Presumably, the tires would be held constant for the purposes of the test. Load rating (# of plys) would vary the weight of identically sized tires.
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Mass concentrated towards the outside of the rotating object matters more than mass closer to the axis of rotation.
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But rotational energy is a give and take situation, while deviations from a direct path are just take, take, take. Every time you hit a pot-hole, the weight of that corner is lifted by a punch from the sprung mass. Wheel alignment/steering play—same thing.
Where does that energy come from, out of your gas tank?