Vehicle DynamicsSuspension Design

Spring & Damper Calculator

Determine wheel rate, coilover spring rate, damping coefficient, static deflection and installation geometry from target ride frequency and suspension motion ratio.

MR = Shock Travel / Wheel TravelLinear 1-DOF Ride ModelStatic Geometry Reference

Engineering Schematic

Coilover Installation Geometry — Front View

DamperSpring
COILOVER / FRONT VIEWVEHICLE CENTERUPPER MOUNTY 280 / Z 420LOWER MOUNTY 480 / Z 160328.0 mmΔZ 260.0 mmΔY 200.0 mm142.4°SHOCK FORCECONTROL ARM

Ride Dynamics

1-DOF
kg

Corner mass

Hz

Ride frequency

-

Shock / Wheel

-

Damping profile

Mount Coordinates

Front View
mm

Lateral pos.

mm

Vertical pos.

mm

Lateral pos.

mm

Vertical pos.

Damper Packaging

mm

Cylinder length

mm

Shaft travel

Calculated Results

Suspension Rates

Wheel Rate

8.3N/mm

8.31 kN/m

Spring Rate

14.8N/mm

MR² = 0.563

Static Wheel Defl.

76.7mm

Under sprung load

Static Shock Defl.

57.5mm

95.8% of stroke

Critical Damping

2614N·s/m

At shock

Target Damping

1699N·s/m

ζ = 0.65

Coilover Geometry & Allocation

Static Length

328.0mm

Install Angle

142.4deg

From vertical

Shock Bump

33.0mm

55% stroke

Shock Rebound

27.0mm

45% stroke

Engineering Check

Review Required

Shock installation angle exceeds 30°. Check packaging and lateral load effects.

Static shock deflection consumes more than 40% of available stroke.

Static shock position is likely too deep in the available stroke.

Engineering Relations

Governing Formula

Kw = (2πfn)² · ms
KwN/m

Wheel Rate

fnHz

Ride Freq

mskg

Mass

Governing Formula

Ks = Kw / MR²
KsN/m

Spring Rate

KwN/m

Wheel Rate

MR-

Ratio

Governing Formula

Cc = 2√(Kw · ms)
CcN·s/m

Crit. Damping

KwN/m

Wheel Rate

mskg

Mass

Governing Formula

C = ζ · Cc
CN·s/m

Target Damping

ζ-

Damping Ratio

CcN·s/m

Crit. Damping

Understanding Vehicle Suspension Rates and Damping

Designing a high-performance suspension system requires balancing ride comfort with handling characteristics. Instead of guessing spring rates, engineers use a targeted Ride Frequency based on the vehicle's purpose—typically ranging from 1.0 Hz for passenger cars to over 2.5 Hz for dedicated race cars.

Motion Ratio and Spring Rate

Because the coilover is rarely mounted directly at the wheel centerline, we must account for the Motion Ratio (MR). The Motion Ratio defines the mechanical advantage the wheel has over the spring. Since the spring rate is related to the wheel rate by the square of the motion ratio ($K_s = K_w / MR^2$), even a small change in suspension geometry dramatically impacts the required spring stiffness.

Critical Damping and Damping Ratio

Springs store energy, but dampers (shock absorbers) dissipate it. Critical Damping ($C_c$) is the exact amount of resistance required to return the suspension to its resting position without oscillating. The Damping Ratio ($\zeta$) determines the system's behavior relative to critical damping. A ratio of 0.65 to 0.70 is typically targeted for a firm, controlled ride without excessive harshness.

Frequently Asked Questions

What is Motion Ratio (MR) in suspension design?

Motion Ratio (MR) is the ratio of shock/spring travel to vertical wheel travel. For example, an MR of 0.75 means the shock compresses 0.75 inches for every 1 inch the wheel moves upward. Because suspension forces act through a lever arm, the required spring rate increases by the square of the inverse of the motion ratio.

Why do I need to calculate the Wheel Rate?

Wheel rate is the effective stiffness of the suspension measured at the tire contact patch. It determines the vehicle's ride frequency and handling characteristics, independent of how the spring is actually mounted. Once you know your desired wheel rate, you can use the motion ratio to find the actual coilover spring rate you need to buy.