# Slip Angle

The slip angle of a vehicle describes the ratio of forward and lateral velocities in the form of an angle and is normally represented by the symbol β (Beta). Slip angle is the angle between a rolling wheel's actual direction of travel and the direction towards which it is pointing. In other words it’s the difference between where car is pointing (heading) and where it’s actually going. This slip angle results in a force perpendicular to the wheel's direction of travel - the cornering force. This cornering force increases approximately linearly for the first few degrees of slip angle, and then increases non-linearly to a maximum before beginning to decrease (as the wheel slips).

A non-zero slip angle arises because of deformation in the tire. As the tire rotates, the friction between the contact patch and the road result in individual tread 'elements' remaining stationary with respect to the road.
This tire deflection gives rise to the slip angle, and to the cornering force.

Because the forces exerted on the wheels by the weight of the car and downforce are not distributed equally, the slip angles of each tire will be different. The ratios between the slip angles will determine the vehicle's behavior in a given turn. If the ratio of front to rear slip angles is greater than 1:1, the vehicle will tend to understeer, while a ratio of less than 1:1 will produce oversteer.
Actual instantaneous slip angles depend on many factors, including the condition of the road surface and tires, acceleration and braking, tire profile size and tire camber, but a vehicle's suspension can be designed to promote specific dynamic characteristics.
A principal means of adjusting developed slip angles is to alter the relative roll front to rear by adjusting the amount of front and rear lateral weight transfer. This can be achieved by modifying the height of the Roll centers, or by adjusting roll stiffness, either through suspension changes or the addition of an anti-roll bar.

What changes a slip angle into a slide angle? Excessive slip angles! That is, a slip angle is so called because the part of the contact patch that is to the outside of your turn is moving faster than the wheel itself is in the direction it (the contact patch) is pointing while the part on the inside is moving more slowly. (Exactly like camber thrust.) Since the outside part is moving faster than the tire it must be slipping. The inside part is gripping better than it would if moving in a straight line. For this reason the contact patch 'walks' itself into the turn.

The greater the slip angle, the larger portion of the contact patch that is slipping. At some point there is so little part of the contact patch that is not slipping that traction is lost and the tire begins to slide. Until shortly before then, slide traction increases. Note, however, that traction is generally not lost all at once. Rather than an abrupt loss of traction, it tends to be lost gradually.
Tires seem to operate at their peak performance when they are under a few degrees of slip angle, they generate the most grip at that particular slip angle. For race and high performance tires this optimum slip angle is around 6 to 10 degrees while this number is a little lower for street tires.
Due to low traction surfaces rally drivers reach even bigger angles. In drifting you probably see the biggest slip angle of all motorsports, sometimes as high as 40 degrees!

Slip Angle Measurement

There are many reasons people want to measure the slip angle of vehicles. Slip angle is used in a variety of objective vehicle dynamics measurements. These include checking
the stability of the vehicle, the feel of the steering, comparing the performance of different tires. One of the most important areas is ESC tuning. Because the sensors in vehicles are not able to accurately derive the slip angle, a we need a model to estimate slip angle. All this model needs tuning with accurate data. But no matter what the data will eventually be used for, there’s one requirement everyone has in common—they want it to be accurate.
The main problem in measuring slip angle is that it is a very small angle. A change of 0.5° is already significant. Slip angle also varies quickly, so fast changes (above 1Hz) are significant.

There are two main ways to measure slip angle of a tire: on a vehicle as it moves, or on a dedicated testing device.
There are a number of devices which can be used to measure slip angle on a vehicle as it moves; some use optical methods, some use inertial methods, some GPS and some both GPS and inertial. Combination of all three is the best.
You should also be aware slip angle accuracy changes with speed.
To calculate an object’s track angle, GPS and inertial measurement systems take the arc tangent of the wheel forward velocity -Vx- and lateral velocity -Vy-.

Bearing in mind these instruments measure velocity with a relatively fixed accuracy of, say 0.1 km/h, it seems obvious a small error like this is proportionally more significant at low speeds. That’s why slip angle accuracy improves with speed.

If you know the speed you want to conduct your slip angle tests at, you can calculate the expected accuracy of any system with the following function:

Other sources of error are down to the installation of the measuring equipment in the vehicle, or the device’s inability to compensate properly. That’s why engineers don’t mind spending time making sure an installation is good enough to capture the data they require.
Road camber is one more source of error that directly affects slip angle and can’t be controlled, but can be seen if the measurement device describes exactly how the vehicle body moves through space. This is one of the reasons inertial navigation based systems offer superior performance in real world testing—because they give users a complete and accurately timed picture of how the vehicle is moving in all axes.

Also, various test machines have been developed to measure slip angle in a controlled environment.

Slip angle and steering angle – Tire slip angle

Assuming grip is maintained, the body of vehicle will tend to follow the direction the steered tires are pointing in but momentum of the vehicle will mean that there will always be a level of tire slip, however minimal this may be. The tire will deform slightly as it makes contact with the road and this deformation may also need to be considered. This can be calculated by measuring the slip angle over the wheel and the actual wheel steering angle (which can be obtained via CAN), then subtracting the slip angle from the wheel steering angle – the result is the tire slip angle. Note that wheel steering angle will need to be measured at each wheel, due to the effects of Ackerman steering.

To know more about car movement in 3D space, read my article about Formula 1 car motions.

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