Sprung Back : Ride Rates in a Vehicle

Ride rate refers to the rate of change of tire normal force with vertical body movement and roll rate refers to the rate of change of tire normal force with body roll about its roll axis. The ride and roll rates of the car affect the wheel loading wrt the body position change. And the wheel load or tire normal force determines the available tire lateral/longitudinal forces which directly impacts the vehicle performance.

Individual suspension components like springs and antiroll bar affect the vehicle ride and roll. The ride performance of the car is many a times in conflict with the roll performance and hence choosing the correct springs and anti roll bar is often a balancing act. The main purpose of the suspension is to keep the tires on the ground while also isolating vibrations. This can be achieved by soft suspension. Too stiff suspension can make the tire airborne in trough cases or unsettle it while going over bump. However, some stiffness is required to limit body roll and improved handling and also to protect vehicle with low ground clearance. Race cars also use it to maintain their ride height.

Hence based on the requirements, arriving at the correct spring and anti-roll bar stiffness is a difficult iterative task.


Every suspension use some sort of spring to get the vertical stiffness in order to keep the wheels on the ground. Broadly speaking a car can be viewed as a lumped vehicle body mass (sprung mass) being balanced on the two left right suspension vertical stiffnesses which connects them to the tires (modeled as lumped unsprung masses) while also having their own tire vertical stiffnesses. Note: the figure also shows the dampers which play a key role but are not the part of present discussion.

Half- Car roll dynamics model. Image courtesy: https://www.mdpi.com/2076-3417/7/6/570/htm

Spring rate: Most of the suspensions use coil spring or leaf spring. the spring rate is the force/ displacement for spring alone.

Motion ratio: However most springs are not mounted vertically in a suspension. They are mounted at an angle in a way that the wheel center movement and the spring compression/elongation are not the same. Motion ratio can be defined as Spring deflection over wheel center displacement. It is generally not static and varies as the suspension moves. Hence the single geometric values from the CAD might not be good approximation for every suspension. For the leaf spring suspension, it has a value of 1. For independent suspensions, it varies around 0.6–0.8

Motion Ratio Image Courtesy: https://deltavee.net/2013/10/wheel-rate-motion-ratio-and-frequency/

Higher motion ratio allows lower spring rates for the same wheel rates which can lead to lighter spring and eventually cost/weight saving.

Wheel rate: force/displacement at wheel center.

This would include the spring rate, motion ratio of spring, parasitic rates of suspension bushings, tire rate etc

Tire rate: force/ displacement of tire at operating load.

All tire manufacturers list a static load radius in their catalog for a specific tire. They will also list that tire’s unloaded diameter. There will also be a chart showing the tire’s maximum load rating. From these numbers the static deflection can easily be calculated and the static rate is maximum_load/deflection. Static loaded radius is the radius at maximum load rating for that tire.

Ride rate: force/displacement at contact patch.

This is equivalent to wheel center rate added to tire rate in series. If the tire is infinitly stiff, this would be equal to wheel center rate.

Parasitic rate : Rate due to the compliances in suspension. The bushings in the suspension can also provide certain vertical stiffness and needs to be accounted for if you want to arrive at the exact spring rate required.

Wheel Travels : The wheel center displacement at a certain load. When the wheel goes in the bump, it is called jounce travel or when it goes in trough its called rebound travel. The maximum allowed jounce and rebound travels are also design specifications that are considered while designing the suspension.

Ride Height: It is a measure of ground clearance and where the vehicle sits under its own weight in the wheel rate curve.

Ride Frequency: The undamped frequency at which the sprung mass will resonate or bounce is called the ride frequency. This is the same as the sprung natural frequency. Since the front and rear will resonate or bounce at different frequencies, we typically reference a front and rear ride frequency. The reason the front and rear have different ride frequencies is to reduce the pitch of the vehicle over bumps. Also the ratio of front/rear is called frequency ratio. The rear ride frequency is typically higher than the front, so that after encountering a bump, the rear will “catch up” with the front, and the front and rear will move in phase.


The process of finding a suitable spring stiffness comprises of following steps:

  1. Ride frequencies and ratio can be used to determine the ride rates with the given sprung mass.
  2. Ride rate from step 1 and the tire rate can give you the wheel rate.
  3. Spring rates then can be determined from the wheel rates with a known motion ratio and parasitic rates.
Process to find out the spring Rate

It is usually an iterative process where different parameters are varied to arrive at a desired solution. Lower frequencies lead to softer suspension while higher frequencies produce hard suspension. Motion ratio can be used to change spring rate for same wheel rate but is usually constrained by packaging and geometry. Tire rates and bushing parasitics can also be changed by adopting different tires/bushes but they are usually bounded by other design criteria.

Preloads in the spring

Compressing or adding the preload in the spring would mean that the spring would not compress further until that extra force due to preload is overcome. In the wheel rate graph, this just offsets the graph upwards (assuming you have force on y and displacement on x) without changing the wheel/ spring rate.

Sample Wheel Rate Curve. Image Courtesy: https://www.1addicts.com/forums/showthread.php?t=1492837

Preloads can change the ride height and jounce/rebound wheel travel. Once the total wheel travel required is determined, ride height of the vehicle/ spring preloads can be adjusted to achieve the desired jounce/rebound travel.

Frequency Ratio

There are recommended value for the ride frequencies and their separation in terms of front and rear. It is common to run a spring frequency higher in the rear than the front. The idea is to have the oscillation of the rear suspension catch up with the front as vehicle bounce is less annoying to human perception than the vehicle pitch.

Image Courtesy: http://www.kaztechnologies.com/wp-content/uploads/2014/03/A-Guide-To-Your-Dampers-Chapter-from-FSAE-Book-by-Jim-Kasprzak.pdf

Since the delay between when the front suspension hits a bump and the rear suspension hits that bump varies according to vehicle speed, the spring frequency increase in the rear also varies with speed.

I guess thats all for now

Written while listening to The Lumineers

Vehicle Dynamics | Self Driving Cars | Comedy https://www.linkedin.com/in/archit-rastogi-2604/

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