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4.1 4.1 BicyclesBicycles

Clicker questionClicker questionWhich vehicle is most stable?

(A) tricycle (B) Bicycle

(C) This chopper bike (D) An SUV

The tricycle and SUV The tricycle and SUV are very good at are very good at standing still.standing still.

But both the SUV and tricycle have But both the SUV and tricycle have major problems turning!major problems turning!

TricycleTricycle

……but a regular bike is very but a regular bike is very stable when turning.stable when turning.

A bike always flops over when it’s A bike always flops over when it’s not moving…not moving…

Statically stableDynamically unstable

Statically unstableDynamically stable

Statically stableDynamically unstable

Statically unstableDynamically stable?

A tricycle is statically stableA tricycle is statically stable

It’s base of support is a triangle defined by the points of contact (tires and ground).

c-o-m

Static stabilityStatic stability is determined by is determined by

1. 1. base of supportbase of support (polygon formed by ground (polygon formed by ground contact points)contact points)

2. 2. center of gravitycenter of gravity (effective point at which (effective point at which gravity acts)gravity acts)

Vehicle’s Static StabilityVehicle’s Static Stability

Stability demosStability demos

Static stability occurs when the center of gravity is

above the base of support

Tips over to a new stable equilibrium

If we go too far…

Energy becomes smaller in this direction

mgh

Gravitational potential energy increases

mgh

Stable equilibrium means that Stable equilibrium means that gravitational potential energy rises gravitational potential energy rises when the object is tippedwhen the object is tipped

Tricycle: statically stable

Bicycle: statically unstable

You can also understand this using torqueYou can also understand this using torque

TricyclesTricycleshave 3 contact pointshave 3 contact pointsare statically stable and hard to tip overare statically stable and hard to tip over

BicyclesBicycleshave only 2 contact pointshave only 2 contact pointsare statically unstable and hard to keep uprightare statically unstable and hard to keep upright

Stationary Vehicles:Stationary Vehicles:Base of support requires at least

three contact points:

Why does an SUV roll?Why does an SUV roll?

Ffriction

r

Too much torque around center of mass! Let’s think about forces and acceleration.

SUVs and tricycles are dynamically unstable because the total force does not point to the center-of-mass.

Support force

Total force

There’s a torque around c-o-m from the friction force!

• Sports car• c-o-m low• Lever arm small

• VW van / SUV• c-o-m high

• Lever arm big

torque

Clicker questionClicker questionWhy does Lance ride Why does Lance ride a bike and not a a bike and not a tricycle?tricycle?

(What makes a bike (What makes a bike dynamically stable?)dynamically stable?)

(A) A cyclist can lean on a bike and change the torque around his center of mass.

(B) The pedals on a bike are connected to the rear wheel (in contrast to the front wheel on a tricycle), making it possible for the cyclist’s feet to work independently of the bike’s motion.

(C) A bicycle has brakes, so the cyclist can change speed quickly.

Leaning during Leaning during turns allows turns allows total force total force to point towards to point towards center of gravity, center of gravity, so no net so no net torques!torques!

Dynamic effects can aid a vehicle’s stabilityDynamic effects can aid a vehicle’s stability

- by shifting base of support to under the center - by shifting base of support to under the center of gravity (meter stick)of gravity (meter stick)

- by dynamically stabilizing an equilibrium, i.e., by dynamically stabilizing an equilibrium, i.e., reduce net torques (bicycle)reduce net torques (bicycle)

Vehicle’s Dynamic Vehicle’s Dynamic StabilityStability

And, can make a And, can make a statically unstable vehicle statically unstable vehicle dynamically stabledynamically stable

A bicycle steers automatically!A bicycle steers automatically!• Acts like a gyroscopic• “Trail” – the shape of the fork

““Trail” is the dominant effect at low speedTrail” is the dominant effect at low speed

A bicycle has A bicycle has some special some special features which features which make it make it incredibly incredibly dynamically dynamically stablestable

One of these is not like the other.One of these is not like the other.

The wheel much touch the ground “behind” the steering axis for the bike to steer properly.

Trail – the shape of the forkTrail – the shape of the fork Chopper bike Chopper bike

GyroscopeGyroscope Gyroscope, suitcaseGyroscope, suitcase

The pennyfarthing was designed to get mechanical advantage from gearinggearing.

GearingGearingGears are another important feature of bicycles (and cars!) not related to stability

Gearing on a pennyfarthing:Gearing on a pennyfarthing:the rider turns her feet through less distance than the wheel travels

Going to the top of a hill: she does the same amount of work, so more force is required to turn the pedals (compared with a smaller front wheel)

This is like a “high” gearThis is like a “high” gear

Gears allow you to exchange force for distance or distance for force in doing Gears allow you to exchange force for distance or distance for force in doing work.work.

On steep hills, you use a gear that requires your feet to move a large On steep hills, you use a gear that requires your feet to move a large distance in exchange for smaller force on the pedals.distance in exchange for smaller force on the pedals.

On flat surfaces, you use a gear that requires your feet to push hard in On flat surfaces, you use a gear that requires your feet to push hard in exchange for a larger distance traveled by the rear wheel.exchange for a larger distance traveled by the rear wheel.

Mechanical AdvantageMechanical Advantage

Hence, the Hence, the invention of invention of the indirect the indirect drivedrive

GearsGears

And the And the freewheel freewheel sprocketsprocket