A contribution to tire rolling resistance which arises from tire tread impact with the roadway is defined. These impact losses depend on the square of the vehicle speed. The physics of the process is revealed using a realistic, simple model coupled with Newton's second law. It is shown how the losses depend on tire characteristics. It is not feasible to determine to high accuracy the magnitude of the effect from such an uncomplicated model, however. The speed independent losses are also discussed in terms of a simple model. Finally, analytic expressions are presented for rolling resistance (speed dependent + speed independent) as a function of tire characteristics.