§ How it works

Take one corner of the car and it is a mass sitting on a spring. Disturb it and it bounces at its natural frequency. That one number says more about how a car rides and responds than the spring rate alone, because it accounts for the weight the spring is carrying.

1 · Wheel rate

Springs are rarely mounted directly over the wheel. The lever effect of the suspension arm is the motion ratio $MR$ , and it counts twice: once for force, once for travel.

k_w = k_s \times MR^{2}

2 · Ride frequency

f_n = \frac{1}{2\pi} \sqrt{\frac{k_w}{m_s}}

with $k_w$ in N/m and sprung mass $m_s$ in kg. Comfortable road cars sit around 1.0 to 1.5 Hz, sports cars 1.5 to 2.0 Hz, and downforce cars go well beyond 3 Hz.

3 · Frequency response

The chart shows transmissibility: how much of the road's vertical motion reaches the body at each frequency. For a frequency ratio $r = f / f_n$ and damping ratio $\zeta$ :

T(r) = \sqrt{ \frac{1 + (2 \zeta r)^{2}}{(1 - r^{2})^{2} + (2 \zeta r)^{2}} }

Well below $f_n$ , $T \approx 1$ : the body simply follows long undulations.
At $f_n$ the system resonates. Damping is what limits the peak.
Every curve crosses $T = 1$ at $r = \sqrt{2}$ . Above that the suspension isolates, falling away at up to 12 dB per octave.
More damping lowers the resonant peak but passes more high-frequency harshness. That trade-off is the whole art of damper tuning.

4 · Damping

c_{\text{crit}} = 2 \sqrt{k_w\, m_s} \qquad\qquad c = \zeta\, c_{\text{crit}}

§ How it works

1 · Wheel rate

Springs are rarely mounted directly over the wheel. The lever effect of the suspension arm is the motion ratio $MR$ , and it counts twice: once for force, once for travel.

k_w = k_s \times MR^{2}

2 · Ride frequency

f_n = \frac{1}{2\pi} \sqrt{\frac{k_w}{m_s}}

with $k_w$ in N/m and sprung mass $m_s$ in kg. Comfortable road cars sit around 1.0 to 1.5 Hz, sports cars 1.5 to 2.0 Hz, and downforce cars go well beyond 3 Hz.

3 · Frequency response

The chart shows transmissibility: how much of the road's vertical motion reaches the body at each frequency. For a frequency ratio $r = f / f_n$ and damping ratio $\zeta$ :

T(r) = \sqrt{ \frac{1 + (2 \zeta r)^{2}}{(1 - r^{2})^{2} + (2 \zeta r)^{2}} }

Well below $f_n$ , $T \approx 1$ : the body simply follows long undulations.
At $f_n$ the system resonates. Damping is what limits the peak.
Every curve crosses $T = 1$ at $r = \sqrt{2}$ . Above that the suspension isolates, falling away at up to 12 dB per octave.
More damping lowers the resonant peak but passes more high-frequency harshness. That trade-off is the whole art of damper tuning.

4 · Damping

c_{\text{crit}} = 2 \sqrt{k_w\, m_s} \qquad\qquad c = \zeta\, c_{\text{crit}}

Spring Rate & Ride Frequency

Inputsdrag · tap · type

Fig. 19Quarter-car model and frequency response

§ How it works

1 · Wheel rate

2 · Ride frequency

3 · Frequency response

4 · Damping

Spring Rate & Ride Frequency

Inputsdrag · tap · type

Fig. 19Quarter-car model and frequency response

§ How it works

1 · Wheel rate

2 · Ride frequency

3 · Frequency response

4 · Damping