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The Bicycle

posted Feb 2, 2015, 1:12 AM by   [ updated Jul 19, 2016, 7:18 PM by Upali Salpadoru ]
“ You look so sweet, upon the seat of a bicycle meant for two”

­So sang the golden oldies ; very easy to sing. But it is not so easy to explain how it goes forward when the pedal is pushed down.  When you consider the transmission of force from pedal to the tyre you will realise that the tyre gets pushed back.  If so how does it go forward ? Why it is easy to balance on the run?

Fig. 1 A bicycle meant for two.                  courtsey:- design boom.

Fig.2 Transfering of the force on pedal to wheel.

The figure shows how the push on the pedal pulls the chain and turns the cog wheel of the rare wheel and makes it rotate .
1.    Push on pedal.    This is the force given by the rider which is often called the ‘effort’.
2.    Pull on the chain.   The cog wheel changes the direction and magnitude of the force.
3.    Push on tyre.  The cog wheel attached to the rare wheel rotates the wheel in an anti clockwise direction.   The upper part of the wheel goes forward while the lower part goes backward.
4.    Friction from ground.  The backward movement is not permitted by the ground due to high friction. So the wheel rotates moving  forward.

When the small cog wheel  completes one turn, the rim which is attached to it by the spokes also must do one turn. As the circumference of the tyre is larger than the circumference of the cog wheel the distance a point on the tyre will move will be much higher than the distance a cog will move. This is proportional  to the ratio of their diameters.  In mechanics in order to gain an advantage of distance there has to be a sacrifice.
The bicycle is a complex machine consisting of several simple machines.  If we start with the  pedal , the pedal and the large cog wheel is the first

  • Machine 1.

The energy given to the pedal is equal to the energy, the cog wheel can use in pulling the chain.  Considering this machine taken out of the bike we can see how the force alters.

Fig.2  Pedal and wheel

Effort is the force used on the pedal. Let this be E.   Load is the force exerted by the cog wheel on the chain. Let this be L.

Work done by effort (energy used) is equal to the work done (energy transmitted) by load.

Work done by effort =  Effort  x 2π R.e.     ( Work done= Force X Displacement)

Work cone by load   = Load x 2π R.l.

Therefore         E x 2π Re.  =   L x 2πR.l.


                                                    effort x 2π R.e

                             Load = -------------------------------  ( 2π  Cancels)


                        Then we get..

                            Load =  Effort x Re  ÷  R,l.



Machine 2.

Transferring of the force from the large cog wheel to the small cog wheel forms the second machine. This increases the force according to the ratio of their diameters .

As there are only a fewer cogs in the second wheel it has to turn a number of rounds for one revolution of the large wheel.

Machine 3

This is a wheel and axle machine.  In a usual wheel and axle there is a mechanical advantage. Here it is the opposite that happens.  As work (energy) is equal to force times distance , here force is lowered to gain distance. The bike is designed not to make travelling easier but to make travelling speedier.

The bike as a single machine.

If you can determine the ratio of distance effort moves : the distance bike moves  we can calculate the highest theoretically possible  (ideal)  mechanical advantage. This is also called ‘velocity ‘ratio’.

There are two methods to do this.

Practical method

Place the bike against a wall and mark the exact position of the bike. Then turn the pedal one complete round, allowing the bike to move forward.. Measure the distance bike has moved and the distance your had has moved. Your hand would have moved the circumference of the circle where  pedal arm is the radius. When you divide the distance hand moved by the distance bike moved will give you the Ideal mechanical advantage or the Velocity Ratio.


The answer will be a fraction as the bike is not designed for a mechanical advantage.

Theoretical method

Make the following measurements as accurately as possible.

Radius of the pedal arm =  …………(lets call it R1)

Radius of the wheel          =…………..(Let it be R2)

Number of cogs in the large  Cog wheel     =  …………. ( let it be N1)

Number of cogs in the small cog wheel      = ………..  (N2)


Distance effort moves =  2 Π x  R1

Distance load moves   = 2 Π x  R2

The ratio  N1 : N2    gives the number of rotations of the small wheel for 1 round of the large wheel

Therefore the total distance load moves  =  2 Π x  R2 (N1/N2) 

Total distance Effort moves                         = 2 Π x  R1


                                          2 Π x  R1

Velocity ratio    =---------------------------------                 

                                       2 Π x  R2 (N1/N2) 



                            = --------------------------------------

                                      R2 (N1 / N2)


Real Mechanical advantage

This can be obtained by a practical method.

The Mechanical Advantage is the ratio of  Load : Effort  (Load / Effort)


The bike has to be lifted or turned upside down so  that the wheel may turn freely. Fig.3. Then hand two pans, one from the pedal where the effort is used and another from the end of the wheel that’s going up.

Enter the results in this table.


500g (5 N)

10 N

15 N

20 N

25 N

30 N








Illustrate the results using a graph.


Frequently asked questions.

Why is it easier to balance while riding?
  1. I got the answer to this question at the age of 4 or 5. I was playing with a spinning top while my father was watching along with a friend. Father remarked,  “ Somebody probably got the idea of a bike from a turning top”  ‘Whats the connection ?’ his friend inquired.  “ As long as the top is spinning it can remain vertical. Moment the speed of rotation goes down it drops into a horizontal position”

    A rotating object has kinetic energy, particles are trying to escape sideways but unable to do so due to the binding of neighbouring molecules. So they go round and round, Gravity becomes negligible under these conditions.

    In the same way when the wheels of the bike has rotational kinetic energy it can remen in the same plane.

    A gyroscope is also a development on this principle.

  2. Does friction inhibit a rider?



The answer is "Yes and No."

Broadly speaking, there are two main types of friction. They may be termed as 'Fluid friction and  Sliding friction"

If you are immersed in water and has to wade through, you will have to cut through the water molecules. This kind of opposing force is called 'fluid friction'

Fig. A fast cyclist has to encounter molecules of air in the atmosphere.

The cyclist is also  Fluid friction.immersed in an invisible ocean of air.  Faster he goes harder the air molecules will clash on him.

 Sliding Friction

This affects a rider in two ways.

There is opposing friction at axles where two surfaces rub against each other . This is reduced by having ball bearings,grease or oil.

There is sliding friction  between the ground and the tyre.  If not for this rider cannot move forward. This is increased by using high friction material as rubber and by having treads.

  •  3 
  • If the friction pushes the tyre forward, base of the tyre should turn in the opposite direction to the ike’s motion?  Could you clarify this contradiction?

 It is not the ground friction that makes the wheel turn. In the fig. the wheel is made to turn anti clockwise by the chain. The arrows A,B,C and D show the directions of the angular forces. While A,B and D are free to move C is stopped by the ground. This is friction shown by F.

Now consider a vertical line through the axle. Top of this lines has a force to left. There is a force at the base but cancelled by the ground friction. This system acts like a class two lever. The imaginary lever is shown on the left.
This force on the axle really drives the wheel forward.


  •  History of the Bicycle

 in pictures.