Springs, Part 1

As promised, we’re getting technical now.

This series of posts on springs will focus on vehicle dynamics and tuning issues. We’ll only delve into design and preparation issues (motion ratio, coil bind, material choices, type of spring, etc.) to the extent that they relate to vehicle dynamics and tuning.

So, you ask a race engineer, “What’s your setup on that car?” Usually, one of the very first things you will be told will be the spring rates. There’s no question that there are quite a few other setup choices that have a major influence on handling and grip. But, for nearly every race car, the choice of springs is not only powerful in its own right, but also in the effect it has on a number of other setup choices.

Everyone has their own definition of what springs do. Here’s mine:
1. Allow the wheels to move relative to the chassis
Absorb disturbances from bumps, curbs, etc.
Avoid suspending the car exclusively by the stiff and underdamped tires

2. Allow certain beneficial movement of the chassis relative to the wheels
For vehicle dynamics or aerodynamic reasons
In transient and/or relatively constant situations

3. Conversely, control the movement of the chassis relative to the wheels
Keep response to driver control inputs acceptably quick
Maintain the chassis attitude desired for aerodynamic, geometry, or weight transfer

Here’s a (probably incomplete) list of what we may eventually cover:
-Interactions and relationships with anti-roll bars and shocks.
-Bump rubbers. Either in this, or their own, series. They are, after all, springs.
-Why run stiffer? Why run softer?
-Racing series rules for minimum ride height
-Relationship of spring rates to tire vertical spring rates
-Third spring/damper/bump rubber setups. Either in this, or their own series.
-Preload

To get things started, the first meaty topic in the series:


“Using natural frequency to choose and compare spring rates”


The sprung mass natural frequency of one corner of the car is:

Frequency = (1 / (2 * Pi)) * Square root (Wheel rate / Sprung mass)

See Wikipedia for a brief overview. http://en.wikipedia.org/wiki/Damping. Without fail, read what Bill and Doug Milliken wrote in their book, and Thomas Gillespie in his.

The answer is in cycles per second, abbreviated as Hz (Hertz). Don’t forget to use consistent units, subtract the unsprung weight from the setup pad corner weight, apply the proper constants to convert corner "weight" to corner "mass", and convert the spring rate to wheel rate correctly, using the motion ratio. This idealized formula assumes linear (non-progressive) springs, no friction, and no damping. Lotsa caveats there, but it will do well for the kind of coarse comparisons we have to do.

The reason why sprung mass natural frequency is important is that it lets us compare spring rates between cars. Two cars which are similar in design/race series/performance, may have differing weights and spring motion ratios, but still need a similar natural frequency due to their overriding similarity. OK, to be fair, a heavy car at a given frequency is not the same as a light car at the same frequency. But, it’s a starting point.

Let’s touch on one thing first. Some series have minimum ride height rules for tech inspection. Unless the ride height in the rules is relatively low, cars in these series frequently find themselves on artificially soft springs to allow the car to assume a lower dynamic ride height under the influence of vertical loads from banking and/or aerodynamics, as well as possibly being “pulled” down by rebound damping. That’s for later…

For oval track and road race cars running on pavement, I see four broad categories of cars:

Softer than 2.0 Hz
-Street cars and "showroom stock" racing classes. Autocross, maybe?
-Too floppy for the race track, without big crutches from the bars and shocks

Soft, from 2.0 to 3.0 Hz
-Setup emphasizes mechanical grip
-Little or no vertical load from aerodynamics or banking
-Chassis attitude changes don’t hurt, and may actually help, aerodynamics or vehicle dynamics
-Tires or track surface may have limited grip, or conversely may be just fine

Medium, from 3.0 to 4.5 Hz
-Setup is a compromise of mechanical and aerodynamic grip
-Moderate vertical loads from aerodynamics or banking
-Aero loads may be moderately sensitive to height of underside of car relative to the track
-Suspension geometry may be less than optimal, causing bad behavior with travel
-Good grip from tires and track

Stiff, from 4.5 to 8.0 Hz
-Setup is primarily influenced by aerodynamics
-The car has a high-downforce configuration, or it makes lots of downforce from high speeds
-Aerodynamic loads are highly sensitive to height of the underside of the car relative to the track

Let’s say I’ve been engineering a Daytona Prototype with front and rear motion ratios of 0.90 and I’ve found spring rates that make the car and driver happy. The team then decides to change chassis manufacturers and the new car has front and rear motion ratios of 1.05. Ignoring, for now, the effect this has on the shocks, I’m likely to get a good starting point for the new car by selecting springs that match my old natural frequencies. That’s because the old and new cars are on the same tires, and should have similar downforce amount, power output, total weight, weight distribution, etc. Of course, differences may exist in aerodynamic sensitivity to ride height, suspension geometry, stiffness of the chassis and suspension components, and more.

Nothing is ever simple, though, for my sample Daytona Prototype or for any other car. The front and rear of the car have different tasks to achieve, under different conditions. The need to control the height of an aerodynamically height-sensitive wing or splitter may lead to stiffer front springs. The need for corner exit forward traction may lead to softer rear springs. Certain tracks may have poor grip or a reputation for understeer. Our tire manufacturer may change the rubber compound and/or carcass construction. A change in damping may allow us to run stiffer or softer springs than would previously work.

The list of factors that go into finding the best spring rates is large. No doubt, that’s why it’s likely to be the first thing you hear when you ask, “What’s your setup on that car?”