Tuesday, June 23, 2009

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.

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?”


  1. Hi Buddy, congrats on the great blog, i really enjoy reading it. Just one thing, in this last post about frequency the formula you gave is not working for me. I'm using 150lbs/inch for WR and 135lbs for corner sprung mass and I'm getting 0,16hz. Any math's trick I'm missing here?

  2. Thanks for the kind words, Francisco.

    The formula I posted works for both Metric and Imperial units, but it is critical to get your units correct. You used corner sprung "weight" in pounds of force, not corner sprung mass in slugs. Divide that 135 pounds by 32.16666 * 12 and you'll get the correct answer of 3.296 Hz. Consult your references to see why those are the constants needed.

  3. Thank you very much. I'm in the metric side of Europe so the imperial system still confuses me a bit, though i'm using it to make things simpler as our springs are calibrated in lbs/inch on our Fsae car (found your blog through fsae forums!). My references so far are pirate4x4dotcom's "Coil Over Bible" a great article for the non engineer suspension enthusiastic. This year i just developed the pushrod system, but next I'll design the complete suspension, so Milliken's bible is what I'll be studying during summer.

  4. first of all i really appriciate the knowledge you are putting up here on your blog.
    I have studied vehicle dynamics engineering but gone into finite element analysis as work. anyway recently i picked up a new hobby with radio controlled race cars shaped as touring cars. so i got out all the books and did some calculations on them to get some base figures. this included the natural frequency. my question is i came out at around 10Hz and can't stop to think that this is very much higher those that are indicated for real cars.
    my calculation followed yours and thus does not include the tires yet. the tires will probably have a much lower spring rate as they are not pressurised and and foam filled. would this be the reason for the high frequency?

  5. Tom, the tire rate isn't part of the sprung mass natural frequency calculation discussed in this blog post. So, that's not the reason for your high frequency. I haven't worked with any RC cars, so I don't know what frequency ranges work well for them.

  6. Hi,

    great article and blog.

    What frequency you would choose for an Formula SAE car?

    Maybe different setups for the several competitions(Acceleration, SkidPad, Autocross?)

    What should be the different between front and rear?

  7. I'm not going to answer that question directly, not because I'm a turd (which I may be), but because:
    1-I don't have the desire to study up on what an FSAE car needs. Have my own problems to solve, and plenty of them.
    2-You should read the post again and think about what your car needs. How good is the grip on the surface it will run on? Do the tires need a stiff spring to work them or a soft spring for grip? Who will be driving and what is their preference for support and transient response? Etc. etc. etc.

    You are already thinking creatively, different springs for the different competitions sounds intriguing.

  8. Hello Buddy,first of all thanks for sharing your knowledge with the community.
    I can see other colleagues from FSAE have asked you some questions,about springs.My question is (since we are now designing the car) how can I compare between different ride frequencies/springs and choose the (supposed) right one?We are in the design stage so I can't really ask my driver how he feels abour the car...but I still have to choose/buy some springs.

    Best regards,
    Thanks in advance

  9. Frederico,

    I would expect that your FSAE car would rely heavily on mechanical grip. As such, it shouldn't need a spring that porduces a high frequency. But, I don't have experience with the cars, tires, event venues, etc. I could be wrong...

    It's very difficult to identify the exact spring from calculations alone. For instance, you may choose a setup philosophy that embraces soft springs and stiff AR bars. If you test and find that either the car or driver doesn't work well within that philosophy, then changes are required. Maybe you should initially buy springs over a relatively broad range, test some, then fill in your selection in the range where the car and driver seem to work.

  10. Ok,thanks for your answer Mr. Buddy.
    Best regards,


  11. Buddy Im trying to calculate the frequency of a car with 900 pounds on the corner of unsprung weight and a WR of 186 lb/inch

    900 pounds = unsprung mass of 335.8
    (1/ 2*3.14) * SQRT(186/335.8)

    (1/6.28) * SQRT ( .5539)

    0.159 * 0.744

    .118 Hz

    Where am I messing this simple equation up?

    Any guidance is appreciated

  12. Paul,it's (1/2*pi)*sqrt(k/m). First, "m" is "sprung mass", which is corner weight minus unsprung weight. Then, we have to convert sprung "weight" in pounds force to "mass", then convert units to inches to match the spring rate. Do that by dividing the sprung weight by (32.167*12), which is the acceleration of gravity in in/sec^2. In your example, if the "sprung weight" (not corner weight) is 900 Lb, NatFreq would be 1.42 Hz.

  13. I've written a number of papers on automotive vertical dynamic behavior and related subjects and was pleased to find that you reccomend as sources two of my favorite references: Milliken and Gillespie. May I also reccomend books by Colin Campbell and Donald Bastow...

  14. I am trying to use Motec i2 Pro, does this machine is able to capture the road surface condition such roughness and crack. Because I heard that there could be a method to produce such these data by formula and put in Math Function.

    1. Yusuf, if you have suspension travel pots on the car, or if you have laser or ultrasonic ride height sensors, these will show the "effect on the car" of bumps and curbs. Likewise, you'll see car motion reflected in a Vertical G accelerometer.

    2. quick questions, in Quarter car model it is important to know thr stiffness and coefficient fo the suspension and the tyre. How to calculate suspension stiffness and damper coefficient, similarly for the tyre?.thanks

  15. How car with infinite natural frequency/infinite spring rate will feel on 100% smooth surface (No curbs/No bumps)?
    Will it be faster on corners due to higher roll stiffness?

  16. Well, that's interesting. Roll stiffness distribution would be determined by tire spring rates and chassis torsional stiffness. Aero balance would no long shift with pitch, there being no pitch. Roll center effects would still be valid. Static cambers would need adjusting. I'd expect very sharp turn-in, unless the loss of aero balance shift to the front on brake and decel hurt too much. Hard to say what mid-turn and exit balance you'd have, it would depend on how the roll stiffness sorts out.

  17. Hi Buddy,
    I got asked to be race engineer, and start my career from there.
    What book do you suggest me to read?
    thanks in advance

  18. Daniele, check out the blog post entitled "Recommended Reading". To be honest, that list won't include some recent info, but it's all classic stuff that generally still applies.

  19. thnx fr ur help...can u tell me how to calculate length of double wishbone arms?

  20. A simple method is this. Draw a line between the two inner pickup points. The effective length of the wishbone is the length of a line drawn perpendicular to the line between the pickups and extending to the pivot point at the upright. The kinematics of wishbones where the pivot axis isn't parallel to the car centerline aren't quite that simple, but it will do for many race cars.

  21. Hello mr. Buddy,

    What I am curious to find out is weather those suggested natural undamped frequencies have come more from the knowledge obtained by simulations or from track testing experience (that sadly most of the Students like myself don't possess). If I were to think about it, I would say that it comes mostly from years of experience, rather than endless simulations, but I would be very enlightening if someone with vast experience in the field could tell us about that.

    Thank you in advance,

    1. Hi Mario,
      Those natural frequencies are what are commonly used, in my experience. Not necessarily what I have personally used, just what I've found that teams use. There are plenty of exceptions, found when the needs of a particular car are not typical.

    2. One further comment, Marios. Simulation is quite a useful tool, but depends very much on having a good tire model. Many simulation users in professional racing are using their sims to explore setups and development on cars that they already race and have logged data to compare to the sim. I've done sim work, but never to find a setup from scratch for a new car. That would depend heavily on the tire supplier for data, rather than inferring tire performance from logged data.

  22. Hello mr. Buddy,

    Thank you for the reply and happy new year. Sharing any kind of practical experience is very appreciated.
    I understand what you explained about the required supply of tire data. Do simulation users rely on the Pajesca model (if of course the coefficients are available)?
    The purpose of the simulation is to be done after the conseptual design, if I understand correctly how design works in general. In order to find a new setup, are the steady - state calculations adequate for choosing roll stiffness distribuition, Anti Roll Bar stiffness etc, anti-features etc? The reason I am asking is because I know that steady state calculations are linearized and do not contain solid information about the dynamic response of the racecar, but they seem to be widely used due to their simplicity.

    Thank you in advance,

  23. I've had good results using steady state calcs to pick bar rates after springs have been chosen. Agreed, the method doesn't take a lot into account, but I try to fudge for that in the choices I make. It helps to work out the entire lateral load transfer, not just the suspension roll stiffness.

  24. Buddy, great article. We're trying to size springs for our 1996 dodge neon that we're running as an endurance racer. Quick question for you.... We obviously have Mcpherson struts. Do you ignore the fact that the struts are at an angle to the ground and the spring rate would be impacted by the angle somewhat??? thanks for a great article.

    1. Dave, I've only checked motion ratio on a handful of cars with struts, but I've found them in the .95 to .97 motion ratio range. It's not 1:1 because there is a small bit of camber gain, which gives some wheel travel due to the scrub radius. That travel doesn't move the spring, hence the MR slightly less than 1.0