases even more rapidly
• The balloon reaches a flight ceiling.
• When balloon reaches this altitude it is in
  stable equilibrium and will hover.

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Launching a hot air balloon

• Find a suitable launching point.
• Attach the burner system to the basket.
• Attach the balloon envelope and begin laying it
  out on the ground.

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Next

• Inflate using a powerful fan at the base of the
  envelope.

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Next

• When there is enough air in the balloon, blast
  the burner flame into the envelope mouth.
• Heats the air, building pressure until the
  balloon inflates all the way and starts to lift
  off the ground.
• Hold the basket down until all board.
• Balloon basket is also attached to the ground
  crew vehicle until the last minute, so the
  balloon won't be blown away before it is ready to
  launch.
• Release the balloon and the pilot fires a steady
  flame from the burner.
• As the air heats up, the balloon lifts right off
  the ground.

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Up, up and away!

• Amazingly, this entire process only takes 10 or
  15 minutes!

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Question 5

• Why does a helium balloon float in air?
• How does helium differ from air?
• Doesnt helium have mass and weight?

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Helium vs. Air

• Replacing air particles with helium atoms
• leaves particle density unchanged
• all particles contribute equally to pressure
• reduces the gass density
• helium atoms are less massive than air particles
• leaves the gass pressure unchanged
• helium atoms travel faster hit more often

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Helium Balloon in Air

• A rubber balloon filled with helium
• has same particle density as air
• weighs less than the air it displaces
• experiences an upward net force in air
• floats in air
• FBW
• Its average ?

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Variation of pressure in an incompressible fluid
This is the pressure you feel when you are
submersed in water. Reading material the
physics of SCUBA (see link on course webpage)
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Example Problem

• The envelope and basket of a hot-air balloon have
  a combined weight of 550 lb, and the envelope has
  a capacity of 77,000 ft3. When fully inflated,
  what should be the temperature of the enclosed
  air to give the balloon a lifting capacity of 600
  lb (in addition to its own weight)? Assume that
  the surrounding air, at 20oC, has a weight
  density of 0.0756 lb/ft3.

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Solution
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Summary about Balloons

• Balloons float when their average densities are
  less than that of air
• Helium balloons float because helium atoms are
  lighter than air particles
• Hot-air balloons float because hot air has lower
  particle density than cold air
• Homework 1 (on Rockets) due on Monday Feb 2 on
  WebAssign. Deadline to submit is just before
  class!
• Office hours tomorrow, Tuesday 2-3pm.