Just a little refresher on how these work:
Each wheel experiences it's own coefficient of friction based on the surface under it. Exceed that and the wheel slips providing no additional motive force if you give it more gas.
In addition, there is a static and dynamic coefficient of friction.In most cases the dynamic coefficient is lower, so once a wheel starts to spin, you actually have less traction.
- Standard Slip Differential: Power is applied to both wheels but once one starts slipping, power to the 2nd wheel is limited to the amount sent to the slipping wheel. So if the coefficient of friction is 0.1 and 0.5...you have two wheels applying power based on 0.1. So if you have one wheel on dry pavement and one on slick ice, it's like both are on slick ice in terms of the available traction.
- Limited Slip Differential: Normally works the same but if one wheel starts to spin significantly faster than the other, a clutch mechanism locks the differential, so the 2nd wheel gets as much power. Net result, you have one wheel at 0.1 and one at 0.5 for an average traction of 0.3 (much higher than a standard diff). Downside, because the first wheel is spinning, it might experience a slightly lower coefficient of friction. Now if both wheels are at 0.1, you won't see any significant improvement on available traction
- Manual Locking Differential: Generally used only on poor surfaces as it negates the purpose of a differential (allowing the wheels to travel different distances as you go around corners). This can be bad on dry pavement as it puts a lot of stress on the drivetrain and can burn up tires. This has the advantage, that you can lock the diff and apply power based on the static coefficient of friction, which maximizes the traction available to the axle.
If you punch it with a limited or manual diff, both wheels can slip going into dynamic friction and the rear end gets squirly as they are effectively sliding on the surface. With standard diff, only one wheel typically spins, so the other acts as a rudder to keep the truck in line (there are limits to this effect, so a standard diff truck can still have the rear end get out of control but less likely to happen).
There are also electronic tricks using the brakes that can simulate limited slip. By independently applying just a little bit of braking to a slipping wheel, a standard diff sees more traction on the slipping wheel and sends more power to the non-slipping wheel.
The big take away...if the wheels are on the same surface (with identical Coefficients of Friction), don't expect the diff to have much impact on traction. If they are on different surfaces, it can have a huge difference. Also, spinning the wheels can be fun but almost never provides more traction.
PS: Marginally related, there can be a huge difference between a truck with RV vs truck by itself. Empty, most trucks only have about 40% of the weight on the rear axle. Weight on the wheel times the CoF, determines how much thrust the wheel can provide. If you have a truck camper or trailer applying weight to the rear axle, it can move the distribution up to 50-70% on the rear axle, significantly increasing available traction.
