# Total resistance of a hard tyre rolling in an angle

1. Jul 24, 2013

### Miky2013

Hello,
My problem refers to hard tyres, so assuming none or very little lateral deflection. For a particular tyre on a particular floor there is a rolling resistance against the movement when the tyre is rolling. In a simplified case the resistance can be approximated as a rolling resistance coefficient (let's call it R) times the normal reaction on the tyre (N). If we try to drag the tyre sideways it will not roll, and the resistance will be the well known friction coefficient (μ) times the normal reaction (N). If the tyre moves in a horizontal angle, so neither pure front rolling nor pure lateral dragging, the tyre will roll and drag at the same time, and the resistance will be different than the two pure cases. Think on a car in which one of the rear wheels is misaligned, it will still roll but the resistance will be higher than normal resulting on tyre wear and higher consumption.
I am trying to estimate the resistance as a function of the angle (α) in a simple way as:
Total resistance = (μ*sin(α)+R*cos(α))*N

Anybody knows if that can be a reasonable approximation to the real world?
Particularly for small values of α, before unwanted behaviours start to happen, such as the tyre stopping rolling. The formula produces a high increase in resistance for even small deviations from the straight line.

Thank you,

2. Jul 26, 2013

### xxChrisxx

Depends what you are trying to approximate, and how accurate you need it.

If you are assuming no deflection for a pneumatic tyre then you've lost a huge amount of accuracy.

3. Jul 26, 2013

### Miky2013

Thanks Chris,
I am concerned with really hard tyres, kind of solid polyurethane tyres, that's why I am assuming a very little or negligible deflection. Just think on one of those wheels being pullled and the direction of pulling and wheel longitudinal axis forming a small angle. The wheel will still roll but it won't be pure rolling, it will also be dragged at the same time. I attached a top view drawing of the tyre being pulled. I think the resistance for any angle will be somewhere between the rolling resistance (minimum) and the pure friction (maximum)

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