Free wheels differential power train

Forces

When a vehicle runs on a plane surface it is submitted to two forces in opposition to the moving direction

The forces concerned

They are the aerodynamic load and the rolling force

The aerodynamic load can be divided into two forces: the force due to the body and the force due to the rotation of the wheels

The mass of the vehicle has to be taken into account for the calculation of the rolling force

The reaction of the ground is equal to m g (mass times terrestrial acceleration in newton)

Rolling force formula

Fr is equal to m g m'

Fr    Rolling force in N (newton)

m    Vehicle masse in kg

g    Terrestrial acceleration in m/s2

m'    Rolling friction coefficient without dimension ( m' car = 0.05 - m' bicycle = 0.005)

Dynamometer 25 kg

Measure of the rolling friction coefficient

Measurement is simply done with a commercial dynamometer

Its important to choose a plane surface for the vehicle

It is enough to attach a cord to the hook of towing

To attach the dynamometer and pull it until the vehicle moves

It is also necessary to know the mass of the vehicle

The formula is: m' = md / m

With :

m' Rolling friction coefficient

md Measured mass with the dynamometer

m Vehicle mass , for a bicycle, with the cyclist

For my recumbent bicycle ami-swb, I practised a little differently

As I do not have a dynamometer for this order of magnitude (0.5 to 1 kg)

I took a measurement by using the pedal and masses

I sat down on the bicycle and I hung a bag at the pedal and I gradually loaded the bag until the bicycle advances

At this moment the bag was loaded with 1.825 kg

The ratio of the gear box is 0.75, the plate has 52 teeth and the pinion has 16

Thus the ratio of reduction gearing is 52/16 x 0.75 = 2.44

The lever of the pedal is 0.170 m and the fictitious pinion has a radius of 0.170/2.44 = 0.0697 m

That gives me a couple of 1.83 x 9.81 x 0.0697 = 1.249 Nm

The wheel has 0.25 m of radius, therefore the force on the wheels is 1.249/0.25 = 4.916 N

The bicycle and myself weights 99 kg, which makes 99 x 9.81 = 971.2 N. Now m' = 4.916/971.2 = 0.005062

This measurement includes all the kinematics chain: pedals unit, friction of the chain and friction of the gear box

It is a good thing because it indicates the net force needed for rolling