Why is it difficult to ride a bicycle with a partially inflated or deflated tyre? It is a common observation that riding a bicycle with an inflated tyre is easier than riding one with a deflated tyre but why is it so?
As per my knowledge in an ideal case of no deformation in tyre(when it is inflated) the torque of normal is zero(almost zero in non ideal case) about the axis of rotation whereas in the deflated case the tyre gets deformed and the normal shifts to the front of the tyre and therefore there is a torque of the normal too that our muscles need to overcome.
Is what I thought right and is there any other reason too?
 A: There are several factors that may be taken in account, but the more important is the energy used deforming the tire.
Suppose a deflated tire. As you move forward and the tire rotates, the part of the tire that is starting to touch the ground has to be deformed (since the tire is flat). You have to use an important amount of energy for that. Note that the part of the tire that has just stopped touching the ground also has to be deformed, which recovers some energy. Nonetheless, not all energy is gained due to elastic hysteresis, so we have a net loss. That loss has to be even by the cyclist, which is why it is more difficult to ride a bike with flat tires.
Note that there are other factors that may influence this. I'm quoting Wikipedia here 

Additional contributing factors include wheel diameter, speed, load on wheel, surface adhesion, sliding, and relative micro-sliding between the surfaces of contact. The losses due to hysteresis also depend strongly on the material properties of the wheel or tire and the surface.

You may want to read this article about rolling resistance. Here it suppose a solid (or perfectly inflated) tire and an elastic ground, but it is equivalent.
