suspension-design

name	suspension-design
description	Automotive suspension design — double wishbone, MacPherson, multi-link, kinematics (camber, toe, caster), spring/damper sizing, roll stiffness, natural frequency, handling balance.
metadata	{"priority":7,"promptSignals":{"phrases":["suspension design","suspension kinematics","double wishbone","MacPherson suspension","camber toe caster","spring damper sizing","roll stiffness"],"minScore":3}}

Automotive Suspension Design — Complete Skill

Suspension Types

Double Wishbone (SLA)

Geometry: two triangular links (upper + lower control arms) + strut Kinematics: high design freedom → optimize camber, caster, toe curves Camber change: ≈ -0.5° to -1.5° camber gain per 25mm bump travel (depends on wishbone length ratio) Used: sports cars, performance sedans, front and rear

MacPherson Strut

Geometry: single lower control arm + strut (damper acts as upper link) Advantages: compact (space for engine), low cost, simple Kinematics: less camber control; caster fixed; scrub radius affected by strut angle Used: front suspension majority of FWD vehicles

Multi-Link (5-link)

Geometry: multiple links giving independent control of toe, camber, caster in bump Best kinematic control: each DOF tunable independently Kinematic toe curve: typically mild toe-in on bump for rear → stability Used: rear suspension premium vehicles; some front

Solid Axle / De Dion

Beam axle: front (not used modern); rear pickup trucks De Dion: joints at wheels + rigid tube (reduces unsprung mass vs. solid) Lateral location: Panhard rod (simple), Watts linkage (symmetric)

Wheel Kinematics

Camber: angle between wheel plane and vertical Negative camber (wheel leans in at top): increases cornering grip Dynamic camber change target: -0.5° per 25mm bump (double wishbone)

Caster: angle of kingpin axis rearward from vertical (side view) Positive caster: self-centering (steering returns to center); provides camber gain when steering Modern cars: 3–7° caster

Toe: angle of wheel to vehicle centerline Static toe: slight toe-in front (0–2mm per side) → stability; rear toe-in → oversteer reduction Dynamic toe: rear toe-in on bump (from compliance steer or kinematic) → stability

Scrub radius: distance from steering axis to tire center at ground Zero scrub: best for FWD torque steer; negative scrub: steering returns under braking

Spring Rate and Natural Frequency

Ride frequency: f_ride = (1/2π) × √(k_wheel / m_sprung)

k_wheel = effective spring rate at wheel (motion ratio²× spring rate) Motion ratio MR = spring displacement / wheel displacement (typically 0.6–0.9) k_wheel = k_spring × MR²

Target ride frequencies: Passenger car (comfort): 0.9–1.2 Hz (front); 1.0–1.3 Hz (rear) Sports car: 1.5–2.5 Hz Formula car: 3–8 Hz

Required spring rate: k_spring = m_corner × (2π f_ride)² / MR²

m_corner = sprung corner mass (typically 350–500 kg for passenger car corner)

Damper Sizing

Critical damping: c_crit = 2 √(k_wheel × m_corner) Damping ratio: ζ = c / c_crit (target ζ = 0.25–0.35 comfort; 0.5–0.7 sports; 1.0 racing) Damper coefficient: c = ζ × c_crit

Rebound/compression split: Rebound: 60–70% of total (slower return → better isolation) Compression: 30–40% (stiffer → less bottoming)

Roll Stiffness and Handling Balance

Roll angle: φ = (m × a_y × h_CG) / (K_front + K_rear)

K_front, K_rear = roll stiffness distribution [N·m/deg] h_CG = CG height; a_y = lateral acceleration

Lateral load transfer: ΔFz_front = K_front × φ / t_f + (m × a_y × h_RC,f / t_f) ΔFz_rear = K_rear × φ / t_r + (m × a_y × h_RC,r / t_r)

t_f, t_r = track widths; h_RC = roll center height

Handling balance: % front roll stiffness = K_front / (K_front + K_rear) × 100% More front roll stiffness → understeer tendency (rear holds on longer) More rear roll stiffness → oversteer tendency (rear gives up earlier)

Typical distribution: Understeer car: 60–65% front Neutral: 50–55% front Oversteer car: < 50% front

Anti-Roll Bars (Sway Bars)

Added roll stiffness from ARB: K_ARB = (G J_ARB d²) / (2 L_arm) (simplified; includes bar and droplinks) G = shear modulus of bar; J_ARB = π d⁴/32; L_arm = moment arm length

ARB effect: reduces roll angle without changing ride frequency; increases lateral load transfer

Jounce and Rebound Limits

Jounce bump stop: engagement at full compression; prevents damage Rebound limit: prevents over-extension (droop limiter, rebound bumper) Clearance to bump stop: typically 40–60mm additional travel before contact

Wheel travel: Jounce (bump): 60–120 mm (typical passenger car) Rebound (droop): 80–140 mm

Output

Provide: suspension type selection with rationale, camber/caster/toe specifications, spring rate [N/mm], damper coefficient [N·s/mm], ride frequency [Hz], roll stiffness distribution (% front), ΔFz at 1g lateral [N], roll angle at 1g [deg], understeer gradient assessment.