Springs, dampers and the road

What a spring rate really buys you, why one damping number is a lie, and what a road actually looks like to a wheel.

1. Spring rate, wheel rate, ride frequency: the only three numbersA spring rate on its own tells you almost nothing — it depends on the car's mass and the linkage in between. Ride frequency is the number that lets you compare a Miata to a Dakar truck and have the comparison mean something.
2. Flat ride: why the rear should be stiffer than the frontMatching front and rear ride frequencies is the tidy, symmetrical, obvious thing to do — and it makes the car pitch. The fix is a 1920s idea that still decides how modern cars are sprung.
3. Damping ratio: the number nobody prints on the shockShock manufacturers sell you clicks. What actually matters is ζ — how much damping you have relative to the amount that would stop the car oscillating entirely. Here's how to compute it, and what happens when it's wrong.
4. Digressive dampers: four numbers and a kneeOne damping coefficient can't serve both body control and ride, because those happen at different velocities. A digressive damper solves it by changing slope partway up — and the place it changes is the tuning knob that matters.
5. Bump stops are springs, and they're doing more than you thinkMost people treat the bump stop as a crash pad — the thing that stops metal hitting metal. On a modern car it's a second, progressive spring that's carrying load long before you'd call it 'bottoming out'.
6. Unsprung mass and wheel hop: the second resonanceYour car has two natural frequencies, not one. The body bounces around 1.3 Hz; the wheel bounces around 13 Hz on the tire's own stiffness — and that second one decides whether the tire is touching the road.