Tyre Slip Angle Truth

Uncategorized Dec 20, 2019

In racing, it’s often thought the tyre slip angle is an indication of the tyre losing cornering grip – that the slip angle is formed by the tyres “slipping” or “sliding” on the pavement. 

The truth is, tyres build grip with increasing slip angles up to the point where grip starts to level off, as shown below in the slip angle vs grip diagram.  

It's important to understand a little about how grip is created at the tyres. 

A steering control input from the driver results in the forward momentum of the car being counteracted by frictional forces acting at the tyre contact patches, and so creating tyre slip angles at the contact patches as the car starts to turn and build cornering grip in the tyres.

Tyre slip angles are a property of the pneumatic tyre that creates the lateral force and allows the car to turn. (If we had steel treads, for example, there would be no slip angles, and insufficient friction available to create a cornering force.)

In this diagram, the car is turning left. In cornering the steered angle of the wheel is a little greater than the actual direction the wheel is traveling in. The difference between the two is the slip angle, α, as shown in the diagram. The cornering force is applied at the axle, and the reaction force at the contact patch is the lateral grip.

Note the bag of the tyre flexes sideways, as shown above in end view. There is no twisting of the tyre to form the slip angle. The contact patch just lays down successive “footprints” in line with the direction the wheel is pointing. 

Tyres with greater flex in the side wall operate at higher maximum slip angles. Tyres with less flex in the side wall (e.g. low-profile tyres) are more responsive. They build grip quicker. But they are also “less forgiving” than tyres with a bigger bag. There’s less warning for the driver at the limit of grip.

Yes.  If you push past the limit of grip, the rate of change of slip angle increases markedly, and the tyre does start to slide. 

Starting from the straight ahead, and no tyre slip angles, as you turn the steering wheel to initiate cornering, tyre slip angles start building immediately, then build quickly, subject to your speed of turning the steering wheel: 

The diagram above shows Cornering Force (lbs-force), or grip level on the Y axis versus the Tyre Slip Angle (degrees) on the X axis.

In this example, grip builds initially in a fairly linear fashion.  Around 4 degrees the rate of increase reduces, peaking at around 6 degrees of tyre slip angle, and then falls away. 

Note also that vertical load on the tyre increases the grip potential.  If we doubled the vertical load from 900 to 1800 lbs, for sure, we’d increase the grip a lot, but not quite double it.

The situation shown here, where grip level is fairly constant between 5 and 8 degrees, is typical.  The shape of the curve varies with tyre vertical load as shown.  With maximum weight transfer mid corner, the outside tyre delivers most of the cornering force, but inside tyre grip is still important in achieving best overall grip at that axle.

Maximum grip for this tyre is generated around a slip angle of 6 degrees.  Tyres where maximum grip is achieved around 3 or 4 degrees will be peakier at the top of the graph.  Such tyres, making maximum grip over a smaller range of slip angle, can be considered a “less forgiving” tyre. 

 Any study of how the race car corners should start with tyre slip angles.    

Slip Angle Clarified - The Walking Analogy

This diagram describing the tyre slip angle comes from "Race Car Vehicle Dynamics”, by Bill and Doug Milliken. 

The ability of the tyre to travel out of its plane without appreciable slippage is the result of laying down successive prints, each laterally displaced because of the sideways tyre distortion.

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