Bicycle Ride Balancing

By T.K. NG

        When you started learning to ride a bicycle, had someone told you that you should turn your front wheel to the right if your bicycle undesirably leaned to the right, and the same principle applied for left lean?  You should agree that such balancing act works well and is obviously needed at the beginning of a ride.  But, have you ever thought of the reason behind it?

        The reason why such balancing act works lies in the design of the steering shaft and fork assembly attached to the front wheel of the bicycle.  If you look closely at your bicycle from the side, you should notice that the steering shaft is at an angle to the vertical and the assembly may slant further forward after emerging from the holding bearing of the body frame, bend sharply forward at the end of the fork near the wheel hub, or be in the form of a curved fork before attaching to the front wheel, etc.  A few examples are shown in Fig 1.  You may wonder why the designers do not make the manufacturing processes easier by adopting a straight shaft and fork assembly.

Fig 1

        Before proceeding to explain how the steering shaft and fork assembly works to balance a ride, let us see how we can keep a stick standing upright on the fingertip.  What you need to do is to move your finger in the same direction as the stick’s lean so as to bring it back to the upright position with your fingertip directly below its centre of mass. 

        In fact, the steering shaft and fork assembly design of a bicycle provides a means for you to balance the bicycle in a similar way as keeping a stick upright on your fingertip.  Fig 2 illustrates how it works. 

Fig 2

        When a bicycle is moving forward and remains in a stable upright position, the combined centre of mass of the bicycle and rider should be directly above the straight line passing through the two points of ground contact of the front and rear wheels (see Top View A of Fig 2).  If the bicycle undesirably leans, say, to the right, the combined centre of mass of the bicycle and rider is no longer above the line of ground contacts, but to the right of it (Top View B of Fig 2).  When the steering handle is turned to the right, the steering shaft and fork assembly causes the hub of the front wheel and hence its ground contact point to move to the right also.  The line of ground contacts is then at an angle to the one before the steering handle is turned and is shifted from the left side of the combined centre of mass to the right side (Top View C of Fig 2).  The bicycle is prevented from leaning further to the right under the circumstance.  Without the need of performing any other action by the rider, the bicycle will return to an upright position due to the reversed positions of the combined centre of mass and line of ground contacts.  The front wheel can then be turned back to enable the bicycle to move forward in the desired direction.

        The aforesaid balancing act is not the only effect that helps prevent a bicycle from toppling.  You should have noticed that little effort needs to be made to balance your moving bicycle when its speed is high enough.  This is because other effects such as gyroscopic precession, etc. have come into play.  If you are interested in the physics of moving bicycles and have an appetite for mathematics,  you can refer to the paper titled “Linearized dynamics equations for the balance and steer of a bicycle: a benchmark and review” by J. P. Meijaard et al. for more details.

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