I can try to explain. Some of this goes against conventional wisdom. I'm not infallible, but conventional wisdom also isn't necessarily a good source of info
The explanation also varies depending on the type of LSD, but the conclusion is similar.
First, how a differential actually works (from a rubber meets the road perspective, not the mechanical inner workings, which are cool but irrelevant to going fast):
Lets start with the case of torque application below the critical torque for the LSD to bias the correct direction:
Say you want to put down 200 ft-lb (after leverage multiplication through the drivetrain) at part throttle on corner exit on a path that is (instantaneously) a 50 ft radius corner.
Say the inside tire can support 200 ft-lb worth of resistance.
OPEN DIFF:
The inside tire turns at 9% lower speed than the outside tire, and both have a scrub percentage around 3%. Energy wasted in the diff is negligible, extra heat in the tires from acceleration torque is negligible, extra wear on the tires from acceleration is negligible. The torque on the inside and outside tires is 100 ft-lb. The sum of the moments about the Z axis due to drive thrust is 0.
Clutch type LSD:
The inside tire turns at 8% lower speed than the outside tire, and the inside tire has a scrub percentage around 4% with the outside at 2% (wild guesses on the numbers). Energy wasted in the diff is not huge, extra heat in the tires from acceleration torque is negligible, extra wear on the tires from the fight going on in the LSD is probably not huge. The sum of the torque on the inside and outside tires is around 200 ft-lb, with the INSIDE tire carrying more torque than the outside.
Gear type LSD (several simplifications here, but the gist of it is correct):
The inside tire turns at around 8% (wild guess) lower speed than the outside tire, and the inside tire has a scrub percentage around 4% with the outside at 2%. Energy wasted in the diff is negligible, extra heat in the tires from acceleration torque is negligible, extra wear on the tires from the fight going on in the LSD is probably not huge. The sum of the torque on the inside and outside tires is around 200 ft-lb, with the INSIDE tire carrying more torque than the outside congruent with the bias ratio.
What's going on here? The LSD doesn't know which direction you are turning or if tires are spinning or anything. It only knows 6 parameters, 1 input speed, 2 output speeds and 3 torque values. In the above case, the torque is going the wrong way until the inside tire spins up to match the outside. Neither clutch type nor gear type can leverage enough torque to spin up the slower tire, but they try.
This is why an LSD adds understeer in tight corners on throttle at a torque below that which would have broken free on an open diff. Below the critical torque, the inside tire is turning too slowly, and gets extra torque, which generates a moment about the Z axis that tends towards understeer.
Next the case of the upper limit of the open diff (well above the critical torque for the LSD):
Say you want to put down 400 ft-lb (after leverage multiplication through the drivetrain) at part throttle on corner exit on a path that is (instantaneously) a 50 ft radius corner.
Say the inside tire can support 200 ft-lb worth of resistance (the outside can support maybe 1200, but you'll never see anything over 200 under these conditions with an open diff).
OPEN DIFF:
The inside tire turns at 9% lower speed than the outside tire, and both have a scrub percentage around 3%. Energy wasted in the diff is negligible, extra heat in the tires from acceleration torque is negligible, extra wear on the tires from acceleration is negligible.
working limited slip DIFF (other than VLSD):
The inside tire turns at roughly the same speed as the outside tire. The inside tire has a scrub percentage around 12%. Energy wasted in the diff is negligible. Extra heat in the inside tire from acceleration torque is significant (can even get greasy if this corner is followed immediately by one the other way). Extra wear on the tires from acceleration is significant. How much horsepower does it take to spin up a tire (one that can pull 1.4g's+ in acceleration) to 40 mph when the road speed is 35? I don't know, but given I don't have a lot to start with..... I mean, at 4000 rpm, where I would be at the bottom of second in this example, I've only got ~75 rwhp to work with....
In this case, what's going on, and what do we care about? Why would changing on open diff to an LSD make a car slower?
Tire wear, power lost due to the scrubbing process and its effect on lap times, handling bias effects that come with this effect (moment about the z axis that counter cornering input.) They are all significant.
More in my next post....