Hi everyone,

My name is Nils and I am a current student at Michigan Tech University, and a member our chassis/suspension sub group. In order to better understand springs and dampers, I have gone through OptimumG’s tech tips, and tried to implement the outlined formulas in Excel, specifically in regards to spring rate calculations. To run through some basic damping calculations, I referenced a presentation/PDF on Damping Calculations presented by KAZ Technologies and Jim Kasprzak (http://www.kaztechnologies.com/wp-co...ns-Seminar.pdf). The questions I have revolve around three main areas; roll gradient calculations, third spring calculations, and damping -- I just noticed that I can't attach excel files here so if anyone on this thread is willing to take a look at it, I would be happy to send it to their email address.

1 - Roll gradient calculations

- How should a negative value for spring rate be interpreted based on tech tip formula; I assume this is wrong?

- Because the tech tips reference a percent and divide by 100 in the final equation to calculate required front and rear ARB rates, I assume I am supposed to enter the percent value (WD and baseline magic number) as a whole number (i.e. 52 not 0.52). Is this correct?

- Going off of that, is the "magic number" (percentage of roll rate taken by the front of the car) fairly subjective, or is there any rhyme or reason as to selecting a value here? Would it be a safe bet to simply leave it at the advised baseline value of front WD+5% ?

- The variable K_w (see cell B35 - needed to calculate total ARB roll rate required to achieve the chosen roll gradient) in the tech tips refers to “wheel rate” in N/m. Since the front and rear wheel rates are different based on the F/R spring rates, am I supposed to assume an average in this case? Or is that incorrect?

- I also read that “A stiffer roll gradient will produce a car that is faster responding in transient conditions, but at the expense of mechanical grip over bumps in a corner”; I’m not sure I completely understand that. Is someone able to explain this principle in a different way?

- In regards to ride frequency; why is it that a higher front ride frequency allows "faster transient response at corner entry, less ride height variation on the front and allows for better rear wheel traction on corner exit" ?

2 - Third Spring Calculations

- I assume F/R ride frequencies refer to the targeted ride frequency of the car (usually between 1.5-2 Hz for non-aero FSAE cars if I’m not mistaken)? Practically speaking, what does wheel bump frequency refer to in this case? How could a baseline value for this be determined/what is a reasonable range for an FSAE car? I did notice that if the targeted ride frequency for a given side of the vehicle is equal to the wheel bump frequency for both tires, then obviously the third spring rate goes to zero, which intuitively makes sense, as the whole purpose of the third spring is to achieve a lower frequency in single wheel bump than overall ride.

- While from a mathematical standpoint it makes sense that motion ratio of the suspension would not play a role in third spring rates since its change is offset by a subsequently different single wheel spring rate, I just wanted to make sure this was correct? Intuitively I would have expected motion ratio to play a role in determining the third spring rate.

3 - Damping

- In attempting to calculate the ideal knee speed - low speed damping turns into high speed damping - I first calculated the undamped system resonant frequency, and then multiplied this frequency by the sq. root of 2 (as referenced in OptimumG tech tip #4) to determine the crossover point in Hz for the transmissibility plot. To relate this frequency to an absolute velocity, I assumed an arbitrary maximum disturbance height (say 0.04m), divided this value by the (crossover frequency/2) (Tech tip: “The time it takes for the wheel to complete the up-down cycle is the frequency divided by two”). While this gave me an “optimal” knee speed abs. velocity, it doesn’t quite make sense to me, because that would mean that if the crossover frequency [Hz] were to increase, the absolute velocity would decrease. Shouldn’t it be the opposite? If I use the definition that a wave period = 1/f (I divide the crossover frequency by 1/f) then this gives me a different knee speed which increases with increasing crossover frequency as I would have expected. Which method is correct here?

Thank you to everyone for your help, and especially those that read the whole post! I’ve been spending a lot of time trying to understand these calculations and these are the questions I had the most trouble with, so any help would be appreciated!

Best regards,

Nils