On this page, Rikutsu-Kone-Taro tries to explain statistically why 4WD (four-wheel drive) is advantageous in sports driving compared to 2WD (two-wheel drive).
Of course, this is my subjective opinion filled with arbitrary judgments and biases based on the views of “Mr. Know-it-all.”
Now, the traditional explanation for the superiority of 4WD over 2WD used to be something like, “Because each wheel in 2WD has less traction, allowing more grip on the tires.” However, I want to explain it using a probabilistic approach rather than the typical explanation that suggests 4WD prevents tire slippage in situations where 2WD might fail due to the struggle to transmit engine power to just two wheels.
Before proceeding, please assume that the discussion below assumes the presence of an appropriate Limited Slip Differential (LSD) unless otherwise stated.
Let’s state the conclusion upfront.
In 2WD, the probability that a tire in contact with the ground is a driving wheel is 50%. However, in 4WD, there are no non-driving wheels, and all tires in contact with the ground are 100% driving wheels. Therefore, 4WD has an advantage over 2WD in transmitting traction to the road.
When only one wheel is in contact with the ground in 2WD, the probability of that tire being a driving wheel is 1/2.
If two wheels are in contact, the probability that both are driving wheels is 1/6, the probability that only one is a driving wheel is 2/3, and the probability that both are non-driving wheels is 1/6.
However, in 4WD, all tires in contact with the ground are always driving wheels.
From this, in situations where the road surface has some irregularities or the coefficient of friction (μ) changes discontinuously, 4WD has a higher probability of having a driving wheel in contact compared to 2WD.
Therefore, the probability of transmitting traction to the road surface is higher in 4WD.
In 4WD, regardless of the number of tires in contact with the ground, all of them are driving wheels. This is the reason why 4WD is advantageous on roads with varying coefficients of friction, such as those encountered in rally competitions.
In the past, when tire performance was low and lacked sufficient grip, excessive engine power could lead to wheel spin, resulting in a lack of traction.
In modern times, with improved tire performance, intentionally spinning the wheels has become a form of entertainment to showcase the power of the engine.
Returning to the main point, in the past when tire performance was low, having only two driving wheels could lead to wheel spin and the inability to move forward. To address this, there was a time when the idea was to distribute engine power to all four tires, allowing even low-performance tires to avoid wheel spin by sharing the traction load among four tires.
Of course, if engine power is distributed to four wheels but still significantly exceeds the performance of the tires, all four wheels may spin, and traction may be lost entirely.
To avoid such situations, there exists a system within the grip of the tires to control the power from the engine. Here, we refer to such a system as the Traction Control System (TCS).
Nowadays, with the significant improvement in tire performance and the ability to implement sophisticated TCS, the rationale for distributing engine power to four tires is less relevant. In fact, it may result in the addition of complex and heavy mechanisms.
With the current level of tire performance, it is sufficient to convert the engine output to traction using only the front two wheels or the rear two wheels. However, this assumption holds only when the road surface has a high coefficient of friction (μ) and is homogeneous without many irregularities.
In reality, homogeneous and smooth roads with a high coefficient of friction do not exist. Roads can have various factors like remaining snow, puddles, manholes, paint, cracks, bumps, grooves, loose gravel, fallen objects, and other elements that make the coefficient of friction uneven and bumpy.
To reiterate the previous points, in scenarios where the coefficient of friction is uneven and there are some irregularities, let’s consider which drive system, 2WD or 4WD, has a higher probability of applying traction to the ground.
Exclude situations where all four wheels are in a jumping state.
In 2WD, even in the luckiest scenario, traction can be applied to a maximum of two wheels.
Depending on the circumstances, it might be only one wheel, and with an open differential, there could be moments of zero-wheel drive.
On the other hand, with an open-differential 4WD, traction can be applied to 0, 1, 2, 3, or 4 wheels at a maximum.
This means that in moments when only one effective tire is in contact with the ground, the probability of it being a driving wheel is twice as likely in 4WD compared to 2WD.
On the same road, if both 2WD and 4WD vehicles are driven, 4WD has twice the probability of applying traction compared to 2WD.
This is the reason why 4WD is advantageous over 2WD. In gravel, dirt, or semi-gravel/semi-dirt courses, 4WD has twice the probability of applying traction to the road.
Even with a complex 4WD system that adds weight to the vehicle, it might be worthwhile. Conversely, even with a lightweight vehicle, it is not ideal to have frequent moments of zero traction.
As mentioned earlier, in scenarios with a homogeneous and flat road, such as a runway or racetrack, where torque cutoff does not occur, elements like 0-60 acceleration or 0-100 straight-line time attack depend on engine output and tire performance. Therefore, there is no inherent advantage for the 4WD system in the GR Yaris.
Moreover, an automatic transmission that doesn’t experience torque cutoff is overwhelmingly advantageous.
The outstanding feature of the GR Yaris RZHP lies in its excellent 4WD system, guaranteeing traction even on uneven and slightly bumpy courses, while allowing significant driver intervention in the vehicle’s behavior through the 6MT (6-speed manual transmission).
This is the most endearing aspect of the GR Yaris, from the perspective of Rikutsu-Kone-Taro.
It might sound similar to the content covered so far, but please bear with me.
That concludes this article.
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