PhysicsMechanics
Velocity Calculator
The Velocity calculator can be used to calculate the particle's velocity by inputting the required values for the formulas
Spring rate and wheel rate aren't the same number, and mixing them up is one of the easier ways to get a suspension setup wrong. The spring rate is what's stamped on the spring. The wheel rate is what the tire actually feels once the suspension linkage has had its way with that force. This calculator handles the conversion by factoring in the motion ratio of your suspension geometry.
Wheel rate is the spring rate as the tire experiences it. The reason it differs from the raw spring rate is that almost every suspension puts a linkage - A-arms, control arms, a strut - between the wheel and the spring, and that linkage creates leverage. The motion ratio measures the leverage. If yours is 0.6, the spring compresses 60mm for every 100mm the wheel moves. Intuitively you might guess the spring feels 60% as stiff at the wheel. It actually feels 36% as stiff, because the ratio gets squared (). The wheel sees less travel AND less force, so the motion ratio shows up twice in the math.
Enter any two of the three values and the third fills in. Spring rate comes off the spring itself or from the manufacturer's spec sheet. Motion ratio either lives in the suspension designer's notes or you measure it yourself: cycle the suspension through a known amount of wheel travel and check how far the spring moves over the same arc. Units switch between metric (N/m, N/mm) and imperial (lbf/in), so you don't need to convert by hand.
The formula:
Worked example: you've installed coilovers rated at 50 N/mm (50,000 N/m) on a track car with a motion ratio of 0.6. Plug it in:
The wheel rate lands at 18,000 N/m, or 18 N/mm. The tire ends up feeling a spring noticeably softer than what's bolted to the car. That's part of why race cars run such absurd-sounding spring rates on paper - the linkage eats a chunk of it. The squared term also makes small geometry changes loud. Bumping the motion ratio from 0.6 to 0.7 with the same spring would push the wheel rate from 18,000 to 24,500 N/m. About a 17% change in MR, but a 36% change at the wheel.
Race teams care about wheel rate because ride frequency and platform stiffness fall directly out of it. On the street side, anyone swapping springs needs the calculation to keep front-to-rear balance reasonable - a stiffer-looking spring with a lower motion ratio can land softer at the wheel than what you replaced. Suspension designers run this math during packaging: a lower motion ratio (say 0.5) lets you tuck the spring further inboard for wider tires, but you'll need a proportionally stiffer spring to hit the same wheel rate. It also comes up whenever you're swapping spring types or designing custom geometry, since spring rate alone doesn't tell you what the car will feel like.
Motion ratios usually land between 0.5 and 0.9 depending on the suspension type. MacPherson struts run on the high end (roughly 0.8 to 0.9) because the spring sits almost in line with the strut. Double wishbones come in lower (0.5 to 0.7) since the geometry gives the designer more freedom to tuck the spring inboard. When you're swapping springs, do the wheel rate math first; just comparing spring rates can mislead you. As a rough target, a comfortable street car wants a ride frequency of about 1.0 to 1.5 Hz. Track cars sit in the 2.0 to 3.0 Hz range.
Because the motion ratio shows up twice in the physics. The spring sees less travel (one factor of MR) and applies less force at the wheel (another factor of MR). Multiply them together and the ratio is squared.
Only when the motion ratio is above 1.0, which is rare in production cars. Most designs sit below 1.0, so the wheel rate ends up softer than the spring rate.
Pull the spring, jack the suspension through a known amount of wheel travel, and measure how much the spring perch moves over the same arc. Spring movement divided by wheel movement is your ratio.
Usually not. Most suspensions are either progressive or regressive, so the ratio shifts as the wheel moves through its travel. The number you plug in here is the average or the static ride-height value.
Not by default. The right front-to-rear balance depends on the weight distribution, the car, and the handling you're chasing. Plenty of performance cars run stiffer fronts to dial out understeer.
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Wheel Rate Calculator
Work out the wheel rate of a suspension from spring rate and motion ratio. Useful for setup work, tuning, and design - converts between metric and imperial automatically.
https://hexacalculator.com/calculators/physics/mechanics/wheel-rate-calculator
Physics
Mechanics