The reason why tyres exhibit such unpredictable behaviour is because they are made of rubber which is a viscoelastic material. To get our heads round this we first need to understand elastic and viscous materials.

Elastic material

Elastic materials deform linearly when a load is applied. Once this load is removed it returns back to its original shape. A good example is a spring; when you push it, the spring compresses and when you let go, it expands back to its original length. The harder you push the spring, the more it compresses, therefore the displacement is proportional to the applied force. By applying a cycle of compression and extension forces to the spring and plotting the results we can see below that the displacement (yellow) is in phase with the force (red).