If you are looking for the safety of an open with the fun of the traditional limited slip you can use a Torsen style differential. If a wheel completely loses traction(like on ice) it acts like an open differential but it takes using the e-brake to get you out of situations like having one tire in the mud and the other on dry pavement.
He's still not convinced. He wants me to show him some evidence like a report claiming that a closed rearend is more dangerous in slick conditions.
The question is: Will a vehicle with limited slip lose traction at both rear wheels when cornering in slick conditions with less torque applied to the driveshaft than an identical vehicle with and open rear end?
I believe the above statement to be true, but I need evidence.
Direct answer to your question is no. It actually takes more but not much more.
There are 3 amounts of torque to be considered between the two.
If the torque applied isn't enough to break the tires loose they'll act the same.
If torque is increased to just enough to break the open loose, under the same conditions, the limited slip should hold traction. This is a VERY small window when it is slick. Dry you have a much bigger window and that's where LSD usually wins.
If torque is increased further the inside tire will continue to just spin faster while the limited slip will break the rear loose almost any car can do this. Now, even an open rear, given enough side force, can go into a slide like an LSD equipped car can. Once both tires are loose an open can usually keep them both spinning.
I'm swapping out the open rear for a limited slip in about a month. I like the open at times because when I'm just playing around I can punch the gas and peel out while staying straight because the other side is rolling. However, I've landed myself in a few places off-road that would have been easier to get out of with LSD.
When I first put a LSD into my 455-powered Buick, I was on my way home from school and did a 1-2 WOT shift in "misty" weather. I had a pretty stiff shift kit in my TH400, so the next thing I realized I was spun out facing the opposite direction. That had never happened with my open diff.
This was about 20 years ago, I was younger and stupider at the time... (but I probably had more fun)
It sounds like most people are describing about a LOCKING differential not a mechanical or viscous LSD. I installed a mechanical 25% LSD on the back of my BMW and it makes the car a lot easier to drive on snow and ice especially when you hit ice with just one side of the car. Also, I've never seen a pickup truck with a factory LSD. All the ones I've seen have either automatic or manual LOCKING differentials. When that thing locks on ice watch out.
My comparisons were my 2002 GMC Sierra 1500 with open diff vs. my dad's 2002 Toyota Tundra Limited TRD with original equipment Limited Slip. I'm 95% sure that his limited slip is NOT a locking diff, just a limited slip diff.
It would probably be even worse with an automatic locking diff like the G80 found on some GMs.
A little off topic, but could LSD cause the rear end of a vehicle, going straight, to whip out to the side? This has happened to me several times in the ranger when hitting a bump just right while applying a gas. I thought it was just one of the quirks of a light backside and solid axle. After reading up on LSDs, now I'm not sure about that.
Ford offers factory LSD, called Traction-lok. Cost as much as an after market locker though.