What is the difference between ride and roll stiffness? Are they separate or closely related?

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"Ride stiffness" refers to the spring rate, or road feel, of the entire vehicle. Does a rough road jar your teeth?

"Roll stiffness" might be created by anti-roll or anti-sway bars, and refers to the resistance of the body vehicle to "leaning" over due to weight transfer when cornering.

It's worth noting that nothing can be done to prevent weight transfer; it's a simple law of physics. What an anti-roll bar does is remove some of the independence of the suspension on that axle, such that the inevitable weight transfer during cornering limits change in the suspension geometry relative to the road surface - keeping the tire [hopefully] flatter and maintaining a larger contact patch with more useful traction.

They are separate and not really related. A "bump" that affects both wheels of an axle (e.g. speed bump/sleeping policeman) is not influenced by an anti-roll device, as both wheel suspensions are compressed in unison. An anti-roll bar will not contribute to ride stiffness.

Only when suspension compression on one wheel of an axle pair will the anti-roll bar come into play. The difference in compression creates a twisting force on the center section of the anti-roll bar, and transfers some of the compression to the other wheel. As the diameter of the center section of the bar increases, the "spring" stiffness or resistance to twist increases exponentially - I believe to the fourth power.

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