When I used to hang out, too many years ago to admit, with a German master tool and die maker (this guy was brilliant in the fab and design world) we tested dino and syn oils. His method was pretty simple: Used each as cutting fluid on lathe and milling operations. The syn's, and this is back in the day, ability to significantly reduce surface friction made it not such a good cutting fluid.
Another little test another similar type of guy showed me back in the day: He would take a metal pan with a film of oil in it and heat the bottom with a flame. The hot spot on the pan would cause different oils to move away from the hot spot at different rates. The worst performers were from multi-viscosities. IOW a 10W40 would move away from the heat source sooner and more aggressively than a straight weight. But we never 'tested' syns just dynos. Like I said it was too many years ago to admit

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But for differentials especially I think, as some of you have stated, it makes more sense particularly in our relatively mild climate and our type of use, to use the cheap stuff and drain it out after every trip with axle deep water crossings. Its amazing how fast, even with properly vented diff housings, cold water gets sucked past seals by the hot diff!!!
Any cheap but clean oil/lube beats dirty and/or contaminated expensive syn oil in our climate!
However I do use syn in my auto trans. I did notice slightly better shifts after I converted. But it could be all in my head

And I use syn in the motor for its extended oil change intervals...and this last year with 20k+ miles on the Hundy it sure made life a little easier
