Suspension

Suspension keeps tyres on the road and occupants comfortable. Learn springs, dampers and the quarter-car model, ride frequency, wheel hop, damping ratio, motion ratio, suspension types (MacPherson, double wishbone, multilink), anti-roll bars and active systems.

Roads are never perfectly smooth. The suspension isolates the body from bumps (comfort) while keeping each tyre firmly pressed on the road (grip and control). These goals conflict — suspension tuning is the art of balancing them.

A simple quarter-car model with a spring, a damper and two masses explains most of the behaviour.

An analogy

A good suspension is like a skilled skier's knees: absorbing bumps so the upper body stays level, while keeping the skis in contact with the snow.

Springs and dampers

Springs (coil, leaf, torsion bar, air) carry the car's weight and store bump energy. Dampers (shock absorbers) turn that energy into heat so the body doesn't keep bouncing. Without damping a car would oscillate after every bump.

Ride frequency and damping

Comfort cars: ride frequencies ≈ 1.0–1.5 Hz; sports cars 1.5–2.5 Hz; race cars with downforce 3–5+ Hz. Damping ratio ≈ 0.2–0.4 balances comfort and control. Wheel hop (unsprung mass bouncing on the tyre) is at 10–15 Hz — low unsprung mass improves grip on rough roads.

Suspension types

Solid axles (trucks, off-road — robust), MacPherson strut (compact, cheap — most front axles), double wishbone (precise camber control — performance cars), multilink (tunable, comfortable — rear axles), twist beam (low-cost rear). Anti-roll bars add roll stiffness without affecting ride over single-wheel bumps less.

Kinematics, compliance and active systems

Suspension geometry sets camber gain, roll centre height, anti-dive/anti-squat and bump steer; bushings add compliance for comfort but alter steering response. Adaptive dampers (magnetorheological, valved), air suspension with levelling, and fully active systems with road preview cameras further break the comfort–handling compromise.

Formulas

• Ride frequency: f = (1/2π) √(k/m_s)
• Wheel-hop frequency: f_hop ≈ (1/2π) √((k + k_t)/m_u)
• Damping: c = 2 ζ √(k m_s)
• Spring rate from wheel rate: k_spring = k_wheel / MR²
• Static deflection: δ = m_s g / k (f ≈ 0.5/√δ[m])

Worked example: Ride frequency and wheel hop

Given: Sprung mass 400 kg/corner, wheel rate 25 kN/m; Unsprung 40 kg, tyre 200 kN/m

Find: Ride and hop frequencies.

• f = (1/2π)√(25 000/400) = 1.26 Hz
• f_hop = (1/2π)√(225 000/40) = 11.9 Hz

Answer: 1.26 Hz ride, 11.9 Hz hop

Worked example: Damper and spring

Given: ζ = 0.3; Motion ratio 0.7

Find: Damping coefficient (at wheel) and actual spring rate.

• c = 2 × 0.3 × √(25 000 × 400) = 1897 N·s/m
• k_spring = 25 000/0.7² = 51 kN/m

Answer: ≈ 1.9 kN·s/m; spring ≈ 51 kN/m

Common mistakes

• Wrong: Specifying spring rate as wheel rate. — Right: Convert with motion ratio: k_spring = k_wheel/MR².
• Wrong: Adding heavy wheels and brakes without retuning. — Right: Unsprung mass lowers hop frequency and grip on rough roads.

Applications

• Passenger cars: MacPherson front + multilink rear; adaptive dampers on premium models.
• Trucks & buses: Air suspension with ride-height control and load levelling.
• Motorsport: High-rate springs, 3rd springs/heave dampers for aero platforms.

Key takeaways

• f = (1/2π)√(k/m); target 1–2.5 Hz for cars.
• c = 2ζ√(km), ζ ≈ 0.2–0.4.
• k_spring = k_wheel/MR².
• Balance comfort, grip and control; minimise unsprung mass.

Going further

• Skyhook damping: Semi-active control that mimics a damper attached to an inertial reference, greatly improving comfort.
• Roll-centre & anti-geometry: Link geometry sets how lateral and longitudinal loads transfer between springs and links.
• Road preview: Camera-scanned roads let active suspensions prepare for bumps before the wheels reach them.