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Old 08-23-2011, 08:45 AM   #5
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grambles423's Avatar
Drives: 2008.5 BMP GTI
Join Date: Jun 2009
Location: Balls Deep
Posts: 18,424
Please refer to this thread for more discussion

Now a lot of the main stuff is handed down from the big guys such as wheelbase target, Lateral and Logitudanol Force Targets, Ground height, Moment Roll, roll pitch, roll center, center of Gravity, etc. etc.

With a lot of known variables we can start solving, or at least get an idea of where we are at and deteremine suspension feasibility and performance characteristics before the vehicle is even made. Once prototyping begins, we can always tweak things to get exactly what we want.

So Lets start:

What is the one talked about topic on car enthusiasts forums? Lowering Right? Or from what I gather at least. Most people say "Stock GTI handles so good, there is no need to modify it." Right and Wrong, for everyday use right. For tracking wrong. There is literally an infinite route you can go to make your car perform well on the tracck, but at what cost to the daily driveability do you want to spend?

I dont have any measurements for my suspension so I cant get any final numbers, but if anyone is willing, go for it.

From my suspension notes:
"A vehicle with a suspension is not a rigid body. The unsprung mass stays (mainly) on the ground. The sprung mass does not roll about the center of gravity. The sprung mass rolls about a kinematic point known as the ‘roll center’ which is defined by suspension geometry. (For preliminary design, without other domain knowledge, take roll center to be at height of axles.) If the roll center is above ground, then the lateral force on the tires in a turn must be directed towards the turn’s center of rotation in order to maintain the vehicle’s equilibrium. The tires scrub to the outside to generate this force. If the roll center is at the ground, there is no tire scrub. If the roll center is below ground, the lateral force is oppositely directed, and the tires scrub into the turn. This causes a break in traction, and the vehicle motion becomes unstable. Roll centers are placed enough above ground that no combination of driving or failure will cause them to move below ground. Roll centers in rear suspension are usually placed higher than those in front suspension so that the rear will be more stable than the front, and the rear will not want to over-rotate (oversteer)."

How do you calculate the roll center?
Moment of Roll (How hard you're vehicle rolls) = Roll Stiffness * Roll angle

Roll Stiffness = Front Roll Stiffness + Rear Roll Stiffness = FRS + RRS

FRS = 0.5 * Wheel Rate * Front Trackwidth^2 + Stiffness of Front Sway

RRS = 0.5 * Wheel Rate * Rear Trackwidth^2 + Stiffness of Rear Sway

*Sway thickness can be forund on the internet if you google Sway stiffness formula

*Assume your wheel rates are the same on each side

Moment of Roll = Sprung Mass * Gravity * (D) * Roll Angle + Sprung Mass * Laterall Acceleration * (D)

Lateral Acceleration = Speed into the turn / Radius of the Turn

(D) = Height of center of gravity above roll center (if roll center is above CG, d < 0 )

*This part is a little hard to determine WHERE exaclty the roll center is, but I will help you. From Happian-Smith (An Introduction to Modern Vehicle Design, 2002):

"The Roll center for a MacPherson Strut suspension lies on the upper defining line of the moment of inertia of the upper mount of the strut perpendicular to the strut axis." I'll discuss further:

The front roll center of a car with the Mustang's MacPherson strut suspension can be found as follows:

- Draw a line at an angle of 90 degrees from the top of the front strut
- Draw a second line through the lower control arm. The point where these lines intersect is the instantaneous center
- Draw a third line from the instantaneous center to the center of the tire contact patch. The point where this third line crosses the car's centerline at the roll center.

This will be your (D) for the front.

"The roll center for a trailing arm suspension lies in the ground plane on the center line of the vehicle" MEANING...its basically on the ground. Your (D) would equal the distance from the COG to the ground.

Just connect to the two dots...and you get your roll axis:

This is what your car rolls about when you turn. FYI that is just an example....but you get the idea.

What does this all mean?

You know your roll stiffness, now you need to find your Roll Moment, but in order to do that you must solve for your roll angle. AND in order to do that, you must solve an average roll center between the front and rear. Shouldnt be hard, Front + Rear divided by 2. Then just rearrange that roll angle formula:

Roll Angle = [Sprung mass * Laterall Acceleration * (Daverage) ] Divided by [Roll stiffness (Front+Rear) * Sprung Mass * gravity * (Daverage)]

And guess what? We're not done. You can now take this formula and find your wheel deflection:

Wheel Deflection = roll angle * trackwidth / 2, You can homogenize to either the front or rear, but then you'd have to break up the roll angle formula and just use the (D) for each specific case.

Wheel deflection of the front = roll angle of the front * front trackwidth / 2
and ditto for the rear.

What does this Ultimately entail? can seen it can get pretty hairy, but as long as you pace through it, its not so bad.

I can safely say now, you can see theres an affect going on when lowering your vehicle. When lowering you drop the effective roll angle closer to the center of gravity and you stiffen the roll. Meaning, you can have hard springs and hard dampers and never see your car roll. Obviously the more roll, the more wheel deflection you get thus removing how much power you put to the ground when coming out of a turn. Thats it.....thats the whole idea of wanting a stiff suspension while tracking.

Now for daily driving, you can sacrifice some stiffness for some body roll. This helps for a smooth ride and happy passengers. I myself use Bilsteins on my new MKV but they're a little stiff. But DAMN do they handle nicely. They deflect the wheel barely an inch coming hard into turns. Do I track the car much? Not really, so in my honest opinion, I will be getting rid of them and sacrificing that performance for a better ride. But others will do differently.

Obviously all the equations are limited to suspension geometry. Meaning, you cant slap the wrong hardware and expect ultimate performance. Its all a matter of balance.

Lateral Load Transfer

This is a bit harder to explain. You have many many many many factors to consider. But its a good idea to touch on this for those you have a grasp on the concept.

Here are some references to read if you're curious:

Heres just a reference formula to blow your mind:

Front Turning Force = [mass of the vehicle * distance between CG and front trackwidth* Lateral Acceleration * height of CG above ground] / [wheelbase * front trackwidth]

Front Turning Force = All of that mess above + [Roll stiffness * Sprung mass * Lateral Acceleration * (Dfront)] / [front trackwidth * (roll stiffness - sprung mass * gravity * (Dfront))]

Ugh......then you can do the same for the rear. Now that you have both Front and Rear Turning Forces you can do the following:

If, Front Turning Force + Rear Turning Force > (vehicle mass * gravity) /2

Then the vehicle rolls over.

Eventually you'll get to a point where your suspension can handle the force its taking from the turn, but your tires cant. Keep that in mind when you're tracking the vehicle. Always have some nice sticky tires.

I KNOW I've missed some stuff and probably confused the hell out of most of you, but people have wanted to see if for quite some time. Any questions? Post them!

This should offer some insight as well:

Enough chit chat....Lets continue. Again, I will keep this vague with as little mathematical derivation as possible. But, should you want to dive further I would definitely brush up on differential equations and basic physics.

I have found my interest lies within the damping aspect to determine my ride quality.

Relationship between spring and wheel rates

In general the relationship between spring deflections and wheel displacements in suspensions is non linear, which means that a desired wheel-rate (related to natural frequency) has to be interpreted into a spring-rate.

Suspension or motion ratio = Spring force/ Wheel force ******(Not the same as spring rates or wheel rates)

To find ANY motion ratio, jack the car up and let the suspension hang. Measure the spring length at this very moment. Then use the jack and deflect the wheel a given amount of inches. Once you do so record that and then measure spring length again. Use those numbers and relate it to this newly derived formula:

Motion ratio (R) = [Final spring length - Intial spring length] / Wheel deflection

Normally, you will know your spring rates. its as easy as searching on google. If you know your spring rates, then you can relate them to a spring energy formula....for the sake of no confusion I've derived it into its simplest form:

Wheel rate = Spring rate / [Motion ratio^2]

Motion ratio results from the same kinematic suspension analysis that gives camber gain and roll center. Note that R is usually greater than 1, so the wheel rate is less than the spring rate. R is not constant; it varies as a function of v. But on an front handling car, it will be close to the ride height value at both full bump and full droop. Once the desired kw is known, and R has been determined from a candidate suspension geometry, ks may be determined. Note that the spring’s own free length (i.e., under no load) corresponds to full droop and not to ride height.

Dampening and Natural Frequency

From Happian Smith:
Frequently called shock absorbers, dampers are the main energy dissipators in a vehicle suspension. They are required to dampen vibration after a wheel strikes a pothole and to provide a good compormise between low spring mass acceleration and adequate control of the unsprung mass to provide good road handling.

Might Wanna Look at Wiki too.....Click Me

Twin tube vs. Monotube

Good Read: Twin Tube vs. Monotube....CLICK ME

Basically Twin tube = comfort; Monotube = Performance

Back to the good stuff. While skipping the boring and tedious derivations, the undamped natural frequency is:

Nat. Frequency (omega) = Square root(wheel rate / sprung mass)

If the wheel rate is maintain constant, the natural freq decreases as the payload increases. It is possible to determine a variable wheel-rate which will ensure that the natural frequency ramains constant as the sprung mass increases. (More on that later)

Effective corner damping coefficients may be set by the damping ratio:

damping ratio (ζ) = effective wheel damping ratio / (2*omega*mass of the vehicle)

- Critical damping (ζ=1) is the boundary limiting oscillation after disturbance.
- Slightly overdamped (ζ=1.2) will keep the wheels hard-pressed to the ground.
- Slightly underdamped (ζ=0.6) will allow more rapid response to disturbance say rolling into a turn) without much oscillation.
- More underdamped (ζ=0.35) will allow rapid wheel deflection, such as necessary to follow a rough surface.

This part is hard because companies do not give these values. But you can calculate a critical damping ratio and go from there. You can see that there is A LOT of fine tuning that goes into this.

Look at this pic:

Normally you want to find that range of overshoot to not allow the car to go haywire when you hit a bump, but also you dont want to car to overshoot and bounce like a pogo stick when hitting a bump and returning on the rebound. Again, you can solve for which damping ratio you'd like and find a coefficient of damping and go from there. You might be able to ask companies for their values, but be warned, they might not give it to you.

In dealing with road surface undulations in the bump direction (damper being compressed) relatively low levels of damping are required when compared with the rebound motion(damper being extended). This is because the damping force produced in bump tends to aid the acceleration of the spring mass, while in rebound an increased level of damping is required to dissipate the energy stored in the suspension spring.

What is the ultimate design? A controllable suspension (DCC) that electronically controls the adjustment forms of the basis of improving ride and handling. AKA Sport Standard and Comfort. Most companies design for the middle, but what the user wants to decide between tracking and daily driving? This system provails.

The biggest is when you chose a static spring and shock setup that has to balance the two: Comfort and Sport. Thats where multivariable input shocks such as Koni FSDs come into play. Basically just a valve that has high limits that soak up the major bumps in the road, but at slow compressions, such as during turns, they act as a performance shock. Still....when does the valve open? Thats left for some interpretation and subjective reasoning to deteremine "ride quality"

Reference PDF

An objective approach to ride quality will be discussed further, when I can collaborate my notes a little better....Stay tuned.......
UnNaturally Aspirated
APR Stage 1- ECS Dogbone
Driver Gear Springs-Tyrol Rigid Collar Subframe Kit
Centric Blank Rotors-Stoptech SP Pads

Last edited by grambles423; 12-07-2011 at 09:46 AM.
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