Library / Automotive and vehicle dynamics / VEH-52
Automotive and vehicle dynamics
Equivalent vertical damping at the wheel
Damping at the wheel from a linear damper coefficient cd and the motion ratio MR, the damper speed divided by the vertical wheel speed.
- Ref
- VEH-52
- Rev
- v1
- Field
- Automotive and vehicle dynamics
- Result
- cw [N s/m]
The same motion-ratio argument applies to a damper: its speed is MR times the wheel speed and the wheel feels its force divided by MR, so the equivalent wheel damping is cw = cd·MR². It holds for a linear damper; real dampers are nonlinear and different in compression and rebound, so this is the slope at a chosen speed.
Damping at the wheel from a linear damper coefficient cd and the motion ratio MR, the damper speed divided by the vertical wheel speed. It holds for small motion about the operating position; compression and rebound may need separate values.
Calculator
- Wheel force at a wheel speed of 0.1 m/s98 N
- Damper speed at a wheel speed of 0.1 m/s0.07 m/s
- Fraction of the damper coefficient felt at the wheel, MR²0.49
What drives the result
Each variable is moved across its typical range while the others stay at the values above. The longest bar is the key driver.
- The wheel sees 980 N s/m from a 2,000 N s/m damper, so a wheel speed of 0.1 m/s gives 98 N at the wheel.
- Because the ratio is squared, small installation changes move the damping strongly; check the ratio at the design ride height, not only at one extreme.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (N s/m) | Local step | Change in result |
|---|---|---|---|---|---|---|
| cd Damper coefficient | 100 to 20,000 N s/m | 49 | 9,800 | 9,751 | +10% | +10 % |
| MR Motion ratio (damper speed per wheel speed) | 0.2 to 1.5 | 80 | 4,500 | 4,420 | +10% | +21 % |
Sweep of Motion ratio (damper speed per wheel speed)
| Motion ratio (damper speed per wheel speed) | Wheel damping (N s/m) |
|---|---|
| 0.2 | 80 |
| 0.3625 | 262.8 |
| 0.525 | 551.3 |
| 0.6875 | 945.3 |
| 0.85 | 1,445 |
| 1.012 | 2,050 |
| 1.175 | 2,761 |
| 1.337 | 3,578 |
| 1.5 | 4,500 |
Sweep one variable
Variables and how each one contributes
Wheel damping
What the equation gives you. Everything else feeds it.
Damper coefficient
The damper coefficient, in N s/m. Raises the wheel damping in direct proportion. Raising it by 10 % (to 2,200) moves the result by +10 %, from 980 to 1,078 N s/m.
Motion ratio (damper speed per wheel speed)
The motion ratio, the damper speed per unit wheel speed. Raises the wheel damping with its square. Raising it by 10 % (to 0.77) moves the result by +21 %, from 980 to 1,186 N s/m.
Worked example with the values above
- Square the ratio: MR² = 0.7² = 0.49.
- cw = cd × MR² = 2,000 × 0.49.
- cw = 980 N s/m.
Assumptions and limits
- A linear suspension with small motion about the design ride height and a constant motion ratio.
- Rigid links and negligible bush compliance, and no preload or geometric stiffness unless stated.
Common mistakes
- Forgetting to square the motion ratio.
- Using the inverse motion ratio, wheel travel per spring travel, in place of spring travel per wheel travel.
- Adding spring and anti-roll-bar stiffness at different points without converting them to the same reference.
Statistics and uncertainty
Spring rates and installation ratios are usually known to about 3 % to 5 %, but the motion ratio enters squared, so a 3 % error in it becomes about 6 % in wheel rate.
Where it is used
- Converting spring and damper settings to wheel rate and wheel damping.
- Setting roll stiffness and front-to-rear roll balance.
Maths you need
- Motion ratio: spring travel per unit wheel travel
- Series springs: 1/k = 1/k₁ + 1/k₂
- Roll stiffness: roll moment per radian of roll