Toe-out

[StewartG]

Peter, what are the pros and cons of toe-in and toe-out and why does a little toe-out help braking?

[Peter Carmichael]

Urgh! I am going to get found out soon for making it up.

 

The effect I was talking about under braking is a bit like dihedral on aeroplane wings (wings sloping upwards forming a V-shape). It is a self stabilising condition, keeping the car in a straight line. It is fairly easy to make empirical observations about the limit state braking condition because you are wanting to get the last little bit out of the friction circles. The effect of toe on turn-in and straight line stability requires a bit more imagination.

 

Going into a bit more detail on the braking...

 

In the limit state braking condition, the calipers are providing the same hydraulic clamping force on each wheel on an axle and therefore the same retarding force. If the centre of gravity of the car is off-centre, these forces are going to deliver a yaw turning moment to the car. With the driver's weight offset to the right, the car is going to try and yaw to the left. Ideal behaviour would be for the car to be stable in a straight line under braking, so how can the correcting moment be delivered to the chassis?

 

Looking at the friction circles, the driver's side of the car is carrying more weight, so the friction circles are larger. The same braking force is being applied on each side, so there is more grip left over on the driver's side than on the more lightly loaded side. The yaw moment being applied by the braking is going to turn into a small yaw angle to the left - as that angle is taken up, you want the leftover grip to come into play and provide a stabilising yaw moment. At the rear : the toed-in LHS wheel will be turned by the yaw angle to run straight on, removing the side force that it was previously developing (this will actually release a bit of friction circle which can be used for braking); the toed-in RHS wheel will be brought more across the direction of travel, developing a greater side force and contributing to the righting yaw moment; this net side force must be corrected by the front tyres. At the front, toe-in would have an opposite effect with the excess grip contributing a force in the same direction: a slight corrective touch of steering can bring a toed-out LHS wheel into line and the toed-out RHS wheel will use its excess grip to provide a righting moment and an opposing side force to cancel out the side force at the rear.

 

This is obviously a dynamic and imperfect equilibrium, but it is a better state than if the rear was straightahead or toed out.

 

In practice, the steering correction is hardly ever applied in a way which contributes to this equilibrium and brake bias is set to leave a bit of extra grip for both rear wheels so that instabilities in either yaw direction are stabilised. If you lock up the rear, then the toe-in does not have any extra friction circle to use to correct any instability and that is why the car suddenly tries to swap ends. If the front wheels are set to straightahead, they will tend to take up force in the bushes to establish a bit of toe-out under braking.