HaulingAss
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True, the lower the traction, the less binding that can happen.The damage that can be done using lockers on pavement, especially while turning can be very severe and expensive. Don't do it. If you want to test your lockers find a dirt or gravel road or a dirt parking area to try it out.
Locking differentials are a serious tool that come with some big advantages and disadvantages. Even on a low-traction surface they will significantly increase your turning radius (assuming the front wheels are also on a low traction surface). That's because a locked rear axle wants to go straight ahead, putting a side load on your front contact patches when trying to steer. If it's slippery, that will result in your front wheels having more of a tendency to plow straight ahead (scrub) even though they are turned. Try to reduce the sharpness of turning required when any lockers are engaged.
Locked differentials will also increase battery consumption/reduce range while increasing tread wear. They should be used very judiciously, and only when beneficial (which is less often than many people think). Even damp dirt can have very high levels of grip, causing strong binding and wear or breakage of drivetrain components. Dry, dusty surfaces, or slick wet surfaces, are safer than damp hard-packed ground which can have almost as much traction as pavement.
The rear locking differential is the most useful of the two, there are limited applications for the front locking differential, primarily slippery, rugged ground on very steep terrain where the rear locking differential is not enough. Because the lockers will lock the left and right wheels on each axle together, they are best used when not turning sharply.
Locking the differential can cause problems when in very slippery conditions like snow and ice when used on off-camber paths (when there is a side slope to the direction of travel). That's because they will cause both tires to break traction, either due to application of power or when the wheels need to turn at different rates due to a steering input or even due to the terrain (a wheel going over obstacles has to travel further than a wheel on a smooth, flat line). This can cause the locked axle to slide sideways downhill more readily than if the differential were left open (but you will have more forward drive to help compensate).
One last tip: They will be harder to engage/disengage if your tire pressures are not equal left to right. Even small pressure differentials will cause your tires to have a different effective circumference, which will load a locked differential when traveling straight ahead on flat ground. Keep your tires at identical pressures on the same axle. If you know one tire is at a lower pressure than the other, the locker will disengage easier if you steer in the direction of the low pressure tire, putting it on the inside of the turn to compensate for it's smaller circumference.
If you don't need your differentials locked, then don't lock them.
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