Originally Posted by The HACK
The answer is FAR more complicated that one can answer on a forum. You're much better off taking a few car control clinics that most BMW CCA chapters offer throughout the year to learn this stuff.
But I'll take a stab at it.
Imagine your car as a 3 axis pendulum, with 2 of the axis attached by springs. The car is capable of rotating or swinging in these three axis: It'll rock left and right, it'll dive front and rear, and when it spins, it'll pivot on the axle that has grip. The two axis that are controlled by springs are the rocking left and right, and the dive and squat front and rear.
If none of this stuff makes any sense, pick up a toy model car and imagine it moving in space. If you're familiar with flying, these three axis are pitch, yaw, and rotate.
In a car, since two of the axis is limited and controlled by springs mounted on dampers, and the tire's contact patch acting as control for the rotation of the car while the tires act as the spring, the end result is when the parameters of the car's operation is pushed beyond the limit of a single component to control, any component, the end result is OSCILLATION, which is the violent rocking back and forth you describe.
If you're still reading at this point, the simple answer to your question is yes, all of the above, some of the above, and none of the above. If this doesn't make any sense, I'll try to confuse you more...
The three axis rotation on a car works as a system. Every single movement is determined by movement of the other axis. How the car yaws depends on both the pitch and rotation. So yes an LSD will likely help since it controls the distribution of power to both rear wheels (controls pitch, the squatting and diving of the car, as well as the rotation, the rocking left and right of the car to a lessor extent), therefore it will ultimately control the yaw of the car. M3 bits in the rear limit the movement of the suspension and increases camber, thus altering the way the car's yaw rate in the middle of the turn, hence altering the pitch and rotation...etc. I hope you get the idea.
Ultimately though, NONE of the parts mentioned above controls the 3 axis like how YOU should be able to control the three axis. If your input overwhelms any of the linked parameters, it will start a chain reaction that ultimately results in oscillation. In other words, take a car like a Formula 1 race car. It's got, by comparison to normal street cars, almost unlimited grip and power. Yet put it in the hands of an untrained driver, it'll probably spin out before it leaves the pits, despite all the parameters of the equipment being magnitudes higher than what a typical street car is equipped with. At that point, ALL the equipment in the world is already installed on the race car to prevent the parameters being overwhelmed, yet those parameters will still be overwhelmed by any novice driver that do not know what they're doing.
IF you're still reading. If none of what I said above made any sense, stop now, go attend a few Car Control Clinics. None of what I say now will make much sense nor help you control your car better. But if you're interested, I can sort of explain to you what is happening.
As you exit out of a turn, weight of the vehicle is transferred to the outside wheels and forcing the outside springs to compress. And as you accelerate, weight of the vehicle is further transferred to the back of the car, making the outside, rear wheel bearing the brunt of the weight of the vehicle. So the rear, outside springs are likely fully compressed, or compressed more than the other corners, and the dampers doing its best to prevent it from REBOUNDING as you exit the turn. Now, as you apply MOAR throttle the rear wheels will eventually break loose and start spinning. At this point, since the rear tires are spinning freely you are no longer accelerating as quickly as you were prior to the tires breaking loose. The end result is, some of that weight comes off of the rear axle, and all that energy that was stored up in the compressed spring is allowed to rebound and send that force back the other way as the rear continues to lose traction from being overpowered by the engine.
This part is the slide.
What comes next, as you catch the slide by counter steering, weight of the vehicle starts to transfer to the INSIDE tire, and now the inside tire all of a sudden regains grip and catches, sending your car's polar momentum going the other way. Combined with the forces being unloaded by the rear outside springs plus the inside tire regaining traction, the two forces add and multiply and again overwhelms the rear tires, now going in the OPPOSITE direction starting an oscillation of the yaw of the car.
This part is the "tank slapper."
Now, in a car that is equipped without an LSD, relying on rear brakes to simulate the effects of an LSD, and DTC acting on its own to prevent the owner of the car from killing him/herself, in the above situation DTC and the e-Diff will act by providing forces moving in the OPPOSITE direction of the forces being applied in a spin. DTC will cut power to the rear to attempt to minimize the wheel spin to the OUTSIDE of the turn, while e-Diff will attempt to brake the inside wheel to prevent power from being diverted from the INSIDE of the turn, and this all act in conjunction to create that bucking sensation instead of a car spinning freely out of control one way or another on a sprung car.
This stuff is hard to visualize. It is best practiced on a big empty parking lot, ideally wetted down with soapy water to decrease grip to allow for prolonged spins. You know, like a Car Control Clinic from a BMW CCA chapter.
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