Bicycles

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Bicycles
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Introductory Question

• How would raising the height of a sport utility
  vehicle affect its turning stability?
• Make it less likely to tip over
• Make it more likely to tip over
• Have no overall effect on its stability

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Observations about Bicycles

• They are hard to keep upright while stationary
• They stay upright easily while moving forward
• They require leaning during turns
• They can be ridden without hands

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5 Questions about Bicycles

• Why is a stationary tricycle so stable?
• Why is stationary bicycle so unstable?
• Why does a moving tricycle flip during turns?
• Why must you lean a bicycle during turns?
• Why can you ride a bicycle without hands?

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Question 1

• Why is a stationary tricycle so stable?

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Tricycles Static Stability (Part 1)

• An upright tricycle has a base of support
• the polygon formed by its ground contact points
• A tricycle has a center of gravity
• the effective point at which its weight is
  located
• When center of gravity is above base of support,
• the tricycle is in a stable equilibrium,
• its gravitational potential rises whenever its
  tipped,
• it accelerates in the direction opposite the tip,
• and it returns to equilibrium

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Tricycles Static Stability (Part 2)

• When its center of gravity isnt above the base,
• the tricycle is not in equilibrium,
• its gravitational potential energy drops when it
  tips,
• it accelerates in the direction of the tip,
• and it falls over
• When its center of gravity is above edge of base,
• the tricycle is in an unstable equilibrium,
• to which it never returns after being tipped

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Question 2

• Why is stationary bicycle so unstable?

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Bicycles Static Instability

• A base of support requires 3 contact points
• An upright bicycle has only 2 contact points
• An upright bicycle is in an unstable equilibrium
• A stationary bicycle tips over easily

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Question 3

• Why does a moving tricycle flip during turns?

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Tricycles Dynamic Instability

• When a tricycle is moving,
• its velocity can point opposite its acceleration,
• so a stable equilibrium doesnt ensure stability
• During a high speed turn,
• the rider travels straight ahead,
• the tricycle starts to tip,
• the acceleration opposite the tip is too slow,
• and the tricycle tips over anyway

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Introductory Question

• How would raising the height of a sport utility
  vehicle affect its turning stability?
• Make it less likely to tip over
• Make it more likely to tip over
• Have no overall effect on its stability

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Question 4

• Why must you lean a bicycle during turns?

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Bicycles Dynamic Stability

• When a bicycle makes a high speed turn,
• the riders initial velocity is straight ahead,
• leaning inward makes the rider accelerate inward,
• and the rider and bicycle turn together safely
• The bicycle drives under the overall center of
  gravity to return to the unstable equilibrium
• Motion can make a bicycle stable!

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Question 5

• Why can you ride a bicycle without hands?

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A Bicycles Automatic Steering

• It naturally steers under its center of gravity
• due to gyroscopic precession of the front
  wheel(the grounds torque on spinning wheel
  steers it)
• due to the design of its rotating front fork(the
  fork steers to reduce total potential energy)
• A forward-moving bicycle that begins to tip
• automatically returns to its unstable
  equilibrium,
• and thus exhibits wonderful dynamic stability

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Summary about Bicycles

• Tricycles
• have static stability
• can flip during turns
• Bicycles
• are statically unstable
• can lean during turns to avoid flipping
• automatically steer back to unstable equilibrium
• have remarkable dynamic stability