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Open diffs and brakes for "torque vectoring"

TL;DR Brake based torque vectoring doesn’t actually vector torque, it just absorbs the torque going to the low traction tire that couldn’t be used anyway which allows the high traction tire to use all the torque that it gets.

Engineering Explained posted a video talking about the McClaren P1's open diff and explaining how the brakes are used to mimic an LSD / torque vectoring differential. HHFP posted an awesome explanation of how differentials work a while back that bears reviewing. If you have a handle on that post my following ramblings might make sense.

We know that an open differential always has a 50/50 torque split. If you put 200 lb-ft of torque into the differential you get 100 lb-ft to each tire. Things go south when one tire can only put down 10 lb-ft. Once that happens each tire only gets 10 lb-ft since there is a 50/50 torque split and we can only use 20 lb-ft of our torque. If we engage the brakes on the side that can only absorb 10 lb-ft we can dissipate the excess torque as heat. Assuming the brakes are capable of absorbing all the excess torque we can still put 200 lb-ft into the diff. Both tires still get 100 lb-ft of torque because of the 50/50 torque split, but the low traction side has 90 lb-ft of torque absorbed by the brakes while only 10 lb-ft of torque gets transferred to the ground.

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For some reason the EE video finally made it click in my head that the brakes are absorbing the torque that goes to the low traction tire, they don’t vector torque to the other side.

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