# Proportionality of Traction and Wheel Slip

1. Jul 27, 2013

### DelToro

Hi All!
I've been doing some research in an attempt to uncover the proportionality between usable traction, which is defined as the the product of coefficient of static friction and the normal force, and the wheel slip. Given the nature of the the equation for usable traction, I expected that wheel slip would decrease directly as traction went up. However, after some experimentation of my own, the proportionality is inverse. That is, Wheel slip is inversely proportional to traction.

So, as you increase mass in a linear fashion I have found that wheel slip decreases in an inverse fashion. Is there anyone here who can point me in the right direction as to why traction is inversely related to wheel slip?

2. Jul 29, 2013

### Baluncore

The optimum way to plough a field with a given tractor and plough is to drive with a constant wheel slip. If I remember correctly, it is about 10% slip. What is optimised I forget, fuel consumption, driver wages or tractor wear.
If you google tractor wheel slip you should find plenty of information.

3. Jul 29, 2013

### tduell

I suggest searching out material on the Pacejka empirical model.
If you can find a paper that describes the model you will see that the relationships between normal force, traction and slip are non linear. For many tyres and conditions, somewhere around 20% slip gives the maximum tractive force.
It may also be described as the "Magic formula".

Cheers,
Terry