Rates, Math, & Geometry
Take a steel rod, wrap it into a spiral shape, throw some engineered heat-treating in the mix, and you've got yourself a coil spring. That spring can be used as part of your suspension to support the weight of the vehicle. How you use these simple devices and choose their size can have a huge impact on the performance of your suspension.
When an OEM manufacturer designs a suspension, they often choose a spring rate that focuses heavily on ride comfort, while offering proper stability control to keep the vehicle behavior safe under a variety of terrain conditions.
We often have other needs to satisfy, be that wanting to tackle sandy whoops at high speed or maintaining traction control on a nasty dirt obstacle. Choosing spring rates on a vehicle can be somewhat tricky, and that's why proper suspension setup is no trivial task if you want high levels of off-road performance.
We're not going to talk about how to choose your initial vehicle coil spring rates but more about the effects of the various spring rate choices. We'll explore some of the physics involved with how effective spring rates vary based on suspension design and coil or coilover placement.
First, it's helpful to briefly understand what determines the spring rate of a coil spring, expressed in pounds per inch (lb/in) of spring travel. Rate depends on three main physical dimensions: coil wire diameter, coil spring mean diameter, and number of active coils. The spring rate increases as wire diameter increases, but the coil rate decreases as the mean diameter increases. The spring rate decreases as the number of active coils increases, and fewer active coils yield a stiffer spring rate.
For example, we can calculate the spring rate for a coil spring with a coil diameter of 0.600 inches, a mean diameter of 4.5 inches, and 8 active coils. Using the equation below gives us a spring rate of about 250 lb/in. This means that 250 pounds of force is needed to compress the coil one inch in height.
When one or more stacked coils is used, such as in a coilover shock, it's possible to have more than one spring rate as the shock moves through its range of travel. For example, a dual-rate coilover is one that has two springs stacked one atop the other. Both springs compress during the initial portion of the compressive shock travel. The effective spring rate is a combination of the two springs and is less than the rated value of either coil, based on this formula:
The lighter rated coil will compress more as the suspension compresses, and a coilover has an adjustable stop ring that can be set to stop the compression movement of the upper (lighter rate) spring. Once the upper coil is stopped, the spring rate of the shock is simply the spring rate of the lower (higher rated) coil. When using a 200-lb/in upper coil and a 300-lb/in lower coil, the initial spring rate would be 120 lb/in. Once the upper coil is stopped, the final spring rate would jump to 300 lb/in for the remaining distance of shock travel.
Choosing Spring Rates
When dealing with an engineered lift kit, coil springs are usually provided by the manufacturer and have been chosen to suit the intended use of the kit. However, some suppliers may offer several coil spring rates to further tweak the setup for various off-road applications. A rockcrawler may want a fairly soft rate for slow-speed articulation, whereas a high-speed rig may lean toward a stiffer rate for better resistance to bottoming in big whoops or landing from jumps.
Rates can also be dependent on shock length, target ride height, comfort, and roll resistance. If relatively short shocks are used, spring rates may need to be stiffer to better utilize the short shock travel. Ride height comes into play when setting the coil rates and where a coilover sits in its range of travel at rest. Softer rates may offer more comfort but increase body roll beyond what is desired.
It's possible to have a coilover shock whose travel closely matches the travel distance of the axle or wheel. Or, a shock may travel far less than the distance the wheel travels. A perfect example of this is a shock mounted on an independent suspension. The shock is mounted inboard on the lower control arm, while the wheel is placed further out on this lever arm. The vertical wheel travel will exceed the travel distance of the shock. Additionally, in a scenario like this, the coil spring rate must be increased over the rate of a system where this lever action is not present, such as on a live front axle.
Another physical factor to consider when talking spring rates (and shock travel) is the angle of the coils or shocks with respect to the direction of wheel travel. When wheel travel is vertical but a coilover is positioned at an angle from vertical, its effective coil rate is reduced. The effective (reduced) rate can be calculated as the spring coil rate multiplied by the cosine of the angle the shock deviates from vertical.
An additional property of vehicle design is that of suspension frequency. Imagine having coil springs at all four corners and no shock action or damping in place. If you were to rock the vehicle and observe the resulting spring oscillation, you would observe the suspension frequency. Soft spring rates typically result in a slow frequency, while stiffer springs offer a higher, or more rapid, frequency. Coil rates can be chosen to affect the suspension frequency based on the speed and terrain you want to tackle. For high-speed rigs, it's also common to choose different suspension frequencies front to rear to help dampen the tendency of the vehicle to buck in rough terrain.
You can imagine a soft low-frequency spring rate might work fine for slow crawling but would react too slowly to effectively track rapidly changing terrain at high speed. A stiffer higher-frequency spring may tackle the fast whoops under control but be too stiff to offer anything but a harsh ride in the rocks.
Selecting Coil Spring Rates
The selection of spring rates, even preliminary spring rates, can be tricky. Rates can be chosen with an eye toward achieving a certain ride height or, more importantly, with an emphasis placed on a desired suspension frequency. We need to choose springs that physically fit in our allotted locations, have sufficient length for our desired travel, get us to a desired ride height at static compression, and offer the proper stiffness for the intended use.
Some spring-rate calculators exist online and from coilover manufacturers. To calculate starting coil rates, you typically need to specify sprung vehicle weight, suspension ride height or frequency, and shock angle geometry. This is where a knowledgeable shock or coil spring supplier can help you get started with initial coil rates.