A car touches the road through four tires.
On real roads, the four contact patches can each have a different coefficient of friction, or μ.
The right-front tire may be on dry asphalt while the left-front tire is crossing wet road paint.
The front tires may be on a wet surface while the rear tires are still on dry pavement.
One side of the car may pass over snow, gravel, or another low-grip surface.
What matters in these situations is how much of the grip available at all four contact patches can be converted into driving force.
In automotive engineering, a condition in which the left and right wheels are on surfaces with different friction levels is commonly called split-μ.
This article considers split-μ as well as broader situations in which grip differs from front to rear and from one contact patch to another.
The car discussed here is the Toyota GR Yaris RZ High Performance (RZHP), which combines the GR-FOUR all-wheel-drive system with Torsen limited-slip differentials at both the front and rear.
GR-FOUR distributes drive between the front and rear axles, while the two Torsen LSDs create torque differences between the left and right wheels on each axle.
Together, they increase the range of available tire grip that can be used for propulsion when μ differs around the car.
What Is μ?
The symbol μ, pronounced “mu,” represents the coefficient of friction between the tire and the road.
At a higher-μ contact patch, the tire can generally generate greater driving, braking, and lateral force.
At a lower-μ contact patch, the amount of force the tire can transmit to the road is smaller.
The actual μ depends on several factors, including:
- road surface condition,
- tire type,
- temperature,
- water film,
- snow condition,
- and ice condition.
In this article:
Grip means the available frictional capacity at a tire’s contact patch.
Driving force means the portion of that available grip used to propel the car.
Grip Can Differ at All Four Contact Patches
Road conditions can change over very short distances.
Examples include:
- standing water,
- wet pavement,
- patches of snow or ice,
- gravel or sand,
- manhole covers,
- and painted road markings.
Only the tires on one side of the car may cross a puddle.
The front tires may pass over wet paint while the rear tires are still on dry asphalt.
During real-world driving, the available grip at the:
- right-front,
- left-front,
- right-rear,
- and left-rear
contact patches can therefore differ at the same moment.
Which of those tires can be used for propulsion directly affects available traction.
A 2WD Car Concentrates Propulsion on One Axle
In a front-wheel-drive car, the two front tires are driven.
In a rear-wheel-drive car, the two rear tires are driven.
Consider an open-differential FWD car with its left-front tire on wet road paint and its right-front tire on dry asphalt.
An open differential sends approximately equal torque to both sides.
If the low-μ left-front tire can support only a small amount of drive torque, the torque available to the high-μ right-front tire is also limited to a similar level.
The right-front tire may still have substantial unused grip, while only part of that capacity can be converted into propulsion.
A 2WD car with an LSD can make better use of the higher-grip wheel by creating a torque difference across the driven axle.
Its propulsion, however, is still concentrated on one axle: the front axle in FWD or the rear axle in RWD.
GR-FOUR Can Use Grip at Both Axles
The GR-FOUR system in the RZHP uses an electronically controlled multi-plate clutch to distribute drive between the front and rear axles.
When grip at the front axle is lower, available grip at the rear axle can also be used for propulsion.
When grip at the rear axle is lower, the front axle remains available to contribute driving force.
GR-FOUR therefore allows available grip at both axles to contribute to propulsion.
This becomes particularly valuable when μ differs from front to rear or changes rapidly as the car moves across the road surface.
The amount of torque transmitted to each axle is determined by the GR-FOUR system and the capacity of its electronically controlled coupling.
Front and Rear Torsen LSDs Use Left-to-Right Grip Differences
The RZHP also has Torsen limited-slip differentials at both the front and rear.
Their roles can be separated clearly:
GR-FOUR electronically controlled multi-plate clutch
→ distributes drive between the front and rear axles
Front and rear Torsen LSDs
→ bias torque between the left and right wheels on each axle
A Torsen LSD uses the reaction torque available at the lower-grip wheel as the basis for biasing more torque toward the higher-grip wheel.
For example, if the right-front tire moves onto a low-μ surface while the left-front tire retains more grip, the front Torsen LSD can create a torque difference and make greater use of the grip available at the left-front tire.
At the same time, GR-FOUR can make use of grip available at the rear axle.
The RZHP therefore works in two directions:
GR-FOUR manages front-to-rear drive distribution.
The front and rear Torsen LSDs manage left-to-right torque bias within each axle.
This two-stage arrangement allows more of the grip remaining at the four contact patches to contribute to propulsion.
The RZHP Can Make Use of a Wider Range of Available Grip
The amount of grip available at each tire changes from moment to moment.
The RZHP has a drivetrain architecture capable of responding to:
- available grip at the front axle,
- available grip at the rear axle,
- left-to-right grip differences at the front,
- and left-to-right grip differences at the rear.
As a result, it can use a wider range of the grip available across the four contact patches for propulsion than a 2WD layout can.
That is the central advantage of combining GR-FOUR with front and rear Torsen LSDs on mixed-grip surfaces.
This article focuses on that hardware architecture and the way it distributes driving force.
A Uniform High-μ Surface Brings Different Strengths to the Foreground
On a dry racetrack, all four tires may have high grip with relatively small differences between the four contact patches.
Under those conditions, AWD traction becomes especially relevant during situations such as standing starts and hard acceleration out of corners, where drive can be shared between both axles.
An AWD system also adds drivetrain components such as differentials, a coupling, and a propeller shaft, which contribute additional mass.
Performance on a uniform high-μ surface therefore reflects a combination of factors including:
- AWD traction,
- vehicle mass,
- engine output,
- tires,
- and circuit layout.
Performance on mixed-μ surfaces and speed on a uniform high-grip surface reveal different aspects of the RZHP’s drivetrain.
A Standing 400-Meter Run Measures a Different Capability
A standing 400-meter acceleration test on uniform pavement measures launch traction and acceleration performance.
Testing performance when μ differs from wheel to wheel requires different grip conditions at the four contact patches.
The GR-FOUR and dual-Torsen arrangement becomes especially relevant when:
the four tires are operating under different grip conditions.
Roads containing a mixture of rainwater, partial snow cover, gravel, painted markings, or other changing surfaces create this type of environment.
Rally stages, where grip conditions can change repeatedly over a short distance, make the same drivetrain characteristic particularly relevant.
Conclusion
A car meets the road through four tire contact patches.
Each of those four contact patches can have a different μ.
Split-μ is one important example, in which the left and right sides of the car experience different friction levels.
The GR Yaris RZ High Performance combines:
- GR-FOUR for front-to-rear drive distribution,
- a front Torsen LSD for left-to-right torque bias at the front axle,
- and a rear Torsen LSD for left-to-right torque bias at the rear axle.
This arrangement increases the range of grip available across the four contact patches that can be converted into driving force when μ varies around the car.
That two-stage distribution of drive—front to rear through GR-FOUR and left to right through the Torsen LSDs—is the reason the GR Yaris RZ High Performance has a strong drivetrain advantage on mixed-grip surfaces.
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