{ 4.1 Bicycles

Clicker question Which vehicle is most stable? (A) tricycle (B) Bicycle (C) This chopper bike (D) An SUV

The tricycle and SUV are very good at standing still.

But both the SUV and tricycle have major problems turning! Tricycle …but a regular bike is very stable when turning. A bike always flops over when it’s not moving…

Statically stable Dynamically unstable Statically unstable Dynamically stable Statically stable Dynamically unstable Statically unstable Dynamically stable?

A 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 stability is determined by 1. base of support (polygon formed by ground contact points) 2. center of gravity (effective point at which gravity acts) Vehicle’s Static Stability Stability 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 mg h Stable equilibrium means that gravitational potential energy rises when the object is tipped

Tricycle: statically stable Bicycle: statically unstable You can also understand this using torque

Tricycles have 3 contact points are statically stable and hard to tip over Bicycles have only 2 contact points are statically unstable and hard to keep upright Stationary Vehicles: Base of support requires at least three contact points:

Why does an SUV roll? F friction 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 question Why does Lance ride a bike and not a tricycle? (What makes a bike 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 turns allows total force to point towards center of gravity, so no net torques!

Dynamic effects can aid a vehicle’s stability - by shifting base of support to under the center of gravity (meter stick) - by dynamically stabilizing an equilibrium, i.e., reduce net torques (bicycle) Vehicle’s Dynamic Stability And, can make a statically unstable vehicle dynamically stable And, can make a statically unstable vehicle dynamically stable

A bicycle steers automatically! Acts like a gyroscopic “Trail” – the shape of the fork “Trail” is the dominant effect at low speed A bicycle has some special features which make it incredibly dynamically stable

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 fork Chopper bike

Gyroscope Gyroscope, suitcase

gearing The pennyfarthing was designed to get mechanical advantage from gearing. Gearing Gears are another important feature of bicycles (and cars!) not related to stability

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” gear

 Gears allow you to exchange force for distance or distance for force in doing work.  On steep hills, you use a gear that requires your feet to move a large distance in exchange for smaller force on the pedals.  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. Mechanical Advantage

Hence, the invention of the indirect drive Gears

And the freewheel sprocket