Damping ratio: the number nobody prints on the shock

Shock 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.

A spring stores energy and gives it all back. Left alone, a car on springs would bounce until friction gave up — which is why the earliest cars, on leaf springs with nothing else, were so unpleasant that people rode them standing.

The damper’s job is to take that energy out. The question is how much, and the answer is not a number you’ll find on the box.

Critical damping, and why it’s the reference

There is exactly one amount of damping that returns the body to rest in the shortest possible time without overshooting. That’s critical damping:

c_{\text{crit}} = 2\sqrt{k_{\text{wheel}} \cdot m_{\text{sprung}}}

Everything else is quoted relative to it. The damping ratio is:

\zeta = \frac{c}{c_{\text{crit}}}

ζ = 1 is critical. Below 1, the body overshoots and oscillates before settling — under-damped. Above 1, it creeps back slowly without overshooting — over-damped, which sounds safe and is not.

Worked example. The front corner of the layout in the app has a wheel rate of 23 210 N/m and 349 kg sprung:

c_{\text{crit}} = 2\sqrt{23\,210 \times 349} = 5692\ \text{N·s/m at the wheel}

The damper is quoted at the damper, not the wheel, so — exactly like spring rate in chapter 10 — it arrives scaled by MR²:

\zeta = \frac{c_{\text{damper}} \times \text{MR}^2}{c_{\text{crit}}}

The preset’s front slow compression is 8000 N·s/m at MR 0.936:

\zeta_{\text{comp}} = \frac{8000 \times 0.876}{5692} = 1.23

And slow rebound at 14 800 N·s/m gives ζ = 2.28.

Those numbers are wrong, and the app says so

An average ζ of 1.75 is not a tuning choice. It’s over-damped by a factor of three or four, and the app’s advisor flags it directly: “Over-damped — the front is harsh and skates over bumps. Lower slow compression & rebound.”

This is worth dwelling on rather than quietly fixing, because it’s the most common real-world error in amateur damper selection: more damping feels like more control, right up until it isn’t. An over-damped car doesn’t float or wallow, so it feels tied down in the showroom. What it actually does is refuse to let the wheel move at the speeds that matter, so over a series of bumps the suspension never returns to its ride position — it packs down — and the tire spends its life skipping rather than following the road.

Here’s what the front corner would need for sensible values:

Target ζ	Damper setting needed
0.25 (soft, comfort)	1624 N·s/m
0.30	1949 N·s/m
0.40 (a good default)	2599 N·s/m
0.70 (firm, track)	4548 N·s/m
as shipped, compression	8000 N·s/m — ζ 1.23 on its own
as shipped, rebound	14 800 N·s/m — ζ 2.28

Those two are what average to the 1.75 above; the compression and rebound sides are graded separately because a damper is not one number.

On compression alone the preset is running roughly 1.8 times the damping of a firm track setup, and three times the sensible road default. Treat it as a fault to fix in chapter 15’s exercise, not as a reference.

The two-jobs problem

Why not just pick one ζ and be done? Because the damper has two jobs with different answers.

Body control wants ζ around 0.6–0.7. That’s what stops the car pitching and rolling sloppily, and it’s what makes a car feel connected when you turn in.

Ride wants ζ around 0.2–0.3. Low damping lets the wheel move freely over sharp inputs so the body doesn’t feel them.

Those are different numbers and one shock has to do both. That conflict is the entire reason dampers aren’t simply linear, and it’s the subject of the next chapter — the trick is that body motions and road inputs happen at different velocities, so a damper that changes its coefficient with speed can serve both.

Rebound versus compression

Notice the preset uses different numbers for compression (8000) and rebound (14 800) — a ratio of 1.85:1. That asymmetry is deliberate and near-universal.

Compression damping resists the wheel moving up, which means resisting the bump itself. Too much and every road input goes straight into the body. Rebound damping resists the wheel moving down, controlling the spring’s release, and the body barely feels it — so you can afford much more.

The app grades the ratio directly, wanting roughly 1.5–2.5:1. Below about 1.2:1 the spring returns uncontrolled; above 3.5:1 the suspension packs down over rapid bumps, because the wheel can’t extend fast enough to reach the next hollow before the next crest arrives.

Go look at it

Open the strut layout on the Springs/Shocks tab.

In the setup panel, find Front damping — it reads about ζ 1.75, graded amber with the over-damped warning.

Set Slow Comp to 2600 and Slow Reb to 4800. Watch ζ fall to roughly 0.40 with a rebound ratio near 1.85:1. The advisory should go green.

Run ▶ Play over Urban Road both before and after, comparing RMS Accel (g) and the body-movement trace. The over-damped version transmits more, not less.

Now go too far the other way: Slow Comp 600, Slow Reb 1100 — about ζ 0.1. Run it again and watch the body keep oscillating after each input. That’s under-damped, and it’s the failure people expect damping problems to look like.

Settle somewhere near ζ 0.4 and note how much of the “improvement” came from removing damping rather than adding it.

The same bump, three damping ratios. Under-damped rings; over-damped creeps back and skates over the next bump. The useful range is narrower than people expect.

Fix the over-damped preset yourself →

What it costs you

Damping is the one suspension parameter that is nearly free in weight, packaging and money — and it’s the one most often set by guesswork, because the number that matters is never on the label. Shocks are sold in clicks, and a click means nothing without the mass and rate it’s working against.

The real cost of getting it wrong is asymmetric. Under-damped is obvious and everybody notices — the car floats and wallows. Over-damped is invisible from the driver’s seat in the way that matters: the car feels firm and controlled, while the tire loses contact over every rough patch and you lose grip you never knew you had. It’s the more dangerous error precisely because it feels like the safe one.

Rules of thumb

Road car: ζ 0.2–0.3 for ride comfort, accepting some float.
Sports / track-day: ζ 0.3–0.5. The app grades 0.28–0.7 as good.
Race car: ζ 0.5–0.7, chasing body control over comfort.
Never above ζ 0.8 on anything that drives on real roads. Above that you’re not damping, you’re locking.
Rebound:rebound ratio: 1.5–2.5:1 rebound to compression.
Rally-raid and desert: low ζ by road-car standards over the working range — often 0.2–0.3 — because the wheel must be free to move over huge inputs. Control comes from position-sensitive bypass damping and bump stops instead of from a high base coefficient. Damping a half-meter-travel wheel like a road car would make it skip across the desert rather than follow it.

Try this

Compute ζ for your own car. You need corner mass, wheel rate and the damper’s slow-speed coefficient — the last is the hard one, and if you can’t find it, that’s the point of this chapter.
Set the front and rear to the same ζ and run a road. Then deliberately mismatch them by 0.2 and see what the advisor says about it.
Find the ζ where RMS Accel (g) is lowest on Urban Road. Is it where you expected? Is it the same value that feels best when you watch the body trace?

Next: how one shock serves both of the jobs in this chapter — by changing its mind at a specific velocity.

Preset spring and damper values are illustrative starting points. The damping in this preset is deliberately left as shipped so you can see the advisor catch it.