A MacPherson suspension uses a structural telescopic strut, coil spring and lower arm to support and locate the wheel. Explore that arrangement and compare spring rate with wheel rate using an entered local motion ratio.
Defined Motion-Ratio Wheel-Rate Calculator
Enter spring rate, local spring/wheel displacement ratio and a small wheel displacement. Results use a constant local ratio and linear spring; they do not predict MacPherson geometry, camber, ride frequency, handling or safe component selection.
Equation Used
- The entered motion ratio is defined as incremental spring displacement divided by incremental wheel displacement.
- The spring is linear over the entered displacement and the ratio is treated as constant locally.
- Tire, bushings, damper force, bump stops, anti-roll bar, unsprung mass, preload and full suspension geometry are excluded.
The motion ratio here means spring displacement divided by wheel displacement. With a constant local ratio, its square relates the linear spring rate to the spring contribution at the wheel.
Structural strut and lower-arm topology
Patent descriptions identify an upright strut with an outer tube carrying the road-wheel member, a shock absorber and piston rod connected at the upper body mount, and a coil spring retained around the strut. A lower arm and joint locate the lower wheel member. On a steered application the upper mount permits rotation.
The animation shows those relationships schematically. Its vertical motion is illustrative and does not solve a particular suspension's ball-joint, tie-rod, steering-axis or camber geometry.
Defined local arithmetic only
Use the calculator only when a compatible local spring/wheel displacement ratio is already known or measured. Real spring and damper selection requires the exact vehicle masses, suspension geometry over travel, tire, bushings, anti-roll bar, bump stops, preload, damping and manufacturer limits.
Constant local displacement ratio
Under lossless virtual work, spring force is Ksxs and wheel force is that force multiplied by m. This is a local linearization, not a universal MacPherson ratio.
Arithmetic example
For Ks=60 N/mm, m=0.90 and xw=25 mm, the defined wheel rate is 48.60 N/mm, spring displacement is 22.50 mm, incremental wheel force is 1,215 N and spring energy is 15.19 J.
Model boundary
The calculator does not determine camber, steering axis, scrub radius, roll center, ride frequency or handling.
MacPherson wheel-rate questions
Is motion ratio always less than one?
No. It depends on the definition and local geometry; this page explicitly defines m as spring displacement divided by wheel displacement.
Does the result include the tire or anti-roll bar?
No. It is the isolated linear spring contribution under the stated ratio.
Can this calculate camber change?
No. Camber requires the actual top mount, lower-arm, ball-joint, knuckle and compliance geometry.
Primary references
- US Patent 2,660,449, Wheel suspension for motor vehicles: E. S. MacPherson's strut suspension patent and geometry.
- US Patent 4,482,135, MacPherson strut front suspension: identifies the upright strut, shock absorber, body mount, coil spring and spring seats.
- US Patent 4,828,237, Reduced-length MacPherson strut: states that the strut combines spring and shock-absorber functions and serves as a structural suspension link.
- US 2021/0129614 A1, Vehicle suspension system: describes a single control arm, telescopic strut, wheel carrier and top-mount/lower-joint steering axis.
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