Faster car drifting (motorsport) when using limited slip vs welded differential

I have been drifting RWD (rear wheel drive) cars for some years now. I tend to think about every engineering solution that other drivers use and how does it work before applying it to my car.

What has been baffling me from some time now is: Why using LSD (limited slip differential) results in bigger speeds when drifting?

Food for thought:

• Welded differentials (100% lock) are very common in this motorsport since you are dealing with kinetic friction on rear tires anyway - which is constant regardless of their rotation speed (unless you match tire speed to ground and grip using static friction).

• Open differentials (0% lock) on the other hand practically make drifting (powersliding) unusable as almost all of the engine torque is routed to unloaded wheel resulting in slowing down.

• Slow motion drifting video: https://www.youtube.com/watch?v=OG0cyjqDJCw

• Out of curiosity, what do Torsen differentials do in that situation? – TimWescott Oct 29 '19 at 16:43
• @TimWescott Torsen "gears" two wheels together (acting contrariwise to open diff), while LSD tries to lock them AFAIK. For some reason it is not used in competitive drifting. Nice idea to explore though... – Tomasz Sulkowski Oct 30 '19 at 12:05

To facilitate my explanation I'll follow the same scenario and the following definitions:
I'll consider all explanation considering the car doing a left curve.
$$W_{rL} =$$ For Left Rear Wheel
$$W_{rR} =$$ For Right Rear Wheel
$$WD =$$ for Welded differential
$$LD =$$ for Limited-slip differential (btw Torsen is a type of $$LD$$)
$$OD =$$ for Open differential
$$r_v =$$ for rotation speed on the wheel
$$L_F =$$ for Lateral force (byproduct of the mass of the vehicle)

When you start cornering what makes the car slip (drifting) is the resultant force from the sum of the force from rotation of the wheel and the lateral force resultant from the mass of the vehicle.

In the normal cornering (without drift) the $$W_{rL}$$ will rotate slower than the $$W_{rR}$$. And the lateral force will be concentrated on the right side of the car.
The $$W_{rR}$$ will be subjected to more lateral force than $$W_{rL}$$.

With $$OD$$ the car will first accelerate $$W_{rR}$$ until the wheel start slipping. On this moment almost all the power of the car goes to $$W_{rR}$$ and your car will desacelerate until the slipping stops (and if you continue accelerating) there will be a loop without never slipping on $$W_{rL}$$, and so no driftting here.

With $$WD$$ the car will start the drifting with the same speed on both wheels. In this case the minimum speed to get a true drift will need to surpass the minimum threshold from $$W_{rL}$$. But the $$W_{rR}$$ will rotate with the same speed from $$W_{rL}$$ ($$r_v$$ is distributed 50% on $$W_{rL}$$ and 50% on $$W_{rR}$$). But our lateral force is not the same with let's say $$L_F$$=20% on $$W_{rL}$$ and $$L_F$$=80% on $$W_{rR}$$ (the correct $$L_F$$ will vary acording with entry speed on curve and curve angle).
The result in this case is that with $$WD$$ the tire grip on $$W_{rL}$$ is better than the grip on $$W_{rR}$$ because of the inbalance of the sum of the forces.

With $$LD$$ the car will start drifting first on $$W_{rR}$$ like with $$OD$$ but our $$LD$$ will garantee that some power remains in $$W_{rL}$$ and the speed keeps increasing until $$W_{rL}$$ starts slipping too.
The moment the drifting start, the $$LD$$ will distribute the $$r_v$$ on both wheels to get a balance in the resultant force. So the values now will be something close to:
- on $$W_{rL}$$: $$L_F$$=20% + $$r_v$$=80%
- on $$W_{rR}$$: $$L_F$$=80% + $$r_v$$=20%
With this combination the grip on the wheels will be the same and no lost power like with $$W_{rR}$$ like with the $$WD$$.

Sorry by the lack of images to help the understanding.
I'm new with stackexchange and I need to fiddle more with the commands to learn how to create some helping image and put here.

• "... need to fiddle more with the commands to learn how to create some helping image ..." Just press the image icon on the editor toolbar. You can upload an image or paste a URL. Don't forget to add a credit with link for anything that's not your own work. – Transistor Dec 1 '19 at 9:30
• You didn't specify which corner you take in your example (I suspect its right hand corner, in which case WrL can be just "the outside wheel"), but I get the idea... and I think you are right! :) In your detailed description, the devil is in the initiation: LSD will "hold" rear of the car longer when using power-over technique! This "grip" effect can also be felt during transition from one slide to another. More of this "grip" == faster, simple. Thank You! – Tomasz Sulkowski Dec 3 '19 at 7:39

Because with a lsd, when one wheel slips the other wheel actually turns faster, due to the way the differential works.

• But that argument could be applied to open differentials, and they are "unusable"! – TimWescott Oct 29 '19 at 16:43
• @TimWescott what do you think the "limited" bit does? – Solar Mike Oct 29 '19 at 16:47
• I feel the explanation lacks depth, because as written it is consistent with the action of either an open or a limited slip differential. Certainly with an open differential, when one wheel slips the other turns faster, just as with a limited slip. – TimWescott Oct 29 '19 at 17:48
• As @TimWescott pointed out, open diffs make the unloaded (inner) wheel spinning even faster when compared to LSD (aka. one wheel burnout) resulting in less grip. I think the secret lies on the usage of the loaded (outer) wheels lateral grip. – Tomasz Sulkowski Oct 30 '19 at 12:15