The following formula can be used to determine the maximum force of friction present:

Here, is the coefficient of static friction, is the normal force

On assuming that initially bicycle is on a flat ground, we know that the normal force in perpendicular therefore the sum of the frictional forces acting on the bicycle is:

Deceleration at which the bike will tip over:

This is the time when the rear wheel lifts off the ground. This will be an important factor to consider since any value of deceleration higher than this will no longer be efficient braking leading to higher chances of accidents.

When the rear wheel just starts to lift off the ground, the clockwise moment force is equal to the counter clockwise moment force. Therefore,

Therefore the clockwise moment force can be derived considering, where Fis the braking force, m is the combined mass (rider and bike) and a is the acceleration due to braking. The clockwise moment will be

Where H1 is the perpendicular distance to the line of action

The counter clockwise moment force will be

Where mg is the weight and L2 the perpendicular distance to the line of action.

By equating the 2,

Thus, a ( the maximum acceleration permitted) = =

VARIABLES:

INDEPENDENT VARIABLE

Weight distribution

CONTROLLED VARIABLES

Tyre air pressure

Brakes

Brake force

Surface conditions

Surface

DEPENDANT VARIABLE:

Maximum deceleration before either skid or tip over

APPARATUS:

Free ride bicycle with front functioning brakes

Tape measurer

Newton scale

Motion detector (to sense the acceleration) and vernier software

Laptop/Computer

String

Backpack

Air pump

Wooden board

In the above theory, it is assumed that the Centre of Mass is known, but in the real situation, it is not so, therefore, first the Centre of Mass has to be determined.

Horizontal positioning of Centre of Mass:

Measure the wheelbase of the bicycle (distance between the points of contact)

Measure the mass of the bicycle using a scale.

Measure the mass of the rider using a scale.

Tie a string to the rider’s waist and the stem of steering tube whilst the bike is at rest. Measure and record the length of the string from the rider’s waist to the steering tube.

Place a scale under the front wheel while ensuring that the string remains stretched. Record the reading.

Steps 4 and 5 to be repeated using 8 different lengths of string and the results to be recorded accordingly.

Calculate the Centre of Mass using the following formula:

Vertical positioning of Centre of Mass (rider):

Using a board, place one end on a scale.

The rider is to lie on this board with the end of his head at the of the board on the side with the scale.

Place rider in riding position

Place an object the same height as the scale under the board where the rider’s feet end.

Record the value visible on the scale.

Calculate the Centre of Mass by the following formula:

Vertical positioning of Centre of Mass (bike):

Hang the bike from one point and drop a string with a weight. Mark generally the lone on the bike frame

Repeat step 1 twice from different points

Measure the height of each from the ground and combine them

Use the formula to calculate the maximum acceleration.